REGULARIZED MESHLESS METHOD FOR SOLVING LAPLACE EQUATION WITH MULTIPLE HOLES

Abstract

In this paper, a regularized meshless method (RMM) is developed to solve the two-dimension Laplace problem with multiply-connected domain. The solution is represented by using the double layer potential. The source points can be located on the real boundary by using the proposed regularized technique to regularize the singularity and hypersingularity of the kernel functions. The difficulty of the coincidence of the source and collocation points in traditional method of fundamental solutions is avoided and thereby the diagonal terms of influence matrices are easily determined. The numerical results demonstrate the accuracy of the solutions after comparing with those of exact solution and BEM for the Dirichlet, mixed-type and arbitrary-shape problems with multiple holes. Good agreements are observed.