A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation
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 iterativ...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2020-10-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/60872/43981 |
| _version_ | 1828491792818896896 |
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| author | Evgenii Vasil'evich Vorozhtsov Vasiliy Pavlovich Shapeev |
| author_facet | Evgenii Vasil'evich Vorozhtsov Vasiliy Pavlovich Shapeev |
| author_sort | Evgenii Vasil'evich Vorozhtsov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T11:09:01Z |
| format | Article |
| id | doaj.art-6c5263d81a194302a3fabea53e97a105 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-11T11:09:01Z |
| publishDate | 2020-10-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-6c5263d81a194302a3fabea53e97a1052022-12-22T01:09:36ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812020-10-0124354257310.14498/vsgtu175855736A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementationEvgenii Vasil'evich Vorozhtsov0Vasiliy Pavlovich Shapeev1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of SciencesKhristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of SciencesThe 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.https://journals.eco-vector.com/1991-8615/article/viewFile/60872/43981preconditioningkrylov subspacesmultigrid algorithmsnavier–stokes equationsthe method of collocations and least squares |
| spellingShingle | Evgenii Vasil'evich Vorozhtsov Vasiliy Pavlovich Shapeev A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki preconditioning krylov subspaces multigrid algorithms navier–stokes equations the method of collocations and least squares |
| title | A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation |
| title_full | A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation |
| title_fullStr | A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation |
| title_full_unstemmed | A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation |
| title_short | A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation |
| title_sort | divergence free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation |
| topic | preconditioning krylov subspaces multigrid algorithms navier–stokes equations the method of collocations and least squares |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/60872/43981 |
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