Parameter-Robust Convergence Analysis of Fixed-Stress Split Iterative Method for Multiple-Permeability Poroelasticity System

Priv.-Doz. Dr. Johannes Kraus

March 5, 2019, 3:30 p.m. S2 416-1

We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing mulitple-network flow and
deformation in a poroelastic medium, also referred to as MPET models. We present a convergence analysis of the fixed-stress split
iteration, a commonly used coupling technique for the flow and mechanics equations defining poromechanical systems. We formulate
the fixed-stress split method in this 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. This 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.