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
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.
An overview over cashocs and its capabilities can be found in Blauth, cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software. Moreover, note that the full cashocs documentation is available at https://cashocs.readthedocs.io/en/latest/index.html.
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 now (starting with release 1.3.2) automatically installed with anaconda.
- 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 4.4.
- You might also want to install Gmsh, version 4.8. cashocs does not necessarily need this to work 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
python3 -m pytest tests/
or simply
pytest tests/
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.
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.
If you use cashocs for your research, I would be grateful if you would cite the following paper
cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software Sebastian Blauth SoftwareX, Volume 13, 2021 https://doi.org/10.1016/j.softx.2020.100646
Additionally, if you are using the nonlinear conjugate gradient methods for shape optimization implemented in cashocs, please cite the following paper
Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics Sebastian Blauth SIAM Journal on Optimization, Volume 31, Issue 3, 2021 https://doi.org/10.1137/20M1367738
If you are using BibTeX, you can use the following entries:
@Article{Blauth2021cashocs,
author = {Sebastian Blauth},
journal = {SoftwareX},
title = {{cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software}},
year = {2021},
issn = {2352-7110},
pages = {100646},
volume = {13},
doi = {https://doi.org/10.1016/j.softx.2020.100646},
keywords = {PDE constrained optimization, Adjoint approach, Shape optimization, Optimal control},
}
as well as
@Article{Blauth2021Nonlinear,
author = {Sebastian Blauth},
journal = {SIAM J. Optim.},
title = {{N}onlinear {C}onjugate {G}radient {M}ethods for {PDE} {C}onstrained {S}hape {O}ptimization {B}ased on {S}teklov-{P}oincaré-{T}ype {M}etrics},
year = {2021},
number = {3},
pages = {1658--1689},
volume = {31},
doi = {10.1137/20M1367738},
fjournal = {SIAM Journal on Optimization},
}
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/.
I'm Sebastian Blauth, a scientific employee at Fraunhofer ITWM. I have developed this project as part of my PhD thesis. If you have any questions / suggestions / feedback, etc., you can contact me via sebastian.blauth@itwm.fraunhofer.de or sebastianblauth@web.de.