Module: tide.staggered

Staggered-grid CPML profile builders for 2D and 3D propagation.

Functions

• set_pml_profiles
• setup_pml_profiles_1d
• set_pml_profiles_3d

set_pml_profiles

2D helper that returns 12 tensors:

• a/b profiles: ay, ayh, ax, axh, by, byh, bx, bxh
• kappa profiles: ky, kyh, kx, kxh

Output tensors are reshaped for broadcasting against [batch, ny, nx] fields.

setup_pml_profiles_1d

Builds 1D CPML profiles for integer and half-grid points. Useful for isolated profile testing.

set_pml_profiles_3d

3D helper that returns:

• 12 a/b profile tensors for z/y/x integer and half grids
• 6 kappa profile tensors

Derivative helpers

The module also contains staggered first-derivative operators:

• diffx1, diffy1, and diffz1 evaluate at integer grid points.
• diffxh1, diffyh1, and diffzh1 evaluate at half-grid points.

Their reciprocal-spacing tensors must be broadcast-compatible with the field, and stencil selects the finite-difference coefficients.

Intended use

These functions are public for numerical studies and backend parity tests, but most applications should obtain CPML and staggered updates through MaxwellTM or Maxwell3D. Calling profile builders directly requires the caller to preserve axis order, integer versus half-grid placement, dtype, device, and padded-domain sizes.

For a profile study, inspect both integer and half-grid tensors and verify that coefficients are inactive in the physical interior and vary smoothly through each absorbing layer.