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 PDE-based fast local level set method
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Paraxial eikonal solvers for anisotropic quasi-P travel times
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Journal of Scientific Computing
A level set based Eulerian method for paraxial multivalued traveltimes
Journal of Computational Physics
A Local Level Set Method for Paraxial Geometrical Optics
SIAM Journal on Scientific Computing
Short note: Fast geodesics computation with the phase flow method
Journal of Computational Physics
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction
IEEE Transactions on Visualization and Computer Graphics
Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications
IEEE Transactions on Visualization and Computer Graphics
Journal of Scientific Computing
Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
Journal of Computational Physics
Anisotropic mesh adaptation on Lagrangian Coherent Structures
Journal of Computational Physics
An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
We propose efficient Eulerian methods for approximating the finite-time Lyapunov exponent (FTLE). The idea is to compute the related flow map using the Level Set Method and the Liouville equation. There are several advantages of the proposed approach. Unlike the usual Lagrangian-type computations, the resulting method requires the velocity field defined only at discrete locations. No interpolation of the velocity field is needed. Also, the method automatically stops a particle trajectory in the case when the ray hits the boundary of the computational domain. The computational complexity of the algorithm is O(@Dx^-^(^d^+^1^)) with d the dimension of the physical space. Since there are the same number of mesh points in the x-t space, the computational complexity of the proposed Eulerian approach is optimal in the sense that each grid point is visited for only O(1) time. We also extend the algorithm to compute the FTLE on a co-dimension one manifold. The resulting algorithm does not require computation on any local coordinate system and is simple to implement even for an evolving manifold.