Module: tide.utils

Core physical constants and low-level coefficient builders.

Constants

• EP0
• MU0

Also exposed internally:

• C0 (speed of light in vacuum)

Functions

• setup_pml
• setup_pml_half

prepare_parameters

Builds electromagnetic update coefficients from model parameters:

• ca and cb for electric-field update
• cq for magnetic-field update

compile_material_coefficients

Compiles coefficient dictionaries for default and Debye-dispersive materials.

Returns keys including:

• ca, cb, cq
• has_dispersion
• debye (when dispersion is enabled)

setup_pml / setup_pml_half

Generates CPML profile tensors used by staggered-grid kernels.

These functions are generally consumed through tide.staggered helpers rather than called directly.

Material coefficient equations

For the standard conductive electric-field update, prepare_parameters constructs coefficients equivalent to

$$c_a = \frac{1-\sigma\Delta t/(2\epsilon)} {1+\sigma\Delta t/(2\epsilon)},\qquad c_b = \frac{\Delta t/\epsilon} {1+\sigma\Delta t/(2\epsilon)}.$$

The implementation uses relative material tensors together with EP0 and MU0 to form physical coefficients. cq supplies the magnetic-field update scale.

ca, cb, cq = tide.utils.prepare_parameters(
    epsilon,
    sigma,
    mu,
    dt,
)

Compiled material dictionaries

compile_material_coefficients validates material inputs and returns the coefficient set required by the selected constitutive path. With Debye dispersion, the dictionary also contains auxiliary update data and marks has_dispersion=True.

linearize_material_coefficients applies the coefficient derivative for depsilon_r and dsigma. It is used by tangent propagation so the JVP follows the same discrete material update as the nonlinear solver.

Low-level boundary profiles

setup_pml and setup_pml_half construct one-dimensional CPML a, b, and k profiles for integer and half-grid locations. Most callers should use tide.staggered, which reshapes and orders these profiles for 2D or 3D field updates.