CASHOCS

CASHOCS is a computational adjoint-based shape optimization and optimal control software for python.

CASHOCS is based on the finite element package FEniCS and uses its high-level unified form language UFL to treat general PDE constrained optimization problems, in particular, shape optimization and optimal control problems.

Note, that we assume that you are (at least somewhat) familiar with PDE constrained optimization and FEniCS. For a introduction to these topics, we can recommend the textbooks

• Optimal Control and general PDE constrained optimization

  • Hinze, Ulbrich, Ulbrich, and Pinnau, Optimization with PDE Constraints
  • Tröltzsch, Optimal Control of Partial Differential Equations

• Shape Optimization

  • Delfour and Zolesio, Shapes and Geometries
  • Sokolowski and Zolesio, Introduction to Shape Optimization

• FEniCS

  • Logg, Mardal, and Wells, Automated Solution of Differential Equations by the Finite Element Method
  • The FEniCS demos

However, the CASHOCS tutorial also gives many references either to the underlying theory of PDE constrained optimization or to relevant demos and documentation of FEniCS.

Note, that the full CASHOCS documentation is available at https://cashocs.readthedocs.io/en/latest/index.html.

Installation

Via conda-forge

CASHOCS is available via the anaconda package manager, and you can install it with :

conda install -c conda-forge cashocs

Alternatively, you might want to create a new, clean conda environment with the command :

conda create -n <ENV_NAME> -c conda-forge cashocs

where <ENV_NAME> is the desired name of the new environment.

Note

Gmsh is not automatically installed with anaconda, as this is not intrinsically linked to CASHOCS. Instead, cashocs only provides an interface for importing meshes generated with Gmsh. If you want to use Gmsh with cashocs, please use Gmsh 4.6 or higher. See https://gmsh.info/ for possibilities to install Gmsh.

Manual Installation

• First, install FEniCS, version 2019.1. Note, that FEniCS should be compiled with PETSc and petsc4py.
• Then, install meshio, with a h5py version that matches the HDF5 version used in FEniCS, and matplotlib. The version of meshio should be at least 4, but for compatibility it is recommended to use meshio 4.2.
• You might also want to install Gmsh, version 4.6. CASHOCS does not necessarily need this to function properly, but it is required for the remeshing functionality.

Note

If you are having trouble with using the conversion tool cashocs-convert from the command line, then you most likely encountered a problem with hdf5 and h5py. This can (hopefully) be resolved by following the suggestions from this thread, i.e., you should try to install meshio using the command :

pip3 install meshio[all] --no-binary=h5py

• You can install CASHOCS via the PYPI:

  pip3 install cashocs

  You can install the newest (development) version of CASHOCS with:

  pip3 install git+https://github.com/sblauth/cashocs.git

• To get the latest (development) version of CASHOCS, clone this repository with git and install it with pip :

  git clone https://github.com/sblauth/cashocs.git
  cd cashocs
  pip3 install .

Note

To verify that the installation was successful, run the tests for CASHOCS with :

cd tests
python3 -m pytest

from the source / repository root directory. Note, that it might take some time to perform all of these tests for the very first time, as FEniCS compiles the necessary code. However, on subsequent iterations the compiled code is retrieved from a cache, so that the tests are singificantly faster.

Usage

The complete CASHOCS documentation is available here https://cashocs.readthedocs.io/en/latest/index.html. For a detailed introduction, see the CASHOCS tutorial. The python source code for the demo programs is located inside the "demos" folder.

License

CASHOCS is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

CASHOCS is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with CASHOCS. If not, see https://www.gnu.org/licenses/.

Contact / About

I'm Sebastian Blauth, a PhD student at Fraunhofer ITWM and TU Kaiserslautern, and I developed this project as part of my work. If you have any questions / suggestions / feedback, etc., you can contact me via sebastian.blauth@itwm.fraunhofer.de or sebastianblauth@web.de.