Geodesic
Parallel algorithms for solving 3-d elasticity problem and sparse linear systems
Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 10-28.

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The paper is devoted to the problem of parallelization of algorithms. In the first part, the general ideas of parallelization and some parallel direct methods for solving the sparse linear systems are considered. The second part is devoted to parallelization of the algorithm for solving the three-dimensional boundary value problem of elasticity by the boundary integral equations method and its implementation on the Parallel Computer Systems Mчу–100 and Mчу–1000. 
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E. N. Akimova. Parallel algorithms for solving 3-d elasticity problem and sparse linear systems. Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 10-28. http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a1/

[1] V. V. Voevodin, Matematicheskie modeli i metody v parallelnykh protsessakh, Nauka, M., 1986, 296 pp.

[2] V. N. Faddeeva, D. K. Faddeev, “Parallelnye vychisleniya v lineinoi algebre – 1”, Kibernetika, 1977, no. 6, 28–40 | MR | Zbl

[3] V. N. Faddeeva, D. K. Faddeev, “Parallelnye vychisleniya v lineinoi algebre – 2”, Kibernetika, 1982, no. 3, 18–31 | MR | Zbl

[4] E. Valyakh, Posledovatelno-parallelnye vychisleniya, Mir, M., 1985, 456 pp.

[5] I. N. Molchanov, Vvedenie v algoritmy parallelnykh vychislenii, Naukova Dumka, Kiev, 1990, 127 pp.

[6] Dzh. Ortega, Vvedenie v parallelnye i vektornye metody resheniya lineinykh sistem, Mir, M., 1991, 366 pp. | MR

[7] Parallelnye vychisleniya, ed. G. Rodrig, Nauka, M., 1986, 374 pp. | MR

[8] Sistemy parallelnoi obrabotki, ed. D. Ivens, Mir, M., 1985, 414 pp.

[9] N. N. Mirenkov, Parallelnoe programmirovanie dlya mnogomodulnykh vychislitelnykh sistem, Radio i svyaz, M., 1989, 320 pp. | MR | Zbl

[10] A. V. Zabrodin, V. K. Levin, V. V. Korneev, “The Massively Parallel Processing System MBC –100”, Proceedings of the Third International Conference (PaCT-95), ed. V. Malyshkin, Springer –Verlag, Berlin, 1995, 341–355

[11] E. S. Nikolaev, A. A. Samarskii, Metody resheniya setochnykh ellipticheskikh uravnenii v neregulyarnykh oblastyakh, Preprint IPM im.M.V.Keldysha, No63, Nauka, M., 1979, 23 pp.

[12] Yu. A. Kuznetsov, “Vychislitelnye metody v podprostranstvakh”, Vychislitelnye protsessy i sistemy, no. 2, Nauka, M., 1985, 265–350

[13] A. M. Matsokin, Metody fiktivnykh komponent i alternirovaniya po podoblastyam, Preprint VTs SO AN SSSR, No114, Novosibirsk, 1985, 16 pp.

[14] V. I. Lebedev, V. I. Agoshkov, Variatsionnye algoritmy metoda razdeleniya oblasti, Preprint OVM AN SSSR, No54, Nauka, M., 1983, 24 pp. | MR

[15] A. A. Samarskii, E. S. Nikolaev, Metody resheniya setochnykh uravnenii, Nauka, M., 1978, 590 pp. | MR

[16] D. Lawrie, A. Sameh, “The Computation and Communication Complexity of a Parallel Banded System Solver”, ACM Trans. Math., Softwere 10 (1984), 185–195 | DOI | MR | Zbl

[17] L. Johnsson, “Solving Narrow Banded Systems on Ensemble Architectures”, ACM Trans. Math., Softwere 11 (1985), 271–288 | DOI | MR | Zbl

[18] R. Khokni, K. Dzhesskhoup, Parallelnye EVM, Radio i svyaz, M., 1986, 390 pp.

[19] H. Stone, “Parallel Tridiagonal Equation Solvers”, ACM Trans. Math., Softwere 1 (1975), 289–307 | DOI | MR | Zbl

[20] A. Dzhordzh, Dzh. Lyu, Chislennoe reshenie bolshikh razrezhennykh sistem uravnenii, Mir, M., 1984, 334 pp. | MR

[21] N. N. Yanenko, A. N. Konovalov, A. N. Bugrov, G. V. Shustov, “Ob organizatsii parallelnykh vychislenii i rasparallelivanii progonki”, Chislennye metody mekhaniki sploshnoi sredy, 9, no. 7, VTs i ITiPM SO AN SSSR, Novosibirsk, 1978, 139–146

[22] E. N. Akimova, “Rasparallelivanie algoritma matrichnoi progonki”, Matematicheskoe modelirovanie, 6, no. 9, Nauka, M., 1994, 61–67 | MR

[23] V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, T. V. Burchuladze, Trekhmernye zadachi matematicheskoi teorii uprugosti i termouprugosti, Nauka, M., 1976, 663 pp. | MR

[24] V. V. Vasin, T. I. Serezhnikova, E. N. Akimova, Kompleks programm resheniya prostranstvennykh zadach uprugosti metodom granichnykh integralnykh uravnenii (MGIU-2), Otchet IMM UrO RAN, Ekaterinburg, 1996, 107 pp.

[25] L. B. Tsvik, “Obobschenie algoritma Shvartsa na sluchai oblastei, sopryazhennykh bez naleganiya”, DAN, 224:2 (1975), 309–312 | MR | Zbl

[26] V. V. Vasin, E. N. Akimova, “Parallelnye algoritmy resheniya trekhmernoi zadachi uprugosti”, Algoritmy i programmnye sredstva parallelnykh vychislenii, 3, Ekaterinburg, 1999, 34–47