TY - JOUR
T1 - Hybridized Discontinuous Galerkin/Hybrid Mixed Methods for a Multiple Network Poroelasticity Model with Application in Biomechanics
AU - Kraus, Johannes
AU - Lederer, Philip L.
AU - Lymbery, Maria
AU - Osthues, Kevin
AU - Schoberl, Joachim
N1 - Publisher Copyright:
© by SIAM. Unauthorized reproduction of this article is prohibited.
PY - 2023/12/31
Y1 - 2023/12/31
N2 - The quasi-static multiple-network poroelastic theory (MPET) model, first introduced in the context of geomechanics [G. Barenblatt, G. Zheltov, and I. Kochina, J. Appl. Math. Mech., 24 (1960), pp. 1286-1303], has recently found new applications in biomechanics. In practice, the parameters in the MPET equations can vary over several orders of magnitude which makes their stable discretization and fast solution a challenging task. Here, a new efficient parameter-robust hybridized discontinuous Galerkin method, which also features fluid mass conservation, is proposed for the MPET model. Its stability analysis, crucial for the well-posedness of the discrete problem, is performed, and cost-efficient parameter-robust preconditioners are derived. We present a series of numerical computations for a four-network MPET model of a human brain which demonstrate the performance of the new algorithms.
AB - The quasi-static multiple-network poroelastic theory (MPET) model, first introduced in the context of geomechanics [G. Barenblatt, G. Zheltov, and I. Kochina, J. Appl. Math. Mech., 24 (1960), pp. 1286-1303], has recently found new applications in biomechanics. In practice, the parameters in the MPET equations can vary over several orders of magnitude which makes their stable discretization and fast solution a challenging task. Here, a new efficient parameter-robust hybridized discontinuous Galerkin method, which also features fluid mass conservation, is proposed for the MPET model. Its stability analysis, crucial for the well-posedness of the discrete problem, is performed, and cost-efficient parameter-robust preconditioners are derived. We present a series of numerical computations for a four-network MPET model of a human brain which demonstrate the performance of the new algorithms.
KW - 2024 OA procedure
KW - hybrid mixed methods
KW - MPET model
KW - norm-equivalent preconditioners
KW - parameter-
KW - robust LBB stability
KW - strongly mass-conserving high-order discretizations
KW - hybrid discontinuous Galerkin methods
UR - http://www.scopus.com/inward/record.url?scp=85178076453&partnerID=8YFLogxK
U2 - 10.1137/22M149764X
DO - 10.1137/22M149764X
M3 - Article
AN - SCOPUS:85178076453
SN - 1064-8275
VL - 45
SP - B802-B827
JO - SIAM journal on scientific computing
JF - SIAM journal on scientific computing
IS - 6
ER -