A Finite Element Approach to Reaction-Diffusion Systems
Description:
This was my project in Will Mitchell’s Partial Differential Equations (MATH 494) class in Fall 2024.
I wanted to explore numerical solvers for partial differential equations. In particular, I looked into how the finite element method of solving PDEs can be applied to reaction-diffusion systems, which often feature highly nonlinear parts that are hard to numerically solve. In Python, I wrote my own reaction diffusion solver. I especially focused on computational efficiency. Using spare matrices, vectorized functions, and efficient linear algebra solvers specific to the features of the problem, the code runs fast, even for large systems.
Solutions to a reaction diffusion equation over time on various domains.