Bridging the gap between geometric and algebraic multi-grid methods

D. Feuchter; I. Heppner; S. A. Sauter; G. Wittum

doi:10.1007/s00791-003-0102-3

Bridging the gap between geometric and algebraic multi-grid methods

D. Feuchter, I. Heppner, S. A. Sauter, G. Wittum

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this paper, a multi-grid solver for the discretisation of partial differential equations on complicated domains will be developed. The algorithm requires as input only the given discretisation instead of a hierarchy of discretisations on coarser grids. Such auxiliary grids and discretisations will be generated in a black-box fashion and will be 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.

Original language	English (US)
Pages (from-to)	1-13
Number of pages	13
Journal	Computing and Visualization in Science
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/s00791-003-0102-3
State	Published - Jun 2003
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgements. This work was supported by the National Science Foundation Grant 21-058891.99 and by the Swiss Federal Office for Education and Science Grant 01.0025-1/2 (as a part of the HMS 2000-Research Training Network “Homogenization and Multiple Scales” of the European Union).

ASJC Scopus subject areas

Theoretical Computer Science
Software
Modeling and Simulation
General Engineering
Computer Vision and Pattern Recognition
Computational Theory and Mathematics

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Bridging the gap between geometric and algebraic multi-grid methods

Abstract

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