Iterative substructuring preconditioners for mortar element methods in two dimensions

Yves Achdou, Yvon Maday, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

The mortar methods are based on domain decomposition and they allow for the coupling of different variational approximations in different subdomains. The resulting methods are nonconforming but still yield optimal approximations. In this paper, we will discuss iterative substructuring algorithms for the algebraic systems arising from the discretization of symmetric, second-order, elliptic equations in two dimensions. Both spectral and finite element methods, for geometrically conforming as well as nonconforming domain decompositions, are studied. In each case, we obtain a polylogarithmic bound on the condition number of the preconditioned matrix.

Original languageEnglish (US)
Pages (from-to)551-580
Number of pages30
JournalSIAM Journal on Numerical Analysis
Volume36
Issue number2
DOIs
StatePublished - Jan 1 1999

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Keywords

  • Domain decomposition
  • Iterative substructuring
  • Mortar finite element method

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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