6 papers · 1 filter
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…