Conjugate Direction Methods for Parallel Deflation

Yana Gurieva, Valery Il’in

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

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.

Язык оригиналаанглийский
Название основной публикацииParallel Computational Technologies - 15th International Conference, PCT 2021, Revised Selected Papers
РедакторыLeonid Sokolinsky, Mikhail Zymbler
ИздательSpringer Science and Business Media Deutschland GmbH
Страницы194-207
Число страниц14
ISBN (печатное издание)9783030816902
DOI
СостояниеОпубликовано - 2021
Событие15th International Conference on Parallel Computational Technologies, PCT 2021 - Virtual, Online
Продолжительность: 30 мар 20211 апр 2021

Серия публикаций

НазваниеCommunications in Computer and Information Science
Том1437
ISSN (печатное издание)1865-0929
ISSN (электронное издание)1865-0937

Конференция

Конференция15th International Conference on Parallel Computational Technologies, PCT 2021
ГородVirtual, Online
Период30.03.202101.04.2021

Предметные области OECD FOS+WOS

  • 1.01 МАТЕМАТИКА
  • 1.02 КОМПЬЮТЕРНЫЕ И ИНФОРМАЦИОННЫЕ НАУКИ

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