The Sinh Transformation for Curved Elements Using theGeneral Distance Function

作者：Jia-He Lv, Yu Miao, Wenyong Gong, Huiqing Zhu · 发表于：Computer Modeling in Engineering & Sciences · 年份：2013 · DOI：10.3970/cmes.2013.093.113 · 被引用次数：11 · 研究领域：Numerical methods in engineering、Electromagnetic Simulation and Numerical Methods、Fatigue and fracture mechanics

Accurate numerical evaluation of the nearly singular boundary inte- grals is a major concerned issue in the implementation of boundary element method (BEM). In this paper, a general distance function independent on the nearly singular point is proposed. Combined with an iteration process, the position of the nearly singular point can be obtained more easily. Then, an extended form of the sinh transformation using the general distance function, which automatically takes into account the intrinsic coordinate of the nearly singular point and the minimum dis- tance from source point to the element in the intrinsic parameter plane, is developed to deal with the nearly singular integrals. The iterated sinh transformation can also be achieved in a straightforward fashion. Results obtained by the one and two it- erations of sinh transformation for various orders of singularities demonstrate the high efficiency and accuracy of presented method. Comparisons with other variable transformation methods are also carried out to show the superiority of the presented method.