Numerical quadrature over triangles with weak singularities

Abstract

SUMMARYThe present paper studies in a uniÿed way the numerical computation of integrals over triangles with weak singularities arising from the ln r and 1=r kernels present in the boundary element method by mapping the triangle into a square and thus obtaining a regularizing e ect. Three types of co-ordinate transformations are evaluated and their performance with respect to numerical quadrature is assessed.