We compute and visualize solutions to the Optimal Transportation(OT)problem for a wide class of cost functions.The standard linear programming(LP)discretization of the continuous problem becomes intractable for modera...We compute and visualize solutions to the Optimal Transportation(OT)problem for a wide class of cost functions.The standard linear programming(LP)discretization of the continuous problem becomes intractable for moderate grid sizes.A grid refinement method results in a linear cost algorithm.Weak convergence of solutions is established and barycentric projection of transference plans is used to improve the accuracy of solutions.Optimal maps between nonconvex domains,partial OT free boundaries,and high accuracy barycenters are presented.展开更多
We build finite difference schemes for a class of fully nonlinear parabolic equations. The schemes are polyhedral and grid aligned. While this is a restrictive class of schemes, a wide class of equations are well appr...We build finite difference schemes for a class of fully nonlinear parabolic equations. The schemes are polyhedral and grid aligned. While this is a restrictive class of schemes, a wide class of equations are well approximated by equations from this class. For regular （C2,α） solutions of uniformly parabolic equations, we also establish of convergence rate of O（α）. A case study along with supporting numerical results is included.展开更多
文摘We compute and visualize solutions to the Optimal Transportation(OT)problem for a wide class of cost functions.The standard linear programming(LP)discretization of the continuous problem becomes intractable for moderate grid sizes.A grid refinement method results in a linear cost algorithm.Weak convergence of solutions is established and barycentric projection of transference plans is used to improve the accuracy of solutions.Optimal maps between nonconvex domains,partial OT free boundaries,and high accuracy barycenters are presented.
文摘We build finite difference schemes for a class of fully nonlinear parabolic equations. The schemes are polyhedral and grid aligned. While this is a restrictive class of schemes, a wide class of equations are well approximated by equations from this class. For regular （C2,α） solutions of uniformly parabolic equations, we also establish of convergence rate of O（α）. A case study along with supporting numerical results is included.
