Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D

Abstract

We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations on these results.