Dual-primal FETI methods for linear elasticity

Axel Klawonn, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

Dual-primal FETI methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations, as in primal iterative substructuring methods, while most of the constraints are enforced by Lagrange multipliers, as in one-level FETI methods. These methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems. The purpose of this article is to develop strategies for selecting these constraints, which are enforced throughout the iterations, such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them. The algorithms are described in terms of a change of basis that has proven to be quite robust in practice. A theoretical analysis is provided for the case of linear elasticity, and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the Young's modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain. The strategies have already proven quite successful in large-scale implementations of these iterative methods.

Original languageEnglish (US)
Pages (from-to)1523-1572
Number of pages50
JournalCommunications on Pure and Applied Mathematics
Volume59
Issue number11
DOIs
StatePublished - Nov 2006

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Primal-dual
Linear Elasticity
Iterative methods
Elasticity
Domain decomposition methods
Lagrange multipliers
Iteration
Elastic moduli
Iterative Substructuring
Stiffness
Nonoverlapping Domain Decomposition
Young's Modulus
Domain Decomposition Method
Condition number
System of equations
Theoretical Analysis
Jump
Finite Element
Unknown
Strategy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Dual-primal FETI methods for linear elasticity. / Klawonn, Axel; Widlund, Olof B.

In: Communications on Pure and Applied Mathematics, Vol. 59, No. 11, 11.2006, p. 1523-1572.

Research output: Contribution to journalArticle

Klawonn, Axel ; Widlund, Olof B. / Dual-primal FETI methods for linear elasticity. In: Communications on Pure and Applied Mathematics. 2006 ; Vol. 59, No. 11. pp. 1523-1572.
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