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Polynomial Interpolation of a Vector Field on a Convex Polyhedral Domain

组织者

马修·伯菲特 , 李京艳 , Pravin Kumar , 吴杰

演讲者

Junyan Chu

时间

2026年04月02日 15:00 至 16:00

地点

A3-4-301

线上

Zoom 518 868 7656 (BIMSA)

摘要

We present a computational method for reconstructing a vector field on a convex polytope $\mathcal{P} \subset \mathbb{R}^d$ of arbitrary dimension from discrete samples. We specifically address the scenario where the vector field is subject to a no-penetration (slip) boundary condition, requiring it to be tangent to the boundary $\partial \mathcal{P}$. Given a degree bound $k$, our algorithm computes a polynomial vector field of degree at most $k$ that fits the observed data in the least-squares sense while exactly satisfying the tangency constraints. Central to our approach is an explicit characterization of the module of polynomial vector fields tangent to $\partial \mathcal{P}$, derived using algebraic concepts from the theory of hyperplane arrangements.