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A Multilevel Method for the Solution of Time Dependent Optimal Transport

Published online by Cambridge University Press:  03 March 2015

Eldad Haber and
Raya Horesh
Eldad Haber*
Affiliation:
Department of Mathematics & Department of Earth and Ocean Science, The University of British Columbia, Vancouver, BC, Canada; IBM research, NY, USA
Raya Horesh
Affiliation:
Department of Mathematics & Department of Earth and Ocean Science, The University of British Columbia, Vancouver, BC, Canada; IBM research, NY, USA
*
*Email address: haber@math.ubc.ca (E. Haber)

Abstract

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In this paper we present a new computationally efficient numerical scheme for the minimizing flow for the computation of the optimal L2 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.

Keywords

15A1265F1065F15Optimal mass transportinverse problemsstaggered grids

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 1 , February 2015, pp. 97 - 111
Copyright
Copyright © Global-Science Press 2015 

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