cashocs 2.1.3

Computational Adjoint-Based Shape Optimization and Optimal Control Software

cashocs is a finite element software for the automated solution of shape optimization and optimal control problems. It is used to solve problems in fluid dynamics and multiphysics contexts. Its name is an acronym for computational adjoint-based shape optimization and optimal control software and the software is written in Python.

• Introduction

• Installation

  • Via conda-forge

  • Manual Installation

• Usage

• Citing

• License

• Contact / About

Introduction

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.

For some applications and further information about cashocs, we also refer to the website Fluid Dynamical Shape Optimization with cashocs.

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

• Topology Optimization

  • Sokolowski and Novotny - Topological Derivatives in Shape Optimization

  • Amstutz - An Introduction to the Topological Derivative

• 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.

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.

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 now (starting with release 1.3.2) automatically installed with anaconda.

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 4.4.

• 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 as follows

  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.

Usage

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

Citing

If you use cashocs for your research, please cite the following papers

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

as well as

Version 2.0 - cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software
Sebastian Blauth
SoftwareX, Volume 24, 2023
https://doi.org/10.1016/j.softx.2023.101577

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 the space mapping methods for shape optimization, please cite the paper

Space Mapping for PDE Constrained Shape Optimization
Sebastian Blauth
SIAM Journal on Optimization, Volume 33, Issue 3, 2023
https://doi.org/10.1137/22M1515665

and if you are using the topology optimization methods implemented in cashocs, please cite the paper

Quasi-Newton Methods for Topology Optimization Using a Level-Set Method
Sebastian Blauth and Kevin Sturm
Structural and Multidisciplinary Optimization, Volume 66, 2023
https://doi.org/10.1007/s00158-023-03653-2

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},
}

@Article{Blauth2023Version,
  author   = {Sebastian Blauth},
  journal  = {SoftwareX},
  title    = {{Version 2.0 - cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software}},
  year     = {2023},
  issn     = {2352-7110},
  pages    = {101577},
  volume   = {24},
  doi      = {https://doi.org/10.1016/j.softx.2023.101577},
  keywords = {PDE constrained optimization, Shape optimization, Topology optimization, Space mapping},
}

@Article{Blauth2021Nonlinear,
  author   = {Sebastian Blauth},
  journal  = {SIAM J. Optim.},
  title    = {{Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov-Poincaré-Type Metrics}},
  year     = {2021},
  number   = {3},
  pages    = {1658--1689},
  volume   = {31},
  doi      = {10.1137/20M1367738},
  fjournal = {SIAM Journal on Optimization},
}

@Article{Blauth2023Space,
  author   = {Blauth, Sebastian},
  journal  = {SIAM J. Optim.},
  title    = {{Space Mapping for PDE Constrained Shape Optimization}},
  year     = {2023},
  issn     = {1052-6234,1095-7189},
  number   = {3},
  pages    = {1707--1733},
  volume   = {33},
  doi      = {10.1137/22M1515665},
  fjournal = {SIAM Journal on Optimization},
  mrclass  = {49Q10 (35Q93 49M41 65K05)},
  mrnumber = {4622415},
}

@Article{Blauth2023Quasi,
  author   = {Blauth, Sebastian and Sturm, Kevin},
  journal  = {Struct. Multidiscip. Optim.},
  title    = {{Quasi-Newton methods for topology optimization using a level-set method}},
  year     = {2023},
  issn     = {1615-147X,1615-1488},
  number   = {9},
  pages    = {203},
  volume   = {66},
  doi      = {10.1007/s00158-023-03653-2},
  fjournal = {Structural and Multidisciplinary Optimization},
  mrclass  = {99-06},
  mrnumber = {4635978},
}

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 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 [e-mail]. For more information, visit my website at https://sblauth.github.io/.