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

[摘要] 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.

[学科分类] 应用数学

[关键词] boundary element method;Galerkin discretization;Helmholtz equation;hypersingular boundary integral equation