This article surveys the recent developments in computational methods for second order
fully nonlinear partial differential equations (PDEs), a relatively new subarea within …

A numerical method for the solution of the elliptic Monge–Ampère Partial Differential
Equation, with boundary conditions corresponding to the Optimal Transportation (OT) …

The elliptic Monge–Ampère equation is a fully nonlinear partial differential equation that
originated in geometric surface theory and has been applied in dynamic meteorology …

The theory of viscosity solutions has been effective for representing and approximating weak
solutions to fully nonlinear partial differential equations such as the elliptic Monge--Ampère …

In this article we introduce a novel numerical method to solve the problem of optimal
transport and the related elliptic Monge--Ampère equation. It is one of the few numerical …

The problem of optimal mass transport arises in numerous applications, including image
registration, mesh generation, reflector design, and astrophysics. One approach to solving …

In modern optical design, the central challenge is to facilitate the efficient transport of light
from A to B. Guiding light transport is important for the design of lamps, cameras and …

We present a unified mathematical framework for sixteen fundamental optical systems. The
systems have a parallel or point source and a parallel, point, near-field or far-field target …

The direct formulation of a freeform optical surface for producing a prescribed irradiance
from a point source is very complicated. Instead of directly determining the freeform optical …

We build convergent discretizations and semi-implicit solvers for the Infinity Laplacian and
the game theoretical p-Laplacian. The discretizations simplify and generalize earlier ones …