A direct method for evaluating arbitrary high-order singular curved boundary integrals

摘要

In this paper, an efficient method for numerical evaluation of all kinds of singular curved boundary integrals from 2D/3D BEM analysis is proposed based on an operation technique on a projection line/plane. Firstly, geometry variables on a curved line or surface element are expressed by parameters on the projection line/plane, and then all singularities are analytically removed by expressing the non-singular part of the integration kernel as a power series in a local distance defined on the projection line/plane. Also, a set of important relationships computing derivatives of intrinsic coordinates with respect to local orthogonal coordinates is derived. A few examples are provided to demonstrate the correctness and the stability of the proposed method.