Performance and robustness of block constraint preconditioners in finite element coupled consolidation problems

Block constraint preconditioners are a most recent development for the iterative solution to large-scale, often ill-conditioned, coupled consolidation problems. A major limitation to their practical use, however, is the somewhat difficult selection of a number of user-defined parameters (at least 4) in a more or less optimal way. The present paper investigates the robustness of three variants of the block constraint preconditioning in relation to the above parameters. A theoretical analysis of the eigenspectrum of the preconditioned matrix provides relatively simple bounds of the eigenvalues as a function of these parameters. A number of test problems used to validate the theoretical results show that both the mixed constraint preconditioner (MCP) combined with the symmetric quasi-minimal residual (SQMR) solver and the MCP triangular variant (T-MCP) combined with the bi-conjugate gradient stabilized (Bi-CGSTAB) are efficient and robust tools for the solution to difficult Finite Element-discretized coupled consolidation problems. Moreover, the practical selection of the user-defined parameters is relatively easy as a stable behavior is observed for a wide range of fill-in degree values. The theoretical bounds on the eigenspectrum of the preconditioned matrix may help to suggest the most appropriate parameter combination.