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A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework

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Abstract

We give a mathematically rigorous definition of a grid for algorithms solving partial differential equations. Unlike previous approaches (Benger 2005, PhD thesis; Berti 2000, PhD thesis), our grids have a hierarchical structure. This makes them suitable for geometric multigrid algorithms and hierarchical local grid refinement. The description is also general enough to include geometrically non-conforming grids. The definitions in this article serve as the basis for an implementation of an abstract grid interface as C++ classes in the framework (Bastian et al. 2008, this issue).

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References

  1. Bastian P, Blatt M, Dedner A, Engwer C, Klöfkorn R, Kornhuber R, Ohlberger M, Sander O (2008) A generic grid interface for parallel and adaptive scientific computing. Part II: Implementation and tests in DUNE. Computing (this issue)

  2. Benger W (2005) Visualization of general relativistic tensor fields via a Fiber Bundle Data Model. PhD thesis, Freie Universität Berlin

  3. Berti G (2000) Generic software components for scientific computing. PhD thesis, BTU Cottbus

  4. Botta N, Ionescu C, Linstead C, Klein R (2006) Structuring distributed relation-based computations with SCDRC. Technical report, PIK Report No. 103, Potsdam Institute for Climate Impact Research

  5. DUNE – Distributed and Unified Numerics Environment. http://dune-project.org/

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Authors and Affiliations

  1. Institut für Parallele und Verteilte Systeme, Universität Stuttgart, Stuttgart, Germany

    P. Bastian, M. Blatt & C. Engwer

  2. Abteilung für Angewandte Mathematik, Universität Freiburg, Freiburg, Germany

    A. Dedner & R. Klöfkorn

  3. Institut für Numerische und Angewandte Mathematik, Universität Münster, Münster, Germany

    M. Ohlberger

  4. Institut für Mathematik, Freie Universität Berlin, DFG Research Center Matheon, Berlin, Germany

    O. Sander

Authors
  1. P. Bastian
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  2. M. Blatt
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  3. A. Dedner
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  4. C. Engwer
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  5. R. Klöfkorn
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  6. M. Ohlberger
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  7. O. Sander
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Corresponding author

Correspondence to P. Bastian.

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Bastian, P., Blatt, M., Dedner, A. et al. A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework. Computing 82, 103–119 (2008). https://doi.org/10.1007/s00607-008-0003-x

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  • DOI: https://doi.org/10.1007/s00607-008-0003-x

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