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arXiv · 2008.12815

Numerical Analysis of the 1-D Parabolic Optimal Transport Problem

Abigail Brauer·Megan Krawick·Manuel Santana
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Abstract

Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution of the optimal transport problem. This suggests a fast numerical algorithm for computing optimal maps; we investigate such an algorithm here in the 1-dimensional case. Specifically, we use a finite difference scheme to solve the time-dependent optimal transport problem and carry out an error analysis of the scheme. A collection of numerical examples is also presented and discussed.

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Abigail Brauer, Megan Krawick, Manuel Santana. 2020-08-28. Numerical Analysis of the 1-D Parabolic Optimal Transport Problem. https://doi.org/10.1137/20s1367155

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