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

• Published in: Computing Vol. 82; no. 2-3; pp. 103 - 119
• Main Authors: Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.07.2008; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; C plus plus; Computer Appl. in Administrative Data Processing; Computer Communication Networks; Computer Science; Euclidean space; Information Systems Applications (incl.Internet); Linear algebra; Numerical analysis; Partial differential equations; Software; Software Engineering; Studies; Finite elements; Father relation; 52C99; DUNE; Finite volumes; 65Y05; Hierarchical grids; Geometric realization; Index maps; Interface; Entity complex; Parallelization; 65N30
• ISSN: 0010-485X; 1436-5057
• DOI: 10.1007/s00607-008-0003-x

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).