CutFEMx is a cut finite element library for FEniCSx. It is developed to support cut finite element methods as described in

@article{CutFEM2015,
  title={CutFEM: discretizing geometry and partial differential equations},
  author={Burman, Erik and Claus, Susanne and Hansbo, Peter and Larson, Mats G and Massing, Andr{\'e}},
  journal={International Journal for Numerical Methods in Engineering},
  volume={104},
  number={7},
  pages={472--501},
  year={2015},
  publisher={Wiley Online Library}
}

The current version supports FEniCSx 0.9 with a customised ffcx version for runtime quadrature at ffcx-runtime.

Poisson problem in a circular domain described by a level set function.

Features

• Unfitted Discretization: Solve PDEs on geometries defined by level set functions without remeshing.
• Runtime Quadrature: Automatically generates quadrature rules on cut elements using the CutCells library and a custom FFCX backend.
• Stabilization: Implements Ghost Penalty stabilization to ensure condition number robustness independent of cut geometry..
• Parallel Support: Fully compatible with MPI for large-scale distributed simulations.

Installation Instructions

The CutFEMx library requires a FEniCSx installation version 0.9.0 with an extended version of ffcx from here git clone git@github.com:sclaus2/ffcx-runtime-0.9.0.git . CutFEMx also requires CutCells. The installation instructions using conda to manage the dependencies are detailed below. Make sure to use python 3.12.

1. Create and activate a new conda environment:

   conda create -n cutfemx python=3.12
   conda activate cutfemx

2. Install general packages required for the build:

   conda install -c conda-forge cxx-compiler cmake python pkg-config pip nanobind

3. Install dependencies:

   conda install -c conda-forge numpy scipy sympy numba pyvista pytest
   conda install -c conda-forge blas blas-devel lapack libblas libcblas liblapack liblapacke libtmglib
   conda install -c conda-forge mpi mpich kahip libboost-devel parmetis libscotch libptscotch pugixml spdlog ccache
   conda install -c conda-forge mpi4py petsc4py slepc4py scikit-build-core 
   conda install -c conda-forge 'hdf5=*=mpi*' 'petsc=*=*real*' 'slepc=*=*real*' 'libadios2=*=mpi*'

4. Install Basix:

   git clone git@github.com:FEniCS/basix.git
   cd basix
   git checkout v0.9.0
   
   cd cpp
   cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX="$CONDA_PREFIX" -B build-dir -S .
   cmake --build build-dir
   cmake --install build-dir
   
   cd ../python
   pip install .
   cd ../..

5. Install UFL:

   git clone https://github.com/FEniCS/ufl.git
   cd ufl
   git checkout 2024.2.0
   pip install .
   cd ..

6. Install runtime integral extended FFCX:

   git clone git@github.com:sclaus2/ffcx-runtime-0.9.0.git
   cd ffcx-runtime-0.9.0
   pip install .
   cd ..

7. Install DOLFINx:

   git clone git@github.com:FEniCS/dolfinx.git
   cd dolfinx
   git checkout v0.9.0
   
   cd cpp
   cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX="$CONDA_PREFIX" -B build-dir -S .
   cmake --build build-dir
   cmake --install build-dir
   
   cd ../python
   pip install -r build-requirements.txt
   pip install --check-build-dependencies --no-build-isolation .

8. Install CutCells:

   git clone git@github.com:sclaus2/cutcells.git
   
   cd cutcells/cpp
   cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX="$CONDA_PREFIX" -B build-dir -S .
   cmake --build build-dir
   cmake --install build-dir
   
   cd ../python
   pip install .

9. Install CutFEMx:

   git clone https://github.com/sclaus2/CutFEMx
   cd CutFEMx
   
   # 1. Install C++ library and headers (Required for C++ demos/tests)
   cd cpp
   cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX="$CONDA_PREFIX" -B build-dir -S .
   cmake --build build-dir
   cmake --install build-dir
   cd ..
   
   # 2. Install Python interface
   python -m pip install --check-build-dependencies --no-build-isolation -v .

Available Demos

The python/demo directory contains several examples illustrating the usage of CutFEMx:

• Poisson Equation (demo_cut_poisson.py): Solving the Poisson equation on a circular domain using Nitsche's method and ghost penalty stabilization.
• Stokes Flow (demo_stokes.py): Simulating Stokes flow around a cylinder using P1-P1 elements. Features include:
  • Global Continuous Interior Penalty (CIP) stabilization for pressure.
  • Ghost penalty stabilization for velocity.
  • VTX output for parallel visualization.
• Moving Domain (demo_moving_poisson.py): solving a time-dependent problem with a moving interface, demonstrating how to update quadrature rules and integration domains dynamically at each time step.
• Distance from STL (demo_stl_distance.py): Computing a signed distance field from an arbitrary STL surface using a parallel Fast Marching Method. Automatically refining a background mesh around an STL surface to improve geometric resolution.
• Level Set Reinitialization (demo_reinit.py): Converting a distorted level set function (e.g., parabolic) into a clean signed distance field using parallel FMM.

Geometry and Level Sets

CutFEMx provides robust tools for handling complex geometries via level set functions. The library can generate distance fields from standard STL files and adaptively refine the mesh around them.

Example: Signed distance field computed from a dino STL surface on an adaptively refined mesh using `demo_stl_distance.py`.