Optimized Schwarz Methods for curl-curl time-harmonic Maxwells equationsReport as inadecuate

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1 JAD - Laboratoire Jean Alexandre Dieudonné 2 Section de mathématiques Genève 3 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621 4 OSU - Ohio State University Columbus

Abstract : Like the Helmholtz equation, the high frequency time-harmonic Maxwell-s equa- tions are difficult to solve by classical iterative methods. Domain decomposition methods are currently most promising: following the first provably convergent method in 4, various optimized Schwarz methods were developed over the last decade 2, 3, 10, 11, 1, 6, 13, 14, 16, 8. There are however two basic formulations for Maxwell-s equation: the first order formulation, for which complete optimized results are known 6, and the second order, or curl-curl formulation, with partial optimization results 1, 13, 16. We show in this paper that the convergence factors and the optimization process for the two formulations are the same. We then show by numerical experiments that the Fourier analysis predicts very well the behavior of the algorithms for a Yee scheme discretization, which corresponds to Nedelec edge elements on a tensor product mesh, in the curl-curl formulation. When using however mixed type Nedelec elements on an irregular tetrahedral mesh, numerical experiments indicate that transverse magnetic TM modes are less well resolved for high frequencies than transverse electric TE modes, and a heuristic can then be used to compensate for this in the optimization.

Author: Victorita Dolean - Martin Gander - Stéphane Lanteri - Jin-Fa Lee - Zhen Peng -

Source: https://hal.archives-ouvertes.fr/


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