Source code for pina.problem.timedep_problem
"""Module for the TimeDependentProblem class"""
from abc import abstractmethod
from .abstract_problem import AbstractProblem
[docs]
class TimeDependentProblem(AbstractProblem):
"""
The class for the definition of time-dependent problems, i.e., for problems
depending on time.
Here's an example of a 1D wave problem.
:Example:
>>> from pina.problem import SpatialProblem, TimeDependentProblem
>>> from pina.operators import grad, laplacian
>>> from pina.equation import Equation, FixedValue
>>> from pina import Condition
>>> from pina.geometry import CartesianDomain
>>> import torch
>>>
>>>
>>> class Wave(TimeDependentSpatialProblem):
>>>
>>> output_variables = ['u']
>>> spatial_domain = CartesianDomain({'x': [0, 3]})
>>> 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'])
>>> delta_u = laplacian(output_, input_, components=['u'], d=['x'])
>>> return delta_u - u_tt
>>>
>>> def initial_condition(input_, output_):
>>> u_expected = (-3*torch.sin(2*torch.pi*input_.extract(['x']))
>>> + 5*torch.sin(8/3*torch.pi*input_.extract(['x'])))
>>> u = output_.extract(['u'])
>>> return u - u_expected
>>>
>>> conditions = {
>>> 't0': Condition(CartesianDomain({'x': [0, 3], 't':0}), Equation(initial_condition)),
>>> 'gamma1': Condition(CartesianDomain({'x':0, 't':[0, 1]}), FixedValue(0.)),
>>> 'gamma2': Condition(CartesianDomain({'x':3, 't':[0, 1]}), FixedValue(0.)),
>>> 'D': Condition(CartesianDomain({'x': [0, 3], 't':[0, 1]}), Equation(wave_equation))}
"""
[docs]
@abstractmethod
def temporal_domain(self):
"""
The temporal domain of the problem.
"""
pass
@property
def temporal_variable(self):
"""
The time variable of the problem.
"""
return self.temporal_domain.variables