# A Convergent Numerical Method for the Reflector Antenna Problem via Optimal Transport on the Sphere

@article{Hamfeldt2021ACN, title={A Convergent Numerical Method for the Reflector Antenna Problem via Optimal Transport on the Sphere}, author={Brittany Froese Hamfeldt and Axel G. R. Turnquist}, journal={ArXiv}, year={2021}, volume={abs/2108.00088} }

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 ‖x− y‖. At each point on the sphere, we replace the surface PDE with a generalized Monge-Ampère type equation posed on the local tangent plane. We then utilize a provably convergent finite difference scheme to approximate the solution and construct the reflector. The method is easily adapted to take into account highly…

## One Citation

Adaptive Mesh Methods on Compact Manifolds via Optimal Transport and Optimal Information Transport

- Computer Science, MathematicsArXiv
- 2021

This manuscript performs the first side-by-side comparison of using Optimal Transport and Optimal Information Transport on the sphere for adaptive mesh problems and introduces how to generalize these computations to more general manifolds.

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