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.
@article{arxiv.1812.11809,
title = {Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems},
author = {Qingguo Hong and Johannes Kraus and Maria Lymbery and Mary Fanett Wheeler},
journal= {arXiv preprint arXiv:1812.11809},
year = {2019}
}