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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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26
examples/problems/poisson.py
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@@ -5,35 +5,49 @@ from pina.problem import SpatialProblem
from pina.operators import nabla
from pina import Condition, Span
# ===================================================== #
# #
# This script implements the two dimensional #
# Poisson problem. The Poisson class is defined #
# inheriting from SpatialProblem. We denote: #
# u --> field variable #
# x,y --> spatial variables #
# #
# ===================================================== #
class Poisson(SpatialProblem):
# assign output/ spatial variables
output_variables = ['u']
spatial_domain = Span({'x': [0, 1], 'y': [0, 1]})
# define the laplace equation
def laplace_equation(input_, output_):
force_term = (torch.sin(input_.extract(['x'])*torch.pi) *
torch.sin(input_.extract(['y'])*torch.pi))
nabla_u = nabla(output_.extract(['u']), input_)
return nabla_u - force_term
# define nill dirichlet boundary conditions
def nil_dirichlet(input_, output_):
value = 0.0
return output_.extract(['u']) - value
# problem condition statement
conditions = {
'gamma1': Condition(Span({'x': [0, 1], 'y': 1}), nil_dirichlet),
'gamma2': Condition(Span({'x': [0, 1], 'y': 0}), nil_dirichlet),
'gamma3': Condition(Span({'x': 1, 'y': [0, 1]}), nil_dirichlet),
'gamma4': Condition(Span({'x': 0, 'y': [0, 1]}), nil_dirichlet),
'D': Condition(Span({'x': [0, 1], 'y': [0, 1]}), laplace_equation),
'gamma1': Condition(location=Span({'x': [0, 1], 'y': 1}), function=nil_dirichlet),
'gamma2': Condition(location=Span({'x': [0, 1], 'y': 0}), function=nil_dirichlet),
'gamma3': Condition(location=Span({'x': 1, 'y': [0, 1]}),function=nil_dirichlet),
'gamma4': Condition(location=Span({'x': 0, 'y': [0, 1]}), function=nil_dirichlet),
'D': Condition(location=Span({'x': [0, 1], 'y': [0, 1]}), function=laplace_equation),
}
# real poisson solution
def poisson_sol(self, pts):
return -(
torch.sin(pts.extract(['x'])*torch.pi)*
torch.sin(pts.extract(['y'])*torch.pi)
)/(2*torch.pi**2)
#return -(np.sin(x*np.pi)*np.sin(y*np.pi))/(2*np.pi**2)
truth_solution = poisson_sol