In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a structure-preserving finite-element approximation with standard Nedelec--Raviart--Thomas elements in space and a Crank--Nicolson scheme in time to approximate the electric and magnetic fields. We focus on two types of block preconditioners. The first type is based on the well-posedness results of the discrete problem. The second uses an exact block factorization of the linear system, for which the structure-preserving discretization yields sparse Schur complements. We prove robustness and optimality of these block preconditioners, and provide supporting numerical tests.
@article{arxiv.1605.00156,
title = {Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions},
author = {James H. Adler and Xiaozhe Hu and Ludmil T. Zikatanov},
journal= {arXiv preprint arXiv:1605.00156},
year = {2016}
}