Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems

Owe Axelsson, Radim Blaheta, Petr Byczanski, J. Karátson, Bashir Ahmad

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Saddle point problems arise in the modeling of many important practical situations. Preconditioners for the corresponding matrices of block-triangular form, based on coupled inner-outer iteration methods, are analyzed and applied to a Darcy flow problem, possibly with strong heterogeneity and non-symmetric saddle point systems. Using proper regularized forms of the given matrix and its preconditioner, it is shown that the eigenvalues cluster about one or two points on the real axis for large values of the regularization parameters and that eigenvalue bounds do not depend on this variation. Therefore, just two outer iterations can suffice. On the other hand, several iterations may be needed to solve the inner iteration systems.

Original languageEnglish
Pages (from-to)141-157
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume280
DOIs
Publication statusPublished - May 15 2015

Fingerprint

Darcy Flow
Saddle Point Problems
Preconditioner
Iteration
Saddle Point Systems
Eigenvalue Bounds
Regularization Parameter
Iteration Method
Triangular
Eigenvalue
Modeling
Form

Keywords

  • Darcy flow
  • Heterogeneous coefficients
  • Inner-outer iterations
  • Preconditioners
  • Regularized saddle point

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems. / Axelsson, Owe; Blaheta, Radim; Byczanski, Petr; Karátson, J.; Ahmad, Bashir.

In: Journal of Computational and Applied Mathematics, Vol. 280, 15.05.2015, p. 141-157.

Research output: Contribution to journalArticle

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