Direct, partitioned and projected solution to finite element consolidation models

Direct, partitioned, and projected (conjugate gradient-like) solution approaches are compared on unsymmetric indefinite systems arising from the finite element integration of coupled consolidation equations. The direct method is used in its most recent and computationally efficient implementations of the Harwell Software Library. The partitioned approach designed for coupled problems is especially attractive as it addresses two separate positive definite problems of a smaller size that can be solved by symmetric conjugate gradients. However, it may stagnate and when converging it does not prove competitive with a global projection method such as Bi-CGSTAB, which may take full advantage of its flexibility in working on scaled and reordered equations, and thus may greatly improve its computational performance in terms of both robustness and convergence rate. The Bi-CGSTAB superiority to the other approaches is discussed and demonstrated with a few representative examples in two-dimensional (2-D) and three-dimensional (3-D) coupled consolidation problems.