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

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

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

2018

On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

Joachim Krieger

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on

\mathbb{R}^{3+1}

constructed in [28], [27] are stable along a co-dimension three manifold of radial data perturbations in a suit ...

2018

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

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 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

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Jean-Philippe Lucien Montillet

Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...

Int Center Scientific Research & Studies2017

Stochastic partial differential equations driven by Lévy white noises

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Multi-index Monte Carlo: when sparsity meets sampling

Fabio Nobile

We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a s ...

2016

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model

Hoài-Minh Nguyên

This paper concerns approximate cloaking by mapping for a full, but scalar wave equation, when one allows for physically relevant frequency dependence of the material properties of the cloak. The paper is a natural continuation of [20], but here we employ ...

Elsevier2016

The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

Fabio Rinaldi

In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction, of strength beta, centred at 0 (the bottom of the confining parabolic potential), that was rigorou ...

Iop Publishing Ltd2016

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

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

On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Dynamical Low Rank approximation of PDEs with random parameters

Structure preserving model reduction of parametric Hamiltonian systems

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Stochastic partial differential equations driven by Lévy white noises

Multi-index Monte Carlo: when sparsity meets sampling

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model

The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Stochastic partial differential equations driven by Lévy white noises

The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

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

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Dynamical Low Rank approximation of PDEs with random parameters

Structure preserving model reduction of parametric Hamiltonian systems

Multi-index Monte Carlo: when sparsity meets sampling

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model