39 lines
1.2 KiB
Python
39 lines
1.2 KiB
Python
import torch
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from pina.problem import TimeDependentProblem, SpatialProblem
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from pina.operators import grad
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from pina import Condition
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from pina.span import Span
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class Burgers1D(TimeDependentProblem, SpatialProblem):
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spatial_variables = ['x']
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temporal_variable = ['t']
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output_variables = ['u']
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domain = Span({'x': [-1, 1], 't': [0, 1]})
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def burger_equation(input_, output_):
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grad_u = grad(output_['u'], input_)
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grad_x, grad_t = grad(output_['u'], input_).T
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gradgrad_u_x = grad(grad_u['x'], input_)
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return (
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grad_u['t'] + output_['u']*grad_u['x'] -
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(0.01/torch.pi)*gradgrad_u_x['x']
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)
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def nil_dirichlet(input_, output_):
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u_expected = 0.0
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return output_['u'] - u_expected
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def initial_condition(input_, output_):
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u_expected = -torch.sin(torch.pi*input_['x'])
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return output_['u'] - u_expected
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conditions = {
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'gamma1': Condition(Span({'x': -1, 't': [0, 1]}), nil_dirichlet),
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'gamma2': Condition(Span({'x': 1, 't': [0, 1]}), nil_dirichlet),
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't0': Condition(Span({'x': [-1, 1], 't': 0}), initial_condition),
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'D': Condition(Span({'x': [-1, 1], 't': [0, 1]}), burger_equation),
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}
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