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 high-order 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
   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
   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 .

5. Install UFL:

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

6. Install runtime integral extended FFCX:

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

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
   export CMAKE_PREFIX_PATH=$CONDA_PREFIX
   export CMAKE_INSTALL_PREFIX=$CONDA_PREFIX
   
   # Install CutFEMx  (triggers C++ build via scikit-build-core)
   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.