pihnn.bc.dirichlet_laplace_bc

class pihnn.bc.dirichlet_laplace_bc

Bases: scalar_bc

Dirichlet-Laplace boundary condition:

\[u=u_d, \nabla^2 u = u_l,\]

where \(u\) is the solution and \(u_d,u_l\) are the assigned RHS values.

To be used for the biharmonic 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.