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

Authors:
P. Bastian;M. Blatt;A. Dedner;C. Engwer;R. Klöfkorn;M. Ohlberger;O. Sander
Affiliations:
Universität Stuttgart, Institut für Parallele und Verteilte Systeme, Stuttgart, Germany;Universität Stuttgart, Institut für Parallele und Verteilte Systeme, Stuttgart, Germany;Universität Freiburg, Abteilung für Angewandte Mathematik, Freiburg, Germany;Universität Stuttgart, Institut für Parallele und Verteilte Systeme, Stuttgart, Germany;Universität Freiburg, Abteilung für Angewandte Mathematik, Freiburg, Germany;Universität Münster, Institut für Numerische und Angewandte Mathematik, Münster, Germany;Freie Universität Berlin, DFG Research Center Matheon, Institut für Mathematik, Berlin, Germany
Venue:
Computing
Year:
2008

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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).