pihnn.bc.interface_bc#

class pihnn.bc.interface_bc#

Bases: scalar_bc, linear_elasticity_bc

Interface condition for DD-PIHNNs.

For scalar problems:

$$[u]=[\mathrm{\nabla }u\cdot n]=0,$$

where $u$ is the solution and $n$ is the outward normal vector.

For linear elasticity:

$$[u]=[\sigma \cdot n]=0,$$

where $u$ is the displacement vector, $\sigma$ is the stress tensor and $n$ is the outward normal vector.

In both cases, $[\cdot ]$ denotes the discontinuity across 2 domains.

__call__(*args)#

Calculate residual of the boundary condition.

It employs call_for_scalar() or call_for_linear_elasticity() based on the types of arguments.

call_for_scalar(z, u, normal, rhs)#

Calculate residual of the boundary condition (for scalar problems).

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.

call_for_linear_elasticity(z, sxx, syy, sxy, ux, uy, normal, rhs)#

Calculate residual of the boundary condition (for linear elasticity problems).

Parameters:

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

• sxx (torch.tensor) – ${\sigma }_{xx}$ evaluated at the ‘z’ coordinates.

• syy (torch.tensor) – ${\sigma }_{yy}$ evaluated at the ‘z’ coordinates.

• sxy (torch.tensor) – ${\sigma }_{xy}$ evaluated at the ‘z’ coordinates.

• ux (torch.tensor) – $u_x$ evaluated at the ‘z’ coordinates.

• uy (torch.tensor) – $u_y$ 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.