SLMath Research Talk: A Numerical Study of the Dirichlet Problem for the Elliptic Monge-Ampere Equation in 2D

The Dirichlet problem for the real elliptic Monge-Ampère equation in two dimensions arises in many important applications including optimal transport, machine learning, and geometry. In this talk, I will discuss the performance of two numerical methods for the solution of this problem. The first method is an augmented Lagrangian based method that reformulates the problem as a saddle point problem. The second method is a relaxation algorithm using a least squares formulation. This work is part of an ongoing undergraduate research project, and I will present preliminary numerical experiments in two dimensions comparing the two methods with respect to accuracy, convergence behavior, and computational cost.

Work by J.C. Meza and Isaic Cruse, UC Merced.