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arXiv · 1605.00156

Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions

James H. Adler·Xiaozhe Hu·Ludmil T. Zikatanov
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Abstract

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.

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James H. Adler, Xiaozhe Hu, Ludmil T. Zikatanov. 2016-04-30. Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions. https://arxiv.org/abs/1605.00156

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