A Simplified Approach for the Evaluation of Nearly singular integrals in Boundary Element Method

摘要

The accurate and efficient evaluation of nearly singular integrals is one of the major concerned problems in the implementation of the boundary element method. Among the various commonly used nonlinear transformation methods, the distance transformation technique seems to be a promising method to dealing with various orders of nearly singular integrals both in potential and elasticity problems. In this paper, some drawbacks of the conventional distance transformation, such as the sensitivity to the position of projection point, are investigated by numerical tests. And a general distance transformation technique is developed to circumvent these drawbacks, which is aimed to remove or weaken the limitations of the projection point. Numerical examples are presented for curved line elements to validate the accuracy and efficiency of our method.