I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns on lizard surfaces emerge. The image below shows real geckos and their simulation counterparts.
The author of the article told me that his code is not ready to be shared publicly and is unsure when or if it will ever be ready - which is such a pity as it happens quite often. Nevertheless, he told me that he has used Trilinos library (https://trilinos.github.io/) and Deal.ii (https://www.dealii.org/) package to perform the simulations and that both libraries have received frequent updates since he published the article.
To all the Mathematica aficionados who love solving PDEs numerically, I am wondering whether the current capabilities of Mathematica allow solving PDEs of such kind (reaction-diffusion, heat equation) over surface of a mesh. From what I know,
NDSolve complains when you feed it a mesh that has
RegionDimension of 2 (essentially a surface) while the
RegionEmbeddingDimension is 3.
It would be wonderful if such problems can be tackled with the burgeoning Finite Elements capability in Mathematica. My question, is it possible?
Note: one can easily download a similar geometry or surface mesh from https://www.thingiverse.com/thing:1363148