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

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 com...

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Bibliographic Details
Published in:arXiv.org 2018-12
Main Authors: Hong, Qingguo, Kraus, Johannes, Lymbery, Maria, Wheeler, Mary Fanett
Format: Article
Language:English
Subjects:
Convergence
Elastic deformation
Elastic media
Iterative methods
Mathematical models
Parameter robustness
Permeability
Physical properties
Poroelasticity
Porosity
Preconditioning
Robustness (mathematics)
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Summary: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.
ISSN:2331-8422