Bridging the gap between geometric and algebraic multi-grid methods

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

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalComputing and Visualization in Science
Volume6
Issue number1
DOIs
StatePublished - Jan 1 2003

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics

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