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update examples

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This commit is contained in:
Dario Coscia
2023-05-29 15:34:23 +02:00
committed by Nicola Demo
parent 37e9658211
commit eb531747e5
11 changed files with 331 additions and 216 deletions
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51
examples/problems/parametric_elliptic_optimal_control_alpha_variable.py
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@@ -5,22 +5,42 @@ from pina import Span, Condition
from pina.problem import SpatialProblem, ParametricProblem
from pina.operators import grad, nabla
# ===================================================== #
# #
# This script implements the two dimensional #
# Parametric Elliptic Optimal Control problem. #
# The ParametricEllipticOptimalControl class is #
# inherited from TimeDependentProblem, SpatialProblem #
# and we denote: #
# u --> field variable #
# p --> field variable #
# y --> field variable #
# x1, x2 --> spatial variables #
# mu, alpha --> problem parameters #
# #
# More info in https://arxiv.org/pdf/2110.13530.pdf #
# Section 4.2 of the article #
# ===================================================== #
class ParametricEllipticOptimalControl(SpatialProblem, ParametricProblem):
# setting spatial variables ranges
xmin, xmax, ymin, ymax = -1, 1, -1, 1
x_range = [xmin, xmax]
y_range = [ymin, ymax]
# setting parameters range
amin, amax = 0.0001, 1
mumin, mumax = 0.5, 3
mu_range = [mumin, mumax]
a_range = [amin, amax]
x_range = [xmin, xmax]
y_range = [ymin, ymax]
# setting field variables
output_variables = ['u', 'p', 'y']
# setting spatial and parameter domain
spatial_domain = Span({'x1': x_range, 'x2': y_range})
parameter_domain = Span({'mu': mu_range, 'alpha': a_range})
# equation terms as in https://arxiv.org/pdf/2110.13530.pdf
def term1(input_, output_):
laplace_p = nabla(output_, input_, components=['p'], d=['x1', 'x2'])
return output_.extract(['y']) - input_.extract(['mu']) - laplace_p
@@ -37,21 +57,22 @@ class ParametricEllipticOptimalControl(SpatialProblem, ParametricProblem):
p_exp = 0.0
return output_.extract(['p']) - p_exp
# setting problem condition formulation
conditions = {
'gamma1': Condition(
Span({'x1': x_range, 'x2': 1, 'mu': mu_range, 'alpha': a_range}),
[state_dirichlet, adj_dirichlet]),
location=Span({'x1': x_range, 'x2': 1, 'mu': mu_range, 'alpha': a_range}),
function=[state_dirichlet, adj_dirichlet]),
'gamma2': Condition(
Span({'x1': x_range, 'x2': -1, 'mu': mu_range, 'alpha': a_range}),
[state_dirichlet, adj_dirichlet]),
location=Span({'x1': x_range, 'x2': -1, 'mu': mu_range, 'alpha': a_range}),
function=[state_dirichlet, adj_dirichlet]),
'gamma3': Condition(
Span({'x1': 1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
[state_dirichlet, adj_dirichlet]),
location=Span({'x1': 1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
function=[state_dirichlet, adj_dirichlet]),
'gamma4': Condition(
Span({'x1': -1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
[state_dirichlet, adj_dirichlet]),
location=Span({'x1': -1, 'x2': y_range, 'mu': mu_range, 'alpha': a_range}),
function=[state_dirichlet, adj_dirichlet]),
'D': Condition(
Span({'x1': x_range, 'x2': y_range,
location=Span({'x1': x_range, 'x2': y_range,
'mu': mu_range, 'alpha': a_range}),
[term1, term2]),
}
function=[term1, term2]),
}