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Numerical analysis of the method of fundamental solution for harmonic problems in annular domains
Author(s) -
Tsangaris Th.,
Smyrlis Y.S.,
Karageorghis A.
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20104
Subject(s) - mathematics , method of fundamental solutions , domain decomposition methods , eigenvalues and eigenvectors , partial differential equation , convergence (economics) , dirichlet boundary condition , laplace transform , boundary value problem , mathematical analysis , laplace's equation , computation , matrix (chemical analysis) , dirichlet problem , fourier transform , domain (mathematical analysis) , harmonic , boundary element method , algorithm , finite element method , singular boundary method , physics , materials science , quantum mechanics , economics , composite material , thermodynamics , economic growth
In this study, we investigate the application of the method of fundamental solutions (MFS) to the Dirichlet problem for Laplace's equation in an annular domain. We examine the properties of the resulting coefficient matrix and its eigenvalues. The convergence of the method is proved for analytic boundary data. An efficient matrix decomposition algorithm using fast Fourier transforms (FFTs) is developed for the computation of the MFS approximation. We also tested the algorithm numerically on several problems confirming the theoretical predictions. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005