4 papers
A Constrained Least-Squares Ghost Sample Points (CLS-GSP) Method for Differential Operators on Point Clouds
Ningchen Ying, Kwunlun Chu, Shingyu Leung
We introduce a novel meshless method called the Constrained Least-Squares Ghost Sample Points (CLS-GSP) method for solving partial differential equations on irregular domains or ma…
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…
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…