2020/03/21 by Eleonora Piersanti, Jeonghun J. Lee, Piersanti, Eleonora +7 · 1 citation
Computer Science · Engineering · #65M22 #65M60 #92C10 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2003.09641
openalex publication_date 2020/03/21 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The mechanical behaviour of a poroelastic medium permeated by multiple\ninteracting fluid networks can be described by a system of time-dependent\npartial differential equations known as the multiple-network poroelasticity\n(MPET) equations or multi-porosity/multi-permeability systems. These equations\ngeneralize Biot's equations, which describe the mechanics of the one-network\ncase. The efficient numerical solution of the MPET equations is challenging, in\npart due to the complexity of the system and in part due to the presence of\ninteracting parameter regimes. In this paper, we present a new strategy for\nefficiently and robustly solving the MPET equations numerically. In particular,\nwe introduce a new approach to formulating finite element methods and\nassociated preconditioners for the MPET equations. The approach is based on\ndesigning transformations of variables that simultaneously diagonalize (by\ncongruence) the equations' key operators and subsequently constructing\nparameter-robust block-diagonal preconditioners for the transformed system. Our\nmethodology is supported by theoretical considerations as well as by numerical\nresults.\n