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
StatePublished - 1999

Fingerprint

Iterative Substructuring
Mortar
Domain Decomposition
Preconditioner
Two Dimensions
Mortar Method
Decomposition
Variational Approximation
Spectral Element Method
Second Order Elliptic Equations
Optimal Approximation
Condition number
Discretization
Finite Element Method
Finite element method

Keywords

  • Domain decomposition
  • Iterative substructuring
  • Mortar finite element method

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Iterative substructuring preconditioners for mortar element methods in two dimensions. / Achdou, Yves; Maday, Yvon; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 36, No. 2, 1999, p. 551-580.

Research output: Contribution to journalArticle

Achdou, Yves ; Maday, Yvon ; Widlund, Olof B. / Iterative substructuring preconditioners for mortar element methods in two dimensions. In: SIAM Journal on Numerical Analysis. 1999 ; Vol. 36, No. 2. pp. 551-580.
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