Gustafsson, Ivar; Lindskog, Gunhild A preconditioning technique based on element matrix factorizations. (English) Zbl 0576.65022 Comput. Methods Appl. Mech. Eng. 55, 201-220 (1986). The task of making an incomplete factorization of the finite element stiffness matrix using only element matrices is concerned. We present a technique for realizing this and obtain a method which, for many problems solved in practice, requires an amount of core storage that is independent of the number of unknowns in the discrete model, i.e., of the mesh size parameter. On the other hand data transfers from/to the desk and more arithmetic operations than in a corresponding completely-in-core method are required. Theoretical estimates of the rate of convergence of the corresponding preconditioned conjugate gradient method are derived for a model problem and a number of test examples are examined. Cited in 5 Documents MSC: 65F10 Iterative numerical methods for linear systems 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74S05 Finite element methods applied to problems in solid mechanics 15A23 Factorization of matrices Keywords:incomplete factorization; finite element stiffness matrix; data transfers; rate of convergence; preconditioned conjugate gradient method; test examples PDF BibTeX XML Cite \textit{I. Gustafsson} and \textit{G. Lindskog}, Comput. Methods Appl. Mech. Eng. 55, 201--220 (1986; Zbl 0576.65022) Full Text: DOI OpenURL References: [1] Axelsson, O., A class of iterative methods for finite element equations, Comput. meths. appl. mech. engrg., 9, 123-137, (1976) · Zbl 0334.65028 [2] Axelsson, O.; Gustafsson, I., Preconditioning and two-level multigrid methods of arbitrary degree of approximation, Math. comp., 40, 219-242, (1983) · Zbl 0511.65079 [3] Argyris, J.H.; Brönlund, O.E., The natural factor formulation of the stiffness for the matrix displacement methods, Comput. meths. appl. mech. engrg., 5, 97-119, (1975) · Zbl 0291.73051 [4] () [5] Gustafsson, I., Modified incomplete Cholesky (MIC) methods, (), 265-293 · Zbl 0767.65017 [6] Hughes, T.; Levit, I.; Winget, J., An element-by-element solution algorithm for problems of structural and solid mechanics, Comput. meths. appl. mech. engrg., 36, 241-254, (1983) · Zbl 0487.73083 [7] Irons, B.M., A frontal solution program for finite element analysis, Internat. J. numer. meths. engrg., 2, 5-32, (1970) · Zbl 0252.73050 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.