Dual-primal feti methods for three-dimensional elliptic problems with heterogeneous coefficients

Axel Klawonn, Olof B. Widlund, Maksymilian Dryja

Research output: Contribution to journalArticle

Abstract

In this paper, certain iterative substructuring methods with Lagrange multipliers are considered for elliptic problems in three dimensions. The algorithms belong to the family of dual-primal finite element tearing and interconnecting (FETI) methods which recently have been introduced and analyzed successfully for elliptic problems in the plane. The family of algorithms for three dimensions is extended and a full analysis is provided for the new algorithms. Particular attention is paid to finding algorithms with a small primal subspace since that subspace represents the only global part of the dual-primal preconditioner. It is shown that the condition numbers of several of the dual-primal FETI methods can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains, the mesh size, and jumps in the coefficients. These results closely parallel those of other successful iterative substructuring methods of primal as well as dual type.

Original languageEnglish (US)
Pages (from-to)159-179
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume40
Issue number1
DOIs
StatePublished - Apr 2002

Keywords

  • Domain decomposition
  • Dual-primal methods
  • Elliptic equations
  • FETI
  • Finite elements
  • Heterogeneous coefficients
  • Lagrange multipliers
  • Preconditioners

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Dual-primal feti methods for three-dimensional elliptic problems with heterogeneous coefficients'. Together they form a unique fingerprint.

  • Cite this