A unified approach to parallel space decomposition methods

Andreas Frommer, Rosemary Renaut

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We consider (relaxed) additive and multiplicative iterative space decomposition methods for the minimization of sufficiently smooth functionals without constraints. We develop a general framework which unites existing approaches from both parallel optimization and finite elements. Specifically this work unifies earlier research on the parallel variable distribution method in minimization, space decomposition methods for convex functionals, algebraic Schwarz methods for linear systems and splitting methods for linear least squares. We develop a general convergence theory within this framework, which provides several new results as well as including known convergence results.

Original languageEnglish (US)
Pages (from-to)205-223
Number of pages19
JournalJournal of Computational and Applied Mathematics
Volume110
Issue number1
DOIs
StatePublished - Oct 15 1999

Keywords

  • 65H10
  • Block Jacobi
  • Block SOR
  • Finite elements
  • Minimization* Coordinate descent
  • Multisplittings* Parallel computation
  • Parallel variable distribution
  • Space decomposition methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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