On the Implementation of the h-p Boundary Element Method on Curved Surfaces

We consider the h-p Galerkin boundary element method applied to a weakly singular integral equation of the rst kind on an open curved surface. We focus on the eeective computation of the Galerkin matrix, i.e. we introduce a numerical qudrature rule which is shown (for a model case) to converge exponentially fast with the number of kernel evaluations. Numerical experiments show that the application of this quadrature rule preserves the exponential convergence of our h-p Galerkin scheme.