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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…
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 , found in disciplines like optics, computer graphics, and comp…
On the Reduction in Accuracy of Finite Difference Schemes on Manifolds without Boundary
Brittany Froese Hamfeldt, Axel G. R. Turnquist
We investigate error bounds for numerical solutions of divergence structure linear elliptic PDEs on compact manifolds without boundary. Our focus is on a class of monotone finite d…
Adaptive Mesh Methods on Compact Manifolds via Optimal Transport and Optimal Information Transport
Axel G. R. Turnquist
Moving mesh methods are designed to redistribute a mesh in a regular way. This applied problem can be considered to overlap with the problem of finding a diffeomorphic mapping betw…
A Convergent Numerical Method for the Reflector Antenna Problem via Optimal Transport on the Sphere
Brittany Froese Hamfeldt, Axel G R Turnquist
We consider a PDE approach to numerically solving the reflector antenna problem by solving an Optimal Transport problem on the unit sphere with cost function $c(x,y) = -2\log \left…
A Convergent Finite Difference Method for Optimal Transport on the Sphere
Brittany Froese Hamfeldt, Axel G. R. Turnquist
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (a…
A convergence framework for optimal transport on the sphere
Brittany Froese Hamfeldt, Axel G. R. Turnquist
We consider a PDE approach to numerically solving the optimal transportation problem on the sphere. We focus on both the traditional squared geodesic cost and a logarithmic cost, w…