Mathematics

The mechanical behaviour of a poroelastic medium permeated by multiple interactingfluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or multi-porosity/multi-permeability systems. These equations generalize Biot's equations, which describe the mechanics of the one–network case. The efficient numerical solution of the MPET equations is challenging, in part due to the complexity of the system and in part due to the presence of interacting parameter regimes. In this talk, we present a new strategy for efficiently and robustly solving the MPET equations numerically.In particular, we introduce a new approach to formulating finite element methods and associatedpreconditioners for the MPET equations. The approach is based on designing transformations of variables that simultaneously diagonalize (by congruence) the equations' key operators and subsequently constructing parameter-robust block-diagonal preconditioners for the transformed system. Finally we will show some numerical results that support the theory.