56 lines
2.3 KiB
Python
56 lines
2.3 KiB
Python
""" Parametric Poisson problem. """
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# ===================================================== #
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# #
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# This script implements the two dimensional #
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# Parametric Poisson problem. The ParametricPoisson #
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# class is defined inheriting from SpatialProblem and #
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# ParametricProblem. We denote: #
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# u --> field variable #
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# x,y --> spatial variables #
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# mu1, mu2 --> parameter variables #
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# #
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# ===================================================== #
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from pina.domain import CartesianDomain
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from pina.problem import SpatialProblem, ParametricProblem
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from pina.operators import laplacian
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from pina.equation import FixedValue, Equation
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from pina import Condition
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import torch
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class ParametricPoisson(SpatialProblem, ParametricProblem):
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# assign output/ spatial and parameter variables
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output_variables = ['u']
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spatial_domain = CartesianDomain({'x': [-1, 1], 'y': [-1, 1]})
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parameter_domain = CartesianDomain({'mu1': [-1, 1], 'mu2': [-1, 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.exp(
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- 2*(input_.extract(['x']) - input_.extract(['mu1']))**2
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- 2*(input_.extract(['y']) - input_.extract(['mu2']))**2)
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return laplacian(output_.extract(['u']), input_, d=['x','y']) - force_term
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# problem condition statement
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conditions = {
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'gamma1': Condition(
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location=CartesianDomain({'x': [-1, 1], 'y': 1, 'mu1': [-1, 1], 'mu2': [-1, 1]}),
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equation=FixedValue(0.)),
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'gamma2': Condition(
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location=CartesianDomain({'x': [-1, 1], 'y': -1, 'mu1': [-1, 1], 'mu2': [-1, 1]}),
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equation=FixedValue(0.)),
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'gamma3': Condition(
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location=CartesianDomain({'x': 1, 'y': [-1, 1], 'mu1': [-1, 1], 'mu2': [-1, 1]}),
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equation=FixedValue(0.)),
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'gamma4': Condition(
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location=CartesianDomain({'x': -1, 'y': [-1, 1], 'mu1': [-1, 1], 'mu2': [-1, 1]}),
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equation=FixedValue(0.)),
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'D': Condition(
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location=CartesianDomain({'x': [-1, 1], 'y': [-1, 1], 'mu1': [-1, 1], 'mu2': [-1, 1]}),
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equation=Equation(laplace_equation)),
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}
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