Cancellation-Errorless Double-Layer Approach for Static Electric and Magnetic Problems

Abstract

In the boundary element method (BEM), we deal with the direct and indirect boundary integral equations. The indirect BEM requires less degree of freedom compared with the direct BEM and has been used for a long time. It has been numerically proven that the Double-Layer Approach (DLA) possesses superior features to analyze static electric and magnetic problems. However, the indirect BEM suffers from the so-called cancellation-error. While the Surface Charge Method (SCM) has to deal with the cancellation-error, when evaluating the electric and magnetic fields in the medium, the DLA does so when evaluating the field in the surrounding medium. In order to avoid the cancellation-error in the DLA, we propose an approach suitable for both electric and magnetic problems by preparing a post-processing based on the direct BEM. Using simple but suitable models and generalizing the DLA, we study how to avoid the errors in a post-processing stage in both static electric and magnetic problems. A comparison with a magnetostatic FEM model is also presented.