Abstract

We present cubature methods for the approximation of surface integrals arising from Galerkin discretizations of 3-D boundary integral equations. This numerical integrator is fully implicit in the sense that the form of the kernel function, the surface parametrization, the trial and test space, and the order of the singularity of the kernel functions are not used explicitly. Different kernels can be treated by just replacing the subroutine which evaluates the kernel function in certain surface points.
Furthermore, the implementation of the integrator is relatively easy since it can be checked on simple test kernels as, e.g., polynomials where the exact integrals are available. We discuss the convergence of the cubature methods together with a stability and consistency analysis in order to determine the minimal cubature orders a priori.