Numerical solution of the Helmholtz equation in an infinite strip by Wiener‐Hopf factorization |
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| Authors: | Marcello Lucia Fabio Maggio Giuseppe Rodriguez |
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| Affiliation: | 1. Mathematics Department, The City University of New York, CSI, Staten Island, New York 10314;2. CRS4 Bioinformatica, Parco Scientifico e Tecnologico, 09010 Pula (CA), Italy;3. Dip. di Matematica e Informatica, Università di Cagliari, 09123 Cagliari, Italy |
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| Abstract: | 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. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 |
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| Keywords: | block Toeplitz matrices finite difference approximation Helmholtz equation matrix polynomials Wiener‐Hopf factorization |
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