Numerical Integration of Functions with Endpoint Singularities and/or Complex Poles in 3D Galerkin Boundary Element Methods

Abstract

In this paper we propose special strategies to compute 1D integrals of functions having weakly or strong singularities at the endpoints of the interval of integration or complex poles close to the domain of integration. As application of the proposed strategies, we compute a four dimensional integral arising from 3D Galerkin boundary element methods (BEM) applied to hypersingular boundary integral equations.