Performance of block-ILU factorization preconditioners based on block-size reduction for 2D elasticity systems

Tony F. Chan*, Svetozar D. Margenov, Panayot S. Vassilevski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The performance of the block-ILU factorization preconditioners that exploit block-size reduction (introduced in [T.F. Chan and P.S. Vassilevski, Math. Comp., 64 (1995), pp. 129-156]) is studied in the case of block-tridiagonal finite element matrices arising from the discretization of the two-dimensional (2D) Navier equations of elasticity. Conforming triangle finite elements are used for discretizing the differential problem. For the model problem, an estimate of the relative condition number is derived. The efficiency of this incomplete factorization is based on the Sherman-Morrison-Woodbury formula, and, of particular importance, this factorization exists for symmetric and positive definite block-tridiagonal matrices that are not necessarily M-matrices. The convergence rate of the preconditioner is controlled by the block-size reduction parameter which, however, reflects the cost. The numerical tests presented illustrate a strategy for coarse grid size selection; we have also tested the problem for values of the Poisson ratio (v ∈ (0, 1/2)) close to the incompressible limit (e.g., ṽ= 0.9, where v = ṽ/1-ṽ) with the expense of about four times more iterations than for the scalar Poisson equation with the same quality preconditioner.

Original languageEnglish (US)
Pages (from-to)1355-1366
Number of pages12
JournalSIAM Journal of Scientific Computing
Volume18
Issue number5
DOIs
StatePublished - Jan 1 1997
Externally publishedYes

Keywords

  • Almost incompressible elasticity
  • Block-incomplete factorization
  • Preconditioning

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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