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A nonoverlapping domain decomposition method for Maxwell’s equations in three dimensions. (English) Zbl 1057.65097
From the authors’ summary: We propose a nonoverlapping domain decomposition method for solving the three-dimensional Maxwell equations, based on the edge element discretization. For the Schur complement system on the interface, we construct an efficient preconditioner by introducing two special coarse subspaces defined on the nonoverlapping subdomains. It is shown that the condition number of the preconditioned system grows only polylogarithmically with the ratio between the subdomain diameter and the finite element mesh size but possibly depends on the jumps of the coefficients.
MSC:
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65F10Iterative methods for linear systems
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
35Q60PDEs in connection with optics and electromagnetic theory
78A25General electromagnetic theory
78M10Finite element methods (optics)