Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Convergent Numerical Method for the Reflector Antenna Problem via
  Optimal Transport on the Sphere   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 $c(x,y) = -2\log \left\Vert x - y \right\Vert$. At each point on the
sphere, we replace the surface PDE with a generalized Monge-Amp\`ere 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
nonsmooth data and solutions, which makes it particularly well adapted to
real-world optics problems. Computational examples demonstrate the success of
this method in computing reflectors for a range of challenging problems
including discontinuous intensities and intensities supported on complicated
geometries.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat