ROBUST PRECONDITIONERS FOR LINEAR ELASTICITY FEM ANALYSES

This paper deals with two forms of preconditioner which can be easily used with a Conjugate Gradient solver to replace a direct solution sub routine in a traditional engineering finite element package; they are tested in such a package (FINAL) over a range of 2-D and 3-D elasticit y problems from geotechnical engineering. Quadratic basis functions ar e used. A number of modifications to the basic Incomplete Choleski [IC (0)] factorization preconditioner are considered. An algorithm to redu ce positive off-diagonal entries is shown in numerical experiments to ensure stability, but at the expense of slow convergence. An alternati ve algorithm of Jennings and Malik is more successful, and a relaxatio n parameter omega is introduced which can make a further significant i mprovement in performance while maintaining stability. A heuristic for determining a near-optimal value of omega is proposed. A second form of preconditioning, symmetrically scaled element by element, due to Ba rtelt, is also shown to perform robustly over a range of problems; it does not require assembly of the global stiffness matrix, and has grea t potential for parallelization. (C) 1997 by John Wiley & Sons, Ltd.