3 research outputs found
Port-Hamiltonian formulations of poroelastic network models
We investigate an energy-based formulation of the two-field poroelasticity
model and the related multiple-network model as they appear in geosciences or
medical applications. We propose a port-Hamiltonian formulation of the system
equations, which is beneficial for preserving important system properties after
discretization or model-order reduction. For this, we include the commonly
omitted second-order term and consider the corresponding first-order
formulation. The port-Hamiltonian formulation of the quasi-static case is then
obtained by (formally) setting the second-order term zero. Further, we
interpret the poroelastic equations as an interconnection of a network of
submodels with internal energies, adding a control-theoretic understanding of
the poroelastic equations
Semi-explicit discretization schemes for weakly-coupled elliptic-parabolic problems
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as well as multiple-network models used in medical applications. The semi-explicit approach decouples the system such that each time step requires the solution of two small and well-structured linear systems rather than the solution of one large system. The decoupling improves the computational efficiency without decreasing the convergence rates. The presented convergence proof is based on an interpretation of the scheme as an implicit method applied to a constrained partial differential equation with delay term. Here, the delay time equals the used step size. This connection also allows a deeper understanding of the weak coupling condition, which we accomplish to quantify explicitly