TimeDependentProblem

Module for the TimeDependentProblem class

class TimeDependentProblem

Bases: 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))}

abstract temporal_domain()

The temporal domain of the problem.

property temporal_variable

The time variable of the problem.