Numerical solution of the Helmholtz equation in an infinite strip by Wiener-Hopf factorization
Numerical Methods for Partial Differential Equations, Volume 26, Number 6, page 1247–1274 - november 2010
We describe an algorithm to compute numerically the solution of the Helmholtz equation: Δu + κu = f, u ∈ H01(S), where S is an infinite strip and κ a given bounded function. By using the finite difference approximation on the entire strip, we are led to solve an infinite linear system. When κ 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 κ is constant outside a bounded domain of the strip. Numerical results are given to assess the performance of our method.
Références BibTex
@Article{LMR10,
author = {Lucia, M. and Maggio, F. and Rodriguez, G.},
title = {Numerical solution of the Helmholtz equation in an infinite strip by Wiener-Hopf factorization},
journal = {Numerical Methods for Partial Differential Equations},
number = {6},
volume = {26},
pages = {1247–1274},
month = {november},
year = {2010},
publisher = {Wiley Periodicals, Inc.},
keywords = {block Toeplitz matrices;finite difference approximation;Helmholtz equation;matrix polynomials;Wiener-Hopf factorization},
issn = {1098-2426},
doi = {10.1002/num.20484},
url = {https://publications.crs4.it/pubdocs/2010/LMR10},
}