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

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.