  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.
