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

We give a mathematically rigorous definition of a grid for algorithms solving partial differential equations. Unlike previous approaches [2, 3], 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 framework [1]