Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 97-111.
Published online: 2015-08
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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 $L_2$ 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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w02si}, url = {http://global-sci.org/intro/article_detail/nmtma/12401.html} }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.