ee39b39805
* modify examples/problems * modify tutorials --------- Co-authored-by: Dario Coscia <dariocoscia@dhcp-235.eduroam.sissa.it> Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
58 lines
2.0 KiB
Python
58 lines
2.0 KiB
Python
""" Poisson problem. """
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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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import torch
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from pina.geometry import CartesianDomain
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from pina import Condition
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from pina.problem import SpatialProblem
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from pina.operators import laplacian
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from pina.equation import FixedValue, Equation
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class Poisson(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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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 = laplacian(output_.extract(['u']), input_)
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return nabla_u - force_term
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conditions = {
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'gamma1': Condition(
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location=CartesianDomain({'x': [0, 1], 'y': 1}),
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equation=FixedValue(0.0)),
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'gamma2': Condition(
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location=CartesianDomain({'x': [0, 1], 'y': 0}),
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equation=FixedValue(0.0)),
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'gamma3': Condition(
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location=CartesianDomain({'x': 1, 'y': [0, 1]}),
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equation=FixedValue(0.0)),
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'gamma4': Condition(
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location=CartesianDomain({'x': 0, 'y': [0, 1]}),
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equation=FixedValue(0.0)),
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'D': Condition(
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location=CartesianDomain({'x': [0, 1], 'y': [0, 1]}),
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equation=Equation(laplace_equation)),
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}
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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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