Robust block diagonal preconditioners for poroelastic problems with strongly heterogeneous material

Abstract

This paper focuses on the analysis and the solution of the saddle‐point problem arising from a three‐field formulation of Biot's model of poroelasticity, discretized in time by the implicit Euler method. A block diagonal‐preconditioner, based on the Schur complement, is analyzed on a functional level and compared with two other block‐diagonal preconditioners having a similar structure. The problem is discretized in space using mixed finite elements and solved with appropriate iterative solvers, incorporating the investigated preconditioners. The solvers are tested on numerical examples inspired by geotechnical practice, with particular attention devoted to the solvers' robustness concerning strong heterogeneity in permeability.