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Mathematics of Computation

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An optimal domain decomposition preconditioner
for low-frequency time-harmonic
Maxwell equations

Authors: Ana Alonso and Alberto Valli
Journal: Math. Comp. 68 (1999), 607-631
MSC (1991): Primary 65N55, 65N30; Secondary 35Q60
MathSciNet review: 1609607
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Abstract: The time-harmonic Maxwell equations are considered in the low-frequency case. A finite element domain decomposition approach is proposed for the numerical approximation of the exact solution. This leads to an iteration-by-subdomain procedure, which is proven to converge. The rate of convergence turns out to be independent of the mesh size, showing that the preconditioner implicitly defined by the iterative procedure is optimal. For obtaining this convergence result it has been necessary to prove a regularity theorem for Dirichlet and Neumann harmonic fields.

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Additional Information

Ana Alonso
Affiliation: Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy

Alberto Valli
Affiliation: Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy

Keywords: Domain decomposition methods, Maxwell equations
Received by editor(s): December 2, 1996
Received by editor(s) in revised form: July 30, 1997
Additional Notes: Partially supported by H.C.M. contract CHRX 0930407
Article copyright: © Copyright 1999 American Mathematical Society