# Port-Hamiltonian formulations of poroelastic network models

@article{Altmann2021PortHamiltonianFO, title={Port-Hamiltonian formulations of poroelastic network models}, author={R. Altmann and Volker Mehrmann and B. Unger}, journal={Mathematical and Computer Modelling of Dynamical Systems}, year={2021}, volume={27}, pages={429 - 452} }

ABSTRACT 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…

## 12 Citations

A decoupling and linearizing discretization for poroelasticity with nonlinear permeability

- MathematicsArXiv
- 2021

A semi-explicit time discretization scheme of first order for poroelasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled leads to a decoupling of the equations and linearizes the nonlinearity without the need of further inner iteration steps.

A Decoupling and Linearizing Discretization for Weakly Coupled Poroelasticity with Nonlinear Permeability

- MathematicsSIAM Journal on Scientific Computing
- 2022

A semi-explicit time discretization scheme of first order for poroelasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled leads to a decoupling of the equations and linearizes the nonlinearity without the need of further inner iteration steps.

Local and global canonical forms for differential-algebraic equations with symmetries

- MathematicsArXiv
- 2022

Local and global canonical forms under congruence are presented and used to classify the geometric properties of the flow associated with the differential equation as symplectic or generalized orthogonal flow, applied to the analysis of dissipative Hamiltonian systems arising from circuit simulation and incompressible flow.

Passivity preserving model reduction via spectral factorization

- Computer Science, MathematicsAutomatica
- 2022

Port-Hamiltonian Dynamic Mode Decomposition

- MathematicsArXiv
- 2022

. We present a novel physics-informed system identiﬁcation method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the…

Port-Hamiltonian Fluid-Structure Interaction Modeling and Structure-Preserving Model Order Reduction of a Classical Guitar

- PhysicsArXiv
- 2022

A fluid-structure interaction model in a port-Hamiltonian representation is derived for a classical guitar. We combine the laws of continuum mechanics for solids and fluids within a unified…

Computation of the nearest structured matrix triplet with common null space

- MathematicsArXiv
- 2021

This work will use characterizations of dissipative Hamiltonian systems and related matrix pencils for the development of computational methods to compute distances via methods that follow the flow of a differential equation converging to the smallest perturbation that destroys the property of regularity, index one or stability.

Matrix pencils with coefficients that have positive semidefinite Hermitian part

- MathematicsArXiv
- 2021

This work introduces matrix pencils with coefficients that have positive semidefinite Hermitian parts and relates the Kronecker structure of these pencils to that of an underlying skew-Hermitian pencil and discusses their regularity, index, numerical range, and location of eigenvalues.

On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs

- Mathematics, Computer ScienceArXiv
- 2021

Different cases of dissipative Hamiltonian diﬀerential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization are discussed and iterative methods based on eﬁnite three-term recurrences are illustrated.

Splitting schemes for the semi-linear wave equation with dynamic boundary conditions

- MathematicsArXiv
- 2021

Novel splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type with reinterpretation of the system equations as a coupled system are introduced.

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