an:03921817
Zbl 0576.65022
Gustafsson, Ivar; Lindskog, Gunhild
A preconditioning technique based on element matrix factorizations
EN
Comput. Methods Appl. Mech. Eng. 55, 201-220 (1986).
00150834
1986
j
65F10 65N30 74S05 15A23
incomplete factorization; finite element stiffness matrix; data transfers; rate of convergence; preconditioned conjugate gradient method; test examples
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.