Contour surgery: a topological reconnection scheme for extended integrations using contour dynamics
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
An algorithm for monotone piecewise bicubic interpolation
SIAM Journal on Numerical Analysis
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Mathematical aspects of classical and celestial mechanics (2nd ed.)
Mathematical aspects of classical and celestial mechanics (2nd ed.)
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Fast Sweeping Methods for Static Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
Journal of Computational Physics
Isoline retrieval: An optimal sounding method for validation of advected contours
Computers & Geosciences
The combined Lagrangian advection method
Journal of Computational Physics
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
Journal of Computational Physics
Journal of Computational Physics
An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems
Journal of Computational Physics
Hi-index | 31.45 |
We propose a new Eulerian tool to study complicated dynamical systems based on the average growth in the surface area of a family of level surfaces represented implicitly by a level set function. Since this proposed quantity determines the temporal variation of the averaged surface area of all level surfaces, we name the quantity the Variation of the Integral over Area of Level Surfaces (VIALS). Numerically, all these infinitely many level surfaces are advected according to the given dynamics by solving one single linear advection equation. To develop a computationally efficient approach, we apply the coarea formula and rewrite the surface area integral as a simple integral relating the total variation (TV) of the level set function. The proposed method can be easily incorporated with a recent Eulerian algorithm for efficient computation of flow maps to speed up our approach. We will also prove that the proposed VIALS is closely related to the computation of the finite time Lyapunov exponent (FTLE) in the Lagrangian coherent structure (LCS) extraction. This connects our proposed Eulerian approach to widely used Lagrangian techniques for understanding complicated dynamical systems.