collaborators

8 papers

math.NA2026

PH2T-splines, Part I: A Reasonable Mesh Assumption

Bingru Huang, Yue Xi

This paper is the first in a three-part series on the construction of polynomial splines with the highest order of smoothness over hierarchical T-meshes, referred to as $\PHtwoT$-s…

math.NA2026

Sharp Dimension Bounds for Spline Spaces over T-meshes with Highest Order of Smoothness

Bingru Huang, Falai Chen

The dimension of a polynomial spline space of bi-degree over a T-mesh with the highest order of smoothness depends on both mesh topology a…

math.NA2026

A Homological Decomposition for the Dimension and Dimensional Stability of Polynomial Spline Spaces over T-Meshes

Bingru Huang

We study the dimension and dimensional stability of polynomial spline spaces of bi-degree with prescribed smoothness orders over planar T-meshes. The homological dimension…

math.NA2026

Dimension Calculation for Spline Spaces over Rectilinear Partitions via Smoothing Cofactor Method

Bingru Huang, Falai Chen

This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach exten…

math.NA2025

Basis Construction for Spline Spaces over Arbitrary Partitions from a Dimensional Stable Perspective

Bingru Huang

This paper introduces a novel framework for constructing basis functions for polynomial spline spaces of degree over arbitrary planar polygonal partitions, overturning th…

math.NA2025

Basis construction for polynomial spline spaces over arbitrary T-meshes

Shicong Zhong, Bingru Huang, Falai Chen

This paper presents the first method for constructing bases for polynomial spline spaces over an arbitrary T-meshes (PT-splines for short). We construct spline basis functions for…

math.NA2025

A Preliminary Study on the Dimensional Stability Classification of Polynomial Spline Spaces over T-meshes

Bingru Huang, Falai Chen

This paper studies dimensional stability of polynomial spline spaces over T-meshes with highest-order smoothness. Dimensional stability is defined as the invariance of the dimensio…

math.NA2025

Dimension of Bi-degree Spline Spaces with the Highest Order of Smoothness over Hierarchical T-Meshes

Bingru Huang, Falai Chen

In this article, we study the dimension of the spline space of di-degree with the highest order of smoothness over a hierarchical T-mesh using the smoothing co…