autopdex.models.d_alembert_fos

autopdex.models.d_alembert_fos(wave_number_fun, spacing)[source]

Constructs a first-order system for the space-time d’Alembert operator with wave speed c.

This function returns a PDE function representing the d’Alembert operator for one temporal dimension and (n-1) spatial dimensions, with augmented conditions to ensure a fully H1 coercive functional.

Parameters:

  • wave_number_fun (function) – A function that computes the wave number (inverse of wave speed) given spatial coordinates.

  • spacing (float) – The spatial spacing parameter used to scale the augmented conditions.

Returns:

A function that evaluates the first-order system of PDEs for the d’Alembert operator, which includes:

  • The primary d’Alembert operator.

  • Substituted derivative fields.

  • Additional constraints for stabilization (curl conditions).

Return type:

function

Notes: - The last dimension of the input coordinates x is considered the time dimension; the remaining dimensions are spatial dimensions. - This models works for DOFs as a jnp.ndarray.