In this article we introduce a novel numerical method to solve the problem of optimal transport and the related elliptic Monge--Ampère equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments.
Prins, C. R., Thije Boonkkamp, ten, J. H. M., IJzerman, W. L., & Tukker, T. W. (2015). A least-squares method for optimal transport using the Monge-Ampère equation. SIAM Journal on Scientific Computing, 37(6), B937-B961. https://doi.org/10.1137/140986414