Mixed-precision finite element kernels

Documentation

This software generates the numerical results of the manuscript Mixed-precision finite element kernels and assembly: Rounding error analysis and hardware acceleration by M. Croci and G. N. Wells. See ArXiv preprint and techreport in the Zenodo upload for more information.

Important

These codes can only be run on a machine with an Intel Sapphire Rapids CPU!!!

Paper experiments

The code is in src/local_kernel.

Before running the kernel scripts one first has to generate the FFCX kernels and the meshes. These require FEniCSx and gmsh to be installed, but only have to be generated once. The easiest way is to use one of the fenicsproject docker containers.

ALTERNATIVE: Directly download the dataset and software from the Zenodo upload to directly skip to Step 3. The original software is also part of the Zenodo upload and can be used instead of the GitHub version. However, the Zenodo version won't be kept up to date.

1- Generate the FFCX kernels by running the ffcx_codegen.py script in src/ffcx, i.e.,

cd src/ffcx
python3 ffcx_codegen.py

2- Generate the mesh files by running

cd src/local_kernel/meshes
gmsh -3 tet.geo && gmsh -3 cube.geo && python3 get_mesh_coordinates.py

3- Check that all dependencies have been installed (see "Dependencies" below):

cd src/local_kernel
make
./kernel.run

4- Run all the experiments (it takes some time):

python3 run_all_kernels.py

5- Plot results (requires matplotlib):

python3 plot_results.py

Dependencies

Hardware dependency: These codes can only be run on a machine with an Intel Sapphire Rapids CPU!!!

Software dependencies: numpy, [email protected]+binutils and intel-oneapi-mkl (optional). You can use spack to install these with

spack install [email protected]+binutils
spack install intel-oneapi-mkl

NOTES:

• [email protected] can be replaced with [email protected]~libomptarget or [email protected], but the code is untested for these compilers.
• intel-oneapi-mkl is optional and only needed for the gemm tests.