Analysis and Applied Mathematics Seminar
Brittany Froese
New Jersey Institute of Technology
Numerical Optimal Transportation Using the Monge-Ampere Equation
Abstract: The problem of optimal transportation, which involves finding the most cost-efficient mapping between two measures, arises in many different applications. However, the numerical solution of this problem remains extremely challenging. We describe a numerical method for the widely-studied case when the cost is quadratic. The solution is obtained by solving the Monge-Ampere equation, a fully nonlinear elliptic partial differential equation (PDE), coupled to a non-standard implicit boundary condition. Expressing this problem in terms of weak (viscosity) solutions enables us to construct a monotone finite difference approximation that computes the correct solution. A range of challenging computational examples demonstrate the effectiveness of this method, including the recent application of this method to problems in beam shaping and seismic inversion.
Monday February 8, 2016 at 4:00 PM in SEO 636