Projection plane method for evaluation of arbitrary high order singular boundary integrals

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/surface element are expressed in terms of 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 crucial 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.