Parameter-Robust Convergence Analysis of Fixed-Stress Split Iterative Method for Multiple-Permeability Poroelasticity System
Priv.-Doz. Dr. Johannes KrausMarch 5, 2019, 2:30 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.