Parameter Robust Preconditioning by Congruence for Multiple-Network Poroelasticity

The mechanical behavior of a poroelastic medium permeated by multiple interacting fluid networks can be described system time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) or multiporosity/multipermeability systems. These generalize Biot's equations, which describe mechanics one network case. efficient numerical solution MPET is challenging, in part due to complexity and presence parameter regimes. In this paper, we present new strategy for efficiently robustly solving numerically. particular, discuss an approach formulating finite element methods associated preconditioners based on simultaneous diagonalization matrices. We demonstrate technique multicompartment Darcy with large exchange variability, nearly incompressible variability. designing transformations variables that simultaneously diagonalize (by congruence) equations' key operators subsequently constructing parameter-robust block diagonal transformed system. proposed supported theoretical considerations well results.