# Source code for gemseo_umdo.use_cases.heat_equation.configuration

```
# 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.
r"""A configuration for the heat equation model.
[HeatEquationConfiguration][gemseo_umdo.use_cases.heat_equation.configuration.HeatEquationConfiguration]
is used by
[HeatEquationModel][gemseo_umdo.use_cases.heat_equation.model.HeatEquationModel];
read its docstring for more details.
"""
from __future__ import annotations
from dataclasses import dataclass
from dataclasses import field
from numpy import array
from numpy import exp
from numpy import linspace
from numpy import pi
from numpy.typing import NDArray
[docs]@dataclass
class HeatEquationConfiguration:
"""A configuration for the heat equation model."""
mesh_size: int = 100
"""The number of equispaced spatial nodes."""
n_modes: int = 21
"""The number of modes of the truncated Fourier expansion."""
final_time: float = 0.5
"""The time of interest, denoted $t_f$."""
nu_bounds: tuple[float, float] = (0.001, 0.009)
"""The bounds of the thermal diffusivity."""
rod_length: float = 1.0
"""The length of the rod."""
expectation: float = field(init=False)
"""The theoretical expectation of the integral of the temperature along the rod."""
cost: int = field(init=False)
"""The evaluation cost of the
[HeatEquationModel][gemseo_umdo.use_cases.heat_equation.model.HeatEquationModel]."""
mesh: NDArray[float] = field(init=False)
"""The mesh for the
[HeatEquationModel][gemseo_umdo.use_cases.heat_equation.model.HeatEquationModel]."""
def __post_init__(self) -> None:
self.expectation = self.__compute_expectation()
self.cost = self.mesh_size * self.n_modes
self.mesh = linspace(0.0, self.rod_length, num=self.mesh_size)
def __compute_expectation(self) -> float:
"""Compute the expectation of the integral of the temperature along the rod.
From Geraci et al., 2015 (Equation 5.3).
Returns:
The expectation of the integral of the temperature along the rod.
"""
c = array([100 / pi, 98 / 12 / pi, 50 * 98 / 36 / pi, 50 * 98 / 84 / pi])
pi2 = pi**2
n2 = array([1, 3, 9, 21]) ** 2
nu_delta = self.nu_bounds[1] - self.nu_bounds[0]
h = (
exp(-n2 * pi2 * self.nu_bounds[1] * self.final_time)
* (1 - exp(n2 * pi2 * nu_delta * self.final_time))
/ (self.final_time * n2 * pi2 * nu_delta)
)
return -(c * h).sum()
```