A Multilevel Method for the Solution of Time Dependent Optimal Transport

Abstract

AbstractIn 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.