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Numerical Algorithms
Published in: Numerical Algorithms 1/2021

16-03-2020 | Original Paper

Preconditioners and their analyses for edge element saddle-point systems arising from time-harmonic Maxwell’s equations

Authors: Ying Liang, Hua Xiang, Shiyang Zhang, Jun Zou

Published in: Numerical Algorithms | Issue 1/2021

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Abstract

We derive and propose a family of new preconditioners for the saddle-point systems arising from the edge element discretization of the time-harmonic Maxwell’s equations in three dimensions. With the new preconditioners, we show that the preconditioned conjugate gradient method can apply for the saddle-point systems when wave numbers are smaller than a positive critical number, while the iterative methods like the preconditioned MINRES may apply when wave numbers are larger than the critical number. The spectral behaviors of the resulting preconditioned systems for some existing and new preconditioners are analyzed and compared, and several two-dimensional numerical experiments are presented to demonstrate and compare the efficiencies of these preconditioners.
previous article Convergence analysis on matrix splitting iteration algorithm for semidefinite linear complementarity problems
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Metadata
Title
Preconditioners and their analyses for edge element saddle-point systems arising from time-harmonic Maxwell’s equations
Authors
Ying Liang
Hua Xiang
Shiyang Zhang
Jun Zou
Publication date
16-03-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 1/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00889-7

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