24 citations · 65 across the 15 of their papers we have counts for
15 papers
A Moment-Based Eulerian Method for Variance-Based Finite-Time Lyapunov Exponent Computation in Stochastic Flows
Shingyu Leung
Variance-based finite-time Lyapunov exponents (vFTLEs) provide a stochastic analogue of deterministic FTLE by measuring the covariance of stochastic arrival locations. Existing PDF…
Fast Operator-Splitting Methods for Nonlinear Elliptic Equations
Jingyu Yang, Shingyu Leung, Jianliang Qian +1
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite eleme…
Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems
Yun Chen Tsai, Shingyu Leung
The identification and visualization of Lagrangian structures in flows plays a crucial role in the study of dynamic systems and fluid dynamics. The Finite Time Lyapunov Exponent (F…
Hadamard integrators for wave equations in time and frequency domain: Eulerian formulations via butterfly algorithms
Yuxiao Wei, Jin Cheng, Shingyu Leung +2
Starting from the Kirchhoff-Huygens representation and Duhamel's principle of time-domain wave equations, we propose novel butterfly-compressed Hadamard integrators for self-adjoin…
Operator Splitting/Finite Element Methods for the Minkowski Problem
Hao Liu, Shingyu Leung, Jianliang Qian
The classical Minkowski problem for convex bodies has deeply influenced the development of differential geometry. During the past several decades, abundant mathematical theories ha…
A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces
Chun Kit Hung, Shingyu Leung
We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function…
Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems
Wai Ming Chau, Shingyu Leung
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as…
Spherical Essentially Non-Oscillatory (SENO) Interpolation
Ki Wai Fong, Shingyu Leung
We develop two new ideas for interpolation on . In this first part, we will introduce a simple interpolation method named \textit{Spherical Interpolation of orDER} $n…
An Efficient Operator-Splitting Method for the Eigenvalue Problem of the Monge-Ampère Equation
Hao Liu, Shingyu Leung, Jianliang Qian
We develop an efficient operator-splitting method for the eigenvalue problem of the Monge-Ampère operator in the Aleksandrov sense. The backbone of our method relies on a convergen…
On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator
Roland Glowinski, Shingyu Leung, Hao Liu +1
In this article, we report the results we obtained when investigating the numerical solution of some nonlinear eigenvalue problems for the Monge-Ampère operator $v\rightarrow \det…
An Alternating Direction Explicit Method for Time Evolution Equations with Applications to Fractional Differential Equations
Hao Liu, Shingyu Leung
We derive and analyze the alternating direction explicit (ADE) method for time evolution equations with the time-dependent Dirichlet boundary condition and with the zero Neumann bo…
Guarantees of Riemannian Optimization for Low Rank Matrix Completion
Ke Wei, Jian-Feng Cai, Tony F. Chan +1
We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from it…
Eulerian Methods for Visualizing Continuous Dynamical Systems using Lyapunov Exponents
Guoqiao You, Tony Wong, Shingyu Leung
We propose a new Eulerian numerical approach for constructing the forward flow maps in continuous dynamical systems. The new algorithm improves the original formulation developed i…
Modified Virtual Grid Difference for Discretizing the Laplace-Beltrami Operator on Point Clouds
Meng Wang, Shingyu Leung, Hongkai Zhao
We propose a new and simple discretization, named the Modified Virtual Grid Difference (MVGD), for numerical approximation of the Laplace-Beltrami (LB) operator on manifolds sample…
Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
Ke Wei, Jian-Feng Cai, Tony F. Chan +1
We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an rank matri…