Convergence of the infinite element methods for the Helmholtz equation in separable domains

Abstract

To the best knowledge of the authors, this work presents the first convergence analysis for the Infinite Element Method (IEM) for the Helmholtz equation in exterior domains. The approximation applies to separable geometries only, combining an arbitrary Finite Element (FE) discretization on the boundary of the domain with a spectral-like approximation in the “radial” direction, with shape functions resulting from the separation of variables. The principal idea of the presented analysis is based on the spectral decomposition of the problem.