| Abstract: |
| Many works have been devoted to understanding and predicting the time evolution of a growing population of cells (bacterial colonies, tumors, etc...). At the macroscopic scale, cell growth is typically modeled through reaction diffusion equations that describe the change in cell density. These equations are stiff, non-linear, and degenerate, making their numerical simulation a significant challenge. A particularly elegant numerical approach is to use an extension of the JKO scheme (a discrete-in-time variational approximation scheme); however, this requires an accurate computation of optimal transport (OT) maps -- a nontrivial task.
In this talk, I will discuss how to solve the resulting JKO scheme using an adaptation of the back-and-forth method (BFM), a recently introduced optimization method that efficiently computes OT problems in their dual form. To illustrate the power of the method, we will focus on a particularly interesting and challenging growth model, where the growth becomes unstable and the cells form dendritic fingering patterns (fractal-like shapes). |
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