A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework
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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).
KeywordsDUNE Hierarchical grids Interface Finite elements Finite volumes Entity complex Geometric realization Father relation Index maps Parallelization
Mathematics Subject Classification (2000)65N30 52C99 65Y05
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