The operator preconditioning framework with various applications to interstitial fluid flow and the aging human brain

The operator preconditioning technique is a constructive framework for designing efficient solution algorithms from the mapping properties of the continuous equations. In this talk we will present the basic framework in an abstract fashion before discussing various applications  where the interstitial fluid flow is studied in the central nervous system. In particular, we will consider problems arising in porous media flow  in elastic media and multi-scale problems representing the coupling between the vasculature and the extra-cellular space of the human  brain. The numerical modelling is motivated by the recently proposed glymphatic system, which is a clearance mechanism where water remove waste associated with Alzheimer disease. The clearance is particularly active during sleep. The numerical investigations employ the finite element method and the software framework FEniCS.