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

doi:10.1007/s00607-008-0003-x

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

2008-04-29

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DOI：10.1007/s00607-008-0003-x

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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).

Keyword:

DUNE

hierarchical grids

interface

finite elements

finite volumes

entity complex

geometric realization

father relation

index maps

parallelization

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

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