Numerical solution of the Optimal Transportation problem using the Monge-Ampère equation

نویسندگان

  • Jean-David Benamou
  • Brittany D. Froese
  • Adam M. Oberman
چکیده

A numerical method for the solution of the elliptic MongeAmpère Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem is presented. A local representation of the OT boundary conditions is combined with a finite difference scheme for the Monge-Ampère equation. Newton’s method is implemented leading to a fast solver, comparable to solving the Laplace equation on the same grid several times. Theoretical justification for the method is given by a convergence proof in the companion paper [BFO12]. In this paper, the algorithm is modified to a simpler compact stencil implementation and details of the implementation are given. Solutions are computed with densities supported on non-convex and disconnected domains. Computational examples demonstrate robust performance on singular solutions and fast computational times.

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عنوان ژورنال:
  • J. Comput. Physics

دوره 260  شماره 

صفحات  -

تاریخ انتشار 2014