Iterative substructuring methods for spectral element discretizations of elliptic systems I: Compressible linear elasticity

Luca F. Pavarino, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

An iterative substructuring method for the system of linear elasticity in three dimensions is introduced and analyzed. The pure displacement formulation for compressible materials is discretized with the spectral element method. The resulting stiffness matrix is symmetric and positive definite. The proposed method provides a domain decomposition preconditioner constructed from local solvers for the interior of each element and for each face of the elements and a coarse, global solver related to the wire basket of the elements. As in the scalar case, the condition number of the preconditioned operator is independent of the number of spectral elements and grows as the square of the logarithm of the spectral degree.

Original languageEnglish (US)
Pages (from-to)353-374
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume37
Issue number2
StatePublished - 2000

Fingerprint

Iterative Substructuring
Spectral Elements
Linear Elasticity
Stiffness matrix
Elliptic Systems
Iterative methods
Elasticity
Discretization
Wire
Decomposition
Spectral Element Method
Domain Decomposition
Stiffness Matrix
Condition number
Logarithm
Preconditioner
Positive definite
Three-dimension
Interior
Scalar

Keywords

  • Gauss-Lobatto-Legendre quadrature
  • Linear elasticity
  • Preconditioned iterative methods substructuring
  • Spectral element methods

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Iterative substructuring methods for spectral element discretizations of elliptic systems I : Compressible linear elasticity. / Pavarino, Luca F.; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 37, No. 2, 2000, p. 353-374.

Research output: Contribution to journalArticle

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