Robust Solvers for Maxwell's Equations with Dissipative Boundary\n Conditions

2016/04/30 by James H. Adler, Adler, James H., Xiaozhe Hu +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1605.00156

openalex publication_date 2016/04/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we design robust and efficient linear solvers for the\nnumerical approximation of solutions to Maxwell's equations with dissipative\nboundary conditions. We consider a structure-preserving finite-element\napproximation with standard Nedelec--Raviart--Thomas elements in space and a\nCrank--Nicolson scheme in time to approximate the electric and magnetic fields.\n We focus on two types of block preconditioners. The first type is based on\nthe well-posedness results of the discrete problem. The second uses an exact\nblock factorization of the linear system, for which the structure-preserving\ndiscretization yields sparse Schur complements. We prove robustness and\noptimality of these block preconditioners, and provide supporting numerical\ntests.\n

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