A modified non--linear transformation method for evaluating weakly singular boundary element integrals

Abstract

Accurate numerical evaluation of boundary integrals is fundamental to producing useful results with the boundary element method. This paper introduces a generalisation of a recently introduced combined method (subtraction of singularity followed by a non-linear transformation), which takes into account the effect of the basis functions. The new method is applied to solve weakly singular integrals which arise in the solution of the two-dimensional Laplace equation. The new method was found, in the cases considered, to be numerically superior to both the combined method and any of the non-linear transformation methods.