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

An optimal preconditioned FFT-accelerated finite element solver for homogenization

We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...

ELSEVIER SCIENCE INC2023

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Martin Vetterli, Paul Hurley, Eric Bezzam, Sepand Kashani, Matthieu Martin Jean-André Simeoni

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...

2022

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

Gaspard Ohlmann

We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...

EPFL2021

Correcting for non-periodic behaviour in perturbative experiments: application to heat pulse propagation and modulated gas-puff experiments

Federico Alberto Alfredo Felici, Cristian Galperti

This paper introduces a recent innovation in dealing with non-periodic behavior often referred to as transients in perturbative experiments. These transients can be the result from the unforced response due to the initial condition and other slow trends in ...

2020

Fourier Sampling in Signal Processing and Numerical Linear Algebra

Amir Zandieh

This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...

EPFL2020

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

Méthodes numériques liées à la distribution d'alumine dans une cuve d'électrolyse d'aluminium

Thomas Frédéric Hilke

Metallic aluminium plays a key role in our modern economy. Primary metallic aluminium is produced by the transformation of aluminium oxide using the Hall-Héroult industrial process. This process, which requires enormous quantities of energy, consists in pe ...

EPFL2019

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

Combining Fourier Analysis And Machine Learning To Estimate The Shallow-Ground Thermal Diffusivity In Switzerland

Jean-Louis Scartezzini, Dan Assouline, Nahid Mohajeri Pour Rayeni

We propose a methodology combining physical modelling and machine learning (ML) to estimate the apparent ground thermal diffusivity at the scale of a country. Based on ground temperature time series at different depths, we estimate the diffusivity at 49 Sw ...

IEEE2018

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

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

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An optimal preconditioned FFT-accelerated finite element solver for homogenization

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

Correcting for non-periodic behaviour in perturbative experiments: application to heat pulse propagation and modulated gas-puff experiments

Fourier Sampling in Signal Processing and Numerical Linear Algebra

Symplectic dynamical low rank approximation of wave equations with random parameters

Méthodes numériques liées à la distribution d'alumine dans une cuve d'électrolyse d'aluminium

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

Combining Fourier Analysis And Machine Learning To Estimate The Shallow-Ground Thermal Diffusivity In Switzerland

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

An optimal preconditioned FFT-accelerated finite element solver for homogenization

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Correcting for non-periodic behaviour in perturbative experiments: application to heat pulse propagation and modulated gas-puff experiments

Symplectic dynamical low rank approximation of wave equations with random parameters

Combining Fourier Analysis And Machine Learning To Estimate The Shallow-Ground Thermal Diffusivity In Switzerland

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

Fourier Sampling in Signal Processing and Numerical Linear Algebra

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

Méthodes numériques liées à la distribution d'alumine dans une cuve d'électrolyse d'aluminium