OptimiSM is a library for posing and solving problems in solid mechanics using the finite element method. The central theme of this project is exploring how to get better performance and robustness by taking advantages of the tools of variational calculus. OptimiSM uses Lagrangian field theory to pose hard nonlinear solid mechanics problems as optimization problems, and then uses powerful optimization methods to solve them efficiently and reliably.

To do this, OptimiSM relies on Google's JAX library for automatic differentiation and just-in-time compiling for performance.

These days, there are lots of finite element software libraries out there. Why would you want to use OptimiSM?

• OptimiSM is for rapid development: OptimiSM is written in Python and uses the NumPy/SciPy stack. This means that it's easy to read, understand, and extend. If you're like us, and you prefer working in Python/NumPy to C++, you'll find OptimiSM a more pleasant place to work (and play) than heavily abstracted finite element libraries, even the well-designed ones.
  OptimiSM makes use of Jax's just-in-time compilation to get good performance, so the simplicity of Python coding doesn't condemn you to toy problems.
• OptimiSM provides robust solvers: OptimiSM takes a different approach than most finite element libraries. All problems are formulated by encoding them in a scalar-valued functional and then minimizing that functional. This includes nonlinear phenomena like finite deformations and contact, and even irreversible (dissipative) phenomena like plasticity and viscoelasticity. A big motivation for creating this library was proving to others (and ourselves) that real-world, complex problems could be written in this way, and that it could pay off for solving hard problems. By imposing a minimization structure, the OptimiSM solvers can avoid stagnating in hard problems and also avoid converging to spurious unstable configurations. In other words, OptimiSM helps you find the solutions that should be out there and prevents you from finding "solutions" that really aren't solutions. Check out the examples to see some cases that are difficult or impossible to solve correctly even with commerical codes.
• OptimiSM gives sensitivities for design optimization, inverse analysis, and training of machine learning models.

At the moment, OptimiSM is meant to be used as a development package. First, fork and clone the code repository from GitHub. Next, you have a choice: you can pick a basic installation which requires only a minimal set of dependencies, or the recommended installation, which requires some additional packages. The main difference of the recommended installation is that it requires the scikit-sparse package, which provides a sparse Cholesky preconditioner. This is needed if you want to run large-scale problems; without it, you'll only be able to use a dense matrix preconditioner (which is both slower and uses up much more memory).

• Basic installation: If you just want to try some examples out and test-drive OptimiSM, install the basic installation by navigating into the base project directory and executing

pip install -e .

• Recommended installation: The scikit-sparse package requires the SuiteSparse library to be present. If you have access to a package manager on your system, this is the easiest way to get it. On a Mac platform, this would be done with MacPorts by running

sudo port install SuiteSparse

or with Homebrew by

brew install suite-sparse

On a Fedora system, you would run

sudo dnf install suitesparse-devel

Of course, you could compile the source yourself if you wish. Check to make sure the version you download is supported by the scikit-sparse package. The source is available from the SuiteSparse website (a GitHub link is also provided there).

Once the SuiteSparse library is in place, navigate into the optimism directory and execute

pip install -e ".[sparse]"

Note that you can always start with the basic installation, and if you want to switch to the recommended version later, you can just get SuiteSpase and run the above recommended installation command to get the additional functionality. You don't need to remove the basic package first.

From the optimism directory:

brew install suite-sparse
brew install python-tk 

INC=/usr/local/Cellar/suite-sparse/5.11.0/include
LIB=/usr/local/Cellar/suite-sparse/5.11.0/lib
pip=/usr/local/opt/python/bin/pip3
SUITESPARSE_INCLUDE_DIR=$INC SUITESPARSE_LIBRARY_DIR=$LIB $pip install -e . sparse

Utilizing spack can alleviate some of the steps and headaches encountered in build described above to use spack to build optimism in a development environment, use the following instructions.

If you don't already have spack, you can clone the git repo using the following command

git clone https://github.com/spack/spack.git

Once you have spack you can do the following in the optimism directory

source /path/to/spack/share/spack/setup-env.sh
spack env activate .
spack concretize -f
spack install

The above will install all dependencies needed for optimism (including suite sparse and testing dependencies).

Finally, you can install optimism via pip with

pip install -e .[sparse,test]

Note that in each new terminal you will need to source the setup-env.sh script from spack and activate the env in the optimism folder.

If you use OptimiSM in your research, please cite

@software{OptimiSM,
  author = {Michael R. Tupek and Brandon Talamini},
  title = {{OptimiSM}},
  url = {https://github.com/sandialabs/optimism},
  version = {0.0.1},
  year = {2021},
}

TODO: add citation for contact paper

For details about the OptimiSM API, see the documentation.

OptimiSM was created and is maintained by Michael Tupek [email protected] and Brandon Talamini [email protected].

SCR#: 2709.0