Analysis of a Multigrid Algorithm for Time Harmonic Maxwell Equations

This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a "backslash" multigrid cycle is proven to converge at rates independent of refinement level...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2004-01, Vol.42 (1), p.90-108
Main Authors: Gopalakrishnan, Jayadeep, Pasciak, Joseph E., Demkowicz, Leszek F.
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Approximation
Experiments
Mathematical functions
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Summary:This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a "backslash" multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid error reduction operator with that of a related positive definite multigrid operator. This idea has previously been used in multigrid analysis of indefinite second order elliptic problems. However, the Maxwell application involves a nonelliptic indefinite operator. With the help of a few new estimates, the earlier ideas can still be applied. Some numerical experiments with lowest order Nedelec elements are also reported.
ISSN:0036-1429
1095-7170
DOI:10.1137/S003614290139490X