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@article{MM_2003_15_4_a0, author = {O. Yu. Milyukova}, title = {Parallel iterative methods with factorized preconditioning matrices for discretized elliptic equations on nonuniform grids}, journal = {Matemati\v{c}eskoe modelirovanie}, pages = {3--15}, publisher = {mathdoc}, volume = {15}, number = {4}, year = {2003}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MM_2003_15_4_a0/} }
TY - JOUR AU - O. Yu. Milyukova TI - Parallel iterative methods with factorized preconditioning matrices for discretized elliptic equations on nonuniform grids JO - Matematičeskoe modelirovanie PY - 2003 SP - 3 EP - 15 VL - 15 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MM_2003_15_4_a0/ LA - ru ID - MM_2003_15_4_a0 ER -
%0 Journal Article %A O. Yu. Milyukova %T Parallel iterative methods with factorized preconditioning matrices for discretized elliptic equations on nonuniform grids %J Matematičeskoe modelirovanie %D 2003 %P 3-15 %V 15 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/MM_2003_15_4_a0/ %G ru %F MM_2003_15_4_a0
O. Yu. Milyukova. Parallel iterative methods with factorized preconditioning matrices for discretized elliptic equations on nonuniform grids. Matematičeskoe modelirovanie, Tome 15 (2003) no. 4, pp. 3-15. http://geodesic.mathdoc.fr/item/MM_2003_15_4_a0/
[1] J. A. Meijerink, H. A. van der Vorst, “An iterative solution method for linear systems of which the coefficient matrix is a symmetric $M$-matrix”, Math. Comput., 31:137 (1977), 148–162 | DOI | MR | Zbl
[2] I. Gustafsson, “A class of first order factorization methods”, BIT, 18 (1978), 142–156 | DOI | MR | Zbl
[3] T. Dupont, R. Kendall, H. H. Rachford Jr., “An approximate factorization procedure for solving self-adjoint elliptic difference equations”, SIAM J. Numer. Anal., 5 (1968), 559–573 | DOI | MR | Zbl
[4] O. Axelsson, “A Generalized SSOR Method”, BIT, 13 (1972), 443–467 | DOI | MR
[5] A. B. Kucherov, M. M. Makarov, “Metod priblizhennoi faktorizatsii dlya resheniya raznostnykh smeshannykh kraevykh zadach”, Raznostnye metody matematicheskoi fiziki, MGU, M., 1984, 54–65 | MR
[6] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1989 | MR
[7] A. A. Samarskii, E. S. Nikolaev, Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR | Zbl
[8] Dzh. Ortega, Vedenie v parallelnye i vektornye metody resheniya lineinykh sistem, Mir, M., 1991 | MR
[9] S. Doi, “On parallelism and convergence of incomplete LU factorizations”, Appl. Numer. Math., 7:5 (1991), 417–436 | DOI | MR | Zbl
[10] I. S. Duff, G. A. Meurant, “The effect of ordering on preconditioned conjugate gradients”, BIT, 29 (1989), 635–657 | DOI | MR | Zbl
[11] V. Eijkhout, “Analysis of parallel incomplete point factorizations”, Lin. Alg. Appl., 154–156 (1991), 723–740 | DOI | MR | Zbl
[12] O. Yu. Milyukova, B. N. Chetverushkin, “Parallelnyi variant poperemenno-treugolnogo metoda”, Zhurn. vychisl. matem. i matem. fiziki, 38:2 (1998), 228–238 | MR | Zbl
[13] Y. Notay, “An efficient parallel discrete PDE solver”, Parallel Computing, 21 (1995), 1725–1748 | DOI | MR
[14] S. A. Stotland, J. M. Ortega, “Ordering for parallel conjugate gradient preconditioned”, SIAM J. Sci. Comput., 18:3 (1997), 854–868 | DOI | MR | Zbl
[15] O. Yu. Milyukova, “Parallelnyi variant obobschennogo poperemenno-treugolnogo metoda dlya resheniya ellipticheskikh uravnenii”, Zhurn. vychisl. matem. i matem. fiziki, 38:12 (1998), 2002–2012 | MR | Zbl
[16] Y. Notay, “DRIC: a dinamic version of the RIC method”, Journ. Num. Lin. Alg. with Appl., 1 (1994), 511–533 | DOI | MR
[17] O. Yu. Milyukova, “Parallel approximate factorization method for solving discrete elliptic equations”, Parallel Computing, 27 (2001), 1365–1379 | DOI | MR | Zbl
[18] O. Yu. Milyukova, “Parallelnyi iteratsionnyi metod s faktorizovannoi matritsei predobuslovlivaniya dlya resheniya ellipticheskikh uravnenii”, Differentsialnye uravneniya, 36:7 (2000), 953–962 | MR | Zbl
[19] A. N. Konovalov, Vvedenie v vychislitelnye metody lineinoi algebry, Nauka, Sibirskaya izdatelskaya firma, Novosibirsk, 1993 | MR | Zbl
[20] T. A. Kudryashova, S. V. Polyakov, “O nekotorykh metodakh resheniya kraevykh zadach na mnogoprotsessornykh vychislitelnykh sistemakh”, Matematicheskie modeli nelineinykh vozbuzhdenii, perenosa, dinamiki, upravleniya v kondensirovannykh sistemakh i drugikh sredakh, Sb. trudov 4-oi mezhdunarodnoi nauchnoi konferentsii (M., 27 iyunya–1iyulya 2000 g.), eds. L. A. Uvarova, A. E. Arinshtein, Stankin, M., 2001, 134–145