Mixed constraint preconditioners for the iterative solutions of the FE coupled consolidation equations

The Finite Element (FE) integration of the coupled consolidation equations requires the solution of linear symmetric systems with an indefinite saddle point coefficient matrix. Because of ill-conditioning, the repeated solution in time of the FE equations may be a major computational issue requiring ad hoc preconditioning strategies to guarantee the efficient convergence of Krylov subspace methods. In the present paper a Mixed Constraint Preconditioner (MCP) is developed combining implicit and explicit approximations of the inverse of the structural sub-matrix, with the performance investigated in some representative examples. An upper bound of the eigenvalue distance from unity is theoretically provided in order to give practical indications on how to improve the preconditioner. The MCP is efficiently implemented into a Krylov subspace method with the performance obtained in 2D and 3D examples compared to that of Inexact Constraint Preconditioners and Least Square Logarithm scaled ILUT preconditioners. Two variants of MCP (T-MCP and D-MCP), developed with the aim at reducing the cost of the preconditioner application, are also tested. The results show that the MCP variants constitute a reliable and robust approach for the efficient solution of realistic coupled consolidation FE models, and especially so in severely ill-conditioned problems.