The Monge-Ampère equation is a fully nonlinear degenerate elliptic PDE used in a large number of applications including mesh generation, optical design, and medical image processing. The development of convergent numerical methods for this PDE has been guided by the Barles and Souganidis framework, which guarantees a monotone scheme will converge to the unique weak (viscosity) solution provided the PDE satisfies a comparison principle. However, monotone scemes rely on wide stencils, which traditionally suffer from high computational costs and low accuracy due. We will address these challenges by 1) introducing an improved monotone discretization using an integral representation of the Monge-Ampère operator and 2) developing highly parallelizable nonlinear root finders for monotone schemes. This presentation is based on joint work with Tadanaga Takahashi, Yassine Boubendir, and Brittany Hamfeldt.

https://arizona.zoom.us/j/82763762677