Numerical analysis of the method of fundamental solutions for harmonic problems in annular domains

摘要

In this study, we investigate the application of the method of fundamental solutions (NIFS) 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. (C) 2005 Wiley Periodicals, Inc.