Accurate numerical integration of singular boundary element kernels over boundaries with curvature

Abstract

Abstract Use of the Green function, for the solution of boundary‐value problems, frequently results in singular integral equations. Algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method (BEM). They are based upon the use of appropriately weighted Gaussian quadrature formulae, together with numerical geometrical transformations of the region of integration. The use of high‐order subdomain expansion functions, for interpolation over nonplanar elements, allows boundary curvature to be accommodated. In particular, the handling of Green functions with logarithmic and r −1 behaviour are detailed. Volume integrals, with r −2 singularity, are outlined. Operations are performed on a simplex, thus resulting in generality and ease of automation. This scheme has been incorporated into boundary element method software and successfully applied to a variety of problems.