BIMSA > BIMSA Topology Seminar BIMSA Topology Seminar Polynomial Interpolation of a Vector Field on a Convex Polyhedral Domain
Polynomial Interpolation of a Vector Field on a Convex Polyhedral Domain
Organizers
Matthew Burfitt , Jingyan Li , Pravin Kumar , Jie Wu
Speaker
Junyan Chu
Time
Thursday, April 2, 2026 3:00 PM - 4:00 PM
Venue
A3-4-301
Online
Zoom 518 868 7656 (BIMSA)
Abstract
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.