Axel G. R. Turnquist

collaborators

4 papers

math.NA2026

Pointwise Convergence Analysis for Approximations of Optimal Transport Problems with a Target Measure that Has Unbounded Support

Axel G. R. Turnquist

We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence…

math.AP2024

Optimal Transport Using Cost Functions with Preferential Direction with Applications to Optics Inverse Problems

Axel G. R. Turnquist

We focus on Optimal Transport PDE on the unit sphere $S^{2}$ with a particular type of cost function $c (x, y) = F (x \cdot y, x \cdot e^, y \cdot e^)$ which we call…

math.AP2024

Optimal Transport with Defective Cost Functions with Applications to the Lens Refractor Problem

Axel G. R. Turnquist

We define and discuss the properties of a class of cost functions on the sphere which we term defective cost functions. We then discuss how to extend these definitions and some pro…

math.NA2024

A Volumetric Approach to Monge's Optimal Transport on Surfaces

Richard Tsai, Axel G. R. Turnquist

We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $R^{3}$ , found in disciplines like optics, computer graphics, and comp…