Numerical solution of the second boundary value problem for the Elliptic Monge-Ampère equation

Abstract : This paper introduces a numerical method for the solution of the nonlinear elliptic Monge-Ampére equation. The boundary conditions correspond to the optimal transportation of measures supported on two domains, where one of these sets is convex. The new challenge is implementing the boundary conditions, which are implicit and non-local. These boundary conditions are reformulated as a nonlinear Hamilton-Jacobi PDE on the boundary. This formulation allows us to extend the convergent, wide stencil Monge-Ampére solvers proposed by Froese and Oberman to this problem. Several non-trivial computational examples demonstrate that the method is robust and fast.
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https://hal.inria.fr/hal-00703677
Contributor : Jean-David Benamou <>
Submitted on : Monday, June 4, 2012 - 10:59:55 AM
Last modification on : Wednesday, June 26, 2019 - 4:28:04 PM
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Jean-David Benamou, Adam Oberman, Froese Britanny. Numerical solution of the second boundary value problem for the Elliptic Monge-Ampère equation. [Research Report] INRIA. 2012. ⟨hal-00703677⟩

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