On the use of inexact subdomain solvers for BDDC algorithms

Jing Li, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

The standard BDDC (balancing domain decomposition by constraints) preconditioner is shown to be equivalent to a preconditioner built from a partially subassembled finite element model. This results in a system of linear algebraic equations which is much easier to solve in parallel than the fully assembled model; the cost is then often dominated by that of the problems on the subdomains. An important role is also played, both in theory and practice, by an averaging operator and in addition exact Dirichlet solvers are used on the subdomains in order to eliminate the residual in the interior of the subdomains. The use of inexact solvers for these problems and even the replacement of the Dirichlet solvers by a trivial extension are considered. It is established that one of the resulting algorithms has the same eigenvalues as the standard BDDC algorithm, and the connection of another with the FETI-DP algorithm with a lumped preconditioner is also considered. Multigrid methods are used in the experimental work and under certain assumptions, it is established that the iteration count essentially remains the same as when exact solvers are used, while considerable gains in the speed of the algorithm can be realized since the cost of the exact solvers grows superlinearly with the size of the subdomain problems while the multigrid methods are linear.

Original languageEnglish (US)
Pages (from-to)1415-1428
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Volume196
Issue number8
DOIs
StatePublished - Jan 20 2007

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Decomposition
multigrid methods
decomposition
costs
linear equations
Linear equations
iteration
Costs
eigenvalues
operators

Keywords

  • BDDC
  • Domain decomposition
  • FETI-DP
  • Inexact solvers
  • Multi-level
  • Multigrid
  • Non-overlapping

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

On the use of inexact subdomain solvers for BDDC algorithms. / Li, Jing; Widlund, Olof B.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 8, 20.01.2007, p. 1415-1428.

Research output: Contribution to journalArticle

Li, Jing ; Widlund, Olof B. / On the use of inexact subdomain solvers for BDDC algorithms. In: Computer Methods in Applied Mechanics and Engineering. 2007 ; Vol. 196, No. 8. pp. 1415-1428.
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