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Volume 8, Issue 1
A Multilevel Method for the Solution of Time Dependent Optimal Transport

Eldad Haber & Raya Horesh

DOI: 10.4208/nmtma.2015.w02si

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 97-111.

Published online: 2015-08

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  • Abstract

In this paper we present a new computationally efficient numerical scheme for the minimizing flow for the computation of the optimal $L_2$ mass transport mapping using the fluid approach. We review the method and discuss its numerical properties. We then derive a new scaleable, efficient discretization and a solution technique for the problem and show that the problem is equivalent to a mixed form formulation of a nonlinear fluid flow in porous media. We demonstrate the effectiveness of our approach using a number of numerical experiments.

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@Article{NMTMA-8-97, author = {Eldad Haber and Raya Horesh}, title = {A Multilevel Method for the Solution of Time Dependent Optimal Transport}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {1}, pages = {97--111}, abstract = {

In this paper we present a new computationally efficient numerical scheme for the minimizing flow for the computation of the optimal $L_2$ mass transport mapping using the fluid approach. We review the method and discuss its numerical properties. We then derive a new scaleable, efficient discretization and a solution technique for the problem and show that the problem is equivalent to a mixed form formulation of a nonlinear fluid flow in porous media. We demonstrate the effectiveness of our approach using a number of numerical experiments.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w02si}, url = {http://global-sci.org/intro/article_detail/nmtma/12401.html} }
TY - JOUR T1 - A Multilevel Method for the Solution of Time Dependent Optimal Transport AU - Eldad Haber & Raya Horesh JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 97 EP - 111 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.w02si UR - https://global-sci.org/intro/article_detail/nmtma/12401.html KW - AB -

In this paper we present a new computationally efficient numerical scheme for the minimizing flow for the computation of the optimal $L_2$ mass transport mapping using the fluid approach. We review the method and discuss its numerical properties. We then derive a new scaleable, efficient discretization and a solution technique for the problem and show that the problem is equivalent to a mixed form formulation of a nonlinear fluid flow in porous media. We demonstrate the effectiveness of our approach using a number of numerical experiments.

Eldad Haber and Raya Horesh. (2015). A Multilevel Method for the Solution of Time Dependent Optimal Transport. Numerical Mathematics: Theory, Methods and Applications. 8 (1). 97-111. doi:10.4208/nmtma.2015.w02si
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