Related papers: Structure-Preserving Model-Reduction of Dissipativ…
We investigate the reductions of dispersionless Harry Dym hierarchy to systems of finitely many partial differential equations. These equations must satisfy the compatibility condition and they are diagonalizable and semi-Hamiltonian. By…
This work proposes a structure-preserving model reduction method for marginally stable linear time-invariant (LTI) systems. In contrast to Lyapunov-stability-based approaches---which ensure the poles of the reduced system remain in the open…
In this paper, we present two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After…
We will further develop the study of the dissipation for a Hamilton-Poisson system introduced in \cite{2}. We will give a tensorial form of this dissipation and show that it preserves the Hamiltonian function but not the Poisson geometry of…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
In this paper we study Hamiltonian systems on contact manifolds, which is an appropriate scenario to discuss dissipative systems. We prove a coisotropic reduction theorem similar to the one in symplectic mechanics.
This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional…
We develop a structure-preserving parametric model reduction approach for linearized swing equations where parametrization corresponds to variations in operating conditions. We employ a global basis approach to develop the parametric…
In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…
We study $H_\infty$ control design for linear time-invariant port-Hamiltonian systems. By a modification of the two central algebraic Riccati equations, we ensure that the resulting controller will be port-Hamiltonian. Using these modified…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the…
In order to simulate open quantum systems, many approaches (such as Hamiltonian-based solvers in dynamical mean-field theory) aim for a reproduction of a desired environment spectral density in terms of a discrete set of bath states,…
In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions…
Port-Hamiltonian (pH) systems offer a highly structured and energy-based modular framework for control systems. Many pH systems exhibit non-polynomial non-linearities. We consider the problem of immersing such systems into a…
We consider data assimilation for the heat equation using a finite element space semi-discretization. The approach is optimization based, but the design of regularization operators and parameters rely on techniques from the theory of…
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with…