Analysis and Applied Mathematics Seminar
Gerard Awanou
University of Illinois at Chicago
Discrete Monge-Ampere equations and the second boundary value problem
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.
Monday April 13, 2026 at 4:00 PM in 636 SEO