f67467e5bd
* adding problems * add tests * update doc + formatting --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
68 lines
2.2 KiB
Python
68 lines
2.2 KiB
Python
"""Formulation of the Poisson problem in a square domain."""
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import torch
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from ... import Condition
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from ...operator import laplacian
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from ...problem import SpatialProblem
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from ...domain import CartesianDomain
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from ...equation import Equation, FixedValue
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def laplace_equation(input_, output_):
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"""
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Implementation of the laplace equation.
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:param LabelTensor input_: Input data of the problem.
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:param LabelTensor output_: Output data of the problem.
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:return: The residual of the laplace equation.
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:rtype: LabelTensor
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"""
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force_term = (
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torch.sin(input_.extract(["x"]) * torch.pi)
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* torch.sin(input_.extract(["y"]) * torch.pi)
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* (2 * torch.pi**2)
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)
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delta_u = laplacian(output_, input_, components=["u"], d=["x", "y"])
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return delta_u - force_term
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class Poisson2DSquareProblem(SpatialProblem):
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r"""
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Implementation of the 2-dimensional Poisson problem in the square domain
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:math:`[0, 1] \times [0, 1]`.
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"""
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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": 1.0}),
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"g2": CartesianDomain({"x": [0, 1], "y": 0.0}),
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"g3": CartesianDomain({"x": 1.0, "y": [0, 1]}),
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"g4": CartesianDomain({"x": 0.0, "y": [0, 1]}),
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}
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conditions = {
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"g1": Condition(domain="g1", equation=FixedValue(0.0)),
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"g2": Condition(domain="g2", equation=FixedValue(0.0)),
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"g3": Condition(domain="g3", equation=FixedValue(0.0)),
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"g4": Condition(domain="g4", equation=FixedValue(0.0)),
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"D": Condition(domain="D", equation=Equation(laplace_equation)),
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}
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def solution(self, pts):
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"""
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Implementation of the analytical solution of the Poisson problem.
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:param LabelTensor pts: Points where the solution is evaluated.
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:return: The analytical solution of the Poisson problem.
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:rtype: LabelTensor
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"""
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sol = -(
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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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)
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sol.labels = self.output_variables
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return sol
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