Source code for pina.problem.zoo.poisson_2d_square

"""Formulation of the Poisson problem in a square domain."""

import torch
from ...equation import FixedValue, Poisson
from ...problem import SpatialProblem
from ...domain import CartesianDomain
from ... import Condition


def forcing_term(input_):
    """
    Implementation of the forcing term of the Poisson problem.

    :param LabelTensor input_: The points where the forcing term is evaluated.
    :return: The forcing term of the Poisson problem.
    :rtype: LabelTensor
    """
    return (
        torch.sin(input_.extract(["x"]) * torch.pi)
        * torch.sin(input_.extract(["y"]) * torch.pi)
        * (2 * torch.pi**2)
    )


[docs] class Poisson2DSquareProblem(SpatialProblem): r""" Implementation of the 2-dimensional Poisson problem in the square domain :math:`[0, 1] \times [0, 1]`. :Example: >>> problem = Poisson2DSquareProblem() """ output_variables = ["u"] spatial_domain = CartesianDomain({"x": [0, 1], "y": [0, 1]}) domains = { "D": CartesianDomain({"x": [0, 1], "y": [0, 1]}), "g1": CartesianDomain({"x": [0, 1], "y": 1.0}), "g2": CartesianDomain({"x": [0, 1], "y": 0.0}), "g3": CartesianDomain({"x": 1.0, "y": [0, 1]}), "g4": CartesianDomain({"x": 0.0, "y": [0, 1]}), } conditions = { "g1": Condition(domain="g1", equation=FixedValue(0.0)), "g2": Condition(domain="g2", equation=FixedValue(0.0)), "g3": Condition(domain="g3", equation=FixedValue(0.0)), "g4": Condition(domain="g4", equation=FixedValue(0.0)), "D": Condition(domain="D", equation=Poisson(forcing_term=forcing_term)), }
[docs] def solution(self, pts): """ Implementation of the analytical solution of the Poisson problem. :param LabelTensor pts: The points where the solution is evaluated. :return: The analytical solution of the Poisson problem. :rtype: LabelTensor """ sol = -( torch.sin(pts.extract(["x"]) * torch.pi) * torch.sin(pts.extract(["y"]) * torch.pi) ) sol.labels = self.output_variables return sol