Publications related to Dynamical Reduced Basis Methods for Hamiltonian Systems

Motivic and p-adic Localization Phenomena

In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the

p

-adic pushforward of the Haar measure under a ...

EPFL2017

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

Jan Sickmann Hesthaven, Daniel Henri Baffet

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel reduction method for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our stud ...

Springer Verlag2017

On a Lagrangian Formulation of the Incompressible Euler Equation

Hasan Inci

In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...

Global Science Press2016

Convergence Results For Projected Line-Search Methods On Varieties Of Low-Rank Matrices Via Lojasiewicz Inequality

André Uschmajew

The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety M-

Siam Publications2015

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

L-2-cohomology and complete Hamiltonian manifolds

Tudor Ratiu

A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem st ...

Elsevier2015

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

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

Tangent-based manifold approximation with locally linear models

Pascal Frossard, Sofia Karygianni

In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represent manifold data accurately while preserving the manifold's structure. For this purpo ...

Elsevier2014

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

Dynamical Reduced Basis Methods for Hamiltonian Systems

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Motivic and p-adic Localization Phenomena

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

On a Lagrangian Formulation of the Incompressible Euler Equation

Convergence Results For Projected Line-Search Methods On Varieties Of Low-Rank Matrices Via Lojasiewicz Inequality

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

L-2-cohomology and complete Hamiltonian manifolds

Discrete variational Lie group formulation of geometrically exact beams dynamics

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

Tangent-based manifold approximation with locally linear models

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Motivic and p-adic Localization Phenomena

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

On a Lagrangian Formulation of the Incompressible Euler Equation

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

Discrete variational Lie group formulation of geometrically exact beams dynamics

Convergence Results For Projected Line-Search Methods On Varieties Of Low-Rank Matrices Via Lojasiewicz Inequality

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

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

Tangent-based manifold approximation with locally linear models

L-2-cohomology and complete Hamiltonian manifolds