Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems

Abstract

We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also referred to as MPET models. The focus of the paper is on the convergence analysis of the fixed-stress split iteration, a commonly used coupling technique for the flow and mechanics equations in poromechanics. We formulate the fixed-stress split method in the present context and prove its linear convergence. The contraction rate of this fixed-point iteration does not depend on any of the physical parameters appearing in the model. The theory is confirmed by numerical results which further demonstrate the advantage of the fixed-stress split scheme over a fully implicit method relying on norm-equivalent preconditioning.

References in corpus (2)

• Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media
• Conservative discretizations and parameter-robust preconditioners for Biot and multiple-network flux-based poroelastic models

Cited by in corpus (4)

• The gradient flow structures of thermo-poro-visco-elastic processes in porous media
• A new practical framework for the stability analysis of perturbed saddle-point problems and applications
• Robust block preconditioners for poroelasticity
• Iterative solvers for Biot model under small and large deformation