This project is an effort to demonstrate the capabilities of the finite element method in 3D. The project is written mainly in C++ and OpenGL trough Magnum.
Try it online here: http://envall.xyz/fem3d/
The examined problem is the simplest of the simple; Poisson's equation
-∆u=f
with the weak form
(∇u,∇v)=(fv).
The program supports tetrahedron meshes. Meshes are compiled into the final binary as the program is designed to be a web ready demo only. The load is hardcoded but the user can constrain vertices to zero by clicking or by using the lasso from the ui. The user can visualize either the solution u or the gradient of the solution ∇u.
Meshes are drawn as transparent triangles with the order independent algorithm from here: http://jcgt.org/published/0002/02/09/ Quadratures and other operations are vectorized for maximal speed. The resulting linear system is solved using Eigen's Eigen::SimplicialLLT solver.
To build the project you need Magnum installed on your system. Magnum is split into a number of separate modules.
Magnum also supports WebGL as the rendering backend and WASM via Emscripten.
Here is what is needed for the desktop build:
SDL2 (prebuilt or from source)
https://github.com/ocornut/imgui.git (v1.66b for WASM build)
https://github.com/mosra/corrade.git
https://github.com/mosra/magnum.git
https://github.com/mosra/magnum-plugins.git
https://github.com/mosra/magnum-extras.git
https://github.com/mosra/magnum-integration.git
This project has been developed against the "v2019.01" branch of the above repositories. Pre-built packages can be found for Arch can be found in AUR. "build.sh" might be useful when building from source.
Before the first build you also need a mesh file, see instructions below. After all dependencies are in place this project can be built the common way:
mkdir build
cd build
cmake -DImGui_INCLUDE_DIR=PATH/TO/IMGUI ..
make -j
Thanks to @Henkkis for valuable help with the mesh generation scripts. Two MATLAB scripts are included for generating and saving tetrahedron meshes in a simple ASCII format. In order to have this project also WASM ready, the files are built into the final binary.
The MATLAB script can be run in batchmode with
matlab -nodesktop -nosplash -nodisplay -r "createMesh('cube.stl',0.5);exit"