Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
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
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
Paraxial eikonal solvers for anisotropic quasi-P travel times
Journal of Computational Physics
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
High-frequency wave propagation by the segment projection method
Journal of Computational Physics
Using K-branch entropy solutions for multivalued geometric optics computations
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
An Introduction to Eulerian Geometrical Optics (1992–2002)
Journal of Scientific Computing
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Journal of Scientific Computing
Computing multi-valued velocity and electric fields for 1D Euler--Poisson equations
Applied Numerical Mathematics
Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
Journal of Computational Physics
A grid based particle method for moving interface problems
Journal of Computational Physics
A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations
Journal of Computational Physics
Journal of Computational Physics
Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity
SIAM Journal on Numerical Analysis
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics
An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems
Journal of Computational Physics
Hi-index | 31.48 |
We apply the level-set methodology to compute multivalued solutions of the paraxial eikonal equation in both isotropic and anisotropic metrics. This paraxial equation is obtained from 2D stationary eikonal equations by using one of the spatial directions as the artificial evolution direction. The advection velocity field used to move level sets is obtained by the method of characteristics; therefore, the motion of level sets is defined in a phase space, and the zero level set yields the location of bicharacteristic strips in the reduced phase space. The multivalued traveltime is obtained from solving another advection equation with a source term. The complexity of the algorithm is O(N3 logN) in the worst case and O(N3) in the average case, where N is the number of the sampling points along one of the spatial directions. Numerical experiments including the well-known Marmousi synthetic model illustrate the accuracy and the efficiency of the Eulerian method.