Ewing, Richard E.; Shen, Jian; Vassilevski, Panayot S. Vectorizable preconditioners for mixed finite element solution of second- order elliptic problems. (English) Zbl 0758.65022 Int. J. Comput. Math. 44, No. 1-4, 313-327 (1992). The authors compare the performance of the conjugate gradient (CG) method, the point-wise incomplete factorization preconditioned CG method and the block-incomplete factorization preconditioned CG method for solving problems arising in mixed finite element discretization of second-order elliptic differential equations.Numerical results are presented to show the robustness and vectorizable properties of these methods and also the superiority of the block- incomplete factorization method to other methods both in CPU time and number of iterations. Reviewer: T.C.Mohan (Madras) Cited in 3 Documents MSC: 65F10 Iterative numerical methods for linear systems 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65F35 Numerical computation of matrix norms, conditioning, scaling 65Y05 Parallel numerical computation 35J25 Boundary value problems for second-order elliptic equations Keywords:incomplete factorization; mixed finite element; vectorization; preconditioned conjugate gradient method; performance; second-order elliptic differential equations; Numerical results PDFBibTeX XMLCite \textit{R. E. Ewing} et al., Int. J. Comput. Math. 44, No. 1--4, 313--327 (1992; Zbl 0758.65022) Full Text: DOI References: [1] Axelsson O., CWI Syllabus 4 (1985) [2] DOI: 10.1016/0024-3795(86)90121-7 · Zbl 0622.65023 [3] Axelsson O., Finite Element Solution of Boundary Value Problems (1984) · Zbl 0537.65072 [4] Axelsson O., Algorithms and Applications on Vector and Parallel Computers (1987) [5] DOI: 10.1016/0024-3795(86)90159-X · Zbl 0587.65013 [6] DOI: 10.1007/BF01409783 · Zbl 0661.65110 [7] DOI: 10.1137/0727092 · Zbl 0715.65091 [8] DOI: 10.1007/BF01462238 · Zbl 0645.65074 [9] DOI: 10.1137/0723075 · Zbl 0615.65113 [10] DOI: 10.1090/S0025-5718-1986-0829613-0 [11] Bramble J. H., Math. Comp. [12] DOI: 10.1137/0906018 · Zbl 0556.65022 [13] DOI: 10.1007/BF01399311 · Zbl 0478.65062 [14] DOI: 10.1007/BF01410102 · Zbl 0568.65075 [15] Dryja, M. and Widlund, O. B. January 1990.Parallel Algorithms for PDE’s, Proceedings of the 6th GAMM Seminar, Edited by: Hackbusch, W. January, 16–21. Kiel, Braunschweig-Wiesbaden: Multilevel additive methods for elliptic finite element problems. 58-69 [16] DOI: 10.1016/0167-8191(89)90080-X · Zbl 0692.65024 [17] Ewing R. E., Point-distributed algorithms for second-order elliptic equations in mixed form [18] Ewing R. E., Numerical Methods for Scientific Computing pp 163– (1983) [19] Hackbusch W., Multigrid Methods and Applications, Springer Series in Comput. Math. 4 (1985) · Zbl 0595.65106 [20] Kettler R., Multigrid Methods, Proceedings, Kiln-Porz, 1981 960 pp 502– (1982) [21] Mc Cormick S., Multilevel Adaptive Methods for Partial Differential Equations (1989) [22] Meijerink J. A., Math. Comp. 31 pp 148– (1977) [23] DOI: 10.1007/BF01934919 · Zbl 0556.65023 [24] DOI: 10.1515/rnam.1989.4.6.493 [25] DOI: 10.1007/BFb0064470 [26] Varga R., Matrix Iterative Analysis (1962) · Zbl 0133.08602 [27] Vassilevski P. S., Nearly optimal iterative methods for solving finite element elliptic equations based on the multilevel splitting of the matrix 572 (1989) [28] DOI: 10.1002/nme.1620270312 · Zbl 0712.65020 [29] DOI: 10.1007/BF02242922 · Zbl 0691.65017 [30] Vassilevski P. S., Appl. Math. Comp. [31] Vassilevski P. S., Math. Comp. [32] Wang J., Proceedings, IMACS Conference on Iterative Methods (1991) [33] DOI: 10.1007/BF01389538 · Zbl 0608.65065 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.