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

TL;DR

This paper analyzes the convergence of the fixed-stress split iterative method for complex poroelastic systems with multiple networks, proving parameter-independent linear convergence and demonstrating its advantages over fully implicit methods.

Contribution

The paper provides the first convergence proof for the fixed-stress split method applied to MPET models, showing parameter-robust linear convergence.

Findings

Contraction rate is independent of physical parameters.

Fixed-stress split method converges linearly.

Numerical results confirm theoretical advantages.

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.