Performance and scalability of finite-difference and finite-element wave-propagation modeling on Intel's Xeon Phi

NARCIS (Netherlands)

Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.

2013-01-01

With the rapid developments in parallel compute architectures, algorithms for seismic modeling and imaging need to be reconsidered in terms of parallelization. The aim of this paper is to compare scalability of seismic modeling algorithms: finite differences, continuous mass-lumped finite elements

Different radiation impedance models for finite porous materials

DEFF Research Database (Denmark)

Nolan, Melanie; Jeong, Cheol-Ho; Brunskog, Jonas

2015-01-01

The Sabine absorption coefficients of finite absorbers are measured in a reverberation chamber according to the international standard ISO 354. They vary with the specimen size essentially due to diffraction at the specimen edges, which can be seen as the radiation impedance differing from...... the infinite case. Thus, in order to predict the Sabine absorption coefficients of finite porous samples, one can incorporate models of the radiation impedance. In this study, different radiation impedance models are compared with two experimental examples. Thomasson’s model is compared to Rhazi’s method when...

A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

International Nuclear Information System (INIS)

Ackroyd, R.T.

1987-01-01

A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)

On the spectral properties of random finite difference operators

International Nuclear Information System (INIS)

Kunz, H.; Souillard, B.

1980-01-01

We study a class of random finite difference operators, a typical example of which is the finite difference Schroedinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schroedinger operator with a random potential has pure point spectrum and developps no static conductivity. (orig.)

Hybrid finite difference/finite element immersed boundary method.

Science.gov (United States)

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

Finite-Difference Frequency-Domain Method in Nanophotonics

DEFF Research Database (Denmark)

Ivinskaya, Aliaksandra

Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling...... is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...

The Laguerre finite difference one-way equation solver

Science.gov (United States)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Directory of Open Access Journals (Sweden)

Armando Martínez-Pérez

2017-10-01

Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

Chebyshev Finite Difference Method for Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Boundary

2015-09-01

Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

Finite difference computing with PDEs a modern software approach

CERN Document Server

Langtangen, Hans Petter

2017-01-01

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model

Directory of Open Access Journals (Sweden)

Oluwaseun Egbelowo

2017-05-01

Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.

Modeling seismic wave propagation using staggered-grid mimetic finite differences

Directory of Open Access Journals (Sweden)

Freysimar Solano-Feo

2017-04-01

Full Text Available Mimetic finite difference (MFD approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP. In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.

Elementary introduction to finite difference equations

International Nuclear Information System (INIS)

White, J.W.

1976-01-01

An elementary description is given of the basic vocabulary and concepts associated with finite difference modeling. The material discussed is biased toward the types of large computer programs used at the Lawrence Livermore Laboratory. Particular attention is focused on truncation error and how it can be affected by zoning patterns. The principle of convergence is discussed, and convergence as a tool for improving calculational accuracy and efficiency is emphasized

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

The mimetic finite difference method for elliptic problems

CERN Document Server

Veiga, Lourenço Beirão; Manzini, Gianmarco

2014-01-01

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy.

OpenAIRE

Buttler, Hans-Jurg

1995-01-01

The purpose of this paper is to evaluate numerically the semi-American callable bond by means of finite difference methods. This study implies three results. First, the numerical error is greater for the callable bond price than for the straight bond price, and too large for real applications Secondly, the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points. Thi...

Interactive finite difference preprocessor for three-dimensional fluid flow systems. [PREFLO

Energy Technology Data Exchange (ETDEWEB)

Kleinstreuer, C. (Rensselaer Polytechnic Inst., Troy, NY); Patterson, M.R.

1981-06-01

A preprocessor, called PREFLO, consisting of data processing modules combined with a flexible finite difference grid generator is described. This economical, interactive computer code is a useful research tool contributing significantly to the accurate analysis and modeling of large and/or geometrically complex flow systems. PREFLO (PREprocessor for fluid FLOw problems), written in FORTRAN IV, consists of four modules which in turn call various subroutines. The main programs accomplish the following tasks: (1) system identification and selection of appropriate finite difference algorithms; (2) input devices for storage of natural flow boundaries; (3) interactive generation of finite difference meshes and display of computer graphics; (4) preparation of all data files for the source program. The computation of the velocity field near a power plant site is outlined to illustrate the capabilities and application of PREFLO.

Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements

Science.gov (United States)

Arntsen, B.

2017-12-01

The finite-difference technique for numerical modeling of seismic waves is still important and for some areas extensively used.For exploration purposes is finite-difference simulation at the core of both traditional imaging techniques such as reverse-time migration and more elaborate Full-Waveform Inversion techniques.The accuracy and fidelity of finite-difference simulation of seismic waves are hard to quantify and meaningfully error analysis is really onlyeasily available for simplistic media. A possible alternative to theoretical error analysis is provided by comparing finite-difference simulated data with laboratory data created using a scale model. The advantage of this approach is the accurate knowledge of the model, within measurement precision, and the location of sources and receivers.We use a model made of PVC immersed in water and containing horizontal and tilted interfaces together with several spherical objects to generateultrasonic pressure reflection measurements. The physical dimensions of the model is of the order of a meter, which after scaling represents a model with dimensions of the order of 10 kilometer and frequencies in the range of one to thirty hertz.We find that for plane horizontal interfaces the laboratory data can be reproduced by the finite-difference scheme with relatively small error, but for steeply tilted interfaces the error increases. For spherical interfaces the discrepancy between laboratory data and simulated data is sometimes much more severe, to the extent that it is not possible to simulate reflections from parts of highly curved bodies. The results are important in view of the fact that finite-difference modeling is often at the core of imaging and inversion algorithms tackling complicatedgeological areas with highly curved interfaces.

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

Science.gov (United States)

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Finite difference order doubling in two dimensions

International Nuclear Information System (INIS)

Killingbeck, John P; Jolicard, Georges

2008-01-01

An order doubling process previously used to obtain eighth-order eigenvalues from the fourth-order Numerov method is applied to the perturbed oscillator in two dimensions. A simple method of obtaining high order finite difference operators is reported and an odd parity boundary condition is found to be effective in facilitating the smooth operation of the order doubling process

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-01-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax

Finite Difference Schemes as Algebraic Correspondences between Layers

Science.gov (United States)

Malykh, Mikhail; Sevastianov, Leonid

2018-02-01

For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

KAUST Repository

Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai

2012-01-01

It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

KAUST Repository

Osman, Hossam Omar

2012-06-17

It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

Computational Aero-Acoustic Using High-order Finite-Difference Schemes

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2007-01-01

are solved using the in-house flow solver EllipSys2D/3D which is a second-order finite volume code. The acoustic solution is found by solving the acoustic equations using high-order finite difference schemes. The incompressible flow equations and the acoustic equations are solved at the same time levels......In this paper, a high-order technique to accurately predict flow-generated noise is introduced. The technique consists of solving the viscous incompressible flow equations and inviscid acoustic equations using a incompressible/compressible splitting technique. The incompressible flow equations...

Preconditioned finite-difference frequency-domain for modelling periodic dielectric structures - comparisons with FDTD

NARCIS (Netherlands)

Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.

2008-01-01

Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling

Preconditioned finite-difference frequency-domain for modelling periodic dielectric structures : comparisons with FDTD

NARCIS (Netherlands)

Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.

2008-01-01

Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling

Integral equations with difference kernels on finite intervals

CERN Document Server

Sakhnovich, Lev A

2015-01-01

This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful...

A practical implicit finite-difference method: examples from seismic modelling

International Nuclear Information System (INIS)

Liu, Yang; Sen, Mrinal K

2009-01-01

We derive explicit and new implicit finite-difference formulae for derivatives of arbitrary order with any order of accuracy by the plane wave theory where the finite-difference coefficients are obtained from the Taylor series expansion. The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to that of a (6N + 2)th-order explicit formula for the first-order derivative, and (2N + 2)th-order implicit formula is nearly equivalent to (4N + 2)th-order explicit formula for the second-order derivative. In general, an implicit method is computationally more expensive than an explicit method, due to the requirement of solving large matrix equations. However, the new implicit method only involves solving tridiagonal matrix equations, which is fairly inexpensive. Furthermore, taking advantage of the fact that many repeated calculations of derivatives are performed by the same difference formula, several parts can be precomputed resulting in a fast algorithm. We further demonstrate that a (2N + 2)th-order implicit formulation requires nearly the same memory and computation as a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (6N + 2)th-order explicit formulation for the first-order derivative and that of a (4N + 2)th-order explicit method for the second-order derivative when additional cost of visiting arrays is not considered. This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance. Our analysis of efficiency and numerical modelling results for acoustic and elastic wave propagation validates the effectiveness and practicality of the implicit finite-difference method

Formulation of coarse mesh finite difference to calculate mathematical adjoint flux

International Nuclear Information System (INIS)

Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)

A simple finite-difference scheme for handling topography with the first-order wave equation

NARCIS (Netherlands)

Mulder, W.A.; Huiskes, M.J.

2017-01-01

One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the

Finite element analysis of thermal stress distribution in different ...

African Journals Online (AJOL)

Nigerian Journal of Clinical Practice • Jan-Feb 2016 • Vol 19 • Issue 1. Abstract ... Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ... applications for force analysis and assessment of different.

Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication

Directory of Open Access Journals (Sweden)

Shouquan Pang

2016-01-01

Full Text Available Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.

High-order finite-difference methods for Poisson's equation

NARCIS (Netherlands)

van Linde, Hendrik Jan

1971-01-01

In this thesis finite-difference approximations to the three boundary value problems for Poisson’s equation are given, with discretization errors of O(H^3) for the mixed boundary value problem, O(H^3 |ln(h)| for the Neumann problem and O(H^4)for the Dirichlet problem respectively . First an operator

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics

CERN Document Server

Gedney, Stephen

2011-01-01

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to p

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

KAUST Repository

Gao, Longfei

2018-02-22

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

KAUST Repository

Gao, Longfei; Keyes, David E.

2018-01-01

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

Accuracy of finite-difference harmonic frequencies in density functional theory.

Science.gov (United States)

Liu, Kuan-Yu; Liu, Jie; Herbert, John M

2017-07-15

Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors numbers. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

The computation of pressure waves in shock tubes by a finite difference procedure

International Nuclear Information System (INIS)

Barbaro, M.

1988-09-01

A finite difference solution of one-dimensional unsteady isentropic compressible flow equations is presented. The computer program has been tested by solving some cases of the Riemann shock tube problem. Predictions are in good agreement with those presented by other authors. Some inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment. (author)

Finite difference time domain modelling of particle accelerators

International Nuclear Information System (INIS)

Jurgens, T.G.; Harfoush, F.A.

1989-03-01

Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs

Optimal variable-grid finite-difference modeling for porous media

International Nuclear Information System (INIS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-01-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)

Analysis of equilibrium in a tokamak by the finite-difference method

International Nuclear Information System (INIS)

Kim, K.E.; Jeun, G.D.

1983-01-01

Ideal magnetohydrodynamic equilibrium in a Tokamak having a small radius with an elongated rectangular cross section is studied by applying the finite-difference method to the Grad-Shafranov equation to determine possible limitations for *b=8*pPsup(2)/Bsup(2). The coupled first-order differential equations resulting from the finite-difference Grad-Shafranov equation is solved by the numarical method:1)We concluded that equilibrium consideration alone gives no limitation even for *b approx.1. 2)We have obtained the equilibrium magnetic field configuration charcterized by a set of three parameters;the aspect ratio, *b,and the safety factor. (Author)

The Dirac Equation in the algebraic approximation. VII. A comparison of molecular finite difference and finite basis set calculations using distributed Gaussian basis sets

NARCIS (Netherlands)

Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E

2001-01-01

A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and

Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

Science.gov (United States)

Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

2018-04-01

Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

A simple finite-difference scheme for handling topography with the second-order wave equation

NARCIS (Netherlands)

Mulder, W.A.

2017-01-01

The presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad

2013-01-01

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed

2013-06-01

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

Mimetic finite difference method

Science.gov (United States)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Implementation of compact finite-difference method to parabolized Navier-Stokes equations

International Nuclear Information System (INIS)

Esfahanian, V.; Hejranfar, K.; Darian, H.M.

2005-01-01

The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-04-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

Application of compact finite-difference schemes to simulations of stably stratified fluid flows

Czech Academy of Sciences Publication Activity Database

Bodnár, Tomáš; Beneš, L.; Fraunie, P.; Kozel, Karel

2012-01-01

Roč. 219, č. 7 (2012), s. 3336-3353 ISSN 0096-3003 Institutional support: RVO:61388998 Keywords : stratification * finite- difference * finite-volume * Runge-Kutta Subject RIV: BA - General Mathematics Impact factor: 1.349, year: 2012 http://www.sciencedirect.com/science/article/pii/S0096300311010988

Comparison of finite-difference and variational solutions to advection-diffusion problems

International Nuclear Information System (INIS)

Lee, C.E.; Washington, K.E.

1984-01-01

Two numerical solution methods are developed for 1-D time-dependent advection-diffusion problems on infinite and finite domains. Numerical solutions are compared with analytical results for constant coefficients and various boundary conditions. A finite-difference spectrum method is solved exactly in time for periodic boundary conditions by a matrix operator method and exhibits excellent accuracy compared with other methods, especially at late times, where it is also computationally more efficient. Finite-system solutions are determined from a conservational variational principle with cubic spatial trial functions and solved in time by a matrix operator method. Comparisons of problems with few nodes show excellent agreement with analytical solutions and exhibit the necessity of implementing Lagrangian conservational constraints for physically-correct solutions. (author)

A new fitted operator finite difference method to solve systems of ...

African Journals Online (AJOL)

In recent years, fitted operator finite difference methods (FOFDMs) have been developed for numerous types of singularly perturbed ordinary differential equations. The construction of most of these methods differed though the final outcome remained similar. The most crucial aspect was how the difference operator was ...

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.

Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

Science.gov (United States)

Miyazaki, Yutaka; Tsuchiya, Takao

2012-07-01

The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.

Elastic frequency-domain finite-difference contrast source inversion method

International Nuclear Information System (INIS)

He, Qinglong; Chen, Yong; Han, Bo; Li, Yang

2016-01-01

In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)

Acoustic, finite-difference, time-domain technique development

International Nuclear Information System (INIS)

Kunz, K.

1994-01-01

A close analog exists between the behavior of sound waves in an ideal gas and the radiated waves of electromagnetics. This analog has been exploited to obtain an acoustic, finite-difference, time-domain (AFDTD) technique capable of treating small signal vibrations in elastic media, such as air, water, and metal, with the important feature of bending motion included in the behavior of the metal. This bending motion is particularly important when the metal is formed into sheets or plates. Bending motion does not have an analog in electromagnetics, but can be readily appended to the acoustic treatment since it appears as a single additional term in the force equation for plate motion, which is otherwise analogous to the electromagnetic wave equation. The AFDTD technique has been implemented in a code architecture that duplicates the electromagnetic, finite-difference, time-domain technique code. The main difference in the implementation is the form of the first-order coupled differential equations obtained from the wave equation. The gradient of pressure and divergence of velocity appear in these equations in the place of curls of the electric and magnetic fields. Other small changes exist as well, but the codes are essentially interchangeable. The pre- and post-processing for model construction and response-data evaluation of the electromagnetic code, in the form of the TSAR code at Lawrence Livermore National Laboratory, can be used for the acoustic version. A variety of applications is possible, pending validation of the bending phenomenon. The applications include acoustic-radiation-pattern predictions for a submerged object; mine detection analysis; structural noise analysis for cars; acoustic barrier analysis; and symphonic hall/auditorium predictions and speaker enclosure modeling

Mimetic finite difference method for the stokes problem on polygonal meshes

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA

2009-01-01

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.

Integral and finite difference inequalities and applications

CERN Document Server

Pachpatte, B G

2006-01-01

The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.- Contains a variety of inequalities discovered which find numero

Neutron-proton mass difference in finite nuclei and the Nolen-Schiffer anomaly

International Nuclear Information System (INIS)

Meissner, U.G.; Rakhimov, A.M.; Wirzba, A.; Yakhshiev, U.T.

2008-01-01

The neutron-proton mass difference in finite nuclei is studied in the framework of a medium-modified Skyrme model. The possible interplay between the effective nucleon mass in finite nuclei and the Nolen-Schiffer anomaly is discussed. In particular, we find that a correct description of the properties of mirror nuclei leads to a stringent restriction of possible modifications of the nucleon's effective mass in nuclei. (orig.)

Time-domain finite-difference/finite-element hybrid simulations of radio frequency coils in magnetic resonance imaging

International Nuclear Information System (INIS)

Wang Shumin; Duyn, Jeff H

2008-01-01

A hybrid method that combines the finite-difference time-domain (FDTD) method and the finite-element time-domain (FETD) method is presented for simulating radio-frequency (RF) coils in magnetic resonance imaging. This method applies a high-fidelity FETD method to RF coils, while the human body is modeled with a low-cost FDTD method. Since the FDTD and the FETD methods are applied simultaneously, the dynamic interaction between RF coils and the human body is fully accounted for. In order to simplify the treatment of the highly irregular FDTD/FETD interface, composite elements are proposed. Two examples are provided to demonstrate the validity and effectiveness of the hybrid method in high-field receive-and-transmit coil design. This approach is also applicable to general bio-electromagnetic simulations

A fast finite-difference algorithm for topology optimization of permanent magnets

Science.gov (United States)

Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter

2017-09-01

We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.

Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells

Science.gov (United States)

Deinega, Alexei; John, Sajeev

2012-10-01

We introduce a finite difference discretization of semiconductor drift-diffusion equations using cylindrical partial waves. It can be applied to describe the photo-generated current in radial pn-junction nanowire solar cells. We demonstrate that the cylindrically symmetric (l=0) partial wave accurately describes the electronic response of a square lattice of silicon nanowires at normal incidence. We investigate the accuracy of our discretization scheme by using different mesh resolution along the radial direction r and compare with 3D (x, y, z) discretization. We consider both straight nanowires and nanowires with radius modulation along the vertical axis. The charge carrier generation profile inside each nanowire is calculated using an independent finite-difference time-domain simulation.

High‐order rotated staggered finite difference modeling of 3D elastic wave propagation in general anisotropic media

KAUST Repository

Chu, Chunlei

2009-01-01

We analyze the dispersion properties and stability conditions of the high‐order convolutional finite difference operators and compare them with the conventional finite difference schemes. We observe that the convolutional finite difference method has better dispersion properties and becomes more efficient than the conventional finite difference method with the increasing order of accuracy. This makes the high‐order convolutional operator a good choice for anisotropic elastic wave simulations on rotated staggered grids since its enhanced dispersion properties can help to suppress the numerical dispersion error that is inherent in the rotated staggered grid structure and its efficiency can help us tackle 3D problems cost‐effectively.

An outgoing energy flux boundary condition for finite difference ICRP antenna models

International Nuclear Information System (INIS)

Batchelor, D.B.; Carter, M.D.

1992-11-01

For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods

Temperature Calculation of Annular Fuel Pellet by Finite Difference Method

Energy Technology Data Exchange (ETDEWEB)

Yang, Yong Sik; Bang, Je Geon; Kim, Dae Ho; Kim, Sun Ki; Lim, Ik Sung; Song, Kun Woo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2009-10-15

KAERI has started an innovative fuel development project for applying dual-cooled annular fuel to existing PWR reactor. In fuel design, fuel temperature is the most important factor which can affect nuclear fuel integrity and safety. Many models and methodologies, which can calculate temperature distribution in a fuel pellet have been proposed. However, due to the geometrical characteristics and cooling condition differences between existing solid type fuel and dual-cooled annular fuel, current fuel temperature calculation models can not be applied directly. Therefore, the new heat conduction model of fuel pellet was established. In general, fuel pellet temperature is calculated by FDM(Finite Difference Method) or FEM(Finite Element Method), because, temperature dependency of fuel thermal conductivity and spatial dependency heat generation in the pellet due to the self-shielding should be considered. In our study, FDM is adopted due to high exactness and short calculation time.

Symmetries of the second-difference matrix and the finite Fourier transform

International Nuclear Information System (INIS)

Aguilar, A.; Wolf, K.B.

1979-01-01

The finite Fourier transformation is well known to diagonalize the second-difference matrix and has been thus applied extensively to describe finite crystal lattices and electric networks. In setting out to find all transformations having this property, we obtain a multiparameter class of them. While permutations and unitary scaling of the eigenvectors constitute the trivial freedom of choice common to all diagonalization processes, the second-difference matrix has a larger symmetry group among whose elements we find the dihedral manifest symmetry transformations of the lattice. The latter are nevertheless sufficient for the unique specification of eigenvectors in various symmetry-adapted bases for the constrained lattice. The free symmetry parameters are shown to lead to a complete set of conserved quantities for the physical lattice motion. (author)

Peculiarities of cyclotron magnetic system calculation with the finite difference method using two-dimensional approximation

International Nuclear Information System (INIS)

Shtromberger, N.L.

1989-01-01

To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs

Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

KAUST Repository

Wang, Yi

2016-07-21

Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.

Stability and non-standard finite difference method of the generalized Chua's circuit

KAUST Repository

Radwan, Ahmed G.

2011-08-01

In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua\\'s circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles\\' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.

Energy stable and high-order-accurate finite difference methods on staggered grids

Science.gov (United States)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Modeling of Nanophotonic Resonators with the Finite-Difference Frequency-Domain Method

DEFF Research Database (Denmark)

Ivinskaya, Aliaksandra; Lavrinenko, Andrei; Shyroki, Dzmitry

2011-01-01

Finite-difference frequency-domain method with perfectly matched layers and free-space squeezing is applied to model open photonic resonators of arbitrary morphology in three dimensions. Treating each spatial dimension independently, nonuniform mesh of continuously varying density can be built ea...

Finite difference time domain modeling of spiral antennas

Science.gov (United States)

Penney, Christopher W.; Beggs, John H.; Luebbers, Raymond J.

1992-01-01

The objectives outlined in the original proposal for this project were to create a well-documented computer analysis model based on the finite-difference, time-domain (FDTD) method that would be capable of computing antenna impedance, far-zone radiation patterns, and radar cross-section (RCS). The ability to model a variety of penetrable materials in addition to conductors is also desired. The spiral antennas under study by this project meet these requirements since they are constructed of slots cut into conducting surfaces which are backed by dielectric materials.

A mimetic finite difference method for the Stokes problem with elected edge bubbles

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, K [Los Alamos National Laboratory; Berirao, L [DIPARTMENTO DI MATERMATICA

2009-01-01

A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.

Evaluation of explicit finite-difference techniques for LMFBR safety analysis

International Nuclear Information System (INIS)

Bernstein, D.; Golden, R.D.; Gross, M.B.; Hofmann, R.

1976-01-01

In the past few years, the use of explicit finite-difference (EFD) and finite-element computer programs for reactor safety calculations has steadily increased. One of the major areas of application has been for the analysis of hypothetical core disruptive accidents in liquid metal fast breeder reactors. Most of these EFD codes were derived to varying degrees from the same roots, but the codes are large and have progressed rapidly, so there may be substantial differences among them in spite of a common ancestry. When this fact is coupled with the complexity of HCDA calculations, it is not possible to assure that independent calculations of an HCDA will produce substantially the same results. Given the extreme importance of nuclear safety, it is essential to be sure that HCDA analyses are correct, and additional code validation is therefore desirable. A comparative evaluation of HCDA computational techniques is being performed under an ERDA-sponsored program called APRICOT (Analysis of PRImary COntainment Transients). The philosophy, calculations, and preliminary results from this program are described in this paper

Preliminary research on finite difference method to solve radon field distribution over sandstone-type uranium ore body

International Nuclear Information System (INIS)

Li Bihong; Shuang Na; Liu Qingcheng

2006-01-01

The principle of finite difference method is introduced, and the radon field distribution over sandstone-type uranium deposit is narrated. The radon field distribution theory equation is established. To solve radon field distribution equation using finite difference algorithm is to provide the value computational method for forward calculation about radon field over sandstone-type uranium mine. Study on 2-D finite difference method on the center of either high anomaly radon fields in view of the character of radon field over sandstone-type uranium provide an algorithm for further research. (authors)

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

KAUST Repository

Wu, Zedong

2018-04-05

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.

Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

Directory of Open Access Journals (Sweden)

I. Amirali

2014-01-01

Full Text Available Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.

Hybrid finite difference/finite element solution method development for non-linear superconducting magnet and electrical circuit breakdown transient analysis

International Nuclear Information System (INIS)

Kraus, H.G.; Jones, J.L.

1986-01-01

The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique. (author)

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

Science.gov (United States)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

High-order asynchrony-tolerant finite difference schemes for partial differential equations

Science.gov (United States)

Aditya, Konduri; Donzis, Diego A.

2017-12-01

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

Finite difference computation of Casimir forces

International Nuclear Information System (INIS)

Pinto, Fabrizio

2016-01-01

In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing

Optimal 25-Point Finite-Difference Subgridding Techniques for the 2D Helmholtz Equation

Directory of Open Access Journals (Sweden)

Tingting Wu

2016-01-01

Full Text Available We present an optimal 25-point finite-difference subgridding scheme for solving the 2D Helmholtz equation with perfectly matched layer (PML. This scheme is second order in accuracy and pointwise consistent with the equation. Subgrids are used to discretize the computational domain, including the interior domain and the PML. For the transitional node in the interior domain, the finite difference equation is formulated with ghost nodes, and its weight parameters are chosen by a refined choice strategy based on minimizing the numerical dispersion. Numerical experiments are given to illustrate that the newly proposed schemes can produce highly accurate seismic modeling results with enhanced efficiency.

A perturbational h4 exponential finite difference scheme for the convective diffusion equation

International Nuclear Information System (INIS)

Chen, G.Q.; Gao, Z.; Yang, Z.F.

1993-01-01

A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic

Non Standard Finite Difference Scheme for Mutualistic Interaction Description

OpenAIRE

Gabbriellini, Gianluca

2012-01-01

One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...

Abstract Level Parallelization of Finite Difference Methods

Directory of Open Access Journals (Sweden)

Edwin Vollebregt

1997-01-01

Full Text Available A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”. The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing. This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.

Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

International Nuclear Information System (INIS)

Kriventsev, Vladimir

2000-09-01

Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed

Parallelized implicit propagators for the finite-difference Schrödinger equation

Science.gov (United States)

Parker, Jonathan; Taylor, K. T.

1995-08-01

We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion

Directory of Open Access Journals (Sweden)

O. H. Galal

2013-01-01

Full Text Available This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC. The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using Karhunen-Loève expansion, while the response function is approximated using homogenous chaos expansion. Galerkin projection is used in converting the original stochastic partial differential equation (PDE into a set of coupled deterministic partial differential equations and then solved using finite difference method. Two well-known equations were used for efficiency validation of the method proposed. First one being the linear diffusion equation with stochastic parameter and the second is the nonlinear Burger's equation with stochastic parameter and stochastic initial and boundary conditions. In both of these examples, the probability distribution function of the response manifested close conformity to the results obtained from Monte Carlo simulation with optimized computational cost.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

International Nuclear Information System (INIS)

Tan, Sirui; Huang, Lianjie

2014-01-01

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion

Finite-difference time-domain analysis of time-resolved terahertz spectroscopy experiments

DEFF Research Database (Denmark)

Larsen, Casper; Cooke, David G.; Jepsen, Peter Uhd

2011-01-01

In this paper we report on the numerical analysis of a time-resolved terahertz (THz) spectroscopy experiment using a modified finite-difference time-domain method. Using this method, we show that ultrafast carrier dynamics can be extracted with a time resolution smaller than the duration of the T...

The finite-difference time-domain method for electromagnetics with Matlab simulations

CERN Document Server

Elsherbeni, Atef Z

2016-01-01

This book introduces the powerful Finite-Difference Time-Domain method to students and interested researchers and readers. An effective introduction is accomplished using a step-by-step process that builds competence and confidence in developing complete working codes for the design and analysis of various antennas and microwave devices.

A coarse-mesh nodal method-diffusive-mesh finite difference method

International Nuclear Information System (INIS)

Joo, H.; Nichols, W.R.

1994-01-01

Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper

Stability analysis of single-phase thermosyphon loops by finite difference numerical methods

International Nuclear Information System (INIS)

Ambrosini, W.

1998-01-01

In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs

Application of the finite-difference approximation to electrostatic problems in gaseous proportional counters

International Nuclear Information System (INIS)

Waligorski, M.P.R.; Urbanczyk, K.M.

1975-01-01

The basic principles of the finite-difference approximation applied to the solution of electrostatic field distributions in gaseous proportional counters are given. Using this method, complicated two-dimensional electrostatic problems may be solved, taking into account any number of anodes, each with its own radius, and any cathode shape. A general formula for introducing the anode radii into the calculations is derived and a method of obtaining extremely accurate (up to 0.1%) solutions is developed. Several examples of potential and absolute field distributions for single rectangular and multiwire proportional counters are calculated and compared with exact results according to Tomitani, in order to discuss in detail errors of the finite-difference approximation. (author)

Stability and non-standard finite difference method of the generalized Chua's circuit

KAUST Repository

Radwan, Ahmed G.; Moaddy, K.; Momani, Shaher M.

2011-01-01

In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well

Thermal buckling comparative analysis using Different FE (Finite Element) tools

Energy Technology Data Exchange (ETDEWEB)

Banasiak, Waldemar; Labouriau, Pedro [INTECSEA do Brasil, Rio de Janeiro, RJ (Brazil); Burnett, Christopher [INTECSEA UK, Surrey (United Kingdom); Falepin, Hendrik [Fugro Engineers SA/NV, Brussels (Belgium)

2009-12-19

High operational temperature and pressure in offshore pipelines may lead to unexpected lateral movements, sometimes call lateral buckling, which can have serious consequences for the integrity of the pipeline. The phenomenon of lateral buckling in offshore pipelines needs to be analysed in the design phase using FEM. The analysis should take into account many parameters, including operational temperature and pressure, fluid characteristic, seabed profile, soil parameters, coatings of the pipe, free spans etc. The buckling initiation force is sensitive to small changes of any initial geometric out-of-straightness, thus the modeling of the as-laid state of the pipeline is an important part of the design process. Recently some dedicated finite elements programs have been created making modeling of the offshore environment more convenient that has been the case with the use of general purpose finite element software. The present paper aims to compare thermal buckling analysis of sub sea pipeline performed using different finite elements tools, i.e. general purpose programs (ANSYS, ABAQUS) and dedicated software (SAGE Profile 3D) for a single pipeline resting on an the seabed. The analyses considered the pipeline resting on a flat seabed with a small levels of out-of straightness initiating the lateral buckling. The results show the quite good agreement of results of buckling in elastic range and in the conclusions next comparative analyses with sensitivity cases are recommended. (author)

Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

Science.gov (United States)

Mickens, Ronald E.

1989-01-01

A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.

High-resolution finite-difference algorithms for conservation laws

International Nuclear Information System (INIS)

Towers, J.D.

1987-01-01

A new class of Total Variation Decreasing (TVD) schemes for 2-dimensional scalar conservation laws is constructed using either flux-limited or slope-limited numerical fluxes. The schemes are proven to have formal second-order accuracy in regions where neither u/sub x/ nor y/sub y/ vanishes. A new class of high-resolution large-time-step TVD schemes is constructed by adding flux-limited correction terms to the first-order accurate large-time-step version of the Engquist-Osher scheme. The use of the transport-collapse operator in place of the exact solution operator for the construction of difference schemes is studied. The production of spurious extrema by difference schemes is studied. A simple condition guaranteeing the nonproduction of spurious extrema is derived. A sufficient class of entropy inequalities for a conservation law with a flux having a single inflection point is presented. Finite-difference schemes satisfying a discrete version of each entropy inequality are only first-order accurate

Finite difference evolution equations and quantum dynamical semigroups

International Nuclear Information System (INIS)

Ghirardi, G.C.; Weber, T.

1983-12-01

We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)

Double absorbing boundaries for finite-difference time-domain electromagnetics

Energy Technology Data Exchange (ETDEWEB)

LaGrone, John, E-mail: jlagrone@smu.edu; Hagstrom, Thomas, E-mail: thagstrom@smu.edu

2016-12-01

We describe the implementation of optimal local radiation boundary condition sequences for second order finite difference approximations to Maxwell's equations and the scalar wave equation using the double absorbing boundary formulation. Numerical experiments are presented which demonstrate that the design accuracy of the boundary conditions is achieved and, for comparable effort, exceeds that of a convolution perfectly matched layer with reasonably chosen parameters. An advantage of the proposed approach is that parameters can be chosen using an accurate a priori error bound.

Finite difference program for calculating hydride bed wall temperature profiles

International Nuclear Information System (INIS)

Klein, J.E.

1992-01-01

A QuickBASIC finite difference program was written for calculating one dimensional temperature profiles in up to two media with flat, cylindrical, or spherical geometries. The development of the program was motivated by the need to calculate maximum temperature differences across the walls of the Tritium metal hydrides beds for thermal fatigue analysis. The purpose of this report is to document the equations and the computer program used to calculate transient wall temperatures in stainless steel hydride vessels. The development of the computer code was motivated by the need to calculate maximum temperature differences across the walls of the hydrides beds in the Tritium Facility for thermal fatigue analysis

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

KAUST Repository

Chu, Chunlei

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations. © 2011 Elsevier B.V.

A moving mesh finite difference method for equilibrium radiation diffusion equations

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.

A moving mesh finite difference method for equilibrium radiation diffusion equations

International Nuclear Information System (INIS)

Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian

2015-01-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation

Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data

Science.gov (United States)

Gibbons, T. J.; Öztürk, E.; Sims, N. D.

2018-01-01

Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.

Finite difference method for inner-layer equations in the resistive MagnetoHydroDynamic stability analysis

International Nuclear Information System (INIS)

Tokuda, Shinji; Watanabe, Tomoko.

1996-08-01

The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)

Wing-Body Aeroelasticity Using Finite-Difference Fluid/Finite-Element Structural Equations on Parallel Computers

Science.gov (United States)

Byun, Chansup; Guruswamy, Guru P.; Kutler, Paul (Technical Monitor)

1994-01-01

In recent years significant advances have been made for parallel computers in both hardware and software. Now parallel computers have become viable tools in computational mechanics. Many application codes developed on conventional computers have been modified to benefit from parallel computers. Significant speedups in some areas have been achieved by parallel computations. For single-discipline use of both fluid dynamics and structural dynamics, computations have been made on wing-body configurations using parallel computers. However, only a limited amount of work has been completed in combining these two disciplines for multidisciplinary applications. The prime reason is the increased level of complication associated with a multidisciplinary approach. In this work, procedures to compute aeroelasticity on parallel computers using direct coupling of fluid and structural equations will be investigated for wing-body configurations. The parallel computer selected for computations is an Intel iPSC/860 computer which is a distributed-memory, multiple-instruction, multiple data (MIMD) computer with 128 processors. In this study, the computational efficiency issues of parallel integration of both fluid and structural equations will be investigated in detail. The fluid and structural domains will be modeled using finite-difference and finite-element approaches, respectively. Results from the parallel computer will be compared with those from the conventional computers using a single processor. This study will provide an efficient computational tool for the aeroelastic analysis of wing-body structures on MIMD type parallel computers.

High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves

DEFF Research Database (Denmark)

Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter

2012-01-01

is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied...

A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking

Institute of Scientific and Technical Information of China (English)

ZHANG ZuTao; ZHANG JiaShu

2009-01-01

Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.

A parallel finite-difference method for computational aerodynamics

International Nuclear Information System (INIS)

Swisshelm, J.M.

1989-01-01

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed. 14 refs

High-order finite difference solution for 3D nonlinear wave-structure interaction

DEFF Research Database (Denmark)

Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter

2010-01-01

This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme O...

SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

KAUST Repository

Gao, Longfei

2018-02-16

We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

A simple finite-difference scheme for handling topography with the first-order wave equation

Science.gov (United States)

Mulder, W. A.; Huiskes, M. J.

2017-07-01

One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.

Enhanced finite difference scheme for the neutron diffusion equation using the importance function

International Nuclear Information System (INIS)

Vagheian, Mehran; Vosoughi, Naser; Gharib, Morteza

2016-01-01

Highlights: • An enhanced finite difference scheme for the neutron diffusion equation is proposed. • A seven-step algorithm is considered based on the importance function. • Mesh points are distributed through entire reactor core with respect to the importance function. • The results all proved that the proposed algorithm is highly efficient. - Abstract: Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.

A parallel adaptive finite difference algorithm for petroleum reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Hoang, Hai Minh

2005-07-01

Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)

Stability of finite difference schemes for generalized von Foerster equations with renewal

Directory of Open Access Journals (Sweden)

Henryk Leszczyński

2014-01-01

Full Text Available We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to \\(l^1\\ and \\(l^\\infty\\ norms.

Moving magnets in a micromagnetic finite-difference framework

Science.gov (United States)

Rissanen, Ilari; Laurson, Lasse

2018-05-01

We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.

Biomechanical Evaluations of Hip Fracture Using Finite Element Model that Models Individual Differences of Femur

OpenAIRE

田中, 英一; TANAKA, Eiichi; 山本, 創太; YAMAMOTO, Sota; 坂本, 誠二; SAKAMOTO, Seiji; 中西, 孝文; NAKANISHI, Takafumi; 原田, 敦; HARADA, Atsushi; 水野, 雅士; MIZUNO, Masashi

2004-01-01

This paper is concerned with an individual finite element modeling system for femur and biomechanical evaluations of the influences of loading conditions, bone shape and bone density on risks of hip fracture. Firstly, a method to construct an individual finite element model by morphological parameters that represent femoral shapes was developed. Using the models with different shapes constructed by this method, the effects of fall direction, posture of upper body, femur shape and bone density...

Convergence of finite differences schemes for viscous and inviscid conservation laws with rough coefficients

Energy Technology Data Exchange (ETDEWEB)

Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik

2000-09-01

We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a ''rough'' coefficient function k(x). we show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. (author)

Acoustic Wave Propagation Modeling by a Two-dimensional Finite-difference Summation-by-parts Algorithm

Energy Technology Data Exchange (ETDEWEB)

Kim, K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Petersson, N. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rodgers, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-10-25

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examples and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

Science.gov (United States)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

On the raising and lowering difference operators for eigenvectors of the finite Fourier transform

International Nuclear Information System (INIS)

Atakishiyeva, M K; Atakishiyev, N M

2015-01-01

We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)

Modelling optimization involving different types of elements in finite element analysis

International Nuclear Information System (INIS)

Wai, C M; Rivai, Ahmad; Bapokutty, Omar

2013-01-01

Finite elements are used to express the mechanical behaviour of a structure in finite element analysis. Therefore, the selection of the elements determines the quality of the analysis. The aim of this paper is to compare and contrast 1D element, 2D element, and 3D element used in finite element analysis. A simple case study was carried out on a standard W460x74 I-beam. The I-beam was modelled and analyzed statically with 1D elements, 2D elements and 3D elements. The results for the three separate finite element models were compared in terms of stresses, deformation and displacement of the I-beam. All three finite element models yield satisfactory results with acceptable errors. The advantages and limitations of these elements are discussed. 1D elements offer simplicity although lacking in their ability to model complicated geometry. 2D elements and 3D elements provide more detail yet sophisticated results which require more time and computer memory in the modelling process. It is also found that the choice of element in finite element analysis is influence by a few factors such as the geometry of the structure, desired analysis results, and the capability of the computer

Finite difference method calculations of X-ray absorption fine structure for copper

Energy Technology Data Exchange (ETDEWEB)

Bourke, J.D. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia); Chantler, C.T. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)]. E-mail: chantler@physics.unimelb.edu.au; Witte, C. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)

2007-01-15

The finite difference method is extended to calculate X-ray absorption fine structure (XAFS) for solid state copper. These extensions include the incorporation of a Monte Carlo frozen phonon technique to simulate the effect of thermal vibrations under a correlated Debye-Waller model, and the inclusion of broadening effects from inelastic processes. Spectra are obtained over an energy range in excess of 300 eV above the K absorption edge-more than twice the greatest energy range previously reported for a solid state calculation using this method. We find this method is highly sensitive to values of the photoelectron inelastic mean free path, allowing us to probe the accuracy of current models of this parameter, particularly at low energies. We therefore find that experimental data for the photoelectron inelastic mean free path can be obtained by this method. Our results compare favourably with high precision measurements of the X-ray mass attenuation coefficient for copper, reaching agreement to within 3%, and improving previous results using the finite difference method by an order of magnitude.

Scattering analysis of periodic structures using finite-difference time-domain

CERN Document Server

ElMahgoub, Khaled; Elsherbeni, Atef Z

2012-01-01

Periodic structures are of great importance in electromagnetics due to their wide range of applications such as frequency selective surfaces (FSS), electromagnetic band gap (EBG) structures, periodic absorbers, meta-materials, and many others. The aim of this book is to develop efficient computational algorithms to analyze the scattering properties of various electromagnetic periodic structures using the finite-difference time-domain periodic boundary condition (FDTD/PBC) method. A new FDTD/PBC-based algorithm is introduced to analyze general skewed grid periodic structures while another algor

A finite difference method for space fractional differential equations with variable diffusivity coefficient

KAUST Repository

Mustapha, K.

2017-06-03

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.

A finite difference method for space fractional differential equations with variable diffusivity coefficient

KAUST Repository

Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le

2017-01-01

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.

Finite-difference modeling of commercial aircraft using TSAR

Energy Technology Data Exchange (ETDEWEB)

Pennock, S.T.; Poggio, A.J.

1994-11-15

Future aircraft may have systems controlled by fiber optic cables, to reduce susceptibility to electromagnetic interference. However, the digital systems associated with the fiber optic network could still experience upset due to powerful radio stations, radars, and other electromagnetic sources, with potentially serious consequences. We are modeling the electromagnetic behavior of commercial transport aircraft in support of the NASA Fly-by-Light/Power-by-Wire program, using the TSAR finite-difference time-domain code initially developed for the military. By comparing results obtained from TSAR with data taken on a Boeing 757 at the Air Force Phillips Lab., we hope to show that FDTD codes can serve as an important tool in the design and certification of U.S. commercial aircraft, helping American companies to produce safe, reliable air transportation.

Modeling of NiTiHf using finite difference method

Science.gov (United States)

Farjam, Nazanin; Mehrabi, Reza; Karaca, Haluk; Mirzaeifar, Reza; Elahinia, Mohammad

2018-03-01

NiTiHf is a high temperature and high strength shape memory alloy with transformation temperatures above 100oC. A constitutive model based on Gibbs free energy is developed to predict the behavior of this material. Two different irrecoverable strains including transformation induced plastic strain (TRIP) and viscoplastic strain (VP) are considered when using high temperature shape memory alloys (HTSMAs). The first one happens during transformation at high levels of stress and the second one is related to the creep which is rate-dependent. The developed model is implemented for NiTiHf under uniaxial loading. Finite difference method is utilized to solve the proposed equations. The material parameters in the equations are calibrated from experimental data. Simulation results are captured to investigate the superelastic behavior of NiTiHf. The extracted results are compared with experimental tests of isobaric heating and cooling at different levels of stress and also superelastic tests at different levels of temperature. More results are generated to investigate the capability of the proposed model in the prediction of the irrecoverable strain after full transformation in HTSMAs.

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

Science.gov (United States)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

A multigrid algorithm for the cell-centered finite difference scheme

Science.gov (United States)

Ewing, Richard E.; Shen, Jian

1993-01-01

In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.

Mimetic Finite Differences for Flow in Fractures from Microseismic Data

KAUST Repository

Al-Hinai, Omar; Srinivasan, Sanjay; Wheeler, Mary F.

2015-01-01

We present a method for porous media flow in the presence of complex fracture networks. The approach uses the Mimetic Finite Difference method (MFD) and takes advantage of MFD's ability to solve over a general set of polyhedral cells. This flexibility is used to mesh fracture intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis.

Mimetic Finite Differences for Flow in Fractures from Microseismic Data

KAUST Repository

Al-Hinai, Omar

2015-01-01

We present a method for porous media flow in the presence of complex fracture networks. The approach uses the Mimetic Finite Difference method (MFD) and takes advantage of MFD\\'s ability to solve over a general set of polyhedral cells. This flexibility is used to mesh fracture intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis.

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

Science.gov (United States)

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

Finite-difference solution of the space-angle-lethargy-dependent slowing-down transport equation

Energy Technology Data Exchange (ETDEWEB)

Matausek, M V [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1972-07-01

A procedure has been developed for solving the slowing-down transport equation for a cylindrically symmetric reactor system. The anisotropy of the resonance neutron flux is treated by the spherical harmonics formalism, which reduces the space-angle-Iethargy-dependent transport equation to a matrix integro-differential equation in space and lethargy. Replacing further the lethargy transfer integral by a finite-difference form, a set of matrix ordinary differential equations is obtained, with lethargy-and space dependent coefficients. If the lethargy pivotal points are chosen dense enough so that the difference correction term can be ignored, this set assumes a lower block triangular form and can be solved directly by forward block substitution. As in each step of the finite-difference procedure a boundary value problem has to be solved for a non-homogeneous system of ordinary differential equations with space-dependent coefficients, application of any standard numerical procedure, for example, the finite-difference method or the method of adjoint equations, is too cumbersome and would make the whole procedure practically inapplicable. A simple and efficient approximation is proposed here, allowing analytical solution for the space dependence of the spherical-harmonics flux moments, and hence the derivation of the recurrence relations between the flux moments at successive lethargy pivotal points. According to the procedure indicated above a computer code has been developed for the CDC -3600 computer, which uses the KEDAK nuclear data file. The space and lethargy distribution of the resonance neutrons can be computed in such a detailed fashion as the neutron cross-sections are known for the reactor materials considered. The computing time is relatively short so that the code can be efficiently used, either autonomously, or as part of some complex modular scheme. Typical results will be presented and discussed in order to prove and illustrate the applicability of the

Five-point form of the nodal diffusion method and comparison with finite-difference

International Nuclear Information System (INIS)

Azmy, Y.Y.

1988-01-01

Nodal Methods have been derived, implemented and numerically tested for several problems in physics and engineering. In the field of nuclear engineering, many nodal formalisms have been used for the neutron diffusion equation, all yielding results which were far more computationally efficient than conventional Finite Difference (FD) and Finite Element (FE) methods. However, not much effort has been devoted to theoretically comparing nodal and FD methods in order to explain the very high accuracy of the former. In this summary we outline the derivation of a simple five-point form for the lowest order nodal method and compare it to the traditional five-point, edge-centered FD scheme. The effect of the observed differences on the accuracy of the respective methods is established by considering a simple test problem. It must be emphasized that the nodal five-point scheme derived here is mathematically equivalent to previously derived lowest order nodal methods. 7 refs., 1 tab

Detailed balance principle and finite-difference stochastic equation in a field theory

International Nuclear Information System (INIS)

Kozhamkulov, T.A.

1986-01-01

A finite-difference equation, which is a generalization of the Langevin equation in field theory, has been obtained basing upon the principle of detailed balance for the Markov chain. Advantages of the present approach as compared with the conventional Parisi-Wu method are shown for examples of an exactly solvable problem of zero-dimensional quantum theory and a simple numerical simulation

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

DEFF Research Database (Denmark)

Amini Afshar, Mostafa; Bingham, Harry B.

2017-01-01

. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...

Finite difference applied to the reconstruction method of the nuclear power density distribution

International Nuclear Information System (INIS)

Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.

2016-01-01

Highlights: • A method for reconstruction of the power density distribution is presented. • The method uses discretization by finite differences of 2D neutrons diffusion equation. • The discretization is performed homogeneous meshes with dimensions of a fuel cell. • The discretization is combined with flux distributions on the four node surfaces. • The maximum errors in reconstruction occur in the peripheral water region. - Abstract: In this reconstruction method the two-dimensional (2D) neutron diffusion equation is discretized by finite differences, employed to two energy groups (2G) and meshes with fuel-pin cell dimensions. The Nodal Expansion Method (NEM) makes use of surface discontinuity factors of the node and provides for reconstruction method the effective multiplication factor of the problem and the four surface average fluxes in homogeneous nodes with size of a fuel assembly (FA). The reconstruction process combines the discretized 2D diffusion equation by finite differences with fluxes distribution on four surfaces of the nodes. These distributions are obtained for each surfaces from a fourth order one-dimensional (1D) polynomial expansion with five coefficients to be determined. The conditions necessary for coefficients determination are three average fluxes on consecutive surfaces of the three nodes and two fluxes in corners between these three surface fluxes. Corner fluxes of the node are determined using a third order 1D polynomial expansion with four coefficients. This reconstruction method uses heterogeneous nuclear parameters directly providing the heterogeneous neutron flux distribution and the detailed nuclear power density distribution within the FAs. The results obtained with this method has good accuracy and efficiency when compared with reference values.

The Incorporation of Truncated Fourier Series into Finite Difference Approximations of Structural Stability Equations

Science.gov (United States)

Hannah, S. R.; Palazotto, A. N.

1978-01-01

A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.

Numerical study of water diffusion in biological tissues using an improved finite difference method

International Nuclear Information System (INIS)

Xu Junzhong; Does, Mark D; Gore, John C

2007-01-01

An improved finite difference (FD) method has been developed in order to calculate the behaviour of the nuclear magnetic resonance signal variations caused by water diffusion in biological tissues more accurately and efficiently. The algorithm converts the conventional image-based finite difference method into a convenient matrix-based approach and includes a revised periodic boundary condition which eliminates the edge effects caused by artificial boundaries in conventional FD methods. Simulated results for some modelled tissues are consistent with analytical solutions for commonly used diffusion-weighted pulse sequences, whereas the improved FD method shows improved efficiency and accuracy. A tightly coupled parallel computing approach was also developed to implement the FD methods to enable large-scale simulations of realistic biological tissues. The potential applications of the improved FD method for understanding diffusion in tissues are also discussed. (note)

Computational electrodynamics the finite-difference time-domain method

CERN Document Server

Taflove, Allen

2005-01-01

This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.

Non-linear analysis of skew thin plate by finite difference method

International Nuclear Information System (INIS)

Kim, Chi Kyung; Hwang, Myung Hwan

2012-01-01

This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed

Analysis for pressure transient of coalbed methane reservoir based on Laplace transform finite difference method

Directory of Open Access Journals (Sweden)

Lei Wang

2015-09-01

Full Text Available Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare with the results from the analytical method, the result from Laplace transform finite difference method turns out to be accurate. The influence factors are analyzed, including fractal dimension, fractal index, skin factor, well bore storage coefficient, energy storage ratio, interporosity flow coefficient and the adsorption factor. The calculating error of Laplace transform difference method is small. Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment results and space grid.

Finite Boltzmann schemes

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

Principle of detailed balance and the finite-difference stochastic equation in field theory

International Nuclear Information System (INIS)

Kozhamkulov, T.A.

1986-01-01

The principle of detailed balance for the Markov chain is used to obtain a finite-difference equation which generalizes the Langevin equation in field theory. The advantages of using this approach compared to the conventional Parisi-Wu method are demonstrated for the examples of an exactly solvable problem in zero-dimensional quantum theory and a simple numerical simulation

Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

Science.gov (United States)

Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

2016-08-01

Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

A coupled boundary element-finite difference solution of the elliptic modified mild slope equation

DEFF Research Database (Denmark)

Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.

2011-01-01

The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...

Pricing derivatives under Lévy models modern finite-difference and pseudo-differential operators approach

CERN Document Server

Itkin, Andrey

2017-01-01

This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solvin...

Anisotropic constitutive equation for use in finite difference wave propagation calculations. [Incorporation into TOODY code

Energy Technology Data Exchange (ETDEWEB)

Swegle, J.W.; Hicks, D.L.

1979-05-01

An anisotropic constitutive relation was incorporated into the Lagrangian finite-difference wavecode TOODY. The details of the implementation of the constitutive relation in the wavecode and an example of its use are discussed. 4 figures, 1 table.

Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

International Nuclear Information System (INIS)

Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi

2015-01-01

Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap

Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

Energy Technology Data Exchange (ETDEWEB)

Ibral, Asmaa [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Zouitine, Asmaa [Département de Physique, Ecole Nationale Supérieure d' Enseignement Technique, Université Mohammed V Souissi, B. P. 6207 Rabat-Instituts, Rabat, Royaume du Maroc (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); and others

2015-02-01

Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.

Solving the Schroedinger equation using the finite difference time domain method

International Nuclear Information System (INIS)

Sudiarta, I Wayan; Geldart, D J Wallace

2007-01-01

In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems

Transient analysis of printed lines using finite-difference time-domain method

Energy Technology Data Exchange (ETDEWEB)

Ahmed, Shahid [Thomas Jefferson National Accelerator Facility, 12050 Jefferson Avenue, Suite 704, Newport News, VA, 23606, USA

2012-03-29

Comprehensive studies of ultra-wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full-wave 3D finite-difference time-domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_r = 1) and with (ϵ_r > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Finally, physical interpretations of the simulation results are discussed in the paper.

A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

Directory of Open Access Journals (Sweden)

Taohua Liu

2017-01-01

Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(Klog⁡K. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.

Finite-difference analysis of shells impacting rigid barriers

International Nuclear Information System (INIS)

Pirotin, S.D.; Witmer, E.A.

1977-01-01

Nuclear power plants must be protected from the adverse effects of missile impacts. A significant category of missile impact involves deformable structures (pressure vessel components, whipping pipes) striking relatively rigid targets (concrete walls, bumpers) which act as protective devices. The response and interaction of these structures is needed to assess the adequacy of these barriers for protecting vital safety related equipment. The present investigation represents an initial attempt to develop an efficient numerical procedure for predicting the deformations and impact force time-histories of shells which impact upon a rigid target. The general large-deflection equations of motion of the shell are expressed in finite-difference form in space and integrated in time through application of the central-difference temporal operator. The effect of material nonlinearities is treated by a mechanical sublayer material model which handles the strain-hardening, Bauschinger, and strain-rate effects. The general adequacy of this shell treatment has been validated by comparing predictions with the results of various experiments in which structures have been subjected to well-defined transient forcing functions (typically high-explosive impulse loading). The 'new' ingredient addressed in the present study involves an accounting for impact interaction and response of both the target structure and the attacking body. (Auth.)

An Explicit Finite Difference scheme for numerical solution of fractional neutron point kinetic equation

International Nuclear Information System (INIS)

Saha Ray, S.; Patra, A.

2012-01-01

Highlights: ► In this paper fractional neutron point kinetic equation has been analyzed. ► The numerical solution for fractional neutron point kinetic equation is obtained. ► Explicit Finite Difference Method has been applied. ► Supercritical reactivity, critical reactivity and subcritical reactivity analyzed. ► Comparison between fractional and classical neutron density is presented. - Abstract: In the present article, a numerical procedure to efficiently calculate the solution for fractional point kinetics equation in nuclear reactor dynamics is investigated. The Explicit Finite Difference Method is applied to solve the fractional neutron point kinetic equation with the Grunwald–Letnikov (GL) definition (). Fractional Neutron Point Kinetic Model has been analyzed for the dynamic behavior of the neutron motion in which the relaxation time associated with a variation in the neutron flux involves a fractional order acting as exponent of the relaxation time, to obtain the best operation of a nuclear reactor dynamics. Results for neutron dynamic behavior for subcritical reactivity, supercritical reactivity and critical reactivity and also for different values of fractional order have been presented and compared with the classical neutron point kinetic (NPK) equation as well as the results obtained by the learned researchers .

Transport and dispersion of pollutants in surface impoundments: a finite difference model

Energy Technology Data Exchange (ETDEWEB)

Yeh, G.T.

1980-07-01

A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model.

Finite element analysis of thermal stress distribution in different ...

African Journals Online (AJOL)

Nigerian Journal of Clinical Practice. Journal Home ... Von Mises and thermal stress distributions were evaluated. Results: In all ... distribution. Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ...

Visualization of elastic wavefields computed with a finite difference code

Energy Technology Data Exchange (ETDEWEB)

Larsen, S. [Lawrence Livermore National Lab., CA (United States); Harris, D.

1994-11-15

The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.

A study of unstable rock failures using finite difference and discrete element methods

Science.gov (United States)

Garvey, Ryan J.

Case histories in mining have long described pillars or faces of rock failing violently with an accompanying rapid ejection of debris and broken material into the working areas of the mine. These unstable failures have resulted in large losses of life and collapses of entire mine panels. Modern mining operations take significant steps to reduce the likelihood of unstable failure, however eliminating their occurrence is difficult in practice. Researchers over several decades have supplemented studies of unstable failures through the application of various numerical methods. The direction of the current research is to extend these methods and to develop improved numerical tools with which to study unstable failures in underground mining layouts. An extensive study is first conducted on the expression of unstable failure in discrete element and finite difference methods. Simulated uniaxial compressive strength tests are run on brittle rock specimens. Stable or unstable loading conditions are applied onto the brittle specimens by a pair of elastic platens with ranging stiffnesses. Determinations of instability are established through stress and strain histories taken for the specimen and the system. Additional numerical tools are then developed for the finite difference method to analyze unstable failure in larger mine models. Instability identifiers are established for assessing the locations and relative magnitudes of unstable failure through measures of rapid dynamic motion. An energy balance is developed which calculates the excess energy released as a result of unstable equilibria in rock systems. These tools are validated through uniaxial and triaxial compressive strength tests and are extended to models of coal pillars and a simplified mining layout. The results of the finite difference simulations reveal that the instability identifiers and excess energy calculations provide a generalized methodology for assessing unstable failures within potentially complex

On Forecasting Macro-Economic Indicators with the Help of Finite-Difference Equations and Econometric Methods

Directory of Open Access Journals (Sweden)

Polshkov Yulian M.

2013-11-01

Full Text Available The article considers data on the gross domestic product, consumer expenditures, gross investments and volume of foreign trade for the national economy. It is assumed that time is a discrete variable with one year iteration. The article uses finite-difference equations. It considers models with a high degree of the regulatory function of the state with respect to the consumer market. The econometric component is based on the hypothesis that each of the above said macro-economic indicators for this year depends on the gross domestic product for the previous time periods. Such an assumption gives a possibility to engage the least-squares method for building up linear models of the pair regression. The article obtains the time series model, which allows building point and interval forecasts for the gross domestic product for the next year based on the values of the gross domestic product for the current and previous years. The article draws a conclusion that such forecasts could be considered justified at least in the short-term prospect. From the mathematical point of view the built model is a heterogeneous finite-difference equation of the second order with constant ratios. The article describes specific features of such equations. It illustrates graphically the analytical view of solutions of the finite-difference equation. This gives grounds to differentiate national economies as sustainable growth economies, one-sided, weak or being in the stage of successful re-formation. The article conducts comparison of the listed types with specific economies of modern states.

Finite differences versus finite elements in slab geometry, even-parity transport theory

International Nuclear Information System (INIS)

Miller, W.F. Jr.; Noh, T.

1993-01-01

There continues to be considerable interest in the application of the even-parity transport equation to problems of radiation transfer and neutron transport. The motivation for this interest arises from several potential advantages of this equation when compared with the more traditional first-order form of the equation. First, assuming that the scalar flux is of primary interest, the angular domain under consideration is one-half of that required for the first-order equation. Thus, for the same degree of accuracy, one would hopefully require substantiably fewer unknown values of the dependent variable to be determined. Secondly, the elliptic-like nature of the set of even-parity equations should allow certain parallel computer architectures to be used more readily. In a recent paper, it was shown that for neutron transport applications in slab geometry, finite differencing the even-parity equation on the cell edges yields algebraic equations with numerical properties that are superior to the traditional diamond difference approach. Specifically, a positive, second-order method with a rapidly convergent iteration approach emerged from cell-edge differencing. Additionally, for radiation transfer problems that are optically thick, it was shown that cell-edge differencing demonstrates better behavior than does diamond-differencing. However, some problems in accuracy could occur due to vacuum boundaries as well as at interfaces between very different types of material regions. These problems emerge from a boundary-layer analysis of the so called open-quotes thickclose quotes diffusion limit. For neutronics calculations, which are the subject of this paper, however, the open-quotes thickclose quotes diffusion limit analysis has little applicability, and the cell-edge differencing derived previously seems to have considerable promise. 13 refs., 2 figs., 3 tabs

Iterative solutions of finite difference diffusion equations

International Nuclear Information System (INIS)

Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.

1981-01-01

The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

Hybrid lattice Boltzmann finite difference simulation of mixed convection flows in a lid-driven square cavity

Energy Technology Data Exchange (ETDEWEB)

Bettaibi, Soufiene, E-mail: Bettaibisoufiene@gmail.com [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia); Kuznik, Frédéric [INSA-Lyon, CETHIL, F-69621 Villeurbanne (France); Université de Lyon, CNRS, UMR5008, F-69622 Villeurbanne (France); Sediki, Ezeddine [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia)

2014-06-27

Highlights: • Mixed convection heat transfer in 2D lid-driven cavity is studied numerically. • Hybrid scheme with multiple relaxation time lattice Boltzmann method is used to obtain the velocity field. • Finite difference method is used to compute the temperature. • Effect of both Richardson and Reynolds numbers for mixed convection is studied. - Abstract: Mixed convection heat transfer in two-dimensional lid-driven rectangular cavity filled with air (Pr=0.71) is studied numerically. A hybrid scheme with multiple relaxation time lattice Boltzmann method (MRT-LBM) is used to obtain the velocity field while the temperature field is deduced from energy balance equation by using the finite difference method (FDM). The main objective of this work is to investigate the model effectiveness for mixed convection flow simulation. Results are presented in terms of streamlines, isotherms and Nusselt numbers. Excellent agreement is obtained between our results and previous works. The different comparisons demonstrate the robustness and the accuracy of our proposed approach.

A finite difference approach to despiking in-stationary velocity data - tested on a triple-lidar

DEFF Research Database (Denmark)

Meyer Forsting, Alexander Raul; Troldborg, Niels

2016-01-01

A novel despiking method is presented for in-stationary wind lidar velocity measurements. A finite difference approach yields the upper and lower bounds for a valid velocity reading. The sole input to the algorithm is the velocity series and optionally a far- field reference to the temporal...

Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids

Science.gov (United States)

Housman, Jeffrey A.; Kiris, Cetin

2016-01-01

Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.

Accuracy of spectral and finite difference schemes in 2D advection problems

DEFF Research Database (Denmark)

Naulin, V.; Nielsen, A.H.

2003-01-01

In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy...... that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem....

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced

Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems

International Nuclear Information System (INIS)

Aghababa Mohammad Pourmahmood

2012-01-01

The centrifugal flywheel governor (CFG) is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by sudden change of load torque. It has been shown that this system exhibits very rich and complex dynamics such as chaos. This paper investigates the problem of robust finite-time synchronization of non-autonomous chaotic CFGs. The effects of unknown parameters, model uncertainties and external disturbances are fully taken into account. First, it is assumed that the parameters of both master and slave CFGs have the same value and a suitable adaptive finite-time controller is designed. Second, two CFGs are synchronized with the parameters of different values via a robust adaptive finite-time control approach. Finally, some numerical simulations are used to demonstrate the effectiveness and robustness of the proposed finite-time controllers. (general)

Study of two-dimensional transient cavity fields using the finite-difference time-domain technique

Energy Technology Data Exchange (ETDEWEB)

Crisp, J.L.

1988-06-01

This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs.

Study of two-dimensional transient cavity fields using the finite-difference time-domain technique

International Nuclear Information System (INIS)

Crisp, J.L.

1988-06-01

This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs

GPU-accelerated 3D neutron diffusion code based on finite difference method

Energy Technology Data Exchange (ETDEWEB)

Xu, Q.; Yu, G.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ. (China)

2012-07-01

Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)

GPU-accelerated 3D neutron diffusion code based on finite difference method

International Nuclear Information System (INIS)

Xu, Q.; Yu, G.; Wang, K.

2012-01-01

Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)

Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs

Science.gov (United States)

Zhao, Yan; Belov, Pavel A.; Hao, Yang

2006-06-01

In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the slab with its thickness equal to an integer number of half-wavelengths is capable of transporting images with sub-wavelength resolution from one interface of the slab to another. It is also shown that the operation of such transmission devices is not sensitive to their transverse dimensions, which can be made even comparable to the wavelength. In this case, the edge diffractions are negligible and do not disturb the image formation.

Finite elements and approximation

CERN Document Server

Zienkiewicz, O C

2006-01-01

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

Calculating modes of quantum wire systems using a finite difference technique

Directory of Open Access Journals (Sweden)

T Mardani

2013-03-01

Full Text Available  In this paper, the Schrodinger equation for a quantum wire is solved using a finite difference approach. A new aspect in this work is plotting wave function on cross section of rectangular cross-sectional wire in two dimensions, periodically. It is found that the correct eigen energies occur when wave functions have a complete symmetry. If the value of eigen energy has a small increase or decrease in neighborhood of the correct energy the symmetry will be destroyed and aperturbation value at the first of wave function will be observed. In addition, the demand on computer memory varies linearly with the size of the system under investigation.

Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case

International Nuclear Information System (INIS)

Hojbota, C I; Toşa, V; Mercea, P V

2013-01-01

We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food

TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems

International Nuclear Information System (INIS)

Ikushima, Takeshi

1984-02-01

Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)

Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method

International Nuclear Information System (INIS)

Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong

2014-01-01

In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)

A New Approach for the Statistical Thermodynamic Theory of the Nonextensive Systems Confined in Different Finite Traps

Science.gov (United States)

Tang, Hui-Yi; Wang, Jian-Hui; Ma, Yong-Li

2014-06-01

For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann-Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis's q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal energy. When we investigate the thermodynamics for the interacting nonextensive systems, we obtain the system-bath heat exchange and "uncompensated heat" which are in the thermodynamical level and independent on the detail of the system-bath coupling. For ideal finite systems, with different traps and boundary conditions, we calculate some thermodynamic quantities, such as the specific heat, entropy, and equation of state, etc. Particularly at low temperatures for the small systems, we predict some novel behaviors in the quantum thermodynamics, including internal entropy production, heat exchanges between the system and its surroundings and finite-size effects on the free energy.

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

Science.gov (United States)

Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.

2013-12-01

In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( α 0) and the scaling factor ( β 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1

A finite different field solver for dipole modes

International Nuclear Information System (INIS)

Nelson, E.M.

1992-08-01

A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL

Finite difference time domain solution of electromagnetic scattering on the hypercube

International Nuclear Information System (INIS)

Calalo, R.H.; Lyons, J.R.; Imbriale, W.A.

1988-01-01

Electromagnetic fields interacting with a dielectric or conducting structure produce scattered electromagnetic fields. To model the fields produced by complicated, volumetric structures, the finite difference time domain (FDTD) method employs an iterative solution to Maxwell's time dependent curl equations. Implementations of the FDTD method intensively use memory and perform numerous calculations per time step iteration. The authors have implemented an FDTD code on the California Institute of Technology/Jet Propulsion Laboratory Mark III Hypercube. This code allows to solve problems requiring as many as 2,048,000 unit cells on a 32 node Hypercube. For smaller problems, the code produces solutions in a fraction of the time to solve the same problems on sequential computers

Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs

International Nuclear Information System (INIS)

Bollig, Evan F.; Flyer, Natasha; Erlebacher, Gordon

2012-01-01

This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage GPU accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple GPUs. OpenCL kernels target the GPUs and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity GPU with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes.

Finite flavour groups of fermions

International Nuclear Information System (INIS)

Grimus, Walter; Ludl, Patrick Otto

2012-01-01

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations and character tables. In a specialized part, we attempt to give a fairly comprehensive review of finite subgroups of SO(3) and SU(3), in which we apply and illustrate the general theory. Moreover, we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of U(3) and finite subgroups of SU(3). Although in this review we give a detailed description of a wide range of finite groups, the main focus is on the methods which allow the exploration of their different aspects. (topical review)

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

Science.gov (United States)

Ghil, M.; Balgovind, R.

1979-01-01

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

DETERMINATION OF MOISTURE DIFFUSION COEFFICIENT OF LARCH BOARD WITH FINITE DIFFERENCE METHOD

Directory of Open Access Journals (Sweden)

Qiaofang Zhou

2011-04-01

Full Text Available This paper deals with the moisture diffusion coefficient of Dahurian Larch (Larix gmelinii Rupr. by use of the Finite Difference Method (FDM. To obtain moisture distributions the dimensional boards of Dahurian Larch were dried, from which test samples were cut and sliced evenly into 9 pieces in different drying periods, so that moisture distributions at different locations and times across the thickness of Dahurian Larch were obtained with a weighing method. With these experimental data, FDM was used to solve Fick’s one-dimensional unsteady-state diffusion equation, and the moisture diffusion coefficient across the thickness at specified time was obtained. Results indicated that the moisture diffusion coefficient decreased from the surface to the center of the Dahurian Larch wood, and it decreased with decreasing moisture content at constant wood temperature; as the wood temperature increased, the moisture diffusion coefficient increased, and the effect of the wood temperature on the moisture diffusion coefficient was more significant than that of moisture content. Moisture diffusion coefficients were different for the two experiments due to differing diffusivity of the specimens.

On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

KAUST Repository

Gao, Longfei; Ketcheson, David I.; Keyes, David E.

2017-01-01

We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application

Thermal Analysis of Ball screw Systems by Explicit Finite Difference Method

Energy Technology Data Exchange (ETDEWEB)

Min, Bog Ki [Hanyang Univ., Seoul (Korea, Republic of); Park, Chun Hong; Chung, Sung Chong [KIMM, Daejeon (Korea, Republic of)

2016-01-15

Friction generated from balls and grooves incurs temperature rise in the ball screw system. Thermal deformation due to the heat degrades positioning accuracy of the feed drive system. To compensate for the thermal error, accurate prediction of the temperature distribution is required first. In this paper, to predict the temperature distribution according to the rotational speed, solid and hollow cylinders are applied for analysis of the ball screw shaft and nut, respectively. Boundary conditions such as the convective heat transfer coefficient, friction torque, and thermal contact conductance (TCC) between balls and grooves are formulated according to operating and fabrication conditions of the ball screw. Explicit FDM (finite difference method) is studied for development of a temperature prediction simulator. Its effectiveness is verified through numerical analysis.

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Directory of Open Access Journals (Sweden)

Djordjevich Alexandar

2017-12-01

Full Text Available The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity. Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.

Finite element modelling of Plantar Fascia response during running on different surface types

Science.gov (United States)

Razak, A. H. A.; Basaruddin, K. S.; Salleh, A. F.; Rusli, W. M. R.; Hashim, M. S. M.; Daud, R.

2017-10-01

Plantar fascia is a ligament found in human foot structure located beneath the skin of human foot that functioning to stabilize longitudinal arch of human foot during standing and normal gait. To perform direct experiment on plantar fascia seems very difficult since the structure located underneath the soft tissue. The aim of this study is to develop a finite element (FE) model of foot with plantar fascia and investigate the effect of the surface hardness on biomechanical response of plantar fascia during running. The plantar fascia model was developed using Solidworks 2015 according to the bone structure of foot model that was obtained from Turbosquid database. Boundary conditions were set out based on the data obtained from experiment of ground reaction force response during running on different surface hardness. The finite element analysis was performed using Ansys 14. The results found that the peak of stress and strain distribution were occur on the insertion of plantar fascia to bone especially on calcaneal area. Plantar fascia became stiffer with increment of Young’s modulus value and was able to resist more loads. Strain of plantar fascia was decreased when Young’s modulus increased with the same amount of loading.

DIF3D: a code to solve one-, two-, and three-dimensional finite-difference diffusion theory problems

International Nuclear Information System (INIS)

Derstine, K.L.

1984-04-01

The mathematical development and numerical solution of the finite-difference equations are summarized. The report provides a guide for user application and details the programming structure of DIF3D. Guidelines are included for implementing the DIF3D export package on several large scale computers. Optimized iteration methods for the solution of large-scale fast-reactor finite-difference diffusion theory calculations are presented, along with their theoretical basis. The computational and data management considerations that went into their formulation are discussed. The methods utilized include a variant of the Chebyshev acceleration technique applied to the outer fission source iterations and an optimized block successive overrelaxation method for the within-group iterations. A nodal solution option intended for analysis of LMFBR designs in two- and three-dimensional hexagonal geometries is incorporated in the DIF3D package and is documented in a companion report, ANL-83-1

Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

International Nuclear Information System (INIS)

Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.

1996-01-01

This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

Science.gov (United States)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Finite difference time domain modeling of light matter interaction in light-propelled microtools

DEFF Research Database (Denmark)

Bañas, Andrew Rafael; Palima, Darwin; Aabo, Thomas

2013-01-01

save time as it helps optimize the structures prior to fabrication and experiments. In addition to field distributions, optical forces can also be obtained using the Maxwell stress tensor formulation. By calculating the forces on bent waveguides subjected to tailored static light distributions, we...... may trigger highly localized non linear processes in the surface of a cell. Since these functionalities are strongly dependent on design, it is important to use models that can handle complexities and take in little simplifying assumptions about the system. Hence, we use the finite difference time...

Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation

International Nuclear Information System (INIS)

Sha, Wei; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng

2007-01-01

An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources

Low-Frequency Loudspeaker-Room Simulation Using Finite Differences in the Time Domain-Part 1: Analysis

DEFF Research Database (Denmark)

Celestinos, Adrian; Nielsen, Sofus Birkedal

2008-01-01

Small- and medium-size rectangular rooms have a strong influence on the low-frequency performance of loudspeakers. A simulation program based on the finite-difference time-domain (FDTD) method is introduced to analyze the sound field produced by loudspeakers in rectangular rooms at low frequencies...

Aspects of the generation of finite-difference Green's function sequences for arbitrary 3-D cubic lattice points

NARCIS (Netherlands)

de Hon, B.P.; Arnold, J.M.

2015-01-01

The robust and speedy evaluation of lattice Green's functions LGFs) is crucial to the effectiveness of finite-difference Green's function diakoptics schemes. We have recently determined a generic recurrence scheme for the construction of scalar LGF sequences at arbitrary points on a 3-D cubic

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

Science.gov (United States)

Sohn, Kiho D.; Ip, Shek-Se P.

1988-01-01

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

Three-Dimensional Finite Difference Simulation of Ground Motions from the August 24, 2014 South Napa Earthquake

Energy Technology Data Exchange (ETDEWEB)

Rodgers, Arthur J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States); Dreger, Douglas S. [Univ. of California, Berkeley, CA (United States); Pitarka, Arben [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-06-15

We performed three-dimensional (3D) anelastic ground motion simulations of the South Napa earthquake to investigate the performance of different finite rupture models and the effects of 3D structure on the observed wavefield. We considered rupture models reported by Dreger et al. (2015), Ji et al., (2015), Wei et al. (2015) and Melgar et al. (2015). We used the SW4 anelastic finite difference code developed at Lawrence Livermore National Laboratory (Petersson and Sjogreen, 2013) and distributed by the Computational Infrastructure for Geodynamics. This code can compute the seismic response for fully 3D sub-surface models, including surface topography and linear anelasticity. We use the 3D geologic/seismic model of the San Francisco Bay Area developed by the United States Geological Survey (Aagaard et al., 2008, 2010). Evaluation of earlier versions of this model indicated that the structure can reproduce main features of observed waveforms from moderate earthquakes (Rodgers et al., 2008; Kim et al., 2010). Simulations were performed for a domain covering local distances (< 25 km) and resolution providing simulated ground motions valid to 1 Hz.

Finite-difference Green's functions on a 3-D cubic lattice - Integer versus fixed-precision arithmetic recurrence schemes

NARCIS (Netherlands)

De Hon, B. P.; Arnold, J. M.

2016-01-01

Time-domain 3-D lattice Green's function (LGF) sequences can be evaluated using a single-lattice point recurrence scheme, and play an important role in finite-difference Green's function diakoptics. Asymptotically, at large distances, the LGFs in three dimensions can be described in terms of six

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

Science.gov (United States)

Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk

2018-05-01

Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

KAUST Repository

Gerke, Kirill M.

2018-01-17

Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.

Comparison of numerical dispersion for finite-difference algorithms in transversely isotropic media with a vertical symmetry axis

International Nuclear Information System (INIS)

Liang, Wen-Quan; Wang, Yan-Fei; Yang, Chang-Chun

2015-01-01

Numerical simulation of the wave equation is widely used to synthesize seismograms theoretically and is also the basis of the reverse time migration and full waveform inversion. For the finite difference methods, grid dispersion often exists because of the discretization of the time and the spatial derivatives in the wave equation. How to suppress the grid dispersion is therefore a key problem for finite difference (FD) approaches. The FD operators for the space derivatives are usually obtained in the space domain. However, the wave equations are discretized in the time and space directions simultaneously. So it would be better to design the FD operators in the time–space domain. We improved the time–space domain method for obtaining the FD operators in an acoustic vertically transversely isotropic (VTI) media so as to cover a much wider range of frequencies. Dispersion analysis and seismic numerical simulation demonstrate the effectiveness of the proposed method. (paper)

Finite-difference time-domain simulation of thermal noise in open cavities

International Nuclear Information System (INIS)

Andreasen, Jonathan; Cao Hui; Taflove, Allen; Kumar, Prem; Cao Changqi

2008-01-01

A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes

Finite-time generalized function matrix projective lag synchronization of coupled dynamical networks with different dimensions via the double power function nonlinear feedback control method

International Nuclear Information System (INIS)

Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin

2014-01-01

This paper investigates the problem of finite-time generalized function matrix projective lag synchronization between two different coupled dynamical networks with different dimensions of network nodes. The double power function nonlinear feedback control method is proposed in this paper to guarantee that the state trajectories of the response network converge to the state trajectories of the drive network according to a function matrix in a given finite time. Furthermore, in comparison with the traditional nonlinear feedback control method, the new method improves the synchronization efficiency, and shortens the finite synchronization time. Numerical simulation results are presented to illustrate the effectiveness of this method. (papers)

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

Science.gov (United States)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

International Nuclear Information System (INIS)

Chernyshenko, Dmitri; Fangohr, Hans

2015-01-01

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges

Option Pricing under Risk-Minimization Criterion in an Incomplete Market with the Finite Difference Method

Directory of Open Access Journals (Sweden)

Xinfeng Ruan

2013-01-01

Full Text Available We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE of European option. The finite difference method is employed to compute the European option valuation of PIDE.

Analysis for pressure transient of coalbed methane reservoir based on Laplace transform finite difference method

OpenAIRE

Lei Wang; Hongjun Yin; Xiaoshuang Yang; Chuncheng Yang; Jing Fu

2015-01-01

Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare wi...

Finite-difference numerical simulations of underground explosion cavity decoupling

Science.gov (United States)

Aldridge, D. F.; Preston, L. A.; Jensen, R. P.

2012-12-01

Earth models containing a significant portion of ideal fluid (e.g., air and/or water) are of increasing interest in seismic wave propagation simulations. Examples include a marine model with a thick water layer, and a land model with air overlying a rugged topographic surface. The atmospheric infrasound community is currently interested in coupled seismic-acoustic propagation of low-frequency signals over long ranges (~tens to ~hundreds of kilometers). Also, accurate and efficient numerical treatment of models containing underground air-filled voids (caves, caverns, tunnels, subterranean man-made facilities) is essential. In support of the Source Physics Experiment (SPE) conducted at the Nevada National Security Site (NNSS), we are developing a numerical algorithm for simulating coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite-differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within the fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via a finite-difference operator "order switching" formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Current modeling efforts are oriented toward quantifying the amount of atmospheric infrasound energy generated by various underground seismic sources (explosions and earthquakes). Source depth and orientation, and surface topography play obvious roles. The cavity decoupling problem, where an explosion is detonated within an air-filled void, is of special interest. A point explosion

A Coupled Finite Difference and Moving Least Squares Simulation of Violent Breaking Wave Impact

DEFF Research Database (Denmark)

Lindberg, Ole; Bingham, Harry B.; Engsig-Karup, Allan Peter

2012-01-01

feature of this model is a generalized finite point set method which is applied to the solution of the Poisson equation on an unstructured point distribution. The presented finite point set method is generalized to arbitrary order of approximation. The two models are applied to simulation of steep...

Perbandingan Post Stack TIME Migration Metode Finite Difference dan Metode Kirchoff dengan Parameter Gap Dekonvolusi Data Seismik Darat 2d Line “Srda”

OpenAIRE

Dynza Anggary, Sheyza Rery; Danusaputro, Hernowo; Harmoko, Udi

2015-01-01

Analysis on Post Stack Time Migration (Post-STM) with finite difference method and Kirchoff method with determine gap parameter on deconvolution after stack had been applied to 2D land seismic at line “SRDA”. This research had purpose to applied seismic data processing to get subsurface imaging with high signal-to-noise ratio and analyze how the gap parameter corresponding on deconvolution after stack, and to determine which the appropriate method of migration between migration finite differe...

A finite-difference contrast source inversion method

International Nuclear Information System (INIS)

Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M

2008-01-01

We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium

Finite difference time domain (FDTD) modeling of implanted deep brain stimulation electrodes and brain tissue.

Science.gov (United States)

Gabran, S R I; Saad, J H; Salama, M M A; Mansour, R R

2009-01-01

This paper demonstrates the electromagnetic modeling and simulation of an implanted Medtronic deep brain stimulation (DBS) electrode using finite difference time domain (FDTD). The model is developed using Empire XCcel and represents the electrode surrounded with brain tissue assuming homogenous and isotropic medium. The model is created to study the parameters influencing the electric field distribution within the tissue in order to provide reference and benchmarking data for DBS and intra-cortical electrode development.

Comparison between a finite difference model (PUMA) and a finite element model (DELFIN) for simulation of the reactor of the atomic power plant of Atucha I

International Nuclear Information System (INIS)

Grant, C.R.

1996-01-01

The reactor code PUMA, developed in CNEA, simulates nuclear reactors discretizing space in finite difference elements. Core representation is performed by means a cylindrical mesh, but the reactor channels are arranged in an hexagonal lattice. That is why a mapping using volume intersections must be used. This spatial treatment is the reason of an overestimation of the control rod reactivity values, which must be adjusted modifying the incremental cross sections. Also, a not very good treatment of the continuity conditions between core and reflector leads to an overestimation of channel power of the peripherical fuel elements between 5 to 8 per cent. Another code, DELFIN, developed also in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and current among elements and a more realistic representation of the hexagonal lattice of the reactor. A comparison between results obtained using both methods in done in this paper. (author). 4 refs., 3 figs

PCS: an Euler--Lagrange method for treating convection in pulsating stars using finite difference techniques in two spatial dimensions

International Nuclear Information System (INIS)

Deupree, R.G.

1977-01-01

Finite difference techniques were used to examine the coupling of radial pulsation and convection in stellar models having comparable time scales. Numerical procedures are emphasized, including diagnostics to help determine the range of free parameters

Computer Simulation and Experimental Study of Deformation in a Radial Tire under Different Static Loads Using Finite Element Method

Directory of Open Access Journals (Sweden)

Mir Hamid Reza Ghoreishy

2014-10-01

Full Text Available This research work is devoted to the simulation of a steel-belted radial tire under different static loads. The nonlinear finite element calculations were performed using the MSC.MARC code, installed on a computer system equipped with a parallel processing technology. Hybrid elements in conjunction with two hyperelastic models, namely Marlow and Yeoh, and rebar layer implemented in surface elements were used for the modeling of rubbery and reinforcing parts, respectively. Linear elastic material models were also used for the modeling of the reinforcing elements including steel cord in belts, polyester cord in carcass and nylon cord in cap ply section. Two-dimensional axisymmetric elements were used for the modeling of rim-mounting and inflation and three-dimensional models were developed for the application of the radial, tangential, lateral and torsional loads. Different finite element models were developed, in which both linear and quadratic elements were used in conjunction with different mesh densities in order to find the optimum finite element model. Based on the results of the load deflection (displacement data, the tire stiffness under radial, tangential, lateral and torsional loads were calculated and compared with their corresponding experimentally measured values. The comparison was verified by the accuracy of the measured radial stiffness. However, due to the neglecting of the stiffness in shear and bending modes in cord-rubber composites, modeled with rebar layer methodology, the difference between computed values and real data are not small enough so that a more robust material models and element formulation are required to be developed.

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

Science.gov (United States)

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Perfectly matched layer method in the finite-difference time-domain and frequency-domain calculations

DEFF Research Database (Denmark)

Shyroki, Dzmitry; Lavrinenko, Andrei

2007-01-01

A complex-coordinate method known under the guise of the perfectly matched layer (PML) method for treating unbounded domains in computational electrodynamics is related to similar techniques in fluid dynamics and classical quantum theory. It may also find use in electronic-structure finite......-difference simulations. Straightforward transfer of the PML formulation to other fields does not seem feasible, however, since it is a unique feature of electrodynamics - the natural invariance - that allows analytic trick of complex coordinate scaling to be represented as pure modification of local material parameters...

Analysis of oscillational instabilities in acoustic levitation using the finite-difference time-domain method

DEFF Research Database (Denmark)

Santillan, Arturo Orozco

2011-01-01

The aim of the work described in this paper has been to investigate the use of the finite-difference time-domain method to describe the interactions between a moving object and a sound field. The main objective was to simulate oscillational instabilities that appear in single-axis acoustic...... levitation devices and to describe their evolution in time to further understand the physical mechanism involved. The study shows that the method gives accurate results for steady state conditions, and that it is a promising tool for simulations with a moving object....

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

Science.gov (United States)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

Different Modelling Approaches to Coupling Wall and Floor Panels within a Dynamic Finite Element Model of a Lightweight Building

DEFF Research Database (Denmark)

Kiel, Nikolaj; Andersen, Lars Vabbersgaard; Niu, Bin

2012-01-01

. With the number of modules in the three axial directions defined, wall and floor panels are constructed, placed and coupled in the global model. The core of this modular finite element model consists of connecting the different panels to each other in a rational manner, where the accuracy is as high as possible......, with as many applications as possible, for the least possible computational cost. The coupling method of the structural panels in the above mentioned modular finite element model is in this paper discussed and evaluated. The coupling of the panels are performed using the commercial finite element program....... In this way a well-defined master geometry is present onto which all panels can be tied. But as the skeleton is an element itself, it will have a physical mass and a corresponding stiffness to be included in the linear system of equations. This means that the skeleton will influence the structure...

Evaluation of stress distribution of implant-retained mandibular overdenture with different vertical restorative spaces: A finite element analysis

Science.gov (United States)

Ebadian, Behnaz; Farzin, Mahmoud; Talebi, Saeid; Khodaeian, Niloufar

2012-01-01

Background: Available restorative space and bar height is an important factor in stress distribution of implant-supported overdentures. The purpose of this study was to evaluate the effect of different vertical restorative spaces and different bar heights on the stress distribution around implants by 3D finite element analysis. Materials and Methods: 3D finite element models were developed from mandibular overdentures with two implants in the interforaminal region. In these models, four different bar heights from gingival crest (0.5, 1, 1.5, 2 mm) with 15 mm occlusal plane height and three different occlusal plane heights from gingival crest (9, 12, 15 mm) with 2 mm bar height were analyzed. A vertical unilateral and a bilateral load of 150 N were applied to the central occlusal fossa of the first molar and the stress of bone around implant was analyzed by finite element analysis. Results: By increasing vertical restorative space, the maximum stress values around implants were found to be decreased in unilateral loading models but slightly increased in bilateral loading cases. By increasing bar height from gingival crest, the maximum stress values around implants were found to be increased in unilateral loading models but slightly decreased in bilateral loading cases. In unilateral loading models, maximum stress was found in a model with 9 mm occlusal plane height and 1.5 mm bar height (6.254 MPa), but in bilateral loading cases, maximum stress was found in a model with 15 mm occlusal plane height and 0.5 mm bar height (3.482 MPa). Conclusion: The reduction of bar height and increase in the thickness of acrylic resin base in implant-supported overdentures are biomechanically favorable and may result in less stress in periimplant bone. PMID:23559952

Development of the software Conden 1.0 in finite differences to model electrostatics problems 2D

Directory of Open Access Journals (Sweden)

Wilson Rodríguez Calderón

2004-01-01

Full Text Available The present work consists on the development and implementation of the finite differences method for over-relaxation adapted to irregular meshes to determine the influence of the air frontiers on the potencial values and field electricians, calculated inside a badges parallel condenser, using GID like a pre/post-process platform and Fortran like a programming language of the calculation motor of differences Conden 1.0. The problem domain is constituted by two rectangles that represent the condenser and the air layer that covers it, divided in rectangular meshes no standardize.

Contact Stress Analysis for Gears of Different Helix Angle Using Finite Element Method

Directory of Open Access Journals (Sweden)

Patil Santosh

2014-07-01

Full Text Available The gear contact stress problem has been a great point of interest for many years, but still an extensive research is required to understand the various parameters affecting this stress. Among such parameters, helix angle is one which has played a crucial role in variation of contact stress. Numerous studies have been carried out on spur gear for contact stress variation. Hence, the present work is an attempt to study the contact stresses among the helical gear pairs, under static conditions, by using a 3D finite element method. The helical gear pairs on which the analysis is carried are 0, 5, 15, 25 degree helical gear sets. The Lagrange multiplier algorithm has been used between the contacting pairs to determine the stresses. The helical gear contact stress is evaluated using FE model and results have also been found at different coefficient of friction, varying from 0.0 to 0.3. The FE results have been further compared with the analytical calculations. The analytical calculations are based upon Hertz and AGMA equations, which are modified to include helix angle. The commercial finite element software was used in the study and it was shown that this approach can be applied to gear design efficiently. The contact stress results have shown a decreasing trend, with increase in helix angle.

An interactive algorithm for identifying multiattribute measurable value functions based on finite-order independence of structural difference

International Nuclear Information System (INIS)

Tamura, Hiroyuki; Hikita, Shiro

1985-01-01

In this paper, we develop an interactive algorithm for identifying multiattribute measurable value functions based on the concept of finite-order independence of structural difference. This concept includes Dyer and Sarin's weak difference independence as special cases. The algorithm developed is composed of four major parts: 1) formulation of the problem 2) assessment of normalized conditional value functions and structural difference functions 3) assessment of corner values 4) assessment of the order of independence of structural difference and selection of the model. A hypothetical numerical example of a trade-off analysis for siting a nuclear power plant is included. (author)

A finite difference method for off-fault plasticity throughout the earthquake cycle

Science.gov (United States)

Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash

2017-12-01

We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).

Intercomparison of the finite difference and nodal discrete ordinates and surface flux transport methods for a LWR pool-reactor benchmark problem in X-Y geometry

International Nuclear Information System (INIS)

O'Dell, R.D.; Stepanek, J.; Wagner, M.R.

1983-01-01

The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included

Finite-difference time-domain simulation of electromagnetic bandgap and bi-anisotropic metamaterials

Science.gov (United States)

Bray, Matthew G.

The term "Metamaterial" has been introduced into the electromagnetic lexicon in recent years to describe new artificial materials with electromagnetic properties that are not found in naturally occurring materials. Metamaterials exhibit electromagnetic properties that are not observed in its constituent materials, and/or not observed in nature. This thesis will analyze two different classes of metamaterials through the use of the finite-difference time-domain (FDTD) technique. The first class of metamaterials are artificial magnetic conductors (AMC) which approximate the behavior of a perfect magnetic conductor (PMC) over a finite frequency range. The AMC metamaterials are created through the use of an electromagnetic bandgap (EBG) structure. A periodic FDTD code is used to simulate a full-wave model of the metallodielectric EBG structures. The AMCs developed with the aid of the FDTD tool are then used to create low-profile antenna systems consisting of a dipole antenna in close proximity to an AMC surface. Through the use of this FDTD tool, several original contributions were made to the electromagnetic community. These include the first dual-band independently tunable EBG AMC ground plane and the first linearly polarized single-band and dual-band tunable antenna/EBG systems. The second class of materials analyzed are bi-anisotropic metamaterials. Bi-anisotropic media are the largest class of linear media which is able to describe the macroscopic material properties of artificial dielectrics, artificial magnetics, artificial chiral materials, left-handed materials, and other composite materials. The dispersive properties of these materials can be approximated by the oscillator model. This model assumes a Lorentzian frequency profile for the permittivity and permeability and a Condon model for chirality. A new FDTD formulation is introduced which can simulate this type of bi-anisotropic media. This FDTD method incorporates the dispersive material properties through

Formulation of coarse mesh finite difference to calculate mathematical adjoint flux; Formulacao de diferencas finitas de malha grossa para calculo do fluxo adjunto matematico

Energy Technology Data Exchange (ETDEWEB)

Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)

Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects

CERN Document Server

Alkan, Erdogan; Elsherbeni, Atef

2013-01-01

This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid

Analysis of multi lobe journal bearings with surface roughness using finite difference method

Science.gov (United States)

PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.

2018-04-01

Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.

Implicit time-dependent finite different algorithm for quench simulation

International Nuclear Information System (INIS)

Koizumi, Norikiyo; Takahashi, Yoshikazu; Tsuji, Hiroshi

1994-12-01

A magnet in a fusion machine has many difficulties in its application because of requirement of a large operating current, high operating field and high breakdown voltage. A cable-in-conduit (CIC) conductor is the best candidate to overcome these difficulties. However, there remained uncertainty in a quench event in the cable-in-conduit conductor because of a difficulty to analyze a fluid dynamics equation. Several scientists, then, developed the numerical code for the quench simulation. However, most of them were based on an explicit time-dependent finite difference scheme. In this scheme, a discrete time increment is strictly restricted by CFL (Courant-Friedrichs-Lewy) condition. Therefore, long CPU time was consumed for the quench simulation. Authors, then, developed a new quench simulation code, POCHI1, which is based on an implicit time dependent scheme. In POCHI1, the fluid dynamics equation is linearlized according to a procedure applied by Beam and Warming and then, a tridiagonal system can be offered. Therefore, no iteration is necessary to solve the fluid dynamics equation. This leads great reduction of the CPU time. Also, POCHI1 can cope with non-linear boundary condition. In this study, comparison with experimental results was carried out. The normal zone propagation behavior was investigated in two samples of CIC conductors which had different hydraulic diameters. The measured and simulated normal zone propagation length showed relatively good agreement. However, the behavior of the normal voltage shows a little disagreement. These results indicate necessity to improve the treatment of the heat transfer coefficient in the turbulent flow region and the electric resistivity of the copper stabilizer in high temperature and high field region. (author)

Finite element modelling of different CANDU fuel bundle types in various refuelling conditions

International Nuclear Information System (INIS)

Roman, M. R.; Ionescu, D. V.; Olteanu, G.; Florea, S.; Radut, A. C.

2016-01-01

The objective of this paper is to develop a finite element model for static strength analysis of the CANDU standard with 37 elements fuel bundle and the SEU43 with 43 elements fuel bundle design for various refuelling conditions. The computer code, ANSYS7.1, is used to simulate the axial compression in CANDU type fuel bundles subject to hydraulic drag loads, deflection of fuel elements, stresses and displacements in the end plates. Two possible situations for the fuelling machine side stops are considered in our analyses, as follows: the last fuel bundle is supported by the two side stops and a side stop can be blocked therefore, the last fuel bundle is supported by only one side stop. The results of the analyses performed are briefly presented and also illustrated in a graphical form. The finite element model developed in present study is verified against test results for endplate displacement and element bowing obtained from strength tests with fuel bundle string and fuelling machine side-stop simulators. Comparison of ANSYS model predictions with these experimental results led to a very good agreement. Despite the difference in hydraulic load between SEU43 and CANDU standard fuel bundles strings, the maximum stress in the SEU43 endplate is about the same with the maximum stress in the CANDU standard endplate. The comparative assessment reveals that SEU43 fuel bundle is able to withstand high flow rate without showing a significant geometric instability. (authors)

Finite Element Analysis of Pipe T-Joint

OpenAIRE

P.M.Gedkar; Dr. D.V. Bhope

2012-01-01

This paper reports stress analysis of two pressurized cylindrical intersection using finite element method. The different combinations of dimensions of run pipe and the branch pipe are used to investigate thestresses in pipe at the intersection. In this study the stress analysis is accomplished by finite element package ANSYS.

New way for determining electron energy levels in quantum dots arrays using finite difference method

Science.gov (United States)

Dujardin, F.; Assaid, E.; Feddi, E.

2018-06-01

Electronic states are investigated in quantum dots arrays, depending on the type of cubic Bravais lattice (primitive, body centered or face centered) according to which the dots are arranged, the size of the dots and the interdot distance. It is shown that the ground state energy level can undergo significant variations when these parameters are modified. The results were obtained by means of finite difference method which has proved to be easily adaptable, efficient and precise. The symmetry properties of the lattice have been used to reduce the size of the Hamiltonian matrix.

Finite element methods a practical guide

CERN Document Server

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.

Three-dimensional finite element analysis of different implant configurations for a mandibular fixed prosthesis.

Science.gov (United States)

Fazi, Giovanni; Tellini, Simone; Vangi, Dario; Branchi, Roberto

2011-01-01

The distribution of stresses in bone, implants, and prosthesis were analyzed via three-dimensional finite element modeling in different implant configurations for a fixed implant-supported prosthesis in an edentulous mandible. A finite element model was created with data obtained from computed tomographic scans of a human mandible. Anisotropic characteristics for cortical and cancellous bone were incorporated into the model. Six different configurations of intraforaminal implants were tested, with the number of implants varying from three to five and the distal implants inserted either parallel to the other implants or tilted distally by 17 or 34 degrees. A prosthetic structure connecting the implants was designed, with 20-mm posterior cantilevers for the parallel implant configurations, and a load of 200 N was applied to the distal portion of the cantilevers. Stresses were measured at the level of the implant, the prosthetic structure, and the bone. Bone-level stresses were analyzed at the implant-bone interface, at the external cortical bone surface, distal to the terminal implant, and in the cancellous bone along the implant body. A three-parallel-implant configuration resulted in higher stress in the implant and bone than configurations with four or five parallel implants. Configurations with the distal implants tilted resulted in a more favorable stress distribution at all levels. In parallel-implant configurations for fixed implant-supported mandibular prostheses, four and five implants resulted in similar stress distribution in the bone, framework, and implants. A distribution of four implants with the distal implants tilted 34 degrees (ie, the "All-on-Four" configuration) resulted in a favorable reduction of stresses in the bone, framework, and implants.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

Science.gov (United States)

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

COVE-1: a finite difference creep collapse code for oval fuel pin cladding material

International Nuclear Information System (INIS)

Mohr, C.L.

1975-03-01

COVE-1 is a time-dependent incremental creep collapse code that estimates the change in ovality of a fuel pin cladding tube. It uses a finite difference method of solving the differential equations which describe the deflection of the tube walls as a function of time. The physical problem is nonlinear, both with respect to geometry and material properties, which requires the use of an incremental, analytical, path-dependent solution. The application of this code is intended primarily for tubes manufactured from Zircaloy. Therefore, provision has been made to include some of the effects of anisotropy in the flow equations for inelastic incremental deformations. 10 references. (U.S.)

The use of the Finite Element method for the earthquakes modelling in different geodynamic environments

Science.gov (United States)

Castaldo, Raffaele; Tizzani, Pietro

2016-04-01

Many numerical models have been developed to simulate the deformation and stress changes associated to the faulting process. This aspect is an important topic in fracture mechanism. In the proposed study, we investigate the impact of the deep fault geometry and tectonic setting on the co-seismic ground deformation pattern associated to different earthquake phenomena. We exploit the impact of the structural-geological data in Finite Element environment through an optimization procedure. In this framework, we model the failure processes in a physical mechanical scenario to evaluate the kinematics associated to the Mw 6.1 L'Aquila 2009 earthquake (Italy), the Mw 5.9 Ferrara and Mw 5.8 Mirandola 2012 earthquake (Italy) and the Mw 8.3 Gorkha 2015 earthquake (Nepal). These seismic events are representative of different tectonic scenario: the normal, the reverse and thrust faulting processes, respectively. In order to simulate the kinematic of the analyzed natural phenomena, we assume, under the plane stress approximation (is defined to be a state of stress in which the normal stress, sz, and the shear stress sxz and syz, directed perpendicular to x-y plane are assumed to be zero), the linear elastic behavior of the involved media. The performed finite element procedure consist of through two stages: (i) compacting under the weight of the rock successions (gravity loading), the deformation model reaches a stable equilibrium; (ii) the co-seismic stage simulates, through a distributed slip along the active fault, the released stresses. To constrain the models solution, we exploit the DInSAR deformation velocity maps retrieved by satellite data acquired by old and new generation sensors, as ENVISAT, RADARSAT-2 and SENTINEL 1A, encompassing the studied earthquakes. More specifically, we first generate 2D several forward mechanical models, then, we compare these with the recorded ground deformation fields, in order to select the best boundaries setting and parameters. Finally

Analysis of a finite-difference and a Galerkin technique applied to the simulation of advection and diffusion of air pollutants from a line source

International Nuclear Information System (INIS)

Runca, E.; Melli, P.; Sardei, F.

1985-01-01

A finite-difference scheme and a Galerkin scheme are compared with respect to a very accurate solution describing time-dependent advection and diffusion of air pollutants from a line source in an atmosphere vertically stratified and limited by an inversion layer. The accurate solution was achieved by applying the finite-difference scheme on a very refined grid with a very small time step. The grid size and time step were defined according to stability and accuracy criteria discussed in the text. It is found that for the problem considered the two methods can be considered equally accurate. However, the Galerkin method gives a better approximation in the vicinity of the source. This was assumed to be partly due to the different way the source term is taken into account in the two methods. Improvement of the accuracy of the finite-difference scheme was achieved by approximating, at every step, the contribution of the source term by a Gaussian puff moving and diffusing with the velocity and diffusivity of the source location, instead of utilizing a stepwise function for the numerical approximation of the delta function representing the source term

A 3D finite element model to investigate prosthetic interface stresses of different posterior tibial slope.

Science.gov (United States)

Shen, Yi; Li, Xiaomiao; Fu, Xiaodong; Wang, Weili

2015-11-01

Posterior tibial slope that is created during proximal tibial resection in total knee arthroplasty has emerged as an important factor in the mechanics of the knee joint and the surgical outcome. But the ideal degree of posterior tibial slope for recovery of the knee joint function and preventions of complications remains controversial and should vary in different racial groups. The objective of this paper is to investigate the effects of posterior tibial slope on contact stresses in the tibial polyethylene component of total knee prostheses. Three-dimensional finite element analysis was used to calculate contact stresses in tibial polyethylene component of total knee prostheses subjected to a compressive load. The 3D finite element model of total knee prosthesis was constructed from the images produced by 3D scanning technology. Stresses in tibial polyethylene component were calculated with four different posterior tibial slopes (0°, 3°, 6° and 9°). The 3D finite element model of total knee prosthesis we presented was well validated. We found that the stress distribution in the polythene as evaluated by the distributions of the von Mises stress, the maximum principle stress, the minimum principle stress and the Cpress were more uniform with 3° and 6° posterior tibial slopes than with 0° and 9° posterior tibial slopes. Moreover, the peaks of the above stresses and trends of changes with increasing degree of knee flexion were more ideal with 3° and 6° posterior slopes. The results suggested that the tibial component inclination might be favourable to 7°-10° so far as the stress distribution is concerned. The range of the tibial component inclination also can decrease the wear of polyethylene. Chinese posterior tibial slope is bigger than in the West, and the current domestic use of prostheses is imported from the West, so their demands to tilt back bone cutting can lead to shorten the service life of prostheses; this experiment result is of important

FINITE ELEMENT ANALYSIS OF STRUCTURES

Directory of Open Access Journals (Sweden)

PECINGINA OLIMPIA-MIOARA

2015-05-01

Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.

SLIC: an interactive mesh generator for finite element and finite difference application programs

International Nuclear Information System (INIS)

Gerhard, M.A.; Greenlaw, R.C.

1979-01-01

Computers with extended memory, such as the CDC STAR 100 and the CRAY 1 with mega-word capacities, are greatly enlarging the size of finite element problems which can be solved. The cost of developing and testing large meshes can be prohibitive unless one uses a computer program for mesh generation and plotting. SLIC is an interactive mesh program which builds and plots 2- and 3-D continuum meshes from interactive terminal or disc input. The user inputs coordinates for certain key points and enters commands which complete the description of the geometry. Entire surfaces and volumes are then generated from the geometric skeleton. SLIC allows the user to correct input errors and saves the corrected command list for later reuse. The mesh can be plotted on a video display at any stage of development to evaluate the work in progress. Output is in the form of an input file to a user-selected computer code. Among the available output types are ADINA, SAP4, and NIKE2D. 11 figures

Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak

Energy Technology Data Exchange (ETDEWEB)

Lee, Y. Y.; Ahn, D. [University of Seoul, Seoul (Korea, Republic of)

2012-05-15

A dispersive full-wave finite-difference time-domain (FDTD) model is used to calculate the performance of elliptic cylindrical cloaking devices. The permittivity and the permeability tensors for the cloaking structure are derived by using an effective medium approach in general relativity. The elliptic cylindrical invisibility devices are found to show imperfect cloaking, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of the propagation of those waves, the semi-focal distances and the loss tangents of the meta-material. When the semifocal distance of the elliptic cylinder decreases, the performance of the cloaking becomes very good, with neither noticeable scatterings nor field penetrations. For a larger semi-focal distance, only the TM wave with a specific propagation direction shows good cloaking performance. Realistic cloaking materials with loss still show a cloak that is working, but attenuated back-scattering waves exist.

CASKETSS-HEAT: a finite difference computer program for nonlinear heat conduction problems

International Nuclear Information System (INIS)

Ikushima, Takeshi

1988-12-01

A heat conduction program CASKETSS-HEAT has been developed. CASKETSS-HEAT is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Main features of CASKETSS-HEAT are as follows. (1) One, two and three-dimensional geometries for heat conduction calculation are available. (2) Convection and radiation heat transfer of boundry can be specified. (3) Phase change and chemical change can be treated. (4) Finned surface heat transfer can be treated easily. (5) Data memory allocation in the program is variable according to problem size. (6) The program is a compatible heat transfer analysis program to the stress analysis program SAP4 and SAP5. (7) Pre- and post-processing for input data generation and graphic representation of calculation results are available. In the paper, brief illustration of calculation method, input data and sample calculation are presented. (author)

A finite-difference time-domain simulation of high power microwave generated plasma at atmospheric pressures

International Nuclear Information System (INIS)

Ford, Patrick J.; Beeson, Sterling R.; Krompholz, Hermann G.; Neuber, Andreas A.

2012-01-01

A finite-difference algorithm was developed to calculate several RF breakdown parameters, for example, the formative delay time that is observed between the initial application of a RF field to a dielectric surface and the formation of field-induced plasma interrupting the RF power flow. The analysis is focused on the surface being exposed to a background gas pressure above 50 Torr. The finite-difference algorithm provides numerical solutions to partial differential equations with high resolution in the time domain, making it suitable for simulating the time evolving interaction of microwaves with plasma; in lieu of direct particle tracking, a macroscopic electron density is used to model growth and transport. This approach is presented as an alternative to particle-in-cell methods due to its low complexity and runtime leading to more efficient analysis for a simulation of a microsecond scale pulse. The effect and development of the plasma is modeled in the simulation using scaling laws for ionization rates, momentum transfer collision rates, and diffusion coefficients, as a function of electric field, gas type and pressure. The incorporation of plasma material into the simulation involves using the Z-transform to derive a time-domain algorithm from the complex frequency-dependent permittivity of plasma. Therefore, the effect of the developing plasma on the instantaneous microwave field is calculated. Simulation results are compared with power measurements using an apparatus designed to facilitate surface flashover across a polycarbonate boundary in a controlled N 2 , air, or argon environment at pressures exceeding 50 Torr.

Comparison of SAR calculation algorithms for the finite-difference time-domain method

International Nuclear Information System (INIS)

Laakso, Ilkka; Uusitupa, Tero; Ilvonen, Sami

2010-01-01

Finite-difference time-domain (FDTD) simulations of specific-absorption rate (SAR) have several uncertainty factors. For example, significantly varying SAR values may result from the use of different algorithms for determining the SAR from the FDTD electric field. The objective of this paper is to rigorously study the divergence of SAR values due to different SAR calculation algorithms and to examine if some SAR calculation algorithm should be preferred over others. For this purpose, numerical FDTD results are compared to analytical solutions in a one-dimensional layered model and a three-dimensional spherical object. Additionally, the implications of SAR calculation algorithms for dosimetry of anatomically realistic whole-body models are studied. The results show that the trapezium algorithm-based on the trapezium integration rule-is always conservative compared to the analytic solution, making it a good choice for worst-case exposure assessment. In contrast, the mid-ordinate algorithm-named after the mid-ordinate integration rule-usually underestimates the analytic SAR. The linear algorithm-which is approximately a weighted average of the two-seems to be the most accurate choice overall, typically giving the best fit with the shape of the analytic SAR distribution. For anatomically realistic models, the whole-body SAR difference between different algorithms is relatively independent of the used body model, incident direction and polarization of the plane wave. The main factors affecting the difference are cell size and frequency. The choice of the SAR calculation algorithm is an important simulation parameter in high-frequency FDTD SAR calculations, and it should be explained to allow intercomparison of the results between different studies. (note)

Finite Difference Analysis of Transient Heat Transfer in Surrounding Rock Mass of High Geothermal Roadway

Directory of Open Access Journals (Sweden)

Yuan Zhang

2016-01-01

Full Text Available Based on finite difference method, a mathematical model and a numerical model written by Fortran language were established in the paper. Then a series of experiments were conducted to figure out the evolution law of temperature field in high geothermal roadway. Research results indicate that temperature disturbance range increases gradually as the unsteady heat conduction goes on and it presents power function relationship with dimensionless time. Based on the case analysis, there is no distinct expansion of temperature disturbance range after four years of ventilation, when the temperature disturbance range R=13.6.

Synthesis of hydrocode and finite element technology for large deformation Lagrangian computation

International Nuclear Information System (INIS)

Goudreau, G.L.; Hallquist, J.O.

1979-08-01

Large deformation engineering analysis at Lawrence Livermore Laboratory has benefited from a synthesis of computational technology from the finite difference hydrocodes of the scientific weapons community and the structural finite element methodology of engineering. Two- and three-dimensional explicit and implicit Lagrangian continuum codes have been developed exploiting the strengths of each. The explicit methodology primarily exploits the primitive constant stress (or one point integration) brick element. Similarity and differences with the integral finite difference method are discussed. Choice of stress and finite strain measures, and selection of hour glass viscosity are also considered. The implicit codes also employ a Cauchy formulation, with Newton iteration and a symmetric tangent matrix. A library of finite strain material routines includes hypoelastic/plastic, hyperelastic, viscoelastic, as well as hydrodynamic behavior. Arbitrary finite element topology and a general slide-line treatment significantly extends Lagrangian hydrocode application. Computational experience spans weapons and non-weapons applications

Numerical solution of the state-delayed optimal control problems by a fast and accurate finite difference θ-method

Science.gov (United States)

Hajipour, Mojtaba; Jajarmi, Amin

2018-02-01

Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.

Socio-economic applications of finite state mean field games

KAUST Repository

Gomes, Diogo A.; Machado Velho, Roberto; Wolfram, Marie Therese

2014-01-01

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite

Storm Water Infiltration and Focused Groundwater Recharge in a Rain Garden: Finite Volume Model and Numerical Simulations for Different Configurations and Climates

Science.gov (United States)

Aravena, J.; Dussaillant, A. R.

2006-12-01

Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).

Simulation of natural convection in an inclined polar cavity using a finite-difference lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)

2017-06-15

Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.

Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

International Nuclear Information System (INIS)

Lu Jia; Zhou Huaichun

2016-01-01

To deal with the staircase approximation problem in the standard finite-difference time-domain (FDTD) simulation, the two-dimensional boundary condition equations (BCE) method is proposed in this paper. In the BCE method, the standard FDTD algorithm can be used as usual, and the curved surface is treated by adding the boundary condition equations. Thus, while maintaining the simplicity and computational efficiency of the standard FDTD algorithm, the BCE method can solve the staircase approximation problem. The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders. The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors. Moreover, the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities. (paper)

Quantization and representation theory of finite W algebras

International Nuclear Information System (INIS)

Boer, J. de; Tjin, T.

1993-01-01

In this paper we study the finitely generated algebras underlying W algebras. These so called 'finite W algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of sl 2 into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite W algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite W symmetry. In the second part we BRST quantize the finite W algebras. The BRST cohomoloy is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite W algebras in one stroke. Examples are given. In the last part of the paper we study the representation theory of finite W algebras. It is shown, using a quantum inversion of the generalized Miura transformation, that the representations of finite W algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite W algebras. (orig.)

Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion

Science.gov (United States)

Wu, Guo-Cheng; Baleanu, Dumitru; Zeng, Sheng-Da

2018-04-01

This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

Science.gov (United States)

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

An efficient realization of frequency dependent boundary conditions in an acoustic finite-difference time-domain model

DEFF Research Database (Denmark)

Escolano-Carrasco, José; Jacobsen, Finn; López, J.J.

2008-01-01

The finite-difference time-domain (FDTD) method provides a simple and accurate way of solving initial boundary value problems. However, most acoustic problems involve frequency dependent boundary conditions, and it is not easy to include such boundary conditions in an FDTD model. Although solutions...... to this problem exist, most of them have high computational costs, and stability cannot always be ensured. In this work, a solution is proposed based on "mixing modelling strategies"; this involves separating the FDTD mesh and the boundary conditions (a digital filter representation of the impedance...

Numerical simulation of temperature distribution using finite difference equations and estimation of the grain size during friction stir processing

International Nuclear Information System (INIS)

Arora, H.S.; Singh, H.; Dhindaw, B.K.

2012-01-01

Highlights: ► Magnesium alloy AE42 was friction stir processed under different cooling conditions. ► Heat flow model was developed using finite difference heat equations. ► Generalized MATLAB code was developed for solving heat flow model. ► Regression equation for estimation of grain size was developed. - Abstract: The present investigation is aimed at developing a heat flow model to simulate temperature history during friction stir processing (FSP). A new approach of developing implicit form of finite difference heat equations solved using MATLAB code was used. A magnesium based alloy AE42 was friction stir processed (FSPed) at different FSP parameters and cooling conditions. Temperature history was continuously recorded in the nugget zone during FSP using data acquisition system and k type thermocouples. The developed code was validated at different FSP parameters and cooling conditions during FSP experimentation. The temperature history at different locations in the nugget zone at different instants of time was further utilized for the estimation of grain growth rate and final average grain size of the FSPed specimen. A regression equation relating the final grain size, maximum temperature during FSP and the cooling rate was developed. The metallurgical characterization was done using optical microscopy, SEM, and FIB-SIM analysis. The simulated temperature profiles and final average grain size were found to be in good agreement with the experimental results. The presence of fine precipitate particles generated in situ in the investigated magnesium alloy also contributed in the evolution of fine grain structure through Zener pining effect at the grain boundaries.

Simulation of acoustic streaming by means of the finite-difference time-domain method

DEFF Research Database (Denmark)

Santillan, Arturo Orozco

2012-01-01

Numerical simulations of acoustic streaming generated by a standing wave in a narrow twodimensional cavity are presented. In this case, acoustic streaming arises from the viscous boundary layers set up at the surfaces of the walls. It is known that streaming vortices inside the boundary layer have...... directions of rotation that are opposite to those of the outer streaming vortices (Rayleigh streaming). The general objective of the work described in this paper has been to study the extent to which it is possible to simulate both the outer streaming vortices and the inner boundary layer vortices using...... the finite-difference time-domain method. To simplify the problem, thermal effects are not considered. The motivation of the described investigation has been the possibility of using the numerical method to study acoustic streaming, particularly under non-steady conditions. Results are discussed for channels...

The delay function in finite difference models for nuclear channels thermo-hydraulic transients

International Nuclear Information System (INIS)

Agazzi, A.

1977-01-01

The study of the thermo-hydraulic transients in a nuclear reactor core often requires a bi- or tri-dimensional mathematical simulation of a reactor channel. The equations involved are generally solved by means of finite-difference methods. The determination of the spatial mesh-width and the time interval is strongly conditioned by the necessity of a good accuracy in the description of the delay function which defines the transfer of thermal perturbations along the cooling channel. In this paper the effects of both space and time discretization on the delay function are considered and for the classical cases of inlet temperature step and ramp universal functions and diagrams are given in order to make possible the determination of optimal spatial mesh-width and time interval, once the requested accuracy of the model is fixed in advance

Composite Finite Sums

KAUST Repository

Alabdulmohsin, Ibrahim M.

2018-03-07

In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.

Composite Finite Sums

KAUST Repository

Alabdulmohsin, Ibrahim M.

2018-01-01

In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.

Axial anomaly at finite temperature and finite density

International Nuclear Information System (INIS)

Qian Zhixin; Su Rukeng; Yu, P.K.N.

1994-01-01

The U(1) axial anomaly in a hot fermion medium is investigated by using the real time Green's function method. After calculating the lowest order triangle diagrams, we find that finite temperature as well as finite fermion density does not affect the axial anomaly. The higher order corrections for the axial anomaly are discussed. (orig.)

Finite size effects in simulations of protein aggregation.

Directory of Open Access Journals (Sweden)

Amol Pawar

Full Text Available It is becoming increasingly clear that the soluble protofibrillar species that proceed amyloid fibril formation are associated with a range of neurodegenerative disorders such as Alzheimer's and Parkinson diseases. Computer simulations of the processes that lead to the formation of these oligomeric species are starting to make significant contributions to our understanding of the determinants of protein aggregation. We simulate different systems at constant concentration but with a different number of peptides and we study the how the finite number of proteins affects the underlying free energy of the system and therefore the relative stability of the species involved in the process. If not taken into account, this finite size effect can undermine the validity of theoretical predictions regarding the relative stability of the species involved and the rates of conversion from one to the other. We discuss the reasons that give rise to this finite size effect form both a probabilistic and energy fluctuations point of view and also how this problem can be dealt by a finite size scaling analysis.

Locally Finite Root Supersystems

OpenAIRE

Yousofzadeh, Malihe

2013-01-01

We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.

Investigation of different cage designs and mechano-regulation algorithms in the lumbar interbody fusion process - a finite element analysis.

Science.gov (United States)

Postigo, Sergio; Schmidt, Hendrik; Rohlmann, Antonius; Putzier, Michael; Simón, Antonio; Duda, Georg; Checa, Sara

2014-04-11

Lumbar interbody fusion cages are commonly used to treat painful spinal degeneration and instability by achieving bony fusion. Many different cage designs exist, however the effect of cage morphology and material properties on the fusion process remains largely unknown. This finite element model study aims to investigate the influence of different cage designs on bone fusion using two mechano-regulation algorithms of tissue formation. It could be observed that different cages play a distinct key role in the mechanical conditions within the fusion region and therefore regulate the time course of the fusion process. Copyright © 2014 Elsevier Ltd. All rights reserved.

Simple Finite Sums

KAUST Repository

Alabdulmohsin, Ibrahim M.

2018-01-01

We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.

Simple Finite Sums

KAUST Repository

Alabdulmohsin, Ibrahim M.

2018-03-07

We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.

A mean field theory of study of lattice gauge theory with finite temperature and with finite fermion density

International Nuclear Information System (INIS)

Naik, S.

1990-01-01

We have developed a mean field theory technique to study the confinement-deconfinement phase transition and chiral symmetry restoring phase transition with dynamical fermions and with finite chemical potential and finite temperature. The approximation scheme concerns the saddle point scenario and large space dimension. The static quark-antiquark potentials are identified from the Wilson loop correlation functions in both the fundamental and the adjoint representation of the gauge group with different temperatures. The difference between the responses of the chemical potential to the fermion number with singlet and non-singlet isospin configuration is found. We compare our results with recent Monte Carlo data. (orig.)

Hydrothermal analysis in engineering using control volume finite element method

CERN Document Server

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),

ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

Science.gov (United States)

Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

2008-12-01

We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Science.gov (United States)

Wu, Zuqing; Ping, Jialun; Zong, Hongshi

2017-12-01

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 in the phase diagram, and different values for the charged pion mass (or decay constant) and neutral pion mass (or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses. Supported by National Natural Science Foundation of China (11175088, 11475085, 11535005, 11690030) and the Fundamental Research Funds for the Central Universities (020414380074)

A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene

International Nuclear Information System (INIS)

Brinkman, D.; Heitzinger, C.; Markowich, P.A.

2014-01-01

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses

Evolution operator equation: Integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado

1997-10-01

The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.

Methods for compressible fluid simulation on GPUs using high-order finite differences

Science.gov (United States)

Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer

2017-08-01

We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia

Science.gov (United States)

Mansor, Nur Jariah; Jaffar, Maheran Mohd

2014-07-01

Call warrant is a type of structured warrant in Bursa Malaysia. It gives the holder the right to buy the underlying share at a specified price within a limited period of time. The issuer of the structured warrants usually uses European style to exercise the call warrant on the maturity date. Warrant is very similar to an option. Usually, practitioners of the financial field use Black-Scholes model to value the option. The Black-Scholes equation is hard to solve analytically. Therefore the finite difference approach is applied to approximate the value of the call warrant prices. The central in time and central in space scheme is produced to approximate the value of the call warrant prices. It allows the warrant holder to forecast the value of the call warrant prices before the expiry date.

Chiral anomaly and anomalous finite-size conductivity in graphene

Science.gov (United States)

Shen, Shun-Qing; Li, Chang-An; Niu, Qian

2017-09-01

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two spin degenerate pairs of massless two-dimensional Dirac fermions with different chirality. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of a zigzag nanoribbon and some anomalous transport properties. Here it is proposed that the Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges of Dirac fermions at different valleys can be realized in a confined ribbon of finite width, even in the absence of a magnetic field. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and is inversely proportional to the square of the lateral dimension W, which is different from the finite-size correction inversely proportional to W from the boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and it is measurable experimentally. This finding provides an alternative platform to explore the purely quantum mechanical effect in graphene.

Finite Element Analysis of Increasing Column Section and CFRP Reinforcement Method under Different Axial Compression Ratio

Science.gov (United States)

Jinghai, Zhou; Tianbei, Kang; Fengchi, Wang; Xindong, Wang

2017-11-01

Eight less stirrups in the core area frame joints are simulated by ABAQUS finite element numerical software. The composite reinforcement method is strengthened with carbon fiber and increasing column section, the axial compression ratio of reinforced specimens is 0.3, 0.45 and 0.6 respectively. The results of the load-displacement curve, ductility and stiffness are analyzed, and it is found that the different axial compression ratio has great influence on the bearing capacity of increasing column section strengthening method, and has little influence on carbon fiber reinforcement method. The different strengthening schemes improve the ultimate bearing capacity and ductility of frame joints in a certain extent, composite reinforcement joints strengthening method to improve the most significant, followed by increasing column section, reinforcement method of carbon fiber reinforced joints to increase the minimum.

Groebner Finite Path Algebras

OpenAIRE

Leamer, Micah J.

2004-01-01

Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS

The finite element analysis program MSC Marc/Mentat a first introduction

CERN Document Server

Öchsner, Andreas

2016-01-01

Based on simple examples, this book offers a short introduction to the general-purpose finite element program MSC Marc, a specialized program for non-linear problems (implicit solver) distributed by the MSC Software Corporation, which is commonly used in academia and industry. Today the documentation of all finite element programs includes a variety of step-by-step examples of differing complexity, and in addition, all software companies offer professional workshops on different topics. As such, rather than competing with these, the book focuses on providing simple examples, often single-element problems, which can easily be related to the theory that is discussed in finite element lectures. This makes it an ideal companion book to classical introductory courses on the finite element method.

A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene

KAUST Repository

Brinkman, Daniel; Heitzinger, Clemens Heitzinger; Markowich, Peter A.

2014-01-01

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac-Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac-Poisson system where potentials act as beam splitters or Veselago lenses. © 2013 Elsevier Inc.

Finite difference method and algebraic polynomial interpolation for numerically solving Poisson's equation over arbitrary domains

Directory of Open Access Journals (Sweden)

Tsugio Fukuchi

2014-06-01

Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.

Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion

Directory of Open Access Journals (Sweden)

S. A. Kaschenko

2014-01-01

Full Text Available We study the dynamics of finite-difference approximation on spatial variables of a logistic equation with delay and diffusion. It is assumed that the diffusion coefficient is small and the Malthusian coefficient is large. The question of the existence and asymptotic behavior of attractors was studied with special asymptotic methods. It is shown that there is a rich array of different types of attractors in the phase space: leading centers, spiral waves, etc. The main asymptotic characteristics of all solutions from the corresponding attractors are adduced in this work. Typical graphics of wave fronts motion of different structures are represented in the article.

Eulerian finite-difference calculations of explosions in partially water-filled overstrong cylindrical containment vessels

International Nuclear Information System (INIS)

Thompson, S.L.; Herrmann, W.

1977-01-01

Calculations, using the two-dimensional Eulerian finite-difference code CSQ, were performed for the problem of a small spherical high-explosive charge detonated in a closed heavy-walled cylindrical container partially filled with water. Data from corresponding experiments, specifically performed to validate codes used for hypothetical core disruptive accidents of liquid metal fast breeder reactors, are available in the literature. The calculations were performed specifically to test whether Eulerian methods could handle this type of problem, to determine whether water cavitation, which plays a large role in the loadings on the roof of the containment vessel, could be described adequately by an equilibrium liquid-vapor mixed phase model, and to investigate the trade-off between accuracy and cost of the calculations by using different sizes of computational meshes. Comparison of the experimental and computational data shows that the Eulerian method can handle the problem with ease, giving good predictions of wall and floor loadings. While roof loadings are qualitatively correct, peak impulse appears to be affected by numerical resolution and is underestimated somewhat

The Determining Finite Automata Process

Directory of Open Access Journals (Sweden)

M. S. Vinogradova

2017-01-01

Full Text Available The theory of formal languages widely uses finite state automata both in implementation of automata-based approach to programming, and in synthesis of logical control algorithms.To ensure unambiguous operation of the algorithms, the synthesized finite state automata must be deterministic. Within the approach to the synthesis of the mobile robot controls, for example, based on the theory of formal languages, there are problems concerning the construction of various finite automata, but such finite automata, as a rule, will not be deterministic. The algorithm of determinization can be applied to the finite automata, as specified, in various ways. The basic ideas of the algorithm of determinization can be most simply explained using the representations of a finite automaton in the form of a weighted directed graph.The paper deals with finite automata represented as weighted directed graphs, and discusses in detail the procedure for determining the finite automata represented in this way. Gives a detailed description of the algorithm for determining finite automata. A large number of examples illustrate a capability of the determinization algorithm.

Stress analysis of different prosthesis materials in implant-supported fixed dental prosthesis using 3D finite element method

Directory of Open Access Journals (Sweden)

Pedram Iranmanesh

2014-01-01

Full Text Available Introduction: In the present study, the finite element method (FEM was used to investigate the effects of prosthesis material types on stress distribution of the bone surrounding implants and to evaluate stress distribution in three-unit implant-supported fixed dental prosthesis (FDP. Materials and Methods: A three-dimensional (3D finite element FDP model of the maxillary second premolar to the second molar was designed. Three load conditions were statically applied on the functional cusps in horizontal (57.0 N, vertical (200.0 N, and oblique (400.0 N, θ = 120° directions. Four standard framework materials were evaluated: Polymethyl methacrylate (PMMA, base-metal, porcelain fused to metal, andporcelain. Results: The maximum of von Mises stress in the oblique direction was higher than the vertical and horizontal directions in all conditions. In the bone-crestal section, the maximum von Mises stress (53.78 MPa was observed in PMMA within oblique load. In FDPs, the maximum stress was generated at the connector region in all conditions. Conclusion: A noticeable difference was not observed in the bone stress distribution pattern with different prosthetic materials. Although, higher stress value could be seen in polymethyl methacrylate, all types of prosthesis yielded the same stress distribution pattern in FDP. More clinical studies are needed to evaluate the survival rate of these materials.

Explicit formula of finite difference method to estimate human peripheral tissue temperatures during exposure to severe cold stress.

Science.gov (United States)

Khanday, M A; Hussain, Fida

2015-02-01

During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25 °C, 20 °C, 15 °C, 5 °C, -5 °C and -10 °C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor

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B. Godongwana

2015-01-01

Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.

Basic Finite Element Method

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.

Finite element computation of plasma equilibria

International Nuclear Information System (INIS)

Rivier, M.

1977-01-01

The applicability of the finite element method is investigated for the numerical solution of the nonlinear Grad-Shafranov equation with free boundary for the flux function of a plasma at equilibrium. This method is based on the case of variational principles and finite dimensional subspaces whose elements are piecewise polynomial functions obtained by a Lagrange type interpolation procedure over a triangulation of the domain. Two cases of plasma pressure (exponential and quadratic including a vacuum region) were examined. In both cases the nonuniqueness of the solutions was shown in exhibiting a deeper solution in the case of exponential pressure function, and a non-constant solution for a quadratic pressure function. In order to get this ''other'' solution, two linearization methods were tested with two different constraints. Different cross sections are investigated

Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

Energy Technology Data Exchange (ETDEWEB)

Nakra Mohajer, Soukaina; El Harouny, El Hassan [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); El Khamkhami, Jamal [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); and others

2016-09-15

Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.

Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

International Nuclear Information System (INIS)

Nakra Mohajer, Soukaina; El Harouny, El Hassan; Ibral, Asmaa; El Khamkhami, Jamal

2016-01-01

Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.

3D finite element analysis of tightening process of bolt and nut connections with pitch difference

Science.gov (United States)

Liu, X.; Noda, N.-A.; Sano, Y.; Huang, Y. T.; Takase, Y.

2018-06-01

In a wide industrial field, the bolt-nut joint is unitized as an important machine element and anti-loosening performance is always required. In this paper, the effect of a slight pitch difference between a bolt and nut is studied. Firstly, by varying the pitch difference, the prevailing torque required for the nut rotation, before the nut touches the clamped body, is measured experimentally. Secondly, the tightening torque is determined as a function of the axial force of the bolt after the nut touches the clamped body. The results show that a large value of pitch difference may provide large prevailing torque that causes an anti-loosening effect although a very large pitch difference may deteriorate the bolt axial force under a certain tightening torque. Thirdly, a suitable pitch difference is determined taking into account the anti-loosening and clamping abilities. Furthermore, the chamfered corners at nut ends are considered, and it is found that the 3D finite element analysis with considering the chamfered nut threads has a good agreement with the experimental observation. Finally, the most desirable pitch difference required for improving anti-loosening is proposed.

Using Finite Element Method

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.

Parallel direct solver for finite element modeling of manufacturing processes

DEFF Research Database (Denmark)

Nielsen, Chris Valentin; Martins, P.A.F.

2017-01-01

The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...

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

FDiff3: a finite-difference solver for facilitating understanding of heat conduction and numerical analysis

Energy Technology Data Exchange (ETDEWEB)

Russell, M.B. [University of Hertfordshire, Hatfield (United Kingdom). Department of Aerospace, Automotive and Design Engineering; Probert, S.D. [Cranfield University, Bedfordshire (United Kingdom). School of Engineering

2004-12-01

The growing requirement for energy thrift and hence the increasing emphasis on 'low-purchased-energy' designs are stimulating the need for more accurate insights into the thermal behaviours of buildings and their components. This better understanding is preferably achieved, rather than by using 'closed software' or teaching the relevant mathematics outside heat-transfer lessons, but from embedding the pertinent tutoring while dealing with heat-transfer problems using an open-source code approach. Hence a finite-difference software program (FDiff3) has been composed to show the principles of numerical analysis as well as improve the undergraduates' perception of transient conduction. The pedagogic approach behind the development, its present capabilities and applications to sample test-cases are discussed. (author)

A finite landscape?

International Nuclear Information System (INIS)

Acharya, B.S.; Douglas, M.R.

2006-06-01

We present evidence that the number of string/M theory vacua consistent with experiments is finite. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems. (author)

Fractional finite Fourier transform.

Science.gov (United States)

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

A finite difference Hartree-Fock program for atoms and diatomic molecules

Science.gov (United States)

Kobus, Jacek

2013-03-01

The newest version of the two-dimensional finite difference Hartree-Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree-Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities (αzz, βzzz, γzzzz, Az,zz, Bzz,zz) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Catalogue identifier: ADEB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 171196 No. of bytes in distributed program, including test data, etc.: 9481802 Distribution format: tar.gz Programming language: Fortran 77, C. Computer: any 32- or 64-bit platform. Operating system: Unix/Linux. RAM: Case dependent, from few MB to many GB Classification: 16.1. Catalogue identifier of previous version: ADEB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 98(1996)346 Does the new version supersede the previous version?: Yes Nature of problem: The program finds virtually exact solutions of the Hartree-Fock and density functional theory type equations for atoms, diatomic molecules and their ions

Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation

International Nuclear Information System (INIS)

Lan, Haiqiang; Zhang, Zhongjie

2011-01-01

The finite-difference (FD) method is a powerful tool in seismic wave field modelling for understanding seismic wave propagation in the Earth's interior and interpreting the real seismic data. The accuracy of FD modelling partly depends on the implementation of the free-surface (i.e. traction-free) condition. In the past 40 years, at least six kinds of free-surface boundary condition approximate schemes (such as one-sided, centred finite-difference, composed, new composed, implicit and boundary-modified approximations) have been developed in FD second-order elastodynamic simulation. Herein we simulate seismic wave fields in homogeneous and lateral heterogeneous models using these free-surface boundary condition approximate schemes and evaluate their stability and applicability by comparing with corresponding analytical solutions, and then quantitatively evaluate the accuracies of different approximate schemes from the misfit of the amplitude and phase between the numerical and analytical results. Our results confirm that the composed scheme becomes unstable for the V s /V p ratio less than 0.57, and suggest that (1) the one-sided scheme is only accurate to first order and therefore introduces serious errors for the shorter wavelengths, other schemes are all of second-order precision; (2) the new composed, implicit and boundary-modified schemes are stable even when the V s /V p ratio is less than 0.2; (3) the implicit and boundary-modified schemes are able to deal with laterally varying (heterogeneous) free surface; (4) in the corresponding stability range, the one-sided scheme shows remarkable errors in both phase and amplitude compared to analytical solution (which means larger errors in travel-time and reflection strength), the other five approximate schemes show better performance in travel-time (phase) than strength (amplitude)

Finite Element Residual Stress Analysis of Planetary Gear Tooth

Directory of Open Access Journals (Sweden)

Jungang Wang

2013-01-01

Full Text Available A method to simulate residual stress field of planetary gear is proposed. In this method, the finite element model of planetary gear is established and divided to tooth zone and profile zone, whose different temperature field is set. The gear's residual stress simulation is realized by the thermal compression stress generated by the temperature difference. Based on the simulation, the finite element model of planetary gear train is established, the dynamic meshing process is simulated, and influence of residual stress on equivalent stress of addendum, pitch circle, and dedendum of internal and external meshing planetary gear tooth profile is analyzed, according to non-linear contact theory, thermodynamic theory, and finite element theory. The results show that the equivalent stresses of planetary gear at both meshing and nonmeshing surface are significantly and differently reduced by residual stress. The study benefits fatigue cracking analysis and dynamic optimization design of planetary gear train.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

Science.gov (United States)

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

True Concurrent Thermal Engineering Integrating CAD Model Building with Finite Element and Finite Difference Methods

Science.gov (United States)

Panczak, Tim; Ring, Steve; Welch, Mark

1999-01-01

Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.

Electrokinetic Flow in Microchannels with Finite Reservoir Size Effects

International Nuclear Information System (INIS)

Yan, D; Yang, C; Nguyen, N-T; Huang, X

2006-01-01

In electrokinetically-driven microfluidic applications, reservoirs are indispensable and have finite sizes. During operation processes, as the liquid level difference in reservoirs keeps changing as time elapses, the flow characteristics in a microchannel exhibit a combination of the electroosmotic flow and the time-dependent induced backpressure-driven flow. In this work, an assessment of the finite reservoir size effect on electroosmotic flows is presented theoretically and experimentally. A model is developed to describe the timedependent electrokinetic flow with finite reservoir size effects. The theoretical analysis shows that under certain conditions the finite reservoir size effect is significant. The important parameters that describe the effect of finite reservoir size on the flow characteristics are discussed. A new concept denoted as 'effective pumping period' is introduced to characterize the reservoir size effect. The proposed model clearly identifies the mechanisms of the finitereservoir size effects and is further confirmed by using micro-PIV technique. The results of this study can be used for facilitating the design of microfluidic devices

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

Finite Range Decomposition of Gaussian Processes

CERN Document Server

Brydges, C D; Mitter, P K

2003-01-01

Let $D$ be the finite difference Laplacian associated to the lattice $bZ^{d}$. For dimension $dge 3$, $age 0$ and $L$ a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent $G^{a}:=(a-D)^{-1}$ can be decomposed as an infinite sum of positive semi-definite functions $ V_{n} $ of finite range, $ V_{n} (x-y) = 0$ for $|x-y|ge O(L)^{n}$. Equivalently, the Gaussian process on the lattice with covariance $G^{a}$ admits a decomposition into independent Gaussian processes with finite range covariances. For $a=0$, $ V_{n} $ has a limiting scaling form $L^{-n(d-2)}Gamma_{ c,ast }{bigl (frac{x-y}{ L^{n}}bigr )}$ as $nrightarrow infty$. As a corollary, such decompositions also exist for fractional powers $(-D)^{-alpha/2}$, $0

Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

Directory of Open Access Journals (Sweden)

Navnit Jha

2014-04-01

Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.

Finite rotation shells basic equations and finite elements for Reissner kinematics

CERN Document Server

Wisniewski, K

2010-01-01

This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.

Validation of High Displacement Piezoelectric Actuator Finite Element Models

Science.gov (United States)

Taleghani, B. K.

2000-01-01

The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

Science.gov (United States)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Development and application of a third order scheme of finite differences centered in mesh

International Nuclear Information System (INIS)

Delfin L, A.; Alonso V, G.; Valle G, E. del

2003-01-01

In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

Science.gov (United States)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles

2011-01-01

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Finite difference solution of the time dependent neutron group diffusion equations

International Nuclear Information System (INIS)

Hendricks, J.S.; Henry, A.F.

1975-08-01

In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods

Solution of unidimensional problems from monoenergetics neutrons diffusion through finite differences

International Nuclear Information System (INIS)

Filio Lopez, Carlos.

1979-01-01

A calculation program (URA 6.F4) was elaborated on FORTRAN IV language, that through finite differences solves the unidimensional scalar Helmholtz equation, assuming only one energy group, in spherical cylindrical or plane geometry. The purpose is the determination of the flow distribution in a reactor of spherical cylindrical or plane geometry and the critical dimensions. Feeding as entrance datas to the program the geometry, diffusion coefficients and macroscopic transversals cross sections of absorption and fission for each region. The differential diffusion equation is converted with its boundary conditions, to one system of homogeneous algebraic linear equations using the box integration technique. The investigation on criticality is converted then in a succession of eigenvalue problems for the critical eigenvalue. In general, only is necessary to solve the first eigenvalue and its corresponding eigenvector, employing the power method. The obtained results by the program for the critical dimensions of the clean reactors are admissible, the existing error as respect to the analytic is less of 0.5%; by the analysed reactors of three regions, the relative error with respect to the semianalytic result is less of 0.2%. With this program is possible to obtain one quantitative description of one reactor if the transversal sections that appears in the monoenergetic model are adequatedly averaged by the energy group used. (author)

Aspects of Finite Element Simulation of Axi-Symmetric Hydromechanical Deep Drawing

DEFF Research Database (Denmark)

Jensen, Morten Rikard; Olovsson, Lars; Danckert, Joachim

1999-01-01

A new approach for the Finite Element modelling of the hydromechanical deep drawing process is evaluated. In the model a Finite Difference approximation of Reynold’s equation is solved for the fluid flow between the blank and the draw die in the flange region. The approach is implemented...... as a contact algorithm in an explicit Finite Element code, Exhale2D. The developed model is verified against experiments and good agreement is obtained. It is concluded that the developed model is a promising approach for simulating the hydromechanical deep drawing process using the Finite Element Method....

Conversion and comparison of the mathematical, three-dimensional, finite-difference, ground-water flow model to the modular, three-dimensional, finite-difference, ground-water flow model for the Tesuque aquifer system in northern New Mexico

Science.gov (United States)

Umari, A.M.; Szeliga, T.L.

1989-01-01

The three-dimensional finite-difference groundwater model (using a mathematical groundwater flow code) of the Tesuque aquifer system in northern New Mexico was converted to run using the U.S. Geological Survey 's modular groundwater flow code. Results from the final versions of the predevelopment and 1947 to 2080 transient simulations of the two models are compared. A correlation coefficient of 0.9905 was obtained for the match in block-by-block head-dependent fluxes for predevelopment conditions. There are, however, significant differences in at least two specific cases. In the first case, a difference is associated with the net loss from the Pojoaque River and its tributaries to the aquifer. The net loss by the river is given as 1.134 cu ft/sec using the original groundwater model, which is 38.1% less than the net loss by the river of 1.8319 cu ft/sec computed in this study. In the second case, the large difference is computed for the transient decline in the hydraulic head of a model block near Tesuque Pueblo. The hydraulic-head decline by 2080 is, using the original model, 249 ft, which is 14.7% less than the hydraulic head of 292 ft computed by this study. In general, the differences between the two sets of results are not large enough to lead to different conclusions regarding the behavior of the system at steady state or when pumped. (USGS)

Electromagnetic numerical characterization of the laser-induced liquid crystal lens by finite-difference time domain method

International Nuclear Information System (INIS)

Morisaki, T.; Ono, H.

2005-01-01

A laser-induced liquid-crystal lens is formed by large optical non-linearity and anisotropic complex refractive indices in guest-host liquid crystals. We obtained light wave propagation characteristics of the laser-induced LC lens. Three analytical methods were used to obtain light wave propagation characteristics. Analysis by 3-dimensional heat conduction was applied to determine the refractive index in the liquid-crystal layer. Another method used was to determine light wave propagation characteristics in the laser-induced lens by means of the finite-difference tune domain (FDTD) method and diffraction theory. In this study, we draw a parallel between the experimental results and FDTD. Copyright (2003) AD-TECH - International Foundation for the Advancement of Technology Ltd

Development of a partitioned finite volume-finite element fluid-structure interaction scheme for strongly-coupled problems

CSIR Research Space (South Africa)

Suliman, Ridhwaan

2012-07-01

Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...

Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

Energy Technology Data Exchange (ETDEWEB)

Priimak, Dmitri

2014-12-01

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

International Nuclear Information System (INIS)

Priimak, Dmitri

2014-01-01

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques

Socio-economic applications of finite state mean field games

KAUST Repository

Gomes, Diogo A.

2014-10-06

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.

Finite Difference Solution of Elastic-Plastic Thin Rotating Annular Disk with Exponentially Variable Thickness and Exponentially Variable Density

Directory of Open Access Journals (Sweden)

Sanjeev Sharma

2013-01-01

Full Text Available Elastic-plastic stresses, strains, and displacements have been obtained for a thin rotating annular disk with exponentially variable thickness and exponentially variable density with nonlinear strain hardening material by finite difference method using Von-Mises' yield criterion. Results have been computed numerically and depicted graphically. From the numerical results, it can be concluded that disk whose thickness decreases radially and density increases radially is on the safer side of design as compared to the disk with exponentially varying thickness and exponentially varying density as well as to flat disk.

Finite quantum field theories

International Nuclear Information System (INIS)

Lucha, W.; Neufeld, H.

1986-01-01

We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)

Finite micro-tab system for load control on a wind turbine

International Nuclear Information System (INIS)

Bach, A B; Lennie, M; Nayeri, C N; Paschereit, C O; Pechlivanoglou, G

2014-01-01

Finite micro-tabs have been investigated experimentally to evaluate the potential for load control on wind turbines. Two dimensional full span, as well as multiple finite tabs of various aspect ratios have been studied on an AH93W174 airfoil at different chord wise positions. A force balance was used to measure the aerodynamic loads. Furthermore, the wake vortex system consisting of the Karman vortex street as well as the tab tip vortices was analyzed with a 12-hole probe and hot wire anemometry. Finally, conventional oil paint as well as a quantitative digital flow analysis technique called SMARTviz were used to visualize the flow around the finite tab configurations. Results have shown that the devices are an effective solution to alleviate the airfoils overall load. The influence of the tab height, tab position as well as the finite tab aspect ratio on the lift and lift to drag ratio have been evaluated. It could be shown, that the lift difference can either be varied by changing the tab height as well as by altering the aspect ratio of the finite tabs. The drag of a two-dimensional flap is directly associated with the vortex street, while in the case of the finite tab, the solidity ratio of the tabs has the strongest effect on the drag. Therefore, the application of a finite tab system showed to improve the lift to drag ratio

Differences in the stress distribution in the distal femur between patellofemoral joint replacement and total knee replacement: a finite element study

Directory of Open Access Journals (Sweden)

van Jonbergen Hans-Peter W

2012-06-01

Full Text Available Abstract Background Patellofemoral joint replacement is a successful treatment option for isolated patellofemoral osteoarthritis. However, results of later conversion to total knee replacement may be compromised by periprosthetic bone loss. Previous clinical studies have demonstrated a decrease in distal femoral bone mineral density after patellofemoral joint replacement. It is unclear whether this is due to periprosthetic stress shielding. The main objective of the current study was to evaluate the stress shielding effect of prosthetic replacement with 2 different patellofemoral prosthetic designs and with a total knee prosthesis. Methods We developed a finite element model of an intact patellofemoral joint, and finite element models of patellofemoral joint replacement with a Journey PFJ prosthesis, a Richards II prosthesis, and a Genesis II total knee prosthesis. For each of these 4 finite element models, the average Von Mises stress in 2 clinically relevant regions of interest were evaluated during a simulated squatting movement until 120 degrees of flexion. Results During deep knee flexion, in the anterior region of interest, the average Von Mises stress with the Journey PFJ design was comparable to the physiological knee, while reduced by almost 25% for both the Richards II design and the Genesis II total knee joint replacement design. The average Von Mises stress in the supracondylar region of interest was similar for both patellofemoral prosthetic designs and the physiological model, with slightly lower stress for the Genesis II design. Conclusions Patellofemoral joint replacement results in periprosthetic stress-shielding, although to a smaller degree than in total knee replacement. Specific patellofemoral prosthetic design properties may result in differences in femoral stress shielding.

Differences in the stress distribution in the distal femur between patellofemoral joint replacement and total knee replacement: a finite element study

Science.gov (United States)

2012-01-01

Background Patellofemoral joint replacement is a successful treatment option for isolated patellofemoral osteoarthritis. However, results of later conversion to total knee replacement may be compromised by periprosthetic bone loss. Previous clinical studies have demonstrated a decrease in distal femoral bone mineral density after patellofemoral joint replacement. It is unclear whether this is due to periprosthetic stress shielding. The main objective of the current study was to evaluate the stress shielding effect of prosthetic replacement with 2 different patellofemoral prosthetic designs and with a total knee prosthesis. Methods We developed a finite element model of an intact patellofemoral joint, and finite element models of patellofemoral joint replacement with a Journey PFJ prosthesis, a Richards II prosthesis, and a Genesis II total knee prosthesis. For each of these 4 finite element models, the average Von Mises stress in 2 clinically relevant regions of interest were evaluated during a simulated squatting movement until 120 degrees of flexion. Results During deep knee flexion, in the anterior region of interest, the average Von Mises stress with the Journey PFJ design was comparable to the physiological knee, while reduced by almost 25% for both the Richards II design and the Genesis II total knee joint replacement design. The average Von Mises stress in the supracondylar region of interest was similar for both patellofemoral prosthetic designs and the physiological model, with slightly lower stress for the Genesis II design. Conclusions Patellofemoral joint replacement results in periprosthetic stress-shielding, although to a smaller degree than in total knee replacement. Specific patellofemoral prosthetic design properties may result in differences in femoral stress shielding. PMID:22704638

Comparison of measured and predicted thermal mixing tests using improved finite difference technique

International Nuclear Information System (INIS)

Hassan, Y.A.; Rice, J.G.; Kim, J.H.

1983-01-01

The numerical diffusion introduced by the use of upwind formulations in the finite difference solution of the flow and energy equations for thermal mixing problems (cold water injection after small break LOCA in a PWR) was examined. The relative importance of numerical diffusion in the flow equations, compared to its effect on the energy equation was demonstrated. The flow field equations were solved using both first order accurate upwind, and second order accurate differencing schemes. The energy equation was treated using the conventional upwind and a mass weighted skew upwind scheme. Results presented for a simple test case showed that, for thermal mixing problems, the numerical diffusion was most significant in the energy equation. The numerical diffusion effect in the flow field equations was much less significant. A comparison of predictions using the skew upwind and the conventional upwind with experimental data from a two dimensional thermal mixing text are presented. The use of the skew upwind scheme showed a significant improvement in the accuracy of the steady state predicted temperatures. (orig./HP)

Three-Dimensional Phase Field Simulations of Hysteresis and Butterfly Loops by the Finite Volume Method

International Nuclear Information System (INIS)

Xi Li-Ying; Chen Huan-Ming; Zheng Fu; Gao Hua; Tong Yang; Ma Zhi

2015-01-01

Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg–Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems. (paper)

Application of Mass Lumped Higher Order Finite Elements

International Nuclear Information System (INIS)

J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau

2005-01-01

There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied

Finite fields and applications

CERN Document Server

Mullen, Gary L

2007-01-01

This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications. The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields. Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises rel...

An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels

Science.gov (United States)

Colera, Manuel; Pérez-Saborid, Miguel

2017-09-01

A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.

On finite quantum field theories

International Nuclear Information System (INIS)

Rajpoot, S.; Taylor, J.G.

1984-01-01

The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)

Finite size scaling theory

International Nuclear Information System (INIS)

Rittenberg, V.

1983-01-01

Fischer's finite-size scaling describes the cross over from the singular behaviour of thermodynamic quantities at the critical point to the analytic behaviour of the finite system. Recent extensions of the method--transfer matrix technique, and the Hamiltonian formalism--are discussed in this paper. The method is presented, with equations deriving scaling function, critical temperature, and exponent v. As an application of the method, a 3-states Hamiltonian with Z 3 global symmetry is studied. Diagonalization of the Hamiltonian for finite chains allows one to estimate the critical exponents, and also to discover new phase transitions at lower temperatures. The critical points lambda, and indices v estimated for finite-scaling are given

Numerical solution of recirculating flow by a simple finite element recursion relation

Energy Technology Data Exchange (ETDEWEB)

Pepper, D W; Cooper, R E

1980-01-01

A time-split finite element recursion relation, based on linear basis functions, is used to solve the two-dimensional equations of motion. Recirculating flow in a rectangular cavity and free convective flow in an enclosed container are analyzed. The relation has the advantage of finite element accuracy and finite difference speed and simplicity. Incorporating dissipation parameters in the functionals decreases numerical dispersion and improves phase lag.

Automation of finite element methods

CERN Document Server

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.

Finite difference modelling of the temperature rise in non-linear medical ultrasound fields.

Science.gov (United States)

Divall, S A; Humphrey, V F

2000-03-01

Non-linear propagation of ultrasound can lead to increased heat generation in medical diagnostic imaging due to the preferential absorption of harmonics of the original frequency. A numerical model has been developed and tested that is capable of predicting the temperature rise due to a high amplitude ultrasound field. The acoustic field is modelled using a numerical solution to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, known as the Bergen Code, which is implemented in cylindrical symmetric form. A finite difference representation of the thermal equations is used to calculate the resulting temperature rises. The model allows for the inclusion of a number of layers of tissue with different acoustic and thermal properties and accounts for the effects of non-linear propagation, direct heating by the transducer, thermal diffusion and perfusion in different tissues. The effect of temperature-dependent skin perfusion and variation in background temperature between the skin and deeper layers of the body are included. The model has been tested against analytic solutions for simple configurations and then used to estimate temperature rises in realistic obstetric situations. A pulsed 3 MHz transducer operating with an average acoustic power of 200 mW leads to a maximum steady state temperature rise inside the foetus of 1.25 degrees C compared with a 0.6 degree C rise for the same transmitted power under linear propagation conditions. The largest temperature rise occurs at the skin surface, with the temperature rise at the foetus limited to less than 2 degrees C for the range of conditions considered.

$\\delta$-Expansion at Finite Temperature

OpenAIRE

Ramos, Rudnei O.

1996-01-01

We apply the $\\delta$-expansion perturbation scheme to the $\\lambda \\phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\\delta$-expansion the interaction term is written as $\\lambda (\\phi^{2})^{ 1 + \\delta}$ and $\\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\\delta$. The results are compared with the usual loop-expansion at finite temperature.

A Finite Difference Scheme for Double-Diffusive Unsteady Free Convection from a Curved Surface to a Saturated Porous Medium with a Non-Newtonian Fluid

KAUST Repository

El-Amin, Mohamed

2011-05-14

In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

Analytic Coarse-Mesh Finite-Difference Method Generalized for Heterogeneous Multidimensional Two-Group Diffusion Calculations

International Nuclear Information System (INIS)

Garcia-Herranz, Nuria; Cabellos, Oscar; Aragones, Jose M.; Ahnert, Carol

2003-01-01

In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects.The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors. When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations

Finite spatial volume approach to finite temperature field theory

International Nuclear Information System (INIS)

Weiss, Nathan

1981-01-01

A relativistic quantum field theory at finite temperature T=β -1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned. (auth)

Tomographic reconstruction of melanin structures of optical coherence tomography via the finite-difference time-domain simulation

Science.gov (United States)

Huang, Shi-Hao; Wang, Shiang-Jiu; Tseng, Snow H.

2015-03-01

Optical coherence tomography (OCT) provides high resolution, cross-sectional image of internal microstructure of biological tissue. We use the Finite-Difference Time-Domain method (FDTD) to analyze the data acquired by OCT, which can help us reconstruct the refractive index of the biological tissue. We calculate the refractive index tomography and try to match the simulation with the data acquired by OCT. Specifically, we try to reconstruct the structure of melanin, which has complex refractive indices and is the key component of human pigment system. The results indicate that better reconstruction can be achieved for homogenous sample, whereas the reconstruction is degraded for samples with fine structure or with complex interface. Simulation reconstruction shows structures of the Melanin that may be useful for biomedical optics applications.

Performance Improvements for Coarse Mesh Finite Difference Acceleration L3:RTM.PRT.P13.02

International Nuclear Information System (INIS)

Collins, Benjamin S.; Hamilton, Steven P.; Stimpson, Shane; Yee, Ben; Larsen, Edward W.; Kochunas, Brendan

2016-01-01

The development of VERA-CS in recent years has focused on developing the capability to simulate multiple cycles of operating commercial nuclear power plants. Now that these capabilities have advanced to the point where it is being deployed to users, the focus is on improving the computational performance of various components in VERA-CS. In this work, the focus is on the Coarse Mesh Finite Difference (CMFD) solution in MPACT. CMFD serves multiple purposes in the 2D/1D solution methodology. First, it is a natural mechanism to tie together the radial MOC transport and the axial SP3 solution. Because the CMFD system solves the multigroup three-dimensional core in one system, it pulls together the global response of the system. In addition, the CMFD solution provides a framework to accelerate the convergence of the eigenvalue problem.

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

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

KAUST Repository

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.

Measures with locally finite support and spectrum.

Science.gov (United States)

Meyer, Yves F

2016-03-22

The goal of this paper is the construction of measures μ on R(n)enjoying three conflicting but fortunately compatible properties: (i) μ is a sum of weighted Dirac masses on a locally finite set, (ii) the Fourier transform μ f μ is also a sum of weighted Dirac masses on a locally finite set, and (iii) μ is not a generalized Dirac comb. We give surprisingly simple examples of such measures. These unexpected patterns strongly differ from quasicrystals, they provide us with unusual Poisson's formulas, and they might give us an unconventional insight into aperiodic order.

Finite-dimensional calculus

International Nuclear Information System (INIS)

Feinsilver, Philip; Schott, Rene

2009-01-01

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.

Efficient Finite Element Models for Calculation of the No-load losses of the Transformer

Directory of Open Access Journals (Sweden)

Kamran Dawood

2017-10-01

Full Text Available Different transformer models are examined for the calculation of the no-load losses using finite element analysis. Two-dimensional and three-dimensional finite element analyses are used for the simulation of the transformer. Results of the finite element method are also compared with the experimental results. The Result shows that 3-dimensional provide high accuracy as compared to the 2 dimensional full and half model. However, the 2-dimensional half model is the less time-consuming method as compared to the 3 and 2-dimensional full model. Simulation time duration taken by the different models of the transformer is also compared. The difference between the 3-dimensional finite element method and experimental results are less than 3%. These numerical methods can help transformer designers to minimize the development of the prototype transformers.

Finite element analysis of the three different posterior malleolus fixation strategies in relation to different fracture sizes.

Science.gov (United States)

Anwar, Adeel; Lv, Decheng; Zhao, Zhi; Zhang, Zhen; Lu, Ming; Nazir, Muhammad Umar; Qasim, Wasim

2017-04-01

Appropriate fixation method for the posterior malleolar fractures (PMF) according to the fracture size is still not clear. Aim of this study was to evaluate the outcomes of the different fixation methods used for fixation of PMF by finite element analysis (FEA) and to compare the effect of fixation constructs on the size of the fracture computationally. Three dimensional model of the tibia was reconstructed from computed tomography (CT) images. PMF of 30%, 40% and 50% fragment sizes were simulated through computational processing. Two antero-posterior (AP) lag screws, two postero-anterior (PA) lag screws and posterior buttress plate were analysed for three different fracture volumes. The simulated loads of 350N and 700N were applied to the proximal tibial end. Models were fixed distally in all degrees of freedom. In single limb standing condition, the posterior plate group produced the lowest relative displacement (RD) among all the groups (0.01, 0.03 and 0.06mm). Further nodal analysis of the highest RD fracture group showed a higher mean displacement of 4.77mm and 4.23mm in AP and PA lag screws model (p=0.000). The amounts of stress subjected to these implants, 134.36MPa and 140.75MPa were also significantly lower (p=0.000). There was a negative correlation (p=0.021) between implant stress and the displacement which signifies a less stable fixation using AP and PA lag screws. Progressively increasing fracture size demands more stable fixation construct because RD increases significantly. Posterior buttress plate produces superior stability and lowest RD in PMF models irrespective of the fragment size. Copyright © 2017 Elsevier Ltd. All rights reserved.

A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

KAUST Repository

Wheeler, Mary; Xue, Guangri; Yotov, Ivan

2011-01-01

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields

Star formation through thermal instability of radiative plasma with finite electron inertia and finite Larmor radius corrections

Energy Technology Data Exchange (ETDEWEB)

Kaothekar, Sachin, E-mail: sackaothekar@gmail.com [Department of Physics, Mahakal Institute of Technology, Ujjain-456664, Madhya Pradesh (India)

2016-08-15

I have studied the effects of finite electron inertia, finite ion Larmor radius (FLR) corrections, and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effect of thermal conductivity for star formation in interstellar medium (ISM). A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instability criterion is get modified into radiative instability criterion by inclusion of radiative heat-loss functions with thermal conductivity. The viscosity of medium removes the effect of FLR corrections from the condition of radiative instability. Numerical calculation shows stabilizing effect of heat-loss function, viscosity and FLR corrections, and destabilizing effect of finite electron inertia on the thermal instability. Results carried out in this paper shows that stars are formed in interstellar medium mainly due to thermal instability.

Star formation through thermal instability of radiative plasma with finite electron inertia and finite Larmor radius corrections

Directory of Open Access Journals (Sweden)

Sachin Kaothekar

2016-08-01

Full Text Available I have studied the effects of finite electron inertia, finite ion Larmor radius (FLR corrections, and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effect of thermal conductivity for star formation in interstellar medium (ISM. A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instability criterion is get modified into radiative instability criterion by inclusion of radiative heat-loss functions with thermal conductivity. The viscosity of medium removes the effect of FLR corrections from the condition of radiative instability. Numerical calculation shows stabilizing effect of heat-loss function, viscosity and FLR corrections, and destabilizing effect of finite electron inertia on the thermal instability. Results carried out in this paper shows that stars are formed in interstellar medium mainly due to thermal instability.

A particle finite element method for machining simulations

Science.gov (United States)

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.

Development of a Finite-Difference Time Domain (FDTD) Model for Propagation of Transient Sounds in Very Shallow Water.

Science.gov (United States)

Sprague, Mark W; Luczkovich, Joseph J

2016-01-01

This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating pile, can be used. The cylindrical implementation uses less computation but requires axial symmetry. The Cartesian implementation allows asymmetry. FDTD calculations compare well with those of a split-step parabolic equation. Applications include modeling the propagation of individual fish sounds, fish aggregation sounds, and distributed sources.

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

Science.gov (United States)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

Analysis of Different Positions of Fiber-Reinforced Composite Retainers versus Multistrand Wire Retainers Using the Finite Element Method

Directory of Open Access Journals (Sweden)

Arezoo Jahanbin

2014-01-01

Full Text Available Background. The aim of this study was to evaluate root displacement of the lower incisors fixed with FRC in different positions versus FSW retainers using the finite element method. Materials and Methods. 3D finite element models were designed for a mandibular anterior segment: Model 1: flexible spiral wire bonded to the lingual teeth surfaces, Model 2: FRC bonded to the upper third of lingual teeth surfaces, and Model 3: FRC bonded to the middle third. FE analysis was performed for three models and then tooth displacements were evaluated. Results. In contrast to lateral incisors and canines, the FSW retainer caused the central teeth to move more than the teeth bonded with FRC in both loadings. Comparison between Models 2 and 3 (in vertical loading showed that FRC retainers that bonded at the upper third of lingual teeth surfaces made central and canine teeth move less than FRC retainers bonded at the middle third; however, for lateral teeth it was the opposite. Conclusion. FRC retainers bonded at the upper third of lingual teeth surfaces make central and canine teeth move less than FRC retainers bonded at the middle third in vertical loading; however, for lateral teeth it was the opposite.

Quantiles for Finite Mixtures of Normal Distributions

Science.gov (United States)

Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.

2006-01-01

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes

Science.gov (United States)

Capuano, M.; Bogey, C.; Spelt, P. D. M.

2018-05-01

A computational method for the simulation of viscous and compressible gas-gas flows is presented. It consists in solving the Navier-Stokes equations associated with a convection equation governing the motion of the interface between two gases using high-order finite-difference schemes. A discontinuity-capturing methodology based on sensors and a spatial filter enables capturing shock waves and deformable interfaces. One-dimensional test cases are performed as validation and to justify choices in the numerical method. The results compare well with analytical solutions. Shock waves and interfaces are accurately propagated, and remain sharp. Subsequently, two-dimensional flows are considered including viscosity and thermal conductivity. In Richtmyer-Meshkov instability, generated on an air-SF6 interface, the influence of the mesh refinement on the instability shape is studied, and the temporal variations of the instability amplitude is compared with experimental data. Finally, for a plane shock wave propagating in air and impacting a cylindrical bubble filled with helium or R22, numerical Schlieren pictures obtained using different grid refinements are found to compare well with experimental shadow-photographs. The mass conservation is verified from the temporal variations of the mass of the bubble. The mean velocities of pressure waves and bubble interface are similar to those obtained experimentally.

Nilpotent -local finite groups

Science.gov (United States)

Cantarero, José; Scherer, Jérôme; Viruel, Antonio

2014-10-01

We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.

Optimal Tikhonov Regularization in Finite-Frequency Tomography

Science.gov (United States)

Fang, Y.; Yao, Z.; Zhou, Y.

2017-12-01

The last decade has witnessed a progressive transition in seismic tomography from ray theory to finite-frequency theory which overcomes the resolution limit of the high-frequency approximation in ray theory. In addition to approximations in wave propagation physics, a main difference between ray-theoretical tomography and finite-frequency tomography is the sparseness of the associated sensitivity matrix. It is well known that seismic tomographic problems are ill-posed and regularizations such as damping and smoothing are often applied to analyze the tradeoff between data misfit and model uncertainty. The regularizations depend on the structure of the matrix as well as noise level of the data. Cross-validation has been used to constrain data uncertainties in body-wave finite-frequency inversions when measurements at multiple frequencies are available to invert for a common structure. In this study, we explore an optimal Tikhonov regularization in surface-wave phase-velocity tomography based on minimization of an empirical Bayes risk function using theoretical training datasets. We exploit the structure of the sensitivity matrix in the framework of singular value decomposition (SVD) which also allows for the calculation of complete resolution matrix. We compare the optimal Tikhonov regularization in finite-frequency tomography with traditional tradeo-off analysis using surface wave dispersion measurements from global as well as regional studies.

Nonlinear Conservation Laws and Finite Volume Methods

Science.gov (United States)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level

Implementation of Unsplit Perfectly Matched Layer Absorbing Boundary Condition in 3 Dimensional Finite Difference Time Domain Method

Directory of Open Access Journals (Sweden)

B. U. Musa

2017-04-01

Full Text Available The C++ programming language was used to implement three-dimensional (3-D finite-difference time-domain (FDTD technique to simulate radiation of high frequency electromagnetic waves in free space. To achieve any meaningful results the computational domain of interest should have to be truncated in some way and this is achieved by applying absorbing boundary conditions. A uniaxial perfectly matched layer (UPML absorbing boundary condition is used in this work. The discretised equations of the UPML in FDTD time stepping scheme were derived and has been successfully implemented using the computer program. Simulation results showed that the UPML behaves as an absorber. This was confirmed by comparing the results with another boundary condition, the Mur ABC.

Three-dimensional modeling in the electromagnetic/magnetotelluric methods. Accuracy of various finite-element and finite difference methods; Denjiho MT ho ni okeru sanjigen modeling. Shushu no yugen yosoho to sabunho no seido

Energy Technology Data Exchange (ETDEWEB)

Sasaki, Y [Kyushu University, Fukuoka (Japan). Faculty of Engineering

1997-05-27

To enhance the reliability of electromagnetic/magnetotelluric (MT) survey, calculation results of finite-element methods (FEMs) and finite difference methods (FDMs) were compared. Accuracy of individual methods and convergence of repitition solution were examined. As a result of the investigation, it was found that appropriate accuracy can be obtained from the edge FEM and FDM for the example of vertical magnetic dipole, and that the best accuracy can be obtained from the FDM among four methods for the example of MT survey. It was revealed that the ICBCG (incomplete Cholesky bi-conjugate gradient) method is an excellent method as a solution method of simultaneous equations from the viewpoint of accuracy and calculation time. For the joint FEM, solutions of SOR method converged for both the examples. It was concluded that the cause of error is not due to the error of numerical calculation, but due to the consideration without discontinuity of electric field. The conditions of coefficient matrix increased with decreasing the frequency, which resulted in the unstable numerical calculation. It would be required to incorporate the constraint in a certain form. 4 refs., 12 figs.

Finite size effects in quark-gluon plasma formation

International Nuclear Information System (INIS)

Gopie, Andy; Ogilvie, Michael C.

1999-01-01

Using lattice simulations of quenched QCD we estimate the finite size effects present when a gluon plasma equilibrates in a slab geometry, i.e., finite width but large transverse dimensions. Significant differences are observed in the free energy density for the slab when compared with bulk behavior. A small shift in the critical temperature is also seen. The free energy required to liberate heavy quarks relative to bulk is measured using Polyakov loops; the additional free energy required is on the order of 30 - 40 MeV at 2 - 3 T c

Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling.

Science.gov (United States)

Wilts, Bodo D; Michielsen, Kristel; De Raedt, Hans; Stavenga, Doekele G

2014-03-25

Birds-of-paradise are nature's prime examples of the evolution of color by sexual selection. Their brilliant, structurally colored feathers play a principal role in mating displays. The structural coloration of both the occipital and breast feathers of the bird-of-paradise Lawes' parotia is produced by melanin rodlets arranged in layers, together acting as interference reflectors. Light reflection by the silvery colored occipital feathers is unidirectional as in a classical multilayer, but the reflection by the richly colored breast feathers is three-directional and extraordinarily complex. Here we show that the reflection properties of both feather types can be quantitatively explained by finite-difference time-domain modeling using realistic feather anatomies and experimentally determined refractive index dispersion values of keratin and melanin. The results elucidate the interplay between avian coloration and vision and indicate tuning of the mating displays to the spectral properties of the avian visual system.

Finite Discrete Gabor Analysis

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

Socio-economic applications of finite state mean field games.

Science.gov (United States)

Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese

2014-11-13

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Alternating-time temporal logic with finite-memory strategies

DEFF Research Database (Denmark)

Vester, Steen

2013-01-01

on finite-memory strategies. One where the memory size allowed is bounded and one where the memory size is unbounded (but must be finite). This is motivated by the high complexity of model-checking with perfect recall semantics and the severe limitations of memoryless strategies. We show that both types...... of semantics introduced are different from perfect recall and memoryless semantics and next focus on the decidability and complexity of model-checking in both complete and incomplete information games for ATL/ATL*. In particular, we show that the complexity of model-checking with bounded-memory semantics...... is Delta_2p-complete for ATL and PSPACE-complete for ATL* in incomplete information games just as in the memoryless case. We also present a proof that ATL and ATL* model-checking is undecidable for n >= 3 players with finite-memory semantics in incomplete information games....

A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria

Directory of Open Access Journals (Sweden)

Juan C. Chimal-Eguía

2012-12-01

Full Text Available This work shows the power of the variational approach for studying the efficiency of thermal engines in the context of the Finite Time Thermodynamics (FTT. Using an endoreversible Curzon–Ahlborn (CA heat engine as a model for actual thermal engines, three different criteria for thermal efficiency were analyzed: maximum power output, ecological function, and maximum power density. By means of this procedure, the performance of the CA heat engine with a nonlinear heat transfer law (the Stefan–Boltzmann law was studied to describe the heat exchanges between the working substance and its thermal reservoirs. The specific case of the Müser engine for all the criteria was analyzed. The results confirmed some previous findings using other procedures and additionally new results for the Müser engine performance were obtained.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang

2010-01-01

Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo

2010-01-01

Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

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.

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1977-11-01

The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently

Finite difference methods for reducing numerical diffusion in TEACH-type calculations. [Teaching Elliptic Axisymmetric Characteristics Heuristically

Science.gov (United States)

Syed, S. A.; Chiappetta, L. M.

1985-01-01

A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.

OpenSeesPy: Python library for the OpenSees finite element framework

Science.gov (United States)

Zhu, Minjie; McKenna, Frank; Scott, Michael H.

2018-01-01

OpenSees, an open source finite element software framework, has been used broadly in the earthquake engineering community for simulating the seismic response of structural and geotechnical systems. The framework allows users to perform finite element analysis with a scripting language and for developers to create both serial and parallel finite element computer applications as interpreters. For the last 15 years, Tcl has been the primary scripting language to which the model building and analysis modules of OpenSees are linked. To provide users with different scripting language options, particularly Python, the OpenSees interpreter interface was refactored to provide multi-interpreter capabilities. This refactoring, resulting in the creation of OpenSeesPy as a Python module, is accomplished through an abstract interface for interpreter calls with concrete implementations for different scripting languages. Through this approach, users are able to develop applications that utilize the unique features of several scripting languages while taking advantage of advanced finite element analysis models and algorithms.

Modeling Bidirectional Reflectance Distribution Function of One-dimensional Random Rough Surfaces with the Finite Difference Time Domain Method

Directory of Open Access Journals (Sweden)

Min-Jhong Gu

2014-08-01

Full Text Available This article describes the development of a suite of programs that is capable of simulating the radiation properties of a random rough surface (RRS. The fundamental approach involves the generation, by fast Fourier transform (FFT built with rigorous finite difference time domain (FDTD, as the theoretical basis for the simulation of a bidirectional reflectance distribution function (BRDF of the RRS. The results are compared with the measurements and modeling of existing work to verify the feasibility of customized programming. It was found that the results of this study were a better match to the measurement data than those achieved in other modeling work.

Using finite element modelling to examine the flow process and temperature evolution in HPT under different constraining conditions

International Nuclear Information System (INIS)

Pereira, P H R; Langdon, T G; Figueiredo, R B; Cetlin, P R

2014-01-01

High-pressure torsion (HPT) is a metal-working technique used to impose severe plastic deformation into disc-shaped samples under high hydrostatic pressures. Different HPT facilities have been developed and they may be divided into three distinct categories depending upon the configuration of the anvils and the restriction imposed on the lateral flow of the samples. In the present paper, finite element simulations were performed to compare the flow process, temperature, strain and hydrostatic stress distributions under unconstrained, quasi-constrained and constrained conditions. It is shown there are distinct strain distributions in the samples depending on the facility configurations and a similar trend in the temperature rise of the HPT workpieces

Introduction to finite temperature and finite density QCD

International Nuclear Information System (INIS)

Kitazawa, Masakiyo

2014-01-01

It has been pointed out that QCD (Quantum Chromodynamics) in the circumstances of medium at finite temperature and density shows numbers of phenomena similar to the characteristics of solid state physics, e.g. phase transitions. In the past ten years, the very high temperature and density matter came to be observed experimentally at the heavy ion collisions. At the same time, the numerical QCD analysis at finite temperature and density attained quantitative level analysis possible owing to the remarkable progress of computers. In this summer school lecture, it has been set out to give not only the recent results, but also the spontaneous breaking of the chiral symmetry, the fundamental theory of finite temperature and further expositions as in the following four sections. The first section is titled as 'Introduction to Finite Temperature and Density QCD' with subsections of 1.1 standard model and QCD, 1.2 phase transition and phase structure of QCD, 1.3 lattice QCD and thermodynamic quantity, 1.4 heavy ion collision experiments, and 1.5 neutron stars. The second one is 'Equilibrium State' with subsections of 2.1 chiral symmetry, 2.2 vacuum state: BCS theory, 2.3 NJL (Nambu-Jona-Lasinio) model, and 2.4 color superconductivity. The third one is 'Static fluctuations' with subsections of 3.1 fluctuations, 3.2 moment and cumulant, 3.3 increase of fluctuations at critical points, 3.4 analysis of fluctuations by lattice QCD and Taylor expansion, and 3.5 experimental exploration of QCD phase structure. The fourth one is 'Dynamical Structure' with 4.1 linear response theory, 4.2 spectral functions, 4.3 Matsubara function, and 4.4 analyses of dynamical structure by lattice QCD. (S. Funahashi)

Use of the finite-difference time-domain method in electromagnetic dosimetry

International Nuclear Information System (INIS)

Sullivan, D.M.

1987-01-01

Although there are acceptable methods for calculating whole body electromagnetic absorption, no completely acceptable method for calculating the local specific absorption rate (SAR) at points within the body has been developed. Frequency domain methods, such as the method of moments (MoM) have achieved some success; however, the MoM requires computer storage on the order of (3N) 2 , and computation time on the order of (3N) 3 where N is the number of cells. The finite-difference time-domain (FDTD) method has been employed extensively in calculating the scattering from metallic objects, and recently is seeing some use in calculating the interaction of EM fields with complex, lossy dielectric bodies. Since the FDTD method has storage and time requirements proportional to N, it presents an attractive alternative to calculating SAR distribution in large bodies. This dissertation describes the FDTD method and evaluates it by comparing its results with analytic solutions in 2 and 3 dimensions. The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy. The construction of a data base to provide detailed, inhomogeneous man models for use with the FDTD method is described. Using this construction method, a model of 40,000 1.31 cm. cells is developed for use at 350 MHz, and another model consisting of 5000 2.62 cm. cells is developed for use at 100 MHz. To add more realism to the problem, a ground plane is added to the FDTD software. The needed changes to the software are described, along with a test which confirms its accuracy. Using the CRAY II supercomputer, SAR distributions in human models are calculated using incident frequencies of 100 MHz and 350 MHz for three different cases: (1) A homogeneous man model in free space, (2) an inhomogeneous man model in free space, and (3) an inhomogeneous man model standing on a ground plane

Finite element computational fluid mechanics

International Nuclear Information System (INIS)

Baker, A.J.

1983-01-01

This book analyzes finite element theory as applied to computational fluid mechanics. It includes a chapter on using the heat conduction equation to expose the essence of finite element theory, including higher-order accuracy and convergence in a common knowledge framework. Another chapter generalizes the algorithm to extend application to the nonlinearity of the Navier-Stokes equations. Other chapters are concerned with the analysis of a specific fluids mechanics problem class, including theory and applications. Some of the topics covered include finite element theory for linear mechanics; potential flow; weighted residuals/galerkin finite element theory; inviscid and convection dominated flows; boundary layers; parabolic three-dimensional flows; and viscous and rotational flows

Finite element model updating of concrete structures based on imprecise probability

Science.gov (United States)

Biswal, S.; Ramaswamy, A.

2017-09-01

Imprecise probability based methods are developed in this study for the parameter estimation, in finite element model updating for concrete structures, when the measurements are imprecisely defined. Bayesian analysis using Metropolis Hastings algorithm for parameter estimation is generalized to incorporate the imprecision present in the prior distribution, in the likelihood function, and in the measured responses. Three different cases are considered (i) imprecision is present in the prior distribution and in the measurements only, (ii) imprecision is present in the parameters of the finite element model and in the measurement only, and (iii) imprecision is present in the prior distribution, in the parameters of the finite element model, and in the measurements. Procedures are also developed for integrating the imprecision in the parameters of the finite element model, in the finite element software Abaqus. The proposed methods are then verified against reinforced concrete beams and prestressed concrete beams tested in our laboratory as part of this study.

Designs and finite geometries

CERN Document Server

1996-01-01

Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

A Dyson-Schwinger approach to finite temperature QCD

Energy Technology Data Exchange (ETDEWEB)

Mueller, Jens Andreas

2011-10-26

The different phases of quantum chromodynamics at finite temperature are studied. To this end the nonperturbative quark propagator in Matsubara formalism is determined from its equation of motion, the Dyson-Schwinger equation. A novel truncation scheme is introduced including the nonperturbative, temperature dependent gluon propagator as extracted from lattice gauge theory. In the first part of the thesis a deconfinement order parameter, the dual condensate, and the critical temperature are determined from the dependence of the quark propagator on the temporal boundary conditions. The chiral transition is investigated by means of the quark condensate as order parameter. In addition differences in the chiral and deconfinement transition between gauge groups SU(2) and SU(3) are explored. In the following the quenched quark propagator is studied with respect to a possible spectral representation at finite temperature. In doing so, the quark propagator turns out to possess different analytic properties below and above the deconfinement transition. This result motivates the consideration of an alternative deconfinement order parameter signaling positivity violations of the spectral function. A criterion for positivity violations of the spectral function based on the curvature of the Schwinger function is derived. Using a variety of ansaetze for the spectral function, the possible quasi-particle spectrum is analyzed, in particular its quark mass and momentum dependence. The results motivate a more direct determination of the spectral function in the framework of Dyson-Schwinger equations. In the two subsequent chapters extensions of the truncation scheme are considered. The influence of dynamical quark degrees of freedom on the chiral and deconfinement transition is investigated. This serves as a first step towards a complete self-consistent consideration of dynamical quarks and the extension to finite chemical potential. The goodness of the truncation is verified first

A Dyson-Schwinger approach to finite temperature QCD

International Nuclear Information System (INIS)

Mueller, Jens Andreas

2011-01-01

The different phases of quantum chromodynamics at finite temperature are studied. To this end the nonperturbative quark propagator in Matsubara formalism is determined from its equation of motion, the Dyson-Schwinger equation. A novel truncation scheme is introduced including the nonperturbative, temperature dependent gluon propagator as extracted from lattice gauge theory. In the first part of the thesis a deconfinement order parameter, the dual condensate, and the critical temperature are determined from the dependence of the quark propagator on the temporal boundary conditions. The chiral transition is investigated by means of the quark condensate as order parameter. In addition differences in the chiral and deconfinement transition between gauge groups SU(2) and SU(3) are explored. In the following the quenched quark propagator is studied with respect to a possible spectral representation at finite temperature. In doing so, the quark propagator turns out to possess different analytic properties below and above the deconfinement transition. This result motivates the consideration of an alternative deconfinement order parameter signaling positivity violations of the spectral function. A criterion for positivity violations of the spectral function based on the curvature of the Schwinger function is derived. Using a variety of ansaetze for the spectral function, the possible quasi-particle spectrum is analyzed, in particular its quark mass and momentum dependence. The results motivate a more direct determination of the spectral function in the framework of Dyson-Schwinger equations. In the two subsequent chapters extensions of the truncation scheme are considered. The influence of dynamical quark degrees of freedom on the chiral and deconfinement transition is investigated. This serves as a first step towards a complete self-consistent consideration of dynamical quarks and the extension to finite chemical potential. The goodness of the truncation is verified first

Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

Energy Technology Data Exchange (ETDEWEB)

Martin, Bradley, E-mail: brma7253@colorado.edu; Fornberg, Bengt, E-mail: Fornberg@colorado.edu

2017-04-15

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

Thermal quench at finite 't Hooft coupling

Directory of Open Access Journals (Sweden)

H. Ebrahim

2016-03-01

Full Text Available Using holography we have studied thermal electric field quench for infinite and finite 't Hooft coupling constant. The set-up we consider here is D7-brane embedded in (α′ corrected AdS-black hole background. It is well-known that due to a time-dependent electric field on the probe brane, a time-dependent current will be produced and it will finally relax to its equilibrium value. We have studied the effect of different parameters of the system on equilibration time. As the most important results, for massless fundamental matter, we have observed a universal behaviour in the rescaled equilibration time in the very fast quench regime for different values of the temperature and α′ correction parameter. It seems that in the slow quench regime the system behaves adiabatically. We have also observed that the equilibration time decreases in finite 't Hooft coupling limit.

Aspects of numerical and representational methods related to the finite-difference simulation of advective and dispersive transport of freshwater in a thin brackish aquifer

Science.gov (United States)

Merritt, M.L.

1993-01-01

The simulation of the transport of injected freshwater in a thin brackish aquifer, overlain and underlain by confining layers containing more saline water, is shown to be influenced by the choice of the finite-difference approximation method, the algorithm for representing vertical advective and dispersive fluxes, and the values assigned to parametric coefficients that specify the degree of vertical dispersion and molecular diffusion that occurs. Computed potable water recovery efficiencies will differ depending upon the choice of algorithm and approximation method, as will dispersion coefficients estimated based on the calibration of simulations to match measured data. A comparison of centered and backward finite-difference approximation methods shows that substantially different transition zones between injected and native waters are depicted by the different methods, and computed recovery efficiencies vary greatly. Standard and experimental algorithms and a variety of values for molecular diffusivity, transverse dispersivity, and vertical scaling factor were compared in simulations of freshwater storage in a thin brackish aquifer. Computed recovery efficiencies vary considerably, and appreciable differences are observed in the distribution of injected freshwater in the various cases tested. The results demonstrate both a qualitatively different description of transport using the experimental algorithms and the interrelated influences of molecular diffusion and transverse dispersion on simulated recovery efficiency. When simulating natural aquifer flow in cross-section, flushing of the aquifer occurred for all tested coefficient choices using both standard and experimental algorithms. ?? 1993.

Desain dan Implementasi Variasi Dimensi Slot Pada Mikrostrip Double F Menggunakan Metode Finite Difference Time Domain (FDTD

Directory of Open Access Journals (Sweden)

Nurista Wahyu Kirana

2016-06-01

Full Text Available Pada penelitian ini dirancang antena mikrostrip dengan slot double F, di mana antena ini dapat digunakan untuk perangkat wireless yang bekerja pada frekuensi multiband. Antena mikrostrip double F dirancang dengan simulasi, dipabrikasi dan diukur secara riil. Finite Difference Time Domain (FDTD digunakan untuk menganalisis karakteristik distribusi arus yang tersebar pada mikrostrip. Nilai parameter terbaik dari hasil simulasi untuk return loss adalah -31,09 dB pada frekuensi 2,4 GHz dan VSWR sebesar 1,057 sedangkan hasil pengukurannya sebesar -32,82 dB pada frekuensi 2,4 GHz dan VSWR sebesar 1,045. Penggunaan slot pada patch antena dan pencatuan proximity yang digunakan meningkatkan bandwidth antena sebesar 48,7% dan gain yang dihasilkan sebesar 5,97 dBi.

Finite-Difference Time-Domain Simulation of Light Propagation in 2D Periodic and Quasi-Periodic Photonic Structures

Directory of Open Access Journals (Sweden)

N. Dadashzadeh

2013-09-01

Full Text Available Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We provide an overview of recent theoretical developments in a numerical modeling of Maxwell's equations to analyze the propagation of short laser pulses in photonic structures. The process of short light pulse propagation through 2D periodic and quasi-periodic photonic structures is simulated based on Finite-Difference Time-Domain calculations of Maxwell’s equations.

Finite element analysis to compare complete denture and implant-retained overdentures with different attachment systems.

Science.gov (United States)

Barão, Valentim Adelino Ricardo; Assunção, Wirley Gonçalves; Tabata, Lucas Fernando; Delben, Juliana Aparecida; Gomes, Erica Alves; de Sousa, Edson Antonio Capello; Rocha, Eduardo Passos

2009-07-01

This finite element analysis compared stress distribution on complete dentures and implant-retained overdentures with different attachment systems. Four models of edentulous mandible were constructed: group A (control), complete denture; group B, overdenture retained by 2 splinted implants with bar-clip system; group C, overdenture retained by 2 unsplinted implants with o'ring system; and group D, overdenture retained by 2 splinted implants with bar-clip and 2 distally placed o'ring system. Evaluation was performed on Ansys software, with 100-N vertical load applied on central incisive teeth. The lowest maximum general stress value (in megapascal) was observed in group A (64.305) followed by groups C (119.006), D (258.650), and B (349.873). The same trend occurred in supporting tissues with the highest stress value for cortical bone. Unsplinted implants associated with the o'ring attachment system showed the lowest maximum stress values among all overdenture groups. Furthermore, o'ring system also improved stress distribution when associated with bar-clip system.

Full-Wave Analysis of Traveling-Wave Field-Effect Transistors Using Finite-Difference Time-Domain Method

Directory of Open Access Journals (Sweden)

Koichi Narahara

2012-01-01

Full Text Available Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs, together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.

Staggered-grid finite-difference acoustic modeling with the Time-Domain Atmospheric Acoustic Propagation Suite (TDAAPS).

Energy Technology Data Exchange (ETDEWEB)

Aldridge, David Franklin; Collier, Sandra L. (U.S. Army Research Laboratory); Marlin, David H. (U.S. Army Research Laboratory); Ostashev, Vladimir E. (NOAA/Environmental Technology Laboratory); Symons, Neill Phillip; Wilson, D. Keith (U.S. Army Cold Regions Research Engineering Lab.)

2005-05-01

This document is intended to serve as a users guide for the time-domain atmospheric acoustic propagation suite (TDAAPS) program developed as part of the Department of Defense High-Performance Modernization Office (HPCMP) Common High-Performance Computing Scalable Software Initiative (CHSSI). TDAAPS performs staggered-grid finite-difference modeling of the acoustic velocity-pressure system with the incorporation of spatially inhomogeneous winds. Wherever practical the control structure of the codes are written in C++ using an object oriented design. Sections of code where a large number of calculations are required are written in C or F77 in order to enable better compiler optimization of these sections. The TDAAPS program conforms to a UNIX style calling interface. Most of the actions of the codes are controlled by adding flags to the invoking command line. This document presents a large number of examples and provides new users with the necessary background to perform acoustic modeling with TDAAPS.

Biomechanical evaluation of different abutment-implant connections - A nonlinear finite element analysis

Science.gov (United States)

Ishak, Muhammad Ikman; Shafi, Aisyah Ahmad; Rosli, M. U.; Khor, C. Y.; Zakaria, M. S.; Rahim, Wan Mohd Faizal Wan Abd; Jamalludin, Mohd Riduan

2017-09-01

The success of dental implant surgery is majorly dependent on the stability of prosthesis to anchor to implant body as well as the integration of implant body to bone. The attachment between dental implant body and abutment plays a vital role in attributing to the stability of dental implant system. A good connection between implant body cavity to abutment may minimize the complications of abutment loosening and implant fractures as widely reported in clinical findings. The aim of this paper is to investigate the effect of different abutment-implant connections on stress dispersion within the abutment and implant bodies as well as displacement of implant body via three-dimensional (3-D) finite element analysis (FEA). A 3-D model of mandible was reconstructed from computed tomography (CT) image datasets using an image-processing software with the selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone was modelled as compact (cortical) and porous (cancellous) structures. Besides, three implant bodies and three generic models of abutment with different types of connections - tapered interference fit (TIF), tapered integrated screwed-in (TIS) and screw retention (SR) were created using computer-aided design (CAD) software and all models were then analysed via 3D FEA software. Occlusal forces of 114.6 N, 17.2 N and 23.4 N were applied in the axial, lingual and mesio-distal directions, respectively, on the top surface of first molar crown. All planes of the mandibular bone model were rigidly fixed. The result exhibited that abutment with TIS connection produced the most favourable stress and displacement outcomes as compared to other attachment types. This is due to the existence of integrated screw at the bottom portion of tapered abutment which increases the motion resistance.

Size validity of plasma-metamaterial cloaking monitored by scattering wave in finite-difference time-domain method

Directory of Open Access Journals (Sweden)

Alexandre Bambina

2018-01-01

Full Text Available Limitation of the cloak-size reduction is investigated numerically by a finite-difference time-domain (FDTD method. A metallic pole that imitates an antenna is cloaked with an anisotropic and parameter-gradient medium against electromagnetic-wave propagation in microwave range. The cloaking structure is a metamaterial submerged in a plasma confined in a vacuum chamber made of glass. The smooth-permittivity plasma can be compressed in the radial direction, which enables us to decrease the size of the cloak. Theoretical analysis is performed numerically by comparing scattering waves in various cases; there exists a high reduction of the scattering wave when the radius of the cloak is larger than a quarter of one wavelength. This result indicates that the required size of the cloaking layer is more than an object scale in the Rayleigh scattering regime.

Application of finite difference method in the study of diffusion with chemical kinetics of first order

Directory of Open Access Journals (Sweden)

Beltrán-Prieto Juan Carlos

2016-01-01

Full Text Available The mathematical modelling of diffusion of a bleaching agent into a porous material is studied in the present paper. Law of mass conservation was applied to analize the mass transfer of a reactant from the bulk into the external surface of a solid geometrically described as a flat plate. After diffusion of the reactant, surface reaction following kinetics of first order was considered to take place. The solution of the differential equation that described the process leaded to an equation that represents the concentration profile in function of distance, porosity and Thiele modulus. The case of interfacial mass resistance is also discused. In this case, finite difference method was used for the solution of the differential equation taking into account the respective boundary conditions. The profile of concentration can be obtained after numerical especification of Thiele modulus and Biot number.

Elastic Stress Analysis of Rotating Functionally Graded Annular Disk of Variable Thickness Using Finite Difference Method

Directory of Open Access Journals (Sweden)

Mohammad Hadi Jalali

2018-01-01

Full Text Available Elastic stress analysis of rotating variable thickness annular disk made of functionally graded material (FGM is presented. Elasticity modulus, density, and thickness of the disk are assumed to vary radially according to a power-law function. Radial stress, circumferential stress, and radial deformation of the rotating FG annular disk of variable thickness with clamped-clamped (C-C, clamped-free (C-F, and free-free (F-F boundary conditions are obtained using the numerical finite difference method, and the effects of the graded index, thickness variation, and rotating speed on the stresses and deformation are evaluated. It is shown that using FG material could decrease the value of radial stress and increase the radial displacement in a rotating thin disk. It is also demonstrated that increasing the rotating speed can strongly increase the stress in the FG annular disk.

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)

A multiscale mortar multipoint flux mixed finite element method

KAUST Repository

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.

Convergence analysis of the rebalance methods in multiplying finite slab having periodic boundary conditions

International Nuclear Information System (INIS)

Hong, Ser Gi; Lee, Young Ouk; Song, Jae Seung

2009-01-01

This paper analyzes the convergence of the rebalance iteration methods for the discrete ordinates transport equation in the multiplying finite slab problem. The finite slab is assumed to be homogeneous and it has the periodic boundary conditions. A general formulation is used to include three well-known rebalance methods of the linearized form in a unified way. The rebalance iteration methods considered in this paper are the CMR (Coarse-Mesh Rebalance), the CMFD (Coarse-Mesh Finite Difference), and p-CMFD (Partial Current-Based Coarse Mesh Finite Difference) methods which have been popularly used in the reactor physics. The convergence analysis is performed with the well-known Fourier analysis through a linearization. The analyses are applied for one-group problems. The theoretical analysis shows that there are one fundamental mode and N-1 Eigen-modes which determine the convergence if the finite slab is divided into N uniform meshes. The numerical tests show that the Fourier convergence analysis provides the reasonable estimate of the numerical spectral radii for the model problems and the spectral radius for the finite slab approaches the one for the infinite slab as the thickness of the slab increases. (author)

Method and system employing finite state machine modeling to identify one of a plurality of different electric load types

Science.gov (United States)

Du, Liang; Yang, Yi; Harley, Ronald Gordon; Habetler, Thomas G.; He, Dawei

2016-08-09

A system is for a plurality of different electric load types. The system includes a plurality of sensors structured to sense a voltage signal and a current signal for each of the different electric loads; and a processor. The processor acquires a voltage and current waveform from the sensors for a corresponding one of the different electric load types; calculates a power or current RMS profile of the waveform; quantizes the power or current RMS profile into a set of quantized state-values; evaluates a state-duration for each of the quantized state-values; evaluates a plurality of state-types based on the power or current RMS profile and the quantized state-values; generates a state-sequence that describes a corresponding finite state machine model of a generalized load start-up or transient profile for the corresponding electric load type; and identifies the corresponding electric load type.

Relativistic finite-temperature Thomas-Fermi model

Science.gov (United States)

Faussurier, Gérald

2017-11-01

We investigate the relativistic finite-temperature Thomas-Fermi model, which has been proposed recently in an astrophysical context. Assuming a constant distribution of protons inside the nucleus of finite size avoids severe divergence of the electron density with respect to a point-like nucleus. A formula for the nuclear radius is chosen to treat any element. The relativistic finite-temperature Thomas-Fermi model matches the two asymptotic regimes, i.e., the non-relativistic and the ultra-relativistic finite-temperature Thomas-Fermi models. The equation of state is considered in detail. For each version of the finite-temperature Thomas-Fermi model, the pressure, the kinetic energy, and the entropy are calculated. The internal energy and free energy are also considered. The thermodynamic consistency of the three models is considered by working from the free energy. The virial question is also studied in the three cases as well as the relationship with the density functional theory. The relativistic finite-temperature Thomas-Fermi model is far more involved than the non-relativistic and ultra-relativistic finite-temperature Thomas-Fermi models that are very close to each other from a mathematical point of view.

Determination of excited states of quantum systems by finite difference time domain method (FDTD) with supersymmetric quantum mechanics (SUSY-QM)

Energy Technology Data Exchange (ETDEWEB)

Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id [Physics Study Program, University of Mataram, Jln. Majapahit 62 Mataram, NTB (Indonesia)

2016-04-19

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows

International Nuclear Information System (INIS)

Ansanay-Alex, G.

2009-01-01

The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions

KAUST Repository

Settle, Sean O.

2013-01-01

The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.

Supersymmetric theories and finiteness

International Nuclear Information System (INIS)

Helayel-Neto, J.A.

1989-01-01

We attempt here to present a short survey of the all-order finite Lagrangian field theories known at present in four-and two-dimensional space-times. The question of the possible relevance of these ultraviolet finite models in the formulation of consistent unified frameworks for the fundamental forces is also addressed to. (author)

Solving hyperbolic equations with finite volume methods

CERN Document Server

Vázquez-Cendón, M Elena

2015-01-01

Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software withi...

Three-dimensional body-wave model of Nepal using finite difference tomography

Science.gov (United States)

Ho, T. M.; Priestley, K.; Roecker, S. W.

2017-12-01

The processes occurring during continent-continent collision are still poorly understood. Ascertaining the seismic properties of the crust and uppermost mantle in such settings provides insight into continental rheology and geodynamics. The most active present-day continent-continent collision is that of India with Eurasia which has created the Himalayas and the Tibetan Plateau. Nepal provides an ideal laboratory for imaging the crustal processes resulting from the Indo-Eurasia collision. We build body wave models using local body wave arrivals picked at stations in Nepal deployed by the Department of Mining and Geology of Nepal. We use the tomographic inversion method of Roecker et al. [2006], the key feature of which is that the travel times are generated using a finite difference solution to the eikonal equation. The advantage of this technique is increased accuracy in the highly heterogeneous medium expected for the Himalayas. Travel times are calculated on a 3D Cartesian grid with a grid spacing of 6 km and intragrid times are estimated by trilinear interpolation. The gridded area spans a region of 80-90o longitude and 25-30o latitude. For a starting velocity model, we use IASP91. Inversion is performed using the LSQR algorithm. Since the damping parameter can have a significant effect on the final solution, we tested a range of damping parameters to fully explore its effect. Much of the seismicity is clustered to the West of Kathmandu at depths Small areas of strong fast wavespeeds exist in the centre of the region in the upper 30 km of the crust. At depths of 40-50 km, large areas of slow wavespeeds are present which track along the plate boundary.

PT Symmetry and QCD: Finite Temperature and Density

Directory of Open Access Journals (Sweden)

Michael C. Ogilvie

2009-04-01

Full Text Available The relevance of PT symmetry to quantum chromodynamics (QCD, the gauge theory of the strong interactions, is explored in the context of finite temperature and density. Two significant problems in QCD are studied: the sign problem of finite-density QCD, and the problem of confinement. It is proven that the effective action for heavy quarks at finite density is PT-symmetric. For the case of 1+1 dimensions, the PT-symmetric Hamiltonian, although not Hermitian, has real eigenvalues for a range of values of the chemical potential μ, solving the sign problem for this model. The effective action for heavy quarks is part of a potentially large class of generalized sine-Gordon models which are non-Hermitian but are PT-symmetric. Generalized sine-Gordon models also occur naturally in gauge theories in which magnetic monopoles lead to confinement. We explore gauge theories where monopoles cause confinement at arbitrarily high temperatures. Several different classes of monopole gases exist, with each class leading to different string tension scaling laws. For one class of monopole gas models, the PT-symmetric affine Toda field theory emerges naturally as the effective theory. This in turn leads to sine-law scaling for string tensions, a behavior consistent with lattice simulations.

A first course in finite elements

CERN Document Server

Fish, Jacob

2007-01-01

Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations.  Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts

Features of finite quantum field theories

International Nuclear Information System (INIS)

Boehm, M.; Denner, A.

1987-01-01

We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)

The transient response for different types of erodable surface thermocouples using finite element analysis

Directory of Open Access Journals (Sweden)

Mohammed Hussein

2007-01-01

Full Text Available The transient response of erodable surface thermocouples has been numerically assessed by using a two dimensional finite element analysis. Four types of base metal erodable surface thermocouples have been examined in this study, included type-K (alumel-chromel, type-E (chromel-constantan, type-T (copper-constantan, and type-J (iron-constantan with 50 mm thick- ness for each. The practical importance of these types of thermocouples is to be used in internal combustion engine studies and aerodynamics experiments. The step heat flux was applied at the surface of the thermocouple model. The heat flux from the measurements of the surface temperature can be commonly identified by assuming that the heat transfer within these devices is one-dimensional. The surface temperature histories at different positions along the thermocouple are presented. The normalized surface temperature histories at the center of the thermocouple for different types at different response time are also depicted. The thermocouple response to different heat flux variations were considered by using a square heat flux with 2 ms width, a sinusoidal surface heat flux variation width 10 ms period and repeated heat flux variation with 2 ms width. The present results demonstrate that the two dimensional transient heat conduction effects have a significant influence on the surface temperature history measurements made with these devices. It was observed that the surface temperature history and the transient response for thermocouple type-E are higher than that for other types due to the thermal properties of this thermocouple. It was concluded that the thermal properties of the surrounding material do have an impact, but the properties of the thermocouple and the insulation materials also make an important contribution to the net response.

3-D spherical harmonics code FFT3 by the finite Fourier transformation method

International Nuclear Information System (INIS)

Kobayashi, K.

1997-01-01

In the odd order spherical harmonics method, the rigorous boundary condition at the material interfaces is that the even moments of the angular flux and the normal components of the even order moments of current vectors must be continuous. However, it is difficult to derive spatial discretized equations by the finite difference or finite element methods, which satisfy this material interface condition. It is shown that using the finite Fourier transformation method, space discretized equations which satisfy this interface condition can be easily derived. The discrepancies of the flux distribution near void region between spherical harmonics method codes may be due to the difference of application of the material interface condition. (author)

A General Finite Element Scheme for Limit State Analysis and Optimization

DEFF Research Database (Denmark)

Damkilde, Lars

1999-01-01

Limit State analysis which is based on a perfect material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures....... The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes...... for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem...

Accelerated cardiac cine MRI using locally low rank and finite difference constraints.

Science.gov (United States)

Miao, Xin; Lingala, Sajan Goud; Guo, Yi; Jao, Terrence; Usman, Muhammad; Prieto, Claudia; Nayak, Krishna S

2016-07-01

To evaluate the potential value of combining multiple constraints for highly accelerated cardiac cine MRI. A locally low rank (LLR) constraint and a temporal finite difference (FD) constraint were combined to reconstruct cardiac cine data from highly undersampled measurements. Retrospectively undersampled 2D Cartesian reconstructions were quantitatively evaluated against fully-sampled data using normalized root mean square error, structural similarity index (SSIM) and high frequency error norm (HFEN). This method was also applied to 2D golden-angle radial real-time imaging to facilitate single breath-hold whole-heart cine (12 short-axis slices, 9-13s single breath hold). Reconstruction was compared against state-of-the-art constrained reconstruction methods: LLR, FD, and k-t SLR. At 10 to 60 spokes/frame, LLR+FD better preserved fine structures and depicted myocardial motion with reduced spatio-temporal blurring in comparison to existing methods. LLR yielded higher SSIM ranking than FD; FD had higher HFEN ranking than LLR. LLR+FD combined the complimentary advantages of the two, and ranked the highest in all metrics for all retrospective undersampled cases. Single breath-hold multi-slice cardiac cine with prospective undersampling was enabled with in-plane spatio-temporal resolutions of 2×2mm(2) and 40ms. Highly accelerated cardiac cine is enabled by the combination of 2D undersampling and the synergistic use of LLR and FD constraints. Copyright © 2016 Elsevier Inc. All rights reserved.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II. [LMFBR

Energy Technology Data Exchange (ETDEWEB)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1977-11-01

The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently.

Simulations of Chemotaxis and Random Motility in Finite Domains

National Research Council Canada - National Science Library

Jabbarzadeh, Ehsan; Abrams, Cameron F

2005-01-01

.... The model couples fully time-dependent finite-difference solution of a reaction-diffusion equation for the concentration field of a generic chemoattractant to biased random walks representing individual moving cells...

Optimization of Finite-Differencing Kernels for Numerical Relativity Applications

Directory of Open Access Journals (Sweden)

Roberto Alfieri

2018-05-01

Full Text Available A simple optimization strategy for the computation of 3D finite-differencing kernels on many-cores architectures is proposed. The 3D finite-differencing computation is split direction-by-direction and exploits two level of parallelism: in-core vectorization and multi-threads shared-memory parallelization. The main application of this method is to accelerate the high-order stencil computations in numerical relativity codes. Our proposed method provides substantial speedup in computations involving tensor contractions and 3D stencil calculations on different processor microarchitectures, including Intel Knight Landing.

Strong interaction at finite temperature

Indian Academy of Sciences (India)

Quantum chromodynamics; finite temperature; chiral perturbation theory; QCD sum rules. PACS Nos 11.10. ..... at finite temperature. The self-energy diagrams of figure 2 modify it to ..... method of determination at present. Acknowledgement.

Summability calculus a comprehensive theory of fractional finite sums

CERN Document Server

Alabdulmohsin, Ibrahim M

2018-01-01

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergr...

Mathematical aspects of finite element methods for incompressible viscous flows

Science.gov (United States)

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.

Isobaric expansion coefficient and isothermal compressibility for a finite-size ideal Fermi gas system

International Nuclear Information System (INIS)

Su, Guozhen; Chen, Liwei; Chen, Jincan

2014-01-01

Due to quantum size effects (QSEs), the isobaric thermal expansion coefficient and isothermal compressibility well defined for macroscopic systems are invalid for finite-size systems. The two parameters are redefined and calculated for a finite-size ideal Fermi gas confined in a rectangular container. It is found that the isobaric thermal expansion coefficient and isothermal compressibility are generally anisotropic, i.e., they are generally different in different directions. Moreover, it is found the thermal expansion coefficient may be negative in some directions under the condition that the pressures in all directions are kept constant. - Highlights: • Isobaric thermal expansion coefficient and isothermal compressibility are redefined. • The two parameters are calculated for a finite-size ideal Fermi gas. • The two parameters are generally anisotropic for a finite-size system. • Isobaric thermal expansion coefficient may be negative in some directions

A Fast O(N log N Finite Difference Method for the One-Dimensional Space-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

Treena Basu

2015-10-01

Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Uniform stable conformal convolutional perfectly matched layer for enlarged cell technique conformal finite-difference time-domain method

International Nuclear Information System (INIS)

Wang Yue; Wang Jian-Guo; Chen Zai-Gao

2015-01-01

Based on conformal construction of physical model in a three-dimensional Cartesian grid, an integral-based conformal convolutional perfectly matched layer (CPML) is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain (ECT-CFDTD) method is used to simulate the wave propagation inside a perfect electric conductor (PEC) waveguide. The algorithm has the same numerical stability as the ECT-CFDTD method. For the long-time propagation problems of an evanescent wave in a waveguide, several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML. Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide. (paper)

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

Science.gov (United States)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

Lattice study of finite volume effect in HVP for muon g-2

Directory of Open Access Journals (Sweden)

Izubuchi Taku

2018-01-01

Full Text Available We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp,in lattice QCD by comparison with two different volumes, L4 = (5.44 and (8.14 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a−1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

Lattice study of finite volume effect in HVP for muon g-2

Science.gov (United States)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

A generalized volumetric dispersion model for a class of two-phase separation/reaction: finite difference solutions

Science.gov (United States)

Siripatana, Chairat; Thongpan, Hathaikarn; Promraksa, Arwut

2017-03-01

This article explores a volumetric approach in formulating differential equations for a class of engineering flow problems involving component transfer within or between two phases. In contrast to conventional formulation which is based on linear velocities, this work proposed a slightly different approach based on volumetric flow-rate which is essentially constant in many industrial processes. In effect, many multi-dimensional flow problems found industrially can be simplified into multi-component or multi-phase but one-dimensional flow problems. The formulation is largely generic, covering counter-current, concurrent or batch, fixed and fluidized bed arrangement. It was also intended to use for start-up, shut-down, control and steady state simulation. Since many realistic and industrial operation are dynamic with variable velocity and porosity in relation to position, analytical solutions are rare and limited to only very simple cases. Thus we also provide a numerical solution using Crank-Nicolson finite difference scheme. This solution is inherently stable as tested against a few cases published in the literature. However, it is anticipated that, for unconfined flow or non-constant flow-rate, traditional formulation should be applied.

Finiteness of quantum field theories and supersymmetry

International Nuclear Information System (INIS)

Lucha, W.; Neufeld, H.

1986-01-01

We study the consequences of finiteness for a general renormalizable quantum field theory by analysing the finiteness conditions resulting from the requirement of absence of divergent contributions to the renormalizations of the parameters of an arbitrary gauge theory. In all cases considered, the well-known two-loop finite supersymmetric theories prove to be the unique solution of the finiteness criterion. (Author)

An Efficient Explicit Finite-Difference Scheme for Simulating Coupled Biomass Growth on Nutritive Substrates

Directory of Open Access Journals (Sweden)

G. F. Sun

2015-01-01

Full Text Available A novel explicit finite-difference (FD method is presented to simulate the positive and bounded development process of a microbial colony subjected to a substrate of nutrients, which is governed by a nonlinear parabolic partial differential equations (PDE system. Our explicit FD scheme is uniquely designed in such a way that it transfers the nonlinear terms in the original PDE into discrete sets of linear ones in the algebraic equation system that can be solved very efficiently, while ensuring the stability and the boundedness of the solution. This is achieved through (1 a proper design of intertwined FD approximations for the diffusion function term in both time and spatial variations and (2 the control of the time-step through establishing theoretical stability criteria. A detailed theoretical stability analysis is conducted to reveal that our FD method is indeed stable. Our examples verified the fact that the numerical solution can be ensured nonnegative and bounded to simulate the actual physics. Numerical examples have also been presented to demonstrate the efficiency of the proposed scheme. The present scheme is applicable for solving similar systems of PDEs in the investigation of the dynamics of biological films.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

Energy Technology Data Exchange (ETDEWEB)

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.; Jung, Ki Won; Deng, Zhiqun

2015-10-28

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3D sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.

Observations on finite quantum mechanics

International Nuclear Information System (INIS)

Balian, R.; Itzykson, C.

1986-01-01

We study the canonical transformations of the quantum mechanics on a finite phase space. For simplicity we assume that the configuration variable takes an odd prime number 4 K±1 of distinct values. We show that the canonical group is unitarily implemented. It admits a maximal abelian subgroup of order 4 K, commuting with the finite Fourier transform F, a finite analogue of the harmonic oscillator group. This provides a natural construction of F 1/K and of an orthogonal basis of eigenstates of F [fr

Automatic Construction of Finite Algebras

Institute of Scientific and Technical Information of China (English)

张健

1995-01-01

This paper deals with model generation for equational theories,i.e.,automatically generating (finite)models of a given set of (logical) equations.Our method of finite model generation and a tool for automatic construction of finite algebras is described.Some examples are given to show the applications of our program.We argue that,the combination of model generators and theorem provers enables us to get a better understanding of logical theories.A brief comparison betwween our tool and other similar tools is also presented.

Application of hexagonal element scheme in finite element method to three-dimensional diffusion problem of fast reactors

International Nuclear Information System (INIS)

Ishiguro, Misako; Higuchi, Kenji

1983-01-01

The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)

Toward finite quantum field theories

International Nuclear Information System (INIS)

Rajpoot, S.; Taylor, J.G.

1986-01-01

The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)

Experimental Methods for Implementing Graphene Contacts to Finite Bandgap Semiconductors

DEFF Research Database (Denmark)

Meyer-Holdt, Jakob

Present Ph.D. thesis describes my work on implanting graphene as electrical contact to finite bandgap semiconductors. Different transistor architectures, types of graphene and finite bandgap semiconductors have been employed. The device planned from the beginning of my Ph.D. fellowship...... contacts to semiconductor nanowires, more specifically, epitaxially grown InAs nanowires. First, we tried a top down method where CVD graphene was deposited on substrate supported InAs nanowires followed by selective graphene ashing to define graphene electrodes. While electrical contact between...

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 finite elements

International Nuclear Information System (INIS)

Wachspress, E.

2009-01-01

Triangles and rectangles are the ubiquitous elements in finite element studies. Only these elements admit polynomial basis functions. Rational functions provide a basis for elements having any number of straight and curved sides. Numerical complexities initially associated with rational bases precluded extensive use. Recent analysis has reduced these difficulties and programs have been written to illustrate effectiveness. Although incorporation in major finite element software requires considerable effort, there are advantages in some applications which warrant implementation. An outline of the basic theory and of recent innovations is presented here. (authors)

Characterization of resonances using finite size effects

International Nuclear Information System (INIS)

Pozsgay, B.; Takacs, G.

2006-01-01

We develop methods to extract resonance widths from finite volume spectra of (1+1)-dimensional quantum field theories. Our two methods are based on Luscher's description of finite size corrections, and are dubbed the Breit-Wigner and the improved ''mini-Hamiltonian'' method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in 1+1 dimensions, the extension to physical 3+1 space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra

Calculation of electrical potentials on the surface of a realistic head model by finite differences

International Nuclear Information System (INIS)

Lemieux, L.; McBride, A.; Hand, J.W.

1996-01-01

We present a method for the calculation of electrical potentials at the surface of realistic head models from a point dipole generator based on a 3D finite-difference algorithm. The model was validated by comparing calculated values with those obtained algebraically for a three-shell spherical model. For a 1.25 mm cubic grid size, the mean error was 4.9% for a superficial dipole (3.75 mm from the inner surface of the skull) pointing in the radial direction. The effect of generator discretization and node spacing on the accuracy of the model was studied. Three values of the node spacing were considered: 1, 1.25 and 1.5 mm. The mean relative errors were 4.2, 6.3 and 9.3%, respectively. The quality of the approximation of a point dipole by an array of nodes in a spherical neighbourhood did not depend significantly on the number of nodes used. The application of the method to a conduction model derived from MRI data is demonstrated. (author)

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.

Supersymmetry at finite temperature

International Nuclear Information System (INIS)

Clark, T.E.; Love, S.T.

1983-01-01

Finite-temperature supersymmetry (SUSY) is characterized by unbroken Ward identities for SUSY variations of ensemble averages of Klein-operator inserted imaginary time-ordered products of fields. Path-integral representations of these products are defined and the Feynman rules in superspace are given. The finite-temperature no-renormalization theorem is derived. Spontaneously broken SUSY at zero temperature is shown not to be restored at high temperature. (orig.)

An introduction to finite tight frames

CERN Document Server

Waldron, Shayne F D

2018-01-01

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. Key features and topics: * First book entirely devoted to finite frames * Extensive exercises and MATLAB examples for classroom use * Important examples, such as harmonic and Heisenberg frames, are presented in preliminary chapters, encouraging readers to explore and develop an intuitive feeling for tight frames * Later chapters delve into general theory details and recent research results * Many illustrations showing the special aspects of the geometry of finite frames * Provides an overview of the field of finite tight frames * Discusses future research directions in the field Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook ...

Subshifts of finite type and self-similar sets

Science.gov (United States)

Jiang, Kan; Dajani, Karma

2017-02-01

Let K\\subset {R} be a self-similar set generated by some iterated function system. In this paper we prove, under some assumptions, that K can be identified with a subshift of finite type. With this identification, we can calculate the Hausdorff dimension of K as well as the set of elements in K with unique codings using the machinery of Mauldin and Williams (1988 Trans. Am. Math. Soc. 309 811-29). We give three different applications of our main result. Firstly, we calculate the Hausdorff dimension of the set of points of K with multiple codings. Secondly, in the setting of β-expansions, when the set of all the unique codings is not a subshift of finite type, we can calculate in some cases the Hausdorff dimension of the univoque set. Motivated by this application, we prove that the set of all the unique codings is a subshift of finite type if and only if it is a sofic shift. This equivalent condition was not mentioned by de Vries and Komornik (2009 Adv. Math. 221 390-427, theorem 1.8). Thirdly, for the doubling map with asymmetrical holes, we give a sufficient condition such that the survivor set can be identified with a subshift of finite type. The third application partially answers a problem posed by Alcaraz Barrera (2014 PhD Thesis University of Manchester).

Phase transitions in finite systems

Energy Technology Data Exchange (ETDEWEB)

Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), DSM-CEA / IN2P3-CNRS, 14 - Caen (France); Gulminelli, F. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire

2002-07-01

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)

Phase transitions in finite systems

International Nuclear Information System (INIS)

Chomaz, Ph.; Gulminelli, F.

2002-01-01

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)

Non-linear finite element modeling

DEFF Research Database (Denmark)

Mikkelsen, Lars Pilgaard

The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...

Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays

Directory of Open Access Journals (Sweden)

T. S. Doan

2012-01-01

Full Text Available We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.

An analysis of millimetre-wave interferometry on Hall thruster plumes by finite difference time domain simulations

International Nuclear Information System (INIS)

Lee, Jungpyo; Cappelli, Mark A

2008-01-01

In this paper, we present finite difference time domain (FDTD) simulations of millimetre-wave propagation through the near-field plasma plume of low power Hall thrusters. The simulations are intended to address potential issues (collisions, magnetic fields) that may affect the validity of simple theory used for phase shift determination in the recent measurements of plasma density using microwave interferometry (Cappelli et al 2006 J. Phys. D: Appl. Phys. 39 4582). One-dimensional plane wave FDTD simulations indicate that plasma non-uniformities along the direction of wave propagation have only a minor effect on the phase shifts estimated from collisionless, non-magnetized wave propagation through a path-length averaged plasma slab. Three-dimensional FDTD simulations that also account for electron collisions and magnetic fields indicate that the departure from the use of usual simple models is no more than about 15%, well within the limits of uncertainty in the experimental measurements taken within the near field of these plasma sources

Representation of boundary conditions in thermal reactor global analysis by diffusion theory employing finite difference approximation

International Nuclear Information System (INIS)

Paul, O.P.K.

1978-01-01

An approach to simulate the flux vanishing boundary condition in solving the two group coupled neutron diffusion equations in three dimensions (x, y, z) employed to calculate the flux distribution and keff of the reactor is summarised. This is of particular interest when the flux vanishing boundary in x, y, z directions is not an integral multiple of the mesh spacings in these directions. The method assumes the flux to be negative, hypothetically at the mesh points lying outside the boundary and thus the finite difference formalism for Laplacian operator, taking into account six neighbours of a mesh point in a square mesh arrangement, is expressed in a general form so as to account for the boundary mesh points of the system. This approach has been incorporated in a three dimensional diffusion code similar to TAPPS23 and has been used for IRT-2000 reactor and the results are quite satisfactory. (author)

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

Science.gov (United States)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The finite-dimensional Freeman thesis.

Science.gov (United States)

Rudolph, Lee

2008-06-01

I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.

Sound radiation from finite surfaces

DEFF Research Database (Denmark)

Brunskog, Jonas

2013-01-01

A method to account for the effect of finite size in acoustic power radiation problem of planar surfaces using spatial windowing is developed. Cremer and Heckl presents a very useful formula for the power radiating from a structure using the spatially Fourier transformed velocity, which combined...... with spatially windowing of a plane waves can be used to take into account the finite size. In the present paper, this is developed by means of a radiation impedance for finite surfaces, that is used instead of the radiation impedance for infinite surfaces. In this way, the spatial windowing is included...

Photon propagators at finite temperature

International Nuclear Information System (INIS)

Yee, J.H.

1982-07-01

We have used the real time formalism to compute the one-loop finite temperature corrections to the photon self energies in spinor and scalar QED. We show that, for a real photon, only the transverse components develop the temperature-dependent masses, while, for an external static electromagnetic field applied to the finite temperature system, only the static electric field is screened by thermal fluctuations. After showing how to compute systematically the imaginary parts of the finite temperature Green functions, we have attempted to give a microscopic interpretation of the imaginary parts of the self energies. (author)

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

Science.gov (United States)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

Energy flow in plate assembles by hierarchical version of finite element method

DEFF Research Database (Denmark)

Wachulec, Marcin; Kirkegaard, Poul Henning

method has been proposed. In this paper a modified hierarchical version of finite element method is used for modelling of energy flow in plate assembles. The formulation includes description of in-plane forces so that planes lying in different planes can be modelled. Two examples considered are: L......The dynamic analysis of structures in medium and high frequencies are usually focused on frequency and spatial averages of energy of components, and not the displacement/velocity fields. This is especially true for structure-borne noise modelling. For the analysis of complicated structures...... the finite element method has been used to study the energy flow. The finite element method proved its usefulness despite the computational expense. Therefore studies have been conducted in order to simplify and reduce the computations required. Among others, the use of hierarchical version of finite element...

Quantum Chromodynamic at finite temperature

International Nuclear Information System (INIS)

Magalhaes, N.S.

1987-01-01

A formal expression to the Gibbs free energy of topological defects of quantum chromodynamics (QCD)by using the semiclassical approach in the context of field theory at finite temperature and in the high temperature limit is determined. This expression is used to calculate the free energy of magnetic monopoles. Applying the obtained results to a method in which the free energy of topological defects of a theory may indicate its different phases, its searched for informations about phases of QCD. (author) [pt

Finite element method for neutron diffusion problems in hexagonal geometry

International Nuclear Information System (INIS)

Wei, T.Y.C.; Hansen, K.F.

1975-06-01

The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes

Axial anomaly at finite temperature

International Nuclear Information System (INIS)

Chaturvedi, S.; Gupte, Neelima; Srinivasan, V.

1985-01-01

The Jackiw-Bardeen-Adler anomaly for QED 4 and QED 2 are calculated at finite temperature. It is found that the anomaly is independent of temperature. Ishikawa's method [1984, Phys. Rev. Lett. vol. 53 1615] for calculating the quantised Hall effect is extended to finite temperature. (author)

Collaborative Systems – Finite State Machines

Directory of Open Access Journals (Sweden)

Ion IVAN

2011-01-01

Full Text Available In this paper the finite state machines are defined and formalized. There are presented the collaborative banking systems and their correspondence is done with finite state machines. It highlights the role of finite state machines in the complexity analysis and performs operations on very large virtual databases as finite state machines. It builds the state diagram and presents the commands and documents transition between the collaborative systems states. The paper analyzes the data sets from Collaborative Multicash Servicedesk application and performs a combined analysis in order to determine certain statistics. Indicators are obtained, such as the number of requests by category and the load degree of an agent in the collaborative system.

Robust mixed finite element methods to deal with incompressibility in finite strain in an industrial framework

International Nuclear Information System (INIS)

Al-Akhrass, Dina

2014-01-01

Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)

Finite size effects and symmetry breaking in the evolution of networks of competing Boolean nodes

International Nuclear Information System (INIS)

Liu, M; Bassler, K E

2011-01-01

Finite size effects on the evolutionary dynamics of Boolean networks are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. Previous studies have found that large networks evolve to a statistical steady state that is both critical and highly canalized, and that the evolution of canalization, which is a form of robustness found in genetic regulatory networks, is associated with a particular symmetry of the evolutionary dynamics. Here, it is found that finite size networks evolve in a fundamentally different way than infinitely large networks do. The symmetry of the evolutionary dynamics of infinitely large networks that selects for canalizing Boolean functions is broken in the evolutionary dynamics of finite size networks. In finite size networks, there is an additional selection for input-inverting Boolean functions that output a value opposite to the majority of input values. The reason for the symmetry breaking in the evolutionary dynamics is found to be due to the need for nodes in finite size networks to behave differently in order to cooperate so that the system collectively performs as efficiently as possible. The results suggest that both finite size effects and symmetry are fundamental for understanding the evolution of real-world complex networks, including genetic regulatory networks.

Introduction to nonlinear finite element analysis

CERN Document Server

Kim, Nam-Ho

2015-01-01

This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

Finite element analysis of multilayer coextrusion.

Energy Technology Data Exchange (ETDEWEB)

Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann

2011-09-01

Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.

Finite element solution of two dimensional time dependent heat equation

International Nuclear Information System (INIS)

Maaz

1999-01-01

A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)

Extrusion Process by Finite Volume Method Using OpenFoam Software

International Nuclear Information System (INIS)

Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose; Ivankovic, Alojz

2011-01-01

The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.

Finite p′-nilpotent groups. II

Directory of Open Access Journals (Sweden)

S. Srinivasan

1987-01-01

Full Text Available In this paper we continue the study of finite p′-nilpotent groups that was started in the first part of this paper. Here we give a complete characterization of all finite groups that are not p′-nilpotent but all of whose proper subgroups are p′-nilpotent.

Electrical machine analysis using finite elements

CERN Document Server

Bianchi, Nicola

2005-01-01

OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I

What is finiteness? (Abhishek Banerjee) (Indian Institute of Science)

Indian Academy of Sciences (India)

Do finites get enough respect? • Finiteness is easy, no? • Just count whether 1, 2, 3,... • But then we miss out on the true richness of the concept of finitness. • There's more finiteness around. In fact, finiteness is what helps us really understand things. 5 ...

Finite Metric Spaces of Strictly negative Type

DEFF Research Database (Denmark)

Hjorth, Poul G.

If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...

Stability of the nonequilibrium states of a superconductor with a finite difference between the populations of the electron- and hole-like spectral branches

International Nuclear Information System (INIS)

Gal'perin, Y.M.; Kozub, V.I.; Spivak, B.Z.

1981-01-01

The stability of the nonequilibrium states of a superconductor with a finite difference between the populations of the electron- and hole-like spectral branches is investigated. It is shown that an instability similar to the Cooper instability of a normal metal arises at a sufficiently large value of the imbalance. This eliminates the imbalance within quantum-mechanical (nonkinetic) time periods. The consistency of the allowance for the imbalance in the nonequilibrium Ginzburg-Landau equations is discussed

The effect of finite-difference time-domain resolution and power-loss computation method on SAR values in plane-wave exposure of Zubal phantom

International Nuclear Information System (INIS)

Uusitupa, T M; Ilvonen, S A; Laakso, I M; Nikoskinen, K I

2008-01-01

In this paper, the anatomically realistic body model Zubal is exposed to a plane wave. A finite-difference time-domain (FDTD) method is used to obtain field data for specific-absorption-rate (SAR) computation. It is investigated how the FDTD resolution, power-loss computation method and positioning of the material voxels in the FDTD grid affect the SAR results. The results enable one to estimate the effects due to certain fundamental choices made in the SAR simulation