Author(s)

M.A. Golberg

Abstract

The method of fundamental solutions for Poisson's equation M.A. Golberg Czrc/e ABSTRACT We show how to extend the method of fundamental solutions (MFS) to solve Poisson's equation in 2D without boundary or domain discretization. To do this an approximate particular solution is found by approximating the right hand side by thin plate splines. The particular solution is then subtracted from the complete solution and then Laplace's equation is solved by the usual MFS. Numerical results are obtained for a number of standard boundary value problems with 3-4 figure accuracy attainable by solving fewer than 20 linear equations. 1 INTRODUCTION One of the major advantages of the BEM over the Finite Element and Finite Difference methods is that only boundary discretization is usually required rather than the domain discretization needed in those other meth- ods. However, if the differential equation to be solved is inhomogeneous, the BEM becomes less attractive bec

Keywords