https://www.selleckchem.com/pr....oducts/stat3-in-1.ht
We consider a partial differential equation (PDE) approach to numerically solve the reflector antenna problem by solving an optimal transport problem on the unit sphere with cost function c(x,y)=-2log||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 use a provably convergent finite difference scheme to approximate the solution and construct the reflector. The method is easily adapted to take into account highly nonsmooth data and s
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