Solving Helmholtz problem with a fast numerical strategy based on Toeplitz structure

Abstract

This paper develops primarily an analytical solution for sound, electromagnetic or any other wave propagation described by the Helmholtz equation in the case of N circular obstacles. Then, it proposes a fast iterative numerical method, using Toeplitz block structure, for computing the solution of a complex, dense and large linear system. Finally, it shows the efficiency of this numerical strategy via a numerical study of the convergence rate with respect to different geometrical parameters of the problem.