A new boundary element integration strategy for retarded potential boundary integral equations

Abstract

We consider the retarded potential boundary integral equation, arising from the 3D Dirichlet exterior wave equation problem. For its numerical solution we use compactly supported temporal basis functions in time and a standard collocation method in space. Since the accurate computation of the integrals involved in the numerical scheme is a key issue for the numerical stability, we propose a new efficient and competitive quadrature strategy. We compare this approach with the one that uses the Lubich time convolution quadrature, and show pros and cons of both methods.