36 lines
1.2 KiB
Python
36 lines
1.2 KiB
Python
import numpy as np
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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 Problem2D
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from pina.operators import grad, div, nabla
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class Poisson2D(Problem2D):
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input_variables = ['x', 'y']
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output_variables = ['u']
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spatial_domain = Cube([[0, 1], [0, 1]])
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def laplace_equation(input_, output_):
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force_term = (torch.sin(input_['x']*torch.pi)
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* torch.sin(input_['y']*torch.pi))
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return nabla(output_['u'], input_).flatten() - force_term
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def nil_dirichlet(input_, output_):
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value = 0.0
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return output_['u'] - value
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conditions = {
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'gamma1': {'location': Segment((0, 0), (1, 0)), 'func': nil_dirichlet},
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'gamma2': {'location': Segment((1, 0), (1, 1)), 'func': nil_dirichlet},
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'gamma3': {'location': Segment((1, 1), (0, 1)), 'func': nil_dirichlet},
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'gamma4': {'location': Segment((0, 1), (0, 0)), 'func': nil_dirichlet},
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'D': {'location': Cube([[0, 1], [0, 1]]), 'func': laplace_equation}
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}
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def poisson_sol(self, x, y):
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return -(np.sin(x*np.pi)*np.sin(y*np.pi))/(2*np.pi**2)
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truth_solution = poisson_sol
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