A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework
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 hierarc...
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| Published in | Computing Vol. 82; no. 2-3; pp. 103 - 119 |
|---|---|
| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Vienna
Springer Vienna
01.07.2008
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0010-485X 1436-5057 |
| DOI | 10.1007/s00607-008-0003-x |
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| 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 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). |
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| AbstractList | 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). [PUBLICATION 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 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). |
| Author | Dedner, A. Engwer, C. Ohlberger, M. Blatt, M. Sander, O. Klöfkorn, R. Bastian, P. |
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| Keywords | Finite elements Father relation 52C99 DUNE Finite volumes 65Y05 Hierarchical grids Geometric realization Index maps Interface Entity complex Parallelization 65N30 |
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| References | Benger W (2005) Visualization of general relativistic tensor fields via a Fiber Bundle Data Model. PhD thesis, Freie Universität Berlin Bastian P, Blatt M, Dedner A, Engwer C, Klöfkorn R, Kornhuber R, Ohlberger M, Sander O (2008) A generic grid interface for parallel and adaptive scientific computing. Part II: Implementation and tests in DUNE. Computing (this issue) Botta N, Ionescu C, Linstead C, Klein R (2006) Structuring distributed relation-based computations with SCDRC. Technical report, PIK Report No. 103, Potsdam Institute for Climate Impact Research Berti G (2000) Generic software components for scientific computing. PhD thesis, BTU Cottbus DUNE – Distributed and Unified Numerics Environment. http://dune-project.org 3_CR5 3_CR3 3_CR4 3_CR1 3_CR2 |
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| SubjectTerms | 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 |
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| Title | A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework |
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