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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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examples/problems/wave.py Normal file
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""" Wave equation Problem """
import torch
from pina.geometry import CartesianDomain
from pina import Condition
from pina.problem import SpatialProblem, TimeDependentProblem
from pina.operators import laplacian, grad
from pina.equation import FixedValue, Equation
# ===================================================== #
# #
# This script implements the two dimensional #
# Wave equation. The Wave class is defined inheriting #
# from SpatialProblem and TimeDependentProblem. Let #
# u --> field variable #
# x,y --> spatial variables #
# t --> temporal variables #
# the velocity coefficient is set to one. #
# #
# ===================================================== #
class Wave(TimeDependentProblem, SpatialProblem):
output_variables = ['u']
spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})
temporal_domain = CartesianDomain({'t': [0, 1]})
def wave_equation(input_, output_):
u_t = grad(output_, input_, components=['u'], d=['t'])
u_tt = grad(u_t, input_, components=['dudt'], d=['t'])
nabla_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])
return nabla_u - u_tt
def initial_condition(input_, output_):
u_expected = (torch.sin(torch.pi*input_.extract(['x'])) *
torch.sin(torch.pi*input_.extract(['y'])))
return output_.extract(['u']) - u_expected
conditions = {
'gamma1': Condition(location=CartesianDomain({'x': [0, 1], 'y': 1, 't': [0, 1]}), equation=FixedValue(0.)),
'gamma2': Condition(location=CartesianDomain({'x': [0, 1], 'y': 0, 't': [0, 1]}), equation=FixedValue(0.)),
'gamma3': Condition(location=CartesianDomain({'x': 1, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),
'gamma4': Condition(location=CartesianDomain({'x': 0, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),
't0': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': 0}), equation=Equation(initial_condition)),
'D': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': [0, 1]}), equation=Equation(wave_equation)),
}
def wave_sol(self, pts):
sqrt_2 = torch.sqrt(torch.tensor(2.))
return (torch.sin(torch.pi*pts.extract(['x'])) *
torch.sin(torch.pi*pts.extract(['y'])) *
torch.cos(sqrt_2*torch.pi*pts.extract(['t'])))
truth_solution = wave_sol