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Zbl 1079.78025
Gopalakrishnan, Jayadeep; Pasciak, Joseph E.; Demkowicz, Leszek F.
Analysis of a multigrid algorithm for time harmonic Maxwell equations. (English)
[J] SIAM J. Numer. Anal. 42, No. 1, 90-108 (2004). ISSN 0036-1429; ISSN 1095-7170/e

The authors propose and study a multigrid algorithm for the indefinite linear systems arising from finite element discretizations of time harmonic Maxwell equations. If indefinite block smoothers are used, the proposed method has a convergence rate independent of the refinement level. The analysis is based on comparing the multigrid error reduction operator with that of a related positive definite multigrid operator, an idea previously used in multigrid analysis of indefinite second-order elliptic problems and here extended to the nonelliptic Maxwell operator.
[Luca F. Pavarino (Milano)]

MSC 2000:: *78M10 Finite element methods (optics)
65F10 Iterative methods for linear systems
65N55 Multigrid methods; domain decomposition (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)

Keywords: multigrid; preconditioners; Maxwell equations; indefinite problems; finite elements; Nedelec spaces

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