662 research outputs found
Twenty years of distributed port-Hamiltonian systems:A literature review
The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups
Numerical analysis of a structure-preserving space-discretization for an anisotropic and heterogeneous boundary controlled N-dimensional wave equation as port-Hamiltonian system
The anisotropic and heterogeneous N-dimensional wave equation, controlled and
observed at the boundary, is considered as a port-Hamiltonian system. The
recent structure-preserving Partitioned Finite Element Method is applied,
leading directly to a finite-dimensional port-Hamiltonian system, and its
numerical analysis is done in a general framework, under usual assumptions for
finite element. Compatibility conditions are then exhibited to reach the best
trade off between the convergence rate and the number of degrees of freedom for
both the state error and the Hamiltonian error. Numerical simulations in 2D are
performed to illustrate the optimality of the main theorems among several
choices of classical finite element families.Comment: 36 pages, 1 figure, submitte
Hybrid finite difference/finite element immersed boundary method
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian
description of the structural deformations, stresses, and forces along with an Eulerian description of the
momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary
methods described immersed elastic structures using systems of flexible fibers, and even now, most
immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This
work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian
variables that facilitates independent spatial discretizations for the structure and background grid. This
approach employs a finite element discretization of the structure while retaining a finite difference scheme
for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively
contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases
in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors
that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes.
The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse
structural meshes with the immersed boundary method. This work also contrasts two different weak forms
of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations
facilitated by our coupling approach
Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings
Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and
control of complex dynamical systems, where the complexity might result from
multi-physical couplings, non-trivial domains and diverse nonlinearities. A
major benefit of the PH representation is the explicit formulation of power
interfaces, so-called ports, which allow for a power-preserving interconnection
of subsystems to compose flexible multibody systems in a modular way. In this
work, we present a PH representation of geometrically exact strings with
nonlinear material behaviour. Furthermore, using structure-preserving
discretization techniques a corresponding finite-dimensional PH state space
model is developed. Applying mixed finite elements, the semi-discrete model
retains the PH structure and the ports (pairs of velocities and forces) on the
discrete level. Moreover, discrete derivatives are used in order to obtain an
energy-consistent time-stepping method. The numerical properties of the newly
devised model are investigated in a representative example. The developed PH
state space model can be used for structure-preserving simulation and model
order reduction as well as feedforward and feedback control design.Comment: Submitted as a proceeding to the ECCOMAS Thematic Conference on
Multibody Dynamics 202
Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available
A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control
Many boundary controlled and observed Partial Differential Equations can be represented as port-Hamiltonian systems with dissipation, involving a Stokes-Dirac geometrical structure together with constitutive relations. The Partitioned Finite Element Method, introduced in Cardoso-Ribeiro et al. (2018), is a structure preserving numerical method which defines an underlying Dirac structure, and constitutive relations in weak form, leading to finite-dimensional port-Hamiltonian Differential Algebraic systems (pHDAE). Different types of dissipation are examined: internal damping, boundary damping and also diffusion models
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