autopdex.models.isoparametric_surface_element_galerkin

autopdex.models.isoparametric_surface_element_galerkin(weak_form_fun, ansatz_fun, ref_int_coor, ref_int_weights, tangent_contributions, initial_config=True)[source]

Constructs an isoparametric surface element for Galerkin methods using a given weak form function and DOFs as jnp.ndarray.

This function returns a user element function that evaluates the residual and tangent matrix for an isoparametric surface element based on the provided weak form and ansatz functions. The function can, for example, be used in combination with the weak_form_fun neumann_weak.

Parameters:

  • weak_form_fun (callable) – Function that evaluates the weak form given the integration point, trial ansatz, test ansatz, settings, static settings, and element number.

  • ansatz_fun (callable) – Function that constructs the ansatz (trial and test) functions.

  • ref_int_coor (jnp.ndarray) – Reference integration coordinates for the isoparametric element.

  • ref_int_weights (jnp.ndarray) – Reference integration weights for the isoparametric element.

  • tangent_contributions (bool) – If True, compute the tangent contributions; otherwise, return zero tangent.

  • initial_config (bool, optional) – If True, use the initial configuration for isoparametric mapping. Default is True.

Returns:

A function that evaluates the residual and tangent matrix for the isoparametric surface element.

Return type:

callable

Notes

  • Currently, the weak form function must not contain derivatives wrt. the primary fields.

  • The returned function can be used to evaluate the residual and tangent matrix for the element.

  • The mode parameter in the returned function can be ‘residual’ or ‘tangent’.

The returned function has the following parameters:

  • fI (jnp.ndarray): Element nodal values.

  • xI (jnp.ndarray): Element nodal coordinates.

  • elem_number (int): Element number.

  • settings (dict): Settings for the computation.

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

  • mode (str): Specifies whether to compute the ‘residual’ or ‘tangent’.

Notes

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