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We consider flux-based multiple-porosity/multiple-permeability poroelasticitysystems describing multiple-network flow and deformation in a poro-elasticmedium, sometimes also referred to as MPET models. The focus of the paper is onthe convergence analysis of the fixed-stress split iteration, a commonly usedcoupling technique for the flow and mechanics equations in poromechanics. Weformulate the fixed-stress split method in the present context and prove itslinear convergence. The contraction rate of this fixed-point iteration does notdepend on any of the physical parameters appearing in the model. The theory isconfirmed by numerical results which further demonstrate the advantage of thefixed-stress split scheme over a fully implicit method relying onnorm-equivalent preconditioning.

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