45 lines
1.5 KiB
Python
45 lines
1.5 KiB
Python
""" Definition of the Poisson problem on a square domain."""
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from pina.problem import SpatialProblem
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from pina.operators import laplacian
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from pina import LabelTensor, Condition
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from pina.domain import CartesianDomain
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from pina.equation.equation import Equation
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from pina.equation.equation_factory import FixedValue
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import torch
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def laplace_equation(input_, output_):
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force_term = (torch.sin(input_.extract(['x']) * torch.pi) *
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torch.sin(input_.extract(['y']) * torch.pi))
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delta_u = laplacian(output_.extract(['u']), input_)
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return delta_u - force_term
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my_laplace = Equation(laplace_equation)
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class Poisson2DSquareProblem(SpatialProblem):
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output_variables = ['u']
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spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})
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domains = {
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'D': CartesianDomain({'x': [0, 1], 'y': [0, 1]}),
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'g1': CartesianDomain({'x': [0, 1], 'y': 1}),
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'g2': CartesianDomain({'x': [0, 1], 'y': 0}),
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'g3': CartesianDomain({'x': 1, 'y': [0, 1]}),
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'g4': CartesianDomain({'x': 0, 'y': [0, 1]}),
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}
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conditions = {
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'nil_g1': Condition(domain='D', equation=FixedValue(0.0)),
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'nil_g2': Condition(domain='D', equation=FixedValue(0.0)),
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'nil_g3': Condition(domain='D', equation=FixedValue(0.0)),
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'nil_g4': Condition(domain='D', equation=FixedValue(0.0)),
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'laplace_D': Condition(domain='D', equation=my_laplace),
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}
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def poisson_sol(self, pts):
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return -(torch.sin(pts.extract(['x']) * torch.pi) *
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torch.sin(pts.extract(['y']) * torch.pi))
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