Parallel Adaptive Deflated GMRES

Désiré Nuentsa Wakam, Jocelyne Erhel, William D Gropp

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Many scientific libraries are currently based on the GMRES method as a Krylov subspace iterative method for solving large linear systems. The restarted formulation known as GMRES(m) has been extensively studied and several approaches have been proposed to reduce the negative effects due to the restarting procedure. A common effect in GMRES(m) is a slow convergence rate or a stagnation in the iterative process. In this situation, it is less attractive as a general solver in industrial applications. In this work, we propose an adaptive deflation strategy which retains useful information at time of restart to avoid stagnation in GMRES(m) and improve its convergence rate. We give a parallel implementation in the PETSc package. The provided numerical results show that this approach can be effectively used in the hybrid direct/iterative methods to solve large-scale systems.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XX
EditorsRandolph Bank, Michael Holst, Jinchao Xu, Olof Widlund
Pages631-638
Number of pages8
DOIs
StatePublished - Jul 25 2013

Publication series

NameLecture Notes in Computational Science and Engineering
Volume91
ISSN (Print)1439-7358

Fingerprint

GMRES
Iterative methods
Convergence Rate
Industrial applications
GMRES Method
Linear systems
Iteration
Large scale systems
Deflation
Subspace Methods
Krylov Subspace
Restart
Iterative Process
Large-scale Systems
Parallel Implementation
Industrial Application
Direct Method
Linear Systems
Numerical Results
Formulation

ASJC Scopus subject areas

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

Cite this

Wakam, D. N., Erhel, J., & Gropp, W. D. (2013). Parallel Adaptive Deflated GMRES. In R. Bank, M. Holst, J. Xu, & O. Widlund (Eds.), Domain Decomposition Methods in Science and Engineering XX (pp. 631-638). (Lecture Notes in Computational Science and Engineering; Vol. 91). https://doi.org/10.1007/978-3-642-35275-1_75

Parallel Adaptive Deflated GMRES. / Wakam, Désiré Nuentsa; Erhel, Jocelyne; Gropp, William D.

Domain Decomposition Methods in Science and Engineering XX. ed. / Randolph Bank; Michael Holst; Jinchao Xu; Olof Widlund. 2013. p. 631-638 (Lecture Notes in Computational Science and Engineering; Vol. 91).

Research output: Chapter in Book/Report/Conference proceedingChapter

Wakam, DN, Erhel, J & Gropp, WD 2013, Parallel Adaptive Deflated GMRES. in R Bank, M Holst, J Xu & O Widlund (eds), Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol. 91, pp. 631-638. https://doi.org/10.1007/978-3-642-35275-1_75
Wakam DN, Erhel J, Gropp WD. Parallel Adaptive Deflated GMRES. In Bank R, Holst M, Xu J, Widlund O, editors, Domain Decomposition Methods in Science and Engineering XX. 2013. p. 631-638. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-35275-1_75
Wakam, Désiré Nuentsa ; Erhel, Jocelyne ; Gropp, William D. / Parallel Adaptive Deflated GMRES. Domain Decomposition Methods in Science and Engineering XX. editor / Randolph Bank ; Michael Holst ; Jinchao Xu ; Olof Widlund. 2013. pp. 631-638 (Lecture Notes in Computational Science and Engineering).
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