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Numerical solution of the Helmholtz equation in an infinite strip by Wiener‐Hopf factorization
Author(s) -
Lucia Marcello,
Maggio Fabio,
Rodriguez Giuseppe
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20484
Subject(s) - mathematics , factorization , bounded function , constant (computer programming) , helmholtz equation , mathematical analysis , constant coefficients , domain (mathematical analysis) , helmholtz free energy , matrix (chemical analysis) , toeplitz matrix , incomplete lu factorization , matrix decomposition , pure mathematics , boundary value problem , algorithm , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , computer science , programming language
Abstract We describe an algorithm to compute numerically the solution of the Helmholtz equation: Δ u + κ u = f , u ∈ H 0 1 ( 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. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010