Orestis Vantzos (CS, Technion)
This work proposes an algorithm for computing dense packings of congruent circles inside general 2D containers. Unlike the previous approaches which accept as containers, only simple, symmetric shapes such as circles, rectangles and triangles, our method works for any container with a general, freeform (spline) boundary.
In contrast to most previous approaches which cast the problem into a non-convex optimization problem, our method attempts to maximize the number of packed circles via a perturbation approach and consists of two main phases.
We will discuss a variation of the Ginzburg-Landau functional, a common tool in applications such as image segmentation (Ambrosio-Tortorelli) and phase-field methods in fluid simulation, involving a so-called "double-obstacle" barrier term (first studied by Elliott and Blowey).
We will describe fast (GPU-optimized) variational solvers for gradient flows of these functionals (Allen-Cahn and Cahn-Hilliard equivalents), and also look into certain higher-dimensional generalisations.