Exact Sequences of High Order Hardy Space Infinite Elements for Exterior Maxwell Problems

Abstract

This paper describes the construction of a new family of prismatic infinite elements for electromagnetic scattering and resonance problems. The construction is based on the use of the pole condition to define the equivalent of an “outgoing wave.” Specifically, a function satisfies the pole condition if and only if a certain transformation of this function belongs to a Hardy space. We use tensor products of cochain complexes to obtain four different infinite element spaces which form an exact sequence corresponding to the deRham complex in the exterior domain. Numerical tests indicate superalgebraic convergence in the number of additional unknowns per degree of freedom on the coupling boundary.