Spectral/hp element methods for CFD
Karniadakis, George Em
1999-01-01
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2014-01-01
The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.
Spectral element method for wave propagation on irregular domains
Indian Academy of Sciences (India)
Yan Hui Geng
2018-03-14
Mar 14, 2018 ... Abstract. A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the ...
Spectral element method for wave propagation on irregular domains
Indian Academy of Sciences (India)
A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are ...
Stability estimates for hp spectral element methods for general ...
Indian Academy of Sciences (India)
We establish basic stability estimates for a non-conforming ℎ- spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-conforming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are ...
Convergence analysis of spectral element method for electromechanical devices
Curti, M.; Jansen, J.W.; Lomonova, E.A.
2017-01-01
This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with the
Convergence analysis of spectral element method for magnetic devices
Curti, M.; Jansen, J.W.; Lomonova, E.A.
2018-01-01
This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for modeling a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with
Spectral/ hp element methods: Recent developments, applications, and perspectives
Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.
2018-02-01
The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.
Nonconforming h-p spectral element methods for elliptic problems
Indian Academy of Sciences (India)
In [6,7,13,14] h-p spectral element methods for solving elliptic boundary value problems on polygonal ... Let M denote the number of corner layers and W denote the number of degrees of .... β is given by Theorem 2.2 of [3] which can be stated.
hp Spectral element methods for three dimensional elliptic problems
Indian Academy of Sciences (India)
This is the first of a series of papers devoted to the study of h-p spec- .... element functions defined on mesh elements in the new system of variables with a uni- ... the spectral element functions on these elements and give construction of the stability .... By Hm( ), we denote the usual Sobolev space of integer order m ≥ 0 ...
Spectral element method for vector radiative transfer equation
International Nuclear Information System (INIS)
Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.
2010-01-01
A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.
Spectral Element Method for the Simulation of Unsteady Compressible Flows
Diosady, Laslo Tibor; Murman, Scott M.
2013-01-01
This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin
2017-09-28
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.
hp Spectral element methods for three dimensional elliptic problems
Indian Academy of Sciences (India)
elliptic boundary value problems on non-smooth domains in R3. For Dirichlet problems, ... of variable degree bounded by W. Let N denote the number of layers in the geomet- ric mesh ... We prove a stability theorem for mixed problems when the spectral element functions vanish ..... Applying Theorem 3.1,. ∫ r l. |Mu|2dx −.
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.
Spectral/hp element methods: Recent developments, applications, and perspectives
DEFF Research Database (Denmark)
Xu, Hui; Cantwell, Chris; Monteserin, Carlos
2018-01-01
regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral...... is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain...
Tomar, S.K.
2002-01-01
It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy.
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Directory of Open Access Journals (Sweden)
Luca Bergamaschi
1994-01-01
Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
Stability estimates for hp spectral element methods for elliptic ...
Indian Academy of Sciences (India)
... parallel preconditioners and error estimates for the solution of the minimization problem which are nearly optimal as the condition number of the preconditioned system is polylogarithmic in , the number of processors and the number of degrees of freedom in each variable on each element. Moreover if the data is analytic ...
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively......We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...
International Nuclear Information System (INIS)
Ostachowicz, W; Kudela, P
2010-01-01
A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.
Incompressible spectral-element method: Derivation of equations
Deanna, Russell G.
1993-01-01
A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.
Application of Least-Squares Spectral Element Methods to Polynomial Chaos
Vos, P.E.J.; Gerritsma, M.I.
2006-01-01
This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.
High-precision solution to the moving load problem using an improved spectral element method
Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li
2018-02-01
In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.
The next step in coastal numerical models: spectral/hp element methods?
DEFF Research Database (Denmark)
Eskilsson, Claes; Engsig-Karup, Allan Peter; Sherwin, Spencer J.
2005-01-01
In this paper we outline the application of spectral/hp element methods for modelling nonlinear and dispersive waves. We present one- and two-dimensional test cases for the shallow water equations and Boussinesqtype equations – including highly dispersive Boussinesq-type equations....
Spectral element method for elastic and acoustic waves in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)
2016-12-15
Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.
The Spectral/hp-Finite Element Method for Partial Differential Equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2009-01-01
dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...
Spectral element method for band-structure calculations of 3D phononic crystals
International Nuclear Information System (INIS)
Shi, Linlin; Liu, Na; Zhou, Jianyang; Zhou, Yuanguo; Wang, Jiamin; Liu, Qing Huo
2016-01-01
The spectral element method (SEM) is a special kind of high-order finite element method (FEM) which combines the flexibility of a finite element method with the accuracy of a spectral method. In contrast to the traditional FEM, the SEM exhibits advantages in the high-order accuracy as the error decreases exponentially with the increase of interpolation degree by employing the Gauss–Lobatto–Legendre (GLL) polynomials as basis functions. In this study, the spectral element method is developed for the first time for the determination of band structures of 3D isotropic/anisotropic phononic crystals (PCs). Based on the Bloch theorem, we present a novel, intuitive discretization formulation for Navier equation in the SEM scheme for periodic media. By virtue of using the orthogonal Legendre polynomials, the generalized eigenvalue problem is converted to a regular one in our SEM implementation to improve the efficiency. Besides, according to the specific geometry structure, 8-node and 27-node hexahedral elements as well as an analytic mesh have been used to accurately capture curved PC models in our SEM scheme. To verify its accuracy and efficiency, this study analyses the phononic-crystal plates with square and triangular lattice arrangements, and the 3D cubic phononic crystals consisting of simple cubic (SC), bulk central cubic (BCC) and faced central cubic (FCC) lattices with isotropic or anisotropic scatters. All the numerical results considered demonstrate that SEM is superior to the conventional FEM and can be an efficient alternative method for accurate determination of band structures of 3D phononic crystals. (paper)
The spectral element method for static neutron transport in AN approximation. Part I
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Mund, E.H.; Ravetto, P.
2013-01-01
Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, A N formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2N−1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems
Spectral decomposition in advection-diffusion analysis by finite element methods
International Nuclear Information System (INIS)
Nickell, R.E.; Gartling, D.K.; Strang, G.
1978-01-01
In a recent study of the convergence properties of finite element methods in nonlinear fluid mechanics, an indirect approach was taken. A two-dimensional example with a known exact solution was chosen as the vehicle for the study, and various mesh refinements were tested in an attempt to extract information on the effect of the local Reynolds number. However, more direct approaches are usually preferred. In this study one such direct approach is followed, based upon the spectral decomposition of the solution operator. Spectral decomposition is widely employed as a solution technique for linear structural dynamics problems and can be applied readily to linear, transient heat transfer analysis; in this case, the extension to nonlinear problems is of interest. It was shown previously that spectral techniques were applicable to stiff systems of rate equations, while recent studies of geometrically and materially nonlinear structural dynamics have demonstrated the increased information content of the numerical results. The use of spectral decomposition in nonlinear problems of heat and mass transfer would be expected to yield equally increased flow of information to the analyst, and this information could include a quantitative comparison of various solution strategies, meshes, and element hierarchies
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Efendiev, Yalchin
2011-02-01
In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/Λ*)1/2, where Λ* is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings. © 2010.
A spectral element-FCT method for the compressible Euler equations
International Nuclear Information System (INIS)
Giannakouros, J.; Karniadakis, G.E.
1994-01-01
A new algorithm based on spectral element discretizations and flux-corrected transport concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensions. It is demonstrated through shock-tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. Of particular importance is the fact that dispersion errors are minimal, as show through experiments. From the operational point of view, casting the method in a spectral element formulation provides flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements
Spectral-element Method for 3D Marine Controlled-source EM Modeling
Liu, L.; Yin, C.; Zhang, B., Sr.; Liu, Y.; Qiu, C.; Huang, X.; Zhu, J.
2017-12-01
As one of the predrill reservoir appraisal methods, marine controlled-source EM (MCSEM) has been widely used in mapping oil reservoirs to reduce risk of deep water exploration. With the technical development of MCSEM, the need for improved forward modeling tools has become evident. We introduce in this paper spectral element method (SEM) for 3D MCSEM modeling. It combines the flexibility of finite-element and high accuracy of spectral method. We use Galerkin weighted residual method to discretize the vector Helmholtz equation, where the curl-conforming Gauss-Lobatto-Chebyshev (GLC) polynomials are chosen as vector basis functions. As a kind of high-order complete orthogonal polynomials, the GLC have the characteristic of exponential convergence. This helps derive the matrix elements analytically and improves the modeling accuracy. Numerical 1D models using SEM with different orders show that SEM method delivers accurate results. With increasing SEM orders, the modeling accuracy improves largely. Further we compare our SEM with finite-difference (FD) method for a 3D reservoir model (Figure 1). The results show that SEM method is more effective than FD method. Only when the mesh is fine enough, can FD achieve the same accuracy of SEM. Therefore, to obtain the same precision, SEM greatly reduces the degrees of freedom and cost. Numerical experiments with different models (not shown here) demonstrate that SEM is an efficient and effective tool for MSCEM modeling that has significant advantages over traditional numerical methods.This research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900).
Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method
International Nuclear Information System (INIS)
Zhang Xu; Tan Duowang
2009-01-01
A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)
Direct Numerical Simulation of the Rayleigh−Taylor Instability with the Spectral Element Method
International Nuclear Information System (INIS)
Xu, Zhang; Duo-Wang, Tan
2009-01-01
A novel method is proposed to simulate Rayleigh−Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier–Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh−Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh–Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh−Taylor instabilities of turbulent flows. (fundamental areas of phenomenology (including applications))
Gopalakrishnan, Srinivasan; Roy Mahapatra, Debiprosad
2008-01-01
The use of composites and Functionally Graded Materials (FGMs) in structural applications has increased. FGMs allow the user to design materials for a specified functionality and have many uses in structural engineering. However, the behaviour of these structures under high-impact loading is not well understood. This book is the first to apply the Spectral Finite Element Method (SFEM) to inhomogeneous and anisotropic structures in a unified and systematic manner. It focuses on some of the problems with this media which were previously thought unmanageable. Types of SFEM for regular and damaged 1-D and 2-D waveguides, solution techniques, methods of detecting the presence of damages and their locations, and methods for controlling the wave propagation responses are discussed. Tables, figures and graphs support the theory and case studies are included. This book is of value to senior undergraduates and postgraduates studying in this field, and researchers and practicing engineers in structural integrity.
Eiber, Calvin D; Dokos, Socrates; Lovell, Nigel H; Suaning, Gregg J
2017-05-01
The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.
Energy Technology Data Exchange (ETDEWEB)
Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, 100101 (China); Badal, José, E-mail: badal@unizar.es [Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza (Spain)
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
International Nuclear Information System (INIS)
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-01-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
3D airborne EM modeling based on the spectral-element time-domain (SETD) method
Cao, X.; Yin, C.; Huang, X.; Liu, Y.; Zhang, B., Sr.; Cai, J.; Liu, L.
2017-12-01
In the field of 3D airborne electromagnetic (AEM) modeling, both finite-difference time-domain (FDTD) method and finite-element time-domain (FETD) method have limitations that FDTD method depends too much on the grids and time steps, while FETD requires large number of grids for complex structures. We propose a time-domain spectral-element (SETD) method based on GLL interpolation basis functions for spatial discretization and Backward Euler (BE) technique for time discretization. The spectral-element method is based on a weighted residual technique with polynomials as vector basis functions. It can contribute to an accurate result by increasing the order of polynomials and suppressing spurious solution. BE method is a stable tine discretization technique that has no limitation on time steps and can guarantee a higher accuracy during the iteration process. To minimize the non-zero number of sparse matrix and obtain a diagonal mass matrix, we apply the reduced order integral technique. A direct solver with its speed independent of the condition number is adopted for quickly solving the large-scale sparse linear equations system. To check the accuracy of our SETD algorithm, we compare our results with semi-analytical solutions for a three-layered earth model within the time lapse 10-6-10-2s for different physical meshes and SE orders. The results show that the relative errors for magnetic field B and magnetic induction are both around 3-5%. Further we calculate AEM responses for an AEM system over a 3D earth model in Figure 1. From numerical experiments for both 1D and 3D model, we draw the conclusions that: 1) SETD can deliver an accurate results for both dB/dt and B; 2) increasing SE order improves the modeling accuracy for early to middle time channels when the EM field diffuses fast so the high-order SE can model the detailed variation; 3) at very late time channels, increasing SE order has little improvement on modeling accuracy, but the time interval plays
Using spectral element method to solve variational inequalities with applications in finance
International Nuclear Information System (INIS)
Moradipour, M.; Yousefi, S.A.
2015-01-01
Under the Black–Scholes model, the value of an American option solves a time dependent variational inequality problem (VIP). In this paper, first we discretize the variational inequality of American option in temporal direction by applying the Rannacher time stepping and achieve a sequence of elliptic variational inequalities. Second we discretize the spatial domain of variational inequalities by using spectral element methods with high order Lagrangian polynomials introduced on Gauss–Legendre–Lobatto points. Also by computing integrals by the Gauss–Legendre–Lobatto quadrature rule we derive a sequence of the linear complementarity problems (LCPs) having a positive definite sparse coefficient matrix. To find the unique solutions of the LCPs, we use the projected successive over-relaxation (PSOR) algorithm. Furthermore we present some existence and uniqueness theorems for the variational inequalities and LCPs. Finally, theoretical results are verified on the relevant numerical examples.
International Nuclear Information System (INIS)
Nahavandi, N.; Minuchehr, A.; Zolfaghari, A.; Abbasi, M.
2015-01-01
Highlights: • Powerful hp-SEM refinement approach for P N neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks
Energy Technology Data Exchange (ETDEWEB)
Carella, Alfredo Raul
2012-09-15
Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)
McGill, Matthew J. (Inventor); Scott, Vibart S. (Inventor); Marzouk, Marzouk (Inventor)
2001-01-01
A holographic optical element transforms a spectral distribution of light to image points. The element comprises areas, each of which acts as a separate lens to image the light incident in its area to an image point. Each area contains the recorded hologram of a point source object. The image points can be made to lie in a line in the same focal plane so as to align with a linear array detector. A version of the element has been developed that has concentric equal areas to match the circular fringe pattern of a Fabry-Perot interferometer. The element has high transmission efficiency, and when coupled with high quantum efficiency solid state detectors, provides an efficient photon-collecting detection system. The element may be used as part of the detection system in a direct detection Doppler lidar system or multiple field of view lidar system.
Seismoelectric Effects based on Spectral-Element Method for Subsurface Fluid Characterization
Morency, C.
2017-12-01
Present approaches for subsurface imaging rely predominantly on seismic techniques, which alone do not capture fluid properties and related mechanisms. On the other hand, electromagnetic (EM) measurements add constraints on the fluid phase through electrical conductivity and permeability, but EM signals alone do not offer information of the solid structural properties. In the recent years, there have been many efforts to combine both seismic and EM data for exploration geophysics. The most popular approach is based on joint inversion of seismic and EM data, as decoupled phenomena, missing out the coupled nature of seismic and EM phenomena such as seismoeletric effects. Seismoelectric effects are related to pore fluid movements with respect to the solid grains. By analyzing coupled poroelastic seismic and EM signals, one can capture a pore scale behavior and access both structural and fluid properties.Here, we model the seismoelectric response by solving the governing equations derived by Pride and Garambois (1994), which correspond to Biot's poroelastic wave equations and Maxwell's electromagnetic wave equations coupled electrokinetically. We will show that these coupled wave equations can be numerically implemented by taking advantage of viscoelastic-electromagnetic mathematical equivalences. These equations will be solved using a spectral-element method (SEM). The SEM, in contrast to finite-element methods (FEM) uses high degree Lagrange polynomials. Not only does this allow the technique to handle complex geometries similarly to FEM, but it also retains exponential convergence and accuracy due to the use of high degree polynomials. Finally, we will discuss how this is a first step toward full coupled seismic-EM inversion to improve subsurface fluid characterization. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
A study of flow patterns for staggered cylinders at low Reynolds number by spectral element method
Energy Technology Data Exchange (ETDEWEB)
Hsu, Li-Chieh; Chen, Chien-Lin; Ye, Jian-Zhi [National Yunlin University of Science and Technology, Taiwan (China)
2017-06-15
This study investigates the pattern of flow past two staggered array cylinders using the spectral element method by varying the distance between the cylinders and the angle of incidence (α) at low Reynolds numbers (Re = 100-800). Six flow patterns are identified as Shear layer reattachment (SLR), Induced separation (IS), Vortex impingement (VI), Synchronized vortex shedding (SVS), Vortex pairing and enveloping (VPE), and Vortex pairing splitting and enveloping (VPSE). These flow patterns can be transformed from one to another by changing the distance between the cylinders, the angle of incidence, or Re. SLR, IS and VI flow patterns appear in regimes with small angles of incidence (i.e., α ≤ 30° ) and hold only a single von Karman vortex shedding in a wake with one shedding frequency. SVS, VPE and VPSE flow patterns appear in regimes with large angles of incidence (i.e., 30° ≤ α ≤ 50° ) and present two synchronized von Karman vortices. Quantitative analyses and physical interpretation are also conducted to determine the generation mechanisms of the said flow patterns.
Stability Estimates for h-p Spectral Element Methods for Elliptic Problems
Dutt, Pravir; Tomar, S.K.; Kumar, B.V. Rathish
2002-01-01
In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical mesh. With this mesh we seek a solution which
Dynamic analysis of smart composite beams by using the frequency domain spectral element method
Energy Technology Data Exchange (ETDEWEB)
Park, Il Wook; Lee, Usik [Inha Univ., Incheon (Korea, Republic of)
2012-08-15
To excite or measure the dynamic responses of a laminated composite structure for the active controls of vibrations or noises, wafertype piezoelectric transducers are often bonded on the surface of the composite structure to form a multi layer smart composite structure. Thus, for such smart composite structures, it is very important to develop and use a very reliable mathematical and/or computational model for predicting accurate dynamic characteristics. In this paper, the axial-bending coupled equations of motion and boundary conditions are derived for two layer smart composite beams by using the Hamilton's principle with Lagrange multipliers. The spectral element model is then formulated in the frequency domain by using the variation approach. Through some numerical examples, the extremely high accuracy of the present spectral element model is verified by comparing with the solutions by the conventional finite element model provided in this paper. The effects of the lay up of composite laminates and surface bonded wafer type piezoelectric (PZT) layer on the dynamics and wave characteristics of smart composite beams are investigated. The effective constraint forces at the interface between the base beam and PZT layer are also investigated via Lagrange multipliers.
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.
Karaoǧlu, Haydar; Romanowicz, Barbara
2018-06-01
We present a global upper-mantle shear wave attenuation model that is built through a hybrid full-waveform inversion algorithm applied to long-period waveforms, using the spectral element method for wavefield computations. Our inversion strategy is based on an iterative approach that involves the inversion for successive updates in the attenuation parameter (δ Q^{-1}_μ) and elastic parameters (isotropic velocity VS, and radial anisotropy parameter ξ) through a Gauss-Newton-type optimization scheme that employs envelope- and waveform-type misfit functionals for the two steps, respectively. We also include source and receiver terms in the inversion steps for attenuation structure. We conducted a total of eight iterations (six for attenuation and two for elastic structure), and one inversion for updates to source parameters. The starting model included the elastic part of the relatively high-resolution 3-D whole mantle seismic velocity model, SEMUCB-WM1, which served to account for elastic focusing effects. The data set is a subset of the three-component surface waveform data set, filtered between 400 and 60 s, that contributed to the construction of the whole-mantle tomographic model SEMUCB-WM1. We applied strict selection criteria to this data set for the attenuation iteration steps, and investigated the effect of attenuation crustal structure on the retrieved mantle attenuation structure. While a constant 1-D Qμ model with a constant value of 165 throughout the upper mantle was used as starting model for attenuation inversion, we were able to recover, in depth extent and strength, the high-attenuation zone present in the depth range 80-200 km. The final 3-D model, SEMUCB-UMQ, shows strong correlation with tectonic features down to 200-250 km depth, with low attenuation beneath the cratons, stable parts of continents and regions of old oceanic crust, and high attenuation along mid-ocean ridges and backarcs. Below 250 km, we observe strong attenuation in the
Taneja, Ankur; Higdon, Jonathan
2018-01-01
A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.
Huang, Xin; Yin, Chang-Chun; Cao, Xiao-Yue; Liu, Yun-He; Zhang, Bo; Cai, Jing
2017-09-01
The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell's equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic
International Nuclear Information System (INIS)
Koch, Stephan
2009-01-01
This thesis is concerned with the numerical simulation of electromagnetic fields in the quasi-static approximation which is applicable in many practical cases. Main emphasis is put on higher-order finite element methods. Quasi-static applications can be found, e.g., in accelerator physics in terms of the design of magnets required for beam guidance, in power engineering as well as in high-voltage engineering. Especially during the first design and optimization phase of respective devices, numerical models offer a cheap alternative to the often costly assembly of prototypes. However, large differences in the magnitude of the material parameters and the geometric dimensions as well as in the time-scales of the electromagnetic phenomena involved lead to an unacceptably long simulation time or to an inadequately large memory requirement. Under certain circumstances, the simulation itself and, in turn, the desired design improvement becomes even impossible. In the context of this thesis, two strategies aiming at the extension of the range of application for numerical simulations based on the finite element method are pursued. The first strategy consists in parallelizing existing methods such that the computation can be distributed over several computers or cores of a processor. As a consequence, it becomes feasible to simulate a larger range of devices featuring more degrees of freedom in the numerical model than before. This is illustrated for the calculation of the electromagnetic fields, in particular of the eddy-current losses, inside a superconducting dipole magnet developed at the GSI Helmholtzzentrum fuer Schwerionenforschung as a part of the FAIR project. As the second strategy to improve the efficiency of numerical simulations, a hybrid discretization scheme exploiting certain geometrical symmetries is established. Using this method, a significant reduction of the numerical effort in terms of required degrees of freedom for a given accuracy is achieved. The
Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.
2014-12-01
Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.
Nguyen, Vu-Hieu; Naili, Salah
2012-08-01
This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.
Magnetic modeling of a Linear Synchronous Machine with the spectral element method
Curti, M.; Paulides, J.J.H.; Lomonova, E.
2017-01-01
The field calculus for electrical machines is realized solving subdomain problems. Most often, the latter are solved using either finite element analysis or the semi-analytical solution of a Laplace or Poisson equation obtained by separation of variables. The first option can capture complex
Magnetic modeling of a Linear Synchronous Machine with the spectral element method
Curti, M.; Paulides, J.J.H.; Lomonova, E.
2017-01-01
The field calculus for electrical machines (EMs) is realized solving subdomain problems. Most often, the latter are solved using either finite element analysis (FEA) or the semi-analytical solution of a Laplace or Poisson equation obtained by separation of variables. The first option can capture
Directory of Open Access Journals (Sweden)
Xingjian Dong
2014-02-01
Full Text Available An efficient spectral element (SE with electric potential degrees of freedom (DOF is proposed to investigate the static electromechanical responses of a piezoelectric bimorph for its actuator and sensor functions. A sublayer model based on the piecewise linear approximation for the electric potential is used to describe the nonlinear distribution of electric potential through the thickness of the piezoelectric layers. An equivalent single layer (ESL model based on first-order shear deformation theory (FSDT is used to describe the displacement field. The Legendre orthogonal polynomials of order 5 are used in the element interpolation functions. The validity and the capability of the present SE model for investigation of global and local responses of the piezoelectric bimorph are confirmed by comparing the present solutions with those obtained from coupled 3-D finite element (FE analysis. It is shown that, without introducing any higher-order electric potential assumptions, the current method can accurately describe the distribution of the electric potential across the thickness even for a rather thick bimorph. It is revealed that the effect of electric potential is significant when the bimorph is used as sensor while the effect is insignificant when the bimorph is used as actuator, and therefore, the present study may provide a better understanding of the nonlinear induced electric potential for bimorph sensor and actuator.
Directory of Open Access Journals (Sweden)
Wan-You Li
2014-01-01
Full Text Available A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM and the applicability of the finite element method (FEM, is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.
Wu, Zhijing; Li, Fengming; Zhang, Chuanzeng
2018-05-01
Inspired by the hierarchical structures of butterfly wing surfaces, a new kind of lattice structures with a two-order hierarchical periodicity is proposed and designed, and the band-gap properties are investigated by the spectral element method (SEM). The equations of motion of the whole structure are established considering the macro and micro periodicities of the system. The efficiency of the SEM is exploited in the modeling process and validated by comparing the results with that of the finite element method (FEM). Based on the highly accurate results in the frequency domain, the dynamic behaviors of the proposed two-order hierarchical structures are analyzed. An original and interesting finding is the existence of the distinct macro and micro stop-bands in the given frequency domain. The mechanisms for these two types of band-gaps are also explored. Finally, the relations between the hierarchical periodicities and the different types of the stop-bands are investigated by analyzing the parametrical influences.
Ying, Yingzi; Bean, Christopher J.
2014-05-01
Ocean-generated microseisms are faint Earth tremors associated with the interaction between ocean water waves and the solid Earth. The microseism noise recorded as low frequency ground vibrations by seismometers contains significant information about the Earth's interior and the sea states. In this work, we first aim to investigate the forward propagation of microseisms in a deep-ocean environment. We employ a 3D North-East Atlantic geological model and simulate wave propagation in a coupled fluid-solid domain, using a spectral-element method. The aim is to investigate the effects of the continental shelf on microseism wave propagation. A second goal of this work is to perform noise simulation to calculate synthetic ensemble averaged cross-correlations of microseism noise signals with time reversal method. The algorithm can relieve computational cost by avoiding time stacking and get cross-correlations between the designated master station and all the remaining slave stations, at one time. The origins of microseisms are non-uniform, so we also test the effect of simulated noise source distribution on the determined cross-correlations.
Sudarmaji; Rudianto, Indra; Eka Nurcahya, Budi
2018-04-01
A strong tectonic earthquake with a magnitude of 5.9 Richter scale has been occurred in Yogyakarta and Central Java on May 26, 2006. The earthquake has caused severe damage in Yogyakarta and the southern part of Central Java, Indonesia. The understanding of seismic response of earthquake among ground shaking and the level of building damage is important. We present numerical modeling of 3D seismic wave propagation around Yogyakarta and the southern part of Central Java using spectral-element method on MPI-GPU (Graphics Processing Unit) computer cluster to observe its seismic response due to the earthquake. The homogeneous 3D realistic model is generated with detailed topography surface. The influences of free surface topography and layer discontinuity of the 3D model among the seismic response are observed. The seismic wave field is discretized using spectral-element method. The spectral-element method is solved on a mesh of hexahedral elements that is adapted to the free surface topography and the internal discontinuity of the model. To increase the data processing capabilities, the simulation is performed on a GPU cluster with implementation of MPI (Message Passing Interface).
Ryzhenkov, V.; Ivashchenko, V.; Vinuesa, R.; Mullyadzhanov, R.
2016-10-01
We use the open-source code nek5000 to assess the accuracy of high-order spectral element large-eddy simulations (LES) of a turbulent channel flow depending on the spatial resolution compared to the direct numerical simulation (DNS). The Reynolds number Re = 6800 is considered based on the bulk velocity and half-width of the channel. The filtered governing equations are closed with the dynamic Smagorinsky model for subgrid stresses and heat flux. The results show very good agreement between LES and DNS for time-averaged velocity and temperature profiles and their fluctuations. Even the coarse LES grid which contains around 30 times less points than the DNS one provided predictions of the friction velocity within 2.0% accuracy interval.
International Nuclear Information System (INIS)
FEHL, DAVID LEE; BIGGS, F.; CHANDLER, GORDON A.; STYGAR, WILLIAM A.
2000-01-01
The generalized method of Backus and Gilbert (BG) is described and applied to the inverse problem of obtaining spectra from a 5-channel, filtered array of x-ray detectors (XRD's). This diagnostic is routinely fielded on the Z facility at Sandia National Laboratories to study soft x-ray photons ((le)2300 eV), emitted by high density Z-pinch plasmas. The BG method defines spectral resolution limits on the system of response functions that are in good agreement with the unfold method currently in use. The resolution so defined is independent of the source spectrum. For noise-free, simulated data the BG approximating function is also in reasonable agreement with the source spectrum (150 eV black-body) and the unfold. This function may be used as an initial trial function for iterative methods or a regularization model
He, Yue-Jing; Hung, Wei-Chih; Syu, Cheng-Jyun
2017-12-01
The finite-element method (FEM) and eigenmode expansion method (EEM) were adopted to analyze the guided modes and spectrum of phase-shift fiber Bragg grating at five phase-shift degrees (including zero, 1/4π, 1/2π, 3/4π, and π). In previous studies on optical fiber grating, conventional coupled-mode theory was crucial. This theory contains abstruse knowledge about physics and complex computational processes, and thus is challenging for users. Therefore, a numerical simulation method was coupled with a simple and rigorous design procedure to help beginners and users to overcome difficulty in entering the field; in addition, graphical simulation results were presented. To reduce the difference between the simulated context and the actual context, a perfectly matched layer and perfectly reflecting boundary were added to the FEM and the EEM. When the FEM was used for grid cutting, the object meshing method and the boundary meshing method proposed in this study were used to effectively enhance computational accuracy and substantially reduce the time required for simulation. In summary, users can use the simulation results in this study to easily and rapidly design an optical fiber communication system and optical sensors with spectral characteristics.
Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean
2017-04-01
We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3-D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral-element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.
Spectral element simulation of ultrafiltration
DEFF Research Database (Denmark)
Hansen, M.; Barker, Vincent A.; Hassager, Ole
1998-01-01
for the unknowns at the mesh nodes. This system is solved via a technique combining the penalty method, Newton-Raphson iterations, static condensation, and a solver for banded linear systems. In addition, a smoothing technique is used to handle a singularity in the boundary condition at the membrane...
Numerical and spectral investigations of novel infinite elements
International Nuclear Information System (INIS)
Barai, P.; Harari, I.; Barbonet, P.E.
1998-01-01
Exterior problems of time-harmonic acoustics are addressed by a novel infinite element formulation, defined on a bounded computational domain. For two-dimensional configurations with circular interfaces, the infinite element results match Quell both analytical values and those obtained from. other methods like DtN. Along 1uith the numerical performance of this formulation, of considerable interest are its complex-valued eigenvalues. Hence, a spectral analysis of the present scheme is also performed here, using various infinite elements
Pitton, Giuseppe; Heltai, Luca
2018-01-01
Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential equations, via the Isogeometric Analysis (IGA) paradigm. However, spectral accuracy in IGA is limited to relatively small NURBS patch degrees (roughly p
International Nuclear Information System (INIS)
Lawson, K.; Peacock, N.; Gianella, R.
1998-12-01
The derivation of elemental components of radiated powers and impurity concentrations in bulk tokamak plasmas is complex, often requiring a full description of the impurity transport. A novel, empirical method, the Line Intensity Normalization Technique (LINT) has been developed on the JET (Joint European Torus) tokamak to provide routine information about the impurity content of the plasma and elemental components of radiated power (P rad ). The technique employs a few VUV and XUV resonance line intensities to represent the intrinsic impurity elements in the plasma. From a data base comprising these spectral features, the total bolometric measurement of the radiated power and the Z eff measured by visible spectroscopy, separate elemental components of P rad and Z eff are derived. The method, which converts local spectroscopic signals into global plasma parameters, has the advantage of simplicity, allowing large numbers of pulses to be processed, and, in many operational modes of JET, is found to be both reliable and accurate. It relies on normalizing the line intensities to the absolute calibration of the bolometers and visible spectrometers, using coefficients independent of density and temperature. Accuracies of the order of ± 15% can be achieved for the elemental P rad components of the most significant impurities and the impurity concentrations can be determined to within ±30%. Trace elements can be monitored, although with reduced accuracy. The present paper deals with limiter discharges, which have been the main application to date. As a check on the technique and to demonstrate the value of the LINT results, they have been applied to the transport modelling of intrinsic impurities carried out with the SANCO transport code, which uses atomic data from ADAS. The simulations provide independent confirmation of the concentrations empirically derived using the LINT technique. For this analysis, the simple case of the L-mode regime is considered, the chosen
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...
Symplectic discretization for spectral element solution of Maxwell's equations
International Nuclear Information System (INIS)
Zhao Yanmin; Dai Guidong; Tang Yifa; Liu Qinghuo
2009-01-01
Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.
Nagaso, Masaru; Komatitsch, Dimitri; Moysan, Joseph; Lhuillier, Christian
2018-01-01
ASTRID project, French sodium cooled nuclear reactor of 4th generation, is under development at the moment by Alternative Energies and Atomic Energy Commission (CEA). In this project, development of monitoring techniques for a nuclear reactor during operation are identified as a measure issue for enlarging the plant safety. Use of ultrasonic measurement techniques (e.g. thermometry, visualization of internal objects) are regarded as powerful inspection tools of sodium cooled fast reactors (SFR) including ASTRID due to opacity of liquid sodium. In side of a sodium cooling circuit, heterogeneity of medium occurs because of complex flow state especially in its operation and then the effects of this heterogeneity on an acoustic propagation is not negligible. Thus, it is necessary to carry out verification experiments for developments of component technologies, while such kind of experiments using liquid sodium may be relatively large-scale experiments. This is why numerical simulation methods are essential for preceding real experiments or filling up the limited number of experimental results. Though various numerical methods have been applied for a wave propagation in liquid sodium, we still do not have a method for verifying on three-dimensional heterogeneity. Moreover, in side of a reactor core being a complex acousto-elastic coupled region, it has also been difficult to simulate such problems with conventional methods. The objective of this study is to solve these 2 points by applying three-dimensional spectral element method. In this paper, our initial results on three-dimensional simulation study on heterogeneous medium (the first point) are shown. For heterogeneity of liquid sodium to be considered, four-dimensional temperature field (three spatial and one temporal dimension) calculated by computational fluid dynamics (CFD) with Large-Eddy Simulation was applied instead of using conventional method (i.e. Gaussian Random field). This three-dimensional numerical
International Nuclear Information System (INIS)
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
Żak, A.; Krawczuk, M.; Palacz, M.; Doliński, Ł.; Waszkowiak, W.
2017-11-01
In this work results of numerical simulations and experimental measurements related to the high frequency dynamics of an aluminium Timoshenko periodic beam are presented. It was assumed by the authors that the source of beam structural periodicity comes from periodical alterations to its geometry due to the presence of appropriately arranged drill-holes. As a consequence of these alterations dynamic characteristics of the beam are changed revealing a set of frequency band gaps. The presence of the frequency band gaps can help in the design process of effective sound filters or sound barriers that can selectively attenuate propagating wave signals of certain frequency contents. In order to achieve this a combination of three numerical techniques were employed by the authors. They comprise the application of the Time-domain Spectral Finite Element Method in the case of analysis of finite and semi-infinite computational domains, damage modelling in the case of analysis of drill-hole influence, as well as the Bloch reduction in the case of analysis of periodic computational domains. As an experimental technique the Scanning Laser Doppler Vibrometry was chosen. A combined application of all these numerical and experimental techniques appears as new for this purpose and not reported in the literature available.
Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.
2016-01-01
Recent progress towards developing a new computational capability for accurate and efficient high-fidelity direct numerical simulation (DNS) and large-eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy- stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in a computationally efficient manner on a modern high performance computer architecture. An inflow turbulence generation procedure based on a linear forcing approach has been incorporated in this framework and DNS conducted to study the effect of inflow turbulence on the suction- side separation bubble in low-pressure turbine (LPT) cascades. The T106 series of airfoil cascades in both lightly (T106A) and highly loaded (T106C) configurations at exit isentropic Reynolds numbers of 60,000 and 80,000, respectively, are considered. The numerical simulations are performed using 8th-order accurate spatial and 4th-order accurate temporal discretization. The changes in separation bubble topology due to elevated inflow turbulence is captured by the present method and the physical mechanisms leading to the changes are explained. The present results are in good agreement with prior numerical simulations but some expected discrepancies with the experimental data for the T106C case are noted and discussed.
Chebyshev and Fourier spectral methods
Boyd, John P
2001-01-01
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
Lee, D.; Palha, A.; Gerritsma, M.
2018-01-01
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in
A mass and energy conserving spectral element atmospheric dynamical core on the cubed-sphere grid
International Nuclear Information System (INIS)
Taylor, M A; Edwards, J; Thomas, S; Nair, R
2007-01-01
We present results from a conservative formulation of the spectral element method applied to global atmospheric circulation modeling. Exact local conservation of both mass and energy is obtained via a new compatible formulation of the spectral element method. Compatibility insures that the key integral property of the divergence and gradient operators required to show conservation also hold in discrete form. The spectral element method is used on a cubed-sphere grid to discretize the horizontal directions on the sphere. It can be coupled to any conservative vertical/radial discretization. The accuracy and conservation properties of the method are illustrated using a baroclinic instability test case
Bessel smoothing filter for spectral-element mesh
Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.
2017-06-01
Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the
Spectral shift reactor control method
International Nuclear Information System (INIS)
Impink, A.J. Jr.
1981-01-01
A method of operating a nuclear reactor having a core and coolant displacer elements arranged in the core wherein is established a reator coolant temperature set point at which it is desired to operate said reactor and first reactor coolant temperature band limits are provided within which said set point is located and it is desired to operate said reactor charactrized in that said reactor coolant displacer elements are moved relative to the reactor core for adjusting the volume of reactor coolant in said core as said reactor coolant temperature approaches said first band limits thereby to maintain said reactor coolant temperature near said set point and within said first band limits
Spectral shift reactor control method
International Nuclear Information System (INIS)
Impink, A.J.
1982-01-01
A method of operating a nuclear reactor having a core and coolant displacer elements arranged in the core where there is established a reactor coolant temperature set point at which it is desired to operate the reactor and first reactor coolant temperature band limits within which the set point is characterized. The reactor coolant displacer elements are moved relative to the reactor core for adjusting the volume of reactor coolant in the core as the reactor coolant temperature approaches the first band limits to maintain the reactor coolant temperature near the set point and within the first band limits. The reactivity charges associated with movement of respective coolant displacer element clusters is calculated and compared with a calculated derived reactivity charge in order to select the cluster to be moved. (author)
Spectral methods. Fundamentals in single domains
International Nuclear Information System (INIS)
Canuto, C.
2006-01-01
Since the publication of ''Spectral Methods in Fluid Dynamics'' 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded. (orig.)
Stabilization of numerical interchange in spectral-element magnetohydrodynamics
Sovinec, C. R.
2016-08-01
Auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. The projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code Sovinec et al. [17], provided that the projections introduce numerical dissipation.
Spectral Methods in Numerical Plasma Simulation
DEFF Research Database (Denmark)
Coutsias, E.A.; Hansen, F.R.; Huld, T.
1989-01-01
An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded...
Directory of Open Access Journals (Sweden)
M.H.R. Ghoreishy
2008-02-01
Full Text Available This research work is devoted to the footprint analysis of a steel-belted radial tyre (185/65R14 under vertical static load using finite element method. Two models have been developed in which in the first model the tread patterns were replaced by simple ribs while the second model was consisted of details of the tread blocks. Linear elastic and hyper elastic (Arruda-Boyce material models were selected to describe the mechanical behavior of the reinforcing and rubbery parts, respectively. The above two finite element models of the tyre were analyzed under inflation pressure and vertical static loads. The second model (with detailed tread patterns was analyzed with and without friction effect between tread and contact surfaces. In every stage of the analysis, the results were compared with the experimental data to confirm the accuracy and applicability of the model. Results showed that neglecting the tread pattern design not only reduces the computational cost and effort but also the differences between computed deformations do not show significant changes. However, more complicated variables such as shape and area of the footprint zone and contact pressure are affected considerably by the finite element model selected for the tread blocks. In addition, inclusion of friction even in static state changes these variables significantly.
The spectral cell method in nonlinear earthquake modeling
Giraldo, Daniel; Restrepo, Doriam
2017-12-01
This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.
PIXE-quantified AXSIA: Elemental mapping by multivariate spectral analysis
International Nuclear Information System (INIS)
Doyle, B.L.; Provencio, P.P.; Kotula, P.G.; Antolak, A.J.; Ryan, C.G.; Campbell, J.L.; Barrett, K.
2006-01-01
Automated, nonbiased, multivariate statistical analysis techniques are useful for converting very large amounts of data into a smaller, more manageable number of chemical components (spectra and images) that are needed to describe the measurement. We report the first use of the multivariate spectral analysis program AXSIA (Automated eXpert Spectral Image Analysis) developed at Sandia National Laboratories to quantitatively analyze micro-PIXE data maps. AXSIA implements a multivariate curve resolution technique that reduces the spectral image data sets into a limited number of physically realizable and easily interpretable components (including both spectra and images). We show that the principal component spectra can be further analyzed using conventional PIXE programs to convert the weighting images into quantitative concentration maps. A common elemental data set has been analyzed using three different PIXE analysis codes and the results compared to the cases when each of these codes is used to separately analyze the associated AXSIA principal component spectral data. We find that these comparisons are in good quantitative agreement with each other
Spectral methods in numerical plasma simulation
International Nuclear Information System (INIS)
Coutsias, E.A.; Hansen, F.R.; Huld, T.; Knorr, G.; Lynov, J.P.
1989-01-01
An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed. (orig.)
Logarithmic compression methods for spectral data
Dunham, Mark E.
2003-01-01
A method is provided for logarithmic compression, transmission, and expansion of spectral data. A log Gabor transformation is made of incoming time series data to output spectral phase and logarithmic magnitude values. The output phase and logarithmic magnitude values are compressed by selecting only magnitude values above a selected threshold and corresponding phase values to transmit compressed phase and logarithmic magnitude values. A reverse log Gabor transformation is then performed on the transmitted phase and logarithmic magnitude values to output transmitted time series data to a user.
Spectral response of multi-element silicon detectors
Energy Technology Data Exchange (ETDEWEB)
Ludewigt, B.A.; Rossington, C.S.; Chapman, K. [Univ. of California, Berkeley, CA (United States)
1997-04-01
Multi-element silicon strip detectors, in conjunction with integrated circuit pulse-processing electronics, offer an attractive alternative to conventional lithium-drifted silicon Si(Li) and high purity germanium detectors (HPGe) for high count rate, low noise synchrotron x-ray fluorescence applications. One of the major differences between the segmented Si detectors and the commercially available single-element Si(Li) or HPGe detectors is that hundreds of elements can be fabricated on a single Si substrate using standard silicon processing technologies. The segmentation of the detector substrate into many small elements results in very low noise performance at or near, room temperature, and the count rate of the detector is increased many-fold due to the multiplication in the total number of detectors. Traditionally, a single channel of detector with electronics can handle {approximately}100 kHz count rates while maintaining good energy resolution; the segmented detectors can operate at greater than MHz count rates merely due to the multiplication in the number of channels. One of the most critical aspects in the development of the segmented detectors is characterizing the charge sharing and charge loss that occur between the individual detector strips, and determining how these affect the spectral response of the detectors.
Stochastic Spectral and Conjugate Descent Methods
Kovalev, Dmitry
2018-02-11
The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.
Stochastic Spectral and Conjugate Descent Methods
Kovalev, Dmitry; Gorbunov, Eduard; Gasanov, Elnur; Richtarik, Peter
2018-01-01
The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.
Evolutionary Computing Methods for Spectral Retrieval
Terrile, Richard; Fink, Wolfgang; Huntsberger, Terrance; Lee, Seugwon; Tisdale, Edwin; VonAllmen, Paul; Tinetti, Geivanna
2009-01-01
A methodology for processing spectral images to retrieve information on underlying physical, chemical, and/or biological phenomena is based on evolutionary and related computational methods implemented in software. In a typical case, the solution (the information that one seeks to retrieve) consists of parameters of a mathematical model that represents one or more of the phenomena of interest. The methodology was developed for the initial purpose of retrieving the desired information from spectral image data acquired by remote-sensing instruments aimed at planets (including the Earth). Examples of information desired in such applications include trace gas concentrations, temperature profiles, surface types, day/night fractions, cloud/aerosol fractions, seasons, and viewing angles. The methodology is also potentially useful for retrieving information on chemical and/or biological hazards in terrestrial settings. In this methodology, one utilizes an iterative process that minimizes a fitness function indicative of the degree of dissimilarity between observed and synthetic spectral and angular data. The evolutionary computing methods that lie at the heart of this process yield a population of solutions (sets of the desired parameters) within an accuracy represented by a fitness-function value specified by the user. The evolutionary computing methods (ECM) used in this methodology are Genetic Algorithms and Simulated Annealing, both of which are well-established optimization techniques and have also been described in previous NASA Tech Briefs articles. These are embedded in a conceptual framework, represented in the architecture of the implementing software, that enables automatic retrieval of spectral and angular data and analysis of the retrieved solutions for uniqueness.
The spectral element approach for the solution of neutron transport problems
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Ravetto, P.; Mund, E.H.
2011-01-01
In this paper a possible application of the Spectral Element Method to neutron transport problems is presented. The basic features of the numerical scheme on the one-dimensional diffusion equation are illustrated. Then, the AN model for neutron transport is introduced, and the basic steps for the construction of a bi-dimensional solver are described. The AN equations are chosen for their structure, involving a system of coupled elliptic-type equations. Some calculations are carried out on typical benchmark problems and results are compared with the Finite Element Method, in order to evaluate their performances. (author)
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2003-01-01
We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation
Spectral Analysis Methods of Social Networks
Directory of Open Access Journals (Sweden)
P. G. Klyucharev
2017-01-01
Full Text Available Online social networks (such as Facebook, Twitter, VKontakte, etc. being an important channel for disseminating information are often used to arrange an impact on the social consciousness for various purposes - from advertising products or services to the full-scale information war thereby making them to be a very relevant object of research. The paper reviewed the analysis methods of social networks (primarily, online, based on the spectral theory of graphs. Such methods use the spectrum of the social graph, i.e. a set of eigenvalues of its adjacency matrix, and also the eigenvectors of the adjacency matrix.Described measures of centrality (in particular, centrality based on the eigenvector and PageRank, which reflect a degree of impact one or another user of the social network has. A very popular PageRank measure uses, as a measure of centrality, the graph vertices, the final probabilities of the Markov chain, whose matrix of transition probabilities is calculated on the basis of the adjacency matrix of the social graph. The vector of final probabilities is an eigenvector of the matrix of transition probabilities.Presented a method of dividing the graph vertices into two groups. It is based on maximizing the network modularity by computing the eigenvector of the modularity matrix.Considered a method for detecting bots based on the non-randomness measure of a graph to be computed using the spectral coordinates of vertices - sets of eigenvector components of the adjacency matrix of a social graph.In general, there are a number of algorithms to analyse social networks based on the spectral theory of graphs. These algorithms show very good results, but their disadvantage is the relatively high (albeit polynomial computational complexity for large graphs.At the same time it is obvious that the practical application capacity of the spectral graph theory methods is still underestimated, and it may be used as a basis to develop new methods.The work
Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems
Zuchowski, Loïc; Brun, Michael; De Martin, Florent
2018-05-01
The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.
Energy Technology Data Exchange (ETDEWEB)
Fischer, P.F. [Brown Univ., Providence, RI (United States)
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
Energy Technology Data Exchange (ETDEWEB)
Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.
2014-01-01
This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.
Spectral and spectral-frequency methods of investigating atmosphereless bodies of the Solar system
International Nuclear Information System (INIS)
Busarev, Vladimir V; Prokof'eva-Mikhailovskaya, Valentina V; Bochkov, Valerii V
2007-01-01
A method of reflectance spectrophotometry of atmosphereless bodies of the Solar system, its specificity, and the means of eliminating basic spectral noise are considered. As a development, joining the method of reflectance spectrophotometry with the frequency analysis of observational data series is proposed. The combined spectral-frequency method allows identification of formations with distinctive spectral features, and estimations of their sizes and distribution on the surface of atmospherelss celestial bodies. As applied to investigations of asteroids 21 Lutetia and 4 Vesta, the spectral frequency method has given us the possibility of obtaining fundamentally new information about minor planets. (instruments and methods of investigation)
Numerical Methods for Stochastic Computations A Spectral Method Approach
Xiu, Dongbin
2010-01-01
The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC meth
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Element-specific spectral imaging of multiple contrast agents: a phantom study
Panta, R. K.; Bell, S. T.; Healy, J. L.; Aamir, R.; Bateman, C. J.; Moghiseh, M.; Butler, A. P. H.; Anderson, N. G.
2018-02-01
This work demonstrates the feasibility of simultaneous discrimination of multiple contrast agents based on their element-specific and energy-dependent X-ray attenuation properties using a pre-clinical photon-counting spectral CT. We used a photon-counting based pre-clinical spectral CT scanner with four energy thresholds to measure the X-ray attenuation properties of various concentrations of iodine (9, 18 and 36 mg/ml), gadolinium (2, 4 and 8 mg/ml) and gold (2, 4 and 8 mg/ml) based contrast agents, calcium chloride (140 and 280 mg/ml) and water. We evaluated the spectral imaging performances of different energy threshold schemes between 25 to 82 keV at 118 kVp, based on K-factor and signal-to-noise ratio and ranked them. K-factor was defined as the X-ray attenuation in the K-edge containing energy range divided by the X-ray attenuation in the preceding energy range, expressed as a percentage. We evaluated the effectiveness of the optimised energy selection to discriminate all three contrast agents in a phantom of 33 mm diameter. A photon-counting spectral CT using four energy thresholds of 27, 33, 49 and 81 keV at 118 kVp simultaneously discriminated three contrast agents based on iodine, gadolinium and gold at various concentrations using their K-edge and energy-dependent X-ray attenuation features in a single scan. A ranking method to evaluate spectral imaging performance enabled energy thresholds to be optimised to discriminate iodine, gadolinium and gold contrast agents in a single spectral CT scan. Simultaneous discrimination of multiple contrast agents in a single scan is likely to open up new possibilities of improving the accuracy of disease diagnosis by simultaneously imaging multiple bio-markers each labelled with a nano-contrast agent.
Chebyshev super spectral viscosity method for water hammer analysis
Directory of Open Access Journals (Sweden)
Hongyu Chen
2013-09-01
Full Text Available In this paper, a new fast and efficient algorithm, Chebyshev super spectral viscosity (SSV method, is introduced to solve the water hammer equations. Compared with standard spectral method, the method's advantage essentially consists in adding a super spectral viscosity to the equations for the high wave numbers of the numerical solution. It can stabilize the numerical oscillation (Gibbs phenomenon and improve the computational efficiency while discontinuities appear in the solution. Results obtained from the Chebyshev super spectral viscosity method exhibit greater consistency with conventional water hammer calculations. It shows that this new numerical method offers an alternative way to investigate the behavior of the water hammer in propellant pipelines.
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
Carpenter, Mark H.
2016-01-04
Nonlinearly stable finite element methods of arbitrary type and order, are currently unavailable for discretizations of the compressible Navier-Stokes equations. Summation-by-parts (SBP) entropy stability analysis provides a means of constructing nonlinearly stable discrete operators of arbitrary order, but is currently limited to simple element types. Herein, recent progress is reported, on developing entropy-stable (SS) discontinuous spectral collocation formulations for hexahedral elements. Two complementary efforts are discussed. The first effort generalizes previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort extends previous work on entropy stability to include p-refinement at nonconforming interfaces. A generalization of existing entropy stability theory is required to accommodate the nuances of fully multidimensional SBP operators. The entropy stability of the compressible Euler equations on nonconforming interfaces is demonstrated using the newly developed LG operators and multidimensional interface interpolation operators. Preliminary studies suggest design order accuracy at nonconforming interfaces.
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
Lee, D.; Palha, A.; Gerritsma, M.
2018-03-01
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.
Orthogonal feature selection method. [For preprocessing of man spectral data
Energy Technology Data Exchange (ETDEWEB)
Kowalski, B R [Univ. of Washington, Seattle; Bender, C F
1976-01-01
A new method of preprocessing spectral data for extraction of molecular structural information is desired. This SELECT method generates orthogonal features that are important for classification purposes and that also retain their identity to the original measurements. A brief introduction to chemical pattern recognition is presented. A brief description of the method and an application to mass spectral data analysis follow. (BLM)
Computational Performance of a Parallelized Three-Dimensional High-Order Spectral Element Toolbox
Bosshard, Christoph; Bouffanais, Roland; Clémençon, Christian; Deville, Michel O.; Fiétier, Nicolas; Gruber, Ralf; Kehtari, Sohrab; Keller, Vincent; Latt, Jonas
In this paper, a comprehensive performance review of an MPI-based high-order three-dimensional spectral element method C++ toolbox is presented. The focus is put on the performance evaluation of several aspects with a particular emphasis on the parallel efficiency. The performance evaluation is analyzed with help of a time prediction model based on a parameterization of the application and the hardware resources. A tailor-made CFD computation benchmark case is introduced and used to carry out this review, stressing the particular interest for clusters with up to 8192 cores. Some problems in the parallel implementation have been detected and corrected. The theoretical complexities with respect to the number of elements, to the polynomial degree, and to communication needs are correctly reproduced. It is concluded that this type of code has a nearly perfect speed up on machines with thousands of cores, and is ready to make the step to next-generation petaflop machines.
Rahimi Dalkhani, Amin; Javaherian, Abdolrahim; Mahdavi Basir, Hadi
2018-04-01
Wave propagation modeling as a vital tool in seismology can be done via several different numerical methods among them are finite-difference, finite-element, and spectral-element methods (FDM, FEM and SEM). Some advanced applications in seismic exploration benefit the frequency domain modeling. Regarding flexibility in complex geological models and dealing with the free surface boundary condition, we studied the frequency domain acoustic wave equation using FEM and SEM. The results demonstrated that the frequency domain FEM and SEM have a good accuracy and numerical efficiency with the second order interpolation polynomials. Furthermore, we developed the second order Clayton and Engquist absorbing boundary condition (CE-ABC2) and compared it with the perfectly matched layer (PML) for the frequency domain FEM and SEM. In spite of PML method, CE-ABC2 does not add any additional computational cost to the modeling except assembling boundary matrices. As a result, considering CE-ABC2 is more efficient than PML for the frequency domain acoustic wave propagation modeling especially when computational cost is high and high-level absorbing performance is unnecessary.
Digital spectral analysis parametric, non-parametric and advanced methods
Castanié, Francis
2013-01-01
Digital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature.The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models.An entire chapter is devoted to the non-parametric methods most widely used in industry.High resolution methods a
Use of new spectral analysis methods in gamma spectra deconvolution
International Nuclear Information System (INIS)
Pinault, J.L.
1991-01-01
A general deconvolution method applicable to X and gamma ray spectrometry is proposed. Using new spectral analysis methods, it is applied to an actual case: the accurate on-line analysis of three elements (Ca, Si, Fe) in a cement plant using neutron capture gamma rays. Neutrons are provided by a low activity (5 μg) 252 Cf source; the detector is a BGO 3 in.x8 in. scintillator. The principle of the methods rests on the Fourier transform of the spectrum. The search for peaks and determination of peak areas are worked out in the Fourier representation, which enables separation of background and peaks and very efficiently discriminates peaks, or elements represented by several peaks. First the spectrum is transformed so that in the new representation the full width at half maximum (FWHM) is independent of energy. Thus, the spectrum is arranged symmetrically and transformed into the Fourier representation. The latter is multiplied by a function in order to transform original Gaussian into Lorentzian peaks. An autoregressive filter is calculated, leading to a characteristic polynomial whose complex roots represent both the location and the width of each peak, provided that the absolute value is lower than unit. The amplitude of each component (the area of each peak or the sum of areas of peaks characterizing an element) is fitted by the weighted least squares method, taking into account that errors in spectra are independent and follow a Poisson law. Very accurate results are obtained, which would be hard to achieve by other methods. The DECO FORTRAN code has been developed for compatible PC microcomputers. Some features of the code are given. (orig.)
The use of the spectral method within the fast adaptive composite grid method
Energy Technology Data Exchange (ETDEWEB)
McKay, S.M.
1994-12-31
The use of efficient algorithms for the solution of partial differential equations has been sought for many years. The fast adaptive composite grid (FAC) method combines an efficient algorithm with high accuracy to obtain low cost solutions to partial differential equations. The FAC method achieves fast solution by combining solutions on different grids with varying discretizations and using multigrid like techniques to find fast solution. Recently, the continuous FAC (CFAC) method has been developed which utilizes an analytic solution within a subdomain to iterate to a solution of the problem. This has been shown to achieve excellent results when the analytic solution can be found. The CFAC method will be extended to allow solvers which construct a function for the solution, e.g., spectral and finite element methods. In this discussion, the spectral methods will be used to provide a fast, accurate solution to the partial differential equation. As spectral methods are more accurate than finite difference methods, the ensuing accuracy from this hybrid method outside of the subdomain will be investigated.
Methods for deconvoluting and interpreting complex gamma- and x-ray spectral regions
International Nuclear Information System (INIS)
Gunnink, R.
1983-06-01
Germanium and silicon detectors are now widely used for the detection and measurement of x and gamma radiation. However, some analysis situations and spectral regions have heretofore been too complex to deconvolute and interpret by techniques in general use. One example is the L x-ray spectrum of an element taken with a Ge or Si detector. This paper describes some new tools and methods that were developed to analyze complex spectral regions; they are illustrated with examples
Energy Technology Data Exchange (ETDEWEB)
Koch, Stephan
2009-03-30
This thesis is concerned with the numerical simulation of electromagnetic fields in the quasi-static approximation which is applicable in many practical cases. Main emphasis is put on higher-order finite element methods. Quasi-static applications can be found, e.g., in accelerator physics in terms of the design of magnets required for beam guidance, in power engineering as well as in high-voltage engineering. Especially during the first design and optimization phase of respective devices, numerical models offer a cheap alternative to the often costly assembly of prototypes. However, large differences in the magnitude of the material parameters and the geometric dimensions as well as in the time-scales of the electromagnetic phenomena involved lead to an unacceptably long simulation time or to an inadequately large memory requirement. Under certain circumstances, the simulation itself and, in turn, the desired design improvement becomes even impossible. In the context of this thesis, two strategies aiming at the extension of the range of application for numerical simulations based on the finite element method are pursued. The first strategy consists in parallelizing existing methods such that the computation can be distributed over several computers or cores of a processor. As a consequence, it becomes feasible to simulate a larger range of devices featuring more degrees of freedom in the numerical model than before. This is illustrated for the calculation of the electromagnetic fields, in particular of the eddy-current losses, inside a superconducting dipole magnet developed at the GSI Helmholtzzentrum fuer Schwerionenforschung as a part of the FAIR project. As the second strategy to improve the efficiency of numerical simulations, a hybrid discretization scheme exploiting certain geometrical symmetries is established. Using this method, a significant reduction of the numerical effort in terms of required degrees of freedom for a given accuracy is achieved. The
International Nuclear Information System (INIS)
Skerovic, V; Zarubica, V; Aleksic, M; Zekovic, L; Belca, I
2010-01-01
Realization of the scale of spectral responsivity of the detectors in the Directorate of Measures and Precious Metals (DMDM) is based on silicon detectors traceable to LNE-INM. In order to realize the unit of spectral irradiance in the laboratory for photometry and radiometry of the Bureau of Measures and Precious Metals, the new method based on the calibration of the spectroradiometer by comparison with standard detector has been established. The development of the method included realization of the System of Spectral Comparisons (SSC), together with the detector spectral responsivity calibrations by means of a primary spectrophotometric system. The linearity testing and stray light analysis were preformed to characterize the spectroradiometer. Measurement of aperture diameter and calibration of transimpedance amplifier were part of the overall experiment. In this paper, the developed method is presented and measurement results with the associated measurement uncertainty budget are shown.
Energy Technology Data Exchange (ETDEWEB)
Skerovic, V; Zarubica, V; Aleksic, M [Directorate of measures and precious metals, Optical radiation Metrology department, Mike Alasa 14, 11000 Belgrade (Serbia); Zekovic, L; Belca, I, E-mail: vladanskerovic@dmdm.r [Faculty of Physics, Department for Applied physics and metrology, Studentski trg 12-16, 11000 Belgrade (Serbia)
2010-10-15
Realization of the scale of spectral responsivity of the detectors in the Directorate of Measures and Precious Metals (DMDM) is based on silicon detectors traceable to LNE-INM. In order to realize the unit of spectral irradiance in the laboratory for photometry and radiometry of the Bureau of Measures and Precious Metals, the new method based on the calibration of the spectroradiometer by comparison with standard detector has been established. The development of the method included realization of the System of Spectral Comparisons (SSC), together with the detector spectral responsivity calibrations by means of a primary spectrophotometric system. The linearity testing and stray light analysis were preformed to characterize the spectroradiometer. Measurement of aperture diameter and calibration of transimpedance amplifier were part of the overall experiment. In this paper, the developed method is presented and measurement results with the associated measurement uncertainty budget are shown.
The spectral volume method as applied to transport problems
International Nuclear Information System (INIS)
McClarren, Ryan G.
2011-01-01
We present a new spatial discretization for transport problems: the spectral volume method. This method, rst developed by Wang for computational fluid dynamics, divides each computational cell into several sub-cells and enforces particle balance on each of these sub-cells. Also, these sub-cells are used to build a polynomial reconstruction in the cell. The idea of dividing cells into many cells is a generalization of the simple corner balance and other similar schemes. The spectral volume method preserves particle conservation and preserves the asymptotic diffusion limit. We present results from the method on two transport problems in slab geometry using discrete ordinates and second through sixth order spectral volume schemes. The numerical results demonstrate the accuracy and preservation of the diffusion limit of the spectral volume method. Future work will explore possible bene ts of the scheme for high-performance computing and for resolving diffusive boundary layers. (author)
Nguyen, Vu-Hieu; Naili, Salah
2013-01-01
This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace-Fourier transform, the vibroacoustic problem may be transformed into the frequency-wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.
Jafari, Azadeh; Deville, Michel O.; Fiétier, Nicolas
2008-09-01
This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation.
Performance of spectral fitting methods for vegetation fluorescence quantification
Meroni, M.; Busetto, D.; Colombo, R.; Guanter, L.; Moreno, J.; Verhoef, W.
2010-01-01
The Fraunhofer Line Discriminator (FLD) principle has long been considered as the reference method to quantify solar-induced chlorophyll fluorescence (F) from passive remote sensing measurements. Recently, alternative retrieval algorithms based on the spectral fitting of hyperspectral radiance
Spectral Methods for Immunization of Large Networks
Directory of Open Access Journals (Sweden)
Muhammad Ahmad
2017-11-01
Full Text Available Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbour nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constraint that are immunized (vaccinated, screened, filtered so as the remaining graph is less prone to the epidemic. It is known that the problem is, in all practical models, computationally intractable even for moderate sized graphs. In this paper we employ ideas from spectral graph theory to define relevance and importance of nodes. Using novel graph theoretic techniques, we then design an efficient approximation algorithm to immunize the graph. Theoretical guarantees on the running time of our algorithm show that it is more efficient than any other known solution in the literature. We test the performance of our algorithm on several real world graphs. Experiments show that our algorithm scales well for large graphs and outperforms state of the art algorithms both in quality (containment of epidemic and efficiency (runtime and space complexity.
Discrete elements method of neutron transport
International Nuclear Information System (INIS)
Mathews, K.A.
1988-01-01
In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution
A divisive spectral method for network community detection
International Nuclear Information System (INIS)
Cheng, Jianjun; Li, Longjie; Yao, Yukai; Chen, Xiaoyun; Leng, Mingwei; Lu, Weiguo
2016-01-01
Community detection is a fundamental problem in the domain of complex network analysis. It has received great attention, and many community detection methods have been proposed in the last decade. In this paper, we propose a divisive spectral method for identifying community structures from networks which utilizes a sparsification operation to pre-process the networks first, and then uses a repeated bisection spectral algorithm to partition the networks into communities. The sparsification operation makes the community boundaries clearer and sharper, so that the repeated spectral bisection algorithm extract high-quality community structures accurately from the sparsified networks. Experiments show that the combination of network sparsification and a spectral bisection algorithm is highly successful, the proposed method is more effective in detecting community structures from networks than the others. (paper: interdisciplinary statistical mechanics)
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Structural modeling techniques by finite element method
International Nuclear Information System (INIS)
Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong
1991-01-01
This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.
Chebyshev super spectral viscosity method for a fluidized bed model
International Nuclear Information System (INIS)
Sarra, Scott A.
2003-01-01
A Chebyshev super spectral viscosity method and operator splitting are used to solve a hyperbolic system of conservation laws with a source term modeling a fluidized bed. The fluidized bed displays a slugging behavior which corresponds to shocks in the solution. A modified Gegenbauer postprocessing procedure is used to obtain a solution which is free of oscillations caused by the Gibbs-Wilbraham phenomenon in the spectral viscosity solution. Conservation is maintained by working with unphysical negative particle concentrations
A Spectral Conjugate Gradient Method for Unconstrained Optimization
International Nuclear Information System (INIS)
Birgin, E. G.; Martinez, J. M.
2001-01-01
A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak-Ribiere and the Fletcher-Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented
Spectral method and its high performance implementation
Wu, Zedong
2014-01-01
We have presented a new method that can be dispersion free and unconditionally stable. Thus the computational cost and memory requirement will be reduced a lot. Based on this feature, we have implemented this algorithm on GPU based CUDA for the anisotropic Reverse time migration. There is almost no communication between CPU and GPU. For the prestack wavefield extrapolation, it can combine all the shots together to migration. However, it requires to solve a bigger dimensional problem and more meory which can\\'t fit into one GPU cards. In this situation, we implement it based on domain decomposition method and MPI for distributed memory system.
Analysis of spectral methods for the homogeneous Boltzmann equation
Filbet, Francis
2011-04-01
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.
Analysis of spectral methods for the homogeneous Boltzmann equation
Filbet, Francis; Mouhot, Clé ment
2011-01-01
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.
Spectral element model for 2-D electrostatic fields in a linear synchronous motor
van Beek, T.A.; Curti, M.; Jansen, J.W.; Gysen, B.L.J.; Paulides, J.J.H.; Lomonova, E.A.
2017-01-01
This paper presents a fast and accurate 2-D spectral element model for analyzing electric field distributions in linear synchronous motors. The electric field distribution is derived using the electric scalar potential for static cases. The spatial potential and electric field distributions obtained
Spectral methods for quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Szehr, Oleg
2014-05-08
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods for quantum Markov chains
International Nuclear Information System (INIS)
Szehr, Oleg
2014-01-01
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods in quantum field theory
International Nuclear Information System (INIS)
Graham, Noah; Quandt, Markus; Weigel, Herbert
2009-01-01
This concise text introduces techniques from quantum mechanics, especially scattering theory, to compute the effects of an external background on a quantum field in general, and on the properties of the quantum vacuum in particular. This approach can be succesfully used in an increasingly large number of situations, ranging from the study of solitons in field theory and cosmology to the determination of Casimir forces in nano-technology. The method introduced and applied in this book is shown to give an unambiguous connection to perturbation theory, implementing standard renormalization conditions even for non-perturbative backgrounds. It both gives new theoretical insights, for example illuminating longstanding questions regarding Casimir stresses, and also provides an efficient analytic and numerical tool well suited to practical calculations. Last but not least, it elucidates in a concrete context many of the subtleties of quantum field theory, such as divergences, regularization and renormalization, by connecting them to more familiar results in quantum mechanics. While addressed primarily at young researchers entering the field and nonspecialist researchers with backgrounds in theoretical and mathematical physics, introductory chapters on the theoretical aspects of the method make the book self-contained and thus suitable for advanced graduate students. (orig.)
[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.
Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam
Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa
2017-08-01
In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.
Method of lightening radiation darkened optical elements
International Nuclear Information System (INIS)
Reich, F.R.; Schwankoff, A.R.
1980-01-01
A method of lightening a radiation-darkened optical element in which visible optical energy or electromagnetic radiation having a wavelength in the range of from about 2000 to about 20,000 angstroms is directed into the radiation-darkened optical element; the method may be used to lighten radiation-darkened optical element in-situ during the use of the optical element to transmit data by electronically separating the optical energy from the optical output by frequency filtering, data cooling, or interlacing the optic energy between data intervals
Spectral radiative property control method based on filling solution
International Nuclear Information System (INIS)
Jiao, Y.; Liu, L.H.; Hsu, P.-F.
2014-01-01
Controlling thermal radiation by tailoring spectral properties of microstructure is a promising method, can be applied in many industrial systems and have been widely researched recently. Among various property tailoring schemes, geometry design of microstructures is a commonly used method. However, the existing radiation property tailoring is limited by adjustability of processed microstructures. In other words, the spectral radiative properties of microscale structures are not possible to change after the gratings are fabricated. In this paper, we propose a method that adjusts the grating spectral properties by means of injecting filling solution, which could modify the thermal radiation in a fabricated microstructure. Therefore, this method overcomes the limitation mentioned above. Both mercury and water are adopted as the filling solution in this study. Aluminum and silver are selected as the grating materials to investigate the generality and limitation of this control method. The rigorous coupled-wave analysis is used to investigate the spectral radiative properties of these filling solution grating structures. A magnetic polaritons mechanism identification method is proposed based on LC circuit model principle. It is found that this control method could be used by different grating materials. Different filling solutions would enable the high absorption peak to move to longer or shorter wavelength band. The results show that the filling solution grating structures are promising for active control of spectral radiative properties. -- Highlights: • A filling solution grating structure is designed to adjust spectral radiative properties. • The mechanism of radiative property control is studied for engineering utilization. • Different grating materials are studied to find multi-functions for grating
A conjugate gradient method for the spectral partitioning of graphs
Kruyt, Nicolaas P.
1997-01-01
The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and
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.
International Nuclear Information System (INIS)
Bauer, M.; Weitkamp, C.
1977-01-01
The strongest spectra lines of the 85 stable chemical elements have been compiled and plotted along with lines from other elements that may interfere in applications like spectroscopic multielement analysis. For each line a wavelength range of +- 0.25 A.U. around the line of interest has been considered. The tables contain the wavelength, intensity and assignment to an ionization state of the emitting atom, the plots visualize the lines with a doppler broadening corresponding to 8,000 K. (orig.) [de
Spectral methods for time dependent partial differential equations
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
Fuel elements handling device and method
International Nuclear Information System (INIS)
Jabsen, F.S.
1976-01-01
This invention relates to nuclear equipment and more particularly to methods and apparatus for the non-destructive inspection, manipulation, disassembly and assembly of reactor fuel elements and the like. (author)
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
Review on Finite Element Method * ERHUNMWUN, ID ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and ... residual procedures, are examples of the direct approach ... The paper centred on the "stiffness and deflection of ...
Spectral anomaly methods for aerial detection using KUT nuisance rejection
International Nuclear Information System (INIS)
Detwiler, R.S.; Pfund, D.M.; Myjak, M.J.; Kulisek, J.A.; Seifert, C.E.
2015-01-01
This work discusses the application and optimization of a spectral anomaly method for the real-time detection of gamma radiation sources from an aerial helicopter platform. Aerial detection presents several key challenges over ground-based detection. For one, larger and more rapid background fluctuations are typical due to higher speeds, larger field of view, and geographically induced background changes. As well, the possible large altitude or stand-off distance variations cause significant steps in background count rate as well as spectral changes due to increased gamma-ray scatter with detection at higher altitudes. The work here details the adaptation and optimization of the PNNL-developed algorithm Nuisance-Rejecting Spectral Comparison Ratios for Anomaly Detection (NSCRAD), a spectral anomaly method previously developed for ground-based applications, for an aerial platform. The algorithm has been optimized for two multi-detector systems; a NaI(Tl)-detector-based system and a CsI detector array. The optimization here details the adaptation of the spectral windows for a particular set of target sources to aerial detection and the tailoring for the specific detectors. As well, the methodology and results for background rejection methods optimized for the aerial gamma-ray detection using Potassium, Uranium and Thorium (KUT) nuisance rejection are shown. Results indicate that use of a realistic KUT nuisance rejection may eliminate metric rises due to background magnitude and spectral steps encountered in aerial detection due to altitude changes and geographically induced steps such as at land–water interfaces
A modified sliding spectral method and its application to COSMIC ...
Indian Academy of Sciences (India)
A modified sliding spectral method and its application to COSMIC radio occultation data 1751. The window length with 300 samples is supposed to provide a reasonable resolution. In a spherically symmetric atmosphere, the refractive index n as a function of tangent radius r0 can be computed from the bending angle α as.
Deconvolution of EPR spectral lines with an approximate method
International Nuclear Information System (INIS)
Jimenez D, H.; Cabral P, A.
1990-10-01
A recently reported approximation expression to deconvolution Lorentzian-Gaussian spectral lines. with small Gaussian contribution, is applied to study an EPR line shape. The potassium-ammonium solution line reported in the literature by other authors was used and the results are compared with those obtained by employing a precise method. (Author)
Spectral calculations in magnetohydrodynamics using the Jacobi-Davidson method
Belien, A. J. C.; van der Holst, B.; Nool, M.; van der Ploeg, A.; Goedbloed, J. P.
2001-01-01
For the solution of the generalized complex non-Hermitian eigenvalue problems Ax = lambda Bx occurring in the spectral study of linearized resistive magnetohydrodynamics (MHD) a new parallel solver based on the recently developed Jacobi-Davidson [SIAM J. Matrix Anal. Appl. 17 (1996) 401] method has
[An improved low spectral distortion PCA fusion method].
Peng, Shi; Zhang, Ai-Wu; Li, Han-Lun; Hu, Shao-Xing; Meng, Xian-Gang; Sun, Wei-Dong
2013-10-01
Aiming at the spectral distortion produced in PCA fusion process, the present paper proposes an improved low spectral distortion PCA fusion method. This method uses NCUT (normalized cut) image segmentation algorithm to make a complex hyperspectral remote sensing image into multiple sub-images for increasing the separability of samples, which can weaken the spectral distortions of traditional PCA fusion; Pixels similarity weighting matrix and masks were produced by using graph theory and clustering theory. These masks are used to cut the hyperspectral image and high-resolution image into some sub-region objects. All corresponding sub-region objects between the hyperspectral image and high-resolution image are fused by using PCA method, and all sub-regional integration results are spliced together to produce a new image. In the experiment, Hyperion hyperspectral data and Rapid Eye data were used. And the experiment result shows that the proposed method has the same ability to enhance spatial resolution and greater ability to improve spectral fidelity performance.
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Convergence of spectral methods for nonlinear conservation laws. Final report
International Nuclear Information System (INIS)
Tadmor, E.
1987-08-01
The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows
A three-dimensional spectral element model for the solution of the hydrostatic primitive equations
Iskandarani, M; Levin, J C
2003-01-01
We present a spectral element model to solve the hydrostatic primitive equations governing large-scale geophysical flows. The highlights of this new model include unstructured grids, dual h-p paths to convergence, and good scalability characteristics on present day parallel computers including Beowulf-class systems. The behavior of the model is assessed on three process-oriented test problems involving wave propagation, gravitational adjustment, and nonlinear flow rectification, respectively. The first of these test problems is a study of the convergence properties of the model when simulating the linear propagation of baroclinic Kelvin waves. The second is an intercomparison of spectral element and finite-difference model solutions to the adjustment of a density front in a straight channel. Finally, the third problem considers the comparison of model results to measurements obtained from a laboratory simulation of flow around a submarine canyon. The aforementioned tests demonstrate the good performance of th...
PIXE - a new method for elemental analysis
International Nuclear Information System (INIS)
Johansson, S.A.E.
1983-01-01
With elemental analysis we mean the determination of which chemical elements are present in a sample and of their concentration. This is an old and important problem in chemistry. The earliest methods were purely chemical and many such methods are still used. However, various methods based on physical principles have gradually become more and more important. One such method is neutron activation. When the sample is bombarded with neutrons it becomes radioactive and the various radioactive isotopes produced can be identified by the radiation they emit. From the measured intensity of the radiation one can calculate how much of a certain element that is present in the sample. Another possibility is to study the light emitted when the sample is excited in various ways. A spectroscopic investigation of the light can identify the chemical elements and allows also a determination of their concentration in the sample. In the same way, if a sample can be brought to emit X-rays, this radiation is also characteristic for the elements present and can be used to determine the elemental concentration. One such X-ray method which has been developed recently is PIXE. The name is an acronym for Particle Induced X-ray Emission and indicates the principle of the method. Particles in this context means heavy, charged particles such as protons and a-particles of rather high energy. Hence, in PIXE-analysis the sample is irradiated in the beam of an accelerator and the emitted X-rays are studied. (author)
Recent advances in boundary element methods
Manolis, GD
2009-01-01
Addresses the needs of the computational mechanics research community in terms of information on boundary integral equation-based methods and techniques applied to a variety of fields. This book collects both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the Mesh Reduction Methods (MRM).
Introducing the Boundary Element Method with MATLAB
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Finite element method - theory and applications
International Nuclear Information System (INIS)
Baset, S.
1992-01-01
This paper summarizes the mathematical basis of the finite element method. Attention is drawn to the natural development of the method from an engineering analysis tool into a general numerical analysis tool. A particular application to the stress analysis of rubber materials is presented. Special advantages and issues associated with the method are mentioned. (author). 4 refs., 3 figs
Spectral interference of zirconium on 24 analyte elements using CCD based ICP-AES technique
International Nuclear Information System (INIS)
Adya, V.C.; Sengupta, Arijit; Godbole, S.V.
2014-01-01
In the present studies, the spectral interference of zirconium on different analytical lines of 24 critical analytes using CCD based ICP-AES technique is described. Suitable analytical lines for zirconium were identified along with their detection limits. The sensitivity and the detection limits of analytical channels for different elements in presence of Zr matrix were calculated. Subsequently analytical lines with least interference from Zr and better detection limits were selected for their determinations. (author)
Near-fault earthquake ground motion prediction by a high-performance spectral element numerical code
International Nuclear Information System (INIS)
Paolucci, Roberto; Stupazzini, Marco
2008-01-01
Near-fault effects have been widely recognised to produce specific features of earthquake ground motion, that cannot be reliably predicted by 1D seismic wave propagation modelling, used as a standard in engineering applications. These features may have a relevant impact on the structural response, especially in the nonlinear range, that is hard to predict and to be put in a design format, due to the scarcity of significant earthquake records and of reliable numerical simulations. In this contribution a pilot study is presented for the evaluation of seismic ground-motions in the near-fault region, based on a high-performance numerical code for 3D seismic wave propagation analyses, including the seismic fault, the wave propagation path and the near-surface geological or topographical irregularity. For this purpose, the software package GeoELSE is adopted, based on the spectral element method. The set-up of the numerical benchmark of 3D ground motion simulation in the valley of Grenoble (French Alps) is chosen to study the effect of the complex interaction between basin geometry and radiation mechanism on the variability of earthquake ground motion
Investigation of rare elements by electrochemical methods
International Nuclear Information System (INIS)
Zarinskij, V.A.
1988-01-01
The use of electrochemical methods for the study of complexing, separation of rare element mixtures, their preparation in lower oxidation states, and also for the development of highly sensitive methods of the element determination, is considered in the review. Voltammetric methods of Pt, Au, Re determination are considered, as well as Re preparation in oxidation states +5, +3 by electrolytic methods. The possibility to use electrodialysis methods for purification of insoluble compounds of rare earths (RE) from impurities, and for separation of Re and Mo with simultaneous purification of Re from K and other elements is shown. The application of high-frequency conductometry to analytic chemistry and to the study of Th, In, RE complexing and kinetics of the reactions is considered
Discrete elements method of neutral particle transport
International Nuclear Information System (INIS)
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method
INTEGRATED FUSION METHOD FOR MULTIPLE TEMPORAL-SPATIAL-SPECTRAL IMAGES
Directory of Open Access Journals (Sweden)
H. Shen
2012-08-01
Full Text Available Data fusion techniques have been widely researched and applied in remote sensing field. In this paper, an integrated fusion method for remotely sensed images is presented. Differently from the existed methods, the proposed method has the performance to integrate the complementary information in multiple temporal-spatial-spectral images. In order to represent and process the images in one unified framework, two general image observation models are firstly presented, and then the maximum a posteriori (MAP framework is used to set up the fusion model. The gradient descent method is employed to solve the fused image. The efficacy of the proposed method is validated using simulated images.
Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models
MURILLO, Carol Andrea; THOREL, Luc; CAICEDO, Bernardo
2009-01-01
The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge test...
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Rudianto, Indra; Sudarmaji
2018-04-01
We present an implementation of the spectral-element method for simulation of two-dimensional elastic wave propagation in fully heterogeneous media. We have incorporated most of realistic geological features in the model, including surface topography, curved layer interfaces, and 2-D wave-speed heterogeneity. To accommodate such complexity, we use an unstructured quadrilateral meshing technique. Simulation was performed on a GPU cluster, which consists of 24 core processors Intel Xeon CPU and 4 NVIDIA Quadro graphics cards using CUDA and MPI implementation. We speed up the computation by a factor of about 5 compared to MPI only, and by a factor of about 40 compared to Serial implementation.
Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
Directory of Open Access Journals (Sweden)
Hassan Saberi Nik
2014-01-01
Full Text Available We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.
New mixed finite-element methods
International Nuclear Information System (INIS)
Franca, L.P.
1987-01-01
New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates
Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye
2018-04-01
The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
High order spectral volume and spectral difference methods on unstructured grids
Kannan, Ravishekar
The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed
The finite element response matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-02-01
A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt
Analysing flow structures around a blade using spectral/hp method and HPIV
International Nuclear Information System (INIS)
Stoevesandt, Bernhard; Steigerwald, Christian; Shishkin, Andrei; Wagner, Claus; Peinke, Joachim
2007-01-01
A still difficult, yet pressing task for blade manufacturers and turbine producers is the correct prediction of the effects of turbulent winds on the blade. Reynolds Averaged Numerical Simulations (RANS) are a limited tool for calculating the effects. For large eddy simulations (LES) boundary layer calculation are still difficult therefore the spectral element method seems to be an approach to improve numerical calculations of flow separation. The flow field around an fx79-w151a airfoil has been calculated by the spectral element code NεκTαrusing a direct numerical simulation (DNS) solver. In a first step a laminar inflow on the airfoil at angle of attack of α = 12 0 and a Reynolds number of Re= 33000 was simulated using the 2D Version of the code. The flow pattern was compared to measurements using holographic particle induced velocimetry (HPIV) in a wind tunnel
International Conference on Spectral and High-Order Methods
Dumont, Ney; Hesthaven, Jan
2017-01-01
This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
Efendiev, Yalchin R.
2015-08-01
We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.
A finite element method for neutron transport
International Nuclear Information System (INIS)
Ackroyd, R.T.
1983-01-01
A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour. (author)
Boundary element method for modelling creep behaviour
International Nuclear Information System (INIS)
Zarina Masood; Shah Nor Basri; Abdel Majid Hamouda; Prithvi Raj Arora
2002-01-01
A two dimensional initial strain direct boundary element method is proposed to numerically model the creep behaviour. The boundary of the body is discretized into quadratic element and the domain into quadratic quadrilaterals. The variables are also assumed to have a quadratic variation over the elements. The boundary integral equation is solved for each boundary node and assembled into a matrix. This matrix is solved by Gauss elimination with partial pivoting to obtain the variables on the boundary and in the interior. Due to the time-dependent nature of creep, the solution has to be derived over increments of time. Automatic time incrementation technique and backward Euler method for updating the variables are implemented to assure stability and accuracy of results. A flowchart of the solution strategy is also presented. (Author)
Loading method of core constituting elements
International Nuclear Information System (INIS)
Kasai, Shigeo
1976-01-01
Purpose: To provide a remote-controlled replacing method for core constituting elements in a liquid-metal cooling fast breeder, wherein particularly, the core constituting elements are prevented from being loaded on the core position other than as designated. Constitution: The method comprises a first step which determines a position of a suitable neutron shielding body in order to measure a reference level of complete insertion of the core constituting elements, a second step which inserts a gripper for a fuel exchanger, a third step which decides stroke dimensions of the complete insertion, and a fourth step which discriminates the core constituting elements to begin handling of fuel rods. The method further comprises a fifth step which determines a loading position of fuel rod, and a sixth step which inserts and loads fuel rods into the core. The method still further comprises a seventh step which compares and judges the dimension of loading stroke and the dimension of complete inserting stroke so that when coincided, loading is completed, and when not coincided, loading is not completed and then the cycle of the fourth step is repeated. (Kawakami, Y.)
Image segmentation with a finite element method
DEFF Research Database (Denmark)
Bourdin, Blaise
1999-01-01
regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
A spatial discretization of the MHD equations based on the finite volume - spectral method
International Nuclear Information System (INIS)
Miyoshi, Takahiro
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
Spectral analysis of mammographic images using a multitaper method
International Nuclear Information System (INIS)
Wu Gang; Mainprize, James G.; Yaffe, Martin J.
2012-01-01
Purpose: Power spectral analysis in radiographic images is conventionally performed using a windowed overlapping averaging periodogram. This study describes an alternative approach using a multitaper technique and compares its performance with that of the standard method. This tool will be valuable in power spectrum estimation of images, whose content deviates significantly from uniform white noise. The performance of the multitaper approach will be evaluated in terms of spectral stability, variance reduction, bias, and frequency precision. The ultimate goal is the development of a useful tool for image quality assurance. Methods: A multitaper approach uses successive data windows of increasing order. This mitigates spectral leakage allowing one to calculate a reduced-variance power spectrum. The multitaper approach will be compared with the conventional power spectrum method in several typical situations, including the noise power spectra (NPS) measurements of simulated projection images of a uniform phantom, NPS measurement of real detector images of a uniform phantom for two clinical digital mammography systems, and the estimation of the anatomic noise in mammographic images (simulated images and clinical mammograms). Results: Examination of spectrum variance versus frequency resolution and bias indicates that the multitaper approach is superior to the conventional single taper methods in the prevention of spectrum leakage and variance reduction. More than four times finer frequency precision can be achieved with equivalent or less variance and bias. Conclusions: Without any shortening of the image data length, the bias is smaller and the frequency resolution is higher with the multitaper method, and the need to compromise in the choice of regions of interest size to balance between the reduction of variance and the loss of frequency resolution is largely eliminated.
Crack Propagation by Finite Element Method
Directory of Open Access Journals (Sweden)
Luiz Carlos H. Ricardo
2018-01-01
Full Text Available Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FDandE SAE Keyhole Specimen Test Load Histories by finite element analysis. To understand the crack propagation processes under variable amplitude loading, retardation effects are observed
A Novel Polygonal Finite Element Method: Virtual Node Method
Tang, X. H.; Zheng, C.; Zhang, J. H.
2010-05-01
Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin; Yang, Dinghui; Dong, Xingpeng; Liu, Qiancheng; Zheng, Yongchang
2017-01-01
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint
Solution of the Schroedinger equation by a spectral method
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.; Steiger, A.
1982-01-01
A new computational method for determining the eigenvalues and eigenfunctions of the Schroedinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schroedinger equation. The method requires the computation of a correlation function from a numerical solution psi(r, t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of psi(r, t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon--Heiles potential
Zhang, Lei; Cao, Ling; Zhao, Laishi; Algeo, Thomas J.; Chen, Zhong-Qiang; Li, Zhihong; Lv, Zhengyi; Wang, Xiangdong
2017-08-01
Conodont apatite has long been used in paleoenvironmental studies, often with minimal evaluation of the influence of diagenesis on measured elemental and isotopic signals. In this study, we evaluate diagenetic influences on conodonts using an integrated set of analytical techniques. A total of 92 points in 19 coniform conodonts from Ordovician marine units of South China were analyzed by micro-laser Raman spectroscopy (M-LRS), laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), high-resolution X-ray microdiffraction (HXRD), and secondary ion mass spectrometry (SIMS). Each conodont element was analyzed along its full length, including the albid crown, hyaline crown, and basal body, in either a whole specimen (i.e., reflecting the composition of its outer layer) or a split specimen (i.e., reflecting the composition of its interior). In the conodonts of this study, the outer surfaces consist of hydroxyfluorapatite and the interiors of strontian hydroxyfluorapatite. Ionic substitutions resulted in characteristic Raman spectral shifts in the position (SS1) and width (SS2) of the ν1-PO43- stretching band. Although multiple elements were enriched (Sr2+, Mg2+) and depleted (Fe3+, Mn2+, Ca2+) during diagenesis, geochemical modeling constraints and known Raman spectral patterns suggest that Sr uptake was the dominant influence on diagenetic redshifts of SS1. All study specimens show lower SS2 values than modern bioapatite and synthetic apatite, suggesting that band width decreases with time in ancient bioapatite, possibly through an annealing process that produces larger, more uniform crystal domains. Most specimens consist mainly of amorphous or poorly crystalline apatite, which is inferred to represent the original microstructure of conodonts. In a subset of specimens, some tissues (especially albid crown) exhibit an increased degree of crystallinity developed through aggrading neomorphism. However, no systematic relationship was observed between
Chen, Xiao-Li; Guo, Wen-Zhong; Xue, Xu-Zhang; Wang, Li-Chun; Li, Liang; Chen, Fei
2013-08-01
Mineral elements absorption and content of Lactuca sativa under different spectral component conditions were studied by ICP-AES technology. The results showed that: (1) For Lactuca sativa, the average proportion for Ca : Mg : K : Na : P was 5.5 : 2.5 : 2.3 : 1.5 : 1.0, the average proportion for Fe : Mn : Zn : Cu : B was 25.9 : 5.9 : 2.8 : 1.1 : 1.0; (2) The absorptions for K, P, Ca, Mg and B are the largest under the LED treatment R/B = 1 : 2.75, red light from fluorescent lamps and LED can both promote the absorptions of Fe and Cu; (3)The LED treatments exhibiting relatively higher content of mineral elements are R/B = 1 : 2.75 and R/W = 1 : 1 while higher dry matter accumulations are R/B = 1 : 2.75 and B/W = 1 : 1.
Mixed Element Formulation for the Finite Element-Boundary Integral Method
National Research Council Canada - National Science Library
Meese, J; Kempel, L. C; Schneider, S. W
2006-01-01
A mixed element approach using right hexahedral elements and right prism elements for the finite element-boundary integral method is presented and discussed for the study of planar cavity-backed antennas...
High temperature spectral emissivity measurement using integral blackbody method
Pan, Yijie; Dong, Wei; Lin, Hong; Yuan, Zundong; Bloembergen, Pieter
2016-10-01
Spectral emissivity is a critical material's thermos-physical property for heat design and radiation thermometry. A prototype instrument based upon an integral blackbody method was developed to measure material's spectral emissivity above 1000 °. The system was implemented with an optimized commercial variable-high-temperature blackbody, a high speed linear actuator, a linear pyrometer, and an in-house designed synchronization circuit. A sample was placed in a crucible at the bottom of the blackbody furnace, by which the sample and the tube formed a simulated blackbody which had an effective total emissivity greater than 0.985. During the measurement, the sample was pushed to the end opening of the tube by a graphite rod which was actuated through a pneumatic cylinder. A linear pyrometer was used to monitor the brightness temperature of the sample surface through the measurement. The corresponding opto-converted voltage signal was fed and recorded by a digital multi-meter. A physical model was proposed to numerically evaluate the temperature drop along the process. Tube was discretized as several isothermal cylindrical rings, and the temperature profile of the tube was measurement. View factors between sample and rings were calculated and updated along the whole pushing process. The actual surface temperature of the sample at the end opening was obtained. Taking advantages of the above measured voltage profile and the calculated true temperature, spectral emissivity under this temperature point was calculated.
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
Nonconforming hp spectral element methods for elliptic problems
Indian Academy of Sciences (India)
Geometrical mesh; stability estimate; least-squares solution; preconditioners; condition numbers; exponential accuracy. ... Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur 208 016, India; Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India ...
Effective beam method for element concentrations
International Nuclear Information System (INIS)
Tolhurst, Thomas; Barbi, Mauricio; Tokaryk, Tim
2015-01-01
A method to evaluate chemical element concentrations in samples by generating an effective polychromatic beam using as initial input real monochromatic beam data is presented. There is a great diversity of research being conducted at synchrotron facilities around the world and a diverse set of beamlines to accommodate this research. Time is a precious commodity at synchrotron facilities; therefore, methods that can maximize the time spent collecting data are of value. At the same time the incident radiation spectrum, necessary for some research, may not be known on a given beamline. A preliminary presentation of a method applicable to X-ray fluorescence spectrocopic analyses that overcomes the lack of information about the incident beam spectrum that addresses both of these concerns is given here. The method is equally applicable for other X-ray sources so long as local conditions are considered. It relies on replacing the polychromatic spectrum in a standard fundamental parameters analysis with a set of effective monochromatic photon beams. A beam is associated with each element and can be described by an analytical function allowing extension to elements not included in the necessary calibration measurement(s)
Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models
Murillo, Carol Andrea; Thorel, Luc; Caicedo, Bernardo
2009-06-01
The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge testing is a relevant method to characterize VS near the surface.
Smith, J. A.; Peter, D. B.; Tromp, J.; Komatitsch, D.; Lefebvre, M. P.
2015-12-01
We present both SPECFEM3D_Cartesian and SPECFEM3D_GLOBE open-source codes, representing high-performance numerical wave solvers simulating seismic wave propagation for local-, regional-, and global-scale application. These codes are suitable for both forward propagation in complex media and tomographic imaging. Both solvers compute highly accurate seismic wave fields using the continuous Galerkin spectral-element method on unstructured meshes. Lateral variations in compressional- and shear-wave speeds, density, as well as 3D attenuation Q models, topography and fluid-solid coupling are all readily included in both codes. For global simulations, effects due to rotation, ellipticity, the oceans, 3D crustal models, and self-gravitation are additionally included. Both packages provide forward and adjoint functionality suitable for adjoint tomography on high-performance computing architectures. We highlight the most recent release of the global version which includes improved performance, simultaneous MPI runs, OpenCL and CUDA support via an automatic source-to-source transformation library (BOAST), parallel I/O readers and writers for databases using ADIOS and seismograms using the recently developed Adaptable Seismic Data Format (ASDF) with built-in provenance. This makes our spectral-element solvers current state-of-the-art, open-source community codes for high-performance seismic wave propagation on arbitrarily complex 3D models. Together with these solvers, we provide full-waveform inversion tools to image the Earth's interior at unprecedented resolution.
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2004-01-01
We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least
Terahertz spectral unmixing based method for identifying gastric cancer
Cao, Yuqi; Huang, Pingjie; Li, Xian; Ge, Weiting; Hou, Dibo; Zhang, Guangxin
2018-02-01
At present, many researchers are exploring biological tissue inspection using terahertz time-domain spectroscopy (THz-TDS) techniques. In this study, based on a modified hard modeling factor analysis method, terahertz spectral unmixing was applied to investigate the relationships between the absorption spectra in THz-TDS and certain biomarkers of gastric cancer in order to systematically identify gastric cancer. A probability distribution and box plot were used to extract the distinctive peaks that indicate carcinogenesis, and the corresponding weight distributions were used to discriminate the tissue types. The results of this work indicate that terahertz techniques have the potential to detect different levels of cancer, including benign tumors and polyps.
A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation
Terrana, S.; Vilotte, J. P.; Guillot, L.
2018-04-01
We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm
Crack Propagation by Finite Element Method
H. Ricardo, Luiz Carlos
2017-01-01
Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FD&E SAE Keyh...
Generalization of mixed multiscale finite element methods with applications
Energy Technology Data Exchange (ETDEWEB)
Lee, C S [Texas A & M Univ., College Station, TX (United States)
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
The finite element response Matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-01-01
A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed
Boundary element methods for electrical engineers
POLJAK, D
2005-01-01
In the last couple of decades the Boundary Element Method (BEM) has become a well-established technique that is widely used for solving various problems in electrical engineering and electromagnetics. Although there are many excellent research papers published in the relevant literature that describe various BEM applications in electrical engineering and electromagnetics, there has been a lack of suitable textbooks and monographs on the subject. This book presents BEM in a simple fashion in order to help the beginner to understand the very basic principles of the method. It initially derives B
Boundary element method for internal axisymmetric flow
Directory of Open Access Journals (Sweden)
Gokhman Alexander
1999-01-01
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
The blade element momentum (BEM) method
DEFF Research Database (Denmark)
Branlard, Emmanuel Simon Pierre
2017-01-01
The current chapter presents the blade element momentum (BEM) method. The BEM method for a steady uniform inflow is presented in a first section. Some of the ad-hoc corrections that are usually added to the algorithm are discussed in a second section. An exception is made to the tip-loss correction...... which is introduced early in the algorithm formulation for practical reasons. The ad-hoc corrections presented are: the tip-loss correction, the high-thrust correction (momentum breakdown) and the correction for wake rotation. The formulation of an unsteady BEM code is given in a third section...
A finite element method for neutron transport
International Nuclear Information System (INIS)
Ackroyd, R.T.
1978-01-01
A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)
Chacó n Rebollo, Tomá s; Dia, Ben Mansour
2015-01-01
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
Chacón Rebollo, Tomás
2015-03-01
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
Apparatus and method for assembling fuel elements
International Nuclear Information System (INIS)
Arya, S.P.
1978-01-01
A nuclear fuel element assembling method and apparatus is preferably operable under programmed control unit to receive fuel rods from storage, arrange them into axially aligned stacks of closely monitored length, and transfer the stacks of fuel rods to a loading device for insertion into longitudinal passages in the fuel elements. In order to handle large numbers of one or more classifications of fuel rods or other cylindrical parts, the assembling apparatus includes at least two feed troughs each formed by a pair of screw members with a movable table having a plurality of stacking troughs for alignment with the feed troughs and with a conveyor for delivering the stacks to the loading device, the fuel rods being moved along the stacking troughs upon a fluid cushion. 23 claims, 6 figures
Method of detecting a fuel element failure
International Nuclear Information System (INIS)
Cohen, P.
1975-01-01
A method is described for detecting a fuel element failure in a liquid-sodium-cooled fast breeder reactor consisting of equilibrating a sample of the coolant with a molten salt consisting of a mixture of barium iodide and strontium iodide (or other iodides) whereby a large fraction of any radioactive iodine present in the liquid sodium coolant exchanges with the iodine present in the salt; separating the molten salt and sodium; if necessary, equilibrating the molten salt with nonradioactive sodium and separating the molten salt and sodium; and monitoring the molten salt for the presence of iodine, the presence of iodine indicating that the cladding of a fuel element has failed. (U.S.)
The spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
Spectral Karyotyping. An new method for chromosome analysis
International Nuclear Information System (INIS)
Zhou Liying; Qian Jianxin; Guo Xiaokui; Dai Hong; Liu Yulong; Zhou Jianying
2006-01-01
Spectral Karyotyping (SKY) can reveal fine changes in Chromosome structure which could not be detected by G, R, Q banding before, has become an accurate, sensitive and reliable method for karyotyping, promoted the development of cell genetics to molecular level and has been used in medicine and radiological injury research. It also has the ability of analyzing 24 chromosomes on its once test run and, find implicated structure of chromosome changes, such as metathesis, depletion, amplification, rearrangement, dikinetochore, equiarm and maker-body, detect the abnormal change of stable Chromosome and calculate the bio-dose curve; The abnormal Chromosome detected by SKY can be adopted as early diagnosis, effective indexes of minor remaining changes for use of monitor of treatment and in the duration of follow up. This technique provides us a more advanced and effective method for relative gene cloning and the study of pathological mechanism of cancer. (authors)
Spectral analysis methods for vehicle interior vibro-acoustics identification
Hosseini Fouladi, Mohammad; Nor, Mohd. Jailani Mohd.; Ariffin, Ahmad Kamal
2009-02-01
Noise has various effects on comfort, performance and health of human. Sound are analysed by human brain based on the frequencies and amplitudes. In a dynamic system, transmission of sound and vibrations depend on frequency and direction of the input motion and characteristics of the output. It is imperative that automotive manufacturers invest a lot of effort and money to improve and enhance the vibro-acoustics performance of their products. The enhancement effort may be very difficult and time-consuming if one relies only on 'trial and error' method without prior knowledge about the sources itself. Complex noise inside a vehicle cabin originated from various sources and travel through many pathways. First stage of sound quality refinement is to find the source. It is vital for automotive engineers to identify the dominant noise sources such as engine noise, exhaust noise and noise due to vibration transmission inside of vehicle. The purpose of this paper is to find the vibro-acoustical sources of noise in a passenger vehicle compartment. The implementation of spectral analysis method is much faster than the 'trial and error' methods in which, parts should be separated to measure the transfer functions. Also by using spectral analysis method, signals can be recorded in real operational conditions which conduce to more consistent results. A multi-channel analyser is utilised to measure and record the vibro-acoustical signals. Computational algorithms are also employed to identify contribution of various sources towards the measured interior signal. These achievements can be utilised to detect, control and optimise interior noise performance of road transport vehicles.
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.; Galvis, Juan; Hou, Thomasyizhao
2013-01-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.
2013-10-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
Generalized multiscale finite element method for elasticity equations
Chung, Eric T.
2014-10-05
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2016-01-01
Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.
Viner, K.; Reinecke, P. A.; Gabersek, S.; Flagg, D. D.; Doyle, J. D.; Martini, M.; Ryglicki, D.; Michalakes, J.; Giraldo, F.
2016-12-01
NEPTUNE: the Navy Environmental Prediction sysTem Using the NUMA*corE, is a 3D spectral element atmospheric model composed of a full suite of physics parameterizations and pre- and post-processing infrastructure with plans for data assimilation and coupling components to a variety of Earth-system models. This talk will focus on the initial struggles and solutions in adapting NUMA for stable and accurate integration on the sphere using both the deep atmosphere equations and a newly developed shallow-atmosphere approximation, as demonstrated through idealized test cases. In addition, details of the physics-dynamics coupling methodology will be discussed. NEPTUNE results for test cases from the 2016 Dynamical Core Model Intercomparison Project (DCMIP-2016) will be shown and discussed. *NUMA: Nonhydrostatic Unified Model of the Atmosphere; Kelly and Giraldo 2012, JCP
Buican, Tudor N.; Martin, John C.
1990-01-01
An apparatus and method simultaneously measures a plurality of spectral wavelengths present in electromagnetic radiation. A modulatable birefringent optical element is employed to divide a polarized light beam into two components, thereby producing a phase difference in two resulting light beams such that the two beams can be made to interfere with one another when recombined, the interference pattern providing the wavelength information required for the analysis of the incident light. The interferometer thus created performs in a similar manner to a Michelson interferometer, but with no moving parts, and with a resolution dependent on the degree of phase shift introduced by the modulator.
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Vidyasagar, A.; Tan, W. L.; Kochmann, D. M.
2017-09-01
Understanding the electromechanical response of bulk polycrystalline ferroelectric ceramics requires scale-bridging approaches. Recent advances in fast numerical methods to compute the homogenized mechanical response of materials with heterogeneous microstructure have enabled the solution of hitherto intractable systems. In particular, the use of a Fourier-based spectral method as opposed to the traditional finite element method has gained significant interest in the homogenization of periodic microstructures. Here, we solve the periodic, electro-mechanically-coupled boundary value problem at the mesoscale of polycrystalline ferroelectrics in order to extract the effective response of barium titanate (BaTiO3) and lead zirconate titanate (PZT) under applied electric fields. Results include the effective electric hysteresis and the associated butterfly curve of strain vs. electric field for mean stress-free electric loading. Computational predictions of the 3D polycrystalline response show convincing agreement with our experimental electric cycling and strain hysteresis data for PZT-5A. In addition to microstructure-dependent effective physics, we also show how finite-difference-based approximations in the spectral solution scheme significantly reduce instability and ringing phenomena associated with spectral techniques and lead to spatial convergence with h-refinement, which have been major challenges when modeling high-contrast systems such as polycrystals.
Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems
Streett, C. L.
1987-01-01
Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.
Transport survey calculations using the spectral collocation method
International Nuclear Information System (INIS)
Painter, S.L.; Lyon, J.F.
1989-01-01
A novel transport survey code has been developed and is being used to study the sensitivity of stellarator reactor performance to various transport assumptions. Instead of following one of the usual approaches, the steady-state transport equation are solved in integral form using the spectral collocation method. This approach effectively combine the computational efficiency of global models with the general nature of 1-D solutions. A compact torsatron reactor test case was used to study the convergence properties and flexibility of the new method. The heat transport model combined Shaing's model for ripple-induced neoclassical transport, the Chang-Hinton model for axisymmetric neoclassical transport, and neoalcator scaling for anomalous electron heat flux. Alpha particle heating, radiation losses, classical electron-ion heat flow, and external heating were included. For the test problem, the method exhibited some remarkable convergence properties. As the number of basis functions was increased, the maximum, pointwise error in the integrated power balance decayed exponentially until the numerical noise level as reached. Better than 10% accuracy in the globally-averaged quantities was achieved with only 5 basis functions; better than 1% accuracy was achieved with 10 basis functions. The numerical method was also found to be very general. Extreme temperature gradients at the plasma edge which sometimes arise from the neoclassical models and are difficult to resolve with finite-difference methods were easily resolved. 8 refs., 6 figs
Microlocal methods in the analysis of the boundary element method
DEFF Research Database (Denmark)
Pedersen, Michael
1993-01-01
The application of the boundary element method in numerical analysis is based upon the use of boundary integral operators stemming from multiple layer potentials. The regularity properties of these operators are vital in the development of boundary integral equations and error estimates. We show...
Genetic Algorithms: A New Method for Neutron Beam Spectral Characterization
International Nuclear Information System (INIS)
David W. Freeman
2000-01-01
A revolutionary new concept for solving the neutron spectrum unfolding problem using genetic algorithms (GAs) has recently been introduced. GAs are part of a new field of evolutionary solution techniques that mimic living systems with computer-simulated chromosome solutions that mate, mutate, and evolve to create improved solutions. The original motivation for the research was to improve spectral characterization of neutron beams associated with boron neutron capture therapy (BNCT). The GA unfolding technique has been successfully applied to problems with moderate energy resolution (up to 47 energy groups). Initial research indicates that the GA unfolding technique may well be superior to popular unfolding methods in common use. Research now under way at Kansas State University is focused on optimizing the unfolding algorithm and expanding its energy resolution to unfold detailed beam spectra based on multiple foil measurements. Indications are that the final code will significantly outperform current, state-of-the-art codes in use by the scientific community
Methods of total spectral radiant flux realization at VNIIOFI
Ivashin, Evgeniy; Lalek, Jan; Rybczyński, Andrzej; Ogarev, Sergey; Khlevnoy, Boris; Dobroserdov, Dmitry; Sapritsky, Victor
2018-02-01
VNIIOFI carries out works on realization of independent methods for realization of the total spectral radiant flux (TSRF) of incoherent optical radiation sources - reference high-temperature blackbodies (BB), halogen lamps, and LED with quasi-Lambert spatial distribution of radiance. The paper describes three schemes for measuring facilities using photometers, spectroradiometers and computer-controlled high class goniometer. The paper describes different approaches for TSRF realization at the VNIIOFI National radiometric standard on the basis of high-temperature BB and LED sources, and gonio-spectroradiometer. Further, they are planned to be compared, and the use of fixed-point cells (in particular, based on the high-temperature δ(MoC)-C metal-carbon eutectic with a phase transition temperature of 2583 °C corresponding to the metrological optical “source-A”) as an option instead of the BB is considered in order to enhance calibration accuracy.
Final Report of the Project "From the finite element method to the virtual element method"
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.
Adaptive finite element method for shape optimization
Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco
2012-01-01
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Standard Test Method for Normal Spectral Emittance at Elevated Temperatures
American Society for Testing and Materials. Philadelphia
1972-01-01
1.1 This test method describes a highly accurate technique for measuring the normal spectral emittance of electrically conducting materials or materials with electrically conducting substrates, in the temperature range from 600 to 1400 K, and at wavelengths from 1 to 35 μm. 1.2 The test method requires expensive equipment and rather elaborate precautions, but produces data that are accurate to within a few percent. It is suitable for research laboratories where the highest precision and accuracy are desired, but is not recommended for routine production or acceptance testing. However, because of its high accuracy this test method can be used as a referee method to be applied to production and acceptance testing in cases of dispute. 1.3 The values stated in SI units are to be regarded as the standard. The values in parentheses are for information only. 1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this stan...
The use of spectral methods in bidomain studies.
Trayanova, N; Pilkington, T
1992-01-01
A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour
2015-01-07
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a nite number of modes.
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak
2004-01-01
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel
Spectral-Product Methods for Electronic Structure Calculations (Preprint)
National Research Council Canada - National Science Library
Langhoff, P. W; Mills, J. E; Boatz, J. A
2006-01-01
.... The spectral-product approach to molecular electronic structure avoids the repeated evaluations of the one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices...
Spectral-Product Methods for Electronic Structure Calculations (Postprint)
National Research Council Canada - National Science Library
Langhoff, P. W; Hinde, R. J; Mills, J. D; Boatz, J. A
2007-01-01
.... The spectral-product approach to molecular electronic structure avoids the repeated evaluations of the one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices...
Mixed Generalized Multiscale Finite Element Methods and Applications
Chung, Eric T.
2015-03-03
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
New formulation of the discrete element method
Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon
2018-01-01
A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.
Method of manufacturing nuclear fuel elements
International Nuclear Information System (INIS)
Ishida, Masao; Oguma, Masaomi.
1980-01-01
Purpose: To effectively prevent the bending of nuclear fuel elements in the reactor by grinding the end faces of pellets due to their mutual sliding. Method: In the manufacturing process of nuclear fuel elements, a plurality of pellets whose sides have been polished are fed one by one by way of a feeding mechanism through the central aperture in an electric motor into movable arms and retained horizontally with the central axis by being held on the side. Then, the pellet held by one of the arms is urged to another pellet held by the other of the arms by way of a pressing mechanism and the mating end faces of both of the pellets are polished by mutual sliding. Thereafter, the grinding dusts resulted are eliminated by drawing pressurized air and then the pellets are enforced into a cladding tube. Thus, the pellets are charged into the cladding tube with both polished end faces being contacted to each other, whereby the axial force is uniformly transmitted within the end faces to prevent the bending of the cladding tube. (Kawakami, Y.)
A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems
Liu, X.; Banerjee, J. R.
2017-03-01
A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.
Kärhä, Petri; Vaskuri, Anna; Mäntynen, Henrik; Mikkonen, Nikke; Ikonen, Erkki
2017-08-01
Spectral irradiance data are often used to calculate colorimetric properties, such as color coordinates and color temperatures of light sources by integration. The spectral data may contain unknown correlations that should be accounted for in the uncertainty estimation. We propose a new method for estimating uncertainties in such cases. The method goes through all possible scenarios of deviations using Monte Carlo analysis. Varying spectral error functions are produced by combining spectral base functions, and the distorted spectra are used to calculate the colorimetric quantities. Standard deviations of the colorimetric quantities at different scenarios give uncertainties assuming no correlations, uncertainties assuming full correlation, and uncertainties for an unfavorable case of unknown correlations, which turn out to be a significant source of uncertainty. With 1% standard uncertainty in spectral irradiance, the expanded uncertainty of the correlated color temperature of a source corresponding to the CIE Standard Illuminant A may reach as high as 37.2 K in unfavorable conditions, when calculations assuming full correlation give zero uncertainty, and calculations assuming no correlations yield the expanded uncertainties of 5.6 K and 12.1 K, with wavelength steps of 1 nm and 5 nm used in spectral integrations, respectively. We also show that there is an absolute limit of 60.2 K in the error of the correlated color temperature for Standard Illuminant A when assuming 1% standard uncertainty in the spectral irradiance. A comparison of our uncorrelated uncertainties with those obtained using analytical methods by other research groups shows good agreement. We re-estimated the uncertainties for the colorimetric properties of our 1 kW photometric standard lamps using the new method. The revised uncertainty of color temperature is a factor of 2.5 higher than the uncertainty assuming no correlations.
Martian Radiative Transfer Modeling Using the Optimal Spectral Sampling Method
Eluszkiewicz, J.; Cady-Pereira, K.; Uymin, G.; Moncet, J.-L.
2005-01-01
The large volume of existing and planned infrared observations of Mars have prompted the development of a new martian radiative transfer model that could be used in the retrievals of atmospheric and surface properties. The model is based on the Optimal Spectral Sampling (OSS) method [1]. The method is a fast and accurate monochromatic technique applicable to a wide range of remote sensing platforms (from microwave to UV) and was originally developed for the real-time processing of infrared and microwave data acquired by instruments aboard the satellites forming part of the next-generation global weather satellite system NPOESS (National Polarorbiting Operational Satellite System) [2]. As part of our on-going research related to the radiative properties of the martian polar caps, we have begun the development of a martian OSS model with the goal of using it to perform self-consistent atmospheric corrections necessary to retrieve caps emissivity from the Thermal Emission Spectrometer (TES) spectra. While the caps will provide the initial focus area for applying the new model, it is hoped that the model will be of interest to the wider Mars remote sensing community.
Nuclear analytical methods for platinum group elements
International Nuclear Information System (INIS)
2005-04-01
Platinum group elements (PGE) are of special interest for analytical research due to their economic importance like chemical peculiarities as catalysts, medical applications as anticancer drugs, and possible environmental detrimental impact as exhaust from automobile catalyzers. Natural levels of PGE are so low in concentration that most of the current analytical techniques approach their limit of detection capacity. In addition, Ru, Rh, Pd, Re, Os, Ir, and Pt analyses still constitute a challenge in accuracy and precision of quantification in natural matrices. Nuclear analytical techniques, such as neutron activation analysis, X ray fluorescence, or proton-induced X ray emission (PIXE), which are generally considered as reference methods for many analytical problems, are useful as well. However, due to methodological restrictions, they can, in most cases, only be applied after pre-concentration and under special irradiation conditions. This report was prepared following a coordinated research project and a consultants meeting addressing the subject from different viewpoints. The experts involved suggested to discuss the issue according to the (1) application, hence, the concentration levels encountered, and (2) method applied for analysis. Each of the different fields of application needs special consideration for sample preparation, PGE pre-concentration, and determination. Additionally, each analytical method requires special attention regarding the sensitivity and sample type. Quality assurance/quality control aspects are considered towards the end of the report. It is intended to provide the reader of this publication with state-of-the-art information on the various aspects of PGE analysis and to advise which technique might be most suitable for a particular analytical problem related to platinum group elements. In particular, many case studies described in detail from the authors' laboratory experience might help to decide which way to go. As in many cases
Development of polygon elements based on the scaled boundary finite element method
International Nuclear Information System (INIS)
Chiong, Irene; Song Chongmin
2010-01-01
We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.
Rapid simulation of spatial epidemics: a spectral method.
Brand, Samuel P C; Tildesley, Michael J; Keeling, Matthew J
2015-04-07
Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel. Copyright © 2015 Elsevier Ltd. All rights reserved.
Application of finite-element-methods in food processing
DEFF Research Database (Denmark)
Risum, Jørgen
2004-01-01
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
Method of measuring distance between fuel element
International Nuclear Information System (INIS)
Urata, Megumu.
1991-01-01
The distance between fuel elements contained in a pool is measured in a contactless manner even for a narrow distance less than 1 mm. That is, the equipment for measuring the distance between spent fuel elements of a spent fuel assembly in a nuclear reactor comprises a optical fiber scope, a lens, an industrial TV camera and a monitor TV. The top end of the optical fiber scope is inserted between fuel elements to be measured. The state thereof is displayed on the TV screen to measure the distance between the fuel elements. The measured results are compared with a previously formed calibration curve to determine the value between the fuel elements. Then, the distance between the fuel elements can be determined in the pool of a power plant without dismantling the fuel assembly, to investigate the state of the bending and estimate the fuel working life. (I.S.)
Visual Method for Spectral Energy Distribution Calculation of ...
Indian Academy of Sciences (India)
Abstract. In this work, we propose to use 'The Geometer's Sketchpad' to the fitting of a spectral energy distribution of blazar based on three effective spectral indices, αRO, αOX, and αRX and the flux density in the radio band. It can make us to see the fitting in detail with both the peak frequency and peak luminosity given ...
Towards spectral geometric methods for Euclidean quantum gravity
Panine, Mikhail; Kempf, Achim
2016-04-01
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis, respectively. Of particular interest in this regard is the field of spectral geometry, which studies to which extent the shape of a Riemannian manifold is describable in terms of the spectra of differential operators defined on the manifold. Spectral geometry is hard because it is highly nonlinear, but linearized spectral geometry, i.e., the task to determine small shape changes from small spectral changes, is much more tractable and may be iterated to approximate the full problem. Here, we generalize this approach, allowing, in particular, nonequal finite numbers of shape and spectral degrees of freedom. This allows us to study how well the shape degrees of freedom are encoded in the eigenvalues. We apply this strategy numerically to a class of planar domains and find that the reconstruction of small shape changes from small spectral changes is possible if enough eigenvalues are used. While isospectral nonisometric shapes are known to exist, we find evidence that generically shaped isospectral nonisometric shapes, if existing, are exceedingly rare.
Shuxia, ZHAO; Lei, ZHANG; Jiajia, HOU; Yang, ZHAO; Wangbao, YIN; Weiguang, MA; Lei, DONG; Liantuan, XIAO; Suotang, JIA
2018-03-01
The chemical composition of alloys directly determines their mechanical behaviors and application fields. Accurate and rapid analysis of both major and minor elements in alloys plays a key role in metallurgy quality control and material classification processes. A quantitative calibration-free laser-induced breakdown spectroscopy (CF-LIBS) analysis method, which carries out combined correction of plasma temperature and spectral intensity by using a second-order iterative algorithm and two boundary standard samples, is proposed to realize accurate composition measurements. Experimental results show that, compared to conventional CF-LIBS analysis, the relative errors for major elements Cu and Zn and minor element Pb in the copper-lead alloys has been reduced from 12%, 26% and 32% to 1.8%, 2.7% and 13.4%, respectively. The measurement accuracy for all elements has been improved substantially.
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Calo, Victor M.
2016-03-23
In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Spectral-element Seismic Wave Propagation on CUDA/OpenCL Hardware Accelerators
Peter, D. B.; Videau, B.; Pouget, K.; Komatitsch, D.
2015-12-01
Seismic wave propagation codes are essential tools to investigate a variety of wave phenomena in the Earth. Furthermore, they can now be used for seismic full-waveform inversions in regional- and global-scale adjoint tomography. Although these seismic wave propagation solvers are crucial ingredients to improve the resolution of tomographic images to answer important questions about the nature of Earth's internal processes and subsurface structure, their practical application is often limited due to high computational costs. They thus need high-performance computing (HPC) facilities to improving the current state of knowledge. At present, numerous large HPC systems embed many-core architectures such as graphics processing units (GPUs) to enhance numerical performance. Such hardware accelerators can be programmed using either the CUDA programming environment or the OpenCL language standard. CUDA software development targets NVIDIA graphic cards while OpenCL was adopted by additional hardware accelerators, like e.g. AMD graphic cards, ARM-based processors as well as Intel Xeon Phi coprocessors. For seismic wave propagation simulations using the open-source spectral-element code package SPECFEM3D_GLOBE, we incorporated an automatic source-to-source code generation tool (BOAST) which allows us to use meta-programming of all computational kernels for forward and adjoint runs. Using our BOAST kernels, we generate optimized source code for both CUDA and OpenCL languages within the source code package. Thus, seismic wave simulations are able now to fully utilize CUDA and OpenCL hardware accelerators. We show benchmarks of forward seismic wave propagation simulations using SPECFEM3D_GLOBE on CUDA/OpenCL GPUs, validating results and comparing performances for different simulations and hardware usages.
Peter, Daniel; Videau, Brice; Pouget, Kevin; Komatitsch, Dimitri
2015-04-01
Improving the resolution of tomographic images is crucial to answer important questions on the nature of Earth's subsurface structure and internal processes. Seismic tomography is the most prominent approach where seismic signals from ground-motion records are used to infer physical properties of internal structures such as compressional- and shear-wave speeds, anisotropy and attenuation. Recent advances in regional- and global-scale seismic inversions move towards full-waveform inversions which require accurate simulations of seismic wave propagation in complex 3D media, providing access to the full 3D seismic wavefields. However, these numerical simulations are computationally very expensive and need high-performance computing (HPC) facilities for further improving the current state of knowledge. During recent years, many-core architectures such as graphics processing units (GPUs) have been added to available large HPC systems. Such GPU-accelerated computing together with advances in multi-core central processing units (CPUs) can greatly accelerate scientific applications. There are mainly two possible choices of language support for GPU cards, the CUDA programming environment and OpenCL language standard. CUDA software development targets NVIDIA graphic cards while OpenCL was adopted mainly by AMD graphic cards. In order to employ such hardware accelerators for seismic wave propagation simulations, we incorporated a code generation tool BOAST into an existing spectral-element code package SPECFEM3D_GLOBE. This allows us to use meta-programming of computational kernels and generate optimized source code for both CUDA and OpenCL languages, running simulations on either CUDA or OpenCL hardware accelerators. We show here applications of forward and adjoint seismic wave propagation on CUDA/OpenCL GPUs, validating results and comparing performances for different simulations and hardware usages.
The finite element method in engineering, 2nd edition
International Nuclear Information System (INIS)
Rao, S.S.
1986-01-01
This work provides a systematic introduction to the various aspects of the finite element method as applied to engineering problems. Contents include: introduction to finite element method; solution of finite element equations; solid and structural mechanics; static analysis; dynamic analysis; heat transfer; fluid mechanics and additional applications
Method for inspecting nuclear reactor fuel elements
International Nuclear Information System (INIS)
Jabsen, F.S.
1979-01-01
A technique for disassembling a nuclear reactor fuel element without destroying the individual fuel pins and other structural components from which the element is assembled is described. A traveling bridge and trolley span a water-filled spent fuel storage pool and support a strongback. The strongback is under water and provides a working surface on which the spent fuel element is placed for inspection and for the manipulation that is associated with disassembly and assembly. To remove, in a non-destructive manner, the grids that hold the fuel pins in the proper relative positions within the element, bars are inserted through apertures in the grids with the aid of special tools. These bars are rotated to flex the adjacent grid walls and, in this way relax the physical engagement between protruding portions of the grid walls and the associated fuel pins. With the grid structure so flexed to relax the physical grip on the individual fuel pins, these pins can be withdrawn for inspection or replacement as necessary without imposing a need to destroy fuel element components
Energy Technology Data Exchange (ETDEWEB)
Kirsanov, N. Yu.; Latukhina, N. V., E-mail: natalat@yandex.ru; Lizunkova, D. A.; Rogozhina, G. A. [Samara National Research University (Russian Federation); Stepikhova, M. V. [Russian Academy of Sciences, Institute for Physics of Microstructures (Russian Federation)
2017-03-15
The spectral characteristics of the specular reflectance, photosensitivity, and photoluminescence (PL) of multilayer structures based on porous silicon with rare-earth-element (REE) ions are investigated. It is shown that the photosensitivity of these structures in the wavelength range of 0.4–1.0 μm is higher than in structures free of REEs. The structures with Er{sup 3+} ions exhibit a luminescence response at room temperature in the spectral range from 1.1 to 1.7 μm. The PL spectrum of the erbium impurity is characterized by a fine line structure, which is determined by the splitting of the {sup 4}I{sub 15/2} multiplet of the Er{sup 3+} ion. It is shown that the structures with a porous layer on the working surface have a much lower reflectance in the entire spectral range under study (0.2–1.0 μm).
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan
2012-01-01
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite
Huang, Z.; Chen, Q.; Shen, Y.; Chen, Q.; Liu, X.
2017-09-01
Variational pansharpening can enhance the spatial resolution of a hyperspectral (HS) image using a high-resolution panchromatic (PAN) image. However, this technology may lead to spectral distortion that obviously affect the accuracy of data analysis. In this article, we propose an improved variational method for HS image pansharpening with the constraint of spectral difference minimization. We extend the energy function of the classic variational pansharpening method by adding a new spectral fidelity term. This fidelity term is designed following the definition of spectral angle mapper, which means that for every pixel, the spectral difference value of any two bands in the HS image is in equal proportion to that of the two corresponding bands in the pansharpened image. Gradient descent method is adopted to find the optimal solution of the modified energy function, and the pansharpened image can be reconstructed. Experimental results demonstrate that the constraint of spectral difference minimization is able to preserve the original spectral information well in HS images, and reduce the spectral distortion effectively. Compared to original variational method, our method performs better in both visual and quantitative evaluation, and achieves a good trade-off between spatial and spectral information.
A method for spectral DNS of low Rm channel flows based on the least dissipative modes
Kornet, Kacper; Pothérat, Alban
2015-10-01
We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The main idea is to take advantage of the fact that such structures are dissipative and that their presence should reduce the number of degrees of freedom of the flow, when paradoxically, their fine resolution incurs extra computational cost in most current methods. The principle of this method is to use a functional basis with elements that already include these fine structures so as to avoid these extra costs. This leads us to develop an algorithm to implement a spectral method for arbitrary functional bases, and in particular, non-orthogonal ones. We construct a basic implementation of this algorithm to simulate magnetohydrodynamic (MHD) channel flows with an externally imposed, transverse magnetic field, where very thin boundary layers are known to develop along the channel walls. In this case, the sought functional basis can be built out of the eigenfunctions of the dissipation operator, which incorporate these boundary layers, and it turns out to be non-orthogonal. We validate this new scheme against numerical simulations of freely decaying MHD turbulence based on a finite volume code and it is found to provide accurate results. Its ability to fully resolve wall-bounded turbulence with a number of modes close to that required by the dynamics is demonstrated on a simple example. This opens the way to full-blown simulations of MHD turbulence under very high magnetic fields. Until now such simulations were too computationally expensive. In contrast to traditional methods the computational cost of the proposed method, does not depend on the intensity of the magnetic field.
Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media
Chung, Eric T.
2014-11-13
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to their complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids. In this paper, we present a multiscale finite element method for wave propagation on a coarse grid. The proposed method is based on the generalized multiscale finite element method (GMsFEM) (see [Y. Efendiev, J. Galvis, and T. Hou, J. Comput. Phys., 251 (2012), pp. 116--135]). To construct multiscale basis functions, we start with two snapshot spaces in each coarse-grid block, where one represents the degrees of freedom on the boundary and the other represents the degrees of freedom in the interior. We use local spectral problems to identify important modes in each snapshot space. These local spectral problems are different from each other and their formulations are based on the analysis. To the best of knowledge, this is the first time that multiple snapshot spaces and multiple spectral problems are used and necessary for efficient computations. Using the dominant modes from local spectral problems, multiscale basis functions are constructed to represent the solution space locally within each coarse block. These multiscale basis functions are coupled via the symmetric interior penalty discontinuous Galerkin method which provides a block diagonal mass matrix and, consequently, results in fast computations in an explicit time discretization. Our methods\\' stability and spectral convergence are rigorously analyzed. Numerical examples are presented to show our methods\\' performance. We also test oversampling strategies. In particular, we discuss how the modes from different snapshot spaces can affect the proposed methods\\' accuracy.
Assessment of modern spectral analysis methods to improve wavenumber resolution of F-K spectra
International Nuclear Information System (INIS)
Shirley, T.E.; Laster, S.J.; Meek, R.A.
1987-01-01
The improvement in wavenumber spectra obtained by using high resolution spectral estimators is examined. Three modern spectral estimators were tested, namely the Autoregressive/Maximum Entropy (AR/ME) method, the Extended Prony method, and an eigenstructure method. They were combined with the conventional Fourier method by first transforming each trace with a Fast Fourier Transform (FFT). A high resolution spectral estimator was applied to the resulting complex spatial sequence for each frequency. The collection of wavenumber spectra thus computed comprises a hybrid f-k spectrum with high wavenumber resolution and less spectral ringing. Synthetic and real data records containing 25 traces were analyzed by using the hybrid f-k method. The results show an FFT-AR/ME f-k spectrum has noticeably better wavenumber resolution and more spectral dynamic range than conventional spectra when the number of channels is small. The observed improvement suggests the hybrid technique is potentially valuable in seismic data analysis
International Nuclear Information System (INIS)
Moore, Travis J.; Jones, Matthew R.; Tree, Dale R.; Daniel Maynes, R.; Baxter, Larry L.
2011-01-01
An experimental procedure has been developed to make spectral emittance and temperature measurements. The spectral emittance of an object is calculated using measurements of the spectral emissive power and of the surface temperature of the object obtained using a Fourier transform infrared (FTIR) spectrometer. A calibration procedure is described in detail which accounts for the temperature dependence of the detector. The methods used to extract the spectral emissive power and surface temperature from measured infrared spectra were validated using a blackbody radiator at known temperatures. The average error in the measured spectral emittance was 2.1% and the average difference between the temperature inferred from the recorded spectra and the temperature indicated on the blackbody radiator was 1.2%. The method was used to measure the spectral emittance of oxidized copper at various temperatures.
Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification
Winokur, J.; Kim, D.; Bisetti, Fabrizio; Le Maî tre, O. P.; Knio, Omar
2015-01-01
We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a
Directory of Open Access Journals (Sweden)
Tarasenko Alexandr
2016-01-01
Full Text Available The paper is aimed at determining the possibility of applying the simplified method proposed by the authors to calculate the tank seismic resistance in compliance with current regulations and scientific provisions. The authors propose a highly detailed numerical model for a common oil storage tank RVSPK-50000 that enables static operational loads and dynamic action of earthquakes to be calculated. Within the modal analysis the natural oscillation frequencies in the range of 0-10 Hz were calculated; the results are given for the first ten modes. The model takes into account the effect of impulsive and convective components of hydrodynamic pressure during earthquakes. Within the spectral analysis by generalized response spectra was calculated a general stress-strain state of a structure during earthquakes of 7, 8, 9 intensity degrees on the MSK-64 scale for a completely filled up, a half-filled up to the mark of 8.5 m and an empty RVSPK-50000 tank. The developed finite element model can be used to perform calculations of seismic resistance by the direct dynamic method, which will give further consideration to the impact of individual structures (floating roof, support posts, adjoined elements of added stiffness on the general stress-strain state of a tank.
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
Investigation of elements accumulation in some plants by nuclear-research methods
International Nuclear Information System (INIS)
Azhabov, A.K.; Khushmuradov, Sh.Kh.; Danilova, E.A.; Kist, A.A.; Dekhkanov, T.; Kobzev, A.P.; Muminov, I.T.
2000-01-01
The results of studies on 18 elements in the samples of hugh elecampane, middle-asian mint, field horsetail, mixed grass crop and turkestan dog rose fruits, collected at the two stationary sites A and B of the Bashkizylsaj area of the Chatkalsk biospheric reservation and studied through the neutron-activation (n), γ-activation (γ), X-ray spectral (p) and X-ray fluorescence (x) physical methods, are presented. The root-square errors of the results, obtained by different method and differences in the elements accumulation, depending on the plant type, their part and vegetation place, are evaluated. The coefficients of biological accumulation of 15 elements in the 15 plants under study are determined on the basis of the data on the elements content in plants and corresponding soil samples [ru
A simple finite element method for linear hyperbolic problems
International Nuclear Information System (INIS)
Mu, Lin; Ye, Xiu
2017-01-01
Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.
Different Element Methods in Engineering Practice | Onah | Nigerian ...
African Journals Online (AJOL)
Presented is the most common element methods used for analysis in engineering. The methods are discussed in an overall and general manner so that engineers and scientists who are increasingly, called upon to use element methods to support and check their analyses and/or designs can appreciate the essential ...
A finite element solution method for quadrics parallel computer
International Nuclear Information System (INIS)
Zucchini, A.
1996-08-01
A distributed preconditioned conjugate gradient method for finite element analysis has been developed and implemented on a parallel SIMD Quadrics computer. The main characteristic of the method is that it does not require any actual assembling of all element equations in a global system. The physical domain of the problem is partitioned in cells of n p finite elements and each cell element is assigned to a different node of an n p -processors machine. Element stiffness matrices are stored in the data memory of the assigned processing node and the solution process is completely executed in parallel at element level. Inter-element and therefore inter-processor communications are required once per iteration to perform local sums of vector quantities between neighbouring elements. A prototype implementation has been tested on an 8-nodes Quadrics machine in a simple 2D benchmark problem
Transuranium element recovering method for spent nuclear fuel
International Nuclear Information System (INIS)
Todokoro, Akio; Kihara, Yoshiyuki; Okada, Hisashi
1998-01-01
Spent fuels are dissolved in nitric acid, the obtained dissolution liquid is oxidized by electrolysis, and nitric acid of transuranium elements are precipitated together with nitric acid of uranium elements from the dissolution solution and recovered. Namely, the transuranium elements are oxidized to an atomic value level at which nitric acid can be precipitated by an oxidizing catalyst, and cooled to precipitate nitric acid of transuranium elements together with nitric acid of transuranium elements, accordingly, it is not necessary to use a solvent which has been used so far upon recovering transuranium elements. Since no solvent waste is generated, a recovery method taking the circumstance into consideration can be provided. Further, nitric acid of uranium elements and nitric acid of transuranium elements precipitated and recovered together are dissolved in nitric acid again, cooled and only uranium elements are precipitated selectively, and recovered by filtration. The amount of wastes can be reduced to thereby enabling to mitigate control for processing. (N.H.)
Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Xuqing Zhang
2013-01-01
Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.
A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method
Wang, Xiao-Yen J.
2015-01-01
The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.
Research of flaw assessment methods for beryllium reflector elements
International Nuclear Information System (INIS)
Shibata, Akira; Ito, Masayasu; Takemoto, Noriyuki; Tanimoto, Masataka; Tsuchiya, Kunihiko; Nakatsuka, Masafumi; Ohara, Hiroshi; Kodama, Mitsuhiro
2012-02-01
Reflector elements made from metal beryllium is widely used as neutron reflectors to increase neutron flux in test reactors. When beryllium reflector elements are irradiated by neutron, bending of reflector elements caused by swelling occurs, and beryllium reflector elements must be replaced in several years. In this report, literature search and investigation for non-destructive inspection of Beryllium and experiments for Preliminary inspection to establish post irradiation examination method for research of characteristics of metal beryllium under neutron irradiation were reported. (author)
Zou, Peng; Cheng, Jiubing
2017-01-01
-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour; Chá con-Rebollo, Tomas
2015-01-01
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base
International Nuclear Information System (INIS)
Fehrenbacher, G.; Schuetz, R.; Hahn, K.; Sprunck, M.; Cordes, E.; Biersack, J.P.; Wahl, W.
1999-01-01
A new method for the monitoring of neutron radiation is proposed. It is based on the determination of spectral information on the neutron field in order to derive dose quantities like the ambient dose equivalent, the dose equivalent, or other dose quantities which depend on the neutron energy. The method uses a multi-element system consisting of converter type silicon detectors. The unfolding procedure is based on an artificial neural network (ANN). The response function of each element is determined by a computational model considering the neutron interaction with the dosemeter layers and the subsequent transport of produced ions. An example is given for a multi-element system. The ANN is trained by a given set of neutron spectra and then applied to count responses obtained in neutron fields. Four examples of spectra unfolded using the ANN are presented. (author)
Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
Directory of Open Access Journals (Sweden)
Jinkui Liu
2012-01-01
Full Text Available A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition gkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995 in contrast to the famous CD method, FR method, and PRP method.
A Review of Spectral Methods for Variable Amplitude Fatigue Prediction and New Results
Larsen, Curtis E.; Irvine, Tom
2013-01-01
A comprehensive review of the available methods for estimating fatigue damage from variable amplitude loading is presented. The dependence of fatigue damage accumulation on power spectral density (psd) is investigated for random processes relevant to real structures such as in offshore or aerospace applications. Beginning with the Rayleigh (or narrow band) approximation, attempts at improved approximations or corrections to the Rayleigh approximation are examined by comparison to rainflow analysis of time histories simulated from psd functions representative of simple theoretical and real world applications. Spectral methods investigated include corrections by Wirsching and Light, Ortiz and Chen, the Dirlik formula, and the Single-Moment method, among other more recent proposed methods. Good agreement is obtained between the spectral methods and the time-domain rainflow identification for most cases, with some limitations. Guidelines are given for using the several spectral methods to increase confidence in the damage estimate.
Energy Technology Data Exchange (ETDEWEB)
Fauqueux, S.
2003-02-01
We consider the propagation of elastic waves in unbounded domains. A new formulation of the linear elasticity system as an H (div) - L{sup 2} system enables us to use the 'mixed spectral finite element method', This new method is based on the definition of new spaces of approximation and the use of mass-lumping. It leads to an explicit scheme with reduced storage and provides the same solution as the spectral finite element method. Then, we model unbounded domains by using Perfectly Matched Layers. Instabilities in the PML in the case of particular 2D elastic media are pointed out and investigated. The numerical method is validated and tested in the case of acoustic and elastic realistic models. A plane wave analysis gives results about numerical dispersion and shows that meshes adapted to the physical and geometrical properties of the media are more accurate than the others. Then, an extension of the method to fluid-solid coupling is introduced for 2D seismic propagation. (author)
Aglitskiy, Yefim; Weaver, J. L.; Karasik, M.; Serlin, V.; Obenschain, S. P.; Ralchenko, Yu.
2014-10-01
The spectra of multi-charged ions of Hf, Ta, W, Pt, Au and Bi have been studied on Nike krypton-fluoride laser facility with the help of two kinds of X-ray spectrometers. First, survey instrument covering a spectral range from 0.5 to 19.5 angstroms which allows simultaneous observation of both M- and N- spectra of above mentioned elements with high spectral resolution. Second, an imaging spectrometer with interchangeable spherically bent Quartz crystals that added higher efficiency, higher spectral resolution and high spatial resolution to the qualities of the former one. Multiple spectral lines with X-ray energies as high as 4 keV that belong to the isoelectronic sequences of Fe, Co, Ni, Cu and Zn were identified with the help of NOMAD package developed by Dr. Yu. Ralchenko and colleagues. In our continuous effort to support DOE-NNSA's inertial fusion program, this campaign covered a wide range of plasma conditions that result in production of relatively energetic X-rays. Work supported by the US DOE/NNSA.
Establishing a method to measure bone structure using spectral CT
Ramyar, M.; Leary, C.; Raja, A.; Butler, A. P. H.; Woodfield, T. B. F.; Anderson, N. G.
2017-03-01
Combining bone structure and density measurement in 3D is required to assess site-specific fracture risk. Spectral molecular imaging can measure bone structure in relation to bone density by measuring macro and microstructure of bone in 3D. This study aimed to optimize spectral CT methodology to measure bone structure in excised bone samples. MARS CT with CdTe Medipix3RX detector was used in multiple energy bins to calibrate bone structure measurements. To calibrate thickness measurement, eight different thicknesses of Aluminium (Al) sheets were scanned one in air and the other around a falcon tube and then analysed. To test if trabecular thickness measurements differed depending on scan plane, a bone sample from sheep proximal tibia was scanned in two orthogonal directions. To assess the effect of air on thickness measurement, two parts of the same human femoral head were scanned in two conditions (in the air and in PBS). The results showed that the MARS scanner (with 90μm voxel size) is able to accurately measure the Al (in air) thicknesses over 200μm but it underestimates the thicknesses below 200μm because of partial volume effect in Al-air interface. The Al thickness measured in the highest energy bin is overestimated at Al-falcon tube interface. Bone scanning in two orthogonal directions gives the same trabecular thickness and air in the bone structure reduced measurement accuracy. We have established a bone structure assessment protocol on MARS scanner. The next step is to combine this with bone densitometry to assess bone strength.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
basis functions (called G1FEM here) and quadratic basis functions (called G2FEM) ... mulation of Brookes & Hughes (1982) that implicitly incorporates numerical ..... functions and (c) SUPG method in the (kh − ω t)-plane for explicit Euler.
Residual-driven online generalized multiscale finite element methods
Chung, Eric T.
2015-09-08
The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error. This error decrease is independent of physical parameters, such as the contrast and multiple scales in the problem. The offline spaces are constructed using Generalized Multiscale Finite Element Methods (GMsFEM). We show that if one chooses a sufficient number of offline basis functions, one can guarantee that additional online multiscale basis functions will reduce the error independent of contrast. We note that the construction of online basis functions is motivated by the fact that the offline space construction does not take into account distant effects. Using the residual information, we can incorporate the distant information provided the offline approximation satisfies certain properties. In the paper, theoretical and numerical results are presented. Our numerical results show that if the offline space is sufficiently large (in terms of the dimension) such that the coarse space contains all multiscale spectral basis functions that correspond to small eigenvalues, then the error reduction by adding online multiscale basis function is independent of the contrast. We discuss various ways computing online multiscale basis functions which include a use of small dimensional offline spaces.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
2014-01-01
approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction
Dynamic relaxation method in analysis of reinforced concrete bent elements
Directory of Open Access Journals (Sweden)
Anna Szcześniak
2015-12-01
Full Text Available The paper presents a method for the analysis of nonlinear behaviour of reinforced concrete bent elements subjected to short-term static load. The considerations in the range of modelling of deformation processes of reinforced concrete element were carried out. The method of structure effort analysis was developed using the finite difference method. The Dynamic Relaxation Method, which — after introduction of critical damping — allows for description of the static behaviour of a structural element, was used to solve the system of nonlinear equilibrium equations. In order to increase the method effectiveness in the range of the post-critical analysis, the Arc Length Parameter on the equilibrium path was introduced into the computational procedure.[b]Keywords[/b]: reinforced concrete elements, physical nonlinearity, geometrical nonlinearity, dynamic relaxation method, arc-length method
Oral, Elif; Gélis, Céline; Bonilla, Luis Fabián; Delavaud, Elise
2017-12-01
Numerical modelling of seismic wave propagation, considering soil nonlinearity, has become a major topic in seismic hazard studies when strong shaking is involved under particular soil conditions. Indeed, when strong ground motion propagates in saturated soils, pore pressure is another important parameter to take into account when successive phases of contractive and dilatant soil behaviour are expected. Here, we model 1-D seismic wave propagation in linear and nonlinear media using the spectral element numerical method. The study uses a three-component (3C) nonlinear rheology and includes pore-pressure excess. The 1-D-3C model is used to study the 1987 Superstition Hills earthquake (ML 6.6), which was recorded at the Wildlife Refuge Liquefaction Array, USA. The data of this event present strong soil nonlinearity involving pore-pressure effects. The ground motion is numerically modelled for different assumptions on soil rheology and input motion (1C versus 3C), using the recorded borehole signals as input motion. The computed acceleration-time histories show low-frequency amplification and strong high-frequency damping due to the development of pore pressure in one of the soil layers. Furthermore, the soil is found to be more nonlinear and more dilatant under triaxial loading compared to the classical 1C analysis, and significant differences in surface displacements are observed between the 1C and 3C approaches. This study contributes to identify and understand the dominant phenomena occurring in superficial layers, depending on local soil properties and input motions, conditions relevant for site-specific studies.
An Improved Spectral Analysis Method for Fatigue Damage Assessment of Details in Liquid Cargo Tanks
Zhao, Peng-yuan; Huang, Xiao-ping
2018-03-01
Errors will be caused in calculating the fatigue damages of details in liquid cargo tanks by using the traditional spectral analysis method which is based on linear system, for the nonlinear relationship between the dynamic stress and the ship acceleration. An improved spectral analysis method for the assessment of the fatigue damage in detail of a liquid cargo tank is proposed in this paper. Based on assumptions that the wave process can be simulated by summing the sinusoidal waves in different frequencies and the stress process can be simulated by summing the stress processes induced by these sinusoidal waves, the stress power spectral density (PSD) is calculated by expanding the stress processes induced by the sinusoidal waves into Fourier series and adding the amplitudes of each harmonic component with the same frequency. This analysis method can take the nonlinear relationship into consideration and the fatigue damage is then calculated based on the PSD of stress. Take an independent tank in an LNG carrier for example, the accuracy of the improved spectral analysis method is proved much better than that of the traditional spectral analysis method by comparing the calculated damage results with the results calculated by the time domain method. The proposed spectral analysis method is more accurate in calculating the fatigue damages in detail of ship liquid cargo tanks.
Finite element method for solving neutron transport problems
International Nuclear Information System (INIS)
Ferguson, J.M.; Greenbaum, A.
1984-01-01
A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
International Nuclear Information System (INIS)
Wall, G.J.
1985-01-01
A computer programme (written in BASIC) is described for the evaluation of spectral-line intensities in X-ray-fluorescence spectrometry. The programme is designed to assist the analyst while he is developing new analytical methods, because it facilitates the selection of the following evaluation parameters: calculation models, spectral-line correction factors, calibration curves, calibration ranges, and point deletions. In addition, the programme enables the analyst to undertake routine calculations of data from multi-element analyses in which variable data-reduction parameters are used for each element
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
International Nuclear Information System (INIS)
Chen, Q G; Xu, Y; Zhu, H H; Chen, H; Lin, B
2015-01-01
A quantitative method to discriminate caries lesions for a fluorescence imaging system is proposed in this paper. The autofluorescence spectral investigation of 39 teeth samples classified by the International Caries Detection and Assessment System levels was performed at 405 nm excitation. The major differences in the different caries lesions focused on the relative spectral intensity range of 565–750 nm. The spectral parameter, defined as the ratio of wavebands at 565–750 nm to the whole spectral range, was calculated. The image component ratio R/(G + B) of color components was statistically computed by considering the spectral parameters (e.g. autofluorescence, optical filter, and spectral sensitivity) in our fluorescence color imaging system. Results showed that the spectral parameter and image component ratio presented a linear relation. Therefore, the image component ratio was graded as <0.66, 0.66–1.06, 1.06–1.62, and >1.62 to quantitatively classify sound, early decay, established decay, and severe decay tissues, respectively. Finally, the fluorescence images of caries were experimentally obtained, and the corresponding image component ratio distribution was compared with the classification result. A method to determine the numerical grades of caries using a fluorescence imaging system was proposed. This method can be applied to similar imaging systems. (paper)
Chen, Q. G.; Zhu, H. H.; Xu, Y.; Lin, B.; Chen, H.
2015-08-01
A quantitative method to discriminate caries lesions for a fluorescence imaging system is proposed in this paper. The autofluorescence spectral investigation of 39 teeth samples classified by the International Caries Detection and Assessment System levels was performed at 405 nm excitation. The major differences in the different caries lesions focused on the relative spectral intensity range of 565-750 nm. The spectral parameter, defined as the ratio of wavebands at 565-750 nm to the whole spectral range, was calculated. The image component ratio R/(G + B) of color components was statistically computed by considering the spectral parameters (e.g. autofluorescence, optical filter, and spectral sensitivity) in our fluorescence color imaging system. Results showed that the spectral parameter and image component ratio presented a linear relation. Therefore, the image component ratio was graded as 1.62 to quantitatively classify sound, early decay, established decay, and severe decay tissues, respectively. Finally, the fluorescence images of caries were experimentally obtained, and the corresponding image component ratio distribution was compared with the classification result. A method to determine the numerical grades of caries using a fluorescence imaging system was proposed. This method can be applied to similar imaging systems.
Coupling of smooth particle hydrodynamics with the finite element method
International Nuclear Information System (INIS)
Attaway, S.W.; Heinstein, M.W.; Swegle, J.W.
1994-01-01
A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code ppercase[pronto]. In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within ppercase[pronto] will be outlined. Example SPH ppercase[pronto] calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or ''bow tie'' elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within ppercase[pronto] allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm. ((orig.))
Two-dimensional isostatic meshes in the finite element method
Martínez Marín, Rubén; Samartín, Avelino
2002-01-01
In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's...
Element Free Lattice Boltzmann Method for Fluid-Flow Problems
International Nuclear Information System (INIS)
Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung; Kwon, Young Kwon
2007-01-01
The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented
Element Free Lattice Boltzmann Method for Fluid-Flow Problems
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Kwon, Young Kwon [US Naval Postgraduate School, New York (United States)
2007-10-15
The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented.
Finite element formulation for a digital image correlation method
International Nuclear Information System (INIS)
Sun Yaofeng; Pang, John H. L.; Wong, Chee Khuen; Su Fei
2005-01-01
A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust
Efendiev, Yalchin R.
2015-06-05
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.
A Method of Assembling Wall or Floor Elements
DEFF Research Database (Denmark)
2002-01-01
The invention relates to a method of constructing, at the site of use, a building wall (1) or a building floor (1) using a plurality of prefabricated concrete or lightweight concrete plate-shaped wall of floor elements (10), in particular cast elements, which have a front side and a rear side...
A Note on Symplectic, Multisymplectic Scheme in Finite Element Method
Institute of Scientific and Technical Information of China (English)
GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke
2001-01-01
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
International Nuclear Information System (INIS)
Lakhov, V.M.; Gerling, V.Eh.; Il'ina, L.K.; Trojnina, G.G.; Galisheva, Eh.P.
1987-01-01
The papers on the problems of developing and application of synthetic standard samples (SS), imitating the substance and material (rocks, ores) element composition aimed at calibration, testing and certification of the equipment as well as check on the results of neutron-activation, X-ray spectral, X-ray radiometric, X-ray fluorescence and other nuclear-physical methods of analysis, are reviewed. It is shown that choice of SS preparation method is defined by peculiarities of analysis method for which calibration SS is designed. Experience in application of SS imitators of element composition in interlaboratory comparisons testifies to potential application of synthetic SS for calibration in different methods of analysis including, nuclear-physical ones
Multi-spectral lifetime imaging: methods and applications
Fereidouni, F.
2013-01-01
The aim of this PhD project is to further develop multispectral life time imaging hardware and analyses methods. The hardware system, Lambda-Tau, generates a considerable amount of data at high speed. To fully exploit the power of this new hardware, fast and reliable data analyses methods are
International Nuclear Information System (INIS)
Terry, J.L.; Manning, H.L.; Marmar, E.S.
1986-07-01
Two methods which together allow sensitivity calibration from 20 A to 430 A are described in detail. The first method, useful up to 120 A, uses a low power source to generate Kα x-rays which are alternately viewed by an absolute detector (a proportional counter) and the spectrometer. The second method extends that calibration to 430 A. It relies on the 2:1 brightness ratio of bright doublet lines from impurity ions which have a single outer shell electron and which are present in hot, magnetically confined plasmas. It requires that the absolute sensitivity of the spectrometer be known at one wavelength point, and in practice requires a multi-element spectral detector
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@In this paper, some image processing methods such as directional template (mask) matching enhancement, pseudocolor or false color enhancement, K-L transform enhancement are used to enhance a geological structure, one of important ore-controlling factors, shown in the remote-sensing images.This geological structure is regarded as image anomaly in the remote-sensing image, since considerable differences, based on the spatial spectral distribution pattern, in gray values (spectral), color tones and texture, are always present between the geological structure and background. Therefore,the enhancement of the geological structure in the remotesensing image is that of the spectral spatial difference.
Modified Spectral Fatigue Methods for S-N Curves With MIL-HDBK-5J Coefficients
Irvine, Tom; Larsen, Curtis
2016-01-01
The rainflow method is used for counting fatigue cycles from a stress response time history, where the fatigue cycles are stress-reversals. The rainflow method allows the application of Palmgren-Miner's rule in order to assess the fatigue life of a structure subject to complex loading. The fatigue damage may also be calculated from a stress response power spectral density (PSD) using the semi-empirical Dirlik, Single Moment, Zhao-Baker and other spectral methods. These methods effectively assume that the PSD has a corresponding time history which is stationary with a normal distribution. This paper shows how the probability density function for rainflow stress cycles can be extracted from each of the spectral methods. This extraction allows for the application of the MIL-HDBK-5J fatigue coefficients in the cumulative damage summation. A numerical example is given in this paper for the stress response of a beam undergoing random base excitation, where the excitation is applied separately by a time history and by its corresponding PSD. The fatigue calculation is performed in the time domain, as well as in the frequency domain via the modified spectral methods. The result comparison shows that the modified spectral methods give comparable results to the time domain rainflow counting method.
Continuous non-invasive blood glucose monitoring by spectral image differencing method
Huang, Hao; Liao, Ningfang; Cheng, Haobo; Liang, Jing
2018-01-01
Currently, the use of implantable enzyme electrode sensor is the main method for continuous blood glucose monitoring. But the effect of electrochemical reactions and the significant drift caused by bioelectricity in body will reduce the accuracy of the glucose measurements. So the enzyme-based glucose sensors need to be calibrated several times each day by the finger-prick blood corrections. This increases the patient's pain. In this paper, we proposed a method for continuous Non-invasive blood glucose monitoring by spectral image differencing method in the near infrared band. The method uses a high-precision CCD detector to switch the filter in a very short period of time, obtains the spectral images. And then by using the morphological method to obtain the spectral image differences, the dynamic change of blood sugar is reflected in the image difference data. Through the experiment proved that this method can be used to monitor blood glucose dynamically to a certain extent.
New Spectral Method for Halo Particle Definition in Intense Mis-matched Beams
Energy Technology Data Exchange (ETDEWEB)
Dorf, Mikhail A.; Davidson, Ronald C.; Startsev, Edward A.
2011-04-27
An advanced spectral analysis of a mis-matched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits.
Multi-spectral temperature measurement method for gas turbine blade
Gao, Shan; Feng, Chi; Wang, Lixin; Li, Dong
2016-02-01
One of the basic methods to improve both the thermal efficiency and power output of a gas turbine is to increase the firing temperature. However, gas turbine blades are easily damaged in harsh high-temperature and high-pressure environments. Therefore, ensuring that the blade temperature remains within the design limits is very important. There are unsolved problems in blade temperature measurement, relating to the emissivity of the blade surface, influences of the combustion gases, and reflections of radiant energy from the surroundings. In this study, the emissivity of blade surfaces has been measured, with errors reduced by a fitting method, influences of the combustion gases have been calculated for different operational conditions, and a reflection model has been built. An iterative computing method is proposed for calculating blade temperatures, and the experimental results show that this method has high precision.
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.
2013-01-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
The stochastic finite element methods with applications in geotechnics and rupture mechanics
International Nuclear Information System (INIS)
Baldeweck, Herve
1999-01-01
After having presented and classified the various stochastic finite elements methods, notably by distinguishing reliability methods (first order and second order reliability methods, response surfaces, Monte Carlo) and sensitivity methods (Monte Carlo, spectral development, perturbation, weighted integrals), the author of this research thesis presents basic tools needed for different theoretical developments: hazard representation and method of moments. He also presents the problem which is used all along this work to compare and assess the different sensitivity methods. Then, he reports the theoretical development of these sensitivity methods: the Monte Carlo method, the spectral development method, the perturbation method, and the quadrature method. This last one is a new one aimed at the assessment of statistical moments. The author highlights the relationships between reliability and sensitivity methods. In the third part, several applications and calculations are reported. Applications are in geotechnics (soil-structure interaction, calculation of soil stiffness, application in the field of geo-materials with the calculation of an underground gallery), and in rupture mechanics (international benchmark on the reliability of a nuclear reactor, non linear calculation of a cracked straight pipe, reliability calculation of a cracked plate with a Young modulus being a random field) [fr
Review of Tomographic Imaging using Finite Element Method
Directory of Open Access Journals (Sweden)
Mohd Fua’ad RAHMAT
2011-12-01
Full Text Available Many types of techniques for process tomography were proposed and developed during the past 20 years. This paper review the techniques and the current state of knowledge and experience on the subject, aimed at highlighting the problems associated with the non finite element methods, such as the ill posed, ill conditioned which relates to the accuracy and sensitivity of measurements. In this paper, considerations for choice of sensors and its applications were outlined and descriptions of non finite element tomography systems were presented. The finite element method tomography system as obtained from recent works, suitable for process control and measurement were also presented.
Conjugation of fiber-coupled wide-band light sources and acousto-optical spectral elements
Machikhin, Alexander; Batshev, Vladislav; Polschikova, Olga; Khokhlov, Demid; Pozhar, Vitold; Gorevoy, Alexey
2017-12-01
Endoscopic instrumentation is widely used for diagnostics and surgery. The imaging systems, which provide the hyperspectral information of the tissues accessible by endoscopes, are particularly interesting and promising for in vivo photoluminescence diagnostics and therapy of tumour and inflammatory diseases. To add the spectral imaging feature to standard video endoscopes, we propose to implement acousto-optical (AO) filtration of wide-band illumination of incandescent-lamp-based light sources. To collect maximum light and direct it to the fiber-optic light guide inside the endoscopic probe, we have developed and tested the optical system for coupling the light source, the acousto-optical tunable filter (AOTF) and the light guide. The system is compact and compatible with the standard endoscopic components.
Analysis of concrete beams using applied element method
Lincy Christy, D.; Madhavan Pillai, T. M.; Nagarajan, Praveen
2018-03-01
The Applied Element Method (AEM) is a displacement based method of structural analysis. Some of its features are similar to that of Finite Element Method (FEM). In AEM, the structure is analysed by dividing it into several elements similar to FEM. But, in AEM, elements are connected by springs instead of nodes as in the case of FEM. In this paper, background to AEM is discussed and necessary equations are derived. For illustrating the application of AEM, it has been used to analyse plain concrete beam of fixed support condition. The analysis is limited to the analysis of 2-dimensional structures. It was found that the number of springs has no much influence on the results. AEM could predict deflection and reactions with reasonable degree of accuracy.
Linear finite element method for one-dimensional diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica
2011-07-01
We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)
The Matrix Element Method at Next-to-Leading Order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-01-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...
Spectral methods in chemistry and physics applications to kinetic theory and quantum mechanics
Shizgal, Bernard
2015-01-01
This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficient...
A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas
International Nuclear Information System (INIS)
Vay, Jean-Luc; Haber, Irving; Godfrey, Brendan B.
2013-01-01
Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods
Generalized spectral method for near-field optical microscopy
Energy Technology Data Exchange (ETDEWEB)
Jiang, B.-Y.; Zhang, L. M.; Basov, D. N.; Fogler, M. M. [Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093 (United States); Castro Neto, A. H. [Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215 (United States); Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore 117542 (Singapore)
2016-02-07
Electromagnetic interaction between a sub-wavelength particle (the “probe”) and a material surface (the “sample”) is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with radiative damping included perturbatively.
Methodes spectrales paralleles et applications aux simulations de couches de melange compressibles
Male , Jean-Michel; Fezoui , Loula ,
1993-01-01
La resolution des equations de Navier-Stokes en methodes spectrales pour des ecoulements compressibles peut etre assez gourmande en temps de calcul. On etudie donc ici la parallelisation d'un tel algorithme et son implantation sur une machine massivement parallele, la connection-machine CM-2. La methode spectrale s'adapte bien aux exigences du parallelisme massif, mais l'un des outils de base de cette methode, la transformee de Fourier rapide (lorsqu'elle doit etre appliquee sur les deux dime...
Spectral methods for a nonlinear initial value problem involving pseudo differential operators
International Nuclear Information System (INIS)
Pasciak, J.E.
1982-01-01
Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed
Spectral and thermal behaviours of rare earth element complexes with 3,5-dimethoxybenzoic acid
Directory of Open Access Journals (Sweden)
JANUSZ CHRUŚCIEL
2003-10-01
Full Text Available The conditions for the formation of rare earth element 3,5-dimethytoxybenzoates were studied and their quantitative composition and solubilities in water at 293 K were determined. The complexes are anhydrous or hydrated salts and their solubilities are of the orders of 10-5 10-4 mol dm-3. Their FTIR, FIR and X-ray spectra were recorded. The compounds were also characterized by thermogravimetric studies in air and nitrogen atmospheres and by magnetic measurements. All complexes are crystalline compounds. The carboxylate group in these complexes is a bidentate, chelating ligand. On heating in air to 1173 K, the 3,5-dimethoxybenzoates of rare earth elements decompose in various ways. The hydrated complexes first dehydrate to form anhydrous salts which then decompose in air to the oxides of the respective metals while in nitrogen to mixtures of carbon and oxides of the respective metals. The complexes are more stable in air than in nitrogen.
Numerical experiment on finite element method for matching data
International Nuclear Information System (INIS)
Tokuda, Shinji; Kumakura, Toshimasa; Yoshimura, Koichi.
1993-03-01
Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)
Precise magnetostatic field using the finite element method
International Nuclear Information System (INIS)
Nascimento, Francisco Rogerio Teixeira do
2013-01-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
Energy Technology Data Exchange (ETDEWEB)
Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
A Spectral-Texture Kernel-Based Classification Method for Hyperspectral Images
Directory of Open Access Journals (Sweden)
Yi Wang
2016-11-01
Full Text Available Classification of hyperspectral images always suffers from high dimensionality and very limited labeled samples. Recently, the spectral-spatial classification has attracted considerable attention and can achieve higher classification accuracy and smoother classification maps. In this paper, a novel spectral-spatial classification method for hyperspectral images by using kernel methods is investigated. For a given hyperspectral image, the principle component analysis (PCA transform is first performed. Then, the first principle component of the input image is segmented into non-overlapping homogeneous regions by using the entropy rate superpixel (ERS algorithm. Next, the local spectral histogram model is applied to each homogeneous region to obtain the corresponding texture features. Because this step is performed within each homogenous region, instead of within a fixed-size image window, the obtained local texture features in the image are more accurate, which can effectively benefit the improvement of classification accuracy. In the following step, a contextual spectral-texture kernel is constructed by combining spectral information in the image and the extracted texture information using the linearity property of the kernel methods. Finally, the classification map is achieved by the support vector machines (SVM classifier using the proposed spectral-texture kernel. Experiments on two benchmark airborne hyperspectral datasets demonstrate that our method can effectively improve classification accuracies, even though only a very limited training sample is available. Specifically, our method can achieve from 8.26% to 15.1% higher in terms of overall accuracy than the traditional SVM classifier. The performance of our method was further compared to several state-of-the-art classification methods of hyperspectral images using objective quantitative measures and a visual qualitative evaluation.
International Nuclear Information System (INIS)
Schulte, R T; Fritzen, C-P; Moll, J
2010-01-01
During the last decades, guided waves have shown great potential for Structural Health Monitoring (SHM) applications. These waves can be excited and sensed by piezoelectric elements that can be permanently attached onto a structure offering online monitoring capability. However, the setup of wave based SHM systems for complex structures may be very difficult and time consuming. For that reason there is a growing demand for efficient simulation tools providing the opportunity to design wave based SHM systems in a virtual environment. As usually high frequency waves are used, the associated short wavelength leads to the necessity of a very dense mesh, which makes conventional finite elements not well suited for this purpose. Therefore in this contribution a flat shell spectral element approach is presented. By including electromechanical coupling a SHM system can be simulated entirely from actuator voltage to sensor voltage. Besides a comparison to measured data for anisotropic materials including delamination, a numerical example of a more complex, stiffened shell structure with debonding is presented.
Complex finite element sensitivity method for creep analysis
International Nuclear Information System (INIS)
Gomez-Farias, Armando; Montoya, Arturo; Millwater, Harry
2015-01-01
The complex finite element method (ZFEM) has been extended to perform sensitivity analysis for mechanical and structural systems undergoing creep deformation. ZFEM uses a complex finite element formulation to provide shape, material, and loading derivatives of the system response, providing an insight into the essential factors which control the behavior of the system as a function of time. A complex variable-based quadrilateral user element (UEL) subroutine implementing the power law creep constitutive formulation was incorporated within the Abaqus commercial finite element software. The results of the complex finite element computations were verified by comparing them to the reference solution for the steady-state creep problem of a thick-walled cylinder in the power law creep range. A practical application of the ZFEM implementation to creep deformation analysis is the calculation of the skeletal point of a notched bar test from a single ZFEM run. In contrast, the standard finite element procedure requires multiple runs. The value of the skeletal point is that it identifies the location where the stress state is accurate, regardless of the certainty of the creep material properties. - Highlights: • A novel finite element sensitivity method (ZFEM) for creep was introduced. • ZFEM has the capability to calculate accurate partial derivatives. • ZFEM can be used for identification of the skeletal point of creep structures. • ZFEM can be easily implemented in a commercial software, e.g. Abaqus. • ZFEM results were shown to be in excellent agreement with analytical solutions
Method of removing crud deposited on fuel element clusters
International Nuclear Information System (INIS)
Yokota, Tokunobu; Yashima, Akira; Tajima, Jun-ichiro.
1982-01-01
Purpose: To enable easy elimination of claddings deposited on the surface of fuel element. Method: An operator manipulates a pole from above a platform, engages the longitudinal flange of the cover to the opening at the upper end of a channel box and starts up a suction pump. The suction amount of the pump is set such that water flow becomes within the channel box at greater flow rate than the operational flow rate in the channel box of the fuel element clusters during reactor operation. This enables to remove crud deposited on the surface of individual fuel elements with ease and rapidly without detaching the channel box. (Moriyama, K.)
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Scalable fast multipole methods for vortex element methods
Hu, Qi; Gumerov, Nail A.; Yokota, Rio; Barba, Lorena A.; Duraiswami, Ramani
2012-01-01
work for a scalar heterogeneous FMM algorithm, we develop a new FMM-based vortex method capable of simulating general flows including turbulence on heterogeneous architectures, which distributes the work between multi-core CPUs and GPUs to best utilize
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
Analysis of Piezoelectric Solids using Finite Element Method
Aslam, Mohammed; Nagarajan, Praveen; Remanan, Mini
2018-03-01
Piezoelectric materials are extensively used in smart structures as sensors and actuators. In this paper, static analysis of three piezoelectric solids is done using general-purpose finite element software, Abaqus. The simulation results from Abaqus are compared with the results obtained using numerical methods like Boundary Element Method (BEM) and meshless point collocation method (PCM). The BEM and PCM are cumbersome for complex shape and complicated boundary conditions. This paper shows that the software Abaqus can be used to solve the governing equations of piezoelectric solids in a much simpler and faster way than the BEM and PCM.
Navier-Stokes equations by the finite element method
International Nuclear Information System (INIS)
Portella, P.E.
1984-01-01
A computer program to solve the Navier-Stokes equations by using the Finite Element Method is implemented. The solutions variables investigated are stream-function/vorticity in the steady case and velocity/pressure in the steady state and transient cases. For steady state flow the equations are solved simultaneously by the Newton-Raphson method. For the time dependent formulation, a fractional step method is employed to discretize in time and artificial viscosity is used to preclude spurious oscilations in the solution. The element used is the three node triangle. Some numerical examples are presented and comparisons are made with applications already existent. (Author) [pt
Nucleon matrix elements using the variational method in lattice QCD
International Nuclear Information System (INIS)
Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ., SA
2016-06-01
The extraction of hadron matrix elements in lattice QCD using the standard two- and threepoint correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current g_A, the scalar current g_S and the quark momentum fraction left angle x right angle of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
Mathematical aspects of finite element methods for incompressible viscous flows
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Method for fuel element leak detection in pressurized water reactors
International Nuclear Information System (INIS)
Kunze, U.
1983-01-01
The method is aimed at detecting fuel element leaks during reactor operation. It is based on neutron flux measurements at many points in the core, using at least two detectors at a time. The detectors must be arranged in the direction of the coolant flow. Values obtained from periodic measurements are compared with threshold values. The location of fuel element leaks is determined from those values exceeding the threshold of individual detectors
Nonlinear nonstationary analysis with the finite element method
International Nuclear Information System (INIS)
Vaz, L.E.
1981-01-01
In this paper, after some introductory remarks on numerical methods for the integration of initial value problems, the applicability of the finite element method for transient diffusion analysis as well as dynamic and inelastic analysis is discussed, and some examples are presented. (RW) [de
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been
Discontinuous Galerkin finite element methods for hyperbolic differential equations
van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.
2002-01-01
In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas
Instrumental methods for analysis of some elements in flour
International Nuclear Information System (INIS)
Zagrodzki, P.; Dutkiewicz, E.M.; Malec, P.; Krosniak, M.; Knap, W.
1993-10-01
For ten various brands of flour contents of chosen (heavy) elements were determined by means of ICP, GF-AAS, PIXE and ASV/CSV methods. General performance of participating laboratories as well as pros and cons of different analytical methods were compared and discussed. (author). 6 refs, 6 figs, 7 tabs
Spectral Analysis of Rare Earth Elements using Laser-Induced Breakdown Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Martin, Madhavi Z [ORNL; Fox, Dr. Richard V [Idaho National Laboratory (INL); Miziolek, Andrzej W [United States Army Research Laboratory; DeLucia, Frank C [United States Army Research Laboratory; Andre, Nicolas O [ORNL
2015-01-01
There is growing interest in rapid analysis of rare earth elements (REEs) both due to the need to find new natural sources to satisfy increased demand in their use in various electronic devices, as well as the fact that they are used to estimate actinide masses for nuclear safeguards and nonproliferation. Laser-Induced Breakdown Spectroscopy (LIBS) appears to be a particularly well-suited spectroscopy-based technology to rapidly and accurately analyze the REEs in various matrices at low concentration levels (parts-per-million). Although LIBS spectra of REEs have been reported for a number of years, further work is still necessary in order to be able to quantify the concentrations of various REEs in realworld complex samples. LIBS offers advantages over conventional solution-based radiochemistry in terms of cost, analytical turnaround, waste generation, personnel dose, and contamination risk. Rare earth elements of commercial interest are found in the following three matrix groups: 1) raw ores and unrefined materials, 2) as components in refined products such as magnets, lighting phosphors, consumer electronics (which are mostly magnets and phosphors), catalysts, batteries, etc., and 3) waste/recyclable materials (aka e-waste). LIBS spectra for REEs such as Gd, Nd, and Sm found in rare earth magnets are presented.
Spectral Analysis of Rare Earth Elements using Laser-Induced Breakdown Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Martin, Madhavi Z [ORNL; Fox, Dr. Richard V [Idaho National Laboratory (INL); Miziolek, Andrzej W [United States Army Research Laboratory; DeLucia, Frank C [United States Army Research Laboratory; Andre, Nicolas O [ORNL
2015-01-01
There is growing interest in rapid analysis of rare earth elements (REEs) both due to the need to find new natural sources to satisfy increased demand in their use in various electronic devices, as well as the fact that they are used to estimate actinide masses for nuclear safeguards and nonproliferation. Laser-Induced Breakdown Spectroscopy (LIBS) appears to be a particularly well-suited spectroscopy-based technology to rapidly and accurately analyze the REEs in various matrices at low concentration levels (parts-per-million). Although LIBS spectra of REEs have been reported for a number of years, further work is still necessary in order to be able to quantify the concentrations of various REEs in real-world complex samples. LIBS offers advantages over conventional solution-based radiochemistry in terms of cost, analytical turnaround, waste generation, personnel dose, and contamination risk. Rare earth elements of commercial interest are found in the following three matrix groups: 1) raw ores and unrefined materials, 2) as components in refined products such as magnets, lighting phosphors, consumer electronics (which are mostly magnets and phosphors), catalysts, batteries, etc., and 3) waste/recyclable materials (aka e-waste). LIBS spectra for REEs such as Gd, Nd, and Sm found in rare earth magnets are presented.
A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems
Directory of Open Access Journals (Sweden)
A. Karimi Dizicheh
2013-01-01
wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.
Application of the spectral correction method to reanalysis data in South Africa
DEFF Research Database (Denmark)
Larsén, Xiaoli Guo; Kruger, Andries C.
2014-01-01
of this study is to evaluate the applicability of the method to the relevant region. The impacts from the two aspects are investigated for interior and coastal locations. Measurements from five stations from South Africa are used to evaluate the results from the spectral model S(f)=af−5/3 together...... with the hourly time series of the Climate Forecast System Reanalysis (CFSR) 10 m wind at 38 km resolution over South Africa. The results show that using the spectral correction method to the CFSR wind data produce extreme wind atlases in acceptable agreement with the atlas made from limited measurements across...
The analysis of toxic connections content in water by spectral methods
Plotnikova, I. V.; Chaikovskaya, O. N.; Sokolova, I. V.; Artyushin, V. R.
2017-08-01
The current state of ecology means the strict observance of measures for the utilization of household and industrial wastes that is connected with very essential expenses of means and time. Thanks to spectroscopic devices usage the spectral methods allow to carry out the express quantitative and qualitative analysis in a workplace and field conditions. In a work the application of spectral methods by studying the degradation of toxic organic compounds after preliminary radiation of various sources is shown. Experimental data of optical density of water at various influences are given.
Aborode, Fatai Adigun; Raab, Andrea; Foster, Simon; Lombi, Enzo; Maher, William; Krupp, Eva M; Feldmann, Joerg
2015-07-01
Three month old Thunbergia alata were exposed for 13 days to 10 μM selenite to determine the biotransformation of selenite in their roots. Selenium in formic acid extracts (80 ± 3%) was present as selenopeptides with Se-S bonds and selenium-PC complexes (selenocysteinyl-2-3-dihydroxypropionyl-glutathione, seleno-phytochelatin2, seleno-di-glutathione). An analytical method using HPLC-ICPMS to detect and quantify elemental selenium in roots of T. alata plants using sodium sulfite to quantitatively transform elemental selenium to selenosulfate was also developed. Elemental selenium was determined as 18 ± 4% of the total selenium in the roots which was equivalent to the selenium not extracted using formic acid extraction. The results are in an agreement with the XAS measurements of the exposed roots which showed no occurrence of selenite or selenate but a mixture of selenocysteine and elemental selenium.
Scalable fast multipole methods for vortex element methods
Hu, Qi
2012-11-01
We use a particle-based method to simulate incompressible flows, where the Fast Multipole Method (FMM) is used to accelerate the calculation of particle interactions. The most time-consuming kernelsâ\\'the Biot-Savart equation and stretching term of the vorticity equationâ\\'are mathematically reformulated so that only two Laplace scalar potentials are used instead of six, while automatically ensuring divergence-free far-field computation. Based on this formulation, and on our previous work for a scalar heterogeneous FMM algorithm, we develop a new FMM-based vortex method capable of simulating general flows including turbulence on heterogeneous architectures, which distributes the work between multi-core CPUs and GPUs to best utilize the hardware resources and achieve excellent scalability. The algorithm also uses new data structures which can dynamically manage inter-node communication and load balance efficiently but with only a small parallel construction overhead. This algorithm can scale to large-sized clusters showing both strong and weak scalability. Careful error and timing trade-off analysis are also performed for the cutoff functions induced by the vortex particle method. Our implementation can perform one time step of the velocity+stretching for one billion particles on 32 nodes in 55.9 seconds, which yields 49.12 Tflop/s. © 2012 IEEE.
Tapia-Herrera, R.; Huerta-Lopez, C. I.; Martinez-Cruzado, J. A.
2009-05-01
Results of site characterization for an experimental site in the metropolitan area of Tijuana, B. C., Mexico are presented as part of the on-going research in which time series of earthquakes, ambient noise, and induced vibrations were processed with three different methods: H/V spectral ratios, Spectral Analysis of Surface Waves (SASW), and the Random Decrement Method, (RDM). Forward modeling using the wave propagation stiffness matrix method (Roësset and Kausel, 1981) was used to compute the theoretical SH/P, SV/P spectral ratios, and the experimental H/V spectral ratios were computed following the conventional concepts of Fourier analysis. The modeling/comparison between the theoretical and experimental H/V spectral ratios was carried out. For the SASW method the theoretical dispersion curves were also computed and compared with the experimental one, and finally the theoretical free vibration decay curve was compared with the experimental one obtained with the RDM. All three methods were tested with ambient noise, induced vibrations, and earthquake signals. Both experimental spectral ratios obtained with ambient noise as well as earthquake signals agree quite well with the theoretical spectral ratios, particularly at the fundamental vibration frequency of the recording site. Differences between the fundamental vibration frequencies are evident for sites located at alluvial fill (~0.6 Hz) and at sites located at conglomerate/sandstones fill (0.75 Hz). Shear wave velocities for the soft soil layers of the 4-layer discrete soil model ranges as low as 100 m/s and up to 280 m/s. The results with the SASW provided information that allows to identify low velocity layers, not seen before with the traditional seismic methods. The damping estimations obtained with the RDM are within the expected values, and the dominant frequency of the system also obtained with the RDM correlates within the range of plus-minus 20 % with the one obtained by means of the H/V spectral
Spectral analysis of an algebraic collapsing acceleration for the characteristics method
International Nuclear Information System (INIS)
Le Tellier, R.; Hebert, A.
2005-01-01
A spectral analysis of a diffusion synthetic acceleration called Algebraic Collapsing Acceleration (ACA) was carried out in the context of the characteristics method to solve the neutron transport equation. Two analysis were performed in order to assess the ACA performances. Both a standard Fourier analysis in a periodic and infinite slab-geometry and a direct spectral analysis for a finite slab-geometry were investigated. In order to evaluate its performance, ACA was compared with two competing techniques used to accelerate the convergence of the characteristics method, the Self-Collision Re-balancing technique and the Asymptotic Synthetic Acceleration. In the restricted framework of 1-dimensional slab-geometries, we conclude that ACA offers a good compromise between the reduction of the spectral radius of the iterative matrix and the resources to construct, store and solve the corrective system. A comparison on a monoenergetic 2-dimensional benchmark was performed and tends to confirm these conclusions. (authors)
Nobe, Kazuki; Yoshimoto, Kayo; Yamada, Kenji; Takahashi, Hideya
2018-02-01
Functional gastrointestinal disorders (FGID) are the most common gastrointestinal disorders. The term "functional" is generally applied to disorders where there are no structural abnormalities. One of the major factors for FGID is abnormal gastrointestinal motility. We have proposed a system for assessing the function of gastric motility using a 3D endoscope. In this previous study, we established a method for estimating characteristics of contraction wave extracted from a 3D shape include contraction wave obtained from stereo endoscope. Because it is difficult to fix the tip position of the endoscope during the examination, estimation of the 3D position between the endoscope and the gastric wall is necessary for the accurate assessment. Then, we have proposed a motion compensation method using 3D scene flow. However, since mucosa has few feature points, it is difficult to obtain 3D scene flow from RGB images. So, we focused on spectral imaging that can enhance visualization of mucosal structure. Spectral image can be obtained without switching optical filters by using technique to estimate spectral reflectance by image processing. In this paper, we propose registration method of measured 3D shape in time series using estimated spectral image. The spectral image is estimated from the RGB image for each frame. 3D scene flow of feature points, that is, enhanced mucosal structure calculated by spectral images in a time series. The position change between the endoscope and gastric wall is estimated by 3D scene flow. We experimented to confirm the validity of the proposed method using papers with a grid of colors close to the background color.
A finite element method for SSI time history calculation
International Nuclear Information System (INIS)
Ni, X.; Gantenbein, F.; Petit, M.
1989-01-01
The method which is proposed is based on a finite element modelization for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method is presented, then applications are given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior are described
A stochastic method for computing hadronic matrix elements
Energy Technology Data Exchange (ETDEWEB)
Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computational-based Science and Technology Research Center; Dinter, Simon; Drach, Vincent [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Jansen, Karl [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Hadjiyiannakou, Kyriakos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Renner, Dru B. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Collaboration: European Twisted Mass Collaboration
2013-02-15
We present a stochastic method for the calculation of baryon three-point functions that is more versatile compared to the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume and find a favorable signal-to-noise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements.
Thermohydraulic analysis in pipelines using the finite element method
International Nuclear Information System (INIS)
Costa, L.E.; Idelsohn, S.R.
1984-01-01
The Finite Element Method (FEM) is employed for the numerical solution of fluid flow problems with combined heat transfer mechanisms. Boussinesq approximations are used for the solution of the governing equations. The application of the FEM leads to a set of simultaneous nonlinear equations. The development of the method, for the solution of bidimensional and axisymmetric problems, is presented. Examples of fluid flow in pipes, including natural and forced convection, are solved with the proposed method and discussed in the paper. (Author) [pt
A finite element method for SSI time history calculations
International Nuclear Information System (INIS)
Ni, X.M.; Gantenbein, F.; Petit, M.
1989-01-01
The method which is proposed is based on a finite element modelisation for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method will be presented, then applications will be given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior will be described
Nuclear analytical methods for trace element studies in calcified tissues
International Nuclear Information System (INIS)
Chaudhry, M.A.; Chaudhry, M.N.
2001-01-01
Full text: Various nuclear analytical methods have been developed and applied to determine the elemental composition of calcified tissues (teeth and bones). Fluorine was determined by prompt gamma activation analysis through the 19 F(p,ag) 16 O reaction. Carbon was measured by activation analysis with He-3 ions, and the technique of Proton-Induced X-ray Emission (PIXE) was applied to simultaneously determine Ca, P, and trace elements in well-documented teeth. Dental hard tissues, enamel, dentine, cement, and their junctions, as well as different parts of the same tissue, were examined separately. Furthermore, using a Proton Microprobe, we measured the surface distribution of F and other elements on and around carious lesions on the enamel. The depth profiles of F, and other elements, were also measured right up to the amelodentin junction
(Environmental and geophysical modeling, fracture mechanics, and boundary element methods)
Energy Technology Data Exchange (ETDEWEB)
Gray, L.J.
1990-11-09
Technical discussions at the various sites visited centered on application of boundary integral methods for environmental modeling, seismic analysis, and computational fracture mechanics in composite and smart'' materials. The traveler also attended the International Association for Boundary Element Methods Conference at Rome, Italy. While many aspects of boundary element theory and applications were discussed in the papers, the dominant topic was the analysis and application of hypersingular equations. This has been the focus of recent work by the author, and thus the conference was highly relevant to research at ORNL.
Matlab and C programming for Trefftz finite element methods
Qin, Qing-Hua
2008-01-01
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th
Nuclear-physical methods of investigation of an element composition in samples of soils and plants
International Nuclear Information System (INIS)
Hushmurodov, Sh.; Botaev, N.
2002-01-01
Soil (ground) and vegetative covers of the Earth are one of the most responsive and specific parts of the biosphere with respect to pollution. A proper control after them is of fundamental importance in creating and protecting optical surrounding. Analysis of soils and plants is a necessary and important stage in the process of investigation of microelements' migration in biogeochemical cycles. For this purpose we studied some reserved terrains of Uzbekistan to reveal a level of their contamination by heavy metals, as well as to find out typical and territorial singularities in accumulation of a number of elements by soils and plants. In order to decrease an influence of systematic errors, and to obtain more precise and reliable data, we carried out the element analysis of the samples by different methods, such as gamma-activation analysis, neutron-activation analysis, X-ray spectral analysis, and X-ray fluorescent analysis. As a result of our investigations we have obtained rather great information, which can be used in future to estimate the conditions of the surrounding nature. The investigations allowed us to determine the content of about 40 elements, as well as to show that the data, obtained by different nuclear-physical methods, are in rather good agreement. A reproducibility of the results of the methods, determined in control measurements, depends on the concentration of the analyzed elements, and is equal to 10-35 %. A comparison of the obtained data allowed us to reveal some singularities in element composition of the investigated samples depending on their type and territorial factor. It has been revealed that the data, obtained by different methods, are in rather good agreement. Our investigations allowed us to find out a series of regularities and singularities in accumulation of elements in plants, as well as to show the possibility of using nuclear-physical methods in such investigations
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
Stress and Deformation Analysis in Base Isolation Elements Using the Finite Element Method
Directory of Open Access Journals (Sweden)
Claudiu Iavornic
2011-01-01
Full Text Available In Modern tools as Finite Element Method can be used to study the behavior of elastomeric isolation systems. The simulation results obtained in this way provide a large series of data about the behavior of elastomeric isolation bearings under different types of loads and help in taking right decisions regarding geometrical optimizations needed for improve such kind of devices.
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
A particle finite element method for machining simulations
Sabel, Matthias; Sator, Christian; Müller, Ralf
2014-07-01
The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.
PHARMACOPOEIA METHODS FOR ELEMENTAL ANALYSIS OF MEDICINES: A COMPARATIVE STUDY
Directory of Open Access Journals (Sweden)
Tetiana M. Derkach
2018-01-01
Full Text Available The article is devoted to the problem of quality assurance of medicinal products, namely the determination of elemental impurity concentration compared to permitted daily exposures for and the correct choice analytical methods that are adequate to the formulated tasks. The paper goal is to compare characteristics of four analytical methods recommended by the Pharmacopoeia of various countries to control the content of elemental impurities in medicines, including medicinal plant raw materials and herbal medicines. Both advantages and disadvantages were described for atomic absorption spectroscopy with various atomising techniques, as well as atomic emission spectroscopy and mass spectrometry with inductively coupled plasma. The choice of the most rational analysis method depends on a research task and is reasoned from the viewpoint of analytical objectives, possible complications, performance attributes, and economic considerations. The methods of ICP-MS and GFAAS were shown to provide the greatest potential for determining the low and ultra-low concentrations of chemical elements in medicinal plants and herbal medicinal products. The other two methods, FAAS and ICP-AES, are limited to the analysis of the main essential elements and the largest impurities. The ICP-MS is the most efficient method for determining ultra-low concentrations. However, the interference of mass peaks is typical for ICP-MS. It is formed not only by impurities but also by polyatomic ions with the participation of argon, as well as atoms of gases from the air (C, N and O or matrices (O, N, H, P, S and Cl. Therefore, a correct sample preparation, which guarantees minimisation of impurity contamination and loss of analytes becomes the most crucial stage of analytical applications of ICP-MS. The detections limits for some chemical elements, which content is regulated in modern Pharmacopoeia, were estimated for each method and analysis conditions of medicinal plant raw
The application of the Chebyshev-spectral method in transport phenomena
Guo, Weidong; Narayanan, Ranga
2012-01-01
Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character. When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer. To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems. The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs. The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interes...
A new approach to passivity preserving model reduction : the dominant spectral zero method
Ionutiu, R.; Rommes, J.; Antoulas, A.C.; Roos, J.; Costa, L.R.J.
2010-01-01
A new model reduction method for circuit simulation is presented, which preserves passivity by interpolating dominant spectral zeros. These are computed as poles of an associated Hamiltonian system, using an iterative solver: the subspace accelerated dominant pole algorithm (SADPA). Based on a
Mass anomalous dimension of SU(2) with Nf=8 using the spectral density method
DEFF Research Database (Denmark)
Suorsa, Joni M.; Leino, Viljami; Rantaharju, Jarno
2015-01-01
SU(2) with Nf=8 is believed to have an infrared conformal fixed point. We use the spectral density method to evaluate the coupling constant dependence of the mass anomalous dimension for massless HEX smeared, clover improved Wilson fermions with Schr\\"odinger functional boundary conditions....
Spectral mimetic least-squares method for div-curl systems
Gerritsma, Marc; Palha, Artur; Lirkov, I.; Margenov, S.
2018-01-01
In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test
The spectral method and the central limit theorem for general Markov chains
Nagaev, S. V.
2017-12-01
We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.
Evaluation of methods to determine the spectral variations of aerosol optical thickness
Digital Repository Service at National Institute of Oceanography (India)
Suresh, T.; Talaulikar, M.; Rodrigues, A.; Desa, E.; Chauhan, P.
The methods used to derive spectral variations of aerosol optical thickness, AOT are evaluated. For our analysis we have used the AOT measured using a hand held sunphotometer at the coastal station on the west coast of India, Dona-Paula, Goa...
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
Ethnomathematics elements in Batik Bali using backpropagation method
Lestari, Mei; Irawan, Ari; Rahayu, Wanti; Wayan Parwati, Ni
2018-05-01
Batik is one of traditional arts that has been established by the UNESCO as Indonesia’s cultural heritage. Batik has varieties and motifs, and each motifs has its own uniqueness but seems similar, that makes it difficult to identify. This study aims to develop an application that can identify typical batik Bali with etnomatematics elements on it. Etnomatematics is a study that shows relation between culture and mathematics concepts. Etnomatematics in Batik Bali is more to geometrical concept in line of strong Balinese culture element. The identification process is use backpropagation method. Steps of backpropagation methods are image processing (including scalling and tresholding image process). Next step is insert the processed image to an artificial neural network. This study resulted an accuracy of identification of batik Bali that has Etnomatematics elements on it.
Analysis of Brick Masonry Wall using Applied Element Method
Lincy Christy, D.; Madhavan Pillai, T. M.; Nagarajan, Praveen
2018-03-01
The Applied Element Method (AEM) is a versatile tool for structural analysis. Analysis is done by discretising the structure as in the case of Finite Element Method (FEM). In AEM, elements are connected by a set of normal and shear springs instead of nodes. AEM is extensively used for the analysis of brittle materials. Brick masonry wall can be effectively analyzed in the frame of AEM. The composite nature of masonry wall can be easily modelled using springs. The brick springs and mortar springs are assumed to be connected in series. The brick masonry wall is analyzed and failure load is determined for different loading cases. The results were used to find the best aspect ratio of brick to strengthen brick masonry wall.
Testing the accuracy and stability of spectral methods in numerical relativity
International Nuclear Information System (INIS)
Boyle, Michael; Lindblom, Lee; Pfeiffer, Harald P.; Scheel, Mark A.; Kidder, Lawrence E.
2007-01-01
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the Kidder, Scheel, and Teukolsky (KST) representation of the Einstein evolution equations. The basic 'Mexico City tests' widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error or by truncation error in the time integration. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test
International Nuclear Information System (INIS)
Fiebig, H. Rudolf
2002-01-01
We study various aspects of extracting spectral information from time correlation functions of lattice QCD by means of Bayesian inference with an entropic prior, the maximum entropy method (MEM). Correlator functions of a heavy-light meson-meson system serve as a repository for lattice data with diverse statistical quality. Attention is given to spectral mass density functions, inferred from the data, and their dependence on the parameters of the MEM. We propose to employ simulated annealing, or cooling, to solve the Bayesian inference problem, and discuss the practical issues of the approach
Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification
Directory of Open Access Journals (Sweden)
Xiaofeng Xue
2016-01-01
Full Text Available A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF. It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.
A complex guided spectral transform Lanczos method for studying quantum resonance states
International Nuclear Information System (INIS)
Yu, Hua-Gen
2014-01-01
A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO, and compared to previous calculations
Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression of the gra...
Piezoelectric Accelerometers Modification Based on the Finite Element Method
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
A mixed finite element method for particle simulation in lasertron
International Nuclear Information System (INIS)
Le Meur, G.
1987-03-01
A particle simulation code is being developed with the aim to treat the motion of charged particles in electromagnetic devices, such as Lasertron. The paper describes the use of mixed finite element methods in computing the field components, without derivating them from scalar or vector potentials. Graphical results are shown
Possibilities of Particle Finite Element Methods in Industrial Forming Processes
Oliver, J.; Cante, J. C.; Weyler, R.; Hernandez, J.
2007-04-01
The work investigates the possibilities offered by the particle finite element method (PFEM) in the simulation of forming problems involving large deformations, multiple contacts, and new boundaries generation. The description of the most distinguishing aspects of the PFEM, and its application to simulation of representative forming processes, illustrate the proposed methodology.
Method to fabricate block fuel elements for high temperature reactors
International Nuclear Information System (INIS)
Hrovat, M.; Rachor, L.
1977-01-01
The fabrication of block fuel elements for gas-cooled high temperature reactors can be improved upon by adding 0.2 to 2 wt.% of a hydrocarbon compound to the lubricating mixture prior to pressing. Hexanol or octanol are named as substances. The dimensional accuracy of the block is thus improved. 2 examples illustrate the method. (RW) [de
A mixed finite element method for particle simulation in Lasertron
International Nuclear Information System (INIS)
Le Meur, G.
1987-01-01
A particle simulation code is being developed with the aim to treat the motion of charged particles in electromagnetic devices, such as Lasertron. The paper describes the use of mixed finite element methods in computing the field components, without derivating them from scalar or vector potentials. Graphical results are shown
Three-dimensional wake field analysis by boundary element method
International Nuclear Information System (INIS)
Miyata, K.
1987-01-01
A computer code HERTPIA was developed for the calculation of electromagnetic wake fields excited by charged particles travelling through arbitrarily shaped accelerating cavities. This code solves transient wave problems for a Hertz vector. The numerical analysis is based on the boundary element method. This program is validated by comparing its results with analytical solutions in a pill-box cavity
Deflation in preconditioned conjugate gradient methods for Finite Element Problems
Vermolen, F.J.; Vuik, C.; Segal, A.
2002-01-01
We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous
Method to fabricate block fuel elements for high temperature reactors
International Nuclear Information System (INIS)
Hrovat, M.; Rachor, L.
1978-01-01
The fabrication of block fuel elements for gas-cooled high temperature reactors can be improved upon by adding 0.2 to 2 wt.% of a hydrocarbon compound to the lubricating mixture prior to pressing. Hexanol or octanol are named as substances. The dimensional accuracy of the block is thus improved. 2 examples illustrate the method. (orig./PW)
A Finite Element Removal Method for 3D Topology Optimization
Directory of Open Access Journals (Sweden)
M. Akif Kütük
2013-01-01
Full Text Available Topology optimization provides great convenience to designers during the designing stage in many industrial applications. With this method, designers can obtain a rough model of any part at the beginning of a designing stage by defining loading and boundary conditions. At the same time the optimization can be used for the modification of a product which is being used. Lengthy solution time is a disadvantage of this method. Therefore, the method cannot be widespread. In order to eliminate this disadvantage, an element removal algorithm has been developed for topology optimization. In this study, the element removal algorithm is applied on 3-dimensional parts, and the results are compared with the ones available in the related literature. In addition, the effects of the method on solution times are investigated.
Counting addressing method: Command addressable element and extinguishing module
Directory of Open Access Journals (Sweden)
Ristić Jovan D.
2009-01-01
Full Text Available The specific requirements that appear in addressable fire detection and alarm systems and the shortcomings of the existing addressing methods were discussed. A new method of addressing of detectors was proposed. The basic principles of addressing and responding of a called element are stated. Extinguishing module is specific subsystem in classic fire detection and alarm systems. Appearing of addressable fire detection and alarm systems didn't caused essential change in the concept of extinguishing module because of long calling period of such systems. Addressable fire security system based on counting addressing method reaches high calling rates and enables integrating of the extinguishing module in addressable system. Solutions for command addressable element and integrated extinguishing module are given in this paper. The counting addressing method was developed for specific requirements in fire detection and alarm systems, yet its speed and reliability justifies its use in the acquisition of data on slowly variable parameters under industrial conditions. .
Nakashima, Hiroshi; Takatsu, Yuzuru
The goal of this study is to develop a practical and fast simulation tool for soil-tire interaction analysis, where finite element method (FEM) and discrete element method (DEM) are coupled together, and which can be realized on a desktop PC. We have extended our formerly proposed dynamic FE-DE method (FE-DEM) to include practical soil-tire system interaction, where not only the vertical sinkage of a tire, but also the travel of a driven tire was considered. Numerical simulation by FE-DEM is stable, and the relationships between variables, such as load-sinkage and sinkage-travel distance, and the gross tractive effort and running resistance characteristics, are obtained. Moreover, the simulation result is accurate enough to predict the maximum drawbar pull for a given tire, once the appropriate parameter values are provided. Therefore, the developed FE-DEM program can be applied with sufficient accuracy to interaction problems in soil-tire systems.
Use of the iterative solution method for coupled finite element and boundary element modeling
International Nuclear Information System (INIS)
Koteras, J.R.
1993-07-01
Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element method and the boundary element method, have complementary characteristics for applications to problems of this type. The usefulness of combining these two methods for use as a geomechanics analysis tool has been recognized for some time, and a number of coupling techniques have been proposed. However, not all of them lend themselves to efficient computational implementations for large-scale problems. This report examines a coupling technique that can form the basis for an efficient analysis tool for large scale geomechanics problems through the use of an iterative equation solver
Development and validation of a new fallout transport method using variable spectral winds
International Nuclear Information System (INIS)
Hopkins, A.T.
1984-01-01
A new method was developed to incorporate variable winds into fallout transport calculations. The method uses spectral coefficients derived by the National Meteorological Center. Wind vector components are computed with the coefficients along the trajectories of falling particles. Spectral winds are used in the two-step method to compute dose rate on the ground, downwind of a nuclear cloud. First, the hotline is located by computing trajectories of particles from an initial, stabilized cloud, through spectral winds to the ground. The connection of particle landing points is the hotline. Second, dose rate on and around the hotline is computed by analytically smearing the falling cloud's activity along the ground. The feasibility of using spectral winds for fallout particle transport was validated by computing Mount St. Helens ashfall locations and comparing calculations to fallout data. In addition, an ashfall equation was derived for computing volcanic ash mass/area on the ground. Ashfall data and the ashfall equation were used to back-calculate an aggregated particle size distribution for the Mount St. Helens eruption cloud
Convergence of a residual based artificial viscosity finite element method
Nazarov, Murtazo
2013-02-01
We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.
A code for obtaining temperature distribution by finite element method
International Nuclear Information System (INIS)
Bloch, M.
1984-01-01
The ELEFIB Fortran language computer code using finite element method for calculating temperature distribution of linear and two dimensional problems, in permanent region or in the transient phase of heat transfer, is presented. The formulation of equations uses the Galerkin method. Some examples are shown and the results are compared with other papers. The comparative evaluation shows that the elaborated code gives good values. (M.C.K.) [pt
Parallel Fast Multipole Boundary Element Method for crustal dynamics
International Nuclear Information System (INIS)
Quevedo, Leonardo; Morra, Gabriele; Mueller, R Dietmar
2010-01-01
Crustal faults and sharp material transitions in the crust are usually represented as triangulated surfaces in structural geological models. The complex range of volumes separating such surfaces is typically three-dimensionally meshed in order to solve equations that describe crustal deformation with the finite-difference (FD) or finite-element (FEM) methods. We show here how the Boundary Element Method, combined with the Multipole approach, can revolutionise the calculation of stress and strain, solving the problem of computational scalability from reservoir to basin scales. The Fast Multipole Boundary Element Method (Fast BEM) tackles the difficulty of handling the intricate volume meshes and high resolution of crustal data that has put classical Finite 3D approaches in a performance crisis. The two main performance enhancements of this method: the reduction of required mesh elements from cubic to quadratic with linear size and linear-logarithmic runtime; achieve a reduction of memory and runtime requirements allowing the treatment of a new scale of geodynamic models. This approach was recently tested and applied in a series of papers by [1, 2, 3] for regional and global geodynamics, using KD trees for fast identification of near and far-field interacting elements, and MPI parallelised code on distributed memory architectures, and is now in active development for crustal dynamics. As the method is based on a free-surface, it allows easy data transfer to geological visualisation tools where only changes in boundaries and material properties are required as input parameters. In addition, easy volume mesh sampling of physical quantities enables direct integration with existing FD/FEM code.
A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA
Huang, Jun; Ma, Yong; Mei, Xiaoguang; Fan, Fan
2016-11-01
The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein's unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.
Wang, Wei; Song, Wei-Guo; Liu, Shi-Xing; Zhang, Yong-Ming; Zheng, Hong-Yang; Tian, Wei
2011-04-01
An improved method for detecting cloud combining Kmeans clustering and the multi-spectral threshold approach is described. On the basis of landmark spectrum analysis, MODIS data is categorized into two major types initially by Kmeans method. The first class includes clouds, smoke and snow, and the second class includes vegetation, water and land. Then a multi-spectral threshold detection is applied to eliminate interference such as smoke and snow for the first class. The method is tested with MODIS data at different time under different underlying surface conditions. By visual method to test the performance of the algorithm, it was found that the algorithm can effectively detect smaller area of cloud pixels and exclude the interference of underlying surface, which provides a good foundation for the next fire detection approach.
Ultrafast method of calculating the dynamic spectral line shapes for integrated modelling of plasmas
International Nuclear Information System (INIS)
Lisitsa, V.S.
2009-01-01
An ultrafast code for spectral line shape calculations is presented to be used in the integrated modelling of plasmas. The code is based on the close analogy between two mechanisms: (i) Dicke narrowing of the Doppler-broadened spectral lines and (ii) transition from static to impact regime in the Stark broadening. The analogy makes it possible to describe the dynamic Stark broadening in terms of an analytical functional of the static line shape. A comparison of new method with the widely used Frequency Fluctuating Method (FFM) developed by the Marseille University group (B. Talin, R. Stamm, et al.) shows good agreement, with the new method being faster than the standard FFM by nearly two orders of magnitude. The method proposed may significantly simplify the radiation transport modeling and opens new possibilities for integrated modeling of the edge and divertor plasma in tokamaks. (author)
Hybrid finite element and Brownian dynamics method for charged particles
Energy Technology Data Exchange (ETDEWEB)
Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
2016-04-28
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
Steam generator tube rupture simulation using extended finite element method
Energy Technology Data Exchange (ETDEWEB)
Mohanty, Subhasish, E-mail: smohanty@anl.gov; Majumdar, Saurin; Natesan, Ken
2016-08-15
Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.
Steam generator tube rupture simulation using extended finite element method
International Nuclear Information System (INIS)
Mohanty, Subhasish; Majumdar, Saurin; Natesan, Ken
2016-01-01
Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.
A sparse-mode spectral method for the simulation of turbulent flows
International Nuclear Information System (INIS)
Meneguzzi, M.; Politano, H.; Pouquet, A.; Zolver, M.
1996-01-01
We propose a new algorithm belonging to the family of the sparsemode spectral method to simulate turbulent flows. In this method the number of Fourier modes k increases with k more slowly than k D-1 in dimension D, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burger's equation and two-dimensional incompressible MHD flows
Directory of Open Access Journals (Sweden)
Z. Pashazadeh Atabakan
2013-01-01
Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
Flow Applications of the Least Squares Finite Element Method
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
An implicit finite element method for discrete dynamic fracture
Energy Technology Data Exchange (ETDEWEB)
Gerken, Jobie M. [Colorado State Univ., Fort Collins, CO (United States)
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Finite cover method with mortar elements for elastoplasticity problems
Kurumatani, M.; Terada, K.
2005-06-01
Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.
Nonlinear dynamic analysis using Petrov-Galerkin natural element method
International Nuclear Information System (INIS)
Lee, Hong Woo; Cho, Jin Rae
2004-01-01
According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem
Laser systems configured to output a spectrally-consolidated laser beam and related methods
Koplow, Jeffrey P [San Ramon, CA
2012-01-10
A laser apparatus includes a plurality of pumps each of which is configured to emit a corresponding pump laser beam having a unique peak wavelength. The laser apparatus includes a spectral beam combiner configured to combine the corresponding pump laser beams into a substantially spatially-coherent pump laser beam having a pump spectrum that includes the unique peak wavelengths, and first and second selectively reflective elements spaced from each other to define a lasing cavity including a lasing medium therein. The lasing medium generates a plurality of gain spectra responsive to absorbing the pump laser beam. Each gain spectrum corresponds to a respective one of the unique peak wavelengths of the substantially spatially-coherent pump laser beam and partially overlaps with all other ones of the gain spectra. The reflective elements are configured to promote emission of a laser beam from the lasing medium with a peak wavelength common to each gain spectrum.
Reduction of Musical Noise in Spectral Subtraction Method Using Subframe Phase Randomization
Energy Technology Data Exchange (ETDEWEB)
Seok, J.W.; Bae, K.S. [Kyungpook National University, Taegu (Korea)
1999-06-01
The Subframe phase randomization method is applied to the spectral subtraction method to reduce the musical noise in nonvoicing region after speech enhancement. The musical noise in the spectral subtraction method is the result of the narrowband tonal components that appearing somewhat periodically in the spectrogram of unvoiced and silence regions. Thus each synthesis frame in nonvoicing region is divided into several subframes to broaden the narrowband spectrum, and then phases of silence and unvoiced regions are randomized to eliminate the tonal components in the spectrum while keeping the shape of the amplitude spectrum. Performance assessments based on visual inspection of spectrogram, objective measure, and informal subjective listening tests demonstrate the superiority of the proposed algorithm. (author). 7 refs., 5 figs.
Funamizu, Hideki; Onodera, Yusei; Aizu, Yoshihisa
2018-05-01
In this study, we report color quality improvement of reconstructed images in color digital holography using the speckle method and the spectral estimation. In this technique, an object is illuminated by a speckle field and then an object wave is produced, while a plane wave is used as a reference wave. For three wavelengths, the interference patterns of two coherent waves are recorded as digital holograms on an image sensor. Speckle fields are changed by moving a ground glass plate in an in-plane direction, and a number of holograms are acquired to average the reconstructed images. After the averaging process of images reconstructed from multiple holograms, we use the Wiener estimation method for obtaining spectral transmittance curves in reconstructed images. The color reproducibility in this method is demonstrated and evaluated using a Macbeth color chart film and staining cells of onion.
Zhao, Li-Ting; Xiang, Yu-Hong; Dai, Yin-Mei; Zhang, Zhuo-Yong
2010-04-01
Near infrared spectroscopy was applied to measure the tissue slice of endometrial tissues for collecting the spectra. A total of 154 spectra were obtained from 154 samples. The number of normal, hyperplasia, and malignant samples was 36, 60, and 58, respectively. Original near infrared spectra are composed of many variables, for example, interference information including instrument errors and physical effects such as particle size and light scatter. In order to reduce these influences, original spectra data should be performed with different spectral preprocessing methods to compress variables and extract useful information. So the methods of spectral preprocessing and wavelength selection have played an important role in near infrared spectroscopy technique. In the present paper the raw spectra were processed using various preprocessing methods including first derivative, multiplication scatter correction, Savitzky-Golay first derivative algorithm, standard normal variate, smoothing, and moving-window median. Standard deviation was used to select the optimal spectral region of 4 000-6 000 cm(-1). Then principal component analysis was used for classification. Principal component analysis results showed that three types of samples could be discriminated completely and the accuracy almost achieved 100%. This study demonstrated that near infrared spectroscopy technology and chemometrics method could be a fast, efficient, and novel means to diagnose cancer. The proposed methods would be a promising and significant diagnosis technique of early stage cancer.
Rapid screening of guar gum using portable Raman spectral identification methods.
Srivastava, Hirsch K; Wolfgang, Steven; Rodriguez, Jason D
2016-01-25
Guar gum is a well-known inactive ingredient (excipient) used in a variety of oral pharmaceutical dosage forms as a thickener and stabilizer of suspensions and as a binder of powders. It is also widely used as a food ingredient in which case alternatives with similar properties, including chemically similar gums, are readily available. Recent supply shortages and price fluctuations have caused guar gum to come under increasing scrutiny for possible adulteration by substitution of cheaper alternatives. One way that the U.S. FDA is attempting to screen pharmaceutical ingredients at risk for adulteration or substitution is through field-deployable spectroscopic screening. Here we report a comprehensive approach to evaluate two field-deployable Raman methods--spectral correlation and principal component analysis--to differentiate guar gum from other gums. We report a comparison of the sensitivity of the spectroscopic screening methods with current compendial identification tests. The ability of the spectroscopic methods to perform unambiguous identification of guar gum compared to other gums makes them an enhanced surveillance alternative to the current compendial identification tests, which are largely subjective in nature. Our findings indicate that Raman spectral identification methods perform better than compendial identification methods and are able to distinguish guar gum from other gums with 100% accuracy for samples tested by spectral correlation and principal component analysis. Published by Elsevier B.V.
Mapped Chebyshev Pseudo-Spectral Method for Dynamic Aero-Elastic Problem of Limit Cycle Oscillation
Im, Dong Kyun; Kim, Hyun Soon; Choi, Seongim
2018-05-01
A mapped Chebyshev pseudo-spectral method is developed as one of the Fourier-spectral approaches and solves nonlinear PDE systems for unsteady flows and dynamic aero-elastic problem in a given time interval, where the flows or elastic motions can be periodic, nonperiodic, or periodic with an unknown frequency. The method uses the Chebyshev polynomials of the first kind for the basis function and redistributes the standard Chebyshev-Gauss-Lobatto collocation points more evenly by a conformal mapping function for improved numerical stability. Contributions of the method are several. It can be an order of magnitude more efficient than the conventional finite difference-based, time-accurate computation, depending on the complexity of solutions and the number of collocation points. The method reformulates the dynamic aero-elastic problem in spectral form for coupled analysis of aerodynamics and structures, which can be effective for design optimization of unsteady and dynamic problems. A limit cycle oscillation (LCO) is chosen for the validation and a new method to determine the LCO frequency is introduced based on the minimization of a second derivative of the aero-elastic formulation. Two examples of the limit cycle oscillation are tested: nonlinear, one degree-of-freedom mass-spring-damper system and two degrees-of-freedom oscillating airfoil under pitch and plunge motions. Results show good agreements with those of the conventional time-accurate simulations and wind tunnel experiments.
Finite element method for time-space-fractional Schrodinger equation
Directory of Open Access Journals (Sweden)
Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
Eddy current analysis by the finite element circuit method
International Nuclear Information System (INIS)
Kameari, A.; Suzuki, Y.
1977-01-01
The analysis of the transient eddy current in the conductors by ''Finite Element Circuit Method'' is developed. This method can be easily applied to various geometrical shapes of thin conductors. The eddy currents on the vacuum vessel and the upper and lower support plates of JT-60 machine (which is now being constructed by Japan Atomic Energy Research Institute) are calculated by this method. The magnetic field induced by the eddy current is estimated in the domain occupied by the plasma. And the force exerted to the vacuum vessel is also estimated
Improved determination of hadron matrix elements using the variational method
International Nuclear Information System (INIS)
Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ.
2015-11-01
The extraction of hadron form factors in lattice QCD using the standard two- and three-point correlator functions has its limitations. One of the most commonly studied sources of systematic error is excited state contamination, which occurs when correlators are contaminated with results from higher energy excitations. We apply the variational method to calculate the axial vector current g A and compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
Spectral nodal method for one-speed X,Y-geometry Eigenvalue diffusion problems
International Nuclear Information System (INIS)
Dominguez, Dany S.; Lorenzo, Daniel M.; Hernandez, Carlos G.; Barros, Ricardo C.; Silva, Fernando C. da
2001-01-01
Presented here is a new numerical nodal method for steady-state multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the transverse-integrated nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X and Y directions, and then considering flat approximations for the transverse leakage terms. These flat approximations are the only approximations that we consider in this method; as a result the numerical solutions are completely free from truncation errors in slab geometry. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in a heterogeneous medium. (author)
International Nuclear Information System (INIS)
Mitsuyasu, T.; Ishii, K.; Hino, T.; Aoyama, M.
2009-01-01
Spectral history methods for pin-by-pin core analysis method using the three-dimensional direct response matrix have been developed. The direct response matrix is formalized by four sub-response matrices in order to respond to a core eigenvalue k and thus can be recomposed at each outer iteration in the core analysis. For core analysis, it is necessary to take into account the burn-up effect related to spectral history. One of the methods is to evaluate the nodal burn-up spectrum obtained using the out-going neutron current. The other is to correct the fuel rod neutron production rates obtained the pin-by-pin correction. These spectral history methods were tested in a heterogeneous system. The test results show that the neutron multiplication factor error can be reduced by half during burn-up, the nodal neutron production rates errors can be reduced by 30% or more. The root-mean-square differences between the relative fuel rod neutron production rate distributions can be reduced within 1.1% error. This means that these methods can accurately reflect the effects of intra- and inter-assembly heterogeneities during burn-up and can be used for core analysis. Core analysis with the DRM method was carried out for an ABWR quarter core and it was found that both thermal power and coolant-flow distributions were smoothly converged. (authors)
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2012-11-01
Full Text Available The present work advances the inverse quantum (IQ structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings to more wave behavior (free or covalent bindings. This so-called spectral inverse quantum (Spectral-IQ particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding bands’ assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB and cetyltrimethylammonium bromide (CTAB and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature.
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
Directory of Open Access Journals (Sweden)
Changyong Cao
2015-01-01
Full Text Available An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
Introduction to assembly of finite element methods on graphics processors
International Nuclear Information System (INIS)
Cecka, Cristopher; Lew, Adrian; Darve, Eric
2010-01-01
Recently, graphics processing units (GPUs) have had great success in accelerating numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are presented and discussed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor achieves speedups of 30x or more in comparison to a well optimized serial implementation on the CPU. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite-element discretization.
A collocation finite element method with prior matrix condensation
International Nuclear Information System (INIS)
Sutcliffe, W.J.
1977-01-01
For thin shells with general loading, sixteen degrees of freedom have been used for a previous finite element solution procedure using a Collocation method instead of the usual variational based procedures. Although the number of elements required was relatively small, nevertheless the final matrix for the simultaneous solution of all unknowns could become large for a complex compound structure. The purpose of the present paper is to demonstrate a method of reducing the final matrix size, so allowing solution for large structures with comparatively small computer storage requirements while retaining the accuracy given by high order displacement functions. Collocation points, a number are equilibrium conditions which must be satisfied independently of the overall compatibility of forces and deflections for a complete structure. (Auth.)
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using......The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...
International Nuclear Information System (INIS)
Barros, R.C.; Filho, H.A.; Oliveira, F.B.S.; Silva, F.C. da
2004-01-01
Presented here are the advances in spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: (i) the use of the standard discretized spatial balance SN equations; (ii) the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and (iii) the use of the non-standard spectral Green's function (SGF) auxiliary equations in the non-multiplying regions of the domain, e.g., the reflector. In slab-geometry the hybrid SD-SGF method generates numerical results that are completely free of spatial truncation errors. In X,Y-geometry, we obtain a system of two 'slab-geometry' SN equations for the node-edge average angular fluxes by transverse-integrating the X,Y-geometry SN equations separately in the y- and then in the x-directions within an arbitrary node of the spatial grid set up on the domain. In this paper, we approximate the transverse leakage terms by constants. These are the only approximations considered in the SD-SGF-constant nodal method, as the source terms, that include scattering and eventually fission events, are treated exactly. Moreover, we describe in this paper the progress of the approximate SN albedo boundary conditions for substituting the non-multiplying regions around the nuclear reactor core. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (Author)
Spectral feature characterization methods for blood stain detection in crime scene backgrounds
Yang, Jie; Mathew, Jobin J.; Dube, Roger R.; Messinger, David W.
2016-05-01
Blood stains are one of the most important types of evidence for forensic investigation. They contain valuable DNA information, and the pattern of the stains can suggest specifics about the nature of the violence that transpired at the scene. Blood spectral signatures containing unique reflectance or absorption features are important both for forensic on-site investigation and laboratory testing. They can be used for target detection and identification applied to crime scene hyperspectral imagery, and also be utilized to analyze the spectral variation of blood on various backgrounds. Non-blood stains often mislead the detection and can generate false alarms at a real crime scene, especially for dark and red backgrounds. This paper measured the reflectance of liquid blood and 9 kinds of non-blood samples in the range of 350 nm - 2500 nm in various crime scene backgrounds, such as pure samples contained in petri dish with various thicknesses, mixed samples with different colors and materials of fabrics, and mixed samples with wood, all of which are examined to provide sub-visual evidence for detecting and recognizing blood from non-blood samples in a realistic crime scene. The spectral difference between blood and non-blood samples are examined and spectral features such as "peaks" and "depths" of reflectance are selected. Two blood stain detection methods are proposed in this paper. The first method uses index to denote the ratio of "depth" minus "peak" over"depth" add"peak" within a wavelength range of the reflectance spectrum. The second method uses relative band depth of the selected wavelength ranges of the reflectance spectrum. Results show that the index method is able to discriminate blood from non-blood samples in most tested crime scene backgrounds, but is not able to detect it from black felt. Whereas the relative band depth method is able to discriminate blood from non-blood samples on all of the tested background material types and colors.
Energy Technology Data Exchange (ETDEWEB)
Cai, X C; Marcinkowski, L; Vassilevski, P S
2005-02-10
This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.
Methods for measuring the spectral reflectivity of advanced materials at high temperature
International Nuclear Information System (INIS)
Salikhov, T.P.; Kan, V.V.
1993-01-01
For investigation in the domain of advanced materials as well as for new technologies there is an urgent need for knowledge of the spectral reflectivity of the materials specially at high temperatures. However the methods available are mostly intended for measuring the model materials with specular or diffuse reflection surface. This is not quite correct since advanced materials have mixed specular diffuse reflection surfaces. New methods for reflectivity measurements of materials in the visible, near and middle infrared range at high temperature, regardless of surface texture, have been developed. The advantages of the methods proposed are as flows: (a) the facility of performing the reflectivity measurements for materials with mixed specular diffuse reflectance; (b) wide spectral range 0,38-8 micro m; (c) wide temperature range 300-3000 K; (d) high accuracy and rapid measurements. The methods are based on the following principals (i) Diffuse irradiation of the sample surface and the use of Helkholtz reciprocity principle to determine the directional hemispherical reflectivity ii) Pulse polychromatic probing of the sample by additional light source. The first principle excludes the influence of the angular reflection distribution of sample surface on data obtained. The second principle gives the possibility of simultaneous measurements of the reflectivity. The second principle gives the possibility of simultaneous measurements of the reflectivity in wide spectral range. On the basis of these principles for high temperature reflectometers have been developed and discussed here. (author)
A spectral measurement method for determining white OLED average junction temperatures
Zhu, Yiting; Narendran, Nadarajah
2016-09-01
The objective of this study was to investigate an indirect method of measuring the average junction temperature of a white organic light-emitting diode (OLED) based on temperature sensitivity differences in the radiant power emitted by individual emitter materials (i.e., "blue," "green," and "red"). The measured spectral power distributions (SPDs) of the white OLED as a function of temperature showed amplitude decrease as a function of temperature in the different spectral bands, red, green, and blue. Analyzed data showed a good linear correlation between the integrated radiance for each spectral band and the OLED panel temperature, measured at a reference point on the back surface of the panel. The integrated radiance ratio of the spectral band green compared to red, (G/R), correlates linearly with panel temperature. Assuming that the panel reference point temperature is proportional to the average junction temperature of the OLED panel, the G/R ratio can be used for estimating the average junction temperature of an OLED panel.
[Application of Finite Element Method in Thoracolumbar Spine Traumatology].
Zhang, Min; Qiu, Yong-gui; Shao, Yu; Gu, Xiao-feng; Zeng, Ming-wei
2015-04-01
The finite element method (FEM) is a mathematical technique using modern computer technology for stress analysis, and has been gradually used in simulating human body structures in the biomechanical field, especially more widely used in the research of thoracolumbar spine traumatology. This paper reviews the establishment of the thoracolumbar spine FEM, the verification of the FEM, and the thoracolumbar spine FEM research status in different fields, and discusses its prospects and values in forensic thoracolumbar traumatology.
A finite element method for flow problems in blast loading
International Nuclear Information System (INIS)
Forestier, A.; Lepareux, M.
1984-06-01
This paper presents a numerical method which describes fast dynamic problems in flow transient situations as in nuclear plants. A finite element formulation has been chosen; it is described by a preprocessor in CASTEM system: GIBI code. For these typical flow problems, an A.L.E. formulation for physical equations is used. So, some applications are presented: the well known problem of shock tube, the same one in 2D case and a last application to hydrogen detonation
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
International Nuclear Information System (INIS)
Bourlioux, Anne; Layton, Anita T.; Minion, Michael L.
2003-01-01
Models for reacting flow are typically based on advection-diffusion-reaction (A-D-R) partial differential equations. Many practical cases correspond to situations where the relevant time scales associated with each of the three sub-processes can be widely different, leading to disparate time-step requirements for robust and accurate time-integration. In particular, interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection. The numerical strategy introduced in this paper is a general procedure to account for this time-scale disparity. The proposed methods are high-order multi-implicit generalizations of spectral deferred correction methods (MISDC methods), constructed for the temporal integration of A-D-R equations. Spectral deferred correction methods compute a high-order approximation to the solution of a differential equation by using a simple, low-order numerical method to solve a series of correction equations, each of which increases the order of accuracy of the approximation. The key feature of MISDC methods is their flexibility in handling several sub-processes implicitly but independently, while avoiding the splitting errors present in traditional operator-splitting methods and also allowing for different time steps for each process. The stability, accuracy, and efficiency of MISDC methods are first analyzed using a linear model problem and the results are compared to semi-implicit spectral deferred correction methods. Furthermore, numerical tests on simplified reacting flows demonstrate the expected convergence rates for MISDC methods of orders three, four, and five. The gain in efficiency by independently controlling the sub-process time steps is illustrated for nonlinear problems, where reaction and diffusion are much stiffer than advection. Although the paper focuses on this specific time-scales ordering, the generalization to any ordering combination is straightforward
International Nuclear Information System (INIS)
Koszykowski, M.L.; Pfeffer, G.A.; Noid, D.W.
1987-01-01
Nonlinear dynamics plays a dominant role in a variety of important problems in chemical physics. Examples are unimolecular reactions, infrared multiphoton decomposition of molecules, the pumping process of the gamma ray laser, dissociation of vibrationally excited state-selected van der Waals's complexes, and many other chemical and atomic processes. The present article discusses recent theoretical studies on the quasi-periodic and chaotic dynamic aspects of vibrational-rotational states of atomic, nuclear, and molecular systems using the semiclassical spectral method (SSM). The authors note that the coordinates, momenta, and so on, are found using classical mechanics in the studies included in this review. They outline the semiclassical spectral method and a wide variety of applications. Although this technique was first developed ten years ago, it has proved to be tremendously successful as a tool used in dynamics problems. Applications include problems in nonlinear dynamics, molecular and atomic spectra, surface science, astronomy and stellar dynamics, nuclear physics, and polymer physics
Stable multi-domain spectral penalty methods for fractional partial differential equations
Xu, Qinwu; Hesthaven, Jan S.
2014-01-01
We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.
International Nuclear Information System (INIS)
Coulomb, F.
1989-06-01
The aim of this work is to study methods for solving the diffusion equation, based on a primal or mixed-dual finite elements discretization and well suited for use on multiprocessors computers; domain decomposition methods are the subject of the main part of this study, the linear systems being solved by the block-Jacobi method. The origin of the diffusion equation is explained in short, and various variational formulations are reminded. A survey of iterative methods is given. The elemination of the flux or current is treated in the case of a mixed method. Numerical tests are performed on two examples of reactors, in order to compare mixed elements and Lagrange elements. A theoretical study of domain decomposition is led in the case of Lagrange finite elements, and convergence conditions for the block-Jacobi method are derived; the dissection decomposition is previously the purpose of a particular numerical analysis. In the case of mixed-dual finite elements, a study is led on examples and is confirmed by numerical tests performed for the dissection decomposition; furthermore, after being justified, decompositions along axes of symmetry are numerically tested. In the case of a decomposition into two subdomains, the dissection decomposition and the decomposition with an integrated interface are compared. Alternative directions methods are defined; the convergence of those relative to Lagrange elements is shown; in the case of mixed elements, convergence conditions are found [fr
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.
1989-01-01
We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage
Application of the spectral-correlation method for diagnostics of cellulose paper
Kiesewetter, D.; Malyugin, V.; Reznik, A.; Yudin, A.; Zhuravleva, N.
2017-11-01
The spectral-correlation method was described for diagnostics of optically inhomogeneous biological objects and materials of natural origin. The interrelation between parameters of the studied objects and parameters of the cross correlation function of speckle patterns produced by scattering of coherent light at different wavelengths is shown for thickness, optical density and internal structure of the material. A detailed study was performed for cellulose electric insulating paper with different parameters.
Perturbation method utilization in the analysis of the Convertible Spectral Shift Reactor (RCVS)
International Nuclear Information System (INIS)
Bruna, G.B; Legendre, J.F.; Porta, J.; Doriath, J.Y.
1988-01-01
In the framework of the preliminary faisability studies on a new core concept, techniques derived from perturbation theory show-up very useful in the calculation and physical analysis of project parameters. We show, in the present work, some applications of these methods to the RCVS (Reacteur Convertible a Variation de Spectre - Convertible Spectral Shift Reactor) Concept studies. Actually, we present here the search of a few group project type energy structure and the splitting of reactivity effects into individual components [fr
The spectral induced polarisation method and its application to hydrogeological problems
International Nuclear Information System (INIS)
Hoerdt, A.
2007-01-01
The spectral induced polarisation (SIP) method is an extension of the DC resistivity technique, where an alternating current is injected and the phase shift between voltage and current is measured in addition to the amplitude. In unconsolidated sediments, the phase shift includes complementary information on the structure of the pore space, and thus it should be possible to estimate hydraulic parameters from SIP measurements. Here, I describe some recent developments and give one example where hydraulic conductivity was estimated at the field scale
Performance Evaluation of the Spectral Centroid Downshift Method for Attenuation Estimation
Samimi, Kayvan; Varghese, Tomy
2015-01-01
Estimation of frequency-dependent ultrasonic attenuation is an important aspect of tissue characterization. Along with other acoustic parameters studied in quantitative ultrasound, the attenuation coefficient can be used to differentiate normal and pathological tissue. The spectral centroid downshift (CDS) method is one the most common frequency-domain approaches applied to this problem. In this study, a statistical analysis of this method’s performance was carried out based on a parametric m...
International Nuclear Information System (INIS)
Itagaki, Masafumi; Sahashi, Naoki.
1996-01-01
The multiple reciprocity method (MRM) in conjunction with the boundary element method has been employed to solve one-group eigenvalue problems described by the three-dimensional (3-D) neutron diffusion equation. The domain integral related to the fission source is transformed into a series of boundary-only integrals, with the aid of the higher order fundamental solutions based on the spherical and the modified spherical Bessel functions. Since each degree of the higher order fundamental solutions in the 3-D cases has a singularity of order (1/r), the above series of boundary integrals requires additional terms which do not appear in the 2-D MRM formulation. The critical eigenvalue itself can be also described using only boundary integrals. Test calculations show that Wielandt's spectral shift technique guarantees rapid and stable convergence of 3-D MRM computations. (author)
On the trial functions in nested element method
International Nuclear Information System (INIS)
Altiparmakov, D.V.
1985-01-01
The R-function method is applied to the multidimensional steady-state neutron diffusion equation. Using a variational principle the nested element approximation is formulated. Trial functions taking into account the geometrical shape of material regions are constructed. The influence of both the surrounding regions and the corner singularities at the external boundary is incorporated into the approximate solution. Benchmark calculations show that such an approximation can yield satisfactory results. Moreover, in the case of complex geometry, the presented approach would result in a significant reduction of the number of unknowns compared to other methods
Improved fixed point iterative method for blade element momentum computations
DEFF Research Database (Denmark)
Sun, Zhenye; Shen, Wen Zhong; Chen, Jin
2017-01-01
The blade element momentum (BEM) theory is widely used in aerodynamic performance calculations and optimization applications for wind turbines. The fixed point iterative method is the most commonly utilized technique to solve the BEM equations. However, this method sometimes does not converge...... are addressed through both theoretical analysis and numerical tests. A term from the BEM equations equals to zero at a critical inflow angle is the source of the convergence problems. When the initial inflow angle is set larger than the critical inflow angle and the relaxation methodology is adopted...
Finite element method for simulation of the semiconductor devices
International Nuclear Information System (INIS)
Zikatanov, L.T.; Kaschiev, M.S.
1991-01-01
An iterative method for solving the system of nonlinear equations of the drift-diffusion representation for the simulation of the semiconductor devices is worked out. The Petrov-Galerkin method is taken for the discretization of these equations using the bilinear finite elements. It is shown that the numerical scheme is a monotonous one and there are no oscillations of the solutions in the region of p-n transition. The numerical calculations of the simulation of one semiconductor device are presented. 13 refs.; 3 figs
Energy Technology Data Exchange (ETDEWEB)
Alchimov, A B; Drobot, S I; Drokov, V G; Zarubin, V P; Kazmirov, A D; Skodaev, Y D; Podrezov, A M [Applied Physics Institute of Irkutsk State University, Irkutsk (Russian Federation)
1998-12-31
The comparison of different spectral methods of analysis for wear diagnostics of aircraft engines has been carried out. It is shown that known techniques of determination of metals content in aviation oils with the use the spectrometers MFS (Russia) and MOA (USA) give a low accuracy of measurements. As an alternative the method of wear diagnostics on the base of a scintillation spectrometer is suggested. This method possess far better metrological properties in comparison with those on the base of the spectrometer MFS and MOA. (orig.) 6 refs.
Energy Technology Data Exchange (ETDEWEB)
Alchimov, A.B.; Drobot, S.I.; Drokov, V.G.; Zarubin, V.P.; Kazmirov, A.D.; Skodaev, Y.D.; Podrezov, A.M. [Applied Physics Institute of Irkutsk State University, Irkutsk (Russian Federation)
1997-12-31
The comparison of different spectral methods of analysis for wear diagnostics of aircraft engines has been carried out. It is shown that known techniques of determination of metals content in aviation oils with the use the spectrometers MFS (Russia) and MOA (USA) give a low accuracy of measurements. As an alternative the method of wear diagnostics on the base of a scintillation spectrometer is suggested. This method possess far better metrological properties in comparison with those on the base of the spectrometer MFS and MOA. (orig.) 6 refs.
Detection of the power lines in UAV remote sensed images using spectral-spatial methods.
Bhola, Rishav; Krishna, Nandigam Hari; Ramesh, K N; Senthilnath, J; Anand, Gautham
2018-01-15
In this paper, detection of the power lines on images acquired by Unmanned Aerial Vehicle (UAV) based remote sensing is carried out using spectral-spatial methods. Spectral clustering was performed using Kmeans and Expectation Maximization (EM) algorithm to classify the pixels into the power lines and non-power lines. The spectral clustering methods used in this study are parametric in nature, to automate the number of clusters Davies-Bouldin index (DBI) is used. The UAV remote sensed image is clustered into the number of clusters determined by DBI. The k clustered image is merged into 2 clusters (power lines and non-power lines). Further, spatial segmentation was performed using morphological and geometric operations, to eliminate the non-power line regions. In this study, UAV images acquired at different altitudes and angles were analyzed to validate the robustness of the proposed method. It was observed that the EM with spatial segmentation (EM-Seg) performed better than the Kmeans with spatial segmentation (Kmeans-Seg) on most of the UAV images. Copyright © 2017 Elsevier Ltd. All rights reserved.
Seismic response of three-dimensional topographies using a time-domain boundary element method
Janod, François; Coutant, Olivier
2000-08-01
We present a time-domain implementation for a boundary element method (BEM) to compute the diffraction of seismic waves by 3-D topographies overlying a homogeneous half-space. This implementation is chosen to overcome the memory limitations arising when solving the boundary conditions with a frequency-domain approach. This formulation is flexible because it allows one to make an adaptive use of the Green's function time translation properties: the boundary conditions solving scheme can be chosen as a trade-off between memory and cpu requirements. We explore here an explicit method of solution that requires little memory but a high cpu cost in order to run on a workstation computer. We obtain good results with four points per minimum wavelength discretization for various topographies and plane wave excitations. This implementation can be used for two different aims: the time-domain approach allows an easier implementation of the BEM in hybrid methods (e.g. coupling with finite differences), and it also allows one to run simple BEM models with reasonable computer requirements. In order to keep reasonable computation times, we do not introduce any interface and we only consider homogeneous models. Results are shown for different configurations: an explosion near a flat free surface, a plane wave vertically incident on a Gaussian hill and on a hemispherical cavity, and an explosion point below the surface of a Gaussian hill. Comparison is made with other numerical methods, such as finite difference methods (FDMs) and spectral elements.
Scientific use of the finite element method in Orthodontics
Knop, Luegya; Gandini, Luiz Gonzaga; Shintcovsk, Ricardo Lima; Gandini, Marcia Regina Elisa Aparecida Schiavon
2015-01-01
INTRODUCTION: The finite element method (FEM) is an engineering resource applied to calculate the stress and deformation of complex structures, and has been widely used in orthodontic research. With the advantage of being a non-invasive and accurate method that provides quantitative and detailed data on the physiological reactions possible to occur in tissues, applying the FEM can anticipate the visualization of these tissue responses through the observation of areas of stress created from applied orthodontic mechanics. OBJECTIVE: This article aims at reviewing and discussing the stages of the finite element method application and its applicability in Orthodontics. RESULTS: FEM is able to evaluate the stress distribution at the interface between periodontal ligament and alveolar bone, and the shifting trend in various types of tooth movement when using different types of orthodontic devices. Therefore, it is necessary to know specific software for this purpose. CONCLUSIONS: FEM is an important experimental method to answer questions about tooth movement, overcoming the disadvantages of other experimental methods. PMID:25992996
Directory of Open Access Journals (Sweden)
V. Yu. Kleshnin
2016-01-01
Full Text Available The article describes the matrix algebra libraries based on the modern technologies of parallel programming for the Spectrum software, which can use a spectral method (in the spectral form of mathematical description to analyse, synthesise and identify deterministic and stochastic dynamical systems. The developed matrix algebra libraries use the following technologies for the GPUs: OmniThreadLibrary, OpenMP, Intel Threading Building Blocks, Intel Cilk Plus for CPUs nVidia CUDA, OpenCL, and Microsoft Accelerated Massive Parallelism.The developed libraries support matrices with real elements (single and double precision. The matrix dimensions are limited by 32-bit or 64-bit memory model and computer configuration. These libraries are general-purpose and can be used not only for the Spectrum software. They can also find application in the other projects where there is a need to perform operations with large matrices.The article provides a comparative analysis of the libraries developed for various matrix operations (addition, subtraction, scalar multiplication, multiplication, powers of matrices, tensor multiplication, transpose, inverse matrix, finding a solution of the system of linear equations through the numerical experiments using different CPU and GPU. The article contains sample programs and performance test results for matrix multiplication, which requires most of all computational resources in regard to the other operations.
Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping
2017-07-01
This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.
8th International Conference on Boundary Element Methods
Brebbia, C
1986-01-01
The International Conference on Boundary Element Methods in Engineering was started in 1978 with the following objectives: i) To act as a focus for BE research at a time when the technique wasjust emerging as a powerful tool for engineering analysis. ii) To attract new as weIl as established researchers on Boundary Elements, in order to maintain its vitality and originality. iii) To try to relate the Boundary Element Method to other engineering techniques in an effort to help unify the field of engineering analysis, rather than to contribute to its fragmentation. These objectives were achieved during the last 7 conferences and this meeting - the eighth - has continued to be as innovative and dynamic as any ofthe previous conferences. Another important aim ofthe conference is to encourage the participation of researchers from as many different countries as possible and in this regard it is a policy of the organizers to hold the conference in different locations. It is easy to forget when working on scientific ...
Application of distinct element method of toppling failure of slope
International Nuclear Information System (INIS)
Ishida, Tsuyoshi; Hibino, Satoshi; Kitahara, Yoshihiro; Ito, Hiroshi
1984-01-01
The authors have pointed out, in the latest report, that DEM (Distinct Element Method) seems to be a very helpful numerical method to examine the stability of fissured rock slopes, in which toppling failure would occur during earthquakes. In this report, the applicability of DEM for such rock slopes is examined through the following comparisons between theoretical results and DEM results, referring Voegele's works (1982): (1) Stability of one block on a slope. (2) Failure of a rock block column composed of 10 same size rectangular blocks. (3) Cable force required to make a slope stable. Through above 3 comparisons, it seems that DEM give the reasonable results. Considering that these problems may not be treated by the other numerical methods such as FEM and so on, so DEM seems to be a very useful method for fissured rock slope analysis. (author)
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
A spectral nodal method for discrete ordinates problems in x,y geometry
International Nuclear Information System (INIS)
Barros, R.C. de; Larsen, E.W.
1991-06-01
A new nodal method is proposed for the solution of S N problems in x- y-geometry. This method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated nodal transport equations with no spatial truncation error. Thus, the only approximations in the x, y-geometry nodal method occur in the transverse leakage terms, as in diffusion theory. We approximate these leakage terms using a flat or constant approximation, and we refer to the resulting method as the SGF-Constant Nodal (SGF-CN) method. We show in numerical calculations that the SGF-CN method is much more accurate than other well-known transport nodal methods for coarse-mesh deep-penetration S N problems, even though the transverse leakage terms are approximated rather simply. (author)
International Nuclear Information System (INIS)
Kupka, F.
1997-11-01
This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)
The nonconforming virtual element method for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Gardini, Francesca [Univ. of Pavia (Italy). Dept. of Mathematics; Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vacca, Giuseppe [Univ. of Milano-Bicocca, Milan (Italy). Dept. of Mathematics and Applications
2018-02-05
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L^{2}-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.
Simulation of galvanic corrosion using boundary element method
International Nuclear Information System (INIS)
Zaifol Samsu; Muhamad Daud; Siti Radiah Mohd Kamaruddin; Nur Ubaidah Saidin; Abdul Aziz Mohamed; Mohd Saari Ripin; Rusni Rejab; Mohd Shariff Sattar
2011-01-01
Boundary element method (BEM) is a numerical technique that used for modeling infinite domain as is the case for galvanic corrosion analysis. The use of boundary element analysis system (BEASY) has allowed cathodic protection (CP) interference to be assessed in terms of the normal current density, which is directly proportional to the corrosion rate. This paper was present the analysis of the galvanic corrosion between Aluminium and Carbon Steel in natural sea water. The result of experimental was validated with computer simulation like BEASY program. Finally, it can conclude that the BEASY software is a very helpful tool for future planning before installing any structure, where it gives the possible CP interference on any nearby unprotected metallic structure. (Author)
An adaptive finite element method for steady and transient problems
International Nuclear Information System (INIS)
Benner, R.E. Jr.; Davis, H.T.; Scriven, L.E.
1987-01-01
Distributing integral error uniformly over variable subdomains, or finite elements, is an attractive criterion by which to subdivide a domain for the Galerkin/finite element method when localized steep gradients and high curvatures are to be resolved. Examples are fluid interfaces, shock fronts and other internal layers, as well as fluid mechanical and other boundary layers, e.g. thin-film states at solid walls. The uniform distribution criterion is developed into an adaptive technique for one-dimensional problems. Nodal positions can be updated simultaneously with nodal values during Newton iteration, but it is usually better to adopt nearly optimal nodal positions during Newton iteration upon nodal values. Three illustrative problems are solved: steady convection with diffusion, gradient theory of fluid wetting on a solid surface and Buckley-Leverett theory of two phase Darcy flow in porous media
Energy Technology Data Exchange (ETDEWEB)
Steibler, P.
2000-07-01
The unsteady, turbulent flow is to be calculated in a complex geometry. For this purpose a stabilized finite element formulation in which the same functions for velocity and pressure are used is developed. Thus the process remains independent of the type of elements. This simplifies the application. Above all, it is easier to deal with the boundary conditions. The independency from the elements is also achieved by the extended uzawa-algorithm which uses quadratic functions for velocity and an element-constant pressure. This method is also programmed. In order to produce the unstructured grids, an algorithm is implemented which produces meshes consisting of triangular and tetrahedral elements with flow-dependent adaptation. With standard geometries both calculation methods are compared with results. Finally the flow in a draft tube of a Kaplan turbine is calculated and compared with results from model tests. (orig.) [German] Die instationaere, turbulente Stroemung in einer komplexen Geometrie soll berechnet werden. Dazu wird eine Stabilisierte Finite Element Formulierung entwickelt, bei der die gleichen Ansatzfunktionen fuer Geschwindigkeiten und Druck verwendet werden. Das Verfahren wird damit unabhaengig von der Form der Elemente. Dies vereinfacht die Anwendung. Vor allem wird der Umgang mit den Randbedingungen erleichert. Die Elementunabhaengigkeit erreicht man auch mit dem erweiterten Uzawa-Algorithmus, welcher quadratische Ansatzfunktionen fuer die Geschwindigkeiten und elementweisen konstanten Druck verwendet. Dieses Verfahren wird ebenso implementiert. Zur Erstellung der unstrukturierten Gitter wird ein Algorithmus erzeugt, der Netze aus Dreiecks- und Tetraederelementen erstellt, welche stroemungsabhaengige Groessen besitzen koennen. Anhand einiger Standardgeometrien werden die beiden Berechnungsmethoden mit Ergebnissen aus der Literatur verglichen. Als praxisrelevantes Beispiel wird abschliessend die Stroemung in einem Saugrohr einer Kaplanturbine berechnet
The Mixed Finite Element Multigrid Method for Stokes Equations
Muzhinji, K.; Shateyi, S.; Motsa, S. S.
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
A spectral analysis of the domain decomposed Monte Carlo method for linear systems
Energy Technology Data Exchange (ETDEWEB)
Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)
2013-07-01
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)
A spectral analysis of the domain decomposed Monte Carlo method for linear systems
International Nuclear Information System (INIS)
Slattery, S. R.; Wilson, P. P. H.; Evans, T. M.
2013-01-01
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)
Tesoniero, A.; Leng, K.; Long, M. D.; Nissen-Meyer, T.
2017-12-01
Constraining the nature of the anisotropy in the core-mantle boundary region is a key factor for properly predicting the flow of the lowermost mantle. The lack of seismic waves sampling this region and their uneven azimuthal distribution hamper a correct representation of mantle dynamics. We present preliminary results for a series of SKS-SKKS splitting analysis based on numerical forward synthetic tests in a realistic 3-D Earth model using the software AXISEM3D, a newly developed efficient hybrid spectral element method solver for 3-D structures. The anisotropic property of the computational domain in the bottom 300km of the Earth's mantle is fully described with a fourth-order elastic tensor with 21 independent coefficients. We tested a single crystal mineralogy of postperovskite with different orientations that are consistent with realistic mantle flow models and accounted for a wide coverage of azimuthal seismic raypaths. We take advantage of the computational efficiency of the method to achieve resolutions for seismic periods as low as 8s. Our preliminary results, based on forward full waveform modeling, represent a step forward for validating hypotheses for the anisotropy in the D'' layer derived by direct splitting measurements and ray-theoretical mineral physics based modeling tests. Our study also highlights the capability of AXISEM3D to handle high degrees of model complexity in full anisotropy and its potentials for future endeavours.
Khan, Sami Ullah; Ali, Ishtiaq
2018-03-01
Explicit solutions to delay differential equation (DDE) and stochastic delay differential equation (SDDE) can rarely be obtained, therefore numerical methods are adopted to solve these DDE and SDDE. While on the other hand due to unstable nature of both DDE and SDDE numerical solutions are also not straight forward and required more attention. In this study, we derive an efficient numerical scheme for DDE and SDDE based on Legendre spectral-collocation method, which proved to be numerical methods that can significantly speed up the computation. The method transforms the given differential equation into a matrix equation by means of Legendre collocation points which correspond to a system of algebraic equations with unknown Legendre coefficients. The efficiency of the proposed method is confirmed by some numerical examples. We found that our numerical technique has a very good agreement with other methods with less computational effort.
Applications of the discrete element method in mechanical engineering
International Nuclear Information System (INIS)
Fleissner, Florian; Gaugele, Timo; Eberhard, Peter
2007-01-01
Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples
International Nuclear Information System (INIS)
Jovanovic, S.; Stormark, E.
1966-01-01
Measurements of reactor parameters the Nora reactor by Power Spectral Density (PSD) method are described. In case of critical reactor this method was applied for direct measurement of β/l ratio, β is the effective yield of delayed neutrons and l is the neutron lifetime. In case of subcritical reactor values of α+β-ρ/l were measured, ρ is the negative reactivity. Out coming PSD was measured by a filter or by ISAC. PSD was registered by ISAC as well as the auto-correlation function [sr
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.
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
International Nuclear Information System (INIS)
Foo, Jasmine; Wan Xiaoliang; Karniadakis, George Em
2008-01-01
Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation/cubature grid is prescribed on each element. Both full and sparse tensor product grids based on Gauss and Clenshaw-Curtis quadrature rules are considered. We prove analytically and observe in numerical tests that as the parameter space mesh is refined, the convergence rate of the solution depends on the quadrature rule of each element only through its degree of exactness. In addition, the L 2 error of the tensor product interpolant is examined and an adaptivity algorithm is provided. Numerical examples demonstrating adaptive ME-PCM are shown, including low-regularity problems and long-time integration. We test the ME-PCM on two-dimensional Navier-Stokes examples and a stochastic diffusion problem with various random input distributions and up to 50 dimensions. While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100). The computational cost of ME-PCM is found to be favorable when compared to the cost of other methods including stochastic Galerkin, Monte Carlo and quasi-random sequence methods
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Dilz, R.J.; van Beurden, M.C.
2016-01-01
We propose a mixed spatial spectral method aimed directly at aperiodic, finite scatterers in a layered medium. By using a Gabor frame to discretize the problem a straightforward and fast way to Fourier transform is available. The poles and branchcuts in the spectral-domain Green function can be
Development of experimental methods for measuring fuel elements burnup
International Nuclear Information System (INIS)
PEREDA, C; HENRIQUEZ, C; NAVARRO, G; TORRES, H; KLEIN, J; CALDERON, D; MEDEL, J; MUTIS, O; DAIE, J; ITURRIETA, L; LONCOMILLA, M; ZAMBRANO, J; KESTELMAN, A
2003-01-01
This paper is a summary of the work carried out during the last two years in fuel burning measurements at RECH-1 for different enrichments, cooling times and burning rates. The measurements were made in two gamma-spectrometric facilities, one is installed in a hot cell and the other inside of the secondary pool of the RECH-1, where the element is under 2 meters of water. The hot cell measurements need at least 100 cooling days because of the problems generated by the transport of highly active fuel elements from the Reactor to the cell. This was the main reason for using the in-pool facility because of its capability to measure the burning of fuel elements without having to wait so long, that is with only 5 cooling days. The accumulated experience in measurements achieved in both facilities and the encouraging results show that this measuring method is reliable. The results agreed well with those obtained using the reactor's physics codes, which was the way they were obtained previously (Cw)
Operating method of amorphous thin film semiconductor element
Energy Technology Data Exchange (ETDEWEB)
Mori, Koshiro; Ono, Masaharu; Hanabusa, Akira; Osawa, Michio; Arita, Takashi
1988-05-31
The existing technologies concerning amorphous thin film semiconductor elements are the technologies concerning the formation of either a thin film transistor or an amorphous Si solar cell on a substrate. In order to drive a thin film transistor for electronic equipment control by the output power of an amorphous Si solar cell, it has been obliged to drive the transistor weth an amorphous solar cell which was formed on a substrate different from that for the transistor. Accordingly, the space for the amorphous solar cell, which was formed on the different substrate, was additionally needed on the substrate for the thin film transistor. In order to solve the above problem, this invention proposes an operating method of an amorphous thin film semiconductor element that after forming an amorphous Si solar cell through lamination on the insulation coating film which covers the thin film transistor formed on the substrate, the thin film transistor is driven by the output power of this solar cell. The invention eliminates the above superfluous space and reduces the size of the amorphous thin film semiconductor element including the electric source. (3 figs)
A Finite Element Method for Simulation of Compressible Cavitating Flows
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.
Strength Analysis on Ship Ladder Using Finite Element Method
Budianto; Wahyudi, M. T.; Dinata, U.; Ruddianto; Eko P., M. M.
2018-01-01
In designing the ship’s structure, it should refer to the rules in accordance with applicable classification standards. In this case, designing Ladder (Staircase) on a Ferry Ship which is set up, it must be reviewed based on the loads during ship operations, either during sailing or at port operations. The classification rules in ship design refer to the calculation of the structure components described in Classification calculation method and can be analysed using the Finite Element Method. Classification Regulations used in the design of Ferry Ships used BKI (Bureau of Classification Indonesia). So the rules for the provision of material composition in the mechanical properties of the material should refer to the classification of the used vessel. The analysis in this structure used program structure packages based on Finite Element Method. By using structural analysis on Ladder (Ladder), it obtained strength and simulation structure that can withstand load 140 kg both in static condition, dynamic, and impact. Therefore, the result of the analysis included values of safety factors in the ship is to keep the structure safe but the strength of the structure is not excessive.
Multi-element probabilistic collocation method in high dimensions
International Nuclear Information System (INIS)
Foo, Jasmine; Karniadakis, George Em
2010-01-01
We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order μ and the effective dimension ν, with ν<< N, and N the nominal dimension. Numerical tests for multi-dimensional integration and for stochastic elliptic problems suggest that ν≥μ for monotonic convergence of the method. We also employ MEPCM-A to obtain error bars for the piezometric head at the Hanford nuclear waste site under stochastic hydraulic conductivity conditions. Finally, we compare the cost of MEPCM-A against Monte Carlo in several hundred dimensions, and we find MEPCM-A to be more efficient for up to 600 dimensions for a specific multi-dimensional integration problem involving a discontinuous function.
Seakeeping with the semi-Lagrangian particle finite element method
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2017-07-01
The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Storage system and method for spent fuel elements
International Nuclear Information System (INIS)
Queiser, H.; Eckardt, B.
1981-01-01
The proposal concerns an additional protection against leakage of a FE-transport container for interim storage of spent fuel elements. The gastight container has a second cover placed at a short distance from the first cover. The intermediate hollow space can be connected with a measuring system which indicates if part of the trace gas (mostly helium) added as indicator has escaped from the container due to leakage. The description explains the method and the assembly of required lines and measuring points etc. (UWI) [de
Piezoelectric Analysis of Saw Sensor Using Finite Element Method
Directory of Open Access Journals (Sweden)
Vladimír KUTIŠ
2013-06-01
Full Text Available In this contribution modeling and simulation of surface acoustic waves (SAW sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.
Methods for removing transuranic elements from waste solutions
International Nuclear Information System (INIS)
Slater, S.A.; Chamberlain, D.B.; Connor, C.; Sedlet, J.; Srinivasan, B.; Vandegrift, G.F.
1994-11-01
This report outlines a treatment scheme for separating and concentrating the transuranic (TRU) elements present in aqueous waste solutions stored at Argonne National Laboratory (ANL). The treatment method selected is carrier precipitation. Potential carriers will be evaluated in future laboratory work, beginning with ferric hydroxide and magnetite. The process will result in a supernatant with alpha activity low enough that it can be treated in the existing evaporator/concentrator at ANL. The separated TRU waste will be packaged for shipment to the Waste Isolation Pilot Plant
Finite-element method modeling of hyper-frequency structures
International Nuclear Information System (INIS)
Zhang, Min
1990-01-01
The modelization of microwave propagation problems, including Eigen-value problem and scattering problem, is accomplished by the finite element method with vector functional and scalar functional. For Eigen-value problem, propagation modes in waveguides and resonant modes in cavities can be calculated in a arbitrarily-shaped structure with inhomogeneous material. Several microwave structures are resolved in order to verify the program. One drawback associated with the vector functional is the appearance of spurious or non-physical solutions. A penalty function method has been introduced to reduce spurious' solutions. The adaptive charge method is originally proposed in this thesis to resolve waveguide scattering problem. This method, similar to VSWR measuring technique, is more efficient to obtain the reflection coefficient than the matrix method. Two waveguide discontinuity structures are calculated by the two methods and their results are compared. The adaptive charge method is also applied to a microwave plasma excitor. It allows us to understand the role of different physical parameters of excitor in the coupling of microwave energy to plasma mode and the mode without plasma. (author) [fr
Wang, Zhiheng
2015-01-01
A simple multidomain Chebyshev pseudo-spectral method is developed for two-dimensional fluid flow and heat transfer over square cylinders. The incompressible Navier-Stokes equations with primitive variables are discretized in several subdomains of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the PN-PN method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated by benchmark problems of natural convection in a square cavity. Then the method based on multidomains is applied to simulate fluid flow and heat transfer from square cylinders. The numerical results agree well with the existing results. © Taylor & Francis Group, LLC.
Validation of spectral methods for the seismic analysis of multi-supported structures
International Nuclear Information System (INIS)
Viola, B.
1999-01-01
There are many methodologies for the seismic analysis of buildings. When a seism occurs, structures such piping systems in nuclear power plants are subjected to motions that may be different at each support point. Therefore it is necessary to develop methods that take into account the multi-supported effect. In a first time, a bibliography analysis on the different methods that exist has been carried out. The aim was to find a particular method applicable to the study of piping systems. The second step of this work consisted in developing a program that may be used to test and make comparisons on different selected methods. So spectral methods have the advantage to give an estimation of the maximum values for strain in the structure, in reduced calculation time. The time history analysis is used as the reference for the tests. (author)
Spectral methods for the detection of network community structure: a comparative analysis
International Nuclear Information System (INIS)
Shen, Hua-Wei; Cheng, Xue-Qi
2010-01-01
Spectral analysis has been successfully applied to the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix, the correlation matrix and several other variants of these matrices. However, the comparison between these spectral methods is less reported. More importantly, it is still unclear which matrix is more appropriate for the detection of community structure. This paper answers the question by evaluating the effectiveness of these five matrices against benchmark networks with heterogeneous distributions of node degree and community size. Test results demonstrate that the normalized Laplacian matrix and the correlation matrix significantly outperform the other three matrices at identifying the community structure of networks. This indicates that it is crucial to take into account the heterogeneous distribution of node degree when using spectral analysis for the detection of community structure. In addition, to our surprise, the modularity matrix exhibits very similar performance to the adjacency matrix, which indicates that the modularity matrix does not gain benefits from using the configuration model as a reference network with the consideration of the node degree heterogeneity
International Nuclear Information System (INIS)
Llobet, X.; Appert, K.; Bondeson, A.; Vaclavik, J.
1990-01-01
Finite difference and finite element approximations of eigenvalue problems, under certain circumstances exhibit spectral pollution, i.e. the appearance of eigenvalues that do not converge to the correct value when the mesh density is increased. In the present paper this phenomenon is investigated in a homogeneous case by means of discrete dispersion relations: the polluting modes belong to a branch of the dispersion relation that is strongly distorted by the discretization method employed, or to a new, spurious branch. The analysis is applied to finite difference methods and to finite element methods, and some indications about how to avoiding polluting schemes are given. (author) 5 figs., 10 refs
Generalized multiscale finite element methods for problems in perforated heterogeneous domains
Chung, Eric T.
2015-06-08
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales. Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or nonlinear systems. In this paper, we investigate multiscale approaches that attempt to solve such problems on a coarse grid by constructing multiscale basis functions in each coarse grid, where the coarse grid can contain many perforations. In particular, we are interested in cases when there is no scale separation and the perforations can have different sizes. In this regard, we mention some earlier pioneering works, where the authors develop multiscale finite element methods. In our paper, we follow Generalized Multiscale Finite Element Method (GMsFEM) and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems. We show that with a few basis functions in each coarse block, one can approximate the solution, where each coarse block can contain many small inclusions. We apply our general concept to (1) Laplace equation in perforated domains; (2) elasticity equation in perforated domains; and (3) Stokes equations in perforated domains. Numerical results are presented for these problems using two types of heterogeneous perforated domains. The analysis of the proposed methods will be presented elsewhere. © 2015 Taylor & Francis
Overdetermined shooting methods for computing standing water waves with spectral accuracy
International Nuclear Information System (INIS)
Wilkening, Jon; Yu Jia
2012-01-01
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on standing water waves. We identify new nucleation mechanisms in which isolated large-amplitude solutions, and closed loops of such solutions, suddenly exist for depths below a critical threshold. We also study degenerate and secondary bifurcations related to Wilton's ripples in the traveling case, and explore the breakdown of self-similarity at the crests of extreme standing waves. In shallow water, we find that standing waves take the form of counter-propagating solitary waves that repeatedly collide quasi-elastically. In deep water with surface tension, we find that standing waves resemble counter-propagating depression waves. We also discuss the existence and non-uniqueness of solutions, and smooth versus erratic dependence of Fourier modes on wave amplitude and fluid depth. In the numerical method, robustness is achieved by posing the problem as an overdetermined nonlinear system and using either adjoint-based minimization techniques or a quadratically convergent trust-region method to minimize the objective function. Efficiency is achieved in the trust-region approach by parallelizing the Jacobian computation, so the setup cost of computing the Dirichlet-to-Neumann operator in the variational equation is not repeated for each column. Updates of the Jacobian are also delayed until the previous Jacobian ceases to be useful. Accuracy is maintained using spectral collocation with optional mesh refinement in space, a high-order Runge–Kutta or spectral deferred correction method in time and quadruple precision for improved navigation of delicate regions of parameter space as well as validation of double-precision results. Implementation issues for transferring much of the computation to a graphic processing units are briefly
The current matrix elements from HAL QCD method
Watanabe, Kai; Ishii, Noriyoshi
2018-03-01
HAL QCD method is a method to construct a potential (HAL QCD potential) that reproduces the NN scattering phase shift faithful to the QCD. The HAL QCD potential is obtained from QCD by eliminating the degrees of freedom of quarks and gluons and leaving only two particular hadrons. Therefor, in the effective quantum mechanics of two nucleons defined by HAL QCD potential, the conserved current consists not only of the nucleon current but also an extra current originating from the potential (two-body current). Though the form of the two-body current is closely related to the potential, it is not straight forward to extract the former from the latter. In this work, we derive the the current matrix element formula in the quantum mechanics defined by the HAL QCD potential. As a first step, we focus on the non-relativistic case. To give an explicit example, we consider a second quantized non-relativistic two-channel coupling model which we refer to as the original model. From the original model, the HAL QCD potential for the open channel is constructed by eliminating the closed channel in the elastic two-particle scattering region. The current matrix element formula is derived by demanding the effective quantum mechanics defined by the HAL QCD potential to respond to the external field in the same way as the original two-channel coupling model.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H.
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
An adaptative finite element method for turbulent flow simulations
International Nuclear Information System (INIS)
Arnoux-Guisse, F.; Bonnin, O.; Leal de Sousa, L.; Nicolas, G.
1995-05-01
After outlining the space and time discretization methods used in the N3S thermal hydraulic code developed at EDF/NHL, we describe the possibilities of the peripheral version, the Adaptative Mesh, which comprises two separate parts: the error indicator computation and the development of a module subdividing elements usable by the solid dynamics code ASTER and the electromagnetism code TRIFOU also developed by R and DD. The error indicators implemented in N3S are described. They consist of a projection indicator quantifying the space error in laminar or turbulent flow calculations and a Navier-Stokes residue indicator calculated on each element. The method for subdivision of triangles into four sub-triangles and tetrahedra into eight sub-tetrahedra is then presented with its advantages and drawbacks. It is illustrated by examples showing the efficiency of the module. The last concerns the 2 D case of flow behind a backward-facing step. (authors). 9 refs., 5 figs., 1 tab
Heat Conduction Analysis Using Semi Analytical Finite Element Method
International Nuclear Information System (INIS)
Wargadipura, A. H. S.
1997-01-01
Heat conduction problems are very often found in science and engineering fields. It is of accrual importance to determine quantitative descriptions of this important physical phenomena. This paper discusses the development and application of a numerical formulation and computation that can be used to analyze heat conduction problems. The mathematical equation which governs the physical behaviour of heat conduction is in the form of second order partial differential equations. The numerical resolution used in this paper is performed using the finite element method and Fourier series, which is known as semi-analytical finite element methods. The numerical solution results in simultaneous algebraic equations which is solved using the Gauss elimination methodology. The computer implementation is carried out using FORTRAN language. In the final part of the paper, a heat conduction problem in a rectangular plate domain with isothermal boundary conditions in its edge is solved to show the application of the computer program developed and also a comparison with analytical solution is discussed to assess the accuracy of the numerical solution obtained
A Guide on Spectral Methods Applied to Discrete Data in One Dimension
Directory of Open Access Journals (Sweden)
Martin Seilmayer
2017-01-01
Full Text Available This paper provides an overview about the usage of the Fourier transform and its related methods and focuses on the subtleties to which the users must pay attention. Typical questions, which are often addressed to the data, will be discussed. Such a problem can be the origin of frequency or band limitation of the signal or the source of artifacts, when a Fourier transform is carried out. Another topic is the processing of fragmented data. Here, the Lomb-Scargle method will be explained with an illustrative example to deal with this special type of signal. Furthermore, the time-dependent spectral analysis, with which one can evaluate the point in time when a certain frequency appears in the signal, is of interest. The goal of this paper is to collect the important information about the common methods to give the reader a guide on how to use these for application on one-dimensional data. The introduced methods are supported by the spectral package, which has been published for the statistical environment R prior to this article.