An Introduction to Eulerian Geometrical Optics (1992–2002)

Authors:
Jean-David Benamou
Affiliations:
INRIA-Rocquencourt, B.P. 105, F-78153 Le Chesnay Cedex, France. jean-david.benamou@inria.fr
Venue:
Journal of Scientific Computing
Year:
2003

Citing 16
Cited 7

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
A viscosity solutions approach to shape-from-shading

SIAM Journal on Numerical Analysis
Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary

SIAM Journal on Control and Optimization
Numerical solution of the high frequency asymptotic expansion for the scalar wave equation

Journal of Computational Physics
Multi-phase computations in geometrical optics

Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
The Gaussian moment closure for gas dynamics

SIAM Journal on Applied Mathematics
A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering

SIAM Journal on Control and Optimization
A PDE-based fast local level set method

Journal of Computational Physics
A new Eulerian method for the computation of propagating short acoustic and electromagnetic pulses

Journal of Computational Physics
New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations

Journal of Computational Physics
An Eulerian method for capturing caustics

Journal of Computational Physics
A fixed grid method for capturing the motion of self-intersecting wavefronts and related PDEs

Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
Multivalued solutions to the Eikonal equation in stratified media

Quarterly of Applied Mathematics
High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes

Journal of Scientific Computing
Numerical Discretization of Boundary Conditions for First Order Hamilton--Jacobi Equations

SIAM Journal on Numerical Analysis

A level set based Eulerian method for paraxial multivalued traveltimes

Journal of Computational Physics
Numerical microlocal analysis of harmonic wavefields

Journal of Computational Physics
Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds

Journal of Computational Physics
The phase flow method

Journal of Computational Physics
Efficient level set methods for constructing wavefronts in three spatial dimensions

Journal of Computational Physics
A grid based particle method for moving interface problems

Journal of Computational Physics
Source point discovery through high frequency asymptotic time reversal

Journal of Computational Physics

Quantified Score

Hi-index	0.03

Visualization

Abstract

This document is an attempt at introducing the different “Eulerian” numerical methods which have recently been developed for the simulation of geometric optics and related models.