A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework - Bastian, P.; Blatt, M.; Dedner, A.; Engwer, C.; Klöfkorn, R.; Ohlberger, M.; Sander, O. (Computing, 2008)
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).