🧠 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 Fieatures

Example 1 : Single Load Condition

Example 2 : Multiple Load Condition

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
• Topology optimization using the density method and its optimization algorithm
  • Optimality Criteria (OC) Method
  • (Log-Space) Modified OC Method
  • Lagrangian Method
• able to handle multiple objectives / constraints
• High-performance computation using sparse matrices with Scipy and PyAMG
• has a function to monitor the transition of parameters.

📖 Citation

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

@misc{scikit-topt2025,
  author       = {Watanabe, Kohei},
  title        = {Scikit-Topt: A Python Library for Algorithm Development in Topology Optimization},
  year         = {2025},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.15441499},
  url          = {https://doi.org/10.5281/zenodo.15441499},
  note         = {Version 0.2.0}
}

Usage

Install Package

pip install scikit-topt
poetry add scikit-topt

How to define a task

Load Mesh file from file.

import skfem
import sktopt

mesh_path = "./data/model.msh"
basis = sktopt.mesh.loader.basis_from_file(
  mesh_path, intorder=3
)

Create Mesh.

x_len, y_len, z_len = 1.0, 1.0, 1.0
element_size = 0.1

# import pathlib
# msh_path = "model.msh"
# mesh = skfem.MeshHex.load(pathlib.Path(msh_path))

# define basis
mesh = sktopt.mesh.toy_problem.create_box_hex(
  x_len, y_len, z_len, element_size
)
e = skfem.ElementVector(skfem.ElementHex1())
basis = skfem.Basis(mesh, e, intorder=3)

Set BCs and Force, and define task

# Specify Dirichlet Boundary Conditions
dirichlet_nodes = sktopt.mesh.utils.get_nodes_indices_in_range(
    basis, (0.0, 0.03), (0.0, y_len), (0.0, z_len)
)
dirichlet_dir = "all"

# Define Force Vector
F_nodes = sktopt.mesh.utils.get_nodes_indices_in_range(
    basis,
    (x_len, x_len),
    (y_len*2/5, y_len*3/5),
    (z_len*2/5, z_len*3/5)
)
F_dir = "u^1"
F = 100

# Specify Design Field
design_elements = sktopt.mesh.utils.get_elements_in_box(
    mesh,
    (0.0, x_len), (0.0, y_len), (0.0, z_len)
)

# Define it as a task
tsk = sktopt.mesh.task.TaskConfig.from_nodes(
    210e9,
    0.30,
    basis,
    dirichlet_nodes,
    dirichlet_dir,
    F_nodes,
    F_dir,
    F,
    design_elements
)

Optimize Toy Problem with Python Script

import sktopt

tsk = sktopt.mesh.toy_problem.toy1()
cfg = sktopt.core.LogMOC_Config()

optimizer = sktopt.core.LogMOC_Optimizer(cfg, tsk)

optimizer.parameterize()
optimizer.optimize()

Optimize Toy Problem with command line.

OMP_NUM_THREADS=3 OPENBLAS_NUM_THREADS=3 MKL_NUM_THREADS=3 PYTHONPATH=./scikit-topt python ./sktopt/core/optimizer/logmoc.py \
 --dst_path ./result/base_moc_down \
 --interpolation SIMP \
 --vol_frac 0.40 \
 --eta 0.8 \
 --record_times 100 \
 --max_iters 600 \
 --mu_p 2000 \
 --task_name down_box \
 --solver_option spsolve \
 --rho_min 1e-2 \
 --E0 210e9 \
 --E_min 210e5 \
 --design_dirichlet true

Optiization Algorithm

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

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

ToDo

• Set break point from the optimization loop
• Add other optimizers
  • Evolutionary Algorithms
  • Level Set
  • Phase Field
  • MMA
• Add Multiple BC Conditions
• Add Constraint for Rotation