pihnn.bc.neumann_bc

class pihnn.bc.neumann_bc

Bases: scalar_bc

Neumann boundary condition:

\[\nabla u \cdot n= u_n,\]

where \(u\) is the solution, \(n\) is the outward normal vector and \(u_n\) is the assigned RHS value.

To be used for the Laplace problem.

__call__(z, u, normal, rhs)

Calculate residual of the boundary condition.

Parameters:

• z (torch.tensor) – Coordinates of the points where the BC is evaluated.

• u (torch.tensor) – Solution evaluated at the ‘z’ coordinates.

• normal (torch.tensor) – Boundary outward normal vectors at the ‘z’ coordinates.

• rhs (torch.tensor) – Boundary condition RHS assigned value at the ‘z’ coordinates.

Returns:

• error (torch.tensor) - Residual of the boundary condition at the ‘z’ coordinates.