Adaptive quadrature rules for Galerkin BEM

Abstract

The singular integrals in the Galerkin Boundary Element Method are usually treated using singularity removing transformations. The regularized integrals are approximated by tensor product Gaussian quadrature rules. Although these integrals are smooth, the convergence rate depends strongly on the type of singularity and the aspect ratio of the triangulation. Here an adaptive quadrature scheme is presented that ensures a convergence at a user-specified rate. The effectiveness of the resulting quadrature scheme is compared with the non-adaptive approach.