Numerical Solution of the Helmholtz Equation in an Infinite Strip by Wiener-Hopf Factorization

被引：1

作者：

Lucia, Marcello ^{[1
]}

Maggio, Fabio ^{[2
]}

Rodriguez, Giuseppe ^{[3
]}

机构：

[1] CUNY, CSI, Dept Math, Staten Isl, NY 10314 USA

[2] CRS4 Bioinformat, I-09010 Pula, CA, Italy

[3] Univ Cagliari, Dip Matemat & Informat, I-09123 Cagliari, Italy

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2010年 / 26卷 / 06期

关键词：

block Toeplitz matrices; finite difference approximation; Helmholtz equation; matrix polynomials; Wiener-Hopf factorization; MATRIX POLYNOMIALS; SPECTRAL ANALYSIS; TOEPLITZ; DOMAINS;

D O I：

10.1002/num.20484

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe an algorithm to compute numerically the solution of the Helmholtz equation: Delta u + kappa u = f, u is an element of H-0(1) (S), where S is an infinite strip and kappa a given bounded function. By using the finite difference approximation on the entire strip, we are led to solve an infinite linear system. When. is constant the associated matrix is block Toeplitz and banded and the system can be solved using a Wiener-Hopf factorization. This approach can also be adapted to deal with the case when kappa is constant outside a bounded domain of the strip. Numerical results are given to assess the performance of our method. (C) 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 26: 1247-1274, 2010

引用

页码：1247 / 1274

页数：28

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