Analysis and Applied Mathematics Seminar: Discrete Monge-Ampere equations and the second boundary value problem, by Gerard Awanou
April 13, 2026
4:00 PM - 4:50 PM
Gerard Awanou (University of Illinois at Chicago): Discrete Monge-Ampere equations and the second boundary value problem
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 foundationĀcovering existence, uniqueness, and convergenceĀfor
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.
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Date posted
Apr 14, 2026
Date updated
Apr 14, 2026
Speakers
