44 lines
1.6 KiB
Python
44 lines
1.6 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.problem2d import Problem2D
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from pina.problem import Problem
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class Poisson2DProblem(Problem2D):
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def __init__(self):
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def laplace_equation(input_, output_):
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grad_u = self.grad(output_['u'], input_)
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gradgrad_u_x = self.grad(grad_u['x'], input_)
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gradgrad_u_y = self.grad(grad_u['y'], input_)
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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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force_term = -2*(input_['y']*(1-input_['y']) +
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input_['x']*(1-input_['x']))
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return gradgrad_u_x['x'] + gradgrad_u_y['y'] - 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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self.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(x, y):
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return x*(1-x)*y*(1-y)
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self.input_variables = ['x', 'y']
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self.output_variables = ['u']
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self.truth_solution = poisson_sol
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self.spatial_domain = Cube([[0, 1], [0, 1]])
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#self.check() # Check the problem is correctly set
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