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Scientific article
Open access
English

Analysis of Patch Substructuring Methods

Publication date2007
Abstract

Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains, condensated on the interfaces, to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergence rate than both the algebraic and the geometric one. We complement our results by numerical experiments.

Keywords
  • finite element method
  • finite difference method
  • Schwarz domain decomposition methods
  • Schur complement methods
  • patch substructuring methods
  • optimized Schwarz methods
  • Neumann transmission conditions
  • convergence
  • numerical experiments
Citation (ISO format)
GANDER, Martin Jakob et al. Analysis of Patch Substructuring Methods. In: International Journal of Applied Mathematics and Computer Science, 2007, vol. 17, n° 3, p. 395–402.
Main files (1)
Article (Accepted version)
accessLevelPublic
Identifiers
  • PID : unige:6272
ISSN of the journal1641-876X
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