All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2

Displaying 21 – 35 of 35

Showing per page

The wave map problem. Small data critical regularity

Igor Rodnianski (2005/2006)

Séminaire Bourbaki

The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is ( 2 + 1 ) , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory. As a consequence,...

Time domain simulation of a piano. Part 1: model description

J. Chabassier, A. Chaigne, P. Joly (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The purpose of this study is the time domain modeling of a piano. We aim at explaining the vibratory and acoustical behavior of the piano, by taking into account the main elements that contribute to sound production. The soundboard is modeled as a bidimensional thick, orthotropic, heterogeneous, frequency dependent damped plate, using Reissner Mindlin equations. The vibroacoustics equations allow the soundboard to radiate into the surrounding air, in which we wish to compute the complete acoustical...

Time splitting for wave equations in random media

Guillaume Bal, Lenya Ryzhik (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the simplified...

Time splitting for wave equations in random media

Guillaume Bal, Lenya Ryzhik (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the...

Topological sensitivity analysis for time-dependent problems

Boris Vexler, Takéo Takahashi, Samuel Amstutz (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation...

Topological sensitivity analysis for time-dependent problems

Samuel Amstutz, Takéo Takahashi, Boris Vexler (2007)

ESAIM: Control, Optimisation and Calculus of Variations

The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation...

Currently displaying 21 – 35 of 35

Previous Page 2