An iterative substructuring method for Raviart-Thomas vector fields in three dimensions

Barbara I. Wohlmuth, Andrea Toselli, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

The iterative substructuring methods, also known as Schur complement methods, form one of two important families of domain decomposition algorithms. They are based on a partitioning of a given region, on which the partial differential equation is defined, into nonoverlapping substructures. The preconditioners of these conjugate gradient methods are then given in terms of local problems, defined on individual substructures and pairs of substructures, and, in addition, a global problem of low dimension. An iterative method of this kind is introduced for the lowest order Raviart-Thomas finite elements in three dimensions and it is shown that the condition number of the relevant operator is independent of the number of substructures and grows only as the square of the logarithm of the number of unknowns associated with an individual substructure. The theoretical bounds are confirmed by a series of numerical experiments.

Original languageEnglish (US)
Pages (from-to)1657-1676
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume37
Issue number5
StatePublished - 2000

Fingerprint

Iterative Substructuring
Substructure
Iterative methods
Three-dimension
Vector Field
Conjugate gradient method
Partial differential equations
Decomposition
Schur Complement
Decomposition Algorithm
Conjugate Gradient Method
Domain Decomposition
Condition number
Logarithm
Preconditioner
Experiments
Partitioning
Lowest
Partial differential equation
Numerical Experiment

Keywords

  • Domain decomposition
  • Iterative substructuring methods
  • Raviart-Thomas finite elements

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

An iterative substructuring method for Raviart-Thomas vector fields in three dimensions. / Wohlmuth, Barbara I.; Toselli, Andrea; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 37, No. 5, 2000, p. 1657-1676.

Research output: Contribution to journalArticle

Wohlmuth, BI, Toselli, A & Widlund, OB 2000, 'An iterative substructuring method for Raviart-Thomas vector fields in three dimensions', SIAM Journal on Numerical Analysis, vol. 37, no. 5, pp. 1657-1676.
Wohlmuth, Barbara I. ; Toselli, Andrea ; Widlund, Olof B. / An iterative substructuring method for Raviart-Thomas vector fields in three dimensions. In: SIAM Journal on Numerical Analysis. 2000 ; Vol. 37, No. 5. pp. 1657-1676.
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