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Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations


Authors: Jayadeep Gopalakrishnan and Joseph E. Pasciak
Journal: Math. Comp. 72 (2003), 1-15
MSC (2000): Primary 65F10, 65N55, 65N30
DOI: https://doi.org/10.1090/S0025-5718-01-01406-5
Published electronically: December 5, 2001
MathSciNet review: 1933811
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Abstract: Time harmonic Maxwell equations in lossless media lead to a second order differential equation for the electric field involving a differential operator that is neither elliptic nor definite. A Galerkin method using Nedelec spaces can be employed to get approximate solutions numerically. The problem of preconditioning the indefinite matrix arising from this method is discussed here. Specifically, two overlapping Schwarz methods will be shown to yield uniform preconditioners.


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Additional Information

Jayadeep Gopalakrishnan
Affiliation: Institute for Mathematics and its Applications, Minneapolis, Minnesota 55455
Email: jayg@ima.umn.edu

Joseph E. Pasciak
Affiliation: Texas A&M University, College Station, Texas 77843-3368.
Email: pasciak@math.tamu.edu

DOI: https://doi.org/10.1090/S0025-5718-01-01406-5
Keywords: Schwarz method, indefinite, Maxwell equations, preconditioner, domain decomposition, finite element
Received by editor(s): July 10, 2000
Received by editor(s) in revised form: March 7, 2001
Published electronically: December 5, 2001
Additional Notes: The first author was supported in part by Medtronic Inc
The second author was partially supported by NSF grant number DMS-9973328
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society