A Sigmoidal and Distance Combined Transformation Method for Nearly Singular Integral on Asymmetric Patch

Abstract

This paper is devoted to developing a new computational method for nearly singular integral computation in the application of the boundary element method for the analysis of thin-shell-like structures in mechanical engineering. Based on the traditional distance transformation method, a sigmoidal transformation method is introduced to further cluster the integral points around the source point with respect to the circumferential direction. The combined method provides accurate results without employing a large quantity of integral points. Numerical examples demonstrate that the computational accuracy and efficiency of the proposed method is significantly higher than that of the traditional single distance transformation method, especially in the case of the asymmetric integral patch.