Geodesic
Experimental study of some solvers of 3D boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 429-440 
I. A. Klimonov; V. M. Sveshnikov. Experimental study of some solvers of 3D boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 429-440. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a7/
@article{SJVM_2022_25_4_a7,
     author = {I. A. Klimonov and V. M. Sveshnikov},
     title = {Experimental study of some solvers of {3D} boundary},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {429--440},
     year = {2022},
     volume = {25},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a7/}
}
TY  - JOUR
AU  - I. A. Klimonov
AU  - V. M. Sveshnikov
TI  - Experimental study of some solvers of 3D boundary
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2022
SP  - 429
EP  - 440
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a7/
LA  - ru
ID  - SJVM_2022_25_4_a7
ER  - 
%0 Journal Article
%A I. A. Klimonov
%A V. M. Sveshnikov
%T Experimental study of some solvers of 3D boundary
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2022
%P 429-440
%V 25
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a7/
%G ru
%F SJVM_2022_25_4_a7

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

An experimental study of the efficiency of 3D boundary value problem solvers on the regular subgrids of quasi-structured parallelepipedal grids has been carried out. Five solvers are considered: three iterative: the successive over-relaxation method, the implicit alternating direction method, the implicit incomplete factorization method with acceleration by conjugate gradients, as well as two direct methods: PARDISO and HEMHOLTZ — both from the Intel MKL library. The characteristic features of the conducted research are the following: 1) the subgrids contain a small number of nodes; 2) the efficiency is estimated not only for single calculations, but also mainly for a series of calculations, in each of which a large number of repetitions of solving the problem with different boundary conditions on the same same subgrid. On the basis of numerical experiments, the fastest solver under the given conditions was revealed, which turned out to be the method of successive over-relaxation method.

[1] V. D. Korneev, V. M. Sveshnikov, “Parallel algorithms and domain decomposition techniques for solving three-dimensional boundary value problems on quasi-structured grids”, Numerical Analysis and Applications, 9:2 (2016), 141–149

[2] V. D. Korneev, V. M. Sveshnikov, “Parallelnye tekhnologii i setochnye struktury dannykh dlya resheniya trekhmernykh kraevykh zadach v slozhnykh oblastyakh na kvazistrukturirovannykh setkakh”, Vychislitelnye metody i programmirovanie, 19 (2018), 496–506

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

[4] A. Quarteroni, A. Valli, Domain Decomposition Methods for Partial Differential Equations, Clarendon Press, Oxford, 1999

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

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

[7] N. N. Koval, E. M. Oks, Yu. S. Protasov, N. N. Semashko, Emissionnaya elektronika, ed. Yu.S., Izd-vo MGTU im. N.E. Baumana, M., 2009

[8] V. P. Ilin, Metody konechnykh raznostei i konechnykh ob'emov dlya ellipticheskikh uravnenii, Izd-vo Instituta matematiki, Novosibirsk, 2000

[9] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1977

[10] V. P. Ilin, E. A. Itskovich, “Two explicit incomplete factorization methods”, Bull. Novosibirsk Comp. Center. Ser. Numerical Analysis, 11, Novosibirsk, 2002, 51–59