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

Research output: Contribution to journalResearch articleContributedpeer-review


  • Peter Bastian - , University of Stuttgart (Author)
  • Markus Blatt - , University of Stuttgart (Author)
  • Andreas Dedner - , University of Freiburg (Author)
  • Christian Engwer - , University of Stuttgart (Author)
  • Robert Klöfkorn - , University of Freiburg (Author)
  • Mario Ohlberger - , University of Münster (Author)
  • Oliver Sander - , Free University of Berlin (Author)


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).


Original languageEnglish
Pages (from-to)103-119
JournalComputing (Vienna/New York)
Early online date29 Apr 2008
Publication statusPublished - 2008
Externally publishedYes

External IDs

ORCID /0000-0003-1093-6374/work/146644834
Scopus 47749109856