A Multilevel Method for the Solution of Time Dependent Optimal Transport. Issue 1 (3rd March 2015)

• Record Type: Journal Article
• Authors: Haber, Eldad; Horesh, Raya
• Is Part Of: Numerical mathematics. Volume 8:Issue 1(2015)
• Page Start: 97
• Page End: 111
• Publication Date: 2015-03-03
• Subjects: 15A12, -- 65F10, -- 65F15; Optimal mass transport, -- inverse problems, -- staggered grids; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2015.w02si
• Languages: English
• ISSNs: 1004-8979

Abstract

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.