In this talk we explore numerical methods to efficiently solve problems related to electromagnetic wave propagation. We focus on tailored discretizations and iterative solvers designed for robustness and parallel scalability. In the first part, we present the CHDG method, a hybridizable discontinuous Galerkin variant that employs hybrid variables consistent with impedance transmission conditions. This formulation leads to a contractive fixed-point solver composed of two cell-local operators, making the approach naturally parallelizable. We illustrate the method’s performance using results from a 3D matrix-free implementation and discuss computational aspects. In the second part, we address Maxwell’s equations with anisotropic material tensors for the permittivity and permeability. We present preliminary results toward extending a two-level domain decomposition analysis from the isotropic to the anisotropic setting and identify the key assumptions required for this generalization.