0b7a307cf1
* inverse problem implementation * add tutorial7 for inverse Poisson problem * fix doc in equation, equation_interface, system_equation --------- Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
61 lines
2.3 KiB
Python
61 lines
2.3 KiB
Python
"""Module for the TimeDependentProblem class"""
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from abc import abstractmethod
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from .abstract_problem import AbstractProblem
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class TimeDependentProblem(AbstractProblem):
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"""
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The class for the definition of time-dependent problems, i.e., for problems
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depending on time.
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Here's an example of a 1D wave problem.
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:Example:
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>>> from pina.problem import SpatialProblem, TimeDependentProblem
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>>> from pina.operators import grad, laplacian
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>>> from pina.equation import Equation, FixedValue
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>>> from pina import Condition
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>>> from pina.geometry import CartesianDomain
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>>> import torch
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>>>
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>>>
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>>> class Wave(TimeDependentSpatialProblem):
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>>>
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>>> output_variables = ['u']
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>>> spatial_domain = CartesianDomain({'x': [0, 3]})
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>>> temporal_domain = CartesianDomain({'t': [0, 1]})
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>>>
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>>> def wave_equation(input_, output_):
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>>> u_t = grad(output_, input_, components=['u'], d=['t'])
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>>> u_tt = grad(u_t, input_, components=['dudt'], d=['t'])
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>>> delta_u = laplacian(output_, input_, components=['u'], d=['x'])
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>>> return delta_u - u_tt
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>>>
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>>> def initial_condition(input_, output_):
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>>> u_expected = (-3*torch.sin(2*torch.pi*input_.extract(['x']))
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>>> + 5*torch.sin(8/3*torch.pi*input_.extract(['x'])))
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>>> u = output_.extract(['u'])
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>>> return u - u_expected
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>>>
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>>> conditions = {
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>>> 't0': Condition(CartesianDomain({'x': [0, 3], 't':0}), Equation(initial_condition)),
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>>> 'gamma1': Condition(CartesianDomain({'x':0, 't':[0, 1]}), FixedValue(0.)),
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>>> 'gamma2': Condition(CartesianDomain({'x':3, 't':[0, 1]}), FixedValue(0.)),
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>>> 'D': Condition(CartesianDomain({'x': [0, 3], 't':[0, 1]}), Equation(wave_equation))}
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"""
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@abstractmethod
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def temporal_domain(self):
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"""
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The temporal domain of the problem.
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"""
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pass
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@property
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def temporal_variable(self):
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"""
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The time variable of the problem.
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"""
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return self.temporal_domain.variables
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