TOFEA

Project Overview

TOFEA is a lightweight 2D finite element library for topology optimization. It can solve heat conduction and small deformation elasticity problems and integrates with autograd for automatic differentiation.

Installation

Prerequisites

• Python 3.10+

Steps

1. Clone this repository.
2. Create a virtual environment and activate it:

   python3 -m venv .venv
   source .venv/bin/activate

3. Install the required packages:

   pip install -r requirements.txt

Getting Started

The following example is a minimal heat conduction optimization based on examples/heat_2d.py.

import autograd.numpy as np
import matplotlib.pyplot as plt
import nlopt
from autograd import value_and_grad
from tofea.boundary_conditions import BoundaryConditions
from tofea.fea2d import FEA2D_T

shape = (4, 4)
bc = BoundaryConditions(shape)
bc.fix_edge("top")
bc.apply_uniform_load_on_edge("bottom", 1.0)

fem = FEA2D_T(bc.fixed)
x0 = np.full(shape, 0.5)

@value_and_grad
def objective(x):
    t = fem.temperature(x, bc.load)
    return np.mean(t)

def nlopt_obj(x, grad):
    val, g = objective(x.reshape(shape))
    if grad.size > 0:
        grad[:] = g.ravel()
    return val

opt = nlopt.opt(nlopt.LD_MMA, x0.size)
opt.set_lower_bounds(0)
opt.set_upper_bounds(1)
opt.set_min_objective(nlopt_obj)
opt.set_maxeval(5)
x_final = opt.optimize(x0.ravel()).reshape(shape)

plt.imshow(x_final.T, cmap="gray_r")
plt.show()

This script defines the problem, runs nlopt for a few iterations and displays the optimized density field.

Documentation

The full API reference is built with MkDocs and mkdocstrings. Install the documentation extras and run mkdocs serve to preview the site locally:

pip install -e .[docs]
mkdocs serve