Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
International Journal of Computer Vision
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Blobworld: Image Segmentation Using Expectation-Maximization and Its Application to Image Querying
IEEE Transactions on Pattern Analysis and Machine Intelligence
A level set based Eulerian method for paraxial multivalued traveltimes
Journal of Computational Physics
Short note: Fast geodesics computation with the phase flow method
Journal of Computational Physics
Expectation-Maximization Algorithm with Local Adaptivity
SIAM Journal on Imaging Sciences
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
Journal of Computational Physics
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics
IEEE Transactions on Image Processing
Journal of Visual Communication and Image Representation
Journal of Computational Physics
Hi-index | 31.45 |
We develop an efficient Eulerian numerical approach to extract invariant sets in a continuous dynamical system in the extended phase space (the x-t space). We extend the idea of ergodic partition and propose a concept called coherent ergodic partition for visualizing ergodic components in a continuous flow. Numerically, we first apply the level set method [33] and extend the backward phase flow method [25] to determine the long time flow map. To compute all required long time averages of observables along particle trajectories, we propose an Eulerian approach by simply incorporating flow maps to iteratively interpolate those short time averages. Numerical experiments will demonstrate the effectiveness of the approach. As an application of the method, we apply the approach to the field of geometrical optics for high frequency wave propagation and propose to use the result from the coherent ergodic partition as a criteria for adaptivity in typical Lagrangian ray tracing methods.