Conjugate Direction Methods for Parallel Deflation

Yana Gurieva, Valery Il’in

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

We consider parallel iterative processes in Krylov subspaces for solving symmetric positive definite systems of linear algebraic equations (SLAEs) with sparse ill-conditioned matrices arising under grid approximations of multidimensional initial-boundary value problems. Furthermore, we research the efficiency of the methods of moments for choosing an initial guess and constructing a projective-type preconditioner based on a known basis formed by the direction vectors. As a result, the reduction in the number of iterations implies an increase in their computational complexity, which is effectively minimized by parallelizing vector operations. The approaches under consideration are relevant for the multiple solution of SLAEs with the same matrices and different sequentially determined right-hand sides. Such systems arise in multilevel iterative algorithms, including additive domain decomposition and multigrid approaches. The efficiency of the suggested methods is demonstrated by the results of numerical experiments involving methodological examples.

Original languageEnglish
Title of host publicationParallel Computational Technologies - 15th International Conference, PCT 2021, Revised Selected Papers
EditorsLeonid Sokolinsky, Mikhail Zymbler
PublisherSpringer Science and Business Media Deutschland GmbH
Pages194-207
Number of pages14
ISBN (Print)9783030816902
DOIs
Publication statusPublished - 2021
Event15th International Conference on Parallel Computational Technologies, PCT 2021 - Virtual, Online
Duration: 30 Mar 20211 Apr 2021

Publication series

NameCommunications in Computer and Information Science
Volume1437
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference15th International Conference on Parallel Computational Technologies, PCT 2021
CityVirtual, Online
Period30.03.202101.04.2021

Keywords

  • Conjugate directions
  • Deflation
  • Iterative algorithms
  • Krylov subspaces
  • Numerical experiments
  • Preconditioning matrix

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.02 COMPUTER AND INFORMATION SCIENCES

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