Some computational results for dual-primal FETI methods for elliptic problems in 3D

Axel Klawonn, Oliver Rheinbach, Olof B. Widlund

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Iterative substructuring methods with Lagrange multipliers for elliptic problems are considered. The algorithms belong to the family of dual-primal FETI methods which were introduced for linear elasticity problems in the plane by Farhat et al. [2001] and were later extended to three dimensional elasticity problems by Farhat et al. [2000]. Recently, the family of algorithms for scalar diffusion problems was extended to three dimensions and successfully analyzed by Klawonn et al. [2002a,b]. It was shown that the condition number of these dual-primal FETI algorithms 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 diffusion coefficients. In this article, numerical results for some of these algorithms are presented and their relation to the theoretical bounds is studied. The algorithms have been implemented in PETSc, see Balay et al. [2001], and their parallel scalability is analyzed.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Scienceand Engineering
Pages361-368
Number of pages8
Volume40
StatePublished - 2005

Publication series

NameLecture Notes in Computational Science and Engineering
Volume40
ISSN (Print)14397358

Fingerprint

Primal-dual
Elliptic Problems
Computational Results
Elasticity Problem
Elasticity
Iterative Substructuring
Lagrange multipliers
Diffusion Problem
Linear Elasticity
Condition number
Iterative methods
Diffusion Coefficient
Three-dimension
Scalability
Jump
Scalar
Mesh
Numerical Results
Three-dimensional
Family

ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mathematics
  • Modeling and Simulation
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

Cite this

Klawonn, A., Rheinbach, O., & Widlund, O. B. (2005). Some computational results for dual-primal FETI methods for elliptic problems in 3D. In Domain Decomposition Methods in Scienceand Engineering (Vol. 40, pp. 361-368). (Lecture Notes in Computational Science and Engineering; Vol. 40).

Some computational results for dual-primal FETI methods for elliptic problems in 3D. / Klawonn, Axel; Rheinbach, Oliver; Widlund, Olof B.

Domain Decomposition Methods in Scienceand Engineering. Vol. 40 2005. p. 361-368 (Lecture Notes in Computational Science and Engineering; Vol. 40).

Research output: Chapter in Book/Report/Conference proceedingChapter

Klawonn, A, Rheinbach, O & Widlund, OB 2005, Some computational results for dual-primal FETI methods for elliptic problems in 3D. in Domain Decomposition Methods in Scienceand Engineering. vol. 40, Lecture Notes in Computational Science and Engineering, vol. 40, pp. 361-368.
Klawonn A, Rheinbach O, Widlund OB. Some computational results for dual-primal FETI methods for elliptic problems in 3D. In Domain Decomposition Methods in Scienceand Engineering. Vol. 40. 2005. p. 361-368. (Lecture Notes in Computational Science and Engineering).
Klawonn, Axel ; Rheinbach, Oliver ; Widlund, Olof B. / Some computational results for dual-primal FETI methods for elliptic problems in 3D. Domain Decomposition Methods in Scienceand Engineering. Vol. 40 2005. pp. 361-368 (Lecture Notes in Computational Science and Engineering).
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