Application of Boundera Element Method (Bem) to Two-Dimensional Poisson's Eqation

Abstract

BEM can be used to solve Poisson's equation if the right hand side of the equation is constant because it can easily be transformed to an equivalent Laplace equation. However, if the right hand side is not constant, then such a treatment is impossible and part of the equation can not be transformed over the boundary, hence, the whole domain has to be discretized. Although this takes away important advantages of BEM over the Finite Element Method (FEM) in which the whole domain also has to be discretized, but the results are more accurate, and a much coarser mesh can be employed to obtain an equivalent accuracy with less effort in data preparation. In this paper the application of HEM to two - dimensional Poisson's equation is described. A computer program is developed using linear elements to express the geometry and functions. The program, is used to solve the torsion problem (Poisson's equation) and potential flow around a circle (Laplace's equation), and the results are compared with those of analytical methods and FEM.