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Bridging the gap between geometric and algebraic multi-grid methods


Feuchter, D; Heppner, I; Sauter, S; Wittum, G (2003). Bridging the gap between geometric and algebraic multi-grid methods. Computing and Visualization in Science, 6(1):1-13.

Abstract

In this paper, a multi-grid solver for the discretisation of partial differential equations on complicated domains is developed. The algorithm requires as input the given discretisation only instead of a hierarchy of discretisations on coarser grids. Such auxiliary grids and discretisations are generated in a black-box fashion and are employed to define purely algebraic intergrid transfer operators. The geometric interpretation of the algorithm allows one to use the framework of geometric multigrid methods to prove its convergence. The focus of this paper is on the formulation of the algorithm and the demonstration of its efficiency by numerical experiments, while the analysis is carried out for some model problems.

Abstract

In this paper, a multi-grid solver for the discretisation of partial differential equations on complicated domains is developed. The algorithm requires as input the given discretisation only instead of a hierarchy of discretisations on coarser grids. Such auxiliary grids and discretisations are generated in a black-box fashion and are employed to define purely algebraic intergrid transfer operators. The geometric interpretation of the algorithm allows one to use the framework of geometric multigrid methods to prove its convergence. The focus of this paper is on the formulation of the algorithm and the demonstration of its efficiency by numerical experiments, while the analysis is carried out for some model problems.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Theoretical Computer Science
Physical Sciences > Software
Physical Sciences > Modeling and Simulation
Physical Sciences > General Engineering
Physical Sciences > Computer Vision and Pattern Recognition
Physical Sciences > Computational Theory and Mathematics
Language:English
Date:2003
Deposited On:29 Nov 2010 16:26
Last Modified:06 May 2020 21:14
Publisher:Springer
ISSN:1432-9360
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00791-003-0102-3
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1030.65126
http://www.ams.org/mathscinet-getitem?mr=1985197

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