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

被引：141

作者：

Benamou, Jean-David ^{[1
]}

Froese, Brittany D. ^{[2
]}

Oberman, Adam M. ^{[2
]}

机构：

[1] INRIA, F-78153 Rocquencourt, France

[2] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 260卷

关键词：

Optimal Transportation; Monge Ampere equation; Numerical methods; Finite difference methods; Viscosity solutions; Monotone schemes; Convexity; Fully nonlinear elliptic partial differential equations; FINITE-DIFFERENCE SOLVERS; BOUNDARY-VALUE PROBLEM; VISCOSITY SOLUTIONS; SCHEMES; CONSTRUCTION; GEOMETRY;

D O I：

10.1016/j.jcp.2013.12.015

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A numerical method for the solution of the elliptic Monge-Ampere 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-Ampere 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 [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. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：107 / 126

页数：20

共 45 条

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