Convergence of Hardy Space Infinite Elements for Helmholtz Scattering and Resonance Problems

Abstract

We perform a convergence analysis for discretizations of Helmholtz scattering and resonance problems obtained by Hardy space infinite elements. Superalgebraic convergence rates with respect to the number of Hardy space degrees of freedom are achieved. We consider spheres and piecewise polytopes as transparent boundaries. The analysis is based on a G\aa rding-type inequality and standard operator theoretical results. While the obtained results are related to those for the radial perfectly matched layer method, different techniques are used in the analysis.