A Substructuring Preconditioner for Three-Dimensional Maxwell’s Equations
We propose a new nonoverlapping domain decomposition preconditioner for the discrete system arising from the edge element discretization of the three-dimensional Maxwell’s equations. This preconditioner uses the simplest coarse edge element space induced by the coarse triangulation. We will show that the rate of the PCG convergence with this substructuring preconditioner is quasi-optimal, and is independent of large variations of the coefficients across the local interfaces.
KeywordsDomain Decomposition Domain Decomposition Method Edge Element Local Solver Iterative Substructuring
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QH was supported by the Major Research Plan of Natural Science Foundation of China G91130015, the Key Project of Natural Science Foundation of China G11031006 and National Basic Research Program of China G2011309702. SS was supported by NSFC Project 91130002 and 11171281, the project of Scientific Research Fund of Hunan Provincial Education Department 10C1265 and 11C1219, and the project of Xiangtan University 10XZX03. JZ was substantially supported by Hong Kong RGC grant (Project 405110) and a Direct Grant from Chinese University of Hong Kong.
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