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… 
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