Бездивергентный метод коллокаций и наименьших квадратов для расчета течений несжимаемой жидкости и его эффективная реализация

Translated title of the contribution: A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation

E. V. Vorozhtsov, V. P. Shapeev

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of the acceleration of the iterative process of numerical solution by the collocation and least squares (CLS) method of boundary value problems for partial differential equations is considered. For its solution, it is proposed to apply simultaneously three ways to accelerate the iterative process: preconditioner, multigrid algorithm, and Krylov method. A method for finding the optimal values of the parameters of the two-parameter preconditioner is proposed. The use of the found preconditioner significantly accelerates the iterative process. The influence on the iterative process of all three ways of its acceleration is investigated: each separately, and also at their combined application. The application of the algorithm using Krylov subspaces gives the greatest contribution. The combined use of all three ways to speed up the iteration process of solving boundary value problems for two-dimensional Navier-Stokes equations has reduced the CPU time up to 362 times as compared with the case when only one of them, the preconditioner, was applied.

Translated title of the contributionA divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation
Original languageRussian
Pages (from-to)542-573
Number of pages32
JournalVestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, Seriya Fiziko-Matematicheskie Nauki
Volume24
Issue number3
DOIs
Publication statusPublished - Oct 2020

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