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Hexa2

Bases: Hexa1

Twenty-node quadratic serendipity hexahedral element.

Notes

Node ordering:

    7 -- 14 --  6
   /|          /|
 15 19       13 18
 /  |        /  |
4 -- 12 -- 5    |
|   3 -- 10 |-- 2
16 /        17 /
| 11        | 9
|/          |/
0 --  8 --  1

B(xi) classmethod

Evaluate reference-space derivatives of shape functions by autodiff.

Parameters:

  • xi (Tensor) –

    Reference coordinates. Shape: (iso_dim,) or (n_points, iso_dim).

Returns:

  • Tensor ( Tensor ) –

    Derivatives dN/dxi. Shape: (iso_dim, nodes) or (n_points, iso_dim, nodes).

H(xi) classmethod

Evaluate reference-space second derivatives of shape functions by autodiff.

Parameters:

  • xi (Tensor) –

    Reference coordinates. Shape: (iso_dim,) or (n_points, iso_dim).

Returns:

  • Tensor ( Tensor ) –

    Second derivatives d²N/dxi_i dxi_j. Shape: (iso_dim, iso_dim, nodes) or (n_points, iso_dim, iso_dim, nodes).