Gerard Awanou : Discrete Monge-Ampere equations and the second boundary value problem

Posted by Gerard Awanou , part of the Analysis and Applied Mathematics Seminar.

At

April 13, 2026, 4 p.m.

In

636 SEO

Abstract

The second boundary value problem for the Monge-Ampere equation is central to applications in illumination design, such as the construction of refractors and reflectors. While semi-discrete optimal transport methods have worst-case computational complexity of O(N^2) in dimensions 2 and 3, finite difference methods have linear complexity O(N) when used with a stencil of size independent of the number of mesh points N. This talk will present a complete theoretical foundation—covering existence, uniqueness, and convergence—for a linear-complexity finite-difference discretization based on a reformulation of the second boundary condition that prescribes the asymptotic cone of the epigraph of a convex extension of the solution.