Multi-point constraints with FEniCS-X

Code Coverage Report

Author: Jørgen S. Dokken

This library is an add-on to DOLFINx for imposing multi-point constraints, linear relations between degrees of freedom,

$$ u_s = \sum_j c_{sj}, u_{m_j} + g_s, $$

where each constrained, slave, degree of freedom $u_s$ is given by master degrees of freedom $u_{m_j}$, with known coefficients $c_{sj}$ and an offset $g_s$. A master may carry a Dirichlet condition, and its value is then part of the offset. The constraints are eliminated from the system as it is assembled, so the solution satisfies them exactly.

The library provides:

• Slip conditions, $u\cdot n = 0$ on boundaries not aligned with the axes;
• Periodic conditions, also with a phase, as in Floquet–Bloch conditions;
• Contact conditions between non-matching interfaces, with or without slip;
• Integral conditions, such as a prescribed mean value, boundary average or flow rate;
• Spiders, which tie degrees of freedom to a point, rigidly (RBE2) or as a weighted average (RBE3);
• Constraints between spaces and meshes, with masters in another block of the system, such as a field on a submesh tied to the trace of its parent;
• General constraints, from a map between degrees of freedom, or from slaves, masters and coefficients given directly.

The constraints apply to linear and nonlinear problems, to block systems, assembled as nest or single matrices, for real and complex scalars, in serial and in parallel. The assembly is written in C++, with a Python interface. How the constraints are eliminated is described in the theory section of the documentation.

Documentation

Documentation at https://jorgensd.github.io/dolfinx_mpc

Installation

Spack

DOLFINx MPC is on spack as both a C++ package (dolfinx-mpc) and a Python package (py-dolfinx-mpc). First, clone the spack repository and enable spack

git clone --depth=2 https://github.com/spack/spack.git
# For bash/zsh/sh
. spack/share/spack/setup-env.sh

# For tcsh/csh
source spack/share/spack/setup-env.csh

# For fish
. spack/share/spack/setup-env.fish

Next create an environment:

spack env create mpc_env
spack env activate mpc_env

Find the compilers on the system

spack compiler find

Get the relevant packages repos (FEniCS and Scientific Computing)

spack repo add https://github.com/FEniCS/spack-fenics.git
spack repo add https://github.com/scientificcomputing/spack_repos.git

and install the relevant package

C++

spack add dolfinx-mpc@0.10 ^mpich ^petsc+mumps+hypre
spack concretize
spack install

Python

spack add py-dolfinx-mpc@0.10 ^mpich ^petsc+mumps+hypre ^py-fenics-dolfinx+petsc4py
spack add py-scipy py-pytest py-gmsh
spack concretize
spack install

Finally, note that spack needs some packages already installed on your system. On a clean ubuntu container for example one need to install the following packages before running spack

apt update && apt install gcc unzip git python3-dev g++ gfortran xz-utils libzip2 -y

Conda

The DOLFINx MPC package is now on Conda. The C++ library can be found under libdolfinx_mpc and the Python library under dolfinx_mpc. If you have any issues with these installations, add an issue at dolfinx_mpc feedstock.

Docker

Version 0.10.1 is available as an docker image at Github Packages and can be ran using

docker run -ti -v $(pwd):/root/shared -w /root/shared ghcr.io/jorgensd/dolfinx_mpc:v0.10.1

To change to complex mode run source dolfinx-complex-mode. Similarly, to change back to real mode, call source dolfinx-real-mode.

Source

To install the latest version (main branch), you need to install the latest release of DOLFINx. Easiest way to install DOLFINx is to use docker. The DOLFINx docker images goes under the name dolfinx/dolfinx. Remember to use an appropriate tag to get the correct version of DOLFINx, i.e. (:nightly or :vx.y.z).

To install the dolfinx_mpc-library run the following code from this directory:

cmake -G Ninja -DCMAKE_BUILD_TYPE=Release -B build-dir cpp/
ninja -j3 install -C build-dir
python3 -m pip -v install --config-settings=cmake.build-type="Release" --no-build-isolation ./python -U