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 | References | Similar Articles | Additional Information

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