autopdex.models.central_differences

autopdex.models.central_differences(density_fun, damping)

Constructs weak form contributions for acceleration (and optional damping) term based on central differences.

Parameters:

• density_fun (callable) – Function to compute the density coefficient given spatial coordinates and settings.

• damping (bool) – Whether to turn on damping. Damping requires settings[‘damping coefficient’] to be set.

Returns:

A function that evaluates the weak form contributions.

Return type:

callable

The returned function has the following parameters:

• x (jnp.ndarray): Spatial coordinates at the integration point.

• ansatz (callable): Ansatz function representing the primary field at time step n+1.

• test_ansatz (callable): Test ansatz function representing the test function.

• settings (dict): Settings for the computation, including: - ‘dofs n’: Degrees of freedom at the previous time step. - ‘connectivity’: Connectivity information for the elements. - ‘time increment’: Time increment delta_t.

• static_settings (dict): Static settings for the computation.

• int_point_number (int): Integration point number.

• set: Number of domain

Notes

• Requires settings[‘dofs n], settings[‘dofs n-1’] and settings[‘time increment’].

• This models works for DOFs as a jnp.ndarray.