Publications related to Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

Geometric Model Order Reduction

During the past decade, model order reduction (MOR) has been successfully applied to reduce the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. S ...

EPFL2018

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Structure preserving model reduction of parametric Hamiltonian systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

While reduced-order models (ROMs) are popular for approximately solving large systems of differential equations, the stability of reduced models over long-time integration remains an open question. We present a greedy approach for ROM generation of paramet ...

2017

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

Reduced basis methods are popular for approximately solving large and complex systems of dierential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present ...

2017

The tropical momentum map: a classification of toric log symplectic manifolds

Tudor Ratiu

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...

Springer Verlag2017

Discrete variational Lie group formulation of geometrically exact beams dynamics

Yves Weinand, Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resultin ...

Springer Verlag2015

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

We reformulate the equation characterizing the critical points of the hypersymplectic action functional as solutions of a Hamiltonian system on the iterated loop space. The intent is to gain more insight into dynamics of hyperkahler Floer theory. ...

American Mathematical Society2015

Analysis of adiabatic trapping for quasi-integrable area-preserving maps

Cedric Jean-François Hernalsteens, Massimo Giovannozzi

Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinea ...

American Physical Society2014

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

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Geometric Model Order Reduction

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Structure preserving model reduction of parametric Hamiltonian systems

Dynamical Low Rank approximation of PDEs with random parameters

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

The tropical momentum map: a classification of toric log symplectic manifolds

Discrete variational Lie group formulation of geometrically exact beams dynamics

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

Analysis of adiabatic trapping for quasi-integrable area-preserving maps

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

Analysis of adiabatic trapping for quasi-integrable area-preserving maps

Geometric Model Order Reduction

Structure preserving model reduction of parametric Hamiltonian systems

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Discrete variational Lie group formulation of geometrically exact beams dynamics

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Dynamical Low Rank approximation of PDEs with random parameters

The tropical momentum map: a classification of toric log symplectic manifolds