Conformal distance-sigmoidal transformation for evaluating 3D nearly singular integrals over triangular elements

Nearly singular boundary integrals are involved in many applications of BEM, such as thin structures and contact problems. Therefore, the accurate evaluation of such integrals is an important aspect during the successful implementation of BEM. Recently, a conformal mapping for triangular elements has been constructed to eliminate the distorted shape influence and applied to deal with singular integrals. In this paper, the conformal mapping is extended to deal with the nearly singular integrals over triangular elements by combination of the distance transformation proposed by Ma and Kamiya. An improved sigmoidal transformation is employed to rearrange Gaussian points in angular direction more judiciously, and the conformal mapping is introduced to eliminate the distorted shape influence for elements with large aspect ratio or peak/obtuse angles. Extensive numerical tests and comparisons for both planar and curved triangular elements are given to demonstrate the high efficiency and competitiveness of the method presented in this paper.