57 lines
1.7 KiB
Python
57 lines
1.7 KiB
Python
"""Definition of the Poisson problem on a square domain."""
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import torch
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from ..spatial_problem import SpatialProblem
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from ...operator import laplacian
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from ... import Condition
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from ...domain import CartesianDomain
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from ...equation.equation import Equation
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from ...equation.equation_factory import 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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"""
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force_term = torch.sin(input_.extract(["x"]) * torch.pi) * torch.sin(
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input_.extract(["y"]) * torch.pi
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)
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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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"""
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Implementation of the 2-dimensional Poisson problem on a square domain.
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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}),
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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="g1", equation=FixedValue(0.0)),
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"nil_g2": Condition(domain="g2", equation=FixedValue(0.0)),
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"nil_g3": Condition(domain="g3", equation=FixedValue(0.0)),
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"nil_g4": Condition(domain="g4", 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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"""TODO"""
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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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)
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