5 papers · 1 filter
The Closest Point Heat Method for Solving Eikonal Equations on Implicit Surfaces
Tony Wong, Shingyu Leung, Byungjoon Lee
We introduce the Closest Point Heat Method (CPHM), a novel approach for solving the surface Eikonal equation on general smooth surfaces. Building on the strengths of the classical…
A Spherical Crank-Nicolson Integrator Based on the Exponential Map and the Spherical Linear Interpolation
Shingyu Leung
We propose implicit integrators for solving stiff differential equations on unit spheres. Our approach extends the standard backward Euler and Crank-Nicolson methods in Cartesian s…
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…
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…