Bastian, P. and Blatt, M. and Dedner, A. and Engwer, C. and Klöfkorn, R. and Ohlberger, M. and Sander, O. (2008) A generic grid interface for parallel and adaptive scientific computing. Part I: Abstract framework. Computing, 82 (23). pp. 103119. ISSN 0010485X

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Official URL: http://dx.doi.org/10.1007/s006070080003x
Abstract
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 nonconforming 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).
Item Type:  Article 

Uncontrolled Keywords:  DUNE, hierarchical grids, interface, finite elements, finite volumes, entity complex, geometric realization, father relation, index maps, parallelization 
Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1809 
Deposited By:  Ekaterina Engel 
Deposited On:  19 Feb 2016 09:03 
Last Modified:  03 Mar 2017 14:41 
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