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

A construction of prismatic Hardy space infinite elements to discretize wave equations on unbounded domains $\Omega$ in $H^1_{loc}(\Omega)$, $H_{loc}(curl;\Omega)$ and $H_{loc}(div;\Omega)$ is presented. As our motivation is to solve Maxwell's equations we take care that these infinite elements fit into the discrete de Rham diagram, i.e. they span discrete spaces, which together with the exterior derivative form an exact sequence. Resonance as well as scattering problems are considered in the examples. Numerical tests indicate super-algebraic convergence in the number of additional unknowns per degree of freedom on the coupling boundary that are required to realize the Dirichlet to Neumann map.