求解半空间中Helmholtz方程Cauchy问题的投影法  

Projection Method for the Cauchy Problem of Helmholtz Equation in Half-Space

作　　者：马云云[1] 马富明[1] 

机构地区：[1]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2012年第2期157-166,共10页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10971083)

摘　　要：针对Helmholtz方程Cauchy问题提出一种数值计算方法.借助于Dirichlet-to-Neumann映射,将Cauchy问题转化为求解散射场初值的紧算子方程.先讨论紧算子奇异值的渐近性质,然后将投影法与Tikhonov正则化方法相结合,提出一种求解相应紧算子方程的带有正则化技巧的投影法,并通过数值实验验证了算法的有效性.A numerical method was proposed for the Cauchy problem in accordance with the Helmholtz equation in the half-space.With the help of Dirichlet-to-Neumann map,this problem was transformed into a compact opera tor equation for the initial value of the wave field.The asymptotic behavior of the singular values of the compact operator was rigorously justified firstly.Th en a projection method with regularization was applied to solving the operator e quation.Finally,several numerical examples were presented to illustrate the approach.The results show that the algorithm is effective.

关 键 词：HELMHOLTZ方程 CAUCHY问题 投影法 正则化 

分 类 号：O241[理学—计算数学]