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

Alonso, Ana; Valli, Alberto

doi:10.1090/S0025-5718-99-01013-3

An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
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by Ana Alonso and Alberto Valli PDF

Math. Comp. 68 (1999), 607-631 Request permission

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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