Computing

, Volume 82, Issue 2–3, pp 103–119 | Cite as

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

  • P. Bastian
  • M. Blatt
  • A. Dedner
  • C. Engwer
  • R. Klöfkorn
  • M. Ohlberger
  • O. Sander
Article

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).

Keywords

DUNE Hierarchical grids Interface Finite elements Finite volumes Entity complex Geometric realization Father relation Index maps Parallelization 

Mathematics Subject Classification (2000)

65N30 52C99 65Y05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)Google Scholar
  2. 2.
    Benger W (2005) Visualization of general relativistic tensor fields via a Fiber Bundle Data Model. PhD thesis, Freie Universität BerlinGoogle Scholar
  3. 3.
    Berti G (2000) Generic software components for scientific computing. PhD thesis, BTU CottbusGoogle Scholar
  4. 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 ResearchGoogle Scholar
  5. 5.
    DUNE – Distributed and Unified Numerics Environment. http://dune-project.org/

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • P. Bastian
    • 1
  • M. Blatt
    • 1
  • A. Dedner
    • 2
  • C. Engwer
    • 1
  • R. Klöfkorn
    • 2
  • M. Ohlberger
    • 3
  • O. Sander
    • 4
  1. 1.Institut für Parallele und Verteilte SystemeUniversität StuttgartStuttgartGermany
  2. 2.Abteilung für Angewandte MathematikUniversität FreiburgFreiburgGermany
  3. 3.Institut für Numerische und Angewandte MathematikUniversität MünsterMünsterGermany
  4. 4.Institut für MathematikFreie Universität Berlin, DFG Research Center MatheonBerlinGermany

Personalised recommendations