autopdex.spaces.fem_iso_line_quad_brick

autopdex.spaces.fem_iso_line_quad_brick(x, xI, fI, settings, overwrite_diff, n_dim)[source]

Compute isoparametric finite element shape functions for line, quadrilateral, and brick elements.

Parameters:

  • x (jnp.ndarray) – The position of the evaluation point.

  • xI (jnp.ndarray) – The positions of neighboring nodes.

  • fI (jnp.ndarray) – The data at neighboring nodes.

  • settings (dict) – Dictionary containing various settings (not directly used in this function but passed for compatibility).

  • overwrite_diff (bool) – If True, overwrites the derivative to be with respect to the initial configuration instead of the reference configuration.

  • n_dim (int) – The dimensionality of the elements (1 for line, 2 for quadrilateral, 3 for brick).

Returns:

The computed finite element approximation (sum_i shape_fun_i nodal_values_i)

Return type:

float

Notes

  • This function currently supports line elements up to order 20, quadrilateral elements up to order 20, and brick elements up to order 2.

  • Though the input x is a reference coordinate, its derivative is replaced with respect to the initial configuration when overwrite_diff is True.

  • Warning: Only first-order spatial derivatives are supported in the custom JVP implementation with overwritten derivatives.

  • Warning: The derivatives with respect to xI are set to zero.