🧠 Scikit Topt

A lightweight, flexible Python library for topology optimization built on top of Scikit Libraries

• scipy
• scikit-fem

Documentation

Scikit-Topt Documentation

Examples and Features

Example 1 : Single Load Condition

Example 2 : Multiple Load Condition

Example 3 : Heat Conduction

Progress Report

Features

To contribute to the open-source community and education—which I’ve always benefited from—I decided to start this project.

The currently supported features are as follows:

• Coding with Python
• easy installation with pip/poetry
• Implement FEA on unstructured mesh using scikit-fem
• Structural Analysis / Heat Conduction Analysis
• Topology optimization using the density method and its optimization algorithm
  • Optimality Criteria (OC) Method
  • (Log-Space) Modified OC Method
• able to handle multiple force condition
• High-performance computation using sparse matrices with Scipy and PyAMG
• has a function to monitor the transition of parameters.

SetUp

You can install Scikit-Topt either via pip or Poetry.

Supported Python Versions

Scikit-Topt supports Python 3.10–3.13:

• 3.10–3.12 — fully supported and tested
• 3.13 — core topology optimization works normally,
  but VTK-based features (VTU export & image rendering using PyVista)
  are temporarily unavailable because VTK/PyVista do not yet provide wheels
  for Python 3.13.

You can still run the full optimization workflow on Python 3.13;
only visualization-related features are restricted.

Choose one of the following methods:

Using pip

pip install scikit-topt

With PETSc support:

pip install "scikit-topt[petsc4py]"

The legacy alias below is also available:

pip install "scikit-topt[petsc]"

Using poetry

poetry add scikit-topt

With PETSc support:

poetry add scikit-topt -E petsc4py

petsc4py requires a working PETSc installation. If PETSc is not already available on your system, install PETSc first and then install the extra above.

PETSc Runtime Setup

The petsc4py extra installs the Python bindings only. At runtime, PETSc shared libraries must also be discoverable by your Python environment.

Common environment variables are:

• PETSC_DIR: PETSc installation root
• PETSC_ARCH: PETSc build architecture name
• LD_LIBRARY_PATH: shared-library search path on Linux

Typical Linux example:

export PETSC_DIR=/path/to/petsc
export PETSC_ARCH=arch-linux-c-opt
export LD_LIBRARY_PATH="$PETSC_DIR/$PETSC_ARCH/lib:$LD_LIBRARY_PATH"

If PETSc was installed by a package manager or a preconfigured HPC module, these variables may already be set for you. In that case, no extra manual setup is needed.

You can validate the runtime with:

python -c "from petsc4py import PETSc; print(PETSc.Sys.getVersion())"

If Scikit-Topt cannot load PETSc, first check that:

• petsc4py imports successfully
• the PETSc shared libraries are visible in your library search path
• PETSC_DIR and PETSC_ARCH point to the same PETSc build used for petsc4py

Optional: Enable off-screen rendering

If you want to visualize the optimized density distribution with mesh as an image, you need to enable off-screen rendering using a virtual display.

On Debian/Ubuntu:

sudo apt install xvfb libgl1-mesa-glx

CentOS / RHL

sudo yum install xvfb libgl1-mesa-glx

Usage

See examples in example directory and README.md. README for Usage Examples

Algorithm for Optimization

Optimization Algorithms and Techniques are briefly summarized here.
Optimization Algorithms and Techniques

Contributing

We are happy to welcome any contributions to the library. You can contribute in various ways:

• Reporting bugs, opening pull requests, or starting discussions via GitHub Issues
• Writing new examples
• Improving the tests
• Enhancing the documentation or code readability doc

By contributing code to Scikit-Topt, you agree to release it under the Apache 2.0 License.

Acknowledgements

Standing on the shoulders of proverbial giants

This software does not exist in a vacuum. Scikit-Topt is standing on the shoulders of proverbial giants. In particular, I want to thank the following projects for constituting the technical backbone of the project:

• Scipy
• Scikit-fem
• PyAMG
• Numba
• MeshIO
• Matplotlib
• PyVista
• Topology Optimization Community

📖 Citation

If you use Scikit Topt in your research or software, please cite it as:

@article{Watanabe_Scikit-Topt_A_Python_2025,
author = {Watanabe, Kohei},
doi = {10.21105/joss.09092},
journal = {Journal of Open Source Software},
number = {116},
title = {{Scikit-Topt: A Python Library for Algorithm Development in Topology Optimization}},
volume = {10},
year = {2025}
}

ToDo

• Set break point from the optimization loop
• Add A feature to assign tags to nodes and cells
• Add Level Set
• Add other optimizers
  • Evolutionary Algorithms
  • MMA
• Add Multiple BC Conditions
• Add Unit Test