Analytical evaluation and application of the singularities in boundary element method

In this paper, two alternative approaches to the boundary element method (BEM) are investigated; namely, the contour approach method and the direct approach method. A detailed comparison of these methods is made by evaluating the accuracy of singular boundary integrals. A complete and comprehensive exposition of the derivation leads to the correct implementation. This is in contrast to conventional numerical integration methods, which suffer from the numerical boundary layer. Singularities which are mathematical artifacts are shown to vanish when the contour approach and the direct approach methods are applied. Singularities which arise from the physics are dealt with by way of a complex mapping method in the BEM. The results of seven benchmark problems which are supportive of these conclusions are presented at the end of this article.