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

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