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Adaptive Finite Element Methods for Domain Decomposition on Nonmatching Grids

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Book cover Parallel Solution of Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 120))

Abstract

We consider the parallel solution of elliptic boundary value problems discretized by domain decomposition methods on nonmatching grids involving mortar finite elements. We start from an initial nonoverlapping decomposition of the computational domain and independent triangulations of the subdomains realizing weak continuity conditions on the internal subdomain boundaries by means of appropriately chosen Lagrangian multipliers. The solution process features a preconditioned Lanczos iteration for the resulting saddle point problem using a block diagonal preconditioner and an adaptive local mesh refinement on the basis of efficient and reliable residual based or hierarchical a posteriori error estimators. In the parallel implementation of the code, the data related to the subdomains are appropriately distributed among the available processors. The efficiency of the parallel implementation and the benefits of the adaptive grid refinement process are illustrated by numerical simulation results obtained on a IBM SP2 for some selected test problems including fully potential flow around profiles.

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Authors and Affiliations

  1. Institute of Mathematics, University of Augsburg, Universitaetsstr. 14, D-86159, Augsburg, Germany

    B. Engelmann, R. H. W. Hoppe & B. Wohlmuth

  2. Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, 117333, Moscow, Russia

    Y. Iliash & Y. Vassilevski

  3. Department of Mathematics, University of Houston, Houston, TX, 77204-3476, USA

    Y. A. Kuznetsov

Authors
  1. B. Engelmann
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  2. R. H. W. Hoppe
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  3. Y. Iliash
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  4. Y. A. Kuznetsov
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  5. Y. Vassilevski
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  6. B. Wohlmuth
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Editor information

Editors and Affiliations

  1. Institutt for Informatikk Hoyteknologisenteret, University of Bergen, Bergen, N-5020, Norway

    Petter Bjørstad

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Mitchell Luskin

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Engelmann, B., Hoppe, R.H.W., Iliash, Y., Kuznetsov, Y.A., Vassilevski, Y., Wohlmuth, B. (2000). Adaptive Finite Element Methods for Domain Decomposition on Nonmatching Grids. In: Bjørstad, P., Luskin, M. (eds) Parallel Solution of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1176-1_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1176-1_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7034-8

  • Online ISBN: 978-1-4612-1176-1

  • eBook Packages: Springer Book Archive

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