Introduction

Pytop is a powerful tool designed to extend the capabilities of FEniCS for topology optimization. It provides robust tools for advanced computational design and supports multiphysics simulations. Pytop is fully compatible with MPI, allowing for efficient monitoring of parallel applications.

General Optimization Form

This software scopes following general optimization form:

$$\min_{\bm d} F(\bm d, \bm u) = \int_\Omega f(\bm d, \bm u) \ dV$$ $$G_j(\bm d, \bm u) \leq 0$$

where $\Omega$ is the design domain and $\bm u$ represents specific fields that satisfy governing equations for any physics defined in $\Omega$. For example, $\bm u$ is the displacement vector in an elastic deformation problem. $F$ is the functional that represents the objective of the optimization. $\bm d$ is the design vector, and $G_j$ are the functionals representing the constraints.

NLOpt opt class

This software is designed to construct the nlopt.opt class in NLOpt Python interface. You define design variables as DesignVariables class and optimization problem with PloblemStatement class. Then, extended nlopt.opt class will be defined using NloptOptimizer class with DesignVariables and PloblemStatement. Some local gradient-based optimizers in Nlopt are available, including GCMMA, SLSQP, and CCSA. Please refer detail of each algorithms in NLopt algorithms.

Visualization

Currently, this software does not include unique vilualization methods. However, The XDMF and H5 files can be exported. XDMF file can be visualized the VTK-based visualization software, like paraview.

Container

We provide a container for this repository. The container includes python 3.11, FEniCS bundles, and NLOpt with python interface. The container is avaiable in dockerhub.

Installation

To install Pytop, you need to have Python and FEniCS installed on your system. You can install Pytop via pip:

pip install git+https://github.com/Naruki-Ichihara/pytop.git@main

More detailed installation can be found in this page.

MPI parallelization

This software is designed as parallelization-ready. Problem is automatically divided into partial problems and computed in each cpus. We provide useful detaclass for MPI, MPI_Communicator. You can construct a mpi group use this class,

import pytop as pt
comm_group = pt.MPI_Communicator.comm_world

Single problem must be in the same group. Then, mpirun executes the solving with cpus you mentioned:

mpirun -n 36 python your_problem.py

In the container, you need to give option to allow run as a root user:

mpirun -n 36 --allow-run-as-root python your_problem.py

Above example use 36 cpus.

Working with pygmsh

You can use pygmsh as mesh generator. Documentation of pygmsh is available here.

import pytop as pt
import pygmsh

with pygmsh.geo.Geometry() as geom:
    lcar = 0.1
    p1 = geom.add_point([0.0, 0.0], lcar)
    p2 = geom.add_point([1.0, 0.0], lcar)
    p3 = geom.add_point([1.0, 0.5], lcar)
    p4 = geom.add_point([1.0, 1.0], lcar)
    s1 = geom.add_bspline([p1, p2, p3, p4])

    p2 = geom.add_point([0.0, 1.0], lcar)
    p3 = geom.add_point([0.5, 1.0], lcar)
    s2 = geom.add_spline([p4, p3, p2, p1])

    ll = geom.add_curve_loop([s1, s2])
    pl = geom.add_plane_surface(ll)

    mesh = geom.generate_mesh()

mesh = pt.from_pygmsh(mesh)

Use planation option is used, all z coordinates will be neglected.

mesh = pt.from_pygmsh(mesh, planation=True)