Numerical performance of projection methods in finite element consolidation models

Projection, or conjugate gradient like, methods are becoming increasingly p opular for the efficient solution of large sparse sets of unsymmetric indef inite equations arising from the numerical integration of (initial) boundar y value problems. One such problem is soil consolidation coupling a flow an d a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank-Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low compu tational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi-CGSTAB) is used t o solve FE consolidation equations in 2-D and 3-D settings with variable ti me integration steps. Three different nodal orderings are selected along wi th the preconditioner ILUT based on incomplete triangular factorization and variable fill-in. The overall cost of the solver is made up of the precond itioning cost plus the cost to converge which is in turn related to the num ber of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the performance of Bi-CGSTAB. For normally conditioned consolidation problems Bi-CGSTAB with the best IL UT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, co st-effective and robust alternative to direct methods. Copyright (C) 2001 J ohn Wiley & Sons, Ltd.