Preconditioners for finite element consolidation

The Finite Element (FE) solution to consolidation equations in large geological settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the solver efficiency plays a crucial role: 1- fully coupled consolidation, and 2- non-linear faulted (uncoupled) consolidation. Using a proper nodal numbering the FE matrices exhibit a block (or multilevel) structure. Krylov subspace solvers are attracting a growing attention, provided that a relatively inexpensive and effective preconditioner is available. For both problems possible preconditioners include the Diagonal Scaling (DS), the Incomplete Triangular Factorization (ILU), the Mixed Constraint Preconditioning (MCP) and the Multilevel Incomplete Factorization (MIF). The present communication provides a review and a critical discussion of DS, ILU, MCP and MIF when used as preconditioners for the numerical solution of a consolidation model.