Geodesic
A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 3, pp. 542-573

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: preconditioning, Krylov subspaces, multigrid algorithms, Navier–Stokes equations, the method of collocations and least squares. 
@article{VSGTU_2020_24_3_a6,
     author = {E. V. Vorozhtsov and V. P. Shapeev},
     title = {A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {542--573},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a6/}
}
TY  - JOUR
AU  - E. V. Vorozhtsov
AU  - V. P. Shapeev
TI  - A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2020
SP  - 542
EP  - 573
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a6/
LA  - ru
ID  - VSGTU_2020_24_3_a6
ER  - 
%0 Journal Article
%A E. V. Vorozhtsov
%A V. P. Shapeev
%T A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2020
%P 542-573
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a6/
%G ru
%F VSGTU_2020_24_3_a6
E. V. Vorozhtsov; V. P. Shapeev. A divergence-free method of collocations and least squares for the computation of incompressible fluid flows and its efficient implementation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 3, pp. 542-573. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a6/