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.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
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)
