Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 916-941, January 2020.
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.

中文翻译：

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渗透率多孔弹性系统固定应力分裂迭代法的参数鲁棒收敛性分析

2020年1月，《多尺度建模与仿真》，第18卷，第2期，第916-941页。
我们考虑基于通量的多孔隙度/多渗透率孔隙弹性系统，描述多孔弹性介质中的多网络流动和变形，也称为MPET模型。本文的重点是固定应力分裂迭代的收敛性分析，这是用于定义机械力学系统的流动和力学方程式的常用耦合技术。在这种情况下，我们制定了固定应力分裂方法，并证明了其线性收敛性。定点迭代的收缩率不依赖于模型中出现的任何物理参数。数值结果证实了这一点，该数值结果进一步证明了固定应力拆分方案相对于通过规范等效预处理加速的预处理MinRes求解器的优势。