Convergence of infinite element methods for scalar waveguide problems

TL;DR

This paper provides a unified convergence analysis for PML and Hardy space infinite element methods applied to scalar wave equations in waveguide domains, supported by theoretical error bounds and numerical experiments.

Contribution

It introduces a new unified framework for analyzing the convergence of PML and Hardy space methods for waveguide problems, including diffraction and resonance cases.

Findings

Theoretical error bounds are established for both methods.

Numerical experiments confirm the accuracy of the error estimates.

The analysis applies to both diffraction and resonance problems.

Abstract

We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both the Perfectly Matched Layer (PML) method and the Hardy space infinite element method in a unified framework. We treat both diffraction and resonance problems. The theoretical error bounds are compared with errors in numerical experiments.