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A Two-Level Additive Schwarz Preconditioner for C 0 Interior Penalty Methods for Cahn-Hilliard Equations

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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))

  • 2003 Accesses

Summary

We study a two-level additive Schwarz preconditioner for C 0 interior penalty methods for a biharmonic problem with essential and natural boundary conditions with Cahn-Hilliard type. We show that the condition number of the preconditioned system is bounded by C(1 + (H 3 ∕ δ 3)), where H is the typical diameter of a subdomain, δ measures the overlap among the subdomains, and the positive constant C is independent of the mesh sizes and the number of subdomains.

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Bibliography

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Author information

Authors and Affiliations

  1. University of North Florida, 1 UNF Drive, Jacksonville, FL, 32224, USA

    Kening Wang

Authors
  1. Kening Wang
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Correspondence to Kening Wang .

Editor information

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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Wang, K. (2013). A Two-Level Additive Schwarz Preconditioner for C 0 Interior Penalty Methods for Cahn-Hilliard 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_14

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