Method of fundamental solutions: singular value decomposition analysis
Copyright policy )Method of fundamental solutions: singular value decomposition analysis
AbstractThe method of fundamental solutions (also known as the singularity or the source method) is a useful technique for solving linear partial differential equations such as the Laplace or the Helmholtz equation. The procedure involves only boundary collocation or boundary fitting and hence is a very fast procedure for the solution of these classes of problems. The resulting coefficient matrix, is however ill‐conditioned and hence the solution accuracy is sensitive to the location of the source points. In this paper, an alternative solution procedure based on the singular value decomposition of the coefficient matrix is suggested and it is shown that the numerical results are extremely accurate (often within machine precision) and relatively independent of the location of the source points. Copyright © 2002 John Wiley & Sons, Ltd.
- Washington University in St. Louis United States
- University of Mary United States
collocation, method of fundamental solutions, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, singular value decomposition, boundary methods, boundary fitting, Boundary element methods for boundary value problems involving PDEs, Laplace equation, error bounds, Stability and convergence of numerical methods for boundary value problems involving PDEs, stability, numerical results, pseudo-inverses, Spectral, collocation and related methods for boundary value problems involving PDEs, Helmholtz equation, singularity method
collocation, method of fundamental solutions, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, singular value decomposition, boundary methods, boundary fitting, Boundary element methods for boundary value problems involving PDEs, Laplace equation, error bounds, Stability and convergence of numerical methods for boundary value problems involving PDEs, stability, numerical results, pseudo-inverses, Spectral, collocation and related methods for boundary value problems involving PDEs, Helmholtz equation, singularity method
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