A domain decomposition method with Lagrange multipliers and inexact solvers for linear elasticity

A. Klawonn, O. B. Widlund

Research output: Contribution to journalArticle

Abstract

A new decomposition method with Lagrange multipliers for elliptic problems is introduced. It is based on a reformulation of the well-known finite element tearing and interconnecting (FETI) method as a saddle point problem with both primal and dual variables as unknowns. The resulting linear system is solved with block-structured preconditioners combined with a suitable Krylov subspace method. This approach allows the use of inexact subdomain solvers for the positive definite subproblems. It is shown that the condition number of the preconditioned saddle point problem is bounded independently of the number of subregions and depends only polylogarithmically on the number of degrees of freedom of individual local subproblems. Numerical results are presented for a plane stress cantilever membrane problem.

Original languageEnglish (US)
Pages (from-to)1199-1219
Number of pages21
JournalSIAM Journal on Scientific Computing
Volume22
Issue number4
DOIs
StatePublished - 2001

Fingerprint

Domain decomposition methods
Saddle Point Problems
Lagrange multipliers
Linear Elasticity
Domain Decomposition Method
Linear systems
Elasticity
Decomposition
Membranes
Krylov Subspace Methods
Plane Stress
Cantilever
Condition number
Decomposition Method
Reformulation
Preconditioner
Elliptic Problems
Positive definite
Membrane
Degree of freedom

Keywords

  • Domain decomposition
  • Elliptic systems
  • Finite element tearing and interconnecting
  • Finite elements
  • Lagrange multipliers
  • Preconditioners

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A domain decomposition method with Lagrange multipliers and inexact solvers for linear elasticity. / Klawonn, A.; Widlund, O. B.

In: SIAM Journal on Scientific Computing, Vol. 22, No. 4, 2001, p. 1199-1219.

Research output: Contribution to journalArticle

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