Source code for pina.problem.zoo.helmholtz

"""Formulation of the Helmholtz problem."""

import torch
from ... import Condition
from ...equation import FixedValue, Helmholtz
from ...utils import check_consistency
from ...domain import CartesianDomain
from ...problem import SpatialProblem


[docs] class HelmholtzProblem(SpatialProblem): r""" Implementation of the Helmholtz problem in the square domain :math:`[-1, 1] \times [-1, 1]`. .. seealso:: **Original reference**: Si, Chenhao, et al. *Complex Physics-Informed Neural Network.* arXiv preprint arXiv:2502.04917 (2025). DOI: `arXiv:2502.04917 <https://arxiv.org/abs/2502.04917>`_. :Example: >>> problem = HelmholtzProblem() """ output_variables = ["u"] spatial_domain = CartesianDomain({"x": [-1, 1], "y": [-1, 1]}) domains = { "D": CartesianDomain({"x": [-1, 1], "y": [-1, 1]}), "g1": CartesianDomain({"x": [-1, 1], "y": 1.0}), "g2": CartesianDomain({"x": [-1, 1], "y": -1.0}), "g3": CartesianDomain({"x": 1.0, "y": [-1, 1]}), "g4": CartesianDomain({"x": -1.0, "y": [-1, 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)), } def __init__(self, alpha=3.0): """ Initialization of the :class:`HelmholtzProblem` class. :param alpha: Parameter of the forcing term. :type alpha: float | int """ super().__init__() self.alpha = alpha check_consistency(alpha, (int, float)) def forcing_term(self, input_): """ Implementation of the forcing term. """ return ( (1 - 2 * (self.alpha * torch.pi) ** 2) * torch.sin(self.alpha * torch.pi * input_.extract("x")) * torch.sin(self.alpha * torch.pi * input_.extract("y")) ) self.conditions["D"] = Condition( domain="D", equation=Helmholtz(self.alpha, forcing_term), )
[docs] def solution(self, pts): """ Implementation of the analytical solution of the Helmholtz problem. :param LabelTensor pts: Points where the solution is evaluated. :return: The analytical solution of the Poisson problem. :rtype: LabelTensor """ sol = torch.sin(self.alpha * torch.pi * pts.extract("x")) * torch.sin( self.alpha * torch.pi * pts.extract("y") ) sol.labels = self.output_variables return sol