Parameter-Robust Convergence Analysis of Fixed-Stress Split Iterative Method for Multiple-Permeability Poroelasticity Systems
Qingguo Hong, Johannes Kraus, Maria Lymbery, Mary F. Wheeler
Abstract
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. 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 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 preconditioned MinRes solver accelerated by norm-equivalent preconditioning.