Geodesic
Superfast method with guaranteed accuracy for elliptic equations in rectangular domain
Matematičeskoe modelirovanie, Tome 27 (2015) no. 7, pp. 37-43.

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

In finite-difference solution of elliptic equations we face with algebraic systems of enormous sizes with strongly rarefied matrices. A superfast iterative technique has been proposed that is viable for a wide class of problems. The method is based on the relaxation count for economic evolutionary factorized scheme using special set of steps constructed in logarithmic scale. The iterations convergence is proved to be exponential. The superfast convergence rate makes it possible to solve elliptic equations on multiply densening spatial grids with Richardson extrapolation applied. The latter provides a posteriori asymptotically precise error estimations for the grid solution.
Mots-clés : Elliptic equations
Keywords: evolutional factorization, relaxation count, logarithmic set of steps, Richardson method. 
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A. A. Belov; N. N. Kalitkin. Superfast method with guaranteed accuracy for elliptic equations in rectangular domain. Matematičeskoe modelirovanie, Tome 27 (2015) no. 7, pp. 37-43. http://geodesic.mathdoc.fr/item/MM_2015_27_7_a6/

[1] N. N. Kalitkin, “An improved factorization of parabolic schemes”, Doklady Mathematics, 71:3 (2005), 480–483 | Zbl

[2] A. A. Boltnev, O. A. Kacher, N. N. Kalitkin, “Logarithmically convergent relaxation count”, Doklady Mathematics, 72:2 (2005), 806–809 | Zbl

[3] N. N. Kalitkin, A. A. Belov, “Analogue of the Richardson method for logarithmically converging time marching”, Doklady Mathematics, 88:2 (2013), 596–600 | Zbl

[4] A. A. Belov, N. N. Kalitkin, “Evolutionary factorization and superfast relaxation count”, Mathematical modeling and simulations

[5] A. A. Belov, N. N. Kalitkin, “Evoliutsionnaia faktorizatsiia i sverkhbystryi schet na ustanovlenie”, Keldysh Institute preprints, 2013, 069, 36 pp.

[6] N. N. Kalitkin, P. V. Koriakin, Chislennye metody, V dvukh knigakh, v. 2, Metody matematicheskoi fiziki, Akademiia, M., 2013