46 lines
1.4 KiB
Python
46 lines
1.4 KiB
Python
from pina.problem import SpatialProblem
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from pina import Condition, Span
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from pina.operators import grad
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import torch
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# ===================================================== #
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# #
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# This script implements a simple first order ode. #
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# The FirstOrderODE class is defined inheriting from #
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# SpatialProblem. We denote: #
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# y --> field variable #
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# x --> spatial variable #
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# #
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# ===================================================== #
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class FirstOrderODE(SpatialProblem):
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# variable domain range
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x_rng = [0, 5]
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# field variable
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output_variables = ['y']
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# create domain
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spatial_domain = Span({'x': x_rng})
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# define the ode
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def ode(input_, output_):
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y = output_
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x = input_
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return grad(y, x) + y - x
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# define initial conditions
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def fixed(input_, output_):
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exp_value = 1.
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return output_ - exp_value
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# define real solution
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def solution(self, input_):
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x = input_
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return x - 1.0 + 2*torch.exp(-x)
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# define problem conditions
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conditions = {
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'bc': Condition(location=Span({'x': x_rng[0]}), function=fixed),
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'dd': Condition(location=Span({'x': x_rng}), function=ode),
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}
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truth_solution = solution |