We describe an algorithm to compute numerically the solution of the Helmholtz equation: u + κu = f , u ∈ H10 (S), where S is an infinite strip and κ a given bounded function. By using the finite differenceapproximation 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 aWiener-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.

Numerical solution of the Helmholtz equation in a infinite strip by Wiener-Hopf factorization

RODRIGUEZ, GIUSEPPE
2010

Abstract

We describe an algorithm to compute numerically the solution of the Helmholtz equation: u + κu = f , u ∈ H10 (S), where S is an infinite strip and κ a given bounded function. By using the finite differenceapproximation 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 aWiener-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.
Block Toeplitz matrices; Finite difference approximation; Helmholtz equation; Matrix polynomials; Wiener-Hopf factorization
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/21786
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