Galerkin boundary element method for ezterior problems of the 2-D Helmholtz equation with any wave number
The boundary element method is a simple and effective approach for solving the exterior problems of the Helmholtz equation on unbounded domain. However, when wave number is an eigenvalue of the interior Dirichlet or Neumann problem for the Laplacian, the solution of the corresponding boundary integral equation is not unique even for the exterior problem. So a lot of boundary element approaches avoid the eigenvalue problem. Kleinman proposed a scheme that the combination of the Helmholtz integral equation with its gradient expression is able to achieve the unique solution, but in his paper, there is no detailed computing formulation, no numerical example. In this paper, the complicated computing formulations for Kleinmans scheme are deduced. In order to calculate the integral equation with hyper-singularity, a Galerkin boundary element method is applied. Using the idea of regularization in the sense of distributions, the double normal derivatives for singular kernel are shifted to the boundary rotations of trial function and testing functions in the Galerkin variational formulation, so that the hyper-singular integral to be reduced to a weak one. At last, a least square method is applied to solve the overdetermined linear equation system. The results of numerical examples demonstrate that the scheme presented is practical and effective for the exterior problems of the 2-D Helmholtz equation with any wave number.
Galerkin boundary element method ezterior problems of the Helmholtz equation hyper-singular integral the least square method
ZHU Jialin MA Jianjun LI Maojun
College of Mathematics and Physics,Chongqing University,Chongqing 400030,China
国际会议
南京
英文
1
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）