Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
518385 | Journal of Computational Physics | 2014 | 20 Pages |
Abstract
A numerical method for the solution of the elliptic Monge–Ampère 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. Newtonʼs 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 [4]. Solutions are computed with densities supported on non-convex and disconnected domains. Computational examples demonstrate robust performance on singular solutions and fast computational times.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Jean-David Benamou, Brittany D. Froese, Adam M. Oberman,