# Source code for gemseo.problems.topo_opt.volume_fraction_disc

```
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# INITIAL AUTHORS - API and implementation and/or documentation
# :author: Simone Coniglio
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""A discipline for topology optimization volume fraction."""
from __future__ import annotations
from typing import Sequence
from numpy import array
from numpy import atleast_2d
from numpy import mean
from numpy import ones
from numpy import ones_like
from numpy import size
from gemseo.core.discipline import MDODiscipline
[docs]class VolumeFraction(MDODiscipline):
"""Compute the volume fraction from the density.
Volume fraction is computed as the average of the density value (rho) on each finite
element.
"""
def __init__(
self,
n_x: int = 100,
n_y: int = 100,
empty_elements: Sequence[int] | None = None,
full_elements: Sequence[int] | None = None,
name: str | None = None,
) -> None:
"""
Args:
n_x: The number of elements in the x-direction.
n_y: The number of elements in the y-direction.
empty_elements: The index of the empty element
ids that are not part of the design space.
full_elements: The index of the full element
ids that are not part of the design space.
name: The name of the discipline.
If None, use the class name.
""" # noqa: D205, D212, D415
super().__init__(name=name)
self.n_x = n_x
self.n_y = n_y
self.input_grammar.update(["rho"])
self.output_grammar.update(["volume fraction"])
self.default_inputs = {"rho": ones(n_x * n_y)}
def _run(self) -> None:
rho = self.get_inputs_by_name("rho")
self.local_data["volume fraction"] = array([mean(rho.ravel())])
self._is_linearized = True
self._init_jacobian(with_zeros=True)
self.jac["volume fraction"] = {"rho": atleast_2d(ones_like(rho).T / size(rho))}
```