TY - JOUR
T1 - A Multilevel Method for the Solution of Time Dependent Optimal Transport
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 97
EP - 111
PY - 2015
DA - 2015/08
SN - 8
DO - http://doi.org/10.4208/nmtma.2015.w02si
UR - https://global-sci.org/intro/article_detail/nmtma/12401.html
KW - 
AB - <p style="text-align: justify;">In this paper we present a new computationally efficient numerical scheme
for the minimizing flow for the computation of the optimal $L_2$&nbsp;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.</p>