Accuracy Investigations of Boundary Element Methods for the Solution of Laplace Equations

Boundary element methods (BEMs) are approved methods for an efficient numerical solution of problems, which are based on a Laplace equation. Here, the solution of electrostatic field problems, steady current flow field problems, and magnetostatic field problems is considered. Focus of this paper is on investigations of accuracy of direct formulations, which are based on Green's theorem. Different types of coupling of computational domains are examined with respect to accuracy and convergence behavior of iterative solvers of the linear system of equations. Furthermore, the influence of singular and nearly singular integrals and the influence of matrix compression techniques to the accuracy of the solution are observed.