Boundary Element Method (BEM) and Method of Fundamental Solutions (MFS) for the boundary value problems of the 2-D Laplace's equation

Abstract

Boundary Element Method (BEM) and Method of Fundamental Solutions (MFS) for the boundary value problems of the 2-D Laplace’s equation By Ermes A. Salgado-Ibarra Dr. Li Xin, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas In this thesis we study the solution of the two dimensional Laplace equation by the boundary Element method (BEM) and the method of fundamental solutions (MFS). Both the BEM and MFS used to solve boundary value problems involving the Laplace equation 2-D settings. Both methods rely on the use of fundamental solution of the Laplace’s equation (the solution of Laplace’s equation in the distributional sense). We will contrast and compare the results we get using the BEM with results we get using the MFS.