SIAM Journal on Scientific Computing · 2015 · 83 citations · 11 references
Natural SciencesComputational EngineeringMathematicsOptimizationTransportTransport PhenomenaBoundary Conditions In TransportNumerical Methods For Differential EquationsTransport ModelingTransport ModellingTransportation ProblemsBoundary Condition FormulationsBoundary Value Problems In TransportElliptic FunctionsGrid Cell SizeLeast Squares ApproximationNumerical Simulation Of Flow And TransportOptimal TransportTransport Equations
In this article we introduce a novel numerical method to solve the problem of optimal 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 transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments.
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