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Using a compensation principle in the algebraic multilevel iteration method for finite element matrices
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 2, pp. 127-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper, an improved version of the algebraic multilevel iteration (AMLI) method for finite element matrices, which was offered in [6], is proposed. To improve the quality of the AMLI-preconditioner, or (which is the same) to speed up the rate of convergence, a family of iterative parameters defined on an error compensation principle is proposed and analyzed. The performance results on standard test problems are presented and discussed. 
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M. R. Larin. Using a compensation principle in the algebraic multilevel iteration method for finite element matrices. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 2, pp. 127-142. http://geodesic.mathdoc.fr/item/SJVM_2005_8_2_a3/

[1] Apel T., Anisotropic finite elements: Local estimates and applications, Advances in Num. Math., Teubner, Stutgart–Leipzig, 1999 | MR | Zbl

[2] Axelsson O., Vassilevski P., “Algebraic multilevel preconditioning methods I”, Numer. Math., 56 (1989), 157–177 | DOI | MR | Zbl

[3] Axelsson O., Vassilevski P., “Algebraic multilevel preconditioning methods II”, SIAM J. Numer. Anal., 27 (1990), 1569–1590 | DOI | MR | Zbl

[4] Axelsson O., Eijkhout V., “The nested recursive two-level factorization method for nine-point difference matrices”, SIAM J. Sci. Stat. Comp., 12 (1991), 1373–1400 | DOI | MR | Zbl

[5] Axelsson O., Neytcheva M., “Algebraic multilevel iteration method for Stieltjes matrices”, Numer. Lin. Alg. Appl., 1 (1994), 213–236 | DOI | MR | Zbl

[6] Axelsson O., Larin M., “An algebraic multilevel iteration method for finite element matrices”, J. Comp. Appl. Math., 89 (1997), 135–153 | DOI | MR

[7] Axelsson O., Larin M., “An element-by-element version of variable-step multilevel preconditioning methods”, Sib. J. Num. Math. / Sib. Branch of Russ. Acad. Sci., 6:3 (2003), 209–226 | Zbl

[8] Axelsson O., Padiy A., “On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems”, SIAM J. Sci. Comput., 20 (1999), 1807–1830 | DOI | MR | Zbl

[9] Larin M., “An algebraic multilevel iterative method of incomplete factorization for Stieltjes matrices”, Comput. Math. Math. Physics, 38 (1998), 1011–1025 | MR | Zbl

[10] Notay Y., Ould Amar Z., “A nearly optimal preconditioning based on recursive red-black orderings”, Num. Lin. Alg. Appl., 4 (1997), 369–391 | 3.0.CO;2-A class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[11] Vassilevski P., “Hybrid V-cycle algebraic multilevel preconditioners”, Math. Comp., 58 (1992), 489–512 | DOI | MR | Zbl