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

A Spectral Ansatz for The Long-Time Homogenization of The Wave Equation

Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present wor ...

Ecole Polytechnique2024

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 ...

2020

An Easily Computable Error Estimator In Space And Time For The Wave Equation

Marco Picasso, Olga Gorynina

We propose a cheaper version of a posteriori error estimator from Gorynina et al. (Namer. Anal. (2017)) for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator preserv ...

EDP Sciences2019

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

Marco Picasso, Olga Gorynina

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

Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach

Gérôme Graf

I will try to explain, without going into too much detail, how one can consider a non-linear wave equation as a dynamical system and what it brings to the study of its solutions. We begin by considering our model case, the non-linear Klein-Gordon equation ...

EPFL2019

Joint Estimation Of The Room Geometry And Modes With Compressed Sensing

Pierre Vandergheynst, Hervé Lissek, Helena Peic Tukuljac

Acoustical behavior of a room for a given position of microphone and sound source is usually described using the room impulse response. If we rely on the standard uniform sampling, the estimation of room impulse response for arbitrary positions in the room ...

IEEE2018

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

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations for the wave equation in locally periodic media over long time is derived. In particular, explicit formulas for the effective tensors are provided. To validate the derivation, an a priori error estimate between the effective ...

MATHICSE2017

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

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

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A Spectral Ansatz for The Long-Time Homogenization of The Wave Equation

Symplectic dynamical low rank approximation of wave equations with random parameters

An Easily Computable Error Estimator In Space And Time For The Wave Equation

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

Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach

Joint Estimation Of The Room Geometry And Modes With Compressed Sensing

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

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

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

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

A Spectral Ansatz for The Long-Time Homogenization of The Wave Equation

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach

Symplectic dynamical low rank approximation of wave equations with random parameters

An Easily Computable Error Estimator In Space And Time For The Wave Equation

Joint Estimation Of The Room Geometry And Modes With Compressed Sensing

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

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

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media