Direct and iterative methods in finite element consolidation models

Direct and iterative schemes are currently available to solve the large unsymmetric sets of equations which arise from the Finite Element (FE) integration of coupled consolidation. The present paper provides a comparison of the performance of the most advanced direct and iterative solvers for the solution to a FE consolidation problem. The direct methods are those of the Harwell Software Library especially optimized for large sparse matrices. The iterative methods are Bi-CGSTAB and TFQMR belonging to the class of the preconditioned conjugate gradients. The results from representative large size consolidation examples show that the most efficient direct solvers are at least one order of magnitude more expensive than Bi-CGSTAB and TFQMR. In addition the problem size may become a criticai factor for a direct solver irrespective of the reordering technique used to preprocess the FE matrix with the aim at minimizing the number of elements generated during the elimination procedure.