Parameter-Robust Discretization and Preconditioning of Biot's Consolidation Model

Robust estimates for the approximation of the dynamic consolidation problem

We consider stable discretizations in time and space for the linear dynamic consolidation problem describing the wave propagation in a porous solid skeleton which is fully saturated with an incompressible uid. Introducing the hydrostatic pressure, the ow problem is described by Darcy's law. In particular, we discuss the case of nearly impermeable solids which requires inf-sup stable discretizat...

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 variant of...

Large sparse linear systems arising from mimetic discretization

In this work we perform an experimental study of iterative methods for solving large sparse linear systems arising from a second-order 2D mimetic discretization. The model problem is the 2D Poisson equation with different boundary conditions. We use GMRES with the restarted parameter and BiCGstab as iterative methods. We also use various preconditioning techniques including the robust precondit...

An Efficient Diagonal Preconditioner for Finite Element Solution of Biot's Consolidation Equations

Comparison of MSSOR versus ILU(0) Preconditioners for Biot’s FEM Consolidation Equations

Numerical performance of two different preconditioning approaches, modified SSOR (MSSOR) preconditioner and incomplete factorization with zero fill-in (ILU0) preconditioner, is compared for the iterative solution of symmetric indefinite linear systems arising from finite element discretization of the Biot’s consolidation equations. Numerical results show that the nodal ordering affect the perfo...