Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the mathematical modeling of single-phase natural circulation of the University of Genoa's rectangular loop (LOOP#1) by a computer program and using RELAP5 system code is presented.
92 citations
Book•
24 Jun 1992TL;DR: In this paper, a review of EM problems is presented, including some important theorems of separation of variables, separation of variable variables in Cylindrical Coordinates, and separation of variables in Spherical Coordinates.
Abstract: Fundamental Concepts Introduction Review of Electromagnetic Theory Classification of EM Problems Some Important Theorems Analytical Methods Introduction Separation of Variables Separation of Variables in Rectangular Coordinates Separation of Variables in Cylindrical Coordinates Separation of Variables in Spherical Coordinates Some Useful Orthogonal Functions Series Expansion Practical Applications Attenuation Due to Raindrops Concluding Remarks Finite Difference Methods Introduction Finite Difference Schemes Finite Differencing of Parabolic PDEs Finite Differencing of Hyperbolic PDEs Finite Differencing of Elliptic PDEs Accuracy and Stability of FD Solutions Practical Applications I - Guided Structures Practical Applications II - Wave Scattering (FDTD) Absorbing Boundary Conditions for FDTD Finite Differencing for Nonrectangular Systems Numerical Integration Concluding Remarks Variational Methods Introduction Operators in Linear Spaces Calculus of Variations Construction of Functionals from PDEs Rayleigh-Ritz Method Weighted Residual Method Eigenvalue Problems Practical Applications Concluding Remarks Moment Methods Introduction Integral Equations Green's Functions Applications I - Quasi-Static Problems Applications II - Scattering Problems Applications III- Radiation Problems Applications IV - EM Absorption in the Human Body Concluding Remarks Finite Element Method Introduction Solution of Laplace's Equation Solution of Poisson's Equation Solution of the Wave Equation Automatic Mesh Generation I - Rectangular Domains Automatic Mesh Generation II - Arbitrary Domains Bandwidth Reduction Higher Order Elements Three-Dimensional Elements Finite Element Methods for Exterior Problems Finite-Element Time-Domain Method Concluding Remarks Transmission-line-matrix Method Introduction Transmission-line Equations Solution of Diffusion Equation Solution of Wave Equations Inhomogeneous and Lossy Media in TLM Three-Dimensional TLM Mesh Error Sources and Correction Absorbing Boundary Conditions Concluding Remarks Monte Carlo Methods Introduction Generation of Random Numbers and Variables Evaluation of Error Numerical Integration Solution of Potential Problems Regional Monte Carlo Methods Time-Dependent Problems Concluding Remarks Method of Lines Introduction Solution of Laplace's Equation Solution of Wave Equation Time-Domain Solution Concluding Remarks References Problems APPENDICES Vector Relations Vector Identities Vector Theorems Orthogonal Coordinates Programming in MATLAB MATLAB Fundamentals Using MATLAB to Plot Programming with MATLAB Functions Solving Equations Programming Hints Other Useful MATLAB Commands Solution of Simultaneous Equations Elimination Methods Iterative Methods Matrix Inversion Eigenvalue Problems Answers to Odd-Numbered Problems
92 citations
TL;DR: In this article, the authors compared the accuracies of various finite difference (FD), finite element (FE) and spectral methods (SDF) for the Stokes equations for creeping, highly viscous flows.
92 citations
TL;DR: A time stable discretization is derived for the second-order wave equation with discontinuous coefficients using narrow-diagonal summation by parts operators and patched to its neighbors by using a penalty method, leading to fully explicit time integration.
92 citations
TL;DR: In this paper, a meshless generalized finite difference method (GFDM) was proposed for water wave-structure interactions with multiple bottom-seated-cylinder-array structures based on the moving least squares theory and second-order Taylor series expansion.
91 citations