Comparative Analysis of Parallel Methods for Solving SLAEs in Three-Dimensional Initial-Boundary Value Problems

V. S. Gladkikh, V. P. Ilin, M. S. Pekhterev

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

Аннотация

Iterative methods for solving systems of linear algebraic equations with high-order sparse matrices that arise in absolutely stable implicit finite-volume approximations of three-dimensional initial-boundary value problems for the heat and mass transfer equation on unstructured grids in computational domains with a complex configuration of multiply connected piecewise smooth boundary surfaces and contrasting material properties are considered. At each time step, algebraic systems are solved using parallel preconditioned algorithms for conjugate directions in Krylov subspaces. To speed up the iterative processes, variational methods for choosing initial approximations are applied using numerical solutions from previous time steps. It is discussed how the proposed approaches can be more general formulations of problems, as well as how to increase the productivity of computational methods and technologies in the multiple solution of algebraic systems with sequentially determined different right-hand sides and with the scalable parallelization of algorithms based on the additive methods of domain decomposition. The efficiency of the proposed approaches is investigated for the implicit Euler and Crank–Nicholson schemes based on the results of numerical experiments on a representative series of methodological problems.

Язык оригиналаанглийский
Название основной публикацииParallel Computational Technologies - 16th International Conference, PCT 2022, Revised Selected Papers
РедакторыLeonid Sokolinsky, Mikhail Zymbler
ИздательSpringer Science and Business Media Deutschland GmbH
Страницы59-72
Число страниц14
ISBN (печатное издание)9783031116223
DOI
СостояниеОпубликовано - 2022
Событие16th International Conference on Parallel Computational Technologies, PCT 2022 - Dubna, Российская Федерация
Продолжительность: 29 мар 202231 мар 2022

Серия публикаций

НазваниеCommunications in Computer and Information Science
Том1618 CCIS
ISSN (печатное издание)1865-0929
ISSN (электронное издание)1865-0937

Конференция

Конференция16th International Conference on Parallel Computational Technologies, PCT 2022
СтранаРоссийская Федерация
ГородDubna
Период29.03.202231.03.2022

Предметные области OECD FOS+WOS

  • 1.02 КОМПЬЮТЕРНЫЕ И ИНФОРМАЦИОННЫЕ НАУКИ
  • 1.01 МАТЕМАТИКА

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