Also if you’re new to Julia, the following has a tutorial on optimizing differential equation code, where the big example is a 2D reaction-diffusion. It uses different tricks (no sparsity tricks shown here), and focuses more on the code optimization.
https://tutorials.sciml.ai/html/introduction/03-optimizing_diffeq_code.html
This blog post focuses on GPUs:
And the MTK automatic optimization and parallelism tools all showcase 2D reaction diffusion.