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Domain Decomposition Methods in Science and Engineering XX pp 73–84Cite as

A Substructuring Preconditioner for Three-Dimensional Maxwell’s Equations

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Summary

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.

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Acknowledgements

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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Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing, 100080, China

    Qiya Hu

  2. School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, China

    Shi Shu

  3. Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Jun Zou

Authors
  1. Qiya Hu
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  2. Shi Shu
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  3. Jun Zou
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Corresponding author

Correspondence to Qiya Hu .

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Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Hu, Q., Shu, S., Zou, J. (2013). A Substructuring Preconditioner for Three-Dimensional Maxwell’s Equations. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_7

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