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Examples update for v0.1 (#206)

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* modify examples/problems
* modify tutorials

---------

Co-authored-by: Dario Coscia <dariocoscia@dhcp-235.eduroam.sissa.it>
Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
This commit is contained in:
Dario Coscia
2023-11-14 18:24:07 +01:00
committed by Nicola Demo
parent 0d38de5afe
commit ee39b39805
19 changed files with 605 additions and 613 deletions
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54
examples/problems/poisson.py
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@@ -1,10 +1,5 @@
""" Poisson equation example. """
import numpy as np
import torch
""" Poisson problem. """
from pina.problem import SpatialProblem
from pina.operators import laplacian
from pina import Condition, Span
# ===================================================== #
# #
@@ -17,39 +12,46 @@ from pina import Condition, Span
# ===================================================== #
import torch
from pina.geometry import CartesianDomain
from pina import Condition
from pina.problem import SpatialProblem
from pina.operators import laplacian
from pina.equation import FixedValue, Equation
class Poisson(SpatialProblem):
# assign output/ spatial variables
output_variables = ['u']
spatial_domain = Span({'x': [0, 1], 'y': [0, 1]})
spatial_domain = CartesianDomain({'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))
delta_u = laplacian(output_.extract(['u']), input_)
return delta_u - force_term
torch.sin(input_.extract(['y'])*torch.pi))
nabla_u = laplacian(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(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),
'gamma1': Condition(
location=CartesianDomain({'x': [0, 1], 'y': 1}),
equation=FixedValue(0.0)),
'gamma2': Condition(
location=CartesianDomain({'x': [0, 1], 'y': 0}),
equation=FixedValue(0.0)),
'gamma3': Condition(
location=CartesianDomain({'x': 1, 'y': [0, 1]}),
equation=FixedValue(0.0)),
'gamma4': Condition(
location=CartesianDomain({'x': 0, 'y': [0, 1]}),
equation=FixedValue(0.0)),
'D': Condition(
location=CartesianDomain({'x': [0, 1], 'y': [0, 1]}),
equation=Equation(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