Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition  

作　　者：Haibing Wang Jijun Liu 

机构地区：[1]School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan 411201, China [2]Department of Mathematics, Southeast University, Nanjing 210096, China

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》2007年第3期203-214,共12页

摘　　要：We consider the numerical solution for the Helmholtz equation in R^2 with mixed boundary conditions.The solvability of this mixed boundary value problem is estab- lished by the boundary integral equation method.Based on the Green formula,we express the solution in terms of the boundary data.The key to the numerical real- ization of this method is the computation of weakly singular integrals.Numerical performances show the validity and feasibility of our method.The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.We consider the numerical solution for the Helmholtz equation in R^2 with mixed boundary conditions. The solvability of this mixed boundary value problem is estabished by the boundary integral equation method. Based on the Green formula, we express the solution in terms of the boundary data. The key to the numerical realization of this method is the computation of weakly singular integrals. Numerical performances show the validity and feasibility of our method. The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.

关 键 词：赫尔姆霍茨方程 格林公式 位势理论 边界积分方程 数值解 混合边界条件 

分 类 号：O175.5[理学—数学]