54 lines
2.0 KiB
Python
54 lines
2.0 KiB
Python
import numpy as np
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import torch
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from pina.problem import SpatialProblem
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from pina.operators import nabla
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from pina import Condition, Span
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# ===================================================== #
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# #
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# This script implements the two dimensional #
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# Poisson problem. The Poisson class is defined #
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# inheriting from SpatialProblem. We denote: #
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# u --> field variable #
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# x,y --> spatial variables #
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# #
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# ===================================================== #
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class Poisson(SpatialProblem):
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# assign output/ spatial variables
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output_variables = ['u']
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spatial_domain = Span({'x': [0, 1], 'y': [0, 1]})
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# define the laplace equation
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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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nabla_u = nabla(output_.extract(['u']), input_)
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return nabla_u - force_term
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# define nill dirichlet boundary conditions
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def nil_dirichlet(input_, output_):
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value = 0.0
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return output_.extract(['u']) - value
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# problem condition statement
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conditions = {
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'gamma1': Condition(location=Span({'x': [0, 1], 'y': 1}), function=nil_dirichlet),
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'gamma2': Condition(location=Span({'x': [0, 1], 'y': 0}), function=nil_dirichlet),
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'gamma3': Condition(location=Span({'x': 1, 'y': [0, 1]}),function=nil_dirichlet),
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'gamma4': Condition(location=Span({'x': 0, 'y': [0, 1]}), function=nil_dirichlet),
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'D': Condition(location=Span({'x': [0, 1], 'y': [0, 1]}), function=laplace_equation),
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}
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# real poisson solution
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def poisson_sol(self, pts):
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return -(
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torch.sin(pts.extract(['x'])*torch.pi)*
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torch.sin(pts.extract(['y'])*torch.pi)
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)/(2*torch.pi**2)
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truth_solution = poisson_sol
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