11 papers
A Structure-Preserving Scheme for Computing the Gradient of the Eikonal Equation
Ka Lun Leung, Shingyu Leung
We propose a first-order, structure-preserving method for directly computing the normalized traveltime gradient of the eikonal equation in smooth first-arrival regions. The method…
Geodesic Interpolation on the Grassmann Manifold: GLERP and Recursive GIDER Interpolants
Shingyu Leung
This article develops a geodesic interpolation framework for data on the Grassmann manifold. The motivation is that many matrix-valued data sets represent subspaces rather than fix…
Analytic First Derivatives of SIDER Interpolation
Shingyu Leung
Spherical interpolation is required in numerical and geometric applications in which the unknowns are constrained to remain on the unit sphere. Spherical Interpolation of orDER …
A Quaternion--BCH Framework for the Local Accuracy of SIDER Interpolation
Shingyu Leung
Spherical Interpolation of orDER (SIDER-) is a recursive high-order interpolation method for data on the unit sphere , built from repeated spherical linear int…
Local Consistency and Higher-Order Structure of Spherical Interpolation
Shingyu Leung
Spherical Interpolation of orDER (SIDER-) is a recursive high-order interpolation construction for data on the unit sphere , built from repeated spherical line…
A Semi-Lagrangian Spherical Essentially Non-Oscillatory (SENO) Scheme for Advection Equations of S2-valued Functions
Shingyu Leung
We develop a numerical scheme for solving the advection equation of -valued functions of real variables, which models the time-evolution of a -valued ma…
A multilayer level-set method for eikonal-based traveltime tomography
Wenbin Li, Ken K. T. Hung, Shingyu Leung
We present a novel multilayer level-set method (MLSM) for eikonal-based first-arrival traveltime tomography. Unlike classical level-set approaches that rely solely on the zero-leve…
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…
Solving Partial Differential Equations on Evolving Surfaces via the Constrained Least-Squares and Grid-Based Particle Method
Ningchen Ying, Shingyu Leung
We present a framework for solving partial different equations on evolving surfaces. Based on the grid-based particle method (GBPM) [18], the method can naturally resample the surf…
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…