An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations |
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Authors: | Ana Alonso Alberto Valli |
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Institution: | Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy ; Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy |
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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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Keywords: | Domain decomposition methods Maxwell equations |
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