Publications related to Symplectic dynamical low rank approximation of wave equations with random parameters

Time and space adaptivity of the wave equation discretized in time by a second-order scheme

The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. An error estimate is derived in the ...

2019

Coupled-mode theory for stationary and nonstationary resonant sound propagation

Romain Christophe Rémy Fleury, Theodoros Koutserimpas

In this paper, we present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological coupled-mode theory. We calculate the prop ...

2019

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

Jan Sickmann Hesthaven, Cecilia Pagliantini

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

2018

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

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

Fabio Nobile, Lorenzo Tamellini, Anna Scotti

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs w ...

Elsevier2018

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

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

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

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

Symplectic dynamical low rank approximation of wave equations with random parameters

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Time and space adaptivity of the wave equation discretized in time by a second-order scheme

Coupled-mode theory for stationary and nonstationary resonant sound propagation

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

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

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

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

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

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Dynamical Low Rank approximation of PDEs with random parameters

Stochastic partial differential equations driven by Lévy white noises

Stochastic partial differential equations driven by Lévy white noises

Time and space adaptivity of the wave equation discretized in time by a second-order scheme

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

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

Coupled-mode theory for stationary and nonstationary resonant sound propagation

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

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

Dynamical Low Rank approximation of PDEs with random parameters

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