Relationship Among Coefficient Matrices in Symmetric Galerkin Boundary Element Method for Two-Dimensional Scalar Problems

Abstract

Based on the assumption that solutions from different methods should be the same, the relationship among weakly singular, strongly singular and hypersingular matrices associated with symmetric Galerkin boundary element method (SGBEM) is derived in this paper. Hypersingularity is avoided through matrix manipulations so that only weakly and strongly singularities need to be solved. Compared with the advantages brought about by symmetry, the additional computation caused by matrix manipulations is not so important in many cases, especially for time-domain problems or when one wants to couple BEM with other symmetric schemes. Simplicity is the advantage of the current method over the traditional SGBEM. Both steady-state and time-domain potential problems have been studied, and two numerical examples are included to show the effectiveness and accuracy of the present formulation.