Numerical Analysis of the 1-D Parabolic Optimal Transport Problem*
Published in SIURO, 2021
Recommended citation: Brauer A, Krawick M, and Santana M. (2021). "Numerical Analysis of the 1-D Parabolic Optimal Transport Problem." SIAM SIURO. Vol 14:150-166.
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. [Download paper here](https://www.siam.org/Portals/0/Publications/SIURO/Vol14/S136715PDF.pdf?ver=2021-03-22-130924-857) Recommended citation: Brauer A, Krawick M, and Santana M. (2021). "Numerical Analysis of the 1-D Parabolic Optimal Transport Problem." SIAM SIURO. Vol 14:150-166.