hookeai.simulators.fetorch.element.derivatives.gradients.eval_jacobian

eval_jacobian(element_type, nodes_coords, local_coords, is_check_det=False)[source]

Evaluate finite element Jacobian and determinant at given coordinates.

Parameters:

  • element_type (Element) – FETorch finite element.

  • nodes_coords (torch.Tensor(2d)) – Nodes coordinates stored as torch.Tensor(2d) of shape (n_node, n_dof_node).

  • local_coords (torch.Tensor(1d)) – Local coordinates of point where Jacobian is evaluated.

  • is_check_det (bool, default=False) – If True, then check and raise error if Jacobian determinant is non-positive.

Returns:

  • jacobian (torch.Tensor(2d)) – Element Jacobian evaluated at given local coordinates.

  • jacobian_det (torch.Tensor(0d)) – Determinant of element Jacobian evaluated at given local coordinates.

  • shape_fun_local_deriv (torch.Tensor(2d)) – Shape functions local derivatives evaluated at given local coordinates, sorted according with element nodes. Derivative of the i-th shape function with respect to the j-th local coordinate is stored in shape_fun_local_deriv[i, j].