cmaurini / dolfinx_mpc

Extension for dolfinx to handle multi-point constraints.

Multi-point constraints with FEniCS-X

Author: Jørgen S. Dokken

This library contains an add-on to FEniCS_X enabling the possibilities of enforce multi-point constraints, such as $u_i =\sum_{j=0,i{\not=}j}^n \alpha_j u_j, i\in I_N$

This can be used to for instance enforce slip conditions strongly.

Consider a linear system of the form $Au=b$, with the additional constraints written on the form $K\hat u=u$, where $K$ is a prolongation matrix, $\hat u$ is the vector of unknowns excluding the $I_N$ entries.

We then solve the system $K^T A K \hat u = K^T b$, where $K^T A K$ is symmetric if $A$ was symmetric.

If we include boundary conditions on the form $u=g$, we assemble the system $K^TAK\hat u = K^T(b-A\hat g)$ where $A\hat g$ is an extension of the boundary condition $g$ to all degrees of freedom.

The library performs custom matrix and vector assembly adding the extra constraints to the set of linear equations. All assemblies are local to the process, and no MPI communication except when setting up the multi point constraints.

These assemblers are written in C++, but have equivalent Python assemblers in the optional dolfinx_mpc.numba module.

Installation

Version 0.3.0 is available as an docker image at DockerHub and can be ran using

docker run -ti -v $(pwd):/root/shared -w /root/shared dokken92/dolfinx_mpc:0.3.0

To install the latest version (master 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

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
pip3 install python/. --upgrade