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Domain Decomposition Methods in Science and Engineering XX pp 103–110Cite as

Mesh Regularization in Bank-Holst Parallel hp-Adaptive Meshing

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

Abstract

In this work, we study mesh regularization in Bank-Holst parallel adaptive paradigm when adaptive enrichment in both h (geometry) and p (degree) is used. The paradigm was first introduced by Bank and Holst in [1–3] and later extended to hp-adaptivity in [5]. In short, the paradigm can be summarized in the following steps.

The work of this author was supported by the U.S. National Science Foundation under contract DMS-0915220. The Beowulf cluster used for the numerical experiments was funded by NSF SCREMS-0619173.

The work of this author was supported by the National Science Foundation under contract DMS-0915220 and a grant from the Vietnam Education Foundation (VEF).

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Bibliography

  1. Randolph E. Bank. Some variants of the Bank-Holst parallel adaptive meshing paradigm. Comput. Vis. Sci., 9(3):133–144, 2006.

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  2. Randolph E. Bank and Michael Holst. A new paradigm for parallel adaptive meshing algorithms. SIAM J. Sci. Comput., 22(4):1411–1443 (electronic), 2000.

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  3. Randolph E. Bank and Michael Holst. A new paradigm for parallel adaptive meshing algorithms. SIAM Rev., 45(2):291–323 (electronic), 2003. Reprinted from SIAM J. Sci. Comput. 22 (2000), no. 4, 1411–1443 [MR1797889].

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  4. Randolph E. Bank and Shaoying Lu. A domain decomposition solver for a parallel adaptive meshing paradigm. SIAM J. Sci. Comput., 26(1):105–127 (electronic), 2004.

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  5. Randolph E. Bank and Hieu Nguyen. Domain decomposition and h p-adaptive finite elements. In Yunqing Huang, Ralf Kornhuber, Olof Widlund, and Jinchao Xu, editors, Domain Decomposition Methods in Science and Engineering XIX, Lecture Notes in Computational Science and Engineering, pages 3–13, Berlin, 2011. Springer-Verlag.

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  6. Hieu Nguyen. p-adaptive and automatic h p-adaptive finite element methods for elliptic partial differential equations Ph.D. Thesis, Department of Mathematics, University of California, San Diego, La Jolla, CA, 2010.

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  7. Randolph E. Bank and Hieu Nguyen. h p adaptive finite elements based on derivative recovery and superconvergence. Comput. Vis. Sci., 14(6):287–299, 2011.

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  8. Randolph E. Bank and Jeffrey S. Ovall. Dual functions for a parallel adaptive method. SIAM J. Sci. Comput., 29(4):1511–1524 (electronic), 2007.

    Google Scholar 

  9. Randolph E. Bank and Panayot S. Vassilevski. Convergence analysis of a domain decomposition paradigm. Comput. Vis. Sci., 11(4–6):333–350, 2008.

    Google Scholar 

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Author information

Authors and Affiliations

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

    Randolph E. Bank

  2. Department of Computer Science, University of California, Davis, Davis, California, 95616, USA

    Hieu Nguyen

Authors
  1. Randolph E. Bank
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  2. Hieu Nguyen
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Corresponding author

Correspondence to Randolph E. Bank .

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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Bank, R.E., Nguyen, H. (2013). Mesh Regularization in Bank-Holst Parallel hp-Adaptive Meshing. 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_10

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