Abstract
Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the CrankβNicolson 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 computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Biβ CGSTAB) is used to solve FE consolidation equations in 2βD and 3βD settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fillβin. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of BiβCGSTAB. For normally conditioned consolidation problems BiβCGSTAB with the best ILUT 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, costβeffective and robust alternative to direct methods. Copyright Β© 2001 John Wiley & Sons, Ltd.