README.md

JaxFEM

An exercise to implement a FEM solver using python and JAX Jaxlib only works under Linux so this whole software is only usable under Linux-based operating systems. Some functions are written in Rust for better performance but are kept in another repo. Run the setup_environment.py script first to ensure your enviroment has all the necessary requirements.

Poisson equation

Currently main_poisson.py solves a poisson equation with a right hand side equal to -1 and homogenous Dirichlet b.c.

$\nabla^2 u = -1$

Result is:

Fick's law

main_fick.py Solves the simplest form of the diffusion equation in 2D with homogenous Neumann b.c.

$\frac{\partial u}{\partial t} - \nabla^2 u = 0$

Output is:

Advection-Diffusion

This builds on the previous example by adding an advection term.

main_advection.py is the solver for:

$\frac{\partial u}{\partial t} + \bar{b} \cdot \nabla u - \nabla^2 u = 0$

Where the particular choice for $\bar{b}$ simulates a fluid flow moving from the left to the right with a temperature of 0 degrees. Here the "dominant force" is the advection.

Output: