Numerical Analysis of the 1-D Parabolic Optimal Transport Problem
Numerical Analysis
2021-04-05 v3 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2008.12815,
title = {Numerical Analysis of the 1-D Parabolic Optimal Transport Problem},
author = {Abigail Brauer and Megan Krawick and Manuel Santana},
journal= {arXiv preprint arXiv:2008.12815},
year = {2021}
}
Comments
22 pages, 14 figures. Appendix by Farhan Abedin and Jun Kitagawa. Typos fixed, figures and references updated