50 lines
1.6 KiB
Python
50 lines
1.6 KiB
Python
import numpy as np
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import scipy.io
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import torch
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from pina.segment import Segment
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from pina.cube import Cube
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from pina.problem import TimeDependentProblem, Problem1D
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from pina.operators import grad
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def tmp_grad(output_, input_):
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return torch.autograd.grad(
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output_,
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input_.tensor,
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grad_outputs=torch.ones(output_.size()).to(
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dtype=input_.tensor.dtype,
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device=input_.tensor.device),
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create_graph=True, retain_graph=True, allow_unused=True)[0]
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class Burgers1D(TimeDependentProblem, Problem1D):
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input_variables = ['x', 't']
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output_variables = ['u']
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spatial_domain = Cube([[-1, 1]])
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temporal_domain = Cube([[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 = tmp_grad(output_['u'], input_).T
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gradgrad_u_x = grad(grad_u['x'], input_)
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grad_xx = tmp_grad(grad_x, input_)[:, 0]
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return grad_u['t'] + output_['u']*grad_u['x'] - (0.01/torch.pi)*gradgrad_u_x['x']
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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': {'location': Segment((-1, 0), (-1, 1)), 'func': nil_dirichlet},
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'gamma2': {'location': Segment(( 1, 0), ( 1, 1)), 'func': nil_dirichlet},
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'initia': {'location': Segment((-1, 0), ( 1, 0)), 'func': initial_condition},
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'D': {'location': Cube([[-1, 1],[0,1]]), 'func': burger_equation}
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}
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