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An Alternative Coarse Space Method for Overlapping Schwarz Preconditioners for Raviart-Thomas Vector Fields

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Domain Decomposition Methods in Science and Engineering XX

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

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Summary

The purpose of this paper is to introduce an overlapping Schwarz method for vector field problems discretized with the lowest order Raviart-Thomas finite elements. The coarse component of the preconditioner is based on energy-minimizing discrete harmonic extensions and the local components consist of traditional solvers on overlapping subdomains. The approach has a couple of benefits compared to the previous methods. The algorithm can be implemented in an algebraic manner. Moreover, the method leads to a condition number independent of the values and jumps of the coefficients across the interface between the substructures. Supporting numerical examples to demonstrate the effectiveness are also presented.

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Acknowledgements

The author would like to thank Prof. Olof Widlund for his suggestions and assistance. The author is also grateful to Dr. Clark Dohrmann for his useful comments. The work of the author has been supported by the NSF under Grant DMS-0914954.

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Authors and Affiliations

  1. Louisiana State University, 216 Johnston Hall, Baton Rouge, LA, 70809, USA

    Duk-Soon Oh

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  1. Duk-Soon Oh
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Correspondence to Duk-Soon Oh .

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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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Oh, DS. (2013). An Alternative Coarse Space Method for Overlapping Schwarz Preconditioners for Raviart-Thomas Vector Fields. 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_42

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