阻尼边界条件散射问题的数值解法  

On the Numerical Solution of the Direct Acoustic Scattering Problem for an Impedance Boundary

作　　者：王连堂[1] 杨阿莉[2] 管金友[3] 王青云[1] 张梅东[1] 

机构地区：[1]西北大学数学系,西安710069 [2]西安工程大学理学院,西安710048 [3]铜陵学院基础教育系,安徽铜陵244000

出　　处：《数学物理学报（A辑）》2009年第6期1704-1713,共10页Acta Mathematica Scientia

基　　金：西安工程大学博士启动基金(BS0718)资助

摘　　要：该文研究了光滑区域上二维Helmholtz方程阻尼边界条件外问题的数值解法,应用单双层位势组合来逼近散射场,因此积分方程中含有超奇异算子.给出了超奇异算子的离散化方法,在Holder空间中给出了误差估计和解析边界的收敛性分析.最后针对该方法给出数值实例,以表明该方法的有效性.In this paper, the authors describe a fully discrete method for the numerical solution of the hyper-singular integral equation arising from the combined single and double layer potential approach for the solution of the exterior impedance boundary problem to the twodimensional Helmholtz equation in smooth domains. The equation contains a hyper-singular operator. The authors develop an error analysis in a Hoder space setting with point-wise estimates and prove an exponential convergence rate for analytic boundaries and boundary data. Finally the numerical example is given to show the validity of the method.

关 键 词：HELMHOLTZ方程 阻尼边界条件 积分方程 超奇异算子. 

分 类 号：O175[理学—数学]