9 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
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
Port-Hamiltonian systems result from port-based network modeling of physical
systems and are an important example of passive state-space systems. In this
paper, we develop the framework for model reduction of large-scale
multi-input/multi-output port-Hamiltonian systems via tangential rational
interpolation. The resulting reduced-order model not only is a rational
tangential interpolant but also retains the port-Hamiltonian structure; hence
is passive. This reduction methodology is described in both energy and
co-energy system coordinates. We also introduce an -inspired
algorithm for effectively choosing the interpolation points and tangential
directions. The algorithm leads a reduced port-Hamiltonian model that satisfies
a subset of -optimality conditions. We present several numerical
examples that illustrate the effectiveness of the proposed method showing that
it outperforms other existing techniques in both quality and numerical
efficiency
Interpolation-based H2 Model Reduction for port-Hamiltonian Systems
Port network modeling of physical systems leads directly to an important class of passive state space systems: port-Hamiltonian systems. We consider here methods for model reduction of large scale port-Hamiltonian systems that preserve port-Hamiltonian structure and are capable of yielding reduced order models that satisfy first-order optimality conditions with respect to an H2 system error metric. The methods we consider are closely related to rational Krylov methods and variants are described using both energy and co-energy system coordinates. The resulting reduced models have port-Hamiltonian structure and therefore are guaranteed passive, while still retaining the flexibility to interpolate the true system transfer function at any (complex) frequency points that are desired.
Interpolation-based H2 model reduction for port-Hamiltonian systems
Port network modeling of physical systems leads directly to an important class of passive state space systems: port-Hamiltonian systems. We consider here methods for model reduction of large scale port-Hamiltonian systems that preserve port-Hamiltonian structure and are capable of yielding reduced order models that satisfy first-order optimality conditions with respect to an H2 system error metric. The methods we consider are closely related to rational Krylov methods and variants are described using both energy and co-energy system coordinates. The resulting reduced models have port-Hamiltonian structure and therefore are guaranteed passive, while still retaining the flexibility to interpolate the true system transfer function at any (complex) frequency points that are desired