Geodesic
Experimental study of the efficiency of solving 2D boundary value problems on subgrids of quasistructured rectangular grids
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 3, pp. 277-288 
A. N. Kozyrev; V. M. Sveshnikov. Experimental study of the efficiency of solving 2D boundary value problems on subgrids of quasistructured rectangular grids. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 3, pp. 277-288. http://geodesic.mathdoc.fr/item/SJVM_2021_24_3_a3/
@article{SJVM_2021_24_3_a3,
     author = {A. N. Kozyrev and V. M. Sveshnikov},
     title = {Experimental study of the efficiency of solving {2D} boundary value problems on subgrids of quasistructured rectangular grids},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {277--288},
     year = {2021},
     volume = {24},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2021_24_3_a3/}
}
TY  - JOUR
AU  - A. N. Kozyrev
AU  - V. M. Sveshnikov
TI  - Experimental study of the efficiency of solving 2D boundary value problems on subgrids of quasistructured rectangular grids
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2021
SP  - 277
EP  - 288
VL  - 24
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJVM_2021_24_3_a3/
LA  - ru
ID  - SJVM_2021_24_3_a3
ER  - 
%0 Journal Article
%A A. N. Kozyrev
%A V. M. Sveshnikov
%T Experimental study of the efficiency of solving 2D boundary value problems on subgrids of quasistructured rectangular grids
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2021
%P 277-288
%V 24
%N 3
%U http://geodesic.mathdoc.fr/item/SJVM_2021_24_3_a3/
%G ru
%F SJVM_2021_24_3_a3

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

An experimental study of the solvers efficiency of 2D boundary value problems on subgrids of quasistructured rectangular grids was carried out. A solver is understood as a solution method and its software implementation. Three solvers are considered: one direct solver – the Buneman cyclic reduction method and two iterative ones: the Peaceman-Rachford method and the method of successive over relaxation. Characteristic features of the studies are: 1) the subgrids contain a small number of nodes, namely 8$\times$8, 16$\times$16, 32$\times$32, 64$\times$64; 2) the efficiency is estimated not only for single calculations, but also mainly for series of calculations, in each of which several repetitions of solving the problem with different boundary conditions on the same subgrid are carried out. Based on serial calculations, a combined method is proposed, and recommendations on the use of solvers are given.

[1] Kozyrev A.N., Sveshnikov V.M., “O postroenii dvumernykh lokalno-modifitsirovannykh kvazistrukturirovannykh setok i reshenii na nikh kraevykh zadach v oblastyakh s krivolineinoi granitsei”, Vestnik YuUrGU. Seriya: Vychislitelnaya matematika i informatika, 6:2 (2017), 5–21

[2] Liseikin V.D., Grid Generation Methods, Springer-Verlag, Berlin, 1999 | MR | Zbl

[3] Shokin Yu.I., Danaev N.T., Khakimzyanov G.S., Shokina N.Yu., Lektsii po raznostnym skhemam na podvizhnykh setkakh, v. 2, Izd-vo KazNU im. al-Farabi, Almaty, 2008

[4] Vasilevskii Yu.V., Olshanskii M.A., Kratkii kurs po mnogosetochnym metodam i metodam dekompozitsii oblasti, MGU, M., 2007

[5] Quarteroni A., Valli A., Domain Decomposition Methods for Partial Differential Equations, Clarendon Press, Oxford, 1999 | MR | Zbl

[6] Dolean V., Jolivet P., Nataf F., An Introduction to Domain Decomposition Methods: Algorithms, Theory and Parallel Implementation, SIAM, Philadelphia, USA, 2015 | MR | Zbl

[7] Sveshnikov V.M., “Postroenie pryamykh i iteratsionnykh metodov dekompozitsii”, Sib. zhurn. industr. matem., 12:3 (2009), 99–109 | Zbl

[8] Samarskii A.A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR

[9] Ilin V.P., Metody konechnykh raznostei i konechnykh ob'emov dlya ellipticheskikh uravnenii, Izd-vo IVMiMG SO RAN, Novosibirsk, 2001

[10] Astrelin V.T., Vorobyov M.S., Kozyrev A.N., Sveshnikov V.M., “Numerical simulation of the operation of a wide-aperture electron gun with a grid plasma emitter and beam extraction into the atmosphere”, J. of Applied Mechanics and Technical Physics, 60:5 (2019), 785–792 | DOI | MR