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
Journal of Computational Physics
Multi-phase computations in geometrical optics
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
Convolution-generated motion as a link between cellular automata and continuum pattern dynamics
Journal of Computational Physics
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
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
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
High-Resolution Nonoscillatory Central Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Paraxial eikonal solvers for anisotropic quasi-P travel times
Journal of Computational Physics
High-frequency wave propagation by the segment projection method
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Journal of Computational Physics
A level set based Eulerian method for paraxial multivalued traveltimes
Journal of Computational Physics
Journal of Computational Physics
A fast phase space method for computing creeping rays
Journal of Computational Physics
Journal of Computational Physics
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics
Hi-index | 0.03 |
Traveltime, or geodesic distance, is locally the solution of the eikonal equation of geometric optics. However traveltime between sufficiently distant points is generically multivalued. Finite difference eikonal solvers approximate only the viscosity solution, which is the smallest value of the (multivalued) traveltime (“first arrival time”). The slowness matching method stitches together local single-valued eikonal solutions, approximated by a finite difference eikonal solver, to approximate all values of the traveltime. In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation, so that the eikonal equation may be viewed as an evolution equation in one of the spatial directions. This paraxial assumption simplifies both the efficient computation of local traveltime fields and their combination into global multivalued traveltime fields via the slowness matching algorithm. The cost of slowness matching is on the same order as that of a finite difference solver used to compute the viscosity solution, when traveltimes from many point sources are required as is typical in seismic applications. Adaptive gridding near the source point and a formally third order scheme for the paraxial eikonal combine to give second order convergence of the traveltime branches.