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An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations. (English) Zbl 1043.78554
Summary: 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.
MSC:
78M25Numerical methods in optics
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35Q60PDEs in connection with optics and electromagnetic theory