Geodesic
Robust multigrid technique
Matematičeskoe modelirovanie, Tome 21 (2009) no. 9, pp. 66-79.

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

Robust multigrid method for solving a large class of applied problems on structured grids is offered. 
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S. I. Martynenko. Robust multigrid technique. Matematičeskoe modelirovanie, Tome 21 (2009) no. 9, pp. 66-79. http://geodesic.mathdoc.fr/item/MM_2009_21_9_a6/

[1] Bakhvalov N. S., “O skhodimosti odnogo relaksatsionnogo metoda pri estestvennykh ogranicheniyakh na ellipticheskii operator”, Zhurn. vychisl. matem. i matem. fiz., 6:5 (1966), 861–883 | Zbl

[2] Fedorenko R. P., “Relaksatsionnyi metod resheniya raznostnykh ellipticheskikh uravnenii”, Zhurn. vychisl. matem. i matem. fiz., 1:5 (1961), 922–927 | MR | Zbl

[3] Fedorenko R. P., “Skorost skhodimosti odnogo iteratsionnogo metoda”, Zhurn. vychisl. matem. i matem. fiz., 4:3 (1964), 227–235 | Zbl

[4] Brandt A., “Multi-level adaptive technique (MLAT) for fast numerical solution to boundary value problems”, Proc. 3rd Int. Conf. on Numerical Methods in Fluid Mechanics, Lectures Notes in Physics, 18, eds. H. Cabannes, R. Temam, Springer, Berlin, 1973, 82–89

[5] Brandt A., “Multi-level adaptive solutions to boundary value problems”, Math. Comput., 31 (1977), 333–390 | DOI | MR | Zbl

[6] Wesseling P., An Introduction to Multigrid Methods, Wiley, Chichester, 1991 | MR

[7] Wesseling P., Oosterlee C. W., “Geometric multigrid with applications to computational fluid dynamics”, J. Comput. Appl. Math., 128 (2001), 311–334 | DOI | MR | Zbl

[8] Kalitkin N. N., Chislennye metody, Nauka, M., 1978, 512 pp. | MR

[9] Samarskii A. A., Gulin A. V., Chislennye metody, Nauka, M., 1989, 432 pp. | MR

[10] Martynenko S. I., “Universalnaya mnogosetochnaya tekhnologiya dlya chislennogo resheniya kraevykh zadach na strukturirovannykh setkakh”, Vychislitelnye metody i programmirovanie, t. 1, razdel 1, 2000, 85–104

[11] Samarskii A. A., Teoriya raznostnykh skhem, Uch. pos., Nauka, M., 1983, 616 pp. | MR

[12] Martynenko S. I., “Robust multigrid technique for black box software”, Comput. Meth. in Appl. Math., 6:4 (2006), 413–435 | MR | Zbl

[13] Martynenko S. I., “Rasparallelivanie universalnoi mnogosetochnoi tekhnologii”, Vychislitelnye metody i programmirovanie, t. 4, razdel 1, 2003, 45–51

[14] Bornemann F. A., Deuflhard P., “The cascadic multigrid method for elliptic problems”, Numer. Math., 75 (1996), 135–152 | DOI | MR | Zbl

[15] Deuflhard P., “Cascadic conjugate gradient methods for elliptic partial differential equations. Algorithm and numerical results”, Proceeding of the 7th International Conference on Domain Decomposition Methods, eds. Keyes D., Xu J., AMS, Providence, 1993, 29–42 | MR

[16] Shaidurov V. V., “Some estimates of the rate of convergence for the cascadic conjugate-gradient method”, Comput. Math. Appl., 31 (1996), 161–171 | DOI | MR | Zbl

[17] Shi Z., Xu X., “Cascadic multigrid method for elliptic problems”, East-West J. Numer. Math., 3 (1999), 199–209 | MR | Zbl

[18] Hackbusch W., “Robust multi-grid methods, the frequency decomposition multi-grid algorithm”, Proc. 4th GAMM-seminar (Kiel, 1988), Notes on Numerical Fluid Mechanics, 123, ed. W. Hackbusch, Vieweg, Braunschweig, 1989, 96–104 | MR