Concept

One-way wave equation

Related publications (85)

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

Matthias Ruf

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

Stress wave propagation through a 180° bend junction in a square cross-sectional bar

Jean-François Molinari, Antonio Joaquin Garcia Suarez, Ghatu Subhash

Longitudinal elastic stress wave propagation through a 180° bend junction connecting two square bars is analyzed using analytical and numerical approaches and validated against experiments. The aim is to identify conditions under which the one-dimensional ...

2022

Physics Informed Neural Networks for Surrogate Modelling and Inverse Problems in Geotechnics

Finite elements methods (FEMs) have benefited from decades of development to solve partial differential equations (PDEs) and to simulate physical systems. In the recent years, machine learning (ML) and artificial neural networks (ANN) have shown great pote ...

2021

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

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

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2020

Direct FEM-Domain Decomposition Using Convex-to-Concave Spherical Ports for Space Applications

Juan Ramon Mosig, Javier Rubio

This letter proposes the application of a hybrid numerical technique to two cases of interest in the space business: the reallocation of radiators and scatters on satellite platforms; and the analysis of antennas for mobile communications. It is based on t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

Tobias Schneider, Sajjad Azimi

At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in inner units, the statistica ...

CAMBRIDGE UNIV PRESS2020

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

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

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