Numerical Comparison of Block Preconditioners for Poroelasticity

Poroelastic models describe a coupled solid-fluid interaction between a solid skeleton saturated by some fluid. We consider Biot’s model that describes the deformation of the solid skeleton by linear elasticity and the fluid flow by Darcy’s law. The formulation includes displacements, fluid flux and fluid pressure. After time discretization by the implicit Euler method we obtain a linear system with a matrix of \(3\times 3\) block structure. The focus of the paper is how to solve the so-arising linear system by a preconditioned iterative Krylov subspace iteration method. We analyse a particular Schur complement-based preconditioner, constructed with respect to the pressure variable, and compare its performance with other block preconditioners that arise from various algebraic and functional settings. The numerical experiments are based on geotechnical context inspired by a particular tunnel sealing experiment and test the dependence of the performance of the considered preconditioners on mesh size and permeability.