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3 papers
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…