Geodesic
Adaptive analog-SSOR iterative method for solving grid equations with nonselfadjoint operators
Matematičeskoe modelirovanie, Tome 24 (2012) no. 1, pp. 3-20.

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The work is dedicated to the development of adaptive methods for solving convection-diffusion problems. For this class of problems a version of minimal correction adaptive SSOR was built, as well the convergence rate of the method was estimated, when grid Peclet number is restricted. Numerical results have been presented for the solving real hydrodynamics problem for shallow water basin using parallel algorithm of constructed method.
Keywords: grid equations with nonselfadjoint operator, adaptive SSOR with preconditioning, parallel algorithm
Mots-clés : domain decomposition. 
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A. I. Sukhinov; A. E. Chistyakov. Adaptive analog-SSOR iterative method for solving grid equations with nonselfadjoint operators. Matematičeskoe modelirovanie, Tome 24 (2012) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2012_24_1_a0/

[1] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989

[2] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, Editorial URSS, M., 1999

[3] Konovalov A. N., “K teorii poperemenno-treugolnogo iteratsionnogo metoda”, Sibirskii matematicheskii zhurnal, 43:3 (2002), 552–572 | MR | Zbl

[4] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, Editorial URSS, M., 1999

[5] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978

[6] Sukhinov A. I., “Modifitsirovannyi poperemenno-treugolnyi metod dlya zadach teplo-vodnosti i filtratsii”, Vychislitelnye sistemy i algoritmy, Izd-vo RGU, Rostov-na-Donu, 1984, 52–59

[7] Chistyakov A. E., “Trekhmernaya model dvizheniya vodnoi sredy v Azovskom more s uchetom transporta solei i tepla”, Izvestiya YuFU. Tekhnicheskie nauki. Tematicheskii vypusk «Aktualnye problemy matematicheskogo modelirovaniya», no. 8(97), Izd-vo TTI YuFU, Taganrog, 2009, 75–82

[8] Chistyakov A. E., “Teoreticheskie otsenki uskoreniya i effektivnosti parallelnoi realizatsii PTM skoreishego spuska”, Izvestiya YuFU. Tekhnicheskie nauki. Tematicheskii vypusk «Aktualnye problemy matematicheskogo modelirovaniya», no. 6(107), Izd-vo TTI YuFU, Taganrog, 2010, 237–249

[9] Sukhinov A. I., Shishenya A. V., “Uluchshenie otsenki parametra $\gamma_1$ poperemenno-treugolnogo iteratsionnogo metoda s apriornoi informatsiei”, Izvestiya YuFU. Tekhnicheskie nauki. Tematicheskii vypusk «Aktualnye problemy matematicheskogo modelirovaniya», no. 6(107), Izd-vo TTI YuFU, Taganrog, 2010, 7–15

[10] Sukhinov A. I., Chistyakov A. E., Alekseenko E. V., “Chislennaya realizatsiya trekhmernoi modeli gidrodinamiki dlya melkovodnykh vodoemov na supervychislitelnoi sisteme”, Matematicheskoe modelirovanie, 23:3 (2011), 3–21

[11] Alshina E. A., Boltnev A. A., Kacher O. A., “Gradientnye metody s uskorennoi skhodimostyu”, Zh. vychisl. matem. i matem. fiz., 45:3 (2005), 374–382

[12] Milyukova O. Yu., “Parallelnye iteratsionnye metody s faktorizovannoi matritsei predobuslovlivaniya dlya diskretnykh ellipticheskikh uravnenii na neravnomernoi setke”, Matem. modelirovanie, 15:4 (2003), 3–15

[13] Milyukova O. Yu., “Novye parallelnye iteratsionnye metody s faktorizovannymi matritsami predobuslovlivaniya dlya resheniya ellipticheskikh uravnenii na treugolnykh setkakh”, Matem. modelirovanie, 19:9 (2007), 27–48 | MR | Zbl