TY - GEN A1 - Bastian, Peter A1 - Blatt, Markus A1 - Dedner, Andreas A1 - Engwer, Christian A1 - Klöfkorn, Robert A1 - Ohlberger, Mario A1 - Sander, Oliver T1 - A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part I: Abstract Framework N2 - We give a mathematically rigorous definition of a grid for algorithms solving partial differential equations. Unlike previous approaches, 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 nonconforming grids. The definitions in this article serve as the basis for an implementation of an abstract grid interface as C++ classes in the DUNE. KW - hierarchical grids KW - grid-based methods KW - Dune Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/416 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4162 ER -