Energy Technology Data Exchange (ETDEWEB)
Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.
2006-01-01
Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.
Discrete Orthogonal Transforms and Neural Networks for Image Interpolation
Directory of Open Access Journals (Sweden)
J. Polec
1999-09-01
Full Text Available In this contribution we present transform and neural network approaches to the interpolation of images. From transform point of view, the principles from [1] are modified for 1st and 2nd order interpolation. We present several new interpolation discrete orthogonal transforms. From neural network point of view, we present interpolation possibilities of multilayer perceptrons. We use various configurations of neural networks for 1st and 2nd order interpolation. The results are compared by means of tables.
Dynamic Stability Analysis Using High-Order Interpolation
Directory of Open Access Journals (Sweden)
Juarez-Toledo C.
2012-10-01
Full Text Available A non-linear model with robust precision for transient stability analysis in multimachine power systems is proposed. The proposed formulation uses the interpolation of Lagrange and Newton's Divided Difference. The High-Order Interpolation technique developed can be used for evaluation of the critical conditions of the dynamic system.The technique is applied to a 5-area 45-machine model of the Mexican interconnected system. As a particular case, this paper shows the application of the High-Order procedure for identifying the slow-frequency mode for a critical contingency. Numerical examples illustrate the method and demonstrate the ability of the High-Order technique to isolate and extract temporal modal behavior.
High order discrete ordinates transport in two dimensions
International Nuclear Information System (INIS)
Arkuszewski, J.J.
1980-01-01
A two-dimensional neutron transport equation in (x,y) geometry is solved by the subdomain version of the weighted residual method. The weight functions are chosen to be characteristic functions of computational boxes (subdomains). In the case of bilinear interpolant the conventional diamond relations are obtained, while the quadratic one produces generalized diamond relations containing first derivatives of the solution. The balance equation remains the same. The derivation yields also additional relations for extrapolating boundary values of derivatives and leaves the room for supplementing the interpolant with specially curtailed higher order polynomials. The method requires only slight modifications in inner iteration process used by conventional discrete ordinates programs, and has been introduced as an option into the program DOT2. The paper contains comparisons of the proposed method with conventional one based on calculations of IAEA-CRP transport theory benchmarks. (author)
Design of fractional order differentiator using type-III and type-IV discrete cosine transform
Directory of Open Access Journals (Sweden)
Manjeet Kumar
2017-02-01
Full Text Available In this paper, an interpolation method based on discrete cosine transform (DCT is employed for digital finite impulse response-fractional order differentiator (FIR-FOD design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...
Interpolation of the discrete logarithm in a finite field of characteristic two by Boolean functions
DEFF Research Database (Denmark)
Brandstaetter, Nina; Lange, Tanja; Winterhof, Arne
2005-01-01
We obtain bounds on degree, weight, and the maximal Fourier coefficient of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic....
HIGHLY-ACCURATE MODEL ORDER REDUCTION TECHNIQUE ON A DISCRETE DOMAIN
Directory of Open Access Journals (Sweden)
L. D. Ribeiro
2015-09-01
Full Text Available AbstractIn this work, we present a highly-accurate technique of model order reduction applied to staged processes. The proposed method reduces the dimension of the original system based on null values of moment-weighted sums of heat and mass balance residuals on real stages. To compute these sums of weighted residuals, a discrete form of Gauss-Lobatto quadrature was developed, allowing a high degree of accuracy in these calculations. The locations where the residuals are cancelled vary with time and operating conditions, characterizing a desirable adaptive nature of this technique. Balances related to upstream and downstream devices (such as condenser, reboiler, and feed tray of a distillation column are considered as boundary conditions of the corresponding difference-differential equations system. The chosen number of moments is the dimension of the reduced model being much lower than the dimension of the complete model and does not depend on the size of the original model. Scaling of the discrete independent variable related with the stages was crucial for the computational implementation of the proposed method, avoiding accumulation of round-off errors present even in low-degree polynomial approximations in the original discrete variable. Dynamical simulations of distillation columns were carried out to check the performance of the proposed model order reduction technique. The obtained results show the superiority of the proposed procedure in comparison with the orthogonal collocation method.
Multilevel Fast Multipole Method for Higher Order Discretizations
DEFF Research Database (Denmark)
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik
2014-01-01
The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....
Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
International Nuclear Information System (INIS)
Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Qin, Hong; Sun, Yajuan
2015-01-01
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave
Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
Energy Technology Data Exchange (ETDEWEB)
Xiao, Jianyuan [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Qin, Hong [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA; Liu, Jian [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; He, Yang [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China
2015-11-01
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC.
Institute of Scientific and Technical Information of China (English)
ZHENG Guangguo; ZHOU Dongsheng; WEI Xiaopeng; ZHANG Qiang
2012-01-01
Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.
Directory of Open Access Journals (Sweden)
Maheswari Subramanian
2018-01-01
Full Text Available Information hiding techniques have a significant role in recent application areas. Steganography is the embedding of information within an innocent cover work in a way which cannot be detected by any person without accessing the steganographic key. The proposed work uses a steganographic scheme for useful information with the help of human skin tone regions as cover image. The proposed algorithm has undergone Lagrange interpolation encryption for enhancement of the security of the hidden information. First, the skin tone regions are identified by using YCbCr color space which can be used as a cover image. Image pixels which belong to the skin regions are used to carry more secret bits, and the secret information is hidden in both horizontal and vertical sequences of the skin areas of the cover image. The secret information will hide behind the human skin regions rather than other objects in the same image because the skin pixels have high intensity value. The performance of embedding is done and is quite invisible by the vector discrete wavelet transformation (VDWT technique. A new Lagrange interpolation-based encryption method is introduced to achieve high security of the hidden information with higher payload and better visual quality.
A high order solver for the unbounded Poisson equation
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order...... of convergence consistent with the moments conserved by the applied smoothing function. In the hybrid particle-mesh method of Hockney and Eastwood (HE) the particles are interpolated onto a regular mesh where the unbounded Poisson equation is solved by a discrete non-cyclic convolution of the mesh values...... and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight...
High-order harmonic propagation in gases within the discrete dipole approximation
International Nuclear Information System (INIS)
Hernandez-Garcia, C.; Perez-Hernandez, J. A.; Ramos, J.; Jarque, E. Conejero; Plaja, L.; Roso, L.
2010-01-01
We present an efficient approach for computing high-order harmonic propagation based on the discrete dipole approximation. In contrast with other approaches, our strategy is based on computing the total field as the superposition of the driving field with the field radiated by the elemental emitters of the sample. In this way we avoid the numerical integration of the wave equation, as Maxwell's equations have an analytical solution for an elementary (pointlike) emitter. The present strategy is valid for low-pressure gases interacting with strong fields near the saturation threshold (i.e., partially ionized), which is a common situation in the experiments of high-order harmonic generation. We use this tool to study the dependence of phase matching of high-order harmonics with the relative position between the beam focus and the gas jet.
Adaptive discrete-ordinates algorithms and strategies
International Nuclear Information System (INIS)
Stone, J.C.; Adams, M.L.
2005-01-01
We present our latest algorithms and strategies for adaptively refined discrete-ordinates quadrature sets. In our basic strategy, which we apply here in two-dimensional Cartesian geometry, the spatial domain is divided into regions. Each region has its own quadrature set, which is adapted to the region's angular flux. Our algorithms add a 'test' direction to the quadrature set if the angular flux calculated at that direction differs by more than a user-specified tolerance from the angular flux interpolated from other directions. Different algorithms have different prescriptions for the method of interpolation and/or choice of test directions and/or prescriptions for quadrature weights. We discuss three different algorithms of different interpolation orders. We demonstrate through numerical results that each algorithm is capable of generating solutions with negligible angular discretization error. This includes elimination of ray effects. We demonstrate that all of our algorithms achieve a given level of error with far fewer unknowns than does a standard quadrature set applied to an entire problem. To address a potential issue with other algorithms, we present one algorithm that retains exact integration of high-order spherical-harmonics functions, no matter how much local refinement takes place. To address another potential issue, we demonstrate that all of our methods conserve partial currents across interfaces where quadrature sets change. We conclude that our approach is extremely promising for solving the long-standing problem of angular discretization error in multidimensional transport problems. (authors)
International Nuclear Information System (INIS)
Vargas, L.
1988-01-01
The numerical approximate solution of the space-time nuclear reactor kinetics equation is investigated using a finite-element discretization of the space variable and a high order integration scheme for the resulting semi-discretized parabolic equation. The Galerkin method with spatial piecewise polynomial Lagrange basis functions are used to obtained a continuous time semi-discretized form of the space-time reactor kinetics equation. A temporal discretization is then carried out with a numerical scheme based on the Iterated Defect Correction (IDC) method using piecewise quadratic polynomials or exponential functions. The kinetics equations are thus solved with in a general finite element framework with respect to space as well as time variables in which the order of convergence of the spatial and temporal discretizations is consistently high. A computer code GALFEM/IDC is developed, to implement the numerical schemes described above. This issued to solve a one space dimensional benchmark problem. The results of the numerical experiments confirm the theoretical arguments and show that the convergence is very fast and the overall procedure is quite efficient. This is due to the good asymptotic properties of the numerical scheme which is of third order in the time interval
An Online Method for Interpolating Linear Parametric Reduced-Order Models
Amsallem, David; Farhat, Charbel
2011-01-01
A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.
Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng
2017-04-01
A novel on high-grade CNC machines tools for B Spline curve method of High-speed interpolation arithmetic is introduced. In the high-grade CNC machines tools CNC system existed the type value points is more trouble, the control precision is not strong and so on, In order to solve this problem. Through specific examples in matlab7.0 simulation result showed that that the interpolation error significantly reduced, the control precision is improved markedly, and satisfy the real-time interpolation of high speed, high accuracy requirements.
High-order solution methods for grey discrete ordinates thermal radiative transfer
Energy Technology Data Exchange (ETDEWEB)
Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)
2016-12-15
This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.
Energy Technology Data Exchange (ETDEWEB)
Li, Mao; Qiu, Zihua; Liang, Chunlei; Sprague, Michael; Xu, Min
2017-01-13
In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third-order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for 2D wave equation and Euler equa- tions. Our present results demonstrated that the SDRT method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed- element meshes.
Directory of Open Access Journals (Sweden)
Felix Fritzen
2018-02-01
Full Text Available A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete Empirical Interpolation Method (EIM, DEIM. An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (DEIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.
A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids
Energy Technology Data Exchange (ETDEWEB)
McCorquodale, Peter; Colella, Phillip
2011-01-28
We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.
2013-01-01
on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time
The research on NURBS adaptive interpolation technology
Zhang, Wanjun; Gao, Shanping; Zhang, Sujia; Zhang, Feng
2017-04-01
In order to solve the problems of Research on NURBS Adaptive Interpolation Technology, such as interpolation time bigger, calculation more complicated, and NURBS curve step error are not easy changed and so on. This paper proposed a study on the algorithm for NURBS adaptive interpolation method of NURBS curve and simulation. We can use NURBS adaptive interpolation that calculates (xi, yi, zi). Simulation results show that the proposed NURBS curve interpolator meets the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished. The simulation results show that the algorithm is correct; it is consistent with a NURBS curve interpolation requirements.
Analysis and Design of a High-Order Discrete-Time Passive IIR Low-Pass Filter
Tohidian, M.; Madadi, I.; Staszewski, R.B.
2014-01-01
In this paper, we propose a discrete-time IIR low-pass filter that achieves a high-order of filtering through a charge-sharing rotation. Its sampling rate is then multiplied through pipelining. The first stage of the filter can operate in either a voltage-sampling or charge-sampling mode. It uses
High-Order Finite-Difference Solution of the Poisson Equation with Interface Jump Conditions II
Marques, Alexandre; Nave, Jean-Christophe; Rosales, Rodolfo
2010-11-01
The Poisson equation with jump discontinuities across an interface is of central importance in Computational Fluid Dynamics. In prior work, Marques, Nave, and Rosales have introduced a method to obtain fourth-order accurate solutions for the constant coefficient Poisson problem. Here we present an extension of this method to solve the variable coefficient Poisson problem to fourth-order of accuracy. The extended method is based on local smooth extrapolations of the solution field across the interface. The extrapolation procedure uses a combination of cubic Hermite interpolants and a high-order representation of the interface using the Gradient-Augmented Level-Set technique. This procedure is compatible with the use of standard discretizations for the Laplace operator, and leads to modified linear systems which have the same sparsity pattern as the standard discretizations. As a result, standard Poisson solvers can be used with only minimal modifications. Details of the method and applications will be presented.
Global stability of stochastic high-order neural networks with discrete and distributed delays
International Nuclear Information System (INIS)
Wang Zidong; Fang Jianan; Liu Xiaohui
2008-01-01
High-order neural networks can be considered as an expansion of Hopfield neural networks, and have stronger approximation property, faster convergence rate, greater storage capacity, and higher fault tolerance than lower-order neural networks. In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with discrete and distributed time-delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived, which guarantee the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the stochastic high-order delayed neural networks under consideration are globally asymptotically stable in the mean square if two linear matrix inequalities (LMIs) are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also shown that the main results in this paper cover some recently published works. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria
Scalable Intersample Interpolation Architecture for High-channel-count Beamformers
DEFF Research Database (Denmark)
Tomov, Borislav Gueorguiev; Nikolov, Svetoslav I; Jensen, Jørgen Arendt
2011-01-01
Modern ultrasound scanners utilize digital beamformers that operate on sampled and quantized echo signals. Timing precision is of essence for achieving good focusing. The direct way to achieve it is through the use of high sampling rates, but that is not economical, so interpolation between echo...... samples is used. This paper presents a beamformer architecture that combines a band-pass filter-based interpolation algorithm with the dynamic delay-and-sum focusing of a digital beamformer. The reduction in the number of multiplications relative to a linear perchannel interpolation and band-pass per......-channel interpolation architecture is respectively 58 % and 75 % beamformer for a 256-channel beamformer using 4-tap filters. The approach allows building high channel count beamformers while maintaining high image quality due to the use of sophisticated intersample interpolation....
Transfinite C2 interpolant over triangles
International Nuclear Information System (INIS)
Alfeld, P.; Barnhill, R.E.
1984-01-01
A transfinite C 2 interpolant on a general triangle is created. The required data are essentially C 2 , no compatibility conditions arise, and the precision set includes all polynomials of degree less than or equal to eight. The symbol manipulation language REDUCE is used to derive the scheme. The scheme is discretized to two different finite dimensional C 2 interpolants in an appendix
Evaluation of various interpolants available in DICE
Energy Technology Data Exchange (ETDEWEB)
Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Reu, Phillip L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Crozier, Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-02-01
This report evaluates several interpolants implemented in the Digital Image Correlation Engine (DICe), an image correlation software package developed by Sandia. By interpolants we refer to the basis functions used to represent discrete pixel intensity data as a continuous signal. Interpolation is used to determine intensity values in an image at non - pixel locations. It is also used, in some cases, to evaluate the x and y gradients of the image intensities. Intensity gradients subsequently guide the optimization process. The goal of this report is to inform analysts as to the characteristics of each interpolant and provide guidance towards the best interpolant for a given dataset. This work also serves as an initial verification of each of the interpolants implemented.
High-order discrete ordinate transport in non-conforming 2D Cartesian meshes
International Nuclear Information System (INIS)
Gastaldo, L.; Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J. M.
2009-01-01
We present in this paper a numerical scheme for solving the time-independent first-order form of the Boltzmann equation in non-conforming 2D Cartesian meshes. The flux solution technique used here is the discrete ordinate method and the spatial discretization is based on discontinuous finite elements. In order to have p-refinement capability, we have chosen a hierarchical polynomial basis based on Legendre polynomials. The h-refinement capability is also available and the element interface treatment has been simplified by the use of special functions decomposed over the mesh entities of an element. The comparison to a classical S N method using the Diamond Differencing scheme as spatial approximation confirms the good behaviour of the method. (authors)
Analysis of velocity planning interpolation algorithm based on NURBS curve
Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng
2017-04-01
To reduce interpolation time and Max interpolation error in NURBS (Non-Uniform Rational B-Spline) inter-polation caused by planning Velocity. This paper proposed a velocity planning interpolation algorithm based on NURBS curve. Firstly, the second-order Taylor expansion is applied on the numerator in NURBS curve representation with parameter curve. Then, velocity planning interpolation algorithm can meet with NURBS curve interpolation. Finally, simulation results show that the proposed NURBS curve interpolator meet the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished.
Research of Cubic Bezier Curve NC Interpolation Signal Generator
Directory of Open Access Journals (Sweden)
Shijun Ji
2014-08-01
Full Text Available Interpolation technology is the core of the computer numerical control (CNC system, and the precision and stability of the interpolation algorithm directly affect the machining precision and speed of CNC system. Most of the existing numerical control interpolation technology can only achieve circular arc interpolation, linear interpolation or parabola interpolation, but for the numerical control (NC machining of parts with complicated surface, it needs to establish the mathematical model and generate the curved line and curved surface outline of parts and then discrete the generated parts outline into a large amount of straight line or arc to carry on the processing, which creates the complex program and a large amount of code, so it inevitably introduce into the approximation error. All these factors affect the machining accuracy, surface roughness and machining efficiency. The stepless interpolation of cubic Bezier curve controlled by analog signal is studied in this paper, the tool motion trajectory of Bezier curve can be directly planned out in CNC system by adjusting control points, and then these data were put into the control motor which can complete the precise feeding of Bezier curve. This method realized the improvement of CNC trajectory controlled ability from the simple linear and circular arc to the complex project curve, and it provides a new way for economy realizing the curve surface parts with high quality and high efficiency machining.
Image Interpolation with Geometric Contour Stencils
Directory of Open Access Journals (Sweden)
Pascal Getreuer
2011-09-01
Full Text Available We consider the image interpolation problem where given an image vm,n with uniformly-sampled pixels vm,n and point spread function h, the goal is to find function u(x,y satisfying vm,n = (h*u(m,n for all m,n in Z. This article improves upon the IPOL article Image Interpolation with Contour Stencils. In the previous work, contour stencils are used to estimate the image contours locally as short line segments. This article begins with a continuous formulation of total variation integrated over a collection of curves and defines contour stencils as a consistent discretization. This discretization is more reliable than the previous approach and can effectively distinguish contours that are locally shaped like lines, curves, corners, and circles. These improved contour stencils sense more of the geometry in the image. Interpolation is performed using an extension of the method described in the previous article. Using the improved contour stencils, there is an increase in image quality while maintaining similar computational efficiency.
High Order Semi-Lagrangian Advection Scheme
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Liu, Peilu; Li, Xinghua; Li, Haopeng; Su, Zhikun; Zhang, Hongxu
2017-10-12
In order to improve the accuracy of ultrasonic phased array focusing time delay, analyzing the original interpolation Cascade-Integrator-Comb (CIC) filter, an 8× interpolation CIC filter parallel algorithm was proposed, so that interpolation and multichannel decomposition can simultaneously process. Moreover, we summarized the general formula of arbitrary multiple interpolation CIC filter parallel algorithm and established an ultrasonic phased array focusing time delay system based on 8× interpolation CIC filter parallel algorithm. Improving the algorithmic structure, 12.5% of addition and 29.2% of multiplication was reduced, meanwhile the speed of computation is still very fast. Considering the existing problems of the CIC filter, we compensated the CIC filter; the compensated CIC filter's pass band is flatter, the transition band becomes steep, and the stop band attenuation increases. Finally, we verified the feasibility of this algorithm on Field Programming Gate Array (FPGA). In the case of system clock is 125 MHz, after 8× interpolation filtering and decomposition, time delay accuracy of the defect echo becomes 1 ns. Simulation and experimental results both show that the algorithm we proposed has strong feasibility. Because of the fast calculation, small computational amount and high resolution, this algorithm is especially suitable for applications with high time delay accuracy and fast detection.
Directory of Open Access Journals (Sweden)
Peilu Liu
2017-10-01
Full Text Available In order to improve the accuracy of ultrasonic phased array focusing time delay, analyzing the original interpolation Cascade-Integrator-Comb (CIC filter, an 8× interpolation CIC filter parallel algorithm was proposed, so that interpolation and multichannel decomposition can simultaneously process. Moreover, we summarized the general formula of arbitrary multiple interpolation CIC filter parallel algorithm and established an ultrasonic phased array focusing time delay system based on 8× interpolation CIC filter parallel algorithm. Improving the algorithmic structure, 12.5% of addition and 29.2% of multiplication was reduced, meanwhile the speed of computation is still very fast. Considering the existing problems of the CIC filter, we compensated the CIC filter; the compensated CIC filter’s pass band is flatter, the transition band becomes steep, and the stop band attenuation increases. Finally, we verified the feasibility of this algorithm on Field Programming Gate Array (FPGA. In the case of system clock is 125 MHz, after 8× interpolation filtering and decomposition, time delay accuracy of the defect echo becomes 1 ns. Simulation and experimental results both show that the algorithm we proposed has strong feasibility. Because of the fast calculation, small computational amount and high resolution, this algorithm is especially suitable for applications with high time delay accuracy and fast detection.
Slab geometry spatial discretization schemes with infinite-order convergence
International Nuclear Information System (INIS)
Adams, M.L.; Martin, W.R.
1985-01-01
Spatial discretization schemes for the slab geometry discrete ordinates transport equation have received considerable attention in the past several years, with particular interest shown in developing methods that are more computationally efficient that standard schemes. Here the authors apply to the discrete ordinates equations a spectral method that is significantly more efficient than previously proposed schemes for high-accuracy calculations of homogeneous problems. This is a direct consequence of the exponential (infinite-order) convergence of spectral methods for problems with every smooth solutions. For heterogeneous problems where smooth solutions do not exist and exponential convergence is not observed with spectral methods, a spectral element method is proposed which does exhibit exponential convergence
Interpolation of polytopic control Lyapunov functions for discrete–time linear systems
Nguyen, T.T.; Lazar, M.; Spinu, V.; Boje, E.; Xia, X.
2014-01-01
This paper proposes a method for interpolating two (or more) polytopic control Lyapunov functions (CLFs) for discrete--time linear systems subject to polytopic constraints, thereby combining different control objectives. The corresponding interpolated CLF is used for synthesis of a stabilizing
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Multivariate Discrete First Order Stochastic Dominance
DEFF Research Database (Denmark)
Tarp, Finn; Østerdal, Lars Peter
This paper characterizes the principle of first order stochastic dominance in a multivariate discrete setting. We show that a distribution f first order stochastic dominates distribution g if and only if f can be obtained from g by iteratively shifting density from one outcome to another...
International Nuclear Information System (INIS)
Blok, M. de; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1990-01-01
This report describes a time-interpolator with which time differences can be measured using digital and analog techniques. It concerns a maximum measuring time of 6.4 μs with a resolution of 100 ps. Use is made of Emitter Coupled Logic (ECL) and analogues of high-frequency techniques. The difficulty which accompanies the use of ECL-logic is keeping as short as possible the mutual connections and closing properly the outputs in order to avoid reflections. The digital part of the time-interpolator consists of a continuous running clock and logic which converts an input signal into a start- and stop signal. The analog part consists of a Time to Amplitude Converter (TAC) and an analog to digital converter. (author). 3 refs.; 30 figs
International Nuclear Information System (INIS)
Schuller, S.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1990-01-01
This report presents a description of the design of a digital time meter. This time meter should be able to measure, by means of interpolation, times of 100 ns with an accuracy of 50 ps. In order to determine the best principle for interpolation, three methods were simulated at the computer with a Pascal code. On the basis of this the best method was chosen and used in the design. In order to test the principal operation of the circuit a part of the circuit was constructed with which the interpolation could be tested. The remainder of the circuit was simulated with a computer. So there are no data available about the operation of the complete circuit in practice. The interpolation part however is the most critical part, the remainder of the circuit is more or less simple logic. Besides this report also gives a description of the principle of interpolation and the design of the circuit. The measurement results at the prototype are presented finally. (author). 3 refs.; 37 figs.; 2 tabs
Energy Technology Data Exchange (ETDEWEB)
Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
On the Linear Stability of the Fifth-Order WENO Discretization
Motamed, Mohammad
2010-10-03
We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea
2013-01-01
Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Discrete time-crystalline order in black diamond
Zhou, Hengyun; Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman; Demler, Eugene; Lukin, Mikhail D.
2017-04-01
The interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic ``time-crystalline'' phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of 106 dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions; this order is remarkably stable against perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.
Functions with disconnected spectrum sampling, interpolation, translates
Olevskii, Alexander M
2016-01-01
The classical sampling problem is to reconstruct entire functions with given spectrum S from their values on a discrete set L. From the geometric point of view, the possibility of such reconstruction is equivalent to determining for which sets L the exponential system with frequencies in L forms a frame in the space L^2(S). The book also treats the problem of interpolation of discrete functions by analytic ones with spectrum in S and the problem of completeness of discrete translates. The size and arithmetic structure of both the spectrum S and the discrete set L play a crucial role in these problems. After an elementary introduction, the authors give a new presentation of classical results due to Beurling, Kahane, and Landau. The main part of the book focuses on recent progress in the area, such as construction of universal sampling sets, high-dimensional and non-analytic phenomena. The reader will see how methods of harmonic and complex analysis interplay with various important concepts in different areas, ...
Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Rasmussen, Kim; Henning, D.; Gabriel, H.
1996-01-01
We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...
Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel
2015-01-01
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search
Fractional Delayer Utilizing Hermite Interpolation with Caratheodory Representation
Directory of Open Access Journals (Sweden)
Qiang DU
2018-04-01
Full Text Available Fractional delay is indispensable for many sorts of circuits and signal processing applications. Fractional delay filter (FDF utilizing Hermite interpolation with an analog differentiator is a straightforward way to delay discrete signals. This method has a low time-domain error, but a complicated sampling module than the Shannon sampling scheme. A simplified scheme, which is based on Shannon sampling and utilizing Hermite interpolation with a digital differentiator, will lead a much higher time-domain error when the signal frequency approaches the Nyquist rate. In this letter, we propose a novel fractional delayer utilizing Hermite interpolation with Caratheodory representation. The samples of differential signal are obtained by Caratheodory representation from the samples of the original signal only. So, only one sampler is needed and the sampling module is simple. Simulation results for four types of signals demonstrate that the proposed method has significantly higher interpolation accuracy than Hermite interpolation with digital differentiator.
Technique for image interpolation using polynomial transforms
Escalante Ramírez, B.; Martens, J.B.; Haskell, G.G.; Hang, H.M.
1993-01-01
We present a new technique for image interpolation based on polynomial transforms. This is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. In the discrete case, the image segment within every window of analysis is
SPLINE, Spline Interpolation Function
International Nuclear Information System (INIS)
Allouard, Y.
1977-01-01
1 - Nature of physical problem solved: The problem is to obtain an interpolated function, as smooth as possible, that passes through given points. The derivatives of these functions are continuous up to the (2Q-1) order. The program consists of the following two subprograms: ASPLERQ. Transport of relations method for the spline functions of interpolation. SPLQ. Spline interpolation. 2 - Method of solution: The methods are described in the reference under item 10
Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin
2017-12-01
The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for small time step sizes. Since the critical time step size depends on the viscosity and the spatial resolution, these instabilities limit the robustness of the Navier-Stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.
Preservation properties for the discrete mean residual life ordering
Directory of Open Access Journals (Sweden)
Abdulhakim Al-Babtain
2015-04-01
Full Text Available The purpose of this paper is to prove several preservation properties of stochastic comparisons based on the discrete mean residual life ordering d-MRL under the reliability operations of convolutions, mixtures. Fi nally we introduce a discrete renewal process application
Finite Element Simulation of Sheet Metal Forming Process Using Local Interpolation for Tool Surfaces
International Nuclear Information System (INIS)
Hama, Takayuki; Takuda, Hirohiko; Takamura, Masato; Makinouchi, Akitake; Teodosiu, Cristian
2005-01-01
Treatment of contact between a sheet and tools is one of the most difficult problems to deal with in finite-element simulations of sheet forming processes. In order to obtain more accurate tool models without increasing the number of elements, this paper describes a new formulation for contact problems using interpolation proposed by Nagata for tool surfaces. A contact search algorithm between sheet nodes and the interpolated tool surfaces was developed and was introduced into the static-explicit elastoplastic finite-element method code STAMP3D. Simulations of a square cup deep drawing process with a very coarsely discretized punch model were carried out. The simulated results showed that the proposed algorithm gave the proper drawn shape, demonstrating the validity of the proposed algorithm
FPGA implementation of fractional-order discrete memristor chaotic ...
Indian Academy of Sciences (India)
Anitha Karthikeyan
Corresponding author. E-mail: rkarthiekeyan@gmail.com. MS received 10 August 2017; revised 4 September 2017; accepted 5 September 2017; published online 30 December 2017. Abstract. A new fourth-order memristor chaotic oscillator is taken to investigate its fractional-order discrete synchronisation.
Directory of Open Access Journals (Sweden)
Ram Verma
2016-02-01
Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions.
High order curvilinear finite elements for elastic–plastic Lagrangian dynamics
International Nuclear Information System (INIS)
Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
2014-01-01
This paper presents a high-order finite element method for calculating elastic–plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L 2 projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic–plastic flow
An integral conservative gridding--algorithm using Hermitian curve interpolation.
Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K
2008-11-07
The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to
An integral conservative gridding-algorithm using Hermitian curve interpolation
International Nuclear Information System (INIS)
Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K
2008-01-01
The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to
Study on the algorithm for Newton-Rapson iteration interpolation of NURBS curve and simulation
Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng
2017-04-01
In order to solve the problems of Newton-Rapson iteration interpolation method of NURBS Curve, Such as interpolation time bigger, calculation more complicated, and NURBS curve step error are not easy changed and so on. This paper proposed a study on the algorithm for Newton-Rapson iteration interpolation method of NURBS curve and simulation. We can use Newton-Rapson iterative that calculate (xi, yi, zi). Simulation results show that the proposed NURBS curve interpolator meet the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished. The simulation results show that the algorithm is correct; it is consistent with a NURBS curve interpolation requirements.
Sun, Huafei; Darmofal, David L.
2014-12-01
In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with a dual-consistent output evaluation for elliptic interface problems on interface-conforming meshes, and then extend the method to handle multi-physics interface problems, in particular conjugate heat transfer (CHT) problems. The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process. No assumption is made on the interface shape (other than Lipschitz continuity). We then equip our strategy with an output-based adaptive scheme for an accurate output prediction. Through numerical examples, we demonstrate high-order convergence for elliptic interface problems and CHT problems with both smooth and non-smooth interface shapes.
photon-plasma: A modern high-order particle-in-cell code
International Nuclear Information System (INIS)
Haugbølle, Troels; Frederiksen, Jacob Trier; Nordlund, Åke
2013-01-01
We present the photon-plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation scheme for particle-to-cell interpolation and charge deposition. It includes powerful diagnostics tools with on-the-fly particle tracking, synthetic spectra integration, 2D volume slicing, and a new method to correctly account for radiative cooling in the simulations. A robust technique for imposing (time-dependent) particle and field fluxes on the boundaries is also presented. Using a hybrid OpenMP and MPI approach, the code scales efficiently from 8 to more than 250.000 cores with almost linear weak scaling on a range of architectures. The code is tested with the classical benchmarks particle heating, cold beam instability, and two-stream instability. We also present particle-in-cell simulations of the Kelvin-Helmholtz instability, and new results on radiative collisionless shocks
A Parallel Strategy for High-speed Interpolation of CNC Using Data Space Constraint Method
Directory of Open Access Journals (Sweden)
Shuan-qiang Yang
2013-12-01
Full Text Available A high-speed interpolation scheme using parallel computing is proposed in this paper. The interpolation method is divided into two tasks, namely, the rough task executing in PC and the fine task in the I/O card. During the interpolation procedure, the double buffers are constructed to exchange the interpolation data between the two tasks. Then, the data space constraint method is adapted to ensure the reliable and continuous data communication between the two buffers. Therefore, the proposed scheme can be realized in the common distribution of the operation systems without real-time performance. The high-speed and high-precision motion control can be achieved as well. Finally, an experiment is conducted on the self-developed CNC platform, the test results are shown to verify the proposed method.
Quasi interpolation with Voronoi splines.
Mirzargar, Mahsa; Entezari, Alireza
2011-12-01
We present a quasi interpolation framework that attains the optimal approximation-order of Voronoi splines for reconstruction of volumetric data sampled on general lattices. The quasi interpolation framework of Voronoi splines provides an unbiased reconstruction method across various lattices. Therefore this framework allows us to analyze and contrast the sampling-theoretic performance of general lattices, using signal reconstruction, in an unbiased manner. Our quasi interpolation methodology is implemented as an efficient FIR filter that can be applied online or as a preprocessing step. We present visual and numerical experiments that demonstrate the improved accuracy of reconstruction across lattices, using the quasi interpolation framework. © 2011 IEEE
International Nuclear Information System (INIS)
Misawa, T.; Itakura, H.
1995-01-01
The present article focuses on a dynamical simulation of molecular motion in liquids. In the simulation involving diffusion-controlled reaction with discrete time steps, lack of information regarding the trajectory within the time step may result in a failure to count the number of reactions of the particles within the step. In order to rectify this, an interpolated diffusion process is used. The process is derived from a stochastic interpolation formula recently developed by the first author [J. Math. Phys. 34, 775 (1993)]. In this method, the probability that reaction has occurred during the time step given the initial and final positions of the particles is calculated. Some numerical examples confirm that the theoretical result corresponds to an improvement over the Clifford-Green work [Mol. Phys. 57, 123 (1986)] on the same matter
Scientific data interpolation with low dimensional manifold model
Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley
2018-01-01
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Scientific data interpolation with low dimensional manifold model
International Nuclear Information System (INIS)
Zhu, Wei; Wang, Bao; Barnard, Richard C.; Hauck, Cory D.
2017-01-01
Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries
Dyson, Rodger W.; Goodrich, John W.
2000-01-01
Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.
3D Medical Image Interpolation Based on Parametric Cubic Convolution
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter, which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.
Wavelet-Smoothed Interpolation of Masked Scientific Data for JPEG 2000 Compression
Energy Technology Data Exchange (ETDEWEB)
Brislawn, Christopher M. [Los Alamos National Laboratory
2012-08-13
How should we manage scientific data with 'holes'? Some applications, like JPEG 2000, expect logically rectangular data, but some sources, like the Parallel Ocean Program (POP), generate data that isn't defined on certain subsets. We refer to grid points that lack well-defined, scientifically meaningful sample values as 'masked' samples. Wavelet-smoothing is a highly scalable interpolation scheme for regions with complex boundaries on logically rectangular grids. Computation is based on forward/inverse discrete wavelet transforms, so runtime complexity and memory scale linearly with respect to sample count. Efficient state-of-the-art minimal realizations yield small constants (O(10)) for arithmetic complexity scaling, and in-situ implementation techniques make optimal use of memory. Implementation in two dimensions using tensor product filter banks is straighsorward and should generalize routinely to higher dimensions. No hand-tuning required when the interpolation mask changes, making the method aeractive for problems with time-varying masks. Well-suited for interpolating undefined samples prior to JPEG 2000 encoding. The method outperforms global mean interpolation, as judged by both SNR rate-distortion performance and low-rate artifact mitigation, for data distributions whose histograms do not take the form of sharply peaked, symmetric, unimodal probability density functions. These performance advantages can hold even for data whose distribution differs only moderately from the peaked unimodal case, as demonstrated by POP salinity data. The interpolation method is very general and is not tied to any particular class of applications, could be used for more generic smooth interpolation.
High-order dynamic lattice method for seismic simulation in anisotropic media
Hu, Xiaolin; Jia, Xiaofeng
2018-03-01
The discrete particle-based dynamic lattice method (DLM) offers an approach to simulate elastic wave propagation in anisotropic media by calculating the anisotropic micromechanical interactions between these particles based on the directions of the bonds that connect them in the lattice. To build such a lattice, the media are discretized into particles. This discretization inevitably leads to numerical dispersion. The basic lattice unit used in the original DLM only includes interactions between the central particle and its nearest neighbours; therefore, it represents the first-order form of a particle lattice. The first-order lattice suffers from numerical dispersion compared with other numerical methods, such as high-order finite-difference methods, in terms of seismic wave simulation. Due to its unique way of discretizing the media, the particle-based DLM no longer solves elastic wave equations; this means that one cannot build a high-order DLM by simply creating a high-order discrete operator to better approximate a partial derivative operator. To build a high-order DLM, we carry out a thorough dispersion analysis of the method and discover that by adding more neighbouring particles into the lattice unit, the DLM will yield different spatial accuracy. According to the dispersion analysis, the high-order DLM presented here can adapt the requirement of spatial accuracy for seismic wave simulations. For any given spatial accuracy, we can design a corresponding high-order lattice unit to satisfy the accuracy requirement. Numerical tests show that the high-order DLM improves the accuracy of elastic wave simulation in anisotropic media.
Reduced-order LPV model of flexible wind turbines from high fidelity aeroelastic codes
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Sønderby, Ivan Bergquist; Hansen, Morten Hartvig
2013-01-01
of high-order linear time invariant (LTI) models. Firstly, the high-order LTI models are locally approximated using modal and balanced truncation and residualization. Then, an appropriate coordinate transformation is applied to allow interpolation of the model matrices between points on the parameter...
Occlusion-Aware View Interpolation
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Ince Serdar
2008-01-01
Full Text Available Abstract View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
Occlusion-Aware View Interpolation
Directory of Open Access Journals (Sweden)
Janusz Konrad
2009-01-01
Full Text Available View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
International Nuclear Information System (INIS)
Sulbhewar, Litesh N; Raveendranath, P
2014-01-01
An efficient piezoelectric smart beam finite element based on Reddy’s third-order displacement field and layerwise linear potential is presented here. The present formulation is based on the coupled polynomial field interpolation of variables, unlike conventional piezoelectric beam formulations that use independent polynomials. Governing equations derived using a variational formulation are used to establish the relationship between field variables. The resulting expressions are used to formulate coupled shape functions. Starting with an assumed cubic polynomial for transverse displacement (w) and a linear polynomial for electric potential (φ), coupled polynomials for axial displacement (u) and section rotation (θ) are found. This leads to a coupled quadratic polynomial representation for axial displacement (u) and section rotation (θ). The formulation allows accommodation of extension–bending, shear–bending and electromechanical couplings at the interpolation level itself, in a variationally consistent manner. The proposed interpolation scheme is shown to eliminate the locking effects exhibited by conventional independent polynomial field interpolations and improve the convergence characteristics of HSDT based piezoelectric beam elements. Also, the present coupled formulation uses only three mechanical degrees of freedom per node, one less than the conventional formulations. Results from numerical test problems prove the accuracy and efficiency of the present formulation. (paper)
Fourth-order discrete anisotropic boundary-value problems
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Maciej Leszczynski
2015-09-01
Full Text Available In this article we consider the fourth-order discrete anisotropic boundary value problem with both advance and retardation. We apply the direct method of the calculus of variations and the mountain pass technique to prove the existence of at least one and at least two solutions. Non-existence of non-trivial solutions is also undertaken.
International Nuclear Information System (INIS)
Palau, J.M.; Cathalau, S.; Hudelot, J.P.; Barran, F.; Bellanger, V.; Magnaud, C.; Moreau, F.
2011-01-01
Burnable poisons are extensively used by Light Water Reactor designers in order to preserve the fuel reactivity potential and increase the cycle length (without increasing the uranium enrichment). In the industrial two-steps (assembly 2D transport-core 3D diffusion) calculation schemes these heterogeneities yield to strong flux and cross-sections perturbations that have to be taken into account in the final 3D burn-up calculations. This paper presents the application of an enhanced cross-section interpolation model (implemented in the French CRONOS2 code) to LWR (highly poisoned) depleted core calculations. The principle is to use the absorbers (or actinide) concentrations as the new interpolation parameters instead of the standard local burnup/fluence parameters. It is shown by comparing the standard (burnup/fluence) and new (concentration) interpolation models and using the lattice transport code APOLLO2 as a numerical reference that reactivity and local reaction rate prediction of a 2x2 LWR assembly configuration (slab geometry) is significantly improved with the concentration interpolation model. Gains on reactivity and local power predictions (resp. more than 1000 pcm and 20 % discrepancy reduction compared to the reference APOLLO2 scheme) are obtained by using this model. In particular, when epithermal absorbers are inserted close to thermal poison the 'shadowing' ('screening') spectral effects occurring during control operations are much more correctly modeled by concentration parameters. Through this outstanding example it is highlighted that attention has to be paid to the choice of cross-section interpolation parameters (burnup 'indicator') in core calculations with few energy groups and variable geometries all along the irradiation cycle. Actually, this new model could be advantageously applied to steady-state and transient LWR heterogeneous core computational analysis dealing with strong spectral-history variations under
Time-discrete higher order ALE formulations: a priori error analysis
Bonito, Andrea
2013-03-16
We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds\\' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results. © 2013 Springer-Verlag Berlin Heidelberg.
Input variable selection for interpolating high-resolution climate ...
African Journals Online (AJOL)
Although the primary input data of climate interpolations are usually meteorological data, other related (independent) variables are frequently incorporated in the interpolation process. One such variable is elevation, which is known to have a strong influence on climate. This research investigates the potential of 4 additional ...
Calculation of electromagnetic parameter based on interpolation algorithm
International Nuclear Information System (INIS)
Zhang, Wenqiang; Yuan, Liming; Zhang, Deyuan
2015-01-01
Wave-absorbing material is an important functional material of electromagnetic protection. The wave-absorbing characteristics depend on the electromagnetic parameter of mixed media. In order to accurately predict the electromagnetic parameter of mixed media and facilitate the design of wave-absorbing material, based on the electromagnetic parameters of spherical and flaky carbonyl iron mixture of paraffin base, this paper studied two different interpolation methods: Lagrange interpolation and Hermite interpolation of electromagnetic parameters. The results showed that Hermite interpolation is more accurate than the Lagrange interpolation, and the reflectance calculated with the electromagnetic parameter obtained by interpolation is consistent with that obtained through experiment on the whole. - Highlights: • We use interpolation algorithm on calculation of EM-parameter with limited samples. • Interpolation method can predict EM-parameter well with different particles added. • Hermite interpolation is more accurate than Lagrange interpolation. • Calculating RL based on interpolation is consistent with calculating RL from experiment
Dimension Reduction and Discretization in Stochastic Problems by Regression Method
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
1996-01-01
The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ...
Angular interpolations and splice options for three-dimensional transport computations
International Nuclear Information System (INIS)
Abu-Shumays, I.K.; Yehnert, C.E.
1996-01-01
New, accurate and mathematically rigorous angular Interpolation strategies are presented. These strategies preserve flow and directionality separately over each octant of the unit sphere, and are based on a combination of spherical harmonics expansions and least squares algorithms. Details of a three-dimensional to three-dimensional (3-D to 3-D) splice method which utilizes the new angular interpolations are summarized. The method has been implemented in a multidimensional discrete ordinates transport computer program. Various features of the splice option are illustrated by several applications to a benchmark Dog-Legged Void Neutron (DLVN) streaming and transport experimental assembly
Discrete second order trajectory generator with nonlinear constraints
Morselli, R.; Zanasi, R.; Stramigioli, Stefano
2005-01-01
A discrete second order trajectory generator for motion control systems is presented. The considered generator is a nonlinear system which receives as input a raw reference signal and provides as output a smooth reference signal satisfying nonlinear constraints on the output derivatives as UM-(x) ≤
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Directory of Open Access Journals (Sweden)
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
The interpolation method of stochastic functions and the stochastic variational principle
International Nuclear Information System (INIS)
Liu Xianbin; Chen Qiu
1993-01-01
stochastic finite element equations are not very reasonable. On the other hand, Galerkin Method is hopeful, along with the method, the projection principle had been advanced to solve the stochastic operator equations. In Galerkin Method, by means of projecting the stochastic solution functions into the subspace of the solution function space, the treatment of the stochasticity of the structural physical properties and the loads is reasonable. However, the construction or the selection of the subspace of the solution function space which is a Hilbert Space of stochastic functions is difficult, and furthermore it is short of a reasonable rule to measure whether the approximation of the subspace to the solution function space is fine or not. In stochastic finite element method, the discretization of stochastic functions in space and time shows a very importance, so far, the discrete patterns consist of Local Average Theory, Interpolation Method and Orthogonal Expansion Method. Although the Local Average Theory has already been a success in the stationary random fields, it is not suitable for the non-stationary ones as well. For the general stochastic functions, whether it is stationary or not, interpolation method is available. In the present paper, the authors have shown that the error between the true solution function and its approximation, its projection in the subspace, depends continuously on the errors between the stochastic functions and their interpolation functions, the latter rely continuously on the scales of the discrete elements; so a conclusion can be obtained that the Interpolation method of stochastic functions is convergent. That is to say that the approximation solution functions would limit to the true solution functions when the scales of the discrete elements goes smaller and smaller. Using the Interpolation method, a basis of subspace of the solution function space is constructed in this paper, and by means of combining the projection principle and
Directory of Open Access Journals (Sweden)
Huaiqing Zhang
2014-01-01
Full Text Available The spectral leakage has a harmful effect on the accuracy of harmonic analysis for asynchronous sampling. This paper proposed a time quasi-synchronous sampling algorithm which is based on radial basis function (RBF interpolation. Firstly, a fundamental period is evaluated by a zero-crossing technique with fourth-order Newton’s interpolation, and then, the sampling sequence is reproduced by the RBF interpolation. Finally, the harmonic parameters can be calculated by FFT on the synchronization of sampling data. Simulation results showed that the proposed algorithm has high accuracy in measuring distorted and noisy signals. Compared to the local approximation schemes as linear, quadric, and fourth-order Newton interpolations, the RBF is a global approximation method which can acquire more accurate results while the time-consuming is about the same as Newton’s.
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Pakhnutov I.A.
2017-04-01
Full Text Available the paper deals with iterative interpolation methods in forms of similar recursive procedures defined by a sort of simple functions (interpolation basis not necessarily real valued. These basic functions are kind of arbitrary type being defined just by wish and considerations of user. The studied interpolant construction shows virtue of versatility: it may be used in a wide range of vector spaces endowed with scalar product, no dimension restrictions, both in Euclidean and Hilbert spaces. The choice of basic interpolation functions is as wide as possible since it is subdued nonessential restrictions. The interpolation method considered in particular coincides with traditional polynomial interpolation (mimic of Lagrange method in real unidimensional case or rational, exponential etc. in other cases. The interpolation as iterative process, in fact, is fairly flexible and allows one procedure to change the type of interpolation, depending on the node number in a given set. Linear interpolation basis options (perhaps some nonlinear ones allow to interpolate in noncommutative spaces, such as spaces of nondegenerate matrices, interpolated data can also be relevant elements of vector spaces over arbitrary numeric field. By way of illustration, the author gives the examples of interpolation on the real plane, in the separable Hilbert space and the space of square matrices with vektorvalued source data.
International Nuclear Information System (INIS)
Sims, C.S.; Killough, G.G.
1983-01-01
Various segments of the health physics community advocate the use of different sets of neutron fluence-to-dose equivalent conversion factors as a function of energy and different methods of interpolation between discrete points in those data sets. The major data sets and interpolation methods are used to calculate the spectrum average fluence-to-dose equivalent conversion factors for five spectra associated with the various shielded conditions of the Health Physics Research Reactor. The results obtained by use of the different data sets and interpolation methods are compared and discussed. (author)
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
International Nuclear Information System (INIS)
FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
Fan, W C; Powell, J L
2002-01-01
The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.
International Nuclear Information System (INIS)
Garcia-Santos, J. M.; Torres del rio, S.; Blanco, A.; Rodriguez, R.; Parlorio, E.; Garcia, A.; Girela, E.; Hernandez, M. D.; Canteras, M.
2002-01-01
The purpose of this study was to demonstrate that the use of a high-grade interpolator in the reconstruction of images of the chest increases the resolution, independently of the high-resolution filter. Eight independent observers in two groups (experts and non experts) assessed (two readings separated by a time interval) the same section of the chest reconstructed four times (st-st, st-xs, b-st, b-xs), combining standard (st) and high-resolution (b) filters and standard (st) and high-grade (xs) interpolators. The images were classified from greater to lesser in terms of the resolution perceived. The results were used to compare the degree of resolution introduced by the interpolator and the filter and to determine whether or not there existed variability between observers and between the observations of each, and whether experience played a role in the findings. Six of the eight observers assigned the b-xs images the highest degree of resolution in the majority of cases, followed by the b-st image, the st-xs image and, finally, the st-st image). The other tow observers (one expert and one nonexpert) different only with respect to the order of the st-xs and b-st images, which they assigned the second and third places, respectively. The expert group showed no intra observer variability, while two of the nonexpert observers did. The high-grade interpolator enhances the resolution of images of the chest regardless of who evaluates them, while it does not substantially increase image noise. Thus, its use is recommended in helical computed tomography imaging of the lung. (Author) 10 refs
High-order discrete ordinate transport in hexagonal geometry: A new capability in ERANOS
International Nuclear Information System (INIS)
Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J.M.
2010-01-01
This paper presents the implementation of an arbitrary order discontinuous Galerkin scheme within the framework of a discrete ordinate solver of the neutron transport equation for nuclear reactor calculations. More precisely, it deals with non-conforming spatial meshes for the 2 D and 3 D modeling of core geometries based on hexagonal assemblies. This work aims at improving the capabilities of the ERANOS code system dedicated to fast reactor analysis and design. Both the angular quadrature and spatial scheme peculiarities for hexagonal geometries are presented. A particular focus is set on the spatial non-conforming mesh and variable order capabilities of this scheme in anticipation to the development of spatial adaptiveness algorithms. These features are illustrated on a 3 D numerical benchmark with comparison to a Monte Carlo reference and a 2 D benchmark that shows the potential of this scheme for both h-and p-adaptation.
Discretization of four types of Weyl group orbit functions
International Nuclear Information System (INIS)
Hrivnák, Jiří
2013-01-01
The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented
Multivariate Birkhoff interpolation
Lorentz, Rudolph A
1992-01-01
The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well a...
Gottlieb, Sigal
2015-04-10
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.
High order P-G finite elements for convection-dominated problems
International Nuclear Information System (INIS)
Carmo, E.D. do; Galeao, A.C.
1989-06-01
From the error analysis presented in this paper it is shown that de CCAU method derived by Dutra do Carmo and Galeao [3] preserves the same order of approximation obtained with SUPH (cf. Books and Hughes [2]) when advection-diffusion regular solutions are considered, and improves the accuracy of the approximate boundary layer solution when high order interpolating polynomials are used near sharp layers [pt
Discrete Maximum Principle for Higher-Order Finite Elements in 1D
Czech Academy of Sciences Publication Activity Database
Vejchodský, Tomáš; Šolín, Pavel
2007-01-01
Roč. 76, č. 260 (2007), s. 1833-1846 ISSN 0025-5718 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z20760514 Keywords : discrete maximum principle * discrete Grren´s function * higher-order elements Subject RIV: BA - General Mathematics Impact factor: 1.230, year: 2007
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Rafał Stanisławski
2016-01-01
Full Text Available This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.
Vedadi, Farhang; Shirani, Shahram
2014-01-01
A new method of image resolution up-conversion (image interpolation) based on maximum a posteriori sequence estimation is proposed. Instead of making a hard decision about the value of each missing pixel, we estimate the missing pixels in groups. At each missing pixel of the high resolution (HR) image, we consider an ensemble of candidate interpolation methods (interpolation functions). The interpolation functions are interpreted as states of a Markov model. In other words, the proposed method undergoes state transitions from one missing pixel position to the next. Accordingly, the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing HR pixel positions. We derive a parameter-free probabilistic model for this to-be-estimated sequence of interpolation functions. Then, we solve the estimation problem using a trellis representation and the Viterbi algorithm. Using directional interpolation functions and sequence estimation techniques, we classify the new algorithm as an adaptive directional interpolation using soft-decision estimation techniques. Experimental results show that the proposed algorithm yields images with higher or comparable peak signal-to-noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations.
Improved Multilevel Fast Multipole Method for Higher-Order discretizations
DEFF Research Database (Denmark)
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik
2014-01-01
The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion b...
COMPARISONS BETWEEN DIFFERENT INTERPOLATION TECHNIQUES
Directory of Open Access Journals (Sweden)
G. Garnero
2014-01-01
In the present study different algorithms will be analysed in order to spot an optimal interpolation methodology. The availability of the recent digital model produced by the Regione Piemonte with airborne LIDAR and the presence of sections of testing realized with higher resolutions and the presence of independent digital models on the same territory allow to set a series of analysis with consequent determination of the best methodologies of interpolation. The analysis of the residuals on the test sites allows to calculate the descriptive statistics of the computed values: all the algorithms have furnished interesting results; all the more interesting, notably for dense models, the IDW (Inverse Distance Weighing algorithm results to give best results in this study case. Moreover, a comparative analysis was carried out by interpolating data at different input point density, with the purpose of highlighting thresholds in input density that may influence the quality reduction of the final output in the interpolation phase.
Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming
2017-05-01
The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.
Directory of Open Access Journals (Sweden)
Zhihong Wang
2015-01-01
Full Text Available Considering the varying inertia and load torque in high speed and high accuracy servo systems, a novel discrete second-order sliding mode adaptive controller (DSSMAC based on characteristic model is proposed, and a command observer is also designed. Firstly, the discrete characteristic model of servo systems is established. Secondly, the recursive least square algorithm is adopted to identify time-varying parameters in characteristic model, and the observer is applied to predict the command value of next sample time. Furthermore, the stability of the closed-loop system and the convergence of the observer are analyzed. The experimental results show that the proposed method not only can adapt to varying inertia and load torque, but also has good disturbance rejection ability and robustness to uncertainties.
A 2.9 ps equivalent resolution interpolating time counter based on multiple independent coding lines
International Nuclear Information System (INIS)
Szplet, R; Jachna, Z; Kwiatkowski, P; Rozyc, K
2013-01-01
We present the design, operation and test results of a time counter that has an equivalent resolution of 2.9 ps, a measurement uncertainty at the level of 6 ps, and a measurement range of 10 s. The time counter has been implemented in a general-purpose reprogrammable device Spartan-6 (Xilinx). To obtain both high precision and wide measurement range the counting of periods of a reference clock is combined with a two-stage interpolation within a single period of the clock signal. The interpolation involves a four-phase clock in the first interpolation stage (FIS) and an equivalent coding line (ECL) in the second interpolation stage (SIS). The ECL is created as a compound of independent discrete time coding lines (TCL). The number of TCLs used to create the virtual ECL has an effect on its resolution. We tested ECLs made from up to 16 TCLs, but the idea may be extended to a larger number of lines. In the presented time counter the coarse resolution of the counting method equal to 2 ns (period of the 500 MHz reference clock) is firstly improved fourfold in the FIS and next even more than 400 times in the SIS. The proposed solution allows us to overcome the technological limitation in achievable resolution and improve the precision of conversion of integrated interpolators based on tapped delay lines. (paper)
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Energy Technology Data Exchange (ETDEWEB)
Moulton, J.D.; Ascher, U.M. [Univ. of British Columbia, Vancouver, British Columbia (Canada); Morel, J.E. [Los Alamos National Lab., NM (United States)
1996-12-31
Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.
Directory of Open Access Journals (Sweden)
Kurt James Werner
2016-10-01
Full Text Available The magnitude of the Discrete Fourier Transform (DFT of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions.
Roy, Subrata P.
2014-01-28
The method of moments with interpolative closure (MOMIC) for soot formation and growth provides a detailed modeling framework maintaining a good balance in generality, accuracy, robustness, and computational efficiency. This study presents several computational issues in the development and implementation of the MOMIC-based soot modeling for direct numerical simulations (DNS). The issues of concern include a wide dynamic range of numbers, choice of normalization, high effective Schmidt number of soot particles, and realizability of the soot particle size distribution function (PSDF). These problems are not unique to DNS, but they are often exacerbated by the high-order numerical schemes used in DNS. Four specific issues are discussed in this article: the treatment of soot diffusion, choice of interpolation scheme for MOMIC, an approach to deal with strongly oxidizing environments, and realizability of the PSDF. General, robust, and stable approaches are sought to address these issues, minimizing the use of ad hoc treatments such as clipping. The solutions proposed and demonstrated here are being applied to generate new physical insight into complex turbulence-chemistry-soot-radiation interactions in turbulent reacting flows using DNS. © 2014 Copyright Taylor and Francis Group, LLC.
Interpolation for de-Dopplerisation
Graham, W. R.
2018-05-01
'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.
Image Interpolation Scheme based on SVM and Improved PSO
Jia, X. F.; Zhao, B. T.; Liu, X. X.; Song, H. P.
2018-01-01
In order to obtain visually pleasing images, a support vector machines (SVM) based interpolation scheme is proposed, in which the improved particle swarm optimization is applied to support vector machine parameters optimization. Training samples are constructed by the pixels around the pixel to be interpolated. Then the support vector machine with optimal parameters is trained using training samples. After the training, we can get the interpolation model, which can be employed to estimate the unknown pixel. Experimental result show that the interpolated images get improvement PNSR compared with traditional interpolation methods, which is agrees with the subjective quality.
Anyonic order parameters for discrete gauge theories on the lattice
International Nuclear Information System (INIS)
Bais, F.A.; Romers, J.C.
2009-01-01
We present a new family of gauge invariant non-local order parameters Δ α A for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite group H. These combine magnetic flux-sector labeled by a conjugacy class with an electric representation of the centralizer subgroup that commutes with the flux. In particular, cases like the trivial class for magnetic flux, or the trivial irrep for electric charge, these order parameters reduce to the familiar Wilson and the 't Hooft operators, respectively. It is pointed out that these novel operators are crucial for probing the phase structure of a class of discrete lattice models we define, using Monte Carlo simulations.
Energy Technology Data Exchange (ETDEWEB)
Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701 (South Africa); Gerlach, E. [Lohrmann Observatory, Technical University Dresden, D-01062 Dresden (Germany); Bodyfelt, J.D., E-mail: J.Bodyfelt@massey.ac.nz [Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Albany, Private Bag 102904, North Shore City, Auckland 0745 (New Zealand); Papamikos, G. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Eggl, S. [IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris (France)
2014-05-01
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.
International Nuclear Information System (INIS)
Skokos, Ch.; Gerlach, E.; Bodyfelt, J.D.; Papamikos, G.; Eggl, S.
2014-01-01
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.
Time-discrete higher order ALE formulations: a priori error analysis
Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.
2013-01-01
We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our
On discrete 2D integrable equations of higher order
International Nuclear Information System (INIS)
Adler, V E; Postnikov, V V
2014-01-01
We study two-dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund–Darboux transformations for the lattice equations of Bogoyavlensky type. (paper)
Jiang, Jiamin; Younis, Rami M.
2017-06-01
The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.
Comparing interpolation schemes in dynamic receive ultrasound beamforming
DEFF Research Database (Denmark)
Kortbek, Jacob; Andresen, Henrik; Nikolov, Svetoslav
2005-01-01
In medical ultrasound interpolation schemes are of- ten applied in receive focusing for reconstruction of image points. This paper investigates the performance of various interpolation scheme by means of ultrasound simulations of point scatterers in Field II. The investigation includes conventional...... B-mode imaging and synthetic aperture (SA) imaging using a 192-element, 7 MHz linear array transducer with λ pitch as simulation model. The evaluation consists primarily of calculations of the side lobe to main lobe ratio, SLMLR, and the noise power of the interpolation error. When using...... conventional B-mode imaging and linear interpolation, the difference in mean SLMLR is 6.2 dB. With polynomial interpolation the ratio is in the range 6.2 dB to 0.3 dB using 2nd to 5th order polynomials, and with FIR interpolation the ratio is in the range 5.8 dB to 0.1 dB depending on the filter design...
Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A
2017-08-21
In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.
Interpolation of band-limited discrete-time signals by minimising out-of-band energy
Janssen, A.J.E.M.; Vries, L.B.
1984-01-01
An interpolation method for restoring burst errors in discrete—time, band—limited signals is presented. The restoration is such that the restored signal has minimal out—of—band energy. The filter coefficients depend Only on the burst length and on the size of the band to which the signal is assumed
An Improved Rotary Interpolation Based on FPGA
Directory of Open Access Journals (Sweden)
Mingyu Gao
2014-08-01
Full Text Available This paper presents an improved rotary interpolation algorithm, which consists of a standard curve interpolation module and a rotary process module. Compared to the conventional rotary interpolation algorithms, the proposed rotary interpolation algorithm is simpler and more efficient. The proposed algorithm was realized on a FPGA with Verilog HDL language, and simulated by the ModelSim software, and finally verified on a two-axis CNC lathe, which uses rotary ellipse and rotary parabolic as an example. According to the theoretical analysis and practical process validation, the algorithm has the following advantages: firstly, less arithmetic items is conducive for interpolation operation; and secondly the computing time is only two clock cycles of the FPGA. Simulations and actual tests have proved that the high accuracy and efficiency of the algorithm, which shows that it is highly suited for real-time applications.
Huang, Ai-Mei; Nguyen, Truong
2009-04-01
In this paper, we address the problems of unreliable motion vectors that cause visual artifacts but cannot be detected by high residual energy or bidirectional prediction difference in motion-compensated frame interpolation. A correlation-based motion vector processing method is proposed to detect and correct those unreliable motion vectors by explicitly considering motion vector correlation in the motion vector reliability classification, motion vector correction, and frame interpolation stages. Since our method gradually corrects unreliable motion vectors based on their reliability, we can effectively discover the areas where no motion is reliable to be used, such as occlusions and deformed structures. We also propose an adaptive frame interpolation scheme for the occlusion areas based on the analysis of their surrounding motion distribution. As a result, the interpolated frames using the proposed scheme have clearer structure edges and ghost artifacts are also greatly reduced. Experimental results show that our interpolated results have better visual quality than other methods. In addition, the proposed scheme is robust even for those video sequences that contain multiple and fast motions.
Effective Hamiltonian for travelling discrete breathers
MacKay, Robert S.; Sepulchre, Jacques-Alexandre
2002-05-01
Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.
High order backward discretization of the neutron diffusion equation
Energy Technology Data Exchange (ETDEWEB)
Ginestar, D.; Bru, R.; Marin, J. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion
1997-11-21
Fast codes capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear reactor. We propose a new discretization technique for the time integration of the neutron diffusion equation, based on the backward difference formulas for systems of stiff ordinary differential equations. This method needs to solve a system of linear equations for each integration step, and for this purpose, we have developed an iterative block algorithm combined with a variational acceleration technique. We tested the algorithm with two benchmark problems, and compared the results with those provided by other codes, concluding that the performance and overall agreement are very good. (author).
Anisotropic interpolation theorems of Musielak-Orlicz type
Directory of Open Access Journals (Sweden)
Jinxia Li
2016-10-01
Full Text Available Abstract Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k : k ∈ Z } $\\{A^{k}: k\\in\\mathbb{Z}\\}$ , where A is a real n × n $n\\times n$ matrix with all its eigenvalues λ satisfy | λ | > 1 $|\\lambda|>1$ . Let φ : R n × [ 0 , ∞ → [ 0 , ∞ $\\varphi: \\mathbb{R}^{n}\\times[0, \\infty\\to[0,\\infty$ be an anisotropic Musielak-Orlicz function such that φ ( x , ⋅ $\\varphi(x,\\cdot$ is an Orlicz function and φ ( ⋅ , t $\\varphi(\\cdot,t$ is a Muckenhoupt A ∞ ( A $\\mathbb {A}_{\\infty}(A$ weight. The aim of this article is to obtain two anisotropic interpolation theorems of Musielak-Orlicz type, which are weighted anisotropic extension of Marcinkiewicz interpolation theorems. The above results are new even for the isotropic weighted settings.
An efficient interpolation filter VLSI architecture for HEVC standard
Zhou, Wei; Zhou, Xin; Lian, Xiaocong; Liu, Zhenyu; Liu, Xiaoxiang
2015-12-01
The next-generation video coding standard of High-Efficiency Video Coding (HEVC) is especially efficient for coding high-resolution video such as 8K-ultra-high-definition (UHD) video. Fractional motion estimation in HEVC presents a significant challenge in clock latency and area cost as it consumes more than 40 % of the total encoding time and thus results in high computational complexity. With aims at supporting 8K-UHD video applications, an efficient interpolation filter VLSI architecture for HEVC is proposed in this paper. Firstly, a new interpolation filter algorithm based on the 8-pixel interpolation unit is proposed in this paper. It can save 19.7 % processing time on average with acceptable coding quality degradation. Based on the proposed algorithm, an efficient interpolation filter VLSI architecture, composed of a reused data path of interpolation, an efficient memory organization, and a reconfigurable pipeline interpolation filter engine, is presented to reduce the implement hardware area and achieve high throughput. The final VLSI implementation only requires 37.2k gates in a standard 90-nm CMOS technology at an operating frequency of 240 MHz. The proposed architecture can be reused for either half-pixel interpolation or quarter-pixel interpolation, which can reduce the area cost for about 131,040 bits RAM. The processing latency of our proposed VLSI architecture can support the real-time processing of 4:2:0 format 7680 × 4320@78fps video sequences.
A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems
Matos , Carlos; Ortigueira , Manuel ,
2012-01-01
Part 10: Signal Processing; International audience; In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(sα+p) is proposed. We will show that such fractional-order LTI system can be decomposed into sub-systems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be done using the Laplace transform inversion integr...
Multiple periodic solutions for a fourth-order discrete Hamiltonian system
Directory of Open Access Journals (Sweden)
Yongkun Li
2010-12-01
Full Text Available By means of a three critical points theorem proposed by Brezis and Nirenberg and a general version of Mountain Pass Theorem, we obtain some multiplicity results for periodic solutions of a fourth-order discrete Hamiltonian system Δ4u(t-2+∇ F(t,u(t=0 for all t∈ Z.
High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps
International Nuclear Information System (INIS)
Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.; Chen, Xiao
2017-01-01
This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. It relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.
Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications
Directory of Open Access Journals (Sweden)
Ruyun Ma
2014-01-01
Full Text Available Let T>1 be an integer, and let=1,2,…,T. We discuss the spectrum of discrete linear second-order eigenvalue problems Δ2ut-1+λmtut=0, t∈, u0=uT+1=0, where λ≠0 is a parameter, m:→ℝ changes sign and mt≠0 on . At last, as an application of this spectrum result, we show the existence of sign-changing solutions of discrete nonlinear second-order problems by using bifurcate technique.
Shape-based interpolation of multidimensional grey-level images
International Nuclear Information System (INIS)
Grevera, G.J.; Udupa, J.K.
1996-01-01
Shape-based interpolation as applied to binary images causes the interpolation process to be influenced by the shape of the object. It accomplishes this by first applying a distance transform to the data. This results in the creation of a grey-level data set in which the value at each point represents the minimum distance from that point to the surface of the object. (By convention, points inside the object are assigned positive values; points outside are assigned negative values.) This distance transformed data set is then interpolated using linear or higher-order interpolation and is then thresholded at a distance value of zero to produce the interpolated binary data set. In this paper, the authors describe a new method that extends shape-based interpolation to grey-level input data sets. This generalization consists of first lifting the n-dimensional (n-D) image data to represent it as a surface, or equivalently as a binary image, in an (n + 1)-dimensional [(n + 1)-D] space. The binary shape-based method is then applied to this image to create an (n + 1)-D binary interpolated image. Finally, this image is collapsed (inverse of lifting) to create the n-D interpolated grey-level data set. The authors have conducted several evaluation studies involving patient computed tomography (CT) and magnetic resonance (MR) data as well as mathematical phantoms. They all indicate that the new method produces more accurate results than commonly used grey-level linear interpolation methods, although at the cost of increased computation
First-order discrete Faddeev gravity at strongly varying fields
Khatsymovsky, V. M.
2017-11-01
We consider the Faddeev formulation of general relativity (GR), which can be characterized by a kind of d-dimensional tetrad (typically d = 10) and a non-Riemannian connection. This theory is invariant w.r.t. the global, but not local, rotations in the d-dimensional space. There can be configurations with a smooth or flat metric, but with the tetrad that changes abruptly at small distances, a kind of “antiferromagnetic” structure. Previously, we discussed a first-order representation for the Faddeev gravity, which uses the orthogonal connection in the d-dimensional space as an independent variable. Using the discrete form of this formulation, we considered the spectrum of (elementary) area. This spectrum turns out to be physically reasonable just on a classical background with large connection like rotations by π, that is, with such an “antiferromagnetic” structure. In the discrete first-order Faddeev gravity, we consider such a structure with periodic cells and large connection and strongly changing tetrad field inside the cell. We show that this system in the continuum limit reduces to a generalization of the Faddeev system. The action is a sum of related actions of the Faddeev type and is still reduced to the GR action.
Smooth Phase Interpolated Keying
Borah, Deva K.
2007-01-01
Smooth phase interpolated keying (SPIK) is an improved method of computing smooth phase-modulation waveforms for radio communication systems that convey digital information. SPIK is applicable to a variety of phase-shift-keying (PSK) modulation schemes, including quaternary PSK (QPSK), octonary PSK (8PSK), and 16PSK. In comparison with a related prior method, SPIK offers advantages of better performance and less complexity of implementation. In a PSK scheme, the underlying information waveform that one seeks to convey consists of discrete rectangular steps, but the spectral width of such a waveform is excessive for practical radio communication. Therefore, the problem is to smooth the step phase waveform in such a manner as to maintain power and bandwidth efficiency without incurring an unacceptably large error rate and without introducing undesired variations in the amplitude of the affected radio signal. Although the ideal constellation of PSK phasor points does not cause amplitude variations, filtering of the modulation waveform (in which, typically, a rectangular pulse is converted to a square-root raised cosine pulse) causes amplitude fluctuations. If a power-efficient nonlinear amplifier is used in the radio communication system, the fluctuating-amplitude signal can undergo significant spectral regrowth, thus compromising the bandwidth efficiency of the system. In the related prior method, one seeks to solve the problem in a procedure that comprises two major steps: phase-value generation and phase interpolation. SPIK follows the two-step approach of the related prior method, but the details of the steps are different. In the phase-value-generation step, the phase values of symbols in the PSK constellation are determined by a phase function that is said to be maximally smooth and that is chosen to minimize the spectral spread of the modulated signal. In this step, the constellation is divided into two groups by assigning, to information symbols, phase values
International Nuclear Information System (INIS)
Casa, L D C; Krueger, P S
2013-01-01
Unstructured three-dimensional fluid velocity data were interpolated using Gaussian radial basis function (RBF) interpolation. Data were generated to imitate the spatial resolution and experimental uncertainty of a typical implementation of defocusing digital particle image velocimetry. The velocity field associated with a steadily rotating infinite plate was simulated to provide a bounded, fully three-dimensional analytical solution of the Navier–Stokes equations, allowing for robust analysis of the interpolation accuracy. The spatial resolution of the data (i.e. particle density) and the number of RBFs were varied in order to assess the requirements for accurate interpolation. Interpolation constraints, including boundary conditions and continuity, were included in the error metric used for the least-squares minimization that determines the interpolation parameters to explore methods for improving RBF interpolation results. Even spacing and logarithmic spacing of RBF locations were also investigated. Interpolation accuracy was assessed using the velocity field, divergence of the velocity field, and viscous torque on the rotating boundary. The results suggest that for the present implementation, RBF spacing of 0.28 times the boundary layer thickness is sufficient for accurate interpolation, though theoretical error analysis suggests that improved RBF positioning may yield more accurate results. All RBF interpolation results were compared to standard Gaussian weighting and Taylor expansion interpolation methods. Results showed that RBF interpolation improves interpolation results compared to the Taylor expansion method by 60% to 90% based on the average squared velocity error and provides comparable velocity results to Gaussian weighted interpolation in terms of velocity error. RMS accuracy of the flow field divergence was one to two orders of magnitude better for the RBF interpolation compared to the other two methods. RBF interpolation that was applied to
Application of ordinary kriging for interpolation of micro-structured technical surfaces
International Nuclear Information System (INIS)
Raid, Indek; Kusnezowa, Tatjana; Seewig, Jörg
2013-01-01
Kriging is an interpolation technique used in geostatistics. In this paper we present kriging applied in the field of three-dimensional optical surface metrology. Technical surfaces are not always optically cooperative, meaning that measurements of technical surfaces contain invalid data points because of different effects. These data points need to be interpolated to obtain a complete area in order to fulfil further processing. We present an elementary type of kriging, known as ordinary kriging, and apply it to interpolate measurements of different technical surfaces containing different kinds of realistic defects. The result of the interpolation with kriging is compared to six common interpolation techniques: nearest neighbour, natural neighbour, inverse distance to a power, triangulation with linear interpolation, modified Shepard's method and radial basis function. In order to quantify the results of different interpolations, the topographies are compared to defect-free reference topographies. Kriging is derived from a stochastic model that suggests providing an unbiased, linear estimation with a minimized error variance. The estimation with kriging is based on a preceding statistical analysis of the spatial structure of the surface. This comprises the choice and adaptation of specific models of spatial continuity. In contrast to common methods, kriging furthermore considers specific anisotropy in the data and adopts the interpolation accordingly. The gained benefit requires some additional effort in preparation and makes the overall estimation more time-consuming than common methods. However, the adaptation to the data makes this method very flexible and accurate. (paper)
Mining the multigroup-discrete ordinates algorithm for high quality solutions
International Nuclear Information System (INIS)
Ganapol, B.D.; Kornreich, D.E.
2005-01-01
A novel approach to the numerical solution of the neutron transport equation via the discrete ordinates (SN) method is presented. The new technique is referred to as 'mining' low order (SN) numerical solutions to obtain high order accuracy. The new numerical method, called the Multigroup Converged SN (MGCSN) algorithm, is a combination of several sequence accelerators: Romberg and Wynn-epsilon. The extreme accuracy obtained by the method is demonstrated through self consistency and comparison to the independent semi-analytical benchmark BLUE. (authors)
Coarse-mesh discretized low-order quasi-diffusion equations for subregion averaged scalar fluxes
International Nuclear Information System (INIS)
Anistratov, D. Y.
2004-01-01
In this paper we develop homogenization procedure and discretization for the low-order quasi-diffusion equations on coarse grids for core-level reactor calculations. The system of discretized equations of the proposed method is formulated in terms of the subregion averaged group scalar fluxes. The coarse-mesh solution is consistent with a given fine-mesh discretization of the transport equation in the sense that it preserves a set of average values of the fine-mesh transport scalar flux over subregions of coarse-mesh cells as well as the surface currents, and eigenvalue. The developed method generates numerical solution that mimics the large-scale behavior of the transport solution within assemblies. (authors)
Bifurcation and chaos of a new discrete fractional-order logistic map
Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu
2018-04-01
The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.
Effect of interpolation on parameters extracted from seating interface pressure arrays.
Wininger, Michael; Crane, Barbara
2014-01-01
Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pressure array data and compared against a conventional low-pass filtering operation. Additionally, analysis of the effect of tandem filtering and interpolation, as well as the interpolation degree (interpolating to 2, 4, and 8 times sampling density), was undertaken. The following recommendations are made regarding approaches that minimized distortion of features extracted from the pressure maps: (1) filter prior to interpolate (strong effect); (2) use of cubic interpolation versus linear (slight effect); and (3) nominal difference between interpolation orders of 2, 4, and 8 times (negligible effect). We invite other investigators to perform similar benchmark analyses on their own data in the interest of establishing a community consensus of best practices in pressure array data processing.
Linear Methods for Image Interpolation
Pascal Getreuer
2011-01-01
We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.
Stein, A.
1991-01-01
The theory and practical application of techniques of statistical interpolation are studied in this thesis, and new developments in multivariate spatial interpolation and the design of sampling plans are discussed. Several applications to studies in soil science are
Lagrangian Finite-Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy
DEFF Research Database (Denmark)
Marin, José Manuel Román; Rasmussen, Henrik K.
2009-01-01
system attached to the particles is discretized by ten-node quadratic tetrahedral elements using Cartesian coordinates and the pressure by linear interpolation inside these elements. The spatial discretization of the governing equations follows the mixed Galerkin finite element method. The time integral...... is discretized by a quadratic interpolation in time. The convergence of the method in time and space was demonstrated on the free surface problem of a filament stretched between two plates, considering the axisymmetric case as well as the growth of non-axisymmetric disturbances on the free surface. The scheme...
Linear Methods for Image Interpolation
Directory of Open Access Journals (Sweden)
Pascal Getreuer
2011-09-01
Full Text Available We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
International Nuclear Information System (INIS)
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-01-01
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
Mahmoudzadeh, Amir Pasha; Kashou, Nasser H
2013-01-01
Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.
Directory of Open Access Journals (Sweden)
Amir Pasha Mahmoudzadeh
2013-01-01
Full Text Available Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order and to compare the effect of cost functions (least squares (LS, normalized mutual information (NMI, normalized cross correlation (NCC, and correlation ratio (CR for optimized automatic image registration (OAIR on 3D spoiled gradient recalled (SPGR magnetic resonance images (MRI of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.
Interpolating string field theories
International Nuclear Information System (INIS)
Zwiebach, B.
1992-01-01
This paper reports that a minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles
Undecidability of the Logic of Overlap Relation over Discrete Linear Orderings
DEFF Research Database (Denmark)
Bresolin, Davide; Della Monica, Dario; Goranko, Valentin
2010-01-01
. Still, decidability is the rule for the fragments of HS with only one modal operator, based on an Allen’s relation. In this paper, we show that the logic O of the Overlap relation, when interpreted over discrete linear orderings, is an exception. The proof is based on a reduction from the undecidable...
Real-time interpolation for true 3-dimensional ultrasound image volumes.
Ji, Songbai; Roberts, David W; Hartov, Alex; Paulsen, Keith D
2011-02-01
We compared trilinear interpolation to voxel nearest neighbor and distance-weighted algorithms for fast and accurate processing of true 3-dimensional ultrasound (3DUS) image volumes. In this study, the computational efficiency and interpolation accuracy of the 3 methods were compared on the basis of a simulated 3DUS image volume, 34 clinical 3DUS image volumes from 5 patients, and 2 experimental phantom image volumes. We show that trilinear interpolation improves interpolation accuracy over both the voxel nearest neighbor and distance-weighted algorithms yet achieves real-time computational performance that is comparable to the voxel nearest neighbor algrorithm (1-2 orders of magnitude faster than the distance-weighted algorithm) as well as the fastest pixel-based algorithms for processing tracked 2-dimensional ultrasound images (0.035 seconds per 2-dimesional cross-sectional image [76,800 pixels interpolated, or 0.46 ms/1000 pixels] and 1.05 seconds per full volume with a 1-mm(3) voxel size [4.6 million voxels interpolated, or 0.23 ms/1000 voxels]). On the basis of these results, trilinear interpolation is recommended as a fast and accurate interpolation method for rectilinear sampling of 3DUS image acquisitions, which is required to facilitate subsequent processing and display during operating room procedures such as image-guided neurosurgery.
Gas proportional detectors with interpolating cathode pad readout for high track multiplicities
International Nuclear Information System (INIS)
Yu, Bo.
1991-12-01
New techniques for position encoding in very high rate particle and photon detectors will be required in experiments planned for future particle accelerators such as the Superconducting Super Collider and new, high intensity, synchrotron sources. Studies of two interpolating cathode ''pad'' readout systems are described in this thesis. They are well suited for high multiplicity, two dimensional unambiguous position sensitive detection of minimum ionizing particles and heavy ions as well as detection of x-rays at high counting rates. One of the readout systems uses subdivided rows of pads interconnected by resistive strips as the cathode of a multiwire proportional chamber (MWPC). A position resolution of less than 100 μm rms, for 5.4 keV x-rays, and differential non-linearity of 12% have been achieved. Low mass (∼0.6% of a radiation length) detector construction techniques have been developed. The second readout system uses rows of chevron shaped cathode pads to perform geometrical charge division. Position resolution (FWHM) of about 1% of the readout spacing and differential non-linearity of 10% for 5.4 keV x-rays have been achieved. A review of other interpolating methods is included. Low mass cathode construction techniques are described. In conclusion, applications and future developments are discussed. 54 refs
Pujades-Claumarchirant, Ma Carmen; Granero, Domingo; Perez-Calatayud, Jose; Ballester, Facundo; Melhus, Christopher; Rivard, Mark
2010-03-01
The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose function g L ( r ) and 2D anisotropy function F ( r , θ ) table entries for radial distance r and polar angle θ . The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive g L ( r ) and F ( r , θ ) from the reported data; 2) to determine the minimum number of entries in g L ( r ) and F ( r , θ ) that allow reproduction of dose distributions with sufficient accuracy. Four high-energy photon-emitting brachytherapy sources were studied: 60 Co model Co0.A86, 137 Cs model CSM-3, 192 Ir model Ir2.A85-2, and 169 Yb hypothetical model. The mesh used for r was: 0.25, 0.5, 0.75, 1, 1.5, 2-8 (integer steps) and 10 cm. Four different angular steps were evaluated for F ( r , θ ): 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated for g L ( r ). Linear-linear interpolation was used to obtain F ( r , θ ) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for the four sources with the same grid. Linear interpolation of g L ( r ) provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation of F ( r , θ ) using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for 60 Co, 192 Ir, and 169 Yb, while 137 Cs agreement was ≤ 1.5% for θ energy brachytherapy sources, and was similar to commonly found examples in the published literature. For F ( r , θ ) close to the source longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.
Feature displacement interpolation
DEFF Research Database (Denmark)
Nielsen, Mads; Andresen, Per Rønsholt
1998-01-01
Given a sparse set of feature matches, we want to compute an interpolated dense displacement map. The application may be stereo disparity computation, flow computation, or non-rigid medical registration. Also estimation of missing image data, may be phrased in this framework. Since the features...... often are very sparse, the interpolation model becomes crucial. We show that a maximum likelihood estimation based on the covariance properties (Kriging) show properties more expedient than methods such as Gaussian interpolation or Tikhonov regularizations, also including scale......-selection. The computational complexities are identical. We apply the maximum likelihood interpolation to growth analysis of the mandibular bone. Here, the features used are the crest-lines of the object surface....
Fast image interpolation via random forests.
Huang, Jun-Jie; Siu, Wan-Chi; Liu, Tian-Rui
2015-10-01
This paper proposes a two-stage framework for fast image interpolation via random forests (FIRF). The proposed FIRF method gives high accuracy, as well as requires low computation. The underlying idea of this proposed work is to apply random forests to classify the natural image patch space into numerous subspaces and learn a linear regression model for each subspace to map the low-resolution image patch to high-resolution image patch. The FIRF framework consists of two stages. Stage 1 of the framework removes most of the ringing and aliasing artifacts in the initial bicubic interpolated image, while Stage 2 further refines the Stage 1 interpolated image. By varying the number of decision trees in the random forests and the number of stages applied, the proposed FIRF method can realize computationally scalable image interpolation. Extensive experimental results show that the proposed FIRF(3, 2) method achieves more than 0.3 dB improvement in peak signal-to-noise ratio over the state-of-the-art nonlocal autoregressive modeling (NARM) method. Moreover, the proposed FIRF(1, 1) obtains similar or better results as NARM while only takes its 0.3% computational time.
On an integrable discretization of the modified Korteweg-de Vries equation
Suris, Yuri B.
1997-02-01
We find time discretizations for the two “second flows” of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.
High-order conservative discretizations for some cases of the rigid body motion
International Nuclear Information System (INIS)
Kozlov, Roman
2008-01-01
Modified vector fields can be used to construct high-order structure-preserving numerical integrators for ordinary differential equations. In the present Letter we consider high-order integrators based on the implicit midpoint rule, which conserve quadratic first integrals. It is shown that these integrators are particularly suitable for the rigid body motion with an additional quadratic first integral. In this case high-order integrators preserve all four first integrals of motion. The approach is illustrated on the Lagrange top (a rotationally symmetric rigid body with a fixed point on the symmetry axis). The equations of motion are considered in the space fixed frame because in this frame Lagrange top admits a neat description. The Lagrange top motion includes the spherical pendulum and the planar pendulum, which swings in a vertical plane, as particular cases
Some properties of orders of quaternion algebras with regard to the discrete norm
Czech Academy of Sciences Publication Activity Database
Horníček, J.; Kureš, M.; Macálková, Lenka
2016-01-01
Roč. 141, č. 3 (2016), s. 385-405 ISSN 0862-7959 R&D Projects: GA MŠk(CZ) LO1415; GA MŠk(CZ) LM2010007 Institutional support: RVO:67179843 Keywords : order in an imaginary quadratic field * order in a quaternion algebra * discretely normed ring * isomorphism * primitive algebra Subject RIV: BA - General Mathematics
Discrete mathematics in the high school curriculum
Anderson, I.; Asch, van A.G.; van Lint, J.H.
2004-01-01
In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various
Multiscale empirical interpolation for solving nonlinear PDEs
Calo, Victor M.
2014-12-01
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with multiscale basis functions computed offline. Computing the GMsFEM solution involves calculating the system residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully-resolved fine scale one. The empirical interpolation method uses basis functions which are built by sampling the nonlinear function we want to approximate a limited number of times. The coefficients needed for this approximation are computed in the offline stage by inverting an inexpensive linear system. The proposed multiscale empirical interpolation techniques: (1) divide computing the nonlinear function into coarse regions; (2) evaluate contributions of nonlinear functions in each coarse region taking advantage of a reduced-order representation of the solution; and (3) introduce multiscale proper-orthogonal-decomposition techniques to find appropriate interpolation vectors. We demonstrate the effectiveness of the proposed methods on several nonlinear multiscale PDEs that are solved with Newton\\'s methods and fully-implicit time marching schemes. Our numerical results show that the proposed methods provide a robust framework for solving nonlinear multiscale PDEs on a coarse grid with bounded error and significant computational cost reduction.
Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi
2016-07-01
We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free
Schulte, Friederike A; Lambers, Floor M; Mueller, Thomas L; Stauber, Martin; Müller, Ralph
2014-04-01
Time-lapsed in vivo micro-computed tomography is a powerful tool to analyse longitudinal changes in the bone micro-architecture. Registration can overcome problems associated with spatial misalignment between scans; however, it requires image interpolation which might affect the outcome of a subsequent bone morphometric analysis. The impact of the interpolation error itself, though, has not been quantified to date. Therefore, the purpose of this ex vivo study was to elaborate the effect of different interpolator schemes [nearest neighbour, tri-linear and B-spline (BSP)] on bone morphometric indices. None of the interpolator schemes led to significant differences between interpolated and non-interpolated images, with the lowest interpolation error found for BSPs (1.4%). Furthermore, depending on the interpolator, the processing order of registration, Gaussian filtration and binarisation played a role. Independent from the interpolator, the present findings suggest that the evaluation of bone morphometry should be done with images registered using greyscale information.
Interpolation functions and the Lions-Peetre interpolation construction
International Nuclear Information System (INIS)
Ovchinnikov, V I
2014-01-01
The generalization of the Lions-Peetre interpolation method of means considered in the present survey is less general than the generalizations known since the 1970s. However, our level of generalization is sufficient to encompass spaces that are most natural from the point of view of applications, like the Lorentz spaces, Orlicz spaces, and their analogues. The spaces φ(X 0 ,X 1 ) p 0 ,p 1 considered here have three parameters: two positive numerical parameters p 0 and p 1 of equal standing, and a function parameter φ. For p 0 ≠p 1 these spaces can be regarded as analogues of Orlicz spaces under the real interpolation method. Embedding criteria are established for the family of spaces φ(X 0 ,X 1 ) p 0 ,p 1 , together with optimal interpolation theorems that refine all the known interpolation theorems for operators acting on couples of weighted spaces L p and that extend these theorems beyond scales of spaces. The main specific feature is that the function parameter φ can be an arbitrary natural functional parameter in the interpolation. Bibliography: 43 titles
Contrast-guided image interpolation.
Wei, Zhe; Ma, Kai-Kuang
2013-11-01
In this paper a contrast-guided image interpolation method is proposed that incorporates contrast information into the image interpolation process. Given the image under interpolation, four binary contrast-guided decision maps (CDMs) are generated and used to guide the interpolation filtering through two sequential stages: 1) the 45(°) and 135(°) CDMs for interpolating the diagonal pixels and 2) the 0(°) and 90(°) CDMs for interpolating the row and column pixels. After applying edge detection to the input image, the generation of a CDM lies in evaluating those nearby non-edge pixels of each detected edge for re-classifying them possibly as edge pixels. This decision is realized by solving two generalized diffusion equations over the computed directional variation (DV) fields using a derived numerical approach to diffuse or spread the contrast boundaries or edges, respectively. The amount of diffusion or spreading is proportional to the amount of local contrast measured at each detected edge. The diffused DV fields are then thresholded for yielding the binary CDMs, respectively. Therefore, the decision bands with variable widths will be created on each CDM. The two CDMs generated in each stage will be exploited as the guidance maps to conduct the interpolation process: for each declared edge pixel on the CDM, a 1-D directional filtering will be applied to estimate its associated to-be-interpolated pixel along the direction as indicated by the respective CDM; otherwise, a 2-D directionless or isotropic filtering will be used instead to estimate the associated missing pixels for each declared non-edge pixel. Extensive simulation results have clearly shown that the proposed contrast-guided image interpolation is superior to other state-of-the-art edge-guided image interpolation methods. In addition, the computational complexity is relatively low when compared with existing methods; hence, it is fairly attractive for real-time image applications.
High-temperature behavior of a deformed Fermi gas obeying interpolating statistics.
Algin, Abdullah; Senay, Mustafa
2012-04-01
An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.
Reducing Interpolation Artifacts for Mutual Information Based Image Registration
Soleimani, H.; Khosravifard, M.A.
2011-01-01
Medical image registration methods which use mutual information as similarity measure have been improved in recent decades. Mutual Information is a basic concept of Information theory which indicates the dependency of two random variables (or two images). In order to evaluate the mutual information of two images their joint probability distribution is required. Several interpolation methods, such as Partial Volume (PV) and bilinear, are used to estimate joint probability distribution. Both of these two methods yield some artifacts on mutual information function. Partial Volume-Hanning window (PVH) and Generalized Partial Volume (GPV) methods are introduced to remove such artifacts. In this paper we show that the acceptable performance of these methods is not due to their kernel function. It's because of the number of pixels which incorporate in interpolation. Since using more pixels requires more complex and time consuming interpolation process, we propose a new interpolation method which uses only four pixels (the same as PV and bilinear interpolations) and removes most of the artifacts. Experimental results of the registration of Computed Tomography (CT) images show superiority of the proposed scheme. PMID:22606673
International Nuclear Information System (INIS)
Gao Wen-Wu; Wang Zhi-Gang
2014-01-01
Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions. (general)
Directory of Open Access Journals (Sweden)
A. Jo
2018-04-01
Full Text Available The purpose of this study is to create a new dataset of spatially interpolated monthly climate data for South Korea at high spatial resolution (approximately 30m by performing various spatio-statistical interpolation and comparing with forecast LDAPS gridded climate data provided from Korea Meterological Administration (KMA. Automatic Weather System (AWS and Automated Synoptic Observing System (ASOS data in 2017 obtained from KMA were included for the spatial mapping of temperature and rainfall; instantaneous temperature and 1-hour accumulated precipitation at 09:00 am on 31th March, 21th June, 23th September, and 24th December. Among observation data, 80 percent of the total point (478 and remaining 120 points were used for interpolations and for quantification, respectively. With the training data and digital elevation model (DEM with 30 m resolution, inverse distance weighting (IDW, co-kriging, and kriging were performed by using ArcGIS10.3.1 software and Python 3.6.4. Bias and root mean square were computed to compare prediction performance quantitatively. When statistical analysis was performed for each cluster using 20 % validation data, co kriging was more suitable for spatialization of instantaneous temperature than other interpolation method. On the other hand, IDW technique was appropriate for spatialization of precipitation.
Multiresolution Motion Estimation for Low-Rate Video Frame Interpolation
Directory of Open Access Journals (Sweden)
Hezerul Abdul Karim
2004-09-01
Full Text Available Interpolation of video frames with the purpose of increasing the frame rate requires the estimation of motion in the image so as to interpolate pixels along the path of the objects. In this paper, the specific challenges of low-rate video frame interpolation are illustrated by choosing one well-performing algorithm for high-frame-rate interpolation (Castango 1996 and applying it to low frame rates. The degradation of performance is illustrated by comparing the original algorithm, the algorithm adapted to low frame rate, and simple averaging. To overcome the particular challenges of low-frame-rate interpolation, two algorithms based on multiresolution motion estimation are developed and compared on objective and subjective basis and shown to provide an elegant solution to the specific challenges of low-frame-rate video interpolation.
High precision simple interpolation asynchronous FIFO based on ACEX1K30 for HIRFL-CSRe
International Nuclear Information System (INIS)
Li Guihua; Qiao Weimin; Jing Lan
2008-01-01
High precision simple interpolation asynchronous FIFO of HIRFL-CSRe was developed based on the ACEX1K30 FPGA in VHDL Hardware Description language. The FIFO runs in FPGA of DSP module of HIRFL-CSRe. The input data of FIFO is from DSP data bus and the output data is to DAC data bus. It's kernel adopts double buffer ping-pong mode and it can implement simple interpolation inside FPGA. The module can control out- put data time delay in 40 ns. The experimental results indicate that this module is practical and accurate to HIRFL-CSRe. (authors)
Directory of Open Access Journals (Sweden)
Pang Fubin
2015-09-01
Full Text Available In this paper the origin problem of data synchronization is analyzed first, and then three common interpolation methods are introduced to solve the problem. Allowing for the most general situation, the paper divides the interpolation error into harmonic and transient interpolation error components, and the error expression of each method is derived and analyzed. Besides, the interpolation errors of linear, quadratic and cubic methods are computed at different sampling rates, harmonic orders and transient components. Further, the interpolation accuracy and calculation amount of each method are compared. The research results provide theoretical guidance for selecting the interpolation method in the data synchronization application of electronic transformer.
Monotone piecewise bicubic interpolation
International Nuclear Information System (INIS)
Carlson, R.E.; Fritsch, F.N.
1985-01-01
In a 1980 paper the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone script C 1 piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm. 4 references, 6 figures, 2 tables
A Study on the Improvement of Digital Periapical Images using Image Interpolation Methods
International Nuclear Information System (INIS)
Song, Nam Kyu; Koh, Kwang Joon
1998-01-01
Image resampling is of particular interest in digital radiology. When resampling an image to a new set of coordinate, there appears blocking artifacts and image changes. To enhance image quality, interpolation algorithms have been used. Resampling is used to increase the number of points in an image to improve its appearance for display. The process of interpolation is fitting a continuous function to the discrete points in the digital image. The purpose of this study was to determine the effects of the seven interpolation functions when image resampling in digital periapical images. The images were obtained by Digora, CDR and scanning of Ektaspeed plus periapical radiograms on the dry skull and human subject. The subjects were exposed to intraoral X-ray machine at 60 kVp and 70 kVp with exposure time varying between 0.01 and 0.50 second. To determine which interpolation method would provide the better image, seven functions were compared ; (1) nearest neighbor (2) linear (3) non-linear (4) facet model (5) cubic convolution (6) cubic spline (7) gray segment expansion. And resampled images were compared in terms of SNR (Signal to Noise Ratio) and MTF (Modulation Transfer Function) coefficient value. The obtained results were as follows ; 1. The highest SNR value (75.96 dB) was obtained with cubic convolution method and the lowest SNR value (72.44 dB) was obtained with facet model method among seven interpolation methods. 2. There were significant differences of SNR values among CDR, Digora and film scan (P 0.05). 4. There were significant differences of MTF coefficient values between linear interpolation method and the other six interpolation methods (P<0.05). 5. The speed of computation time was the fastest with nearest neighbor method and the slowest with non-linear method. 6. The better image was obtained with cubic convolution, cubic spline and gray segment method in ROC analysis. 7. The better sharpness of edge was obtained with gray segment expansion method
C1 Rational Quadratic Trigonometric Interpolation Spline for Data Visualization
Directory of Open Access Journals (Sweden)
Shengjun Liu
2015-01-01
Full Text Available A new C1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h3. Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.
A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation
Directory of Open Access Journals (Sweden)
Mingzhu Li
2014-01-01
Full Text Available The main aim of this work is to consider a meshfree algorithm for solving Burgers’ equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.
Multi-dimensional cubic interpolation for ICF hydrodynamics simulation
International Nuclear Information System (INIS)
Aoki, Takayuki; Yabe, Takashi.
1991-04-01
A new interpolation method is proposed to solve the multi-dimensional hyperbolic equations which appear in describing the hydrodynamics of inertial confinement fusion (ICF) implosion. The advection phase of the cubic-interpolated pseudo-particle (CIP) is greatly improved, by assuming the continuities of the second and the third spatial derivatives in addition to the physical value and the first derivative. These derivatives are derived from the given physical equation. In order to evaluate the new method, Zalesak's example is tested, and we obtain successfully good results. (author)
Improved Interpolation Kernels for Super-resolution Algorithms
DEFF Research Database (Denmark)
Rasti, Pejman; Orlova, Olga; Tamberg, Gert
2016-01-01
Super resolution (SR) algorithms are widely used in forensics investigations to enhance the resolution of images captured by surveillance cameras. Such algorithms usually use a common interpolation algorithm to generate an initial guess for the desired high resolution (HR) image. This initial guess...... when their original interpolation kernel is replaced by the ones introduced in this work....
High-Order Model and Dynamic Filtering for Frame Rate Up-Conversion.
Bao, Wenbo; Zhang, Xiaoyun; Chen, Li; Ding, Lianghui; Gao, Zhiyong
2018-08-01
This paper proposes a novel frame rate up-conversion method through high-order model and dynamic filtering (HOMDF) for video pixels. Unlike the constant brightness and linear motion assumptions in traditional methods, the intensity and position of the video pixels are both modeled with high-order polynomials in terms of time. Then, the key problem of our method is to estimate the polynomial coefficients that represent the pixel's intensity variation, velocity, and acceleration. We propose to solve it with two energy objectives: one minimizes the auto-regressive prediction error of intensity variation by its past samples, and the other minimizes video frame's reconstruction error along the motion trajectory. To efficiently address the optimization problem for these coefficients, we propose the dynamic filtering solution inspired by video's temporal coherence. The optimal estimation of these coefficients is reformulated into a dynamic fusion of the prior estimate from pixel's temporal predecessor and the maximum likelihood estimate from current new observation. Finally, frame rate up-conversion is implemented using motion-compensated interpolation by pixel-wise intensity variation and motion trajectory. Benefited from the advanced model and dynamic filtering, the interpolated frame has much better visual quality. Extensive experiments on the natural and synthesized videos demonstrate the superiority of HOMDF over the state-of-the-art methods in both subjective and objective comparisons.
Einstein causal quantum fields on lattices with discrete Lorentz invariance
International Nuclear Information System (INIS)
Baumgaertel, H.
1986-01-01
Results on rigorous construction of quantum fields on the hypercubic lattice Z 4 considered as a lattice in the Minkowski space R 4 are presented. Two associated fields are constructed: The first one having on the lattice points of Z 4 is causal and Poincare invariant in the discrete sense. The second one is an interpolating field over R 4 which is pointlike, translationally covariant and spectral in such a manner that the 'real' lattices field is the restriction of the interpolating field to Z 4 . Furthermore, results on a rigorous perturbation theory of such fields are mentioned
Fabiano, E.; Gori-Giorgi, P.; Seidl, M.W.J.; Della Sala, F.
2016-01-01
We have tested the original interaction-strength-interpolation (ISI) exchange-correlation functional for main group chemistry. The ISI functional is based on an interpolation between the weak and strong coupling limits and includes exact-exchange as well as the Görling–Levy second-order energy. We
Hybrid High-Order methods for finite deformations of hyperelastic materials
Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas
2018-01-01
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.
International Nuclear Information System (INIS)
Zou, Ling; Zhao, Haihua; Zhang, Hongbin
2015-01-01
Highlights: • Using high-resolution spatial scheme in solving two-phase flow problems. • Fully implicit time integrations scheme. • Jacobian-free Newton–Krylov method. • Analytical solution for two-phase water faucet problem. - Abstract: The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists
Peters, Andre; Nehls, Thomas; Wessolek, Gerd
2016-06-01
Weighing lysimeters with appropriate data filtering yield the most precise and unbiased information for precipitation (P) and evapotranspiration (ET). A recently introduced filter scheme for such data is the AWAT (Adaptive Window and Adaptive Threshold) filter (Peters et al., 2014). The filter applies an adaptive threshold to separate significant from insignificant mass changes, guaranteeing that P and ET are not overestimated, and uses a step interpolation between the significant mass changes. In this contribution we show that the step interpolation scheme, which reflects the resolution of the measuring system, can lead to unrealistic prediction of P and ET, especially if they are required in high temporal resolution. We introduce linear and spline interpolation schemes to overcome these problems. To guarantee that medium to strong precipitation events abruptly following low or zero fluxes are not smoothed in an unfavourable way, a simple heuristic selection criterion is used, which attributes such precipitations to the step interpolation. The three interpolation schemes (step, linear and spline) are tested and compared using a data set from a grass-reference lysimeter with 1 min resolution, ranging from 1 January to 5 August 2014. The selected output resolutions for P and ET prediction are 1 day, 1 h and 10 min. As expected, the step scheme yielded reasonable flux rates only for a resolution of 1 day, whereas the other two schemes are well able to yield reasonable results for any resolution. The spline scheme returned slightly better results than the linear scheme concerning the differences between filtered values and raw data. Moreover, this scheme allows continuous differentiability of filtered data so that any output resolution for the fluxes is sound. Since computational burden is not problematic for any of the interpolation schemes, we suggest always using the spline scheme.
Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
Rovny, Jared; Blum, Robert L.; Barrett, Sean E.
2018-05-01
A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.
CMB anisotropies interpolation
Zinger, S.; Delabrouille, Jacques; Roux, Michel; Maitre, Henri
2010-01-01
We consider the problem of the interpolation of irregularly spaced spatial data, applied to observation of Cosmic Microwave Background (CMB) anisotropies. The well-known interpolation methods and kriging are compared to the binning method which serves as a reference approach. We analyse kriging
I. Kuba; J. Zavacky; J. Mihalik
1995-01-01
This paper presents the use of B spline functions in various digital signal processing applications. The theory of one-dimensional B spline interpolation is briefly reviewed, followed by its extending to two dimensions. After presenting of one and two dimensional spline interpolation, the algorithms of image interpolation and resolution increasing were proposed. Finally, experimental results of computer simulations are presented.
An application of gain-scheduled control using state-space interpolation to hydroactive gas bearings
DEFF Research Database (Denmark)
Theisen, Lukas Roy Svane; Camino, Juan F.; Niemann, Hans Henrik
2016-01-01
with a gain-scheduling strategy using state-space interpolation, which avoids both the performance loss and the increase of controller order associated to the Youla parametrisation. The proposed state-space interpolation for gain-scheduling is applied for mass imbalance rejection for a controllable gas...... bearing scheduled in two parameters. Comparisons against the Youla-based scheduling demonstrate the superiority of the state-space interpolation....
Bilinear reduced order approximate model of parabolic distributed solar collectors
Elmetennani, Shahrazed
2015-07-01
This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, by means of a modified gaussian interpolation along the spatial domain. The proposed reduced model, taking the form of a low dimensional bilinear state representation, enables the reproduction of the heat transfer dynamics along the collector tube for system analysis. Moreover, presented as a reduced order bilinear state space model, the well established control theory for this class of systems can be applied. The approximation efficiency has been proven by several simulation tests, which have been performed considering parameters of the Acurex field with real external working conditions. Model accuracy has been evaluated by comparison to the analytical solution of the hyperbolic distributed model and its semi discretized approximation highlighting the benefits of using the proposed numerical scheme. Furthermore, model sensitivity to the different parameters of the gaussian interpolation has been studied.
Energy-Driven Image Interpolation Using Gaussian Process Regression
Directory of Open Access Journals (Sweden)
Lingling Zi
2012-01-01
Full Text Available Image interpolation, as a method of obtaining a high-resolution image from the corresponding low-resolution image, is a classical problem in image processing. In this paper, we propose a novel energy-driven interpolation algorithm employing Gaussian process regression. In our algorithm, each interpolated pixel is predicted by a combination of two information sources: first is a statistical model adopted to mine underlying information, and second is an energy computation technique used to acquire information on pixel properties. We further demonstrate that our algorithm can not only achieve image interpolation, but also reduce noise in the original image. Our experiments show that the proposed algorithm can achieve encouraging performance in terms of image visualization and quantitative measures.
International Nuclear Information System (INIS)
Ding Xiaohua; Su Huan; Liu Mingzhu
2008-01-01
The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found
Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team
2017-11-01
We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).
Zeng, Cheng; Liang, Shan; Xiang, Shuwen
2017-05-01
Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Spatiotemporal Interpolation Methods for Solar Event Trajectories
Filali Boubrahimi, Soukaina; Aydin, Berkay; Schuh, Michael A.; Kempton, Dustin; Angryk, Rafal A.; Ma, Ruizhe
2018-05-01
This paper introduces four spatiotemporal interpolation methods that enrich complex, evolving region trajectories that are reported from a variety of ground-based and space-based solar observatories every day. Our interpolation module takes an existing solar event trajectory as its input and generates an enriched trajectory with any number of additional time–geometry pairs created by the most appropriate method. To this end, we designed four different interpolation techniques: MBR-Interpolation (Minimum Bounding Rectangle Interpolation), CP-Interpolation (Complex Polygon Interpolation), FI-Interpolation (Filament Polygon Interpolation), and Areal-Interpolation, which are presented here in detail. These techniques leverage k-means clustering, centroid shape signature representation, dynamic time warping, linear interpolation, and shape buffering to generate the additional polygons of an enriched trajectory. Using ground-truth objects, interpolation effectiveness is evaluated through a variety of measures based on several important characteristics that include spatial distance, area overlap, and shape (boundary) similarity. To our knowledge, this is the first research effort of this kind that attempts to address the broad problem of spatiotemporal interpolation of solar event trajectories. We conclude with a brief outline of future research directions and opportunities for related work in this area.
Park, K. C.; Belvin, W. Keith
1990-01-01
A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.
Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method
Parsani, Matteo
2012-01-01
Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.
International Nuclear Information System (INIS)
Dubcova, Lenka; Solin, Pavel; Hansen, Glen; Park, HyeongKae
2011-01-01
Multiphysics solution challenges are legion within the field of nuclear reactor design and analysis. One major issue concerns the coupling between heat and neutron flow (neutronics) within the reactor assembly. These phenomena are usually very tightly interdependent, as large amounts of heat are quickly produced with an increase in fission events within the fuel, which raises the temperature that affects the neutron cross section of the fuel. Furthermore, there typically is a large diversity of time and spatial scales between mathematical models of heat and neutronics. Indeed, the different spatial resolution requirements often lead to the use of very different meshes for the two phenomena. As the equations are coupled, one must take care in exchanging solution data between them, or significant error can be introduced into the coupled problem. We propose a novel approach to the discretization of the coupled problem on different meshes based on an adaptive multimesh higher-order finite element method (hp-FEM), and compare it to popular interpolation and projection methods. We show that the multimesh hp-FEM method is significantly more accurate than the interpolation and projection approaches considered in this study.
Research on interpolation methods in medical image processing.
Pan, Mei-Sen; Yang, Xiao-Li; Tang, Jing-Tian
2012-04-01
Image interpolation is widely used for the field of medical image processing. In this paper, interpolation methods are divided into three groups: filter interpolation, ordinary interpolation and general partial volume interpolation. Some commonly-used filter methods for image interpolation are pioneered, but the interpolation effects need to be further improved. When analyzing and discussing ordinary interpolation, many asymmetrical kernel interpolation methods are proposed. Compared with symmetrical kernel ones, the former are have some advantages. After analyzing the partial volume and generalized partial volume estimation interpolations, the new concept and constraint conditions of the general partial volume interpolation are defined, and several new partial volume interpolation functions are derived. By performing the experiments of image scaling, rotation and self-registration, the interpolation methods mentioned in this paper are compared in the entropy, peak signal-to-noise ratio, cross entropy, normalized cross-correlation coefficient and running time. Among the filter interpolation methods, the median and B-spline filter interpolations have a relatively better interpolating performance. Among the ordinary interpolation methods, on the whole, the symmetrical cubic kernel interpolations demonstrate a strong advantage, especially the symmetrical cubic B-spline interpolation. However, we have to mention that they are very time-consuming and have lower time efficiency. As for the general partial volume interpolation methods, from the total error of image self-registration, the symmetrical interpolations provide certain superiority; but considering the processing efficiency, the asymmetrical interpolations are better.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Estimating Frequency by Interpolation Using Least Squares Support Vector Regression
Directory of Open Access Journals (Sweden)
Changwei Ma
2015-01-01
Full Text Available Discrete Fourier transform- (DFT- based maximum likelihood (ML algorithm is an important part of single sinusoid frequency estimation. As signal to noise ratio (SNR increases and is above the threshold value, it will lie very close to Cramer-Rao lower bound (CRLB, which is dependent on the number of DFT points. However, its mean square error (MSE performance is directly proportional to its calculation cost. As a modified version of support vector regression (SVR, least squares SVR (LS-SVR can not only still keep excellent capabilities for generalizing and fitting but also exhibit lower computational complexity. In this paper, therefore, LS-SVR is employed to interpolate on Fourier coefficients of received signals and attain high frequency estimation accuracy. Our results show that the proposed algorithm can make a good compromise between calculation cost and MSE performance under the assumption that the sample size, number of DFT points, and resampling points are already known.
Shape-based grey-level image interpolation
International Nuclear Information System (INIS)
Keh-Shih Chuang; Chun-Yuan Chen; Ching-Kai Yeh
1999-01-01
The three-dimensional (3D) object data obtained from a CT scanner usually have unequal sampling frequencies in the x-, y- and z-directions. Generally, the 3D data are first interpolated between slices to obtain isotropic resolution, reconstructed, then operated on using object extraction and display algorithms. The traditional grey-level interpolation introduces a layer of intermediate substance and is not suitable for objects that are very different from the opposite background. The shape-based interpolation method transfers a pixel location to a parameter related to the object shape and the interpolation is performed on that parameter. This process is able to achieve a better interpolation but its application is limited to binary images only. In this paper, we present an improved shape-based interpolation method for grey-level images. The new method uses a polygon to approximate the object shape and performs the interpolation using polygon vertices as references. The binary images representing the shape of the object were first generated via image segmentation on the source images. The target object binary image was then created using regular shape-based interpolation. The polygon enclosing the object for each slice can be generated from the shape of that slice. We determined the relative location in the source slices of each pixel inside the target polygon using the vertices of a polygon as the reference. The target slice grey-level was interpolated from the corresponding source image pixels. The image quality of this interpolation method is better and the mean squared difference is smaller than with traditional grey-level interpolation. (author)
Chen, Tung-Chien; Ma, Tsung-Chuan; Chen, Yun-Yu; Chen, Liang-Gee
2012-01-01
Accurate spike sorting is an important issue for neuroscientific and neuroprosthetic applications. The sorting of spikes depends on the features extracted from the neural waveforms, and a better sorting performance usually comes with a higher sampling rate (SR). However for the long duration experiments on free-moving subjects, the miniaturized and wireless neural recording ICs are the current trend, and the compromise on sorting accuracy is usually made by a lower SR for the lower power consumption. In this paper, we implement an on-chip spike sorting processor with integrated interpolation hardware in order to improve the performance in terms of power versus accuracy. According to the fabrication results in 90nm process, if the interpolation is appropriately performed during the spike sorting, the system operated at the SR of 12.5 k samples per second (sps) can outperform the one not having interpolation at 25 ksps on both accuracy and power.
Validation of a RANS transition model using a high-order weighted compact nonlinear scheme
Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang
2013-04-01
A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.
Gao, Longfei; Fernandez, David C. Del Rey; Carpenter, Mark; Keyes, David E.
2018-01-01
are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate
[Research on fast implementation method of image Gaussian RBF interpolation based on CUDA].
Chen, Hao; Yu, Haizhong
2014-04-01
Image interpolation is often required during medical image processing and analysis. Although interpolation method based on Gaussian radial basis function (GRBF) has high precision, the long calculation time still limits its application in field of image interpolation. To overcome this problem, a method of two-dimensional and three-dimensional medical image GRBF interpolation based on computing unified device architecture (CUDA) is proposed in this paper. According to single instruction multiple threads (SIMT) executive model of CUDA, various optimizing measures such as coalesced access and shared memory are adopted in this study. To eliminate the edge distortion of image interpolation, natural suture algorithm is utilized in overlapping regions while adopting data space strategy of separating 2D images into blocks or dividing 3D images into sub-volumes. Keeping a high interpolation precision, the 2D and 3D medical image GRBF interpolation achieved great acceleration in each basic computing step. The experiments showed that the operative efficiency of image GRBF interpolation based on CUDA platform was obviously improved compared with CPU calculation. The present method is of a considerable reference value in the application field of image interpolation.
Batty, Christopher
2017-02-01
This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L∞ norm.
5-D interpolation with wave-front attributes
Xie, Yujiang; Gajewski, Dirk
2017-11-01
Most 5-D interpolation and regularization techniques reconstruct the missing data in the frequency domain by using mathematical transforms. An alternative type of interpolation methods uses wave-front attributes, that is, quantities with a specific physical meaning like the angle of emergence and wave-front curvatures. In these attributes structural information of subsurface features like dip and strike of a reflector are included. These wave-front attributes work on 5-D data space (e.g. common-midpoint coordinates in x and y, offset, azimuth and time), leading to a 5-D interpolation technique. Since the process is based on stacking next to the interpolation a pre-stack data enhancement is achieved, improving the signal-to-noise ratio (S/N) of interpolated and recorded traces. The wave-front attributes are determined in a data-driven fashion, for example, with the Common Reflection Surface (CRS method). As one of the wave-front-attribute-based interpolation techniques, the 3-D partial CRS method was proposed to enhance the quality of 3-D pre-stack data with low S/N. In the past work on 3-D partial stacks, two potential problems were still unsolved. For high-quality wave-front attributes, we suggest a global optimization strategy instead of the so far used pragmatic search approach. In previous works, the interpolation of 3-D data was performed along a specific azimuth which is acceptable for narrow azimuth acquisition but does not exploit the potential of wide-, rich- or full-azimuth acquisitions. The conventional 3-D partial CRS method is improved in this work and we call it as a wave-front-attribute-based 5-D interpolation (5-D WABI) as the two problems mentioned above are addressed. Data examples demonstrate the improved performance by the 5-D WABI method when compared with the conventional 3-D partial CRS approach. A comparison of the rank-reduction-based 5-D seismic interpolation technique with the proposed 5-D WABI method is given. The comparison reveals that
International Nuclear Information System (INIS)
Drouin, M.
2009-11-01
This research thesis proposes a new formulation of the relativistic implicit direct method, based on the weak formulation of the wave equation which is solved by means of a Newton algorithm. The first part of this thesis deals with the properties of the explicit particle-in-cell (PIC) methods: properties and limitations of an explicit PIC code, linear analysis of a numerical plasma, numerical heating phenomenon, interest of a higher order interpolation function, and presentation of two applications in high density relativistic laser-plasma interaction. The second and main part of this report deals with adapting the direct implicit method to laser-plasma interaction: presentation of the state of the art, formulating of the direct implicit method, resolution of the wave equation. The third part concerns various numerical and physical validations of the ELIXIRS code: case of laser wave propagation in vacuum, demonstration of the adjustable damping which is a characteristic of the proposed algorithm, influence of space-time discretization on energy conservation, expansion of a thermal plasma in vacuum, two cases of plasma-beam unsteadiness in relativistic regime, and then a case of the overcritical laser-plasma interaction
A Note on Cubic Convolution Interpolation
Meijering, E.; Unser, M.
2003-01-01
We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing.
Sanderse, B.; Verstappen, R.W.C.P.; Koren, B.
2014-01-01
A discretization method for the incompressible Navier–Stokes equations conserving the secondary quantities kinetic energy and vorticity was introduced, besides the primary quantities mass and momentum. This method was extended to fourth order accuracy. In this paper we propose a new consistent
Short-term prediction method of wind speed series based on fractal interpolation
International Nuclear Information System (INIS)
Xiu, Chunbo; Wang, Tiantian; Tian, Meng; Li, Yanqing; Cheng, Yi
2014-01-01
Highlights: • An improved fractal interpolation prediction method is proposed. • The chaos optimization algorithm is used to obtain the iterated function system. • The fractal extrapolate interpolation prediction of wind speed series is performed. - Abstract: In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series
Comparison of the methods for discrete approximation of the fractional-order operator
Directory of Open Access Journals (Sweden)
Zborovjan Martin
2003-12-01
Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.
High-order nonuniformly correlated beams
Wu, Dan; Wang, Fei; Cai, Yangjian
2018-02-01
We have introduced a class of partially coherent beams with spatially varying correlations named high-order nonuniformly correlated (HNUC) beams, as an extension of conventional nonuniformly correlated (NUC) beams. Such beams bring a new parameter (mode order) which is used to tailor the spatial coherence properties. The behavior of the spectral density of the HNUC beams on propagation has been investigated through numerical examples with the help of discrete model decomposition and fast Fourier transform (FFT) algorithm. Our results reveal that by selecting the mode order appropriately, the more sharpened intensity maxima can be achieved at a certain propagation distance compared to that of the NUC beams, and the lateral shift of the intensity maxima on propagation is closed related to the mode order. Furthermore, analytical expressions for the r.m.s width and the propagation factor of the HNUC beams on free-space propagation are derived by means of Wigner distribution function. The influence of initial beam parameters on the evolution of the r.m.s width and the propagation factor, and the relation between the r.m.s width and the occurring of the sharpened intensity maxima on propagation have been studied and discussed in detail.
Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations
International Nuclear Information System (INIS)
Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.
2005-01-01
In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects
Surface interpolation with radial basis functions for medical imaging
International Nuclear Information System (INIS)
Carr, J.C.; Beatson, R.K.; Fright, W.R.
1997-01-01
Radial basis functions are presented as a practical solution to the problem of interpolating incomplete surfaces derived from three-dimensional (3-D) medical graphics. The specific application considered is the design of cranial implants for the repair of defects, usually holes, in the skull. Radial basis functions impose few restrictions on the geometry of the interpolation centers and are suited to problems where interpolation centers do not form a regular grid. However, their high computational requirements have previously limited their use to problems where the number of interpolation centers is small (<300). Recently developed fast evaluation techniques have overcome these limitations and made radial basis interpolation a practical approach for larger data sets. In this paper radial basis functions are fitted to depth-maps of the skull's surface, obtained from X-ray computed tomography (CT) data using ray-tracing techniques. They are used to smoothly interpolate the surface of the skull across defect regions. The resulting mathematical description of the skull's surface can be evaluated at any desired resolution to be rendered on a graphics workstation or to generate instructions for operating a computer numerically controlled (CNC) mill
Parallel optimization of IDW interpolation algorithm on multicore platform
Guan, Xuefeng; Wu, Huayi
2009-10-01
Due to increasing power consumption, heat dissipation, and other physical issues, the architecture of central processing unit (CPU) has been turning to multicore rapidly in recent years. Multicore processor is packaged with multiple processor cores in the same chip, which not only offers increased performance, but also presents significant challenges to application developers. As a matter of fact, in GIS field most of current GIS algorithms were implemented serially and could not best exploit the parallelism potential on such multicore platforms. In this paper, we choose Inverse Distance Weighted spatial interpolation algorithm (IDW) as an example to study how to optimize current serial GIS algorithms on multicore platform in order to maximize performance speedup. With the help of OpenMP, threading methodology is introduced to split and share the whole interpolation work among processor cores. After parallel optimization, execution time of interpolation algorithm is greatly reduced and good performance speedup is achieved. For example, performance speedup on Intel Xeon 5310 is 1.943 with 2 execution threads and 3.695 with 4 execution threads respectively. An additional output comparison between pre-optimization and post-optimization is carried out and shows that parallel optimization does to affect final interpolation result.
Novel structures for Discrete Hartley Transform based on first-order moments
Xiong, Jun; Zheng, Wenjuan; Wang, Hao; Liu, Jianguo
2018-03-01
Discrete Hartley Transform (DHT) is an important tool in digital signal processing. In the present paper, the DHT is firstly transformed into the first-order moments-based form, then a new fast algorithm is proposed to calculate the first-order moments without multiplication. Based on the algorithm theory, the corresponding hardware architecture for DHT is proposed, which only contains shift operations and additions with no need for multipliers and large memory. To verify the availability and effectiveness, the proposed design is implemented with hardware description language and synthesized by Synopsys Design Compiler with 0.18-μm SMIC library. A series of experiments have proved that the proposed architecture has better performance in terms of the product of the hardware consumption and computation time.
The modal surface interpolation method for damage localization
Pina Limongelli, Maria
2017-05-01
The Interpolation Method (IM) has been previously proposed and successfully applied for damage localization in plate like structures. The method is based on the detection of localized reductions of smoothness in the Operational Deformed Shapes (ODSs) of the structure. The IM can be applied to any type of structure provided the ODSs are estimated accurately in the original and in the damaged configurations. If the latter circumstance fails to occur, for example when the structure is subjected to an unknown input(s) or if the structural responses are strongly corrupted by noise, both false and missing alarms occur when the IM is applied to localize a concentrated damage. In order to overcome these drawbacks a modification of the method is herein investigated. An ODS is the deformed shape of a structure subjected to a harmonic excitation: at resonances the ODS are dominated by the relevant mode shapes. The effect of noise at resonance is usually lower with respect to other frequency values hence the relevant ODS are estimated with higher reliability. Several methods have been proposed to reliably estimate modal shapes in case of unknown input. These two circumstances can be exploited to improve the reliability of the IM. In order to reduce or eliminate the drawbacks related to the estimation of the ODSs in case of noisy signals, in this paper is investigated a modified version of the method based on a damage feature calculated considering the interpolation error relevant only to the modal shapes and not to all the operational shapes in the significant frequency range. Herein will be reported the comparison between the results of the IM in its actual version (with the interpolation error calculated summing up the contributions of all the operational shapes) and in the new proposed version (with the estimation of the interpolation error limited to the modal shapes).
Interpolation decoding method with variable parameters for fractal image compression
International Nuclear Information System (INIS)
He Chuanjiang; Li Gaoping; Shen Xiaona
2007-01-01
The interpolation fractal decoding method, which is introduced by [He C, Yang SX, Huang X. Progressive decoding method for fractal image compression. IEE Proc Vis Image Signal Process 2004;3:207-13], involves generating progressively the decoded image by means of an interpolation iterative procedure with a constant parameter. It is well-known that the majority of image details are added at the first steps of iterations in the conventional fractal decoding; hence the constant parameter for the interpolation decoding method must be set as a smaller value in order to achieve a better progressive decoding. However, it needs to take an extremely large number of iterations to converge. It is thus reasonable for some applications to slow down the iterative process at the first stages of decoding and then to accelerate it afterwards (e.g., at some iteration as we need). To achieve the goal, this paper proposed an interpolation decoding scheme with variable (iteration-dependent) parameters and proved the convergence of the decoding process mathematically. Experimental results demonstrate that the proposed scheme has really achieved the above-mentioned goal
Energy Technology Data Exchange (ETDEWEB)
Weston, Brian T. [Univ. of California, Davis, CA (United States)
2017-05-17
This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser
High order spectral difference lattice Boltzmann method for incompressible hydrodynamics
Li, Weidong
2017-09-01
This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.
Xu, Zhuo; Sopher, Daniel; Juhlin, Christopher; Han, Liguo; Gong, Xiangbo
2018-04-01
In towed marine seismic data acquisition, a gap between the source and the nearest recording channel is typical. Therefore, extrapolation of the missing near-offset traces is often required to avoid unwanted effects in subsequent data processing steps. However, most existing interpolation methods perform poorly when extrapolating traces. Interferometric interpolation methods are one particular method that have been developed for filling in trace gaps in shot gathers. Interferometry-type interpolation methods differ from conventional interpolation methods as they utilize information from several adjacent shot records to fill in the missing traces. In this study, we aim to improve upon the results generated by conventional time-space domain interferometric interpolation by performing interferometric interpolation in the Radon domain, in order to overcome the effects of irregular data sampling and limited source-receiver aperture. We apply both time-space and Radon-domain interferometric interpolation methods to the Sigsbee2B synthetic dataset and a real towed marine dataset from the Baltic Sea with the primary aim to improve the image of the seabed through extrapolation into the near-offset gap. Radon-domain interferometric interpolation performs better at interpolating the missing near-offset traces than conventional interferometric interpolation when applied to data with irregular geometry and limited source-receiver aperture. We also compare the interferometric interpolated results with those obtained using solely Radon transform (RT) based interpolation and show that interferometry-type interpolation performs better than solely RT-based interpolation when extrapolating the missing near-offset traces. After data processing, we show that the image of the seabed is improved by performing interferometry-type interpolation, especially when Radon-domain interferometric interpolation is applied.
Interpolation Filter Design for Hearing-Aid Audio Class-D Output Stage Application
DEFF Research Database (Denmark)
Pracný, Peter; Bruun, Erik; Llimos Muntal, Pere
2012-01-01
This paper deals with a design of a digital interpolation filter for a 3rd order multi-bit ΣΔ modulator with over-sampling ratio OSR = 64. The interpolation filter and the ΣΔ modulator are part of the back-end of an audio signal processing system in a hearing-aid application. The aim in this paper...... is to compare this design to designs presented in other state-of-the-art works ranging from hi-fi audio to hearing-aids. By performing comparison, trends and tradeoffs in interpolation filter design are indentified and hearing-aid specifications are derived. The possibilities for hardware reduction...... in the interpolation filter are investigated. Proposed design simplifications presented here result in the least hardware demanding combination of oversampling ratio, number of stages and number of filter taps among a number of filters reported for audio applications....
Image Interpolation with Contour Stencils
Pascal Getreuer
2011-01-01
Image interpolation is the problem of increasing the resolution of an image. Linear methods must compromise between artifacts like jagged edges, blurring, and overshoot (halo) artifacts. More recent works consider nonlinear methods to improve interpolation of edges and textures. In this paper we apply contour stencils for estimating the image contours based on total variation along curves and then use this estimation to construct a fast edge-adaptive interpolation.
Revisiting Veerman’s interpolation method
DEFF Research Database (Denmark)
Christiansen, Peter; Bay, Niels Oluf
2016-01-01
and (c) FEsimulations. A comparison of the determined forming limits yields insignificant differences in the limit strain obtainedwith Veerman’s method or exact Lagrangian interpolation for the two sheet metal forming processes investigated. Theagreement with the FE-simulations is reasonable.......This article describes an investigation of Veerman’s interpolation method and its applicability for determining sheet metalformability. The theoretical foundation is established and its mathematical assumptions are clarified. An exact Lagrangianinterpolation scheme is also established...... for comparison. Bulge testing and tensile testing of aluminium sheets containingelectro-chemically etched circle grids are performed to experimentally determine the forming limit of the sheet material.The forming limit is determined using (a) Veerman’s interpolation method, (b) exact Lagrangian interpolation...
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2017-01-01
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy
Interferometric interpolation of sparse marine data
Hanafy, Sherif M.
2013-10-11
We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green\\'s function and a model-based Green\\'s function for a water-layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up- and downgoing separation of both recorded and model-based Green\\'s functions can help in minimizing artefacts in a virtual shot gather. If the up- and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non-stationary 1D multi-channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f-k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method. © 2013 European Association of Geoscientists & Engineers.
Discrete Curvature Theories and Applications
Sun, Xiang
2016-08-25
Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the
On a class of reductions of the Manakov-Santini hierarchy connected with the interpolating system
International Nuclear Information System (INIS)
Bogdanov, L V
2010-01-01
Using the Lax-Sato formulation of the Manakov-Santini hierarchy, we introduce a class of reductions such that the zero-order reduction of this class corresponds to the dKP hierarchy, and the first-order reduction gives the hierarchy associated with the interpolating system introduced by Dunajski. We present the Lax-Sato form of a reduced hierarchy for the interpolating system and also for the reduction of arbitrary order. Similar to the dKP hierarchy, the Lax-Sato equations for L (the Lax function) split from the Lax-Sato equations for M (the Orlov function) due to the reduction, and the reduced hierarchy for an arbitrary order of reduction is defined by Lax-Sato equations for L only. A characterization of the class of reductions in terms of the dressing data is given. We also consider a waterbag reduction of the interpolating system hierarchy, which defines (1+1)-dimensional systems of hydrodynamic type.
Edge-detect interpolation for direct digital periapical images
International Nuclear Information System (INIS)
Song, Nam Kyu; Koh, Kwang Joon
1998-01-01
The purpose of this study was to aid in the use of the digital images by edge-detect interpolation for direct digital periapical images using edge-deted interpolation. This study was performed by image processing of 20 digital periapical images; pixel replication, linear non-interpolation, linear interpolation, and edge-sensitive interpolation. The obtained results were as follows ; 1. Pixel replication showed blocking artifact and serious image distortion. 2. Linear interpolation showed smoothing effect on the edge. 3. Edge-sensitive interpolation overcame the smoothing effect on the edge and showed better image.
Generalized interpolative quantum statistics
International Nuclear Information System (INIS)
Ramanathan, R.
1992-01-01
A generalized interpolative quantum statistics is presented by conjecturing a certain reordering of phase space due to the presence of possible exotic objects other than bosons and fermions. Such an interpolation achieved through a Bose-counting strategy predicts the existence of an infinite quantum Boltzmann-Gibbs statistics akin to the one discovered by Greenberg recently
A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space
Directory of Open Access Journals (Sweden)
Hongyin Yang
2017-01-01
Full Text Available The presented study proposed an improved interpolating boundary node method (IIBNM for 2D potential problems. The improved interpolating moving least-square (IIMLS method was applied to construct the shape functions, of which the delta function properties and boundary conditions were directly implemented. In addition, any weight function used in the moving least-square (MLS method was also applicable in the IIMLS method. Boundary cells were required in the computation of the boundary integrals, and additional discretization error was not avoided if traditional cells were used to approximate the geometry. The present study applied the parametric cells created in the parameter space to preserve the exact geometry, and the geometry was maintained due to the number of cells. Only the number of nodes on the boundary was required as additional information for boundary node construction. Most importantly, the IIMLS method can be applied in the parameter space to construct shape functions without the requirement of additional computations for the curve length.
Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes
Janssen, A.J.E.M.; Veldhuis, R.N.J.; Vries, L.B.
1986-01-01
The authors present an adaptive algorithm for the restoration of lost sample values in discrete-time signals that can locally be described by means of autoregressive processes. The only restrictions are that the positions of the unknown samples should be known and that they should be embedded in a
Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes
Janssen, A.J.E.M.; Veldhuis, Raymond N.J.; Vries, Lodewijk B.
1986-01-01
This paper presents an adaptive algorithm for the restoration of lost sample values in discrete-time signals that can locally be described by means of autoregressive processes. The only restrictions are that the positions of the unknown samples should be known and that they should be embedded in a
Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model
International Nuclear Information System (INIS)
Wang, Guo-gang; Gan, Zong-liang; Tang, Gui-jin; Cui, Zi-guan; Zhu, Xiu-chang
2016-01-01
A novel model is proposed to overcome the shortages of the classical hypothesis of the two-dimensional discrete hidden Markov model. In the proposed model, the state transition probability depends on not only immediate horizontal and vertical states but also on immediate diagonal state, and the observation symbol probability depends on not only current state but also on immediate horizontal, vertical and diagonal states. This paper defines the structure of the model, and studies the three basic problems of the model, including probability calculation, path backtracking and parameters estimation. By exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1 × 2 order hidden Markov model, several algorithms solving the three questions are theoretically derived. Simulation results further demonstrate the performance of the algorithms. Compared with the two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed model, therefore the proposed model theoretically can more accurately describe some practical problems.
Subramanian, Ramanathan Vishnampet Ganapathi
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme
Spatial interpolation schemes of daily precipitation for hydrologic modeling
Hwang, Y.; Clark, M.R.; Rajagopalan, B.; Leavesley, G.
2012-01-01
Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs. ?? 2011 Springer-Verlag.
Single-Image Super-Resolution Based on Rational Fractal Interpolation.
Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming
2018-08-01
This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.
Directory of Open Access Journals (Sweden)
S. Vukotic
2016-08-01
Full Text Available Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.
Duru, Kenneth; Virta, Kristoffer
2014-01-01
to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions
Mohamed, Mamdouh S.
2016-02-11
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Geostatistical interpolation of available copper in orchard soil as influenced by planting duration.
Fu, Chuancheng; Zhang, Haibo; Tu, Chen; Li, Lianzhen; Luo, Yongming
2018-01-01
Mapping the spatial distribution of available copper (A-Cu) in orchard soils is important in agriculture and environmental management. However, data on the distribution of A-Cu in orchard soils is usually highly variable and severely skewed due to the continuous input of fungicides. In this study, ordinary kriging combined with planting duration (OK_PD) is proposed as a method for improving the interpolation of soil A-Cu. Four normal distribution transformation methods, namely, the Box-Cox, Johnson, rank order, and normal score methods, were utilized prior to interpolation. A total of 317 soil samples were collected in the orchards of the Northeast Jiaodong Peninsula. Moreover, 1472 orchards were investigated to obtain a map of planting duration using Voronoi tessellations. The soil A-Cu content ranged from 0.09 to 106.05 with a mean of 18.10 mg kg -1 , reflecting the high availability of Cu in the soils. Soil A-Cu concentrations exhibited a moderate spatial dependency and increased significantly with increasing planting duration. All the normal transformation methods successfully decreased the skewness and kurtosis of the soil A-Cu and the associated residuals, and also computed more robust variograms. OK_PD could generate better spatial prediction accuracy than ordinary kriging (OK) for all transformation methods tested, and it also provided a more detailed map of soil A-Cu. Normal score transformation produced satisfactory accuracy and showed an advantage in ameliorating smoothing effect derived from the interpolation methods. Thus, normal score transformation prior to kriging combined with planting duration (NSOK_PD) is recommended for the interpolation of soil A-Cu in this area.
Monotone methods for solving a boundary value problem of second order discrete system
Directory of Open Access Journals (Sweden)
Wang Yuan-Ming
1999-01-01
Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.
Nodal DG-FEM solution of high-order Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan S.; Bingham, Harry B.
2006-01-01
We present a discontinuous Galerkin finite element method (DG-FEM) solution to a set of high-order Boussinesq-type equations for modelling highly nonlinear and dispersive water waves in one and two horizontal dimensions. The continuous equations are discretized using nodal polynomial basis...... functions of arbitrary order in space on each element of an unstructured computational domain. A fourth order explicit Runge-Kutta scheme is used to advance the solution in time. Methods for introducing artificial damping to control mild nonlinear instabilities are also discussed. The accuracy...... and convergence of the model with both h (grid size) and p (order) refinement are verified for the linearized equations, and calculations are provided for two nonlinear test cases in one horizontal dimension: harmonic generation over a submerged bar; and reflection of a steep solitary wave from a vertical wall...
Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe
2018-02-01
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.
Fast image interpolation for motion estimation using graphics hardware
Kelly, Francis; Kokaram, Anil
2004-05-01
Motion estimation and compensation is the key to high quality video coding. Block matching motion estimation is used in most video codecs, including MPEG-2, MPEG-4, H.263 and H.26L. Motion estimation is also a key component in the digital restoration of archived video and for post-production and special effects in the movie industry. Sub-pixel accurate motion vectors can improve the quality of the vector field and lead to more efficient video coding. However sub-pixel accuracy requires interpolation of the image data. Image interpolation is a key requirement of many image processing algorithms. Often interpolation can be a bottleneck in these applications, especially in motion estimation due to the large number pixels involved. In this paper we propose using commodity computer graphics hardware for fast image interpolation. We use the full search block matching algorithm to illustrate the problems and limitations of using graphics hardware in this way.
Analysis of Spatial Interpolation in the Material-Point Method
DEFF Research Database (Denmark)
Andersen, Søren; Andersen, Lars
2010-01-01
are obtained using quadratic elements. It is shown that for more complex problems, the use of partially negative shape functions is inconsistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations...
International Nuclear Information System (INIS)
Schneiders, Jan F G; Sciacchitano, Andrea
2017-01-01
The track benchmarking method (TBM) is proposed for uncertainty quantification of particle tracking velocimetry (PTV) data mapped onto a regular grid. The method provides statistical uncertainty for a velocity time-series and can in addition be used to obtain instantaneous uncertainty at increased computational cost. Interpolation techniques are typically used to map velocity data from scattered PTV (e.g. tomographic PTV and Shake-the-Box) measurements onto a Cartesian grid. Recent examples of these techniques are the FlowFit and VIC+ methods. The TBM approach estimates the random uncertainty in dense velocity fields by performing the velocity interpolation using a subset of typically 95% of the particle tracks and by considering the remaining tracks as an independent benchmarking reference. In addition, also a bias introduced by the interpolation technique is identified. The numerical assessment shows that the approach is accurate when particle trajectories are measured over an extended number of snapshots, typically on the order of 10. When only short particle tracks are available, the TBM estimate overestimates the measurement error. A correction to TBM is proposed and assessed to compensate for this overestimation. The experimental assessment considers the case of a jet flow, processed both by tomographic PIV and by VIC+. The uncertainty obtained by TBM provides a quantitative evaluation of the measurement accuracy and precision and highlights the regions of high error by means of bias and random uncertainty maps. In this way, it is possible to quantify the uncertainty reduction achieved by advanced interpolation algorithms with respect to standard correlation-based tomographic PIV. The use of TBM for uncertainty quantification and comparison of different processing techniques is demonstrated. (paper)
Lunardi, Alessandra
2018-01-01
This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
A high-order Petrov-Galerkin method for the Boltzmann transport equation
International Nuclear Information System (INIS)
Pain, C.C.; Candy, A.S.; Piggott, M.D.; Buchan, A.; Eaton, M.D.; Goddard, A.J.H.; Oliveira, C.R.E. de
2005-01-01
We describe a new Petrov-Galerkin method using high-order terms to introduce dissipation in a residual-free formulation. The method is developed following both a Taylor series analysis and a variational principle, and the result has much in common with traditional Petrov-Galerkin, Self Adjoint Angular Flux (SAAF) and Even Parity forms of the Boltzmann transport equation. In addition, we consider the subtleties in constructing appropriate boundary conditions. In sub-grid scale (SGS) modelling of fluids the advantages of high-order dissipation are well known. Fourth-order terms, for example, are commonly used as a turbulence model with uniform dissipation. They have been shown to have superior properties to SGS models based upon second-order dissipation or viscosity. Even higher-order forms of dissipation (e.g. 16.-order) can offer further advantages, but are only easily realised by spectral methods because of the solution continuity requirements that these higher-order operators demand. Higher-order operators are more effective, bringing a higher degree of representation to the solution locally. Second-order operators, for example, tend to relax the solution to a linear variation locally, whereas a high-order operator will tend to relax the solution to a second-order polynomial locally. The form of the dissipation is also important. For example, the dissipation may only be applied (as it is in this work) in the streamline direction. While for many problems, for example Large Eddy Simulation (LES), simply adding a second or fourth-order dissipation term is a perfectly satisfactory SGS model, it is well known that a consistent residual-free formulation is required for radiation transport problems. This motivated the consideration of a new Petrov-Galerkin method that is residual-free, but also benefits from the advantageous features that SGS modelling introduces. We close with a demonstration of the advantages of this new discretization method over standard Petrov
International Nuclear Information System (INIS)
Asadzadeh, M.; Thevenot, L.
2010-01-01
The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.
Fast digital zooming system using directionally adaptive image interpolation and restoration.
Kang, Wonseok; Jeon, Jaehwan; Yu, Soohwan; Paik, Joonki
2014-01-01
This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then selectively used according to the refined edge orientation for removing jagged artifacts in the slanted edge region. A novel image restoration algorithm is also presented for removing blurring artifacts caused by the linear or cubic-spline interpolation using the directionally adaptive truncated constrained least squares (TCLS) filter. Both proposed steerable filter-based interpolation and the TCLS-based restoration filters have a finite impulse response (FIR) structure for real time processing in an image signal processing (ISP) chain. Experimental results show that the proposed digital zooming system provides high-quality magnified images with FIR filter-based fast computational structure.
Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems
Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri
2018-05-01
The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.
Rhie-Chow interpolation in strong centrifugal fields
Bogovalov, S. V.; Tronin, I. V.
2015-10-01
Rhie-Chow interpolation formulas are derived from the Navier-Stokes and continuity equations. These formulas are generalized to gas dynamics in strong centrifugal fields (as high as 106 g) occurring in gas centrifuges.
A disposition of interpolation techniques
Knotters, M.; Heuvelink, G.B.M.
2010-01-01
A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated
Application of Time-Frequency Domain Transform to Three-Dimensional Interpolation of Medical Images.
Lv, Shengqing; Chen, Yimin; Li, Zeyu; Lu, Jiahui; Gao, Mingke; Lu, Rongrong
2017-11-01
Medical image three-dimensional (3D) interpolation is an important means to improve the image effect in 3D reconstruction. In image processing, the time-frequency domain transform is an efficient method. In this article, several time-frequency domain transform methods are applied and compared in 3D interpolation. And a Sobel edge detection and 3D matching interpolation method based on wavelet transform is proposed. We combine wavelet transform, traditional matching interpolation methods, and Sobel edge detection together in our algorithm. What is more, the characteristics of wavelet transform and Sobel operator are used. They deal with the sub-images of wavelet decomposition separately. Sobel edge detection 3D matching interpolation method is used in low-frequency sub-images under the circumstances of ensuring high frequency undistorted. Through wavelet reconstruction, it can get the target interpolation image. In this article, we make 3D interpolation of the real computed tomography (CT) images. Compared with other interpolation methods, our proposed method is verified to be effective and superior.
Node insertion in Coalescence Fractal Interpolation Function
International Nuclear Information System (INIS)
Prasad, Srijanani Anurag
2013-01-01
The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed
On the uncertainty inequality as applied to discrete signals
Directory of Open Access Journals (Sweden)
Y. V. Venkatesh
2006-01-01
Full Text Available Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme for exactly reconstructing it from its discrete samples. We analyze the relationship between concentration (or compactness in the temporal/spectral domains of the (i continuous-time and (ii discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which prescribes a lower bound on the product of effective temporal and spectral spreads of the signal. On the other hand, the discrete-time counterpart seems to exhibit some strange properties, and this provides motivation for the present paper. We consider the following problem: for a bandlimited signal, can the uncertainty inequality be expressed in terms of the samples, using thestandard definitions of the temporal and spectral spreads of the signal? In contrast with the results of the literature, we present a new approach to solve this problem. We also present a comparison of the results obtained using the proposed definitions with those available in the literature.
Duru, Kenneth
2014-12-01
© 2014 Elsevier Inc. In this paper, we develop a stable and systematic procedure for numerical treatment of elastic waves in discontinuous and layered media. We consider both planar and curved interfaces where media parameters are allowed to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions at layer interfaces are imposed weakly using penalties. By deriving lower bounds of the penalty strength and constructing discrete energy estimates we prove time stability. We present numerical experiments in two space dimensions to illustrate the usefulness of the proposed method for simulations involving typical interface phenomena in elastic materials. The numerical experiments verify high order accuracy and time stability.
Single image super resolution algorithm based on edge interpolation in NSCT domain
Zhang, Mengqun; Zhang, Wei; He, Xinyu
2017-11-01
In order to preserve the texture and edge information and to improve the space resolution of single frame, a superresolution algorithm based on Contourlet (NSCT) is proposed. The original low resolution image is transformed by NSCT, and the directional sub-band coefficients of the transform domain are obtained. According to the scale factor, the high frequency sub-band coefficients are amplified by the interpolation method based on the edge direction to the desired resolution. For high frequency sub-band coefficients with noise and weak targets, Bayesian shrinkage is used to calculate the threshold value. The coefficients below the threshold are determined by the correlation among the sub-bands of the same scale to determine whether it is noise and de-noising. The anisotropic diffusion filter is used to effectively enhance the weak target in the low contrast region of the target and background. Finally, the high-frequency sub-band is amplified by the bilinear interpolation method to the desired resolution, and then combined with the high-frequency subband coefficients after de-noising and small target enhancement, the NSCT inverse transform is used to obtain the desired resolution image. In order to verify the effectiveness of the proposed algorithm, the proposed algorithm and several common image reconstruction methods are used to test the synthetic image, motion blurred image and hyperspectral image, the experimental results show that compared with the traditional single resolution algorithm, the proposed algorithm can obtain smooth edges and good texture features, and the reconstructed image structure is well preserved and the noise is suppressed to some extent.
BIMOND3, Monotone Bivariate Interpolation
International Nuclear Information System (INIS)
Fritsch, F.N.; Carlson, R.E.
2001-01-01
1 - Description of program or function: BIMOND is a FORTRAN-77 subroutine for piecewise bi-cubic interpolation to data on a rectangular mesh, which reproduces the monotonousness of the data. A driver program, BIMOND1, is provided which reads data, computes the interpolating surface parameters, and evaluates the function on a mesh suitable for plotting. 2 - Method of solution: Monotonic piecewise bi-cubic Hermite interpolation is used. 3 - Restrictions on the complexity of the problem: The current version of the program can treat data which are monotone in only one of the independent variables, but cannot handle piecewise monotone data
Directory of Open Access Journals (Sweden)
Mahacine Amrani
2008-06-01
Full Text Available Several methods are currently used to optimize edges and contours of geophysical data maps. A resistivity map was expectedto allow the electrical resistivity signal to be imaged in 2D in Moroccan resistivity survey in the phosphate mining domain. Anomalouszones of phosphate deposit “disturbances” correspond to resistivity anomalies. The resistivity measurements were taken at 5151discrete locations. Much of the geophysical spatial analysis requires a continuous data set and this study is designed to create that surface. This paper identifies the best spatial interpolation method to use for the creation of continuous data for Moroccan resistivity data of phosphate “disturbances” zones. The effectiveness of our approach for successfully reducing noise has been used much successin the analysis of stationary geophysical data as resistivity data. The interpolation filtering approach methods applied to modelingsurface phosphate “disturbances” was found to be consistently useful.
Directory of Open Access Journals (Sweden)
Lixin Li
2014-09-01
Full Text Available Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate
Li, Lixin; Losser, Travis; Yorke, Charles; Piltner, Reinhard
2014-01-01
Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed) faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate spatiotemporal interpolation
Li, Lixin; Losser, Travis; Yorke, Charles; Piltner, Reinhard
2014-09-03
Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed) faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate spatiotemporal interpolation
International Nuclear Information System (INIS)
Brown, Peter N.; Shumaker, Dana E.; Woodward, Carol S.
2005-01-01
We present a solution method for fully implicit radiation diffusion problems discretized on meshes having millions of spatial zones. This solution method makes use of high order in time integration techniques, inexact Newton-Krylov nonlinear solvers, and multigrid preconditioners. We explore the advantages and disadvantages of high order time integration methods for the fully implicit formulation on both two- and three-dimensional problems with tabulated opacities and highly nonlinear fusion source terms
Research progress and hotspot analysis of spatial interpolation
Jia, Li-juan; Zheng, Xin-qi; Miao, Jin-li
2018-02-01
In this paper, the literatures related to spatial interpolation between 1982 and 2017, which are included in the Web of Science core database, are used as data sources, and the visualization analysis is carried out according to the co-country network, co-category network, co-citation network, keywords co-occurrence network. It is found that spatial interpolation has experienced three stages: slow development, steady development and rapid development; The cross effect between 11 clustering groups, the main convergence of spatial interpolation theory research, the practical application and case study of spatial interpolation and research on the accuracy and efficiency of spatial interpolation. Finding the optimal spatial interpolation is the frontier and hot spot of the research. Spatial interpolation research has formed a theoretical basis and research system framework, interdisciplinary strong, is widely used in various fields.
Directory of Open Access Journals (Sweden)
C.G. Ozoegwu
2016-01-01
Full Text Available The general least squares model for milling process state term is presented. A discrete map for milling stability analysis that is based on the third-order case of the presented general least squares milling state term model is first studied and compared with its third-order counterpart that is based on the interpolation theory. Both numerical rate of convergence and chatter stability results of the two maps are compared using the single degree of freedom (1DOF milling model. The numerical rate of convergence of the presented third-order model is also studied using the two degree of freedom (2DOF milling process model. Comparison gave that stability results from the two maps agree closely but the presented map demonstrated reduction in number of needed calculations leading to about 30% savings in computational time (CT. It is seen in earlier works that accuracy of milling stability analysis using the full-discretization method rises from first-order theory to second-order theory and continues to rise to the third-order theory. The present work confirms this trend. In conclusion, the method presented in this work will enable fast and accurate computation of stability diagrams for use by machinists.
Analysis of ECT Synchronization Performance Based on Different Interpolation Methods
Directory of Open Access Journals (Sweden)
Yang Zhixin
2014-01-01
Full Text Available There are two synchronization methods of electronic transformer in IEC60044-8 standard: impulsive synchronization and interpolation. When the impulsive synchronization method is inapplicability, the data synchronization of electronic transformer can be realized by using the interpolation method. The typical interpolation methods are piecewise linear interpolation, quadratic interpolation, cubic spline interpolation and so on. In this paper, the influences of piecewise linear interpolation, quadratic interpolation and cubic spline interpolation for the data synchronization of electronic transformer are computed, then the computational complexity, the synchronization precision, the reliability, the application range of different interpolation methods are analyzed and compared, which can serve as guide studies for practical applications.
Distance-two interpolation for parallel algebraic multigrid
International Nuclear Information System (INIS)
Sterck, H de; Falgout, R D; Nolting, J W; Yang, U M
2007-01-01
In this paper we study the use of long distance interpolation methods with the low complexity coarsening algorithm PMIS. AMG performance and scalability is compared for classical as well as long distance interpolation methods on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers
International Nuclear Information System (INIS)
Park, Yujin; Kazantzis, Nikolaos; Parlos, Alexander G.; Chong, Kil To
2013-01-01
Highlights: • Numerical solution for stiff differential equations using matrix exponential method. • The approximation is based on First Order Hold assumption. • Various input examples applied to the point kinetics equations. • The method shows superior useful and effective activity. - Abstract: A system of nonlinear differential equations is derived to model the dynamics of neutron density and the delayed neutron precursors within a point kinetics equation modeling framework for a nuclear reactor. The point kinetic equations are mathematically characterized as stiff, occasionally nonlinear, ordinary differential equations, posing significant challenges when numerical solutions are sought and traditionally resulting in the need for smaller time step intervals within various computational schemes. In light of the above realization, the present paper proposes a new discretization method inspired by system-theoretic notions and technically based on a combination of the matrix exponential method (MEM) and the First-Order Hold (FOH) assumption. Under the proposed time discretization structure, the sampled-data representation of the nonlinear point kinetic system of equations is derived. The performance of the proposed time discretization procedure is evaluated using several case studies with sinusoidal reactivity profiles and multiple input examples (reactivity and neutron source function). It is shown, that by applying the proposed method under a First-Order Hold for the neutron density and the precursor concentrations at each time step interval, the stiffness problem associated with the point kinetic equations can be adequately addressed and resolved. Finally, as evidenced by the aforementioned detailed simulation studies, the proposed method retains its validity and accuracy for a wide range of reactor operating conditions, including large sampling periods dictated by physical and/or technical limitations associated with the current state of sensor and
Energy Technology Data Exchange (ETDEWEB)
Thomas, Edward, E-mail: etjr@auburn.edu; Konopka, Uwe; Lynch, Brian; Adams, Stephen; LeBlanc, Spencer [Physics Department, Auburn University, Auburn, Alabama 36849 (United States); Merlino, Robert L. [Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242 (United States); Rosenberg, Marlene [Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, California 92093 (United States)
2015-11-15
Dusty plasmas have been studied in argon, radio frequency (rf) glow discharge plasmas at magnetic fields up to 2.5 T where the electrons and ions are strongly magnetized. Plasmas are generated between two parallel plate electrodes where the lower, powered electrode is solid and the upper electrode supports a dual mesh consisting of #24 brass and #30 aluminum wire cloth. In this experiment, we study the formation of imposed ordered structures and particle dynamics as a function of magnetic field. Through observations of trapped particles and the quasi-discrete (i.e., “hopping”) motion of particles between the trapping locations, it is possible to make a preliminary estimate of the potential structure that confines the particles to a grid structure in the plasma. This information is used to gain insight into the formation of the imposed grid pattern of the dust particles in the plasma.
Interpolative Boolean Networks
Directory of Open Access Journals (Sweden)
Vladimir Dobrić
2017-01-01
Full Text Available Boolean networks are used for modeling and analysis of complex systems of interacting entities. Classical Boolean networks are binary and they are relevant for modeling systems with complex switch-like causal interactions. More descriptive power can be provided by the introduction of gradation in this model. If this is accomplished by using conventional fuzzy logics, the generalized model cannot secure the Boolean frame. Consequently, the validity of the model’s dynamics is not secured. The aim of this paper is to present the Boolean consistent generalization of Boolean networks, interpolative Boolean networks. The generalization is based on interpolative Boolean algebra, the [0,1]-valued realization of Boolean algebra. The proposed model is adaptive with respect to the nature of input variables and it offers greater descriptive power as compared with traditional models. For illustrative purposes, IBN is compared to the models based on existing real-valued approaches. Due to the complexity of the most systems to be analyzed and the characteristics of interpolative Boolean algebra, the software support is developed to provide graphical and numerical tools for complex system modeling and analysis.
Interpolation of diffusion weighted imaging datasets
DEFF Research Database (Denmark)
Dyrby, Tim B; Lundell, Henrik; Burke, Mark W
2014-01-01
anatomical details and signal-to-noise-ratio for reliable fibre reconstruction. We assessed the potential benefits of interpolating DWI datasets to a higher image resolution before fibre reconstruction using a diffusion tensor model. Simulations of straight and curved crossing tracts smaller than or equal......Diffusion weighted imaging (DWI) is used to study white-matter fibre organisation, orientation and structural connectivity by means of fibre reconstruction algorithms and tractography. For clinical settings, limited scan time compromises the possibilities to achieve high image resolution for finer...... interpolation methods fail to disentangle fine anatomical details if PVE is too pronounced in the original data. As for validation we used ex-vivo DWI datasets acquired at various image resolutions as well as Nissl-stained sections. Increasing the image resolution by a factor of eight yielded finer geometrical...
Directory of Open Access Journals (Sweden)
Jinyang Song
2018-01-01
Full Text Available Many modulated signals exhibit a cyclostationarity property, which can be exploited in direction-of-arrival (DOA estimation to effectively eliminate interference and noise. In this paper, our aim is to integrate the cyclostationarity with the spatial domain and enable the algorithm to estimate more sources than sensors. However, DOA estimation with a sparse array is performed in the coarray domain and the holes within the coarray limit the usage of the complete coarray information. In order to use the complete coarray information to increase the degrees-of-freedom (DOFs, sparsity-aware-based methods and the difference coarray interpolation methods have been proposed. In this paper, the coarray interpolation technique is further explored with cyclostationary signals. Besides the difference coarray model and its corresponding Toeplitz completion formulation, we build up a sum coarray model and formulate a Hankel completion problem. In order to further improve the performance of the structured matrix completion, we define the spatial spectrum sampling operations and the derivative (conjugate correlation subspaces, which can be exploited to construct orthogonal constraints for the autocorrelation vectors in the coarray interpolation problem. Prior knowledge of the source interval can also be incorporated into the problem. Simulation results demonstrate that the additional constraints contribute to a remarkable performance improvement.
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Interpolation Routines Assessment in ALS-Derived Digital Elevation Models for Forestry Applications
Directory of Open Access Journals (Sweden)
Antonio Luis Montealegre
2015-07-01
Full Text Available Airborne Laser Scanning (ALS is capable of estimating a variety of forest parameters using different metrics extracted from the normalized heights of the point cloud using a Digital Elevation Model (DEM. In this study, six interpolation routines were tested over a range of land cover and terrain roughness in order to generate a collection of DEMs with spatial resolution of 1 and 2 m. The accuracy of the DEMs was assessed twice, first using a test sample extracted from the ALS point cloud, second using a set of 55 ground control points collected with a high precision Global Positioning System (GPS. The effects of terrain slope, land cover, ground point density and pulse penetration on the interpolation error were examined stratifying the study area with these variables. In addition, a Classification and Regression Tree (CART analysis allowed the development of a prediction uncertainty map to identify in which areas DEMs and Airborne Light Detection and Ranging (LiDAR derived products may be of low quality. The Triangulated Irregular Network (TIN to raster interpolation method produced the best result in the validation process with the training data set while the Inverse Distance Weighted (IDW routine was the best in the validation with GPS (RMSE of 2.68 cm and RMSE of 37.10 cm, respectively.
Sparse representation based image interpolation with nonlocal autoregressive modeling.
Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming
2013-04-01
Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.
A comparison of different interpolation methods for wind data in Central Asia
Reinhardt, Katja; Samimi, Cyrus
2017-04-01
For the assessment of the global climate change and its consequences, the results of computer based climate models are of central importance. The quality of these results and the validity of the derived forecasts are strongly determined by the quality of the underlying climate data. However, in many parts of the world high resolution data are not available. This is particularly true for many regions in Central Asia, where the density of climatological stations has often to be described as thinned out. Due to this insufficient data base the use of statistical methods to improve the resolution of existing climate data is of crucial importance. Only this can provide a substantial data base for a well-founded analysis of past climate changes as well as for a reliable forecast of future climate developments for the particular region. The study presented here shows a comparison of different interpolation methods for the wind components u and v for a region in Central Asia with a pronounced topography. The aim of the study is to find out whether there is an optimal interpolation method which can equally be applied for all pressure levels or if different interpolation methods have to be applied for each pressure level. The European reanalysis data Era-Interim for the years 1989 - 2015 are used as input data for the pressure levels of 850 hPa, 500 hPa and 200 hPa. In order to improve the input data, two different interpolation procedures were applied: On the one hand pure interpolation methods were used, such as inverse distance weighting and ordinary kriging. On the other hand machine learning algorithms, generalized additive models and regression kriging were applied, considering additional influencing factors, e.g. geopotential and topography. As a result it can be concluded that regression kriging provides the best results for all pressure levels, followed by support vector machine, neural networks and ordinary kriging. Inverse distance weighting showed the worst
Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids
DEFF Research Database (Denmark)
Román Marín, José Manuel; Rasmussen, Henrik K.
2009-01-01
equation is replaced with a temperature dependent pseudo time. The spatial coordinate system attached to the particles is discretized by 10-node quadratic tetrahedral elements using Cartesian coordinates. The temperature and the pressure are discretized by 10-node quadratic and linear interpolation...... utilizing an implicit variable step backwards differencing (BDF2) scheme, obtaining second order convergence of the temperature in time. A quadratic interpolation in time is applied to approximate the time integral in the K-BKZ equation. This type of scheme ensures third order accuracy with respect......, respectively, in the tetrahedral particle elements. The spatial discretization of the governing equations follows a mixed Galerkin finite element method. This type of scheme ensures third order accuracy with respect to the discretization of spatial dimension. The temperature equation is solved in time...
Fuzzy linguistic model for interpolation
International Nuclear Information System (INIS)
Abbasbandy, S.; Adabitabar Firozja, M.
2007-01-01
In this paper, a fuzzy method for interpolating of smooth curves was represented. We present a novel approach to interpolate real data by applying the universal approximation method. In proposed method, fuzzy linguistic model (FLM) applied as universal approximation for any nonlinear continuous function. Finally, we give some numerical examples and compare the proposed method with spline method
Treatment of Outliers via Interpolation Method with Neural Network Forecast Performances
Wahir, N. A.; Nor, M. E.; Rusiman, M. S.; Gopal, K.
2018-04-01
Outliers often lurk in many datasets, especially in real data. Such anomalous data can negatively affect statistical analyses, primarily normality, variance, and estimation aspects. Hence, handling the occurrences of outliers require special attention. Therefore, it is important to determine the suitable ways in treating outliers so as to ensure that the quality of the analyzed data is indeed high. As such, this paper discusses an alternative method to treat outliers via linear interpolation method. In fact, assuming outlier as a missing value in the dataset allows the application of the interpolation method to interpolate the outliers thus, enabling the comparison of data series using forecast accuracy before and after outlier treatment. With that, the monthly time series of Malaysian tourist arrivals from January 1998 until December 2015 had been used to interpolate the new series. The results indicated that the linear interpolation method, which was comprised of improved time series data, displayed better results, when compared to the original time series data in forecasting from both Box-Jenkins and neural network approaches.
Enhancement of low sampling frequency recordings for ECG biometric matching using interpolation.
Sidek, Khairul Azami; Khalil, Ibrahim
2013-01-01
Electrocardiogram (ECG) based biometric matching suffers from high misclassification error with lower sampling frequency data. This situation may lead to an unreliable and vulnerable identity authentication process in high security applications. In this paper, quality enhancement techniques for ECG data with low sampling frequency has been proposed for person identification based on piecewise cubic Hermite interpolation (PCHIP) and piecewise cubic spline interpolation (SPLINE). A total of 70 ECG recordings from 4 different public ECG databases with 2 different sampling frequencies were applied for development and performance comparison purposes. An analytical method was used for feature extraction. The ECG recordings were segmented into two parts: the enrolment and recognition datasets. Three biometric matching methods, namely, Cross Correlation (CC), Percent Root-Mean-Square Deviation (PRD) and Wavelet Distance Measurement (WDM) were used for performance evaluation before and after applying interpolation techniques. Results of the experiments suggest that biometric matching with interpolated ECG data on average achieved higher matching percentage value of up to 4% for CC, 3% for PRD and 94% for WDM. These results are compared with the existing method when using ECG recordings with lower sampling frequency. Moreover, increasing the sample size from 56 to 70 subjects improves the results of the experiment by 4% for CC, 14.6% for PRD and 0.3% for WDM. Furthermore, higher classification accuracy of up to 99.1% for PCHIP and 99.2% for SPLINE with interpolated ECG data as compared of up to 97.2% without interpolation ECG data verifies the study claim that applying interpolation techniques enhances the quality of the ECG data. Crown Copyright © 2012. Published by Elsevier Ireland Ltd. All rights reserved.
Zhang, Zhen; Yan, Peng; Jiang, Huan; Ye, Peiqing
2014-09-01
In this paper, we consider the discrete time-varying internal model-based control design for high precision tracking of complicated reference trajectories generated by time-varying systems. Based on a novel parallel time-varying internal model structure, asymptotic tracking conditions for the design of internal model units are developed, and a low order robust time-varying stabilizer is further synthesized. In a discrete time setting, the high precision tracking control architecture is deployed on a Voice Coil Motor (VCM) actuated servo gantry system, where numerical simulations and real time experimental results are provided, achieving the tracking errors around 3.5‰ for frequency-varying signals. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Homography Propagation and Optimization for Wide-Baseline Street Image Interpolation.
Nie, Yongwei; Zhang, Zhensong; Sun, Hanqiu; Su, Tan; Li, Guiqing
2017-10-01
Wide-baseline street image interpolation is useful but very challenging. Existing approaches either rely on heavyweight 3D reconstruction or computationally intensive deep networks. We present a lightweight and efficient method which uses simple homography computing and refining operators to estimate piecewise smooth homographies between input views. To achieve the goal, we show how to combine homography fitting and homography propagation together based on reliable and unreliable superpixel discrimination. Such a combination, other than using homography fitting only, dramatically increases the accuracy and robustness of the estimated homographies. Then, we integrate the concepts of homography and mesh warping, and propose a novel homography-constrained warping formulation which enforces smoothness between neighboring homographies by utilizing the first-order continuity of the warped mesh. This further eliminates small artifacts of overlapping, stretching, etc. The proposed method is lightweight and flexible, allows wide-baseline interpolation. It improves the state of the art and demonstrates that homography computation suffices for interpolation. Experiments on city and rural datasets validate the efficiency and effectiveness of our method.
Convergence of trajectories in fractal interpolation of stochastic processes
International Nuclear Information System (INIS)
MaIysz, Robert
2006-01-01
The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation
A Novel Entropy-Based Decoding Algorithm for a Generalized High-Order Discrete Hidden Markov Model
Directory of Open Access Journals (Sweden)
Jason Chin-Tiong Chan
2018-01-01
Full Text Available The optimal state sequence of a generalized High-Order Hidden Markov Model (HHMM is tracked from a given observational sequence using the classical Viterbi algorithm. This classical algorithm is based on maximum likelihood criterion. We introduce an entropy-based Viterbi algorithm for tracking the optimal state sequence of a HHMM. The entropy of a state sequence is a useful quantity, providing a measure of the uncertainty of a HHMM. There will be no uncertainty if there is only one possible optimal state sequence for HHMM. This entropy-based decoding algorithm can be formulated in an extended or a reduction approach. We extend the entropy-based algorithm for computing the optimal state sequence that was developed from a first-order to a generalized HHMM with a single observational sequence. This extended algorithm performs the computation exponentially with respect to the order of HMM. The computational complexity of this extended algorithm is due to the growth of the model parameters. We introduce an efficient entropy-based decoding algorithm that used reduction approach, namely, entropy-based order-transformation forward algorithm (EOTFA to compute the optimal state sequence of any generalized HHMM. This EOTFA algorithm involves a transformation of a generalized high-order HMM into an equivalent first-order HMM and an entropy-based decoding algorithm is developed based on the equivalent first-order HMM. This algorithm performs the computation based on the observational sequence and it requires OTN~2 calculations, where N~ is the number of states in an equivalent first-order model and T is the length of observational sequence.
Energy Technology Data Exchange (ETDEWEB)
Yu Jinshan; Zhang Ruitao; Zhang Zhengping; Wang Yonglu; Zhu Can; Zhang Lei; Yu Zhou; Han Yong, E-mail: yujinshan@yeah.net [National Laboratory of Analog IC' s, Chongqing 400060 (China)
2011-01-15
A digital calibration technique for an ultra high-speed folding and interpolating analog-to-digital converter in 0.18-{mu}m CMOS technology is presented. The similar digital calibration techniques are taken for high 3-bit flash converter and low 5-bit folding and interpolating converter, which are based on well-designed calibration reference, calibration DAC and comparators. The spice simulation and the measured results show the ADC produces 5.9 ENOB with calibration disabled and 7.2 ENOB with calibration enabled for high-frequency wide-bandwidth analog input. (semiconductor integrated circuits)
High-order shock-fitted detonation propagation in high explosives
Romick, Christopher M.; Aslam, Tariq D.
2017-03-01
A highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich-von Neumann-Döring (ZND) detonation wave, and Taylor-Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m /s, which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott-Stewart-Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting
Imaging system design and image interpolation based on CMOS image sensor
Li, Yu-feng; Liang, Fei; Guo, Rui
2009-11-01
An image acquisition system is introduced, which consists of a color CMOS image sensor (OV9620), SRAM (CY62148), CPLD (EPM7128AE) and DSP (TMS320VC5509A). The CPLD implements the logic and timing control to the system. SRAM stores the image data, and DSP controls the image acquisition system through the SCCB (Omni Vision Serial Camera Control Bus). The timing sequence of the CMOS image sensor OV9620 is analyzed. The imaging part and the high speed image data memory unit are designed. The hardware and software design of the image acquisition and processing system is given. CMOS digital cameras use color filter arrays to sample different spectral components, such as red, green, and blue. At the location of each pixel only one color sample is taken, and the other colors must be interpolated from neighboring samples. We use the edge-oriented adaptive interpolation algorithm for the edge pixels and bilinear interpolation algorithm for the non-edge pixels to improve the visual quality of the interpolated images. This method can get high processing speed, decrease the computational complexity, and effectively preserve the image edges.
International Nuclear Information System (INIS)
Garcia-Santos, J. M.; Cejudo, J.
2002-01-01
In contrast to conventional computed tomography (CT), helical CT requires the application of interpolators to achieve image reconstruction. This is because the projections processed by the computer are not situated in the same plane. Since the introduction of helical CT. a number of interpolators have been designed in the attempt to maintain the thickness of the reconstructed section as close as possible to the thickness of the X-ray beam. The purpose of this article is to discuss the function of these interpolators, stressing the advantages and considering the possible inconveniences of high-grade curved interpolators with respect to standard linear interpolators. (Author) 7 refs
Validation of China-wide interpolated daily climate variables from 1960 to 2011
Yuan, Wenping; Xu, Bing; Chen, Zhuoqi; Xia, Jiangzhou; Xu, Wenfang; Chen, Yang; Wu, Xiaoxu; Fu, Yang
2015-02-01
Temporally and spatially continuous meteorological variables are increasingly in demand to support many different types of applications related to climate studies. Using measurements from 600 climate stations, a thin-plate spline method was applied to generate daily gridded climate datasets for mean air temperature, maximum temperature, minimum temperature, relative humidity, sunshine duration, wind speed, atmospheric pressure, and precipitation over China for the period 1961-2011. A comprehensive evaluation of interpolated climate was conducted at 150 independent validation sites. The results showed superior performance for most of the estimated variables. Except for wind speed, determination coefficients ( R 2) varied from 0.65 to 0.90, and interpolations showed high consistency with observations. Most of the estimated climate variables showed relatively consistent accuracy among all seasons according to the root mean square error, R 2, and relative predictive error. The interpolated data correctly predicted the occurrence of daily precipitation at validation sites with an accuracy of 83 %. Moreover, the interpolation data successfully explained the interannual variability trend for the eight meteorological variables at most validation sites. Consistent interannual variability trends were observed at 66-95 % of the sites for the eight meteorological variables. Accuracy in distinguishing extreme weather events differed substantially among the meteorological variables. The interpolated data identified extreme events for the three temperature variables, relative humidity, and sunshine duration with an accuracy ranging from 63 to 77 %. However, for wind speed, air pressure, and precipitation, the interpolation model correctly identified only 41, 48, and 58 % of extreme events, respectively. The validation indicates that the interpolations can be applied with high confidence for the three temperatures variables, as well as relative humidity and sunshine duration based
Optimum quantization and interpolation of projections in X-ray computerized tomography
International Nuclear Information System (INIS)
Vajnberg, Eh.I.; Fajngojz, M.L.
1984-01-01
Two methods to increase the accuracy of image reconstruction due to optimization of quantization and interpolation of proections with separate reduction of the main types of errors are described and experimentally studied. A high metrological and calculation efficiency of increasing the count frequency in the reconstructed tomogram 2-4 times is found. The optimum structure of interpolation functions of a minimum extent is calculated
Precipitation interpolation in mountainous areas
Kolberg, Sjur
2015-04-01
Different precipitation interpolation techniques as well as external drift covariates are tested and compared in a 26000 km2 mountainous area in Norway, using daily data from 60 stations. The main method of assessment is cross-validation. Annual precipitation in the area varies from below 500 mm to more than 2000 mm. The data were corrected for wind-driven undercatch according to operational standards. While temporal evaluation produce seemingly acceptable at-station correlation values (on average around 0.6), the average daily spatial correlation is less than 0.1. Penalising also bias, Nash-Sutcliffe R2 values are negative for spatial correspondence, and around 0.15 for temporal. Despite largely violated assumptions, plain Kriging produces better results than simple inverse distance weighting. More surprisingly, the presumably 'worst-case' benchmark of no interpolation at all, simply averaging all 60 stations for each day, actually outperformed the standard interpolation techniques. For logistic reasons, high altitudes are under-represented in the gauge network. The possible effect of this was investigated by a) fitting a precipitation lapse rate as an external drift, and b) applying a linear model of orographic enhancement (Smith and Barstad, 2004). These techniques improved the results only marginally. The gauge density in the region is one for each 433 km2; higher than the overall density of the Norwegian national network. Admittedly the cross-validation technique reduces the gauge density, still the results suggest that we are far from able to provide hydrological models with adequate data for the main driving force.
An Improved Minimum Error Interpolator of CNC for General Curves Based on FPGA
Directory of Open Access Journals (Sweden)
Jiye HUANG
2014-05-01
Full Text Available This paper presents an improved minimum error interpolation algorithm for general curves generation in computer numerical control (CNC. Compared with the conventional interpolation algorithms such as the By-Point Comparison method, the Minimum- Error method and the Digital Differential Analyzer (DDA method, the proposed improved Minimum-Error interpolation algorithm can find a balance between accuracy and efficiency. The new algorithm is applicable for the curves of linear, circular, elliptical and parabolic. The proposed algorithm is realized on a field programmable gate array (FPGA with Verilog HDL language, and simulated by the ModelSim software, and finally verified on a two-axis CNC lathe. The algorithm has the following advantages: firstly, the maximum interpolation error is only half of the minimum step-size; and secondly the computing time is only two clock cycles of the FPGA. Simulations and actual tests have proved that the high accuracy and efficiency of the algorithm, which shows that it is highly suited for real-time applications.
Interpolation of fuzzy data | Khodaparast | Journal of Fundamental ...
African Journals Online (AJOL)
Considering the many applications of mathematical functions in different ways, it is essential to have a defining function. In this study, we used Fuzzy Lagrangian interpolation and natural fuzzy spline polynomials to interpolate the fuzzy data. In the current world and in the field of science and technology, interpolation issues ...
Application of the Arbitrarily High Order Method to Coupled Electron Photon Transport
International Nuclear Information System (INIS)
Duo, Jose Ignacio
2004-01-01
This work is about the application of the Arbitrary High Order Nodal Method to coupled electron photon transport.A Discrete Ordinates code was enhanced and validated which permited to evaluate the advantages of using variable spatial development order per particle.The results obtained using variable spatial development and adaptive mesh refinement following an a posteriori error estimator are encouraging.Photon spectra for clinical accelerator target and, dose and charge depositio profiles are simulated in one-dimensional problems using cross section generated with CEPXS code.Our results are in good agreement with ONELD and MCNP codes
International Nuclear Information System (INIS)
Frank, T D; Mongkolsakulvong, S
2015-01-01
In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)
Bagheri, H.; Sadjadi, S. Y.; Sadeghian, S.
2013-09-01
One of the most significant tools to study many engineering projects is three-dimensional modelling of the Earth that has many applications in the Geospatial Information System (GIS), e.g. creating Digital Train Modelling (DTM). DTM has numerous applications in the fields of sciences, engineering, design and various project administrations. One of the most significant events in DTM technique is the interpolation of elevation to create a continuous surface. There are several methods for interpolation, which have shown many results due to the environmental conditions and input data. The usual methods of interpolation used in this study along with Genetic Algorithms (GA) have been optimised and consisting of polynomials and the Inverse Distance Weighting (IDW) method. In this paper, the Artificial Intelligent (AI) techniques such as GA and Neural Networks (NN) are used on the samples to optimise the interpolation methods and production of Digital Elevation Model (DEM). The aim of entire interpolation methods is to evaluate the accuracy of interpolation methods. Universal interpolation occurs in the entire neighbouring regions can be suggested for larger regions, which can be divided into smaller regions. The results obtained from applying GA and ANN individually, will be compared with the typical method of interpolation for creation of elevations. The resulting had performed that AI methods have a high potential in the interpolation of elevations. Using artificial networks algorithms for the interpolation and optimisation based on the IDW method with GA could be estimated the high precise elevations.
Interpolation of quasi-Banach spaces
International Nuclear Information System (INIS)
Tabacco Vignati, A.M.
1986-01-01
This dissertation presents a method of complex interpolation for familities of quasi-Banach spaces. This method generalizes the theory for families of Banach spaces, introduced by others. Intermediate spaces in several particular cases are characterized using different approaches. The situation when all the spaces have finite dimensions is studied first. The second chapter contains the definitions and main properties of the new interpolation spaces, and an example concerning the Schatten ideals associated with a separable Hilbert space. The case of L/sup P/ spaces follows from the maximal operator theory contained in Chapter III. Also introduced is a different method of interpolation for quasi-Banach lattices of functions, and conditions are given to guarantee that the two techniques yield the same result. Finally, the last chapter contains a different, and more direct, approach to the case of Hardy spaces
Basis set approach in the constrained interpolation profile method
International Nuclear Information System (INIS)
Utsumi, T.; Koga, J.; Yabe, T.; Ogata, Y.; Matsunaga, E.; Aoki, T.; Sekine, M.
2003-07-01
We propose a simple polynomial basis-set that is easily extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation. Thus the solution even on the subgrid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. 3rd and 5th order polynomials are tested on the one-dimensional Schroedinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lower-lying eigenstates. (author)
International Nuclear Information System (INIS)
Cho, Sanghee; Grazioso, Ron; Zhang Nan; Aykac, Mehmet; Schmand, Matthias
2011-01-01
The main focus of our study is to investigate how the performance of digital timing methods is affected by sampling rate, anti-aliasing and signal interpolation filters. We used the Nyquist sampling theorem to address some basic questions such as what will be the minimum sampling frequencies? How accurate will the signal interpolation be? How do we validate the timing measurements? The preferred sampling rate would be as low as possible, considering the high cost and power consumption of high-speed analog-to-digital converters. However, when the sampling rate is too low, due to the aliasing effect, some artifacts are produced in the timing resolution estimations; the shape of the timing profile is distorted and the FWHM values of the profile fluctuate as the source location changes. Anti-aliasing filters are required in this case to avoid the artifacts, but the timing is degraded as a result. When the sampling rate is marginally over the Nyquist rate, a proper signal interpolation is important. A sharp roll-off (higher order) filter is required to separate the baseband signal from its replicates to avoid the aliasing, but in return the computation will be higher. We demonstrated the analysis through a digital timing study using fast LSO scintillation crystals as used in time-of-flight PET scanners. From the study, we observed that there is no significant timing resolution degradation down to 1.3 Ghz sampling frequency, and the computation requirement for the signal interpolation is reasonably low. A so-called sliding test is proposed as a validation tool checking constant timing resolution behavior of a given timing pick-off method regardless of the source location change. Lastly, the performance comparison for several digital timing methods is also shown.
Kisaka, M. Oscar; Mucheru-Muna, M.; Ngetich, F. K.; Mugwe, J.; Mugendi, D.; Mairura, F.; Shisanya, C.; Makokha, G. L.
2016-04-01
Drier parts of Kenya's Central Highlands endure persistent crop failure and declining agricultural productivity. These have, in part, attributed to high temperatures, prolonged dry spells and erratic rainfall. Understanding spatial-temporal variability of climatic indices such as rainfall at seasonal level is critical for optimal rain-fed agricultural productivity and natural resource management in the study area. However, the predominant setbacks in analysing hydro-meteorological events are occasioned by either lack, inadequate, or inconsistent meteorological data. Like in most other places, the sole sources of climatic data in the study region are scarce and only limited to single stations, yet with persistent missing/unrecorded data making their utilization a challenge. This study examined seasonal anomalies and variability in rainfall, drought occurrence and the efficacy of interpolation techniques in the drier regions of eastern Kenyan. Rainfall data from five stations (Machang'a, Kiritiri, Kiambere and Kindaruma and Embu) were sourced from both the Kenya Meteorology Department and on-site primary recording. Owing to some experimental work ongoing, automated recording for primary dailies in Machang'a have been ongoing since the year 2000 to date; thus, Machang'a was treated as reference (for period of record) station for selection of other stations in the region. The other stations had data sets of over 15 years with missing data of less than 10 % as required by the world meteorological organization whose quality check is subject to the Centre for Climate Systems Modeling (C2SM) through MeteoSwiss and EMPA bodies. The dailies were also subjected to homogeneity testing to evaluate whether they came from the same population. Rainfall anomaly index, coefficients of variance and probability were utilized in the analyses of rainfall variability. Spline, kriging and inverse distance weighting interpolation techniques were assessed using daily rainfall data and
Differential Interpolation Effects in Free Recall
Petrusic, William M.; Jamieson, Donald G.
1978-01-01
Attempts to determine whether a sufficiently demanding and difficult interpolated task (shadowing, i.e., repeating aloud) would decrease recall for earlier-presented items as well as for more recent items. Listening to music was included as a second interpolated task. Results support views that serial position effects reflect a single process.…
Congdon, Peter
2014-04-01
Health data may be collected across one spatial framework (e.g. health provider agencies), but contrasts in health over another spatial framework (neighbourhoods) may be of policy interest. In the UK, population prevalence totals for chronic diseases are provided for populations served by general practitioner practices, but not for neighbourhoods (small areas of circa 1500 people), raising the question whether data for one framework can be used to provide spatially interpolated estimates of disease prevalence for the other. A discrete process convolution is applied to this end and has advantages when there are a relatively large number of area units in one or other framework. Additionally, the interpolation is modified to take account of the observed neighbourhood indicators (e.g. hospitalisation rates) of neighbourhood disease prevalence. These are reflective indicators of neighbourhood prevalence viewed as a latent construct. An illustrative application is to prevalence of psychosis in northeast London, containing 190 general practitioner practices and 562 neighbourhoods, including an assessment of sensitivity to kernel choice (e.g. normal vs exponential). This application illustrates how a zero-inflated Poisson can be used as the likelihood model for a reflective indicator.
Recent developments of discrete material optimization of laminated composite structures
DEFF Research Database (Denmark)
Lund, Erik; Sørensen, Rene
2015-01-01
This work will give a quick summary of recent developments of the Discrete Material Optimization approach for structural optimization of laminated composite structures. This approach can be seen as a multi-material topology optimization approach for selecting the best ply material and number...... of plies in a laminated composite structure. The conceptual combinatorial design problem is relaxed to a continuous problem such that well-established gradient based optimization techniques can be applied, and the optimization problem is solved on basis of interpolation schemes with penalization...
International Nuclear Information System (INIS)
Azmy, Yousry; Wang, Yaqi
2013-01-01
The research team has developed a practical, high-order, discrete-ordinates, short characteristics neutron transport code for three-dimensional configurations represented on unstructured tetrahedral grids that can be used for realistic reactor physics applications at both the assembly and core levels. This project will perform a comprehensive verification and validation of this new computational tool against both a continuous-energy Monte Carlo simulation (e.g. MCNP) and experimentally measured data, an essential prerequisite for its deployment in reactor core modeling. Verification is divided into three phases. The team will first conduct spatial mesh and expansion order refinement studies to monitor convergence of the numerical solution to reference solutions. This is quantified by convergence rates that are based on integral error norms computed from the cell-by-cell difference between the code's numerical solution and its reference counterpart. The latter is either analytic or very fine- mesh numerical solutions from independent computational tools. For the second phase, the team will create a suite of code-independent benchmark configurations to enable testing the theoretical order of accuracy of any particular discretization of the discrete ordinates approximation of the transport equation. For each tested case (i.e. mesh and spatial approximation order), researchers will execute the code and compare the resulting numerical solution to the exact solution on a per cell basis to determine the distribution of the numerical error. The final activity comprises a comparison to continuous-energy Monte Carlo solutions for zero-power critical configuration measurements at Idaho National Laboratory's Advanced Test Reactor (ATR). Results of this comparison will allow the investigators to distinguish between modeling errors and the above-listed discretization errors introduced by the deterministic method, and to separate the sources of uncertainty.
SAR image formation with azimuth interpolation after azimuth transform
Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM
2008-07-08
Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Hutchinson, Maxwell; Heinecke, Alexander; Pabst, Hans; Henry, Greg; Parsani, Matteo; Keyes, David E.
2016-01-01
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Hutchinson, Maxwell
2016-06-14
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
Adaptive Residual Interpolation for Color and Multispectral Image Demosaicking.
Monno, Yusuke; Kiku, Daisuke; Tanaka, Masayuki; Okutomi, Masatoshi
2017-12-01
Color image demosaicking for the Bayer color filter array is an essential image processing operation for acquiring high-quality color images. Recently, residual interpolation (RI)-based algorithms have demonstrated superior demosaicking performance over conventional color difference interpolation-based algorithms. In this paper, we propose adaptive residual interpolation (ARI) that improves existing RI-based algorithms by adaptively combining two RI-based algorithms and selecting a suitable iteration number at each pixel. These are performed based on a unified criterion that evaluates the validity of an RI-based algorithm. Experimental comparisons using standard color image datasets demonstrate that ARI can improve existing RI-based algorithms by more than 0.6 dB in the color peak signal-to-noise ratio and can outperform state-of-the-art algorithms based on training images. We further extend ARI for a multispectral filter array, in which more than three spectral bands are arrayed, and demonstrate that ARI can achieve state-of-the-art performance also for the task of multispectral image demosaicking.
Interpolating precipitation and its relation to runoff and non-point source pollution.
Chang, Chia-Ling; Lo, Shang-Lien; Yu, Shaw-L
2005-01-01
When rainfall spatially varies, complete rainfall data for each region with different rainfall characteristics are very important. Numerous interpolation methods have been developed for estimating unknown spatial characteristics. However, no interpolation method is suitable for all circumstances. In this study, several methods, including the arithmetic average method, the Thiessen Polygons method, the traditional inverse distance method, and the modified inverse distance method, were used to interpolate precipitation. The modified inverse distance method considers not only horizontal distances but also differences between the elevations of the region with no rainfall records and of its surrounding rainfall stations. The results show that when the spatial variation of rainfall is strong, choosing a suitable interpolation method is very important. If the rainfall is uniform, the precipitation estimated using any interpolation method would be quite close to the actual precipitation. When rainfall is heavy in locations with high elevation, the rainfall changes with the elevation. In this situation, the modified inverse distance method is much more effective than any other method discussed herein for estimating the rainfall input for WinVAST to estimate runoff and non-point source pollution (NPSP). When the spatial variation of rainfall is random, regardless of the interpolation method used to yield rainfall input, the estimation errors of runoff and NPSP are large. Moreover, the relationship between the relative error of the predicted runoff and predicted pollutant loading of SS is high. However, the pollutant concentration is affected by both runoff and pollutant export, so the relationship between the relative error of the predicted runoff and the predicted pollutant concentration of SS may be unstable.
Liu, Derek; Sloboda, Ron S
2014-05-01
Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.
Energy Technology Data Exchange (ETDEWEB)
Steinbrecher, G. [Association Euratom-Nasti Romania, Dept. of Theoretical Physics, Physics Faculty, University of Craiova (Romania); Reuss, J.D.; Misguich, J.H. [Association Euratom-CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
2001-11-01
We first remind usual physical and mathematical concepts involved in the dynamics of Hamiltonian systems, and namely in chaotic systems described by discrete 2D maps (representing the intersection points of toroidal magnetic lines in a poloidal plane in situations of incomplete magnetic chaos in Tokamaks). Finding the periodic points characterizing chains of magnetic islands is an essential step not only to determine the skeleton of the phase space picture, but also to determine the flux of magnetic lines across semi-permeable barriers like Cantori. We discuss here several computational methods used to determine periodic points in N dimensions, which amounts to solve a set of N nonlinear coupled equations: Newton method, minimization techniques, Laplace or steepest descend method, conjugated direction method and Fletcher-Reeves method. We have succeeded to improve this last method in an important way, without modifying its useful double-exponential convergence. This improved method has been tested and applied to finding periodic points of high order m in the 2D 'Tokamap' mapping, for values of m along rational chains of winding number n/m converging towards a noble value where a Cantorus exists. Such precise positions of periodic points have been used in the calculation of the flux across this Cantorus. (authors)
Rules and Discretion in Monetary Policy: Is the Response of the Stock Market Rational?
Directory of Open Access Journals (Sweden)
Ion-Iulian MARINESCU
2015-04-01
Full Text Available We investigate the effects of the monetary policy conduct on the domestic capital market for a sample of developed countries where the capital market plays a significant role in the economy. We break down the policy rate innovations in rules-based and discretionary components in order to determine the degree of prudentiality in the monetary policy conduct and we study their accounts with respect to capital market rationality. The rules-based component is determined using an interpolated vanilla Taylor-rule policy rate at the event date and the discretionary component is obtained by subtracting the rules-based rate from the target monetary policy rate innovation. Using an event study approach, we analyze the impact of monetary policy components on the returns of the stock market and we determine that the conduct of the monetary policy can cause irrational responses of the capital market. More than that, we show, for the analyzed countries, that if the general level of discretion in the monetary policy is high the response of the stock market becomes increasingly erratic, indicating that forward guidance may help reduce uncertainty on capital markets.
Randomized interpolative decomposition of separated representations
Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory
2015-01-01
We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.
Adaptive Discrete Hypergraph Matching.
Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao
2018-02-01
This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.
Survey: interpolation methods for whole slide image processing.
Roszkowiak, L; Korzynska, A; Zak, J; Pijanowska, D; Swiderska-Chadaj, Z; Markiewicz, T
2017-02-01
Evaluating whole slide images of histological and cytological samples is used in pathology for diagnostics, grading and prognosis . It is often necessary to rescale whole slide images of a very large size. Image resizing is one of the most common applications of interpolation. We collect the advantages and drawbacks of nine interpolation methods, and as a result of our analysis, we try to select one interpolation method as the preferred solution. To compare the performance of interpolation methods, test images were scaled and then rescaled to the original size using the same algorithm. The modified image was compared to the original image in various aspects. The time needed for calculations and results of quantification performance on modified images were also compared. For evaluation purposes, we used four general test images and 12 specialized biological immunohistochemically stained tissue sample images. The purpose of this survey is to determine which method of interpolation is the best to resize whole slide images, so they can be further processed using quantification methods. As a result, the interpolation method has to be selected depending on the task involving whole slide images. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.
Illumination estimation via thin-plate spline interpolation.
Shi, Lilong; Xiong, Weihua; Funt, Brian
2011-05-01
Thin-plate spline interpolation is used to interpolate the chromaticity of the color of the incident scene illumination across a training set of images. Given the image of a scene under unknown illumination, the chromaticity of the scene illumination can be found from the interpolated function. The resulting illumination-estimation method can be used to provide color constancy under changing illumination conditions and automatic white balancing for digital cameras. A thin-plate spline interpolates over a nonuniformly sampled input space, which in this case is a training set of image thumbnails and associated illumination chromaticities. To reduce the size of the training set, incremental k medians are applied. Tests on real images demonstrate that the thin-plate spline method can estimate the color of the incident illumination quite accurately, and the proposed training set pruning significantly decreases the computation.
Pricing Exotic Options under a High-Order Markovian Regime Switching Model
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Wai-Ki Ching
2007-10-01
Full Text Available We consider the pricing of exotic options when the price dynamics of the underlying risky asset are governed by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM. We assume that the market interest rate, the drift, and the volatility of the underlying risky asset's return switch over time according to the states of the HOMM, which are interpreted as the states of an economy. We will then employ the well-known tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale measure for option valuation. Moreover, we will also investigate the impact of the high-order effect of the states of the economy on the prices of some path-dependent exotic options, such as Asian options, lookback options, and barrier options.
Efficient GPU-based texture interpolation using uniform B-splines
Ruijters, D.; Haar Romenij, ter B.M.; Suetens, P.
2008-01-01
This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and
Shape Preserving Interpolation Using C2 Rational Cubic Spline
Directory of Open Access Journals (Sweden)
Samsul Ariffin Abdul Karim
2016-01-01
Full Text Available This paper discusses the construction of new C2 rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parameters αi, βi, and γi. The sufficient conditions for the positivity are derived on one parameter γi while the other two parameters αi and βi are free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation with C2 continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion and C2 continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivatives di, i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the new C2 rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated is ft∈C3t0,tn is also investigated in detail.
A FAST MORPHING-BASED INTERPOLATION FOR MEDICAL IMAGES: APPLICATION TO CONFORMAL RADIOTHERAPY
Directory of Open Access Journals (Sweden)
Hussein Atoui
2011-05-01
Full Text Available A method is presented for fast interpolation between medical images. The method is intended for both slice and projective interpolation. It allows offline interpolation between neighboring slices in tomographic data. Spatial correspondence between adjacent images is established using a block matching algorithm. Interpolation of image intensities is then carried out by morphing between the images. The morphing-based method is compared to standard linear interpolation, block-matching-based interpolation and registrationbased interpolation in 3D tomographic data sets. Results show that the proposed method scored similar performance in comparison to registration-based interpolation, and significantly outperforms both linear and block-matching-based interpolation. This method is applied in the context of conformal radiotherapy for online projective interpolation between Digitally Reconstructed Radiographs (DRRs.
National Research Council Canada - National Science Library
Gibou, Frederic; Fedkiw, Ronald
2004-01-01
In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains...
A Meshfree Cell-based Smoothed Point Interpolation Method for Solid Mechanics Problems
International Nuclear Information System (INIS)
Zhang Guiyong; Liu Guirong
2010-01-01
In the framework of a weakened weak (W 2 ) formulation using a generalized gradient smoothing operation, this paper introduces a novel meshfree cell-based smoothed point interpolation method (CS-PIM) for solid mechanics problems. The W 2 formulation seeks solutions from a normed G space which includes both continuous and discontinuous functions and allows the use of much more types of methods to create shape functions for numerical methods. When PIM shape functions are used, the functions constructed are in general not continuous over the entire problem domain and hence are not compatible. Such an interpolation is not in a traditional H 1 space, but in a G 1 space. By introducing the generalized gradient smoothing operation properly, the requirement on function is now further weakened upon the already weakened requirement for functions in a H 1 space and G 1 space can be viewed as a space of functions with weakened weak (W 2 ) requirement on continuity. The cell-based smoothed point interpolation method (CS-PIM) is formulated based on the W 2 formulation, in which displacement field is approximated using the PIM shape functions, which possess the Kronecker delta property facilitating the enforcement of essential boundary conditions [3]. The gradient (strain) field is constructed by the generalized gradient smoothing operation within the cell-based smoothing domains, which are exactly the triangular background cells. A W 2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is used to derive the discretized system equations. It was found that the CS-PIM possesses the following attractive properties: (1) It is very easy to implement and works well with the simplest linear triangular mesh without introducing additional degrees of freedom; (2) it is at least linearly conforming; (3) this method is temporally stable and works well for dynamic analysis; (4) it possesses a close-to-exact stiffness, which is much softer than the overly-stiff FEM model and
Permanently calibrated interpolating time counter
International Nuclear Information System (INIS)
Jachna, Z; Szplet, R; Kwiatkowski, P; Różyc, K
2015-01-01
We propose a new architecture of an integrated time interval counter that provides its permanent calibration in the background. Time interval measurement and the calibration procedure are based on the use of a two-stage interpolation method and parallel processing of measurement and calibration data. The parallel processing is achieved by a doubling of two-stage interpolators in measurement channels of the counter, and by an appropriate extension of control logic. Such modification allows the updating of transfer characteristics of interpolators without the need to break a theoretically infinite measurement session. We describe the principle of permanent calibration, its implementation and influence on the quality of the counter. The precision of the presented counter is kept at a constant level (below 20 ps) despite significant changes in the ambient temperature (from −10 to 60 °C), which can cause a sevenfold decrease in the precision of the counter with a traditional calibration procedure. (paper)
Integrals of Motion for Discrete-Time Optimal Control Problems
Torres, Delfim F. M.
2003-01-01
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.
Pearce, Mark A
2015-08-01
EBSDinterp is a graphic user interface (GUI)-based MATLAB® program to perform microstructurally constrained interpolation of nonindexed electron backscatter diffraction data points. The area available for interpolation is restricted using variations in pattern quality or band contrast (BC). Areas of low BC are not available for interpolation, and therefore cannot be erroneously filled by adjacent grains "growing" into them. Points with the most indexed neighbors are interpolated first and the required number of neighbors is reduced with each successive round until a minimum number of neighbors is reached. Further iterations allow more data points to be filled by reducing the BC threshold. This method ensures that the best quality points (those with high BC and most neighbors) are interpolated first, and that the interpolation is restricted to grain interiors before adjacent grains are grown together to produce a complete microstructure. The algorithm is implemented through a GUI, taking advantage of MATLAB®'s parallel processing toolbox to perform the interpolations rapidly so that a variety of parameters can be tested to ensure that the final microstructures are robust and artifact-free. The software is freely available through the CSIRO Data Access Portal (doi:10.4225/08/5510090C6E620) as both a compiled Windows executable and as source code.
Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.
2018-01-01
High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.
An adaptive interpolation scheme for molecular potential energy surfaces
Kowalewski, Markus; Larsson, Elisabeth; Heryudono, Alfa
2016-08-01
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
Cuzzone, Joshua K.; Morlighem, Mathieu; Larour, Eric; Schlegel, Nicole; Seroussi, Helene
2018-05-01
Paleoclimate proxies are being used in conjunction with ice sheet modeling experiments to determine how the Greenland ice sheet responded to past changes, particularly during the last deglaciation. Although these comparisons have been a critical component in our understanding of the Greenland ice sheet sensitivity to past warming, they often rely on modeling experiments that favor minimizing computational expense over increased model physics. Over Paleoclimate timescales, simulating the thermal structure of the ice sheet has large implications on the modeled ice viscosity, which can feedback onto the basal sliding and ice flow. To accurately capture the thermal field, models often require a high number of vertical layers. This is not the case for the stress balance computation, however, where a high vertical resolution is not necessary. Consequently, since stress balance and thermal equations are generally performed on the same mesh, more time is spent on the stress balance computation than is otherwise necessary. For these reasons, running a higher-order ice sheet model (e.g., Blatter-Pattyn) over timescales equivalent to the paleoclimate record has not been possible without incurring a large computational expense. To mitigate this issue, we propose a method that can be implemented within ice sheet models, whereby the vertical interpolation along the z axis relies on higher-order polynomials, rather than the traditional linear interpolation. This method is tested within the Ice Sheet System Model (ISSM) using quadratic and cubic finite elements for the vertical interpolation on an idealized case and a realistic Greenland configuration. A transient experiment for the ice thickness evolution of a single-dome ice sheet demonstrates improved accuracy using the higher-order vertical interpolation compared to models using the linear vertical interpolation, despite having fewer degrees of freedom. This method is also shown to improve a model's ability to capture sharp
Improving the visualization of electron-microscopy data through optical flow interpolation
Carata, Lucian
2013-01-01
Technical developments in neurobiology have reached a point where the acquisition of high resolution images representing individual neurons and synapses becomes possible. For this, the brain tissue samples are sliced using a diamond knife and imaged with electron-microscopy (EM). However, the technique achieves a low resolution in the cutting direction, due to limitations of the mechanical process, making a direct visualization of a dataset difficult. We aim to increase the depth resolution of the volume by adding new image slices interpolated from the existing ones, without requiring modifications to the EM image-capturing method. As classical interpolation methods do not provide satisfactory results on this type of data, the current paper proposes a re-framing of the problem in terms of motion volumes, considering the depth axis as a temporal axis. An optical flow method is adapted to estimate the motion vectors of pixels in the EM images, and this information is used to compute and insert multiple new images at certain depths in the volume. We evaluate the visualization results in comparison with interpolation methods currently used on EM data, transforming the highly anisotropic original dataset into a dataset with a larger depth resolution. The interpolation based on optical flow better reveals neurite structures with realistic undistorted shapes, and helps to easier map neuronal connections. © 2011 ACM.
A New Interpolation Approach for Linearly Constrained Convex Optimization
Espinoza, Francisco
2012-08-01
In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard\\'s interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton\\'s method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.
A high-order multiscale finite-element method for time-domain acoustic-wave modeling
Gao, Kai; Fu, Shubin; Chung, Eric T.
2018-05-01
Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.
Mayne, Terence P; Paskaranandavadivel, Niranchan; Erickson, Jonathan C; OGrady, Gregory; Cheng, Leo K; Angeli, Timothy R
2018-02-01
High-resolution mapping of gastrointestinal (GI) slow waves is a valuable technique for research and clinical applications. Interpretation of high-resolution GI mapping data relies on animations of slow wave propagation, but current methods remain as rudimentary, pixelated electrode activation animations. This study aimed to develop improved methods of visualizing high-resolution slow wave recordings that increases ease of interpretation. The novel method of "wavefront-orientation" interpolation was created to account for the planar movement of the slow wave wavefront, negate any need for distance calculations, remain robust in atypical wavefronts (i.e., dysrhythmias), and produce an appropriate interpolation boundary. The wavefront-orientation method determines the orthogonal wavefront direction and calculates interpolated values as the mean slow wave activation-time (AT) of the pair of linearly adjacent electrodes along that direction. Stairstep upsampling increased smoothness and clarity. Animation accuracy of 17 human high-resolution slow wave recordings (64-256 electrodes) was verified by visual comparison to the prior method showing a clear improvement in wave smoothness that enabled more accurate interpretation of propagation, as confirmed by an assessment of clinical applicability performed by eight GI clinicians. Quantitatively, the new method produced accurate interpolation values compared to experimental data (mean difference 0.02 ± 0.05 s) and was accurate when applied solely to dysrhythmic data (0.02 ± 0.06 s), both within the error in manual AT marking (mean 0.2 s). Mean interpolation processing time was 6.0 s per wave. These novel methods provide a validated visualization platform that will improve analysis of high-resolution GI mapping in research and clinical translation.
Kolyaie, S.; Yaghooti, M.; Majidi, G.
2011-12-01
This paper is a part of an ongoing research to examine the capability of geostatistical analysis for mobile networks coverage prediction, simulation and tuning. Mobile network coverage predictions are used to find network coverage gaps and areas with poor serviceability. They are essential data for engineering and management in order to make better decision regarding rollout, planning and optimisation of mobile networks.The objective of this research is to evaluate different interpolation techniques in coverage prediction. In method presented here, raw data collected from drive testing a sample of roads in study area is analysed and various continuous surfaces are created using different interpolation methods. Two general interpolation methods are used in this paper with different variables; first, Inverse Distance Weighting (IDW) with various powers and number of neighbours and second, ordinary kriging with Gaussian, spherical, circular and exponential semivariogram models with different number of neighbours. For the result comparison, we have used check points coming from the same drive test data. Prediction values for check points are extracted from each surface and the differences with actual value are computed. The output of this research helps finding an optimised and accurate model for coverage prediction.
The Atmospheric Data Acquisition And Interpolation Process For Center-TRACON Automation System
Jardin, M. R.; Erzberger, H.; Denery, Dallas G. (Technical Monitor)
1995-01-01
The Center-TRACON Automation System (CTAS), an advanced new air traffic automation program, requires knowledge of spatial and temporal atmospheric conditions such as the wind speed and direction, the temperature and the pressure in order to accurately predict aircraft trajectories. Real-time atmospheric data is available in a grid format so that CTAS must interpolate between the grid points to estimate the atmospheric parameter values. The atmospheric data grid is generally not in the same coordinate system as that used by CTAS so that coordinate conversions are required. Both the interpolation and coordinate conversion processes can introduce errors into the atmospheric data and reduce interpolation accuracy. More accurate algorithms may be computationally expensive or may require a prohibitively large amount of data storage capacity so that trade-offs must be made between accuracy and the available computational and data storage resources. The atmospheric data acquisition and processing employed by CTAS will be outlined in this report. The effects of atmospheric data processing on CTAS trajectory prediction will also be analyzed, and several examples of the trajectory prediction process will be given.
ERRORS MEASUREMENT OF INTERPOLATION METHODS FOR GEOID MODELS: STUDY CASE IN THE BRAZILIAN REGION
Directory of Open Access Journals (Sweden)
Daniel Arana
Full Text Available Abstract: The geoid is an equipotential surface regarded as the altimetric reference for geodetic surveys and it therefore, has several practical applications for engineers. In recent decades the geodetic community has concentrated efforts on the development of highly accurate geoid models through modern techniques. These models are supplied through regular grids which users need to make interpolations. Yet, little information can be obtained regarding the most appropriate interpolation method to extract information from the regular grid of geoidal models. The use of an interpolator that does not represent the geoid surface appropriately can impair the quality of geoid undulations and consequently the height transformation. This work aims to quantify the magnitude of error that comes from a regular mesh of geoid models. The analysis consisted of performing a comparison between the interpolation of the MAPGEO2015 program and three interpolation methods: bilinear, cubic spline and neural networks Radial Basis Function. As a result of the experiments, it was concluded that 2.5 cm of the 18 cm error of the MAPGEO2015 validation is caused by the use of interpolations in the 5'x5' grid.
Alvarez, Otto; Guo, Qinghua; Klinger, Robert C.; Li, Wenkai; Doherty, Paul
2013-01-01
Climate models may be limited in their inferential use if they cannot be locally validated or do not account for spatial uncertainty. Much of the focus has gone into determining which interpolation method is best suited for creating gridded climate surfaces, which often a covariate such as elevation (Digital Elevation Model, DEM) is used to improve the interpolation accuracy. One key area where little research has addressed is in determining which covariate best improves the accuracy in the interpolation. In this study, a comprehensive evaluation was carried out in determining which covariates were most suitable for interpolating climatic variables (e.g. precipitation, mean temperature, minimum temperature, and maximum temperature). We compiled data for each climate variable from 1950 to 1999 from approximately 500 weather stations across the Western United States (32° to 49° latitude and −124.7° to −112.9° longitude). In addition, we examined the uncertainty of the interpolated climate surface. Specifically, Thin Plate Spline (TPS) was used as the interpolation method since it is one of the most popular interpolation techniques to generate climate surfaces. We considered several covariates, including DEM, slope, distance to coast (Euclidean distance), aspect, solar potential, radar, and two Normalized Difference Vegetation Index (NDVI) products derived from Advanced Very High Resolution Radiometer (AVHRR) and Moderate Resolution Imaging Spectroradiometer (MODIS). A tenfold cross-validation was applied to determine the uncertainty of the interpolation based on each covariate. In general, the leading covariate for precipitation was radar, while DEM was the leading covariate for maximum, mean, and minimum temperatures. A comparison to other products such as PRISM and WorldClim showed strong agreement across large geographic areas but climate surfaces generated in this study (ClimSurf) had greater variability at high elevation regions, such as in the Sierra
Positivity for Convective Semi-discretizations
Fekete, Imre
2017-04-19
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.
Discrete ordinates transport methods for problems with highly forward-peaked scattering
International Nuclear Information System (INIS)
Pautz, S.D.
1998-04-01
The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method
Integration and interpolation of sampled waveforms
International Nuclear Information System (INIS)
Stearns, S.D.
1978-01-01
Methods for integrating, interpolating, and improving the signal-to-noise ratio of digitized waveforms are discussed with regard to seismic data from underground tests. The frequency-domain integration method and the digital interpolation method of Schafer and Rabiner are described and demonstrated using test data. The use of bandpass filtering for noise reduction is also demonstrated. With these methods, a backlog of seismic test data has been successfully processed
Bayer Demosaicking with Polynomial Interpolation.
Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil
2016-08-30
Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.
Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen
2015-04-01
This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive
Systems and methods for interpolation-based dynamic programming
Rockwood, Alyn
2013-01-03
Embodiments of systems and methods for interpolation-based dynamic programming. In one embodiment, the method includes receiving an object function and a set of constraints associated with the objective function. The method may also include identifying a solution on the objective function corresponding to intersections of the constraints. Additionally, the method may include generating an interpolated surface that is in constant contact with the solution. The method may also include generating a vector field in response to the interpolated surface.
Systems and methods for interpolation-based dynamic programming
Rockwood, Alyn
2013-01-01
Embodiments of systems and methods for interpolation-based dynamic programming. In one embodiment, the method includes receiving an object function and a set of constraints associated with the objective function. The method may also include identifying a solution on the objective function corresponding to intersections of the constraints. Additionally, the method may include generating an interpolated surface that is in constant contact with the solution. The method may also include generating a vector field in response to the interpolated surface.
Space-Time Discrete KPZ Equation
Cannizzaro, G.; Matetski, K.
2018-03-01
We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.
Yuval, Yuval; Rimon, Yaara; Graber, Ellen R; Furman, Alex
2014-08-01
A large fraction of the fresh water available for human use is stored in groundwater aquifers. Since human activities such as mining, agriculture, industry and urbanisation often result in incursion of various pollutants to groundwater, routine monitoring of water quality is an indispensable component of judicious aquifer management. Unfortunately, groundwater pollution monitoring is expensive and usually cannot cover an aquifer with the spatial resolution necessary for making adequate management decisions. Interpolation of monitoring data is thus an important tool for supplementing monitoring observations. However, interpolating routine groundwater pollution data poses a special problem due to the nature of the observations. The data from a producing aquifer usually includes many zero pollution concentration values from the clean parts of the aquifer but may span a wide range of values (up to a few orders of magnitude) in the polluted areas. This manuscript presents a methodology that can cope with such datasets and use them to produce maps that present the pollution plumes but also delineates the clean areas that are fit for production. A method for assessing the quality of mapping in a way which is suitable to the data's dynamic range of values is also presented. A local variant of inverse distance weighting is employed to interpolate the data. Inclusion zones around the interpolation points ensure that only relevant observations contribute to each interpolated concentration. Using inclusion zones improves the accuracy of the mapping but results in interpolation grid points which are not assigned a value. The inherent trade-off between the interpolation accuracy and coverage is demonstrated using both circular and elliptical inclusion zones. A leave-one-out cross testing is used to assess and compare the performance of the interpolations. The methodology is demonstrated using groundwater pollution monitoring data from the coastal aquifer along the Israeli
Yuval; Rimon, Y.; Graber, E. R.; Furman, A.
2013-07-01
A large fraction of the fresh water available for human use is stored in groundwater aquifers. Since human activities such as mining, agriculture, industry and urbanization often result in incursion of various pollutants to groundwater, routine monitoring of water quality is an indispensable component of judicious aquifer management. Unfortunately, groundwater pollution monitoring is expensive and usually cannot cover an aquifer with the spatial resolution necessary for making adequate management decisions. Interpolation of monitoring data between points is thus an important tool for supplementing measured data. However, interpolating routine groundwater pollution data poses a special problem due to the nature of the observations. The data from a producing aquifer usually includes many zero pollution concentration values from the clean parts of the aquifer but may span a wide range (up to a few orders of magnitude) of values in the polluted areas. This manuscript presents a methodology that can cope with such datasets and use them to produce maps that present the pollution plumes but also delineates the clean areas that are fit for production. A method for assessing the quality of mapping in a way which is suitable to the data's dynamic range of values is also presented. Local variant of inverse distance weighting is employed to interpolate the data. Inclusion zones around the interpolation points ensure that only relevant observations contribute to each interpolated concentration. Using inclusion zones improves the accuracy of the mapping but results in interpolation grid points which are not assigned a value. That inherent trade-off between the interpolation accuracy and coverage is demonstrated using both circular and elliptical inclusion zones. A leave-one-out cross testing is used to assess and compare the performance of the interpolations. The methodology is demonstrated using groundwater pollution monitoring data from the Coastal aquifer along the Israeli
Hoarau, Charlotte; Christophe, Sidonie
2017-05-01
Graphic interfaces of geoportals allow visualizing and overlaying various (visually) heterogeneous geographical data, often by image blending: vector data, maps, aerial imagery, Digital Terrain Model, etc. Map design and geo-visualization may benefit from methods and tools to hybrid, i.e. visually integrate, heterogeneous geographical data and cartographic representations. In this paper, we aim at designing continuous hybrid visualizations between ortho-imagery and symbolized vector data, in order to control a particular visual property, i.e. the photo-realism perception. The natural appearance (colors, textures) and various texture effects are used to drive the control the photo-realism level of the visualization: color and texture interpolation blocks have been developed. We present a global design method that allows to manipulate the behavior of those interpolation blocks on each type of geographical layer, in various ways, in order to provide various cartographic continua.
Interpolation for a subclass of H
Indian Academy of Sciences (India)
|g(zm)| ≤ c |zm − zm |, ∀m ∈ N. Thus it is natural to pose the following interpolation problem for H. ∞. : DEFINITION 4. We say that (zn) is an interpolating sequence in the weak sense for H. ∞ if given any sequence of complex numbers (λn) verifying. |λn| ≤ c ψ(zn,z. ∗ n) |zn − zn |, ∀n ∈ N,. (4) there exists a product fg ∈ H.
The high-level error bound for shifted surface spline interpolation
Luh, Lin-Tian
2006-01-01
Radial function interpolation of scattered data is a frequently used method for multivariate data fitting. One of the most frequently used radial functions is called shifted surface spline, introduced by Dyn, Levin and Rippa in \\cite{Dy1} for $R^{2}$. Then it's extended to $R^{n}$ for $n\\geq 1$. Many articles have studied its properties, as can be seen in \\cite{Bu,Du,Dy2,Po,Ri,Yo1,Yo2,Yo3,Yo4}. When dealing with this function, the most commonly used error bounds are the one raised by Wu and S...
Energy band structure of Cr by the Slater-Koster interpolation scheme
International Nuclear Information System (INIS)
Seifu, D.; Mikusik, P.
1986-04-01
The matrix elements of the Hamiltonian between nine localized wave-functions in tight-binding formalism are derived. The symmetry adapted wave-functions and the secular equations are formed by the group theory method for high symmetry points in the Brillouin zone. A set of interaction integrals is chosen on physical ground and fitted via the Slater-Koster interpolation scheme to the abinito band structure of chromium calculated by the Green function method. Then the energy band structure of chromium is interpolated and extrapolated in the Brillouin zone. (author)
Directory of Open Access Journals (Sweden)
J. K. Cuzzone
2018-05-01
Full Text Available Paleoclimate proxies are being used in conjunction with ice sheet modeling experiments to determine how the Greenland ice sheet responded to past changes, particularly during the last deglaciation. Although these comparisons have been a critical component in our understanding of the Greenland ice sheet sensitivity to past warming, they often rely on modeling experiments that favor minimizing computational expense over increased model physics. Over Paleoclimate timescales, simulating the thermal structure of the ice sheet has large implications on the modeled ice viscosity, which can feedback onto the basal sliding and ice flow. To accurately capture the thermal field, models often require a high number of vertical layers. This is not the case for the stress balance computation, however, where a high vertical resolution is not necessary. Consequently, since stress balance and thermal equations are generally performed on the same mesh, more time is spent on the stress balance computation than is otherwise necessary. For these reasons, running a higher-order ice sheet model (e.g., Blatter-Pattyn over timescales equivalent to the paleoclimate record has not been possible without incurring a large computational expense. To mitigate this issue, we propose a method that can be implemented within ice sheet models, whereby the vertical interpolation along the z axis relies on higher-order polynomials, rather than the traditional linear interpolation. This method is tested within the Ice Sheet System Model (ISSM using quadratic and cubic finite elements for the vertical interpolation on an idealized case and a realistic Greenland configuration. A transient experiment for the ice thickness evolution of a single-dome ice sheet demonstrates improved accuracy using the higher-order vertical interpolation compared to models using the linear vertical interpolation, despite having fewer degrees of freedom. This method is also shown to improve a model's ability
A study of discrete nonlinear systems
International Nuclear Information System (INIS)
Dhillon, H.S.
2001-04-01
An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)
Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers
Directory of Open Access Journals (Sweden)
E. George Walters III
2015-11-01
Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-(time) discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the
Cardinal Basis Piecewise Hermite Interpolation on Fuzzy Data
Directory of Open Access Journals (Sweden)
H. Vosoughi
2016-01-01
Full Text Available A numerical method along with explicit construction to interpolation of fuzzy data through the extension principle results by widely used fuzzy-valued piecewise Hermite polynomial in general case based on the cardinal basis functions, which satisfy a vanishing property on the successive intervals, has been introduced here. We have provided a numerical method in full detail using the linear space notions for calculating the presented method. In order to illustrate the method in computational examples, we take recourse to three prime cases: linear, cubic, and quintic.
Exact discretization of Schrödinger equation
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2016-01-08
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
Exact discretization of Schrödinger equation
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2016-01-01
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
On Multiple Interpolation Functions of the -Genocchi Polynomials
Directory of Open Access Journals (Sweden)
Jin Jeong-Hee
2010-01-01
Full Text Available Abstract Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.
Steady State Stokes Flow Interpolation for Fluid Control
DEFF Research Database (Denmark)
Bhatacharya, Haimasree; Nielsen, Michael Bang; Bridson, Robert
2012-01-01
— suffer from a common problem. They fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. We address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures......Fluid control methods often require surface velocities interpolated throughout the interior of a shape to use the velocity as a feedback force or as a boundary condition. Prior methods for interpolation in computer graphics — velocity extrapolation in the normal direction and potential flow...
Quadratic Interpolation and Linear Lifting Design
Directory of Open Access Journals (Sweden)
Joel Solé
2007-03-01
Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.
Directory of Open Access Journals (Sweden)
Zhao-Qing Wang
2014-01-01
Full Text Available Embedding the irregular doubly connected domain into an annular regular region, the unknown functions can be approximated by the barycentric Lagrange interpolation in the regular region. A highly accurate regular domain collocation method is proposed for solving potential problems on the irregular doubly connected domain in polar coordinate system. The formulations of regular domain collocation method are constructed by using barycentric Lagrange interpolation collocation method on the regular domain in polar coordinate system. The boundary conditions are discretized by barycentric Lagrange interpolation within the regular domain. An additional method is used to impose the boundary conditions. The least square method can be used to solve the overconstrained equations. The function values of points in the irregular doubly connected domain can be calculated by barycentric Lagrange interpolation within the regular domain. Some numerical examples demonstrate the effectiveness and accuracy of the presented method.
Data-adapted moving least squares method for 3-D image interpolation
International Nuclear Information System (INIS)
Jang, Sumi; Lee, Yeon Ju; Jeong, Byeongseon; Nam, Haewon; Lee, Rena; Yoon, Jungho
2013-01-01
In this paper, we present a nonlinear three-dimensional interpolation scheme for gray-level medical images. The scheme is based on the moving least squares method but introduces a fundamental modification. For a given evaluation point, the proposed method finds the local best approximation by reproducing polynomials of a certain degree. In particular, in order to obtain a better match to the local structures of the given image, we employ locally data-adapted least squares methods that can improve the classical one. Some numerical experiments are presented to demonstrate the performance of the proposed method. Five types of data sets are used: MR brain, MR foot, MR abdomen, CT head, and CT foot. From each of the five types, we choose five volumes. The scheme is compared with some well-known linear methods and other recently developed nonlinear methods. For quantitative comparison, we follow the paradigm proposed by Grevera and Udupa (1998). (Each slice is first assumed to be unknown then interpolated by each method. The performance of each interpolation method is assessed statistically.) The PSNR results for the estimated volumes are also provided. We observe that the new method generates better results in both quantitative and visual quality comparisons. (paper)
High-order hydrodynamic algorithms for exascale computing
Energy Technology Data Exchange (ETDEWEB)
Morgan, Nathaniel Ray [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-02-05
Hydrodynamic algorithms are at the core of many laboratory missions ranging from simulating ICF implosions to climate modeling. The hydrodynamic algorithms commonly employed at the laboratory and in industry (1) typically lack requisite accuracy for complex multi- material vortical flows and (2) are not well suited for exascale computing due to poor data locality and poor FLOP/memory ratios. Exascale computing requires advances in both computer science and numerical algorithms. We propose to research the second requirement and create a new high-order hydrodynamic algorithm that has superior accuracy, excellent data locality, and excellent FLOP/memory ratios. This proposal will impact a broad range of research areas including numerical theory, discrete mathematics, vorticity evolution, gas dynamics, interface instability evolution, turbulent flows, fluid dynamics and shock driven flows. If successful, the proposed research has the potential to radically transform simulation capabilities and help position the laboratory for computing at the exascale.
International Nuclear Information System (INIS)
Thompson, K.; Martinez, T.J.
1999-01-01
We present a new approach to first-principles molecular dynamics that combines a general and flexible interpolation method with ab initio evaluation of the potential energy surface. This hybrid approach extends significantly the domain of applicability of ab initio molecular dynamics. Use of interpolation significantly reduces the computational effort associated with the dynamics over most of the time scale of interest, while regions where potential energy surfaces are difficult to interpolate, for example near conical intersections, are treated by direct solution of the electronic Schroedinger equation during the dynamics. We demonstrate the concept through application to the nonadiabatic dynamics of collisional electronic quenching of Li(2p). Full configuration interaction is used to describe the wave functions of the ground and excited electronic states. The hybrid approach agrees well with full ab initio multiple spawning dynamics, while being more than an order of magnitude faster. copyright 1999 American Institute of Physics
Foundations of a discrete physics
International Nuclear Information System (INIS)
McGoveran, D.; Noyes, P.
1988-01-01
Starting from the principles of finiteness, discreteness, finite computability and absolute nonuniqueness, we develop the ordering operator calculus, a strictly constructive mathematical system having the empirical properties required by quantum mechanical and special relativistic phenomena. We show how to construct discrete distance functions, and both rectangular and spherical coordinate systems(with a discrete version of ''π''). The richest discrete space constructible without a preferred axis and preserving translational and rotational invariance is shown to be a discrete 3-space with the usual symmetries. We introduce a local ordering parameter with local (proper) time-like properties and universal ordering parameters with global (cosmological) time-like properties. Constructed ''attribute velocities'' connect ensembles with attributes that are invariant as the appropriate time-like parameter increases. For each such attribute, we show how to construct attribute velocities which must satisfy the '' relativistic Doppler shift'' and the ''relativistic velocity composition law,'' as well as the Lorentz transformations. By construction, these velocities have finite maximum and minimum values. In the space of all attributes, the minimum of these maximum velocities will predominate in all multiple attribute computations, and hence can be identified as a fundamental limiting velocity, General commutation relations are constructed which under the physical interpretation are shown to reduce to the usual quantum mechanical commutation relations. 50 refs., 18 figs
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Trace interpolation by slant-stack migration
International Nuclear Information System (INIS)
Novotny, M.
1990-01-01
The slant-stack migration formula based on the radon transform is studied with respect to the depth steep Δz of wavefield extrapolation. It can be viewed as a generalized trace-interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz > 0 the formula yields the familiar plane-wave decomposition, while for Δz > 0 it provides a robust tool for migration transformation of spatially under sampled wavefields. Using the stationary phase method, it is shown that the slant-stack migration formula degenerates into the Rayleigh-Sommerfeld integral in the far-field approximation. Consequently, even a narrow slant-stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period
Optimized Quasi-Interpolators for Image Reconstruction.
Sacht, Leonardo; Nehab, Diego
2015-12-01
We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use. We go against standard practice and optimize for approximation quality over the entire Nyquist range, rather than focusing exclusively on the asymptotic behavior as the sample spacing goes to zero. In contrast to previous work, we jointly optimize with respect to all degrees of freedom available in both the kernel and the digital filter. We consider linear, quadratic, and cubic schemes, offering different tradeoffs between quality and computational cost. Experiments with compounded rotations and translations over a range of input images confirm that, due to the additional degrees of freedom and the more realistic objective function, our new quasi-interpolators perform better than the state of the art, at a similar computational cost.
Algebraic perturbation theory for dense liquids with discrete potentials
Adib, Artur B.
2007-06-01
A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.
Relaxation approximations to second-order traffic flow models by high-resolution schemes
International Nuclear Information System (INIS)
Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.
2015-01-01
A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers
Discrete gravity as a local theory of the Poincare group in the first-order formalism
Energy Technology Data Exchange (ETDEWEB)
Gionti, Gabriele [Vatican Observatory Research Group, Steward Observatory, 933 North Cherry Avenue, University of Arizona, Tucson, AZ 85721 (United States); Specola Vaticana, V-00120 Citta Del Vaticano (Vatican City State, Holy See,)
2005-10-21
A discrete theory of gravity, locally invariant under the Poincare group, is considered as in a companion paper. We define a first-order theory, in the sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex. We follow the same spirit as the continuum theory of general relativity in the Cartan formalism. The field equations are carefully derived taking in account the constraints of the theory. They look very similar to first-order Einstein continuum equations in the Cartan formalism. It is shown that in the limit of small deficit angles these equations have Regge calculus, locally, as the only solution. A quantum measure is easily defined which does not suffer the ambiguities of Regge calculus, and a coupling with fermionic matter is easily introduced.
Discrete gravity as a local theory of the Poincare group in the first-order formalism
International Nuclear Information System (INIS)
Gionti, Gabriele
2005-01-01
A discrete theory of gravity, locally invariant under the Poincare group, is considered as in a companion paper. We define a first-order theory, in the sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex. We follow the same spirit as the continuum theory of general relativity in the Cartan formalism. The field equations are carefully derived taking in account the constraints of the theory. They look very similar to first-order Einstein continuum equations in the Cartan formalism. It is shown that in the limit of small deficit angles these equations have Regge calculus, locally, as the only solution. A quantum measure is easily defined which does not suffer the ambiguities of Regge calculus, and a coupling with fermionic matter is easily introduced
Interpolating Spline Curve-Based Perceptual Encryption for 3D Printing Models
Directory of Open Access Journals (Sweden)
Giao N. Pham
2018-02-01
Full Text Available With the development of 3D printing technology, 3D printing has recently been applied to many areas of life including healthcare and the automotive industry. Due to the benefit of 3D printing, 3D printing models are often attacked by hackers and distributed without agreement from the original providers. Furthermore, certain special models and anti-weapon models in 3D printing must be protected against unauthorized users. Therefore, in order to prevent attacks and illegal copying and to ensure that all access is authorized, 3D printing models should be encrypted before being transmitted and stored. A novel perceptual encryption algorithm for 3D printing models for secure storage and transmission is presented in this paper. A facet of 3D printing model is extracted to interpolate a spline curve of degree 2 in three-dimensional space that is determined by three control points, the curvature coefficients of degree 2, and an interpolating vector. Three control points, the curvature coefficients, and interpolating vector of the spline curve of degree 2 are encrypted by a secret key. The encrypted features of the spline curve are then used to obtain the encrypted 3D printing model by inverse interpolation and geometric distortion. The results of experiments and evaluations prove that the entire 3D triangle model is altered and deformed after the perceptual encryption process. The proposed algorithm is responsive to the various formats of 3D printing models. The results of the perceptual encryption process is superior to those of previous methods. The proposed algorithm also provides a better method and more security than previous methods.
Interpolation algorithm for asynchronous ADC-data
Directory of Open Access Journals (Sweden)
S. Bramburger
2017-09-01
Full Text Available This paper presents a modified interpolation algorithm for signals with variable data rate from asynchronous ADCs. The Adaptive weights Conjugate gradient Toeplitz matrix (ACT algorithm is extended to operate with a continuous data stream. An additional preprocessing of data with constant and linear sections and a weighted overlap of step-by-step into spectral domain transformed signals improve the reconstruction of the asycnhronous ADC signal. The interpolation method can be used if asynchronous ADC data is fed into synchronous digital signal processing.
Extension Of Lagrange Interpolation
Directory of Open Access Journals (Sweden)
Mousa Makey Krady
2015-01-01
Full Text Available Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
Interpolation and sampling in spaces of analytic functions
Seip, Kristian
2004-01-01
The book is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for H^\\infty, and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem. The book aims at clarifying how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the Helson-Szegő condition. The book is based on six lectures given by the author at the University of Michigan. This is reflected in the exposition, which is a blend of informal explanations with technical details. The book is essentially self-contained. There is an underlying assumption that the reader has a basic knowledge of complex and functional analysis. Beyond that, the reader should have some familiari...
Study on Scattered Data Points Interpolation Method Based on Multi-line Structured Light
International Nuclear Information System (INIS)
Fan, J Y; Wang, F G; W, Y; Zhang, Y L
2006-01-01
Aiming at the range image obtained through multi-line structured light, a regional interpolation method is put forward in this paper. This method divides interpolation into two parts according to the memory format of the scattered data, one is interpolation of the data on the stripes, and the other is interpolation of data between the stripes. Trend interpolation method is applied to the data on the stripes, and Gauss wavelet interpolation method is applied to the data between the stripes. Experiments prove regional interpolation method feasible and practical, and it also promotes the speed and precision
Effect of interpolation on parameters extracted from seating interface pressure arrays
Michael Wininger, PhD; Barbara Crane, PhD, PT
2015-01-01
Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pre...
High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves
DEFF Research Database (Denmark)
Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter
2012-01-01
is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied...
Higher-order schemes for the Laplace transformation method for parabolic problems
Douglas, C.
2011-01-01
In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.
Spectral interpolation - Zero fill or convolution. [image processing
Forman, M. L.
1977-01-01
Zero fill, or augmentation by zeros, is a method used in conjunction with fast Fourier transforms to obtain spectral spacing at intervals closer than obtainable from the original input data set. In the present paper, an interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies. The technique is shown to operate faster than zero fill, since fewer operations are required. The major advantages of interpolation by repetitive convolution are that efficient use of memory is possible (thus avoiding the difficulties encountered in decimation in time FFTs) and that is is easy to implement.
A parameterization of observer-based controllers: Bumpless transfer by covariance interpolation
DEFF Research Database (Denmark)
Stoustrup, Jakob; Komareji, Mohammad
2009-01-01
This paper presents an algorithm to interpolate between two observer-based controllers for a linear multivariable system such that the closed loop system remains stable throughout the interpolation. The method interpolates between the inverse Lyapunov functions for the two original state feedback...
Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion
International Nuclear Information System (INIS)
Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun
2016-01-01
Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.
Impact test data obtained by analysis of high speed camera films
International Nuclear Information System (INIS)
Aquaro, D.; Forasassi, G.
1990-01-01
This paper deals with a high speed film elaboration procedure concerning 9m International Atomic Energy Agency free drop tests of a spent nuclear fuel cask. Drop tests of reduced-scale cask models, performed at the Dipartimento di Construzioni Meccaniche e Nucleari of Pisa, are described. The high speed films recorded during the impact test enabled the authors to obtain the motion law of the cask models. A numerical method implemented in order to perform the first and second differentiation of the displacement-time recorded data is shown. The experimental displacement-time discrete data are approximated with a Langrange interpolation polynomial, and the obtained curve is smoothed with a Butterworth digital low pass filter with M poles, in order to reduce the spurious oscillations caused by different kinds of errors which might be unacceptably amplified in the differentiation processes. Good agreement is obtained between the accelerations derived by the film data analysis and the experimentally-measured ones. The reported technique may be a valuable tool for the analysis of transient dynamic phenomena. (author)
Nonexistence and existence of solutions for a fourth-order discrete ...
Indian Academy of Sciences (India)
3Modern Business and Management Department, Guangdong Construction Vocational. Technology, Guangzhou ... 4Packaging Engineering Institute, Jinan University, Zhuhai 519070, China ... years since they provided a natural description of several discrete models. .... The motivation for the present work stems from the.
Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks
Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.
2013-12-01
Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus
High-Order Wave Propagation Algorithms for Hyperbolic Systems
Ketcheson, David I.
2013-01-22
We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge--Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.
New families of interpolating type IIB backgrounds
Minasian, Ruben; Petrini, Michela; Zaffaroni, Alberto
2010-04-01
We construct new families of interpolating two-parameter solutions of type IIB supergravity. These correspond to D3-D5 systems on non-compact six-dimensional manifolds which are mathbb{T}2 fibrations over Eguchi-Hanson and multi-center Taub-NUT spaces, respectively. One end of the interpolation corresponds to a solution with only D5 branes and vanishing NS three-form flux. A topology changing transition occurs at the other end, where the internal space becomes a direct product of the four-dimensional surface and the two-torus and the complexified NS-RR three-form flux becomes imaginary self-dual. Depending on the choice of the connections on the torus fibre, the interpolating family has either mathcal{N}=2 or mathcal{N}=1 supersymmetry. In the mathcal{N}=2 case it can be shown that the solutions are regular.
Quadratic polynomial interpolation on triangular domain
Li, Ying; Zhang, Congcong; Yu, Qian
2018-04-01
In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.
International Nuclear Information System (INIS)
Li Liyong; Tchelepi, Hamdi A.; Zhang Dongxiao
2003-01-01
We present detailed comparisons between high-resolution Monte Carlo simulation (MCS) and low-order numerical solutions of stochastic moment equations (SMEs) for the first and second statistical moments of pressure. The objective is to quantify the difference between the predictions obtained from MCS and SME. Natural formations with high permeability variability and large spatial correlation scales are of special interest for underground resources (e.g. oil and water). Consequently, we focus on such formations. We investigated fields with variance of log-permeability, σ Y 2 , from 0.1 to 3.0 and correlation scales (normalized by domain length) of 0.05 to 0.5. In order to avoid issues related to statistical convergence and resolution level, we used 9000 highly resolved realizations of permeability for MCS. We derive exact discrete forms of the statistical moment equations. Formulations based on equations written explicitly in terms of permeability (K-based) and log-transformed permeability (Y-based) are considered. The discrete forms are applicable to systems of arbitrary variance and correlation scales. However, equations governing a particular statistical moment depend on higher moments. Thus, while the moment equations are exact, they are not closed. In particular, the discrete form of the second moment of pressure includes two triplet terms that involve log-permeability (or permeability) and pressure. We combined MCS computations with full discrete SME equations to quantify the importance of the various terms that make up the moment equations. We show that second-moment solutions obtained using a low-order Y-based SME formulation are significantly better than those from K-based formulations, especially when σ Y 2 >1. As a result, Y-based formulations are preferred. The two triplet terms are complex functions of the variance level and correlation length. The importance (contribution) of these triplet terms increases dramatically as σ Y 2 increases above one. We
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
Discrete formulation for two-dimensional multigroup neutron diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid
2003-02-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.
Discrete formulation for two-dimensional multigroup neutron diffusion equations
International Nuclear Information System (INIS)
Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid
2003-01-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method
Global sensitivity analysis using sparse grid interpolation and polynomial chaos
International Nuclear Information System (INIS)
Buzzard, Gregery T.
2012-01-01
Sparse grid interpolation is widely used to provide good approximations to smooth functions in high dimensions based on relatively few function evaluations. By using an efficient conversion from the interpolating polynomial provided by evaluations on a sparse grid to a representation in terms of orthogonal polynomials (gPC representation), we show how to use these relatively few function evaluations to estimate several types of sensitivity coefficients and to provide estimates on local minima and maxima. First, we provide a good estimate of the variance-based sensitivity coefficients of Sobol' (1990) [1] and then use the gradient of the gPC representation to give good approximations to the derivative-based sensitivity coefficients described by Kucherenko and Sobol' (2009) [2]. Finally, we use the package HOM4PS-2.0 given in Lee et al. (2008) [3] to determine the critical points of the interpolating polynomial and use these to determine the local minima and maxima of this polynomial. - Highlights: ► Efficient estimation of variance-based sensitivity coefficients. ► Efficient estimation of derivative-based sensitivity coefficients. ► Use of homotopy methods for approximation of local maxima and minima.
High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function
International Nuclear Information System (INIS)
Zhao Hongxia; Ma Shanjun
2008-01-01
In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.
International Nuclear Information System (INIS)
Boukir, K.
1994-06-01
This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs
Image re-sampling detection through a novel interpolation kernel.
Hilal, Alaa
2018-06-01
Image re-sampling involved in re-size and rotation transformations is an essential element block in a typical digital image alteration. Fortunately, traces left from such processes are detectable, proving that the image has gone a re-sampling transformation. Within this context, we present in this paper two original contributions. First, we propose a new re-sampling interpolation kernel. It depends on five independent parameters that controls its amplitude, angular frequency, standard deviation, and duration. Then, we demonstrate its capacity to imitate the same behavior of the most frequent interpolation kernels used in digital image re-sampling applications. Secondly, the proposed model is used to characterize and detect the correlation coefficients involved in re-sampling transformations. The involved process includes a minimization of an error function using the gradient method. The proposed method is assessed over a large database of 11,000 re-sampled images. Additionally, it is implemented within an algorithm in order to assess images that had undergone complex transformations. Obtained results demonstrate better performance and reduced processing time when compared to a reference method validating the suitability of the proposed approaches. Copyright © 2018 Elsevier B.V. All rights reserved.
Interpolation methods for creating a scatter radiation exposure map
International Nuclear Information System (INIS)
Gonçalves, Elicardo A. de S.; Gomes, Celio S.; Lopes, Ricardo T.; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F.
2017-01-01
A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)
Interpolation methods for creating a scatter radiation exposure map
Energy Technology Data Exchange (ETDEWEB)
Gonçalves, Elicardo A. de S., E-mail: elicardo.goncalves@ifrj.edu.br [Instituto Federal do Rio de Janeiro (IFRJ), Paracambi, RJ (Brazil); Gomes, Celio S.; Lopes, Ricardo T. [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F. [Universidade do Estado do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto de Física
2017-07-01
A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)
Out-of-order parallel discrete event simulation for electronic system-level design
Chen, Weiwei
2014-01-01
This book offers readers a set of new approaches and tools a set of tools and techniques for facing challenges in parallelization with design of embedded systems.? It provides an advanced parallel simulation infrastructure for efficient and effective system-level model validation and development so as to build better products in less time.? Since parallel discrete event simulation (PDES) has the potential to exploit the underlying parallel computational capability in today's multi-core simulation hosts, the author begins by reviewing the parallelization of discrete event simulation, identifyin
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
DEFF Research Database (Denmark)
Fyhn, Karsten; Duarte, Marco F.; Jensen, Søren Holdt
2015-01-01
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non...... to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super...... interpolation increases the estimation precision....
Wideband DOA Estimation through Projection Matrix Interpolation
Selva, J.
2017-01-01
This paper presents a method to reduce the complexity of the deterministic maximum likelihood (DML) estimator in the wideband direction-of-arrival (WDOA) problem, which is based on interpolating the array projection matrix in the temporal frequency variable. It is shown that an accurate interpolator like Chebyshev's is able to produce DML cost functions comprising just a few narrowband-like summands. Actually, the number of such summands is far smaller (roughly by factor ten in the numerical ...
Directory of Open Access Journals (Sweden)
Mauricio Castro Franco
2017-07-01
Full Text Available Context: Interpolating soil properties at field-scale in the Colombian piedmont eastern plains is challenging due to: the highly and complex variable nature of some processes; the effects of the soil; the land use; and the management. While interpolation techniques are being adapted to include auxiliary information of these effects, the soil data are often difficult to predict using conventional techniques of spatial interpolation. Method: In this paper, we evaluated and compared six spatial interpolation techniques: Inverse Distance Weighting (IDW, Spline, Ordinary Kriging (KO, Universal Kriging (UK, Cokriging (Ckg, and Residual Maximum Likelihood-Empirical Best Linear Unbiased Predictor (REML-EBLUP, from conditioned Latin Hypercube as a sampling strategy. The ancillary information used in Ckg and REML-EBLUP was indexes calculated from a digital elevation model (MDE. The “Random forest” algorithm was used for selecting the most important terrain index for each soil properties. Error metrics were used to validate interpolations against cross validation. Results: The results support the underlying assumption that HCLc captured adequately the full distribution of variables of ancillary information in the Colombian piedmont eastern plains conditions. They also suggest that Ckg and REML-EBLUP perform best in the prediction in most of the evaluated soil properties. Conclusions: Mixed interpolation techniques having auxiliary soil information and terrain indexes, provided a significant improvement in the prediction of soil properties, in comparison with other techniques.
Discrete Mathematics and Its Applications
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
[Multimodal medical image registration using cubic spline interpolation method].
He, Yuanlie; Tian, Lianfang; Chen, Ping; Wang, Lifei; Ye, Guangchun; Mao, Zongyuan
2007-12-01
Based on the characteristic of the PET-CT multimodal image series, a novel image registration and fusion method is proposed, in which the cubic spline interpolation method is applied to realize the interpolation of PET-CT image series, then registration is carried out by using mutual information algorithm and finally the improved principal component analysis method is used for the fusion of PET-CT multimodal images to enhance the visual effect of PET image, thus satisfied registration and fusion results are obtained. The cubic spline interpolation method is used for reconstruction to restore the missed information between image slices, which can compensate for the shortage of previous registration methods, improve the accuracy of the registration, and make the fused multimodal images more similar to the real image. Finally, the cubic spline interpolation method has been successfully applied in developing 3D-CRT (3D Conformal Radiation Therapy) system.
Velasquez, N.; Ochoa, A.; Castillo, S.; Hoyos Ortiz, C. D.
2017-12-01
The skill of river discharge simulation using hydrological models strongly depends on the quality and spatio-temporal representativeness of precipitation during storm events. All precipitation measurement strategies have their own strengths and weaknesses that translate into discharge simulation uncertainties. Distributed hydrological models are based on evolving rainfall fields in the same time scale as the hydrological simulation. In general, rainfall measurements from a dense and well maintained rain gauge network provide a very good estimation of the total volume for each rainfall event, however, the spatial structure relies on interpolation strategies introducing considerable uncertainty in the simulation process. On the other hand, rainfall retrievals from radar reflectivity achieve a better spatial structure representation but with higher uncertainty in the surface precipitation intensity and volume depending on the vertical rainfall characteristics and radar scan strategy. To assess the impact of both rainfall measurement methodologies on hydrological simulations, and in particular the effects of the rainfall spatio-temporal variability, a numerical modeling experiment is proposed including the use of a novel QPE (Quantitative Precipitation Estimation) method based on disdrometer data in order to estimate surface rainfall from radar reflectivity. The experiment is based on the simulation of 84 storms, the hydrological simulations are carried out using radar QPE and two different interpolation methods (IDW and TIN), and the assessment of simulated peak flow. Results show significant rainfall differences between radar QPE and the interpolated fields, evidencing a poor representation of storms in the interpolated fields, which tend to miss the precise location of the intense precipitation cores, and to artificially generate rainfall in some areas of the catchment. Regarding streamflow modelling, the potential improvement achieved by using radar QPE depends on
Garcia, Matthew; Peters-Lidard, Christa D.; Goodrich, David C.
2008-05-01
Inaccuracy in spatially distributed precipitation fields can contribute significantly to the uncertainty of hydrological states and fluxes estimated from land surface models. This paper examines the results of selected interpolation methods for both convective and mixed/stratiform events that occurred during the North American monsoon season over a dense gauge network at the U.S. Department of Agriculture Agricultural Research Service Walnut Gulch Experimental Watershed in the southwestern United States. The spatial coefficient of variation for the precipitation field is employed as an indicator of event morphology, and a gauge clustering factor CF is formulated as a new, scale-independent measure of network organization. We consider that CF 0 (clustering in the gauge network) will produce errors because of reduced areal representation of the precipitation field. Spatial interpolation is performed using both inverse-distance-weighted (IDW) and multiquadric-biharmonic (MQB) methods. We employ ensembles of randomly selected network subsets for the statistical evaluation of interpolation errors in comparison with the observed precipitation. The magnitude of interpolation errors and differences in accuracy between interpolation methods depend on both the density and the geometrical organization of the gauge network. Generally, MQB methods outperform IDW methods in terms of interpolation accuracy under all conditions, but it is found that the order of the IDW method is important to the results and may, under some conditions, be just as accurate as the MQB method. In almost all results it is demonstrated that the inverse-distance-squared method for spatial interpolation, commonly employed in operational analyses and for engineering assessments, is inferior to the ID-cubed method, which is also more computationally efficient than the MQB method in studies of large networks.
Design of a Control System for a Maglev Planar Motor Based on Two-Dimension Linear Interpolation
Directory of Open Access Journals (Sweden)
Feng Xing
2017-08-01
Full Text Available In order to realize the high speed and high-precision control of a maglev planar motor, a high-precision electromagnetic model is needed in the first place, which can also contribute to meeting the real-time running requirements. Traditionally, the electromagnetic model is based on analytical calculations. However, this neglects the model simplification and the manufacturing errors, which may bring certain errors to the model. Aiming to handle this inaccuracy, this paper proposes a novel design method for a maglev planar motor control system based on two-dimensional linear interpolation. First, the magnetic field is divided into several regions according to the symmetry of the Halbach magnetic array, and the uniform grid method is adopted to partition one of these regions. Second, targeting this region, it is possible to sample the electromagnetic forces and torques on each node of the grid and obtain the complete electromagnetic model in this region through the two-dimensional linear interpolation method. Third, the whole electromagnetic model of the maglev planar motor can be derived according to the symmetry of the magnetic field. Finally, the decoupling method and controller are designed according to this electromagnetic model, and thereafter, the control model can be established. The designed control system is demonstrated through simulations and experiments to feature better accuracy and meet the requirements of real-time control.
Cheng, Jian; Zhang, Fan; Liu, Tiegang
2018-06-01
In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.
Image Retrieval Algorithm Based on Discrete Fractional Transforms
Jindal, Neeru; Singh, Kulbir
2013-06-01
The discrete fractional transforms is a signal processing tool which suggests computational algorithms and solutions to various sophisticated applications. In this paper, a new technique to retrieve the encrypted and scrambled image based on discrete fractional transforms has been proposed. Two-dimensional image was encrypted using discrete fractional transforms with three fractional orders and two random phase masks placed in the two intermediate planes. The significant feature of discrete fractional transforms benefits from its extra degree of freedom that is provided by its fractional orders. Security strength was enhanced (1024!)4 times by scrambling the encrypted image. In decryption process, image retrieval is sensitive for both correct fractional order keys and scrambling algorithm. The proposed approach make the brute force attack infeasible. Mean square error and relative error are the recital parameters to verify validity of proposed method.
Energy Technology Data Exchange (ETDEWEB)
Sun, Yuzhou, E-mail: yuzhousun@126.com; Chen, Gensheng; Li, Dongxia [School of Civil Engineering and Architecture, Zhongyuan University of Technology, Zhengzhou (China)
2016-06-08
This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe the special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.
Kim, Wonhee; Chen, Xu; Lee, Youngwoo; Chung, Chung Choo; Tomizuka, Masayoshi
2018-05-01
A discrete-time backstepping control algorithm is proposed for reference tracking of systems affected by both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. A discrete time DOB, which is constructed based on infinite impulse response filters is applied to compensate for narrow band disturbances at high frequencies. A discrete-time nonlinear damping backstepping controller with an augmented observer is proposed to track the desired output and to compensate for low frequency broadband disturbances along with a disturbance observer, for rejecting narrow band high frequency disturbances. This combination has the merit of simultaneously compensating both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. The performance of the proposed method is validated via experiments.
Discrete PID Tuning Using Artificial Intelligence Techniques
Directory of Open Access Journals (Sweden)
Petr DOLEŽEL
2009-06-01
Full Text Available PID controllers are widely used in industry these days due to their useful properties such as simple tuning or robustness. While they are applicable to many control problems, they can perform poorly in some applications. Highly nonlinear system control with constrained manipulated variable can be mentioned as an example. The point of the paper is to string together convenient qualities of conventional PID control and progressive techniques based on Artificial Intelligence. Proposed control method should deal with even highly nonlinear systems. To be more specific, there is described new method of discrete PID controller tuning in this paper. This method tunes discrete PID controller parameters online through the use of genetic algorithm and neural model of controlled system in order to control successfully even highly nonlinear systems. After method description and some discussion, there is performed control simulation and comparison to one chosen conventional control method.
Interpolation in Spaces of Functions
Directory of Open Access Journals (Sweden)
K. Mosaleheh
2006-03-01
Full Text Available In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces
Conformal Interpolating Algorithm Based on Cubic NURBS in Aspheric Ultra-Precision Machining
International Nuclear Information System (INIS)
Li, C G; Zhang, Q R; Cao, C G; Zhao, S L
2006-01-01
Numeric control machining and on-line compensation for aspheric surface are key techniques in ultra-precision machining. In this paper, conformal cubic NURBS interpolating curve is applied to fit the character curve of aspheric surface. Its algorithm and process are also proposed and imitated by Matlab7.0 software. To evaluate the performance of the conformal cubic NURBS interpolation, we compare it with the linear interpolations. The result verifies this method can ensure smoothness of interpolating spline curve and preserve original shape characters. The surface quality interpolated by cubic NURBS is higher than by line. The algorithm is benefit to increasing the surface form precision of workpieces in ultra-precision machining
Lorenzi, Juan M.; Stecher, Thomas; Reuter, Karsten; Matera, Sebastian
2017-10-01
Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.
An improved local radial point interpolation method for transient heat conduction analysis
Wang, Feng; Lin, Gao; Zheng, Bao-Jing; Hu, Zhi-Qiang
2013-06-01
The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions.
An improved local radial point interpolation method for transient heat conduction analysis
International Nuclear Information System (INIS)
Wang Feng; Lin Gao; Hu Zhi-Qiang; Zheng Bao-Jing
2013-01-01
The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions
Perfect discretization of path integrals
International Nuclear Information System (INIS)
Steinhaus, Sebastian
2012-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Perfect discretization of path integrals
Steinhaus, Sebastian
2012-05-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Chen, Wei-Hsin; Hsu, Hung-Jen; Kumar, Gopalakrishnan; Budzianowski, Wojciech M; Ong, Hwai Chyuan
2017-12-01
This study focuses on the biochar formation and torrefaction performance of sugarcane bagasse, and they are predicted using the bilinear interpolation (BLI), inverse distance weighting (IDW) interpolation, and regression analysis. It is found that the biomass torrefied at 275°C for 60min or at 300°C for 30min or longer is appropriate to produce biochar as alternative fuel to coal with low carbon footprint, but the energy yield from the torrefaction at 300°C is too low. From the biochar yield, enhancement factor of HHV, and energy yield, the results suggest that the three methods are all feasible for predicting the performance, especially for the enhancement factor. The power parameter of unity in the IDW method provides the best predictions and the error is below 5%. The second order in regression analysis gives a more reasonable approach than the first order, and is recommended for the predictions. Copyright © 2017 Elsevier Ltd. All rights reserved.
Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains
Adler, V. E.
2018-04-01
We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.
Abstract interpolation in vector-valued de Branges-Rovnyak spaces
Ball, J.A.; Bolotnikov, V.; ter Horst, S.
2011-01-01
Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83–96, Naukova Dumka, Kiev, 1987) for Schur class functions, we study a general metric constrained interpolation problem for functions from a
Data interpolation for vibration diagnostics using two-variable correlations
International Nuclear Information System (INIS)
Branagan, L.
1991-01-01
This paper reports that effective machinery vibration diagnostics require a clear differentiation between normal vibration changes caused by plant process conditions and those caused by degradation. The normal relationship between vibration and a process parameter can be quantified by developing the appropriate correlation. The differences in data acquisition requirements between dynamic signals (vibration spectra) and static signals (pressure, temperature, etc.) result in asynchronous data acquisition; the development of any correlation must then be based on some form of interpolated data. This interpolation can reproduce or distort the original measured quantity depending on the characteristics of the data and the interpolation technique. Relevant data characteristics, such as acquisition times, collection cycle times, compression method, storage rate, and the slew rate of the measured variable, are dependent both on the data handling and on the measured variable. Linear and staircase interpolation, along with the use of clustering and filtering, provide the necessary options to develop accurate correlations. The examples illustrate the appropriate application of these options
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien
2016-09-01
The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.
Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.
Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G
2016-06-01
This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.
High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media.
Zhao, Shan
2011-08-15
This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media. © 2011 Optical Society of America
Peculiar symmetry structure of some known discrete nonautonomous equations
International Nuclear Information System (INIS)
Garifullin, R N; Habibullin, I T; Yamilov, R I
2015-01-01
We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely discrete equations defined on the square lattice. The first one is a discrete analogue of the dressing chain introduced by Levi and Yamilov. The second one is a nonautonomous generalization of the potential discrete KdV equation or, in other words, the H1 equation of the well-known Adler−Bobenko−Suris list. We demonstrate that these equations have generalized symmetries in both directions if and only if their coefficients, depending on the discrete variables, are periodic. The order of the simplest generalized symmetry in at least one direction depends on the period and may be arbitrarily high. We substantiate this picture by some theorems in the case of small periods. In case of an arbitrarily large period, we show that it is possible to construct two hierarchies of generalized symmetries and conservation laws. The same picture should take place in case of any nonautonomous equation of the Adler−Bobenko−Suris list. (paper)
Performance Analysis of High-Order Numerical Methods for Time-Dependent Acoustic Field Modeling
Moy, Pedro Henrique Rocha
2012-07-01
The discretization of time-dependent wave propagation is plagued with dispersion in which the wavefield is perceived to travel with an erroneous velocity. To remediate the problem, simulations are run on dense and computationally expensive grids yielding plausible approximate solutions. This work introduces an error analysis tool which can be used to obtain optimal simulation parameters that account for mesh size, orders of spatial and temporal discretizations, angles of propagation, temporal stability conditions (usually referred to as CFL conditions), and time of propagation. The classical criteria of 10-15 nodes per wavelength for second-order finite differences, and 4-5 nodes per wavelength for fourth-order spectral elements are shown to be unrealistic and overly-optimistic simulation parameters for different propagation times. This work analyzes finite differences, spectral elements, optimally-blended spectral elements, and isogeometric analysis.
Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo
2017-12-01
A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.
On the Linear Stability of the Fifth-Order WENO Discretization
Motamed, Mohammad; Macdonald, Colin B.; Ruuth, Steven J.
2010-01-01
, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC
Interpolation from Grid Lines: Linear, Transfinite and Weighted Method
DEFF Research Database (Denmark)
Lindberg, Anne-Sofie Wessel; Jørgensen, Thomas Martini; Dahl, Vedrana Andersen
2017-01-01
When two sets of line scans are acquired orthogonal to each other, intensity values are known along the lines of a grid. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid l...
DEFF Research Database (Denmark)
Amini Afshar, Mostafa; Bingham, Harry B.
2017-01-01
. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...
Workload Balancing on Heterogeneous Systems: A Case Study of Sparse Grid Interpolation
Muraraşu, Alin
2012-01-01
Multi-core parallelism and accelerators are becoming common features of today’s computer systems, as they allow for computational power without sacrificing energy efficiency. Due to heterogeneity, tuning for each type of compute unit and adequate load balancing is essential. This paper proposes static and dynamic solutions for load balancing in the context of an application for visualizing high-dimensional simulation data. The application relies on the sparse grid technique for data compression. Its performance critical part is the interpolation routine used for decompression. Results show that our load balancing scheme allows for an efficient acceleration of interpolation on heterogeneous systems containing multi-core CPUs and GPUs.
International Nuclear Information System (INIS)
Aydin, Alhun; Sisman, Altug
2016-01-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Some observations on interpolating gauges and non-covariant gauges
Indian Academy of Sciences (India)
We discuss the viability of using interpolating gauges to deﬁne the non-covariant gauges starting from the covariant ones. We draw attention to the need for a very careful treatment of boundary condition deﬁning term. We show that the boundary condition needed to maintain gauge-invariance as the interpolating parameter ...
Normal scheme for solving the transport equation independently of spatial discretization
International Nuclear Information System (INIS)
Zamonsky, O.M.
1993-01-01
To solve the discrete ordinates neutron transport equation, a general order nodal scheme is used, where nodes are allowed to have different orders of approximation and the whole system reaches a final order distribution. Independence in the election of system discretization and order of approximation is obtained without loss of accuracy. The final equations and the iterative method to reach a converged order solution were implemented in a two-dimensional computer code to solve monoenergetic, isotropic scattering, external source problems. Two benchmark problems were solved using different automatic selection order methods. Results show accurate solutions without spatial discretization, regardless of the initial selection of distribution order. (author)
Reinhardt, Katja; Samimi, Cyrus
2018-01-01
While climatological data of high spatial resolution are largely available in most developed countries, the network of climatological stations in many other regions of the world still constitutes large gaps. Especially for those regions, interpolation methods are important tools to fill these gaps and to improve the data base indispensible for climatological research. Over the last years, new hybrid methods of machine learning and geostatistics have been developed which provide innovative prospects in spatial predictive modelling. This study will focus on evaluating the performance of 12 different interpolation methods for the wind components \\overrightarrow{u} and \\overrightarrow{v} in a mountainous region of Central Asia. Thereby, a special focus will be on applying new hybrid methods on spatial interpolation of wind data. This study is the first evaluating and comparing the performance of several of these hybrid methods. The overall aim of this study is to determine whether an optimal interpolation method exists, which can equally be applied for all pressure levels, or whether different interpolation methods have to be used for the different pressure levels. Deterministic (inverse distance weighting) and geostatistical interpolation methods (ordinary kriging) were explored, which take into account only the initial values of \\overrightarrow{u} and \\overrightarrow{v} . In addition, more complex methods (generalized additive model, support vector machine and neural networks as single methods and as hybrid methods as well as regression-kriging) that consider additional variables were applied. The analysis of the error indices revealed that regression-kriging provided the most accurate interpolation results for both wind components and all pressure heights. At 200 and 500 hPa, regression-kriging is followed by the different kinds of neural networks and support vector machines and for 850 hPa it is followed by the different types of support vector machine and
Efficient Algorithms and Design for Interpolation Filters in Digital Receiver
Directory of Open Access Journals (Sweden)
Xiaowei Niu
2014-05-01
Full Text Available Based on polynomial functions this paper introduces a generalized design method for interpolation filters. The polynomial-based interpolation filters can be implemented efficiently by using a modified Farrow structure with an arbitrary frequency response, the filters allow many pass- bands and stop-bands, and for each band the desired amplitude and weight can be set arbitrarily. The optimization coefficients of the interpolation filters in time domain are got by minimizing the weighted mean squared error function, then converting to solve the quadratic programming problem. The optimization coefficients in frequency domain are got by minimizing the maxima (MiniMax of the weighted mean squared error function. The degree of polynomials and the length of interpolation filter can be selected arbitrarily. Numerical examples verified the proposed design method not only can reduce the hardware cost effectively but also guarantee an excellent performance.
Interpolation-free scanning and sampling scheme for tomographic reconstructions
International Nuclear Information System (INIS)
Donohue, K.D.; Saniie, J.
1987-01-01
In this paper a sampling scheme is developed for computer tomography (CT) systems that eliminates the need for interpolation. A set of projection angles along with their corresponding sampling rates are derived from the geometry of the Cartesian grid such that no interpolation is required to calculate the final image points for the display grid. A discussion is presented on the choice of an optimal set of projection angles that will maintain a resolution comparable to a sampling scheme of regular measurement geometry, while minimizing the computational load. The interpolation-free scanning and sampling (IFSS) scheme developed here is compared to a typical sampling scheme of regular measurement geometry through a computer simulation
A comparison of linear interpolation models for iterative CT reconstruction.
Hahn, Katharina; Schöndube, Harald; Stierstorfer, Karl; Hornegger, Joachim; Noo, Frédéric
2016-12-01
Recent reports indicate that model-based iterative reconstruction methods may improve image quality in computed tomography (CT). One difficulty with these methods is the number of options available to implement them, including the selection of the forward projection model and the penalty term. Currently, the literature is fairly scarce in terms of guidance regarding this selection step, whereas these options impact image quality. Here, the authors investigate the merits of three forward projection models that rely on linear interpolation: the distance-driven method, Joseph's method, and the bilinear method. The authors' selection is motivated by three factors: (1) in CT, linear interpolation is often seen as a suitable trade-off between discretization errors and computational cost, (2) the first two methods are popular with manufacturers, and (3) the third method enables assessing the importance of a key assumption in the other methods. One approach to evaluate forward projection models is to inspect their effect on discretized images, as well as the effect of their transpose on data sets, but significance of such studies is unclear since the matrix and its transpose are always jointly used in iterative reconstruction. Another approach is to investigate the models in the context they are used, i.e., together with statistical weights and a penalty term. Unfortunately, this approach requires the selection of a preferred objective function and does not provide clear information on features that are intrinsic to the model. The authors adopted the following two-stage methodology. First, the authors analyze images that progressively include components of the singular value decomposition of the model in a reconstructed image without statistical weights and penalty term. Next, the authors examine the impact of weights and penalty on observed differences. Image quality metrics were investigated for 16 different fan-beam imaging scenarios that enabled probing various aspects
Interpolation functors and interpolation spaces
Brudnyi, Yu A
1991-01-01
The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the r...
Energy Technology Data Exchange (ETDEWEB)
Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr
2016-03-22
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Directory of Open Access Journals (Sweden)
Zeng Cheng
2014-12-01
Full Text Available Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.
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Othman M. K. Alsmadi
2015-01-01
Full Text Available A robust computational technique for model order reduction (MOR of multi-time-scale discrete systems (single input single output (SISO and multi-input multioutput (MIMO is presented in this paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements of B, C, and D matrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach.
Mist'e, Gianluigi Alberto; Benini, Ernesto
2012-06-01
Compressor map interpolation is usually performed through the introduction of auxiliary coordinates (β). In this paper, a new analytical bivariate β function definition to be used in compressor map interpolation is studied. The function has user-defined parameters that must be adjusted to properly fit to a single map. The analytical nature of β allows for rapid calculations of the interpolation error estimation, which can be used as a quantitative measure of interpolation accuracy and also as a valid tool to compare traditional β function interpolation with new approaches (artificial neural networks, genetic algorithms, etc.). The quality of the method is analyzed by comparing the error output to the one of a well-known state-of-the-art methodology. This comparison is carried out for two different types of compressor and, in both cases, the error output using the method presented in this paper is found to be consistently lower. Moreover, an optimization routine able to locally minimize the interpolation error by shape variation of the β function is implemented. Further optimization introducing other important criteria is discussed.
Anisotropic Third-Order Regularization for Sparse Digital Elevation Models
Lellmann, Jan
2013-01-01
We consider the problem of interpolating a surface based on sparse data such as individual points or level lines. We derive interpolators satisfying a list of desirable properties with an emphasis on preserving the geometry and characteristic features of the contours while ensuring smoothness across level lines. We propose an anisotropic third-order model and an efficient method to adaptively estimate both the surface and the anisotropy. Our experiments show that the approach outperforms AMLE and higher-order total variation methods qualitatively and quantitatively on real-world digital elevation data. © 2013 Springer-Verlag.
Phase Center Interpolation Algorithm for Airborne GPS through the Kalman Filter
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Edson A. Mitishita
2005-12-01
Full Text Available The aerial triangulation is a fundamental step in any photogrammetric project. The surveying of the traditional control points, depending on region to be mapped, still has a high cost. The distribution of control points at the block, and its positional quality, influence directly in the resulting precisions of the aero triangulation processing. The airborne GPS technique has as key objectives cost reduction and quality improvement of the ground control in the modern photogrammetric projects. Nowadays, in Brazil, the greatest photogrammetric companies are acquiring airborne GPS systems, but those systems are usually presenting difficulties in the operation, due to the need of human resources for the operation, because of the high technology involved. Inside the airborne GPS technique, one of the fundamental steps is the interpolation of the position of the phase center of the GPS antenna, in the photo shot instant. Traditionally, low degree polynomials are used, but recent studies show that those polynomials is reduced in turbulent flights, which are quite common, mainly in great scales flights. This paper has as objective to present a solution for that problem, through an algorithm based on the Kalman Filter, which takes into account the dynamic aspect of the problem. At the end of the paper, the results of a comparison between experiments done with the proposed methodology and a common linear interpolator are shown. These results show a significant accuracy gain at the procedure of linear interpolation, when the Kalman filter is used.
Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan
Hussain, Ijaz; Spöck, Gunter; Pilz, Jürgen; Yu, Hwa-Lung
2010-08-01
Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space-time heterogeneity of rainfall observations make space-time estimation of precipitation a challenging task. In this paper we propose a Box-Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space-time monthly precipitation in the monsoon periods during 1974-2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space-time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.
Digital Resonant Controller based on Modified Tustin Discretization Method
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STOJIC, D.
2016-11-01
Full Text Available Resonant controllers are used in power converter voltage and current control due to their simplicity and accuracy. However, digital implementation of resonant controllers introduces problems related to zero and pole mapping from the continuous to the discrete time domain. Namely, some discretization methods introduce significant errors in the digital controller resonant frequency, resulting in the loss of the asymptotic AC reference tracking, especially at high resonant frequencies. The delay compensation typical for resonant controllers can also be compromised. Based on the existing analysis, it can be concluded that the Tustin discretization with frequency prewarping represents a preferable choice from the point of view of the resonant frequency accuracy. However, this discretization method has a shortcoming in applications that require real-time frequency adaptation, since complex trigonometric evaluation is required for each frequency change. In order to overcome this problem, in this paper the modified Tustin discretization method is proposed based on the Taylor series approximation of the frequency prewarping function. By comparing the novel discretization method with commonly used two-integrator-based proportional-resonant (PR digital controllers, it is shown that the resulting digital controller resonant frequency and time delay compensation errors are significantly reduced for the novel controller.
The Convergence Acceleration of Two-Dimensional Fourier Interpolation
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Anry Nersessian
2008-07-01
Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.
Positivity Preserving Interpolation Using Rational Bicubic Spline
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Samsul Ariffin Abdul Karim
2015-01-01
Full Text Available This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE, our partially blended rational bicubic spline is on a par with the established methods.
Gaussian Process Interpolation for Uncertainty Estimation in Image Registration
Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William
2014-01-01
Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127
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Annalisa Di Piazza
2015-04-01
Full Text Available An exhaustive comparison among different spatial interpolation algorithms was carried out in order to derive annual and monthly air temperature maps for Sicily (Italy. Deterministic, data-driven and geostatistics algorithms were used, in some cases adding the elevation information and other physiographic variables to improve the performance of interpolation techniques and the reconstruction of the air temperature field. The dataset is given by air temperature data coming from 84 stations spread around the island of Sicily. The interpolation algorithms were optimized by using a subset of the available dataset, while the remaining subset was used to validate the results in terms of the accuracy and bias of the estimates. Validation results indicate that univariate methods, which neglect the information from physiographic variables, significantly entail the largest errors, while performances improve when such parameters are taken into account. The best results at the annual scale have been obtained using the the ordinary kriging of residuals from linear regression and from the artificial neural network algorithm, while, at the monthly scale, a Fourier-series algorithm has been used to downscale mean annual temperature to reproduce monthly values in the annual cycle.
A Discrete Model for Color Naming
Menegaz, G.; Le Troter, A.; Sequeira, J.; Boi, J. M.
2006-12-01
The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1). Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2), and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.
Restoring the missing features of the corrupted speech using linear interpolation methods
Rassem, Taha H.; Makbol, Nasrin M.; Hasan, Ali Muttaleb; Zaki, Siti Syazni Mohd; Girija, P. N.
2017-10-01
One of the main challenges in the Automatic Speech Recognition (ASR) is the noise. The performance of the ASR system reduces significantly if the speech is corrupted by noise. In spectrogram representation of a speech signal, after deleting low Signal to Noise Ratio (SNR) elements, the incomplete spectrogram is obtained. In this case, the speech recognizer should make modifications to the spectrogram in order to restore the missing elements, which is one direction. In another direction, speech recognizer should be able to restore the missing elements due to deleting low SNR elements before performing the recognition. This is can be done using different spectrogram reconstruction methods. In this paper, the geometrical spectrogram reconstruction methods suggested by some researchers are implemented as a toolbox. In these geometrical reconstruction methods, the linear interpolation along time or frequency methods are used to predict the missing elements between adjacent observed elements in the spectrogram. Moreover, a new linear interpolation method using time and frequency together is presented. The CMU Sphinx III software is used in the experiments to test the performance of the linear interpolation reconstruction method. The experiments are done under different conditions such as different lengths of the window and different lengths of utterances. Speech corpus consists of 20 males and 20 females; each one has two different utterances are used in the experiments. As a result, 80% recognition accuracy is achieved with 25% SNR ratio.
Local discrete symmetries from superstring derived models
International Nuclear Information System (INIS)
Faraggi, A.E.
1996-10-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations
Discrete gradients in discrete classical mechanics
International Nuclear Information System (INIS)
Renna, L.
1987-01-01
A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated
International Nuclear Information System (INIS)
Coelho, Pedro J.
2014-01-01
Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed
Discrete Biogeography Based Optimization for Feature Selection in Molecular Signatures.
Liu, Bo; Tian, Meihong; Zhang, Chunhua; Li, Xiangtao
2015-04-01
Biomarker discovery from high-dimensional data is a complex task in the development of efficient cancer diagnoses and classification. However, these data are usually redundant and noisy, and only a subset of them present distinct profiles for different classes of samples. Thus, selecting high discriminative genes from gene expression data has become increasingly interesting in the field of bioinformatics. In this paper, a discrete biogeography based optimization is proposed to select the good subset of informative gene relevant to the classification. In the proposed algorithm, firstly, the fisher-markov selector is used to choose fixed number of gene data. Secondly, to make biogeography based optimization suitable for the feature selection problem; discrete migration model and discrete mutation model are proposed to balance the exploration and exploitation ability. Then, discrete biogeography based optimization, as we called DBBO, is proposed by integrating discrete migration model and discrete mutation model. Finally, the DBBO method is used for feature selection, and three classifiers are used as the classifier with the 10 fold cross-validation method. In order to show the effective and efficiency of the algorithm, the proposed algorithm is tested on four breast cancer dataset benchmarks. Comparison with genetic algorithm, particle swarm optimization, differential evolution algorithm and hybrid biogeography based optimization, experimental results demonstrate that the proposed method is better or at least comparable with previous method from literature when considering the quality of the solutions obtained. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Accurate B-spline-based 3-D interpolation scheme for digital volume correlation
Ren, Maodong; Liang, Jin; Wei, Bin
2016-12-01
An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.
3-D discrete analytical ridgelet transform.
Helbert, David; Carré, Philippe; Andres, Eric
2006-12-01
In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.
Interpolation problem for the solutions of linear elasticity equations based on monogenic functions
Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii
2017-11-01
Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.
Perfect discretization of path integrals
Steinhaus, Sebastian
2011-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discu...
Spatial interpolation of point velocities in stream cross-section
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Hasníková Eliška
2015-03-01
Full Text Available The most frequently used instrument for measuring velocity distribution in the cross-section of small rivers is the propeller-type current meter. Output of measuring using this instrument is point data of a tiny bulk. Spatial interpolation of measured data should produce a dense velocity profile, which is not available from the measuring itself. This paper describes the preparation of interpolation models.
Discretization vs. Rounding Error in Euler's Method
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Delimiting areas of endemism through kernel interpolation.
Oliveira, Ubirajara; Brescovit, Antonio D; Santos, Adalberto J
2015-01-01
We propose a new approach for identification of areas of endemism, the Geographical Interpolation of Endemism (GIE), based on kernel spatial interpolation. This method differs from others in being independent of grid cells. This new approach is based on estimating the overlap between the distribution of species through a kernel interpolation of centroids of species distribution and areas of influence defined from the distance between the centroid and the farthest point of occurrence of each species. We used this method to delimit areas of endemism of spiders from Brazil. To assess the effectiveness of GIE, we analyzed the same data using Parsimony Analysis of Endemism and NDM and compared the areas identified through each method. The analyses using GIE identified 101 areas of endemism of spiders in Brazil GIE demonstrated to be effective in identifying areas of endemism in multiple scales, with fuzzy edges and supported by more synendemic species than in the other methods. The areas of endemism identified with GIE were generally congruent with those identified for other taxonomic groups, suggesting that common processes can be responsible for the origin and maintenance of these biogeographic units.
Delimiting areas of endemism through kernel interpolation.
Directory of Open Access Journals (Sweden)
Ubirajara Oliveira
Full Text Available We propose a new approach for identification of areas of endemism, the Geographical Interpolation of Endemism (GIE, based on kernel spatial interpolation. This method differs from others in being independent of grid cells. This new approach is based on estimating the overlap between the distribution of species through a kernel interpolation of centroids of species distribution and areas of influence defined from the distance between the centroid and the farthest point of occurrence of each species. We used this method to delimit areas of endemism of spiders from Brazil. To assess the effectiveness of GIE, we analyzed the same data using Parsimony Analysis of Endemism and NDM and compared the areas identified through each method. The analyses using GIE identified 101 areas of endemism of spiders in Brazil GIE demonstrated to be effective in identifying areas of endemism in multiple scales, with fuzzy edges and supported by more synendemic species than in the other methods. The areas of endemism identified with GIE were generally congruent with those identified for other taxonomic groups, suggesting that common processes can be responsible for the origin and maintenance of these biogeographic units.
Shao, Chenxi; Liu, Qingqing; Wang, Tingting; Yin, Peifeng; Wang, Binghong
2013-09-01
Time series is widely exploited to study the innate character of the complex chaotic system. Existing chaotic models are weak in modeling accuracy because of adopting either error minimization strategy or an acceptable error to end the modeling process. Instead, interpolation can be very useful for solving differential equations with a small modeling error, but it is also very difficult to deal with arbitrary-dimensional series. In this paper, geometric theory is considered to reduce the modeling error, and a high-precision framework called Series-NonUniform Rational B-Spline (S-NURBS) model is developed to deal with arbitrary-dimensional series. The capability of the interpolation framework is proved in the validation part. Besides, we verify its reliability by interpolating Musa dataset. The main improvement of the proposed framework is that we are able to reduce the interpolation error by properly adjusting weights series step by step if more information is given. Meanwhile, these experiments also demonstrate that studying the physical system from a geometric perspective is feasible.
Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.
2018-03-01
We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.
Particle Swarm Based Approach of a Real-Time Discrete Neural Identifier for Linear Induction Motors
Directory of Open Access Journals (Sweden)
Alma Y. Alanis
2013-01-01
Full Text Available This paper focusses on a discrete-time neural identifier applied to a linear induction motor (LIM model, whose model is assumed to be unknown. This neural identifier is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high-order neural network (RHONN trained with a novel algorithm based on extended Kalman filter (EKF and particle swarm optimization (PSO, using an online series-parallel con figuration. Real-time results are included in order to illustrate the applicability of the proposed scheme.
Performance of an Interpolated Stochastic Weather Generator in Czechia and Nebraska
Dubrovsky, M.; Trnka, M.; Hayes, M. J.; Svoboda, M. D.; Semeradova, D.; Metelka, L.; Hlavinka, P.
2008-12-01
Met&Roll is a WGEN-like parametric four-variate daily weather generator (WG), with an optional extension allowing the user to generate additional variables (i.e. wind and water vapor pressure). It is designed to produce synthetic weather series representing present and/or future climate conditions to be used as an input into various models (e.g. crop growth and rainfall runoff models). The present contribution will summarize recent experiments, in which we tested the performance of the interpolated WG, with the aim to examine whether the WG may be used to produce synthetic weather series even for sites having no meteorological observations. The experiments being discussed include: (1) the comparison of various interpolation methods where the performance of the candidate methods is compared in terms of the accuracy of the interpolation for selected WG parameters; (2) assessing the ability of the interpolated WG in the territories of Czechia and Nebraska to reproduce extreme temperature and precipitation characteristics; (3) indirect validation of the interpolated WG in terms of the modeled crop yields simulated by STICS crop growth model (in Czechia); and (4) indirect validation of interpolated WG in terms of soil climate regime characteristics simulated by the SoilClim model (Czechia and Nebraska). The experiments are based on observed daily weather series from two regions: Czechia (area = 78864 km2, 125 stations available) and Nebraska (area = 200520 km2, 28 stations available). Even though Nebraska exhibits a much lower density of stations, this is offset by the state's relatively flat topography, which is an advantage in using the interpolated WG. Acknowledgements: The present study is supported by the AMVIS-KONTAKT project (ME 844) and the GAAV Grant Agency (project IAA300420806).
Limit sets for the discrete spectrum of complex Jacobi matrices
International Nuclear Information System (INIS)
Golinskii, L B; Egorova, I E
2005-01-01
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the matrix elements ensuring the finiteness of the discrete spectrum is found. An example of a Jacobi matrix with discrete spectrum having a unique limit point is constructed. These results are discrete analogues of Pavlov's well-known results on Schroedinger operators with complex potential on a half-axis.
Introducing Discrete Frequency Infrared Technology for High-Throughput Biofluid Screening
Hughes, Caryn; Clemens, Graeme; Bird, Benjamin; Dawson, Timothy; Ashton, Katherine M.; Jenkinson, Michael D.; Brodbelt, Andrew; Weida, Miles; Fotheringham, Edeline; Barre, Matthew; Rowlette, Jeremy; Baker, Matthew J.
2016-02-01
Accurate early diagnosis is critical to patient survival, management and quality of life. Biofluids are key to early diagnosis due to their ease of collection and intimate involvement in human function. Large-scale mid-IR imaging of dried fluid deposits offers a high-throughput molecular analysis paradigm for the biomedical laboratory. The exciting advent of tuneable quantum cascade lasers allows for the collection of discrete frequency infrared data enabling clinically relevant timescales. By scanning targeted frequencies spectral quality, reproducibility and diagnostic potential can be maintained while significantly reducing acquisition time and processing requirements, sampling 16 serum spots with 0.6, 5.1 and 15% relative standard deviation (RSD) for 199, 14 and 9 discrete frequencies respectively. We use this reproducible methodology to show proof of concept rapid diagnostics; 40 unique dried liquid biopsies from brain, breast, lung and skin cancer patients were classified in 2.4 cumulative seconds against 10 non-cancer controls with accuracies of up to 90%.
High-order above-threshold dissociation of molecules
Lu, Peifen; Wang, Junping; Li, Hui; Lin, Kang; Gong, Xiaochun; Song, Qiying; Ji, Qinying; Zhang, Wenbin; Ma, Junyang; Li, Hanxiao; Zeng, Heping; He, Feng; Wu, Jian
2018-03-01
Electrons bound to atoms or molecules can simultaneously absorb multiple photons via the above-threshold ionization featured with discrete peaks in the photoelectron spectrum on account of the quantized nature of the light energy. Analogously, the above-threshold dissociation of molecules has been proposed to address the multiple-photon energy deposition in the nuclei of molecules. In this case, nuclear energy spectra consisting of photon-energy spaced peaks exceeding the binding energy of the molecular bond are predicted. Although the observation of such phenomena is difficult, this scenario is nevertheless logical and is based on the fundamental laws. Here, we report conclusive experimental observation of high-order above-threshold dissociation of H2 in strong laser fields where the tunneling-ionized electron transfers the absorbed multiphoton energy, which is above the ionization threshold to the nuclei via the field-driven inelastic rescattering. Our results provide an unambiguous evidence that the electron and nuclei of a molecule as a whole absorb multiple photons, and thus above-threshold ionization and above-threshold dissociation must appear simultaneously, which is the cornerstone of the nowadays strong-field molecular physics.
Discrete mKdV and discrete sine-Gordon flows on discrete space curves
International Nuclear Information System (INIS)
Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro
2014-01-01
In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)
Xiao, Yong; Gu, Xiaomin; Yin, Shiyang; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Niu, Yong
2016-01-01
Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R(2)) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial-proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001-2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.
A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets
Directory of Open Access Journals (Sweden)
Min Deng
2016-02-01
Full Text Available Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984–2009. Experimental results show that, for these datasets, the proposed method outperforms three state-of-the-art methods—e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.
International Nuclear Information System (INIS)
Thompson, K.G.
2000-01-01
In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a
Periodic Properties of 1D FE Discrete Models in High Frequency Dynamics
Directory of Open Access Journals (Sweden)
A. Żak
2016-01-01
Full Text Available Finite element discrete models of various engineering 1D structures may be considered as structures of certain periodic characteristics. The source of this periodicity comes from the discontinuity of stress/strain field between the elements. This behaviour remains unnoticeable, when low frequency dynamics of these structures is investigated. At high frequency regimes, however, its influence may be strong enough to dominate calculated structural responses distorting or even falsifying them completely. In this paper, certain computational aspects of structural periodicity of 1D FE discrete models are discussed by the authors. In this discussion, the authors focus their attention on an exemplary problem of 1D rod modelled according to the elementary theory.
Ensemble simulations with discrete classical dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2013-01-01
For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\\tilde{H}$ with energy $\\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\\tilde{H}$. $\\tilde......{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics...
Can a polynomial interpolation improve on the Kaplan-Yorke dimension?
International Nuclear Information System (INIS)
Richter, Hendrik
2008-01-01
The Kaplan-Yorke dimension can be derived using a linear interpolation between an h-dimensional Lyapunov exponent λ (h) >0 and an h+1-dimensional Lyapunov exponent λ (h+1) <0. In this Letter, we use a polynomial interpolation to obtain generalized Lyapunov dimensions and study the relationships among them for higher-dimensional systems
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Interpolant Tree Automata and their Application in Horn Clause Verification
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Bishoksan Kafle
2016-07-01
Full Text Available This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this paper. The role of an interpolant tree automaton is to provide a generalisation of a spurious counterexample during refinement, capturing a possibly infinite set of spurious counterexample traces. In our approach these traces are then eliminated using a transformation of the Horn clauses. We compare this approach with two other methods; one of them uses interpolant tree automata in an algorithm for trace abstraction and refinement, while the other uses abstract interpretation over the domain of convex polyhedra without the generalisation step. Evaluation of the results of experiments on a number of Horn clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead.
Design of interpolation functions for subpixel-accuracy stereo-vision systems.
Haller, Istvan; Nedevschi, Sergiu
2012-02-01
Traditionally, subpixel interpolation in stereo-vision systems was designed for the block-matching algorithm. During the evaluation of different interpolation strategies, a strong correlation was observed between the type of the stereo algorithm and the subpixel accuracy of the different solutions. Subpixel interpolation should be adapted to each stereo algorithm to achieve maximum accuracy. In consequence, it is more important to propose methodologies for interpolation function generation than specific function shapes. We propose two such methodologies based on data generated by the stereo algorithms. The first proposal uses a histogram to model the environment and applies histogram equalization to an existing solution adapting it to the data. The second proposal employs synthetic images of a known environment and applies function fitting to the resulted data. The resulting function matches the algorithm and the data as best as possible. An extensive evaluation set is used to validate the findings. Both real and synthetic test cases were employed in different scenarios. The test results are consistent and show significant improvements compared with traditional solutions. © 2011 IEEE
A temporal interpolation approach for dynamic reconstruction in perfusion CT
International Nuclear Information System (INIS)
Montes, Pau; Lauritsch, Guenter
2007-01-01
This article presents a dynamic CT reconstruction algorithm for objects with time dependent attenuation coefficient. Projection data acquired over several rotations are interpreted as samples of a continuous signal. Based on this idea, a temporal interpolation approach is proposed which provides the maximum temporal resolution for a given rotational speed of the CT scanner. Interpolation is performed using polynomial splines. The algorithm can be adapted to slow signals, reducing the amount of data acquired and the computational cost. A theoretical analysis of the approximations made by the algorithm is provided. In simulation studies, the temporal interpolation approach is compared with three other dynamic reconstruction algorithms based on linear regression, linear interpolation, and generalized Parker weighting. The presented algorithm exhibits the highest temporal resolution for a given sampling interval. Hence, our approach needs less input data to achieve a certain quality in the reconstruction than the other algorithms discussed or, equivalently, less x-ray exposure and computational complexity. The proposed algorithm additionally allows the possibility of using slow rotating scanners for perfusion imaging purposes
NOAA Optimum Interpolation 1/4 Degree Daily Sea Surface Temperature (OISST) Analysis, Version 2
National Oceanic and Atmospheric Administration, Department of Commerce — This high-resolution sea surface temperature (SST) analysis product was developed using an optimum interpolation (OI) technique. The SST analysis has a spatial grid...
Subsurface temperature maps in French sedimentary basins: new data compilation and interpolation
International Nuclear Information System (INIS)
Bonte, D.; Guillou-Frottier, L.; Garibaldi, C.; Bourgine, B.; Lopez, S.; Bouchot, V.; Garibaldi, C.; Lucazeau, F.
2010-01-01
Assessment of the underground geothermal potential requires the knowledge of deep temperatures (1-5 km). Here, we present new temperature maps obtained from oil boreholes in the French sedimentary basins. Because of their origin, the data need to be corrected, and their local character necessitates spatial interpolation. Previous maps were obtained in the 1970's using empirical corrections and manual interpolation. In this study, we update the number of measurements by using values collected during the last thirty years, correct the temperatures for transient perturbations and carry out statistical analyses before modelling the 3D distribution of temperatures. This dataset provides 977 temperatures corrected for transient perturbations in 593 boreholes located in the French sedimentary basins. An average temperature gradient of 30.6 deg. C/km is obtained for a representative surface temperature of 10 deg. C. When surface temperature is not accounted for, deep measurements are best fitted with a temperature gradient of 25.7 deg. C/km. We perform a geostatistical analysis on a residual temperature dataset (using a drift of 25.7 deg. C/km) to constrain the 3D interpolation kriging procedure with horizontal and vertical models of variograms. The interpolated residual temperatures are added to the country-scale averaged drift in order to get a three dimensional thermal structure of the French sedimentary basins. The 3D thermal block enables us to extract isothermal surfaces and 2D sections (iso-depth maps and iso-longitude cross-sections). A number of anomalies with a limited depth and spatial extension have been identified, from shallow in the Rhine graben and Aquitanian basin, to deep in the Provence basin. Some of these anomalies (Paris basin, Alsace, south of the Provence basin) may be partly related to thick insulating sediments, while for some others (southwestern Aquitanian basin, part of the Provence basin) large-scale fluid circulation may explain superimposed
Interpolant tree automata and their application in Horn clause verification
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick
2016-01-01
This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this ......This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way...... clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead....
Directory of Open Access Journals (Sweden)
J.-M. Beckers
2014-10-01
Full Text Available We present a method in which the optimal interpolation of multi-scale processes can be expanded into a succession of simpler interpolations. First, we prove how the optimal analysis of a superposition of two processes can be obtained by different mathematical formulations involving iterations and analysis focusing on a single process. From the different mathematical equivalent formulations, we then select the most efficient ones by analyzing the behavior of the different possibilities in a simple and well-controlled test case. The clear guidelines deduced from this experiment are then applied to a real situation in which we combine large-scale analysis of hourly Spinning Enhanced Visible and Infrared Imager (SEVIRI satellite images using data interpolating empirical orthogonal functions (DINEOF with a local optimal interpolation using a Gaussian covariance. It is shown that the optimal combination indeed provides the best reconstruction and can therefore be exploited to extract the maximum amount of useful information from the original data.
Gao, Longfei
2018-02-16
We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.
Digital x-ray tomosynthesis with interpolated projection data for thin slab objects
Ha, S.; Yun, J.; Kim, H. K.
2017-11-01
In relation with a thin slab-object inspection, we propose a digital tomosynthesis reconstruction with fewer numbers of measured projections in combinations with additional virtual projections, which are produced by interpolating the measured projections. Hence we can reconstruct tomographic images with less few-view artifacts. The projection interpolation assumes that variations in cone-beam ray path-lengths through an object are negligible and the object is rigid. The interpolation is performed in the projection-space domain. Pixel values in the interpolated projection are the weighted sum of pixel values of the measured projections considering their projection angles. The experimental simulation shows that the proposed method can enhance the contrast-to-noise performance in reconstructed images while sacrificing the spatial resolving power.
Directory of Open Access Journals (Sweden)
Marta Béjar-Pizarro
2016-11-01
Full Text Available Land subsidence resulting from groundwater extractions is a global phenomenon adversely affecting many regions worldwide. Understanding the governing processes and mitigating associated hazards require knowing the spatial distribution of the implicated factors (piezometric levels, lithology, ground deformation, usually only known at discrete locations. Here, we propose a methodology based on the Kriging with External Drift (KED approach to interpolate sparse point measurements of variables influencing land subsidence using high density InSAR measurements. In our study, located in the Alto Guadalentín basin, SE Spain, these variables are GPS vertical velocities and the thickness of compressible soils. First, we estimate InSAR and GPS rates of subsidence covering the periods 2003–2010 and 2004–2013, respectively. Then, we apply the KED method to the discrete variables. The resulting continuous GPS velocity map shows maximum subsidence rates of 13 cm/year in the center of the basin, in agreement with previous studies. The compressible deposits thickness map is significantly improved. We also test the coherence of Sentinel-1 data in the study region and evaluate the applicability of this methodology with the new satellite, which will improve the monitoring of aquifer-related subsidence and the mapping of variables governing this phenomenon.
Strip interpolation in silicon and germanium strip detectors
International Nuclear Information System (INIS)
Wulf, E. A.; Phlips, B. F.; Johnson, W. N.; Kurfess, J. D.; Lister, C. J.; Kondev, F.; Physics; Naval Research Lab.
2004-01-01
The position resolution of double-sided strip detectors is limited by the strip pitch and a reduction in strip pitch necessitates more electronics. Improved position resolution would improve the imaging capabilities of Compton telescopes and PET detectors. Digitizing the preamplifier waveform yields more information than can be extracted with regular shaping electronics. In addition to the energy, depth of interaction, and which strip was hit, the digitized preamplifier signals can locate the interaction position to less than the strip pitch of the detector by looking at induced signals in neighboring strips. This allows the position of the interaction to be interpolated in three dimensions and improve the imaging capabilities of the system. In a 2 mm thick silicon strip detector with a strip pitch of 0.891 mm, strip interpolation located the interaction of 356 keV gamma rays to 0.3 mm FWHM. In a 2 cm thick germanium detector with a strip pitch of 5 mm, strip interpolation of 356 keV gamma rays yielded a position resolution of 1.5 mm FWHM
Effect of raingage density, position and interpolation on rainfall-discharge modelling
Ly, S.; Sohier, C.; Charles, C.; Degré, A.
2012-04-01
Precipitation traditionally observed using raingages or weather stations, is one of the main parameters that have direct impact on runoff production. Precipitation data require a preliminary spatial interpolation prior to hydrological modeling. The accuracy of modelling result depends on the accuracy of the interpolated spatial rainfall which differs according to different interpolation methods. The accuracy of the interpolated spatial rainfall is usually determined by cross-validation method. The objective of this study is to assess the different interpolation methods of daily rainfall at the watershed scale through hydrological modelling and to explore the best methods that provide a good long term simulation. Four versions of geostatistics: Ordinary Kriging (ORK), Universal Kriging (UNK), Kriging with External Dridft (KED) and Ordinary Cokriging (OCK) and two types of deterministic methods: Thiessen polygon (THI) and Inverse Distance Weighting (IDW) are used to produce 30-year daily rainfall inputs for a distributed physically-based hydrological model (EPIC-GRID). This work is conducted in the Ourthe and Ambleve nested catchments, located in the Ardennes hilly landscape in the Walloon region, Belgium. The total catchment area is 2908 km2, lies between 67 and 693 m in elevation. The multivariate geostatistics (KED and OCK) are also used by incorporating elevation as external data to improve the rainfall prediction. This work also aims at analysing the effect of different raingage densities and position used for interpolation, on the stream flow modelled to get insight in terms of the capability and limitation of the geostatistical methods. The number of raingage varies from 70, 60, 50, 40, 30, 20, 8 to 4 stations located in and surrounding the catchment area. In the latter case, we try to use different positions: around the catchment and only a part of the catchment. The result shows that the simple method like THI fails to capture the rainfall and to produce
Interpolation of rational matrix functions
Ball, Joseph A; Rodman, Leiba
1990-01-01
This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an indepe...
Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun
2018-07-01
Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.