# A least-squares method for optimal transport using the Monge-Ampère equation

C.R. Prins, J.H.M. Thije Boonkkamp, ten, W.L. IJzerman, T.W. Tukker

### Uittreksel

In this article we introduce a novel numerical method to solve the problem of optimal mass 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 boundary conditions. It scales well with the grid size and has the additional advantage that the target domain may be non-convex. We present the method and several numerical experiments.
Originele taal-2 Engels Eindhoven Technische Universiteit Eindhoven 24 Gepubliceerd - 2014

### Publicatie series

Naam CASA-report 1429 0926-4507

### Vingerafdruk

Numerical methods
Mass transfer
Boundary conditions
Experiments

### Citeer dit

Prins, C. R., Thije Boonkkamp, ten, J. H. M., IJzerman, W. L., & Tukker, T. W. (2014). A least-squares method for optimal transport using the Monge-Ampère equation. (CASA-report; Vol. 1429). Eindhoven: Technische Universiteit Eindhoven.
Prins, C.R. ; Thije Boonkkamp, ten, J.H.M. ; IJzerman, W.L. ; Tukker, T.W. / A least-squares method for optimal transport using the Monge-Ampère equation. Eindhoven : Technische Universiteit Eindhoven, 2014. 24 blz. (CASA-report).
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abstract = "In this article we introduce a novel numerical method to solve the problem of optimal mass transport and the related elliptic Monge-Amp{\`e}re equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper boundary conditions. It scales well with the grid size and has the additional advantage that the target domain may be non-convex. We present the method and several numerical experiments.",
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Prins, CR, Thije Boonkkamp, ten, JHM, IJzerman, WL & Tukker, TW 2014, A least-squares method for optimal transport using the Monge-Ampère equation. CASA-report, vol. 1429, Technische Universiteit Eindhoven, Eindhoven.
Eindhoven : Technische Universiteit Eindhoven, 2014. 24 blz. (CASA-report; Vol. 1429).

TY - BOOK

T1 - A least-squares method for optimal transport using the Monge-Ampère equation

AU - Prins, C.R.

AU - Thije Boonkkamp, ten, J.H.M.

AU - IJzerman, W.L.

AU - Tukker, T.W.

PY - 2014

Y1 - 2014

N2 - In this article we introduce a novel numerical method to solve the problem of optimal mass 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 boundary conditions. It scales well with the grid size and has the additional advantage that the target domain may be non-convex. We present the method and several numerical experiments.

AB - In this article we introduce a novel numerical method to solve the problem of optimal mass 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 boundary conditions. It scales well with the grid size and has the additional advantage that the target domain may be non-convex. We present the method and several numerical experiments.

M3 - Report

T3 - CASA-report

BT - A least-squares method for optimal transport using the Monge-Ampère equation

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -

Prins CR, Thije Boonkkamp, ten JHM, IJzerman WL, Tukker TW. A least-squares method for optimal transport using the Monge-Ampère equation. Eindhoven: Technische Universiteit Eindhoven, 2014. 24 blz. (CASA-report).