HelmholtzProblem#

Formulation of the Helmholtz problem.

class HelmholtzProblem(alpha=3.0)[source]#

Bases: SpatialProblem

Implementation of the Helmholtz problem in the square domain \([-1, 1] \times [-1, 1]\).

See also

Original reference: Si, Chenhao, et al. Complex Physics-Informed Neural Network. arXiv preprint arXiv:2502.04917 (2025). DOI: arXiv:2502.04917.

Example:
>>> problem = HelmholtzProblem()

Initialization of the HelmholtzProblem class.

Parameters:

alpha (float | int) – Parameter of the forcing term.

solution(pts)[source]#

Implementation of the analytical solution of the Helmholtz problem.

Parameters:

pts (LabelTensor) – Points where the solution is evaluated.

Returns:

The analytical solution of the Poisson problem.

Return type:

LabelTensor