ee39b39805
* 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>
57 lines
2.6 KiB
Python
57 lines
2.6 KiB
Python
""" 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 |