A comparison of solution methods for finite element Biot consolidation equations

Direct and iterative schemes are cmrently available to solve the large asymmetric 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 TFQNIR, which belong to the class of the preconditioned conjugate gradients. The resuIts from representative large size consolidation examples show that the most effìcient 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 re-ordering technique used to pre-process the FE matrix with the aim of minimizing the number of elements generated during the elimination procedure.