AdvectionProblem

Formulation of the advection problem.

class AdvectionProblem(c=1.0)

Bases: SpatialProblem, TimeDependentProblem

Implementation of the advection problem in the spatial interval \([0, 2 \pi]\) and temporal interval \([0, 1]\).

See also

Original reference: Wang, Sifan, et al. An expert’s guide to training physics-informed neural networks. arXiv preprint arXiv:2308.08468 (2023). DOI: arXiv:2308.08468.

Example:

>>> problem = AdvectionProblem(c=1.0)

Initialization of the AdvectionProblem.

Parameters:

c (float | int) – The advection velocity parameter.

solution(pts)

Implementation of the analytical solution of the advection problem.

Parameters:

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

Returns:

The analytical solution of the advection problem.

Return type:

LabelTensor