The Galerkin boundary element method for exterior problems of 2-D Helmholtz equation with arbitrary wavenumber

摘要

Among many efforts put into the problems of eigenvalue for the Helmholtz equation with boundary integral equations, Kleinman proposed a scheme using the simultaneous equations of the Helmholtz integral equation with its boundary normal derivative equation. In this paper, the detailed formulation is given following Kleinman's scheme. In order to solve the integral equation with hypersingularity, a Galerkin boundary element method is proposed and the idea of regularization in the sense of distributions is applied to transform the hypersingular integral to a weak one. At last, a least square method is applied to solve the overdetermined linear equation system. Several numerical examples testified that the scheme presented is practical and effective for the exterior problems of the 2-D Helmholtz equation with arbitrary wavenumber.