A PRECONDITIONING TECHNIQUE BASED ON ELEMENT MATRIX FACTORIZATIONS

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 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 datatransfers from/to secondary storage and more arithmetic operations than in a corresponding completely-in-core method are required. For many problems solved in practice even the total requirement of storage for the stiffness and preconditioning matrices is independent of the size of the mesh. 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.