A new mixed preconditioning method for finite element computations

Tayfun E. Tezduyar, M. Behr, S. K. Aliabadi, S. Mittal, S. E. Ray

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

A new mixed clustered element-by-element (CEBE)/cluster companion (CC) preconditioning method for finite element computations is introduced. In the CEBE preconditioning, the elements are merged into clusters of elements, and the preconditioners are defined as series products of cluster level matrices. The CC preconditioning method, which is also introduced in this paper, shares a common philosophy with the multi-grid methods. The CC preconditioners are based on companion meshes associated with different levels of clustering. For each level of clustering, we construct a CEBE preconditioner and an associated CC preconditioner. Because these two preconditioners in a sense complement each other, when they are used in a mixed way, they can be expected to give better performance. In fact, our numerical tests, for two- and three-dimensional problems governed by the Poisson equation, demonstrate that the mixed CEBE/CC preconditioning results in convergence rates which are, in most cases, significantly better than the convergence rates obtained with the best of the CEBE and CC preconditioning methods.

Original languageEnglish
Pages (from-to)27-42
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume99
Issue number1
DOIs
Publication statusPublished - 1992
Externally publishedYes

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preconditioning
Poisson equation
multigrid methods
complement
mesh
products
matrices

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

A new mixed preconditioning method for finite element computations. / Tezduyar, Tayfun E.; Behr, M.; Aliabadi, S. K.; Mittal, S.; Ray, S. E.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 99, No. 1, 1992, p. 27-42.

Research output: Contribution to journalArticle

Tezduyar, Tayfun E. ; Behr, M. ; Aliabadi, S. K. ; Mittal, S. ; Ray, S. E. / A new mixed preconditioning method for finite element computations. In: Computer Methods in Applied Mechanics and Engineering. 1992 ; Vol. 99, No. 1. pp. 27-42.
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