integrands Namespace Reference

Functions
	vec3 (x, y, z)
	zero3 ()
	zero3x3 ()
	shape_rad (node_idx, zeta)
	shape_rad_vec (node_idx, xi_eta_zeta)
	shape_lat (node_idx, xi, eta)
	shape_lat_vec (node_idx, xi_eta_zeta)
	shape (node_idx, xi, eta, zeta)
	shape_vec (node_idx, xi_eta_zeta)
	grad_shape_rad (node_idx)
	grad_shape_lat_xi (node_idx)
	grad_shape_lat_eta (node_idx)
	grad_shape (node_idx, xi, eta, zeta)
	grad_shape_vec (node_idx, xi_eta_zeta)
	shape_rad_coarse (coarse_node_idx, fine_radial_wedge_idx, zeta_fine)
	shape_lat_coarse (coarse_node_idx, fine_lateral_wedge_idx, xi_fine, eta_fine)
	shape_coarse (coarse_node_idx, fine_radial_wedge_idx, fine_lateral_wedge_idx, xi_fine, eta_fine, zeta_fine)
	shape_coarse_vec (coarse_node_idx, fine_radial_wedge_idx, fine_lateral_wedge_idx, xi_eta_zeta_fine)
	grad_shape_rad_coarse (coarse_node_idx, fine_radial_wedge_idx)
	grad_shape_lat_coarse_xi (coarse_node_idx, fine_lateral_wedge_idx)
	grad_shape_lat_coarse_eta (coarse_node_idx, fine_lateral_wedge_idx)
	grad_shape_coarse (node_idx, fine_radial_wedge_idx, fine_lateral_wedge_idx, xi, eta, zeta)
	grad_shape_coarse_vec (node_idx, fine_radial_wedge_idx, fine_lateral_wedge_idx, xi_eta_zeta_fine)
	forward_map_rad (r_1, r_2, zeta)
	grad_forward_map_rad (r_1, r_2)
	forward_map_lat (p1_phy, p2_phy, p3_phy, xi, eta)
	grad_forward_map_lat_xi (p1_phy, p2_phy, p3_phy)
	grad_forward_map_lat_eta (p1_phy, p2_phy, p3_phy)
	jac_lat (p1_phy, p2_phy, p3_phy, xi, eta)
	jac_rad (r_1, r_2, zeta)
	jac (p1_phy, p2_phy, p3_phy, r_1, r_2, xi, eta, zeta)
	jac_from_array (p_phy, r_1, r_2, xi_eta_zeta_fine)
	symmetric_grad (J_inv_transposed, quad_point, dof, dim)

Function Documentation

forward_map_lat()

integrands.forward_map_lat	(		p1_phy,
			p2_phy,
			p3_phy,
			xi,
			eta
	)

p*_phy are 3x1 Matrix or sequences.
Returns a 3x1 Matrix: barycentric mapping (1-xi-eta)*p1 + xi*p2 + eta*p3

forward_map_rad()

integrands.forward_map_rad	(		r_1,
			r_2,
			zeta
	)

grad_forward_map_lat_eta()

integrands.grad_forward_map_lat_eta	(		p1_phy,
			p2_phy,
			p3_phy
	)

grad_forward_map_lat_xi()

integrands.grad_forward_map_lat_xi	(		p1_phy,
			p2_phy,
			p3_phy
	)

grad_forward_map_rad()

integrands.grad_forward_map_rad	(		r_1,
			r_2
	)

grad_shape()

integrands.grad_shape	(		node_idx,
			xi,
			eta,
			zeta
	)

Returns a 3x1 SymPy Matrix:
  [ d/dxi N_j,
    d/deta N_j,
    d/dzeta N_j ]
following:
  d/dxi N_j  = N^rad_j * d/dxi N^lat_j
  d/deta N_j = N^rad_j * d/deta N^lat_j
  d/dzeta N_j = N^lat_j * d/dzeta N^rad_j

grad_shape_coarse()

integrands.grad_shape_coarse	(		node_idx,
			fine_radial_wedge_idx,
			fine_lateral_wedge_idx,
			xi,
			eta,
			zeta
	)

grad_shape_coarse_vec()

integrands.grad_shape_coarse_vec	(		node_idx,
			fine_radial_wedge_idx,
			fine_lateral_wedge_idx,
			xi_eta_zeta_fine
	)

grad_shape_lat_coarse_eta()

integrands.grad_shape_lat_coarse_eta	(		coarse_node_idx,
			fine_lateral_wedge_idx
	)

grad_shape_lat_coarse_xi()

integrands.grad_shape_lat_coarse_xi	(		coarse_node_idx,
			fine_lateral_wedge_idx
	)

grad_shape_lat_eta()

integrands.grad_shape_lat_eta

(

node_idx

)

d/deta of N^lat: [-1, 0, 1] indexed by node_idx % 3

grad_shape_lat_xi()

integrands.grad_shape_lat_xi

(

node_idx

)

d/dxi of N^lat: [-1, 1, 0] indexed by node_idx % 3

grad_shape_rad()

integrands.grad_shape_rad

(

node_idx

)

Returns derivative d/dzeta of N^rad for the given node index:
grad_N_rad = [-0.5, 0.5]
indexed by node_idx // 3

grad_shape_rad_coarse()

integrands.grad_shape_rad_coarse	(		coarse_node_idx,
			fine_radial_wedge_idx
	)

grad_shape_vec()

integrands.grad_shape_vec	(		node_idx,
			xi_eta_zeta
	)

jac()

integrands.jac	(		p1_phy,
			p2_phy,
			p3_phy,
			r_1,
			r_2,
			xi,
			eta,
			zeta
	)

jac_from_array()

integrands.jac_from_array	(		p_phy,
			r_1,
			r_2,
			xi_eta_zeta_fine
	)

jac_lat()

integrands.jac_lat	(		p1_phy,
			p2_phy,
			p3_phy,
			xi,
			eta
	)

jac_rad()

integrands.jac_rad	(		r_1,
			r_2,
			zeta
	)

shape()

integrands.shape	(		node_idx,
			xi,
			eta,
			zeta
	)

shape_coarse()

integrands.shape_coarse	(		coarse_node_idx,
			fine_radial_wedge_idx,
			fine_lateral_wedge_idx,
			xi_fine,
			eta_fine,
			zeta_fine
	)

shape_coarse_vec()

integrands.shape_coarse_vec	(		coarse_node_idx,
			fine_radial_wedge_idx,
			fine_lateral_wedge_idx,
			xi_eta_zeta_fine
	)

shape_lat()

integrands.shape_lat	(		node_idx,
			xi,
			eta
	)

Equivalent of C++: shape_lat(node_idx, xi, eta)
N_lat = [1 - xi - eta, xi, eta]
returns N_lat[node_idx % 3]

shape_lat_coarse()

integrands.shape_lat_coarse	(		coarse_node_idx,
			fine_lateral_wedge_idx,
			xi_fine,
			eta_fine
	)

Matches the C++ nested switch on coarse_node_idx % 3 and fine_lateral_wedge_idx.

shape_lat_vec()

integrands.shape_lat_vec	(		node_idx,
			xi_eta_zeta
	)

Overload that accepts a 3-vector; uses xi_eta_zeta[0], xi_eta_zeta[1].

shape_rad()

integrands.shape_rad	(		node_idx,
			zeta
	)

Equivalent of C++: shape_rad(node_idx, zeta)
N_rad = [0.5*(1 - zeta), 0.5*(1 + zeta)]
returns N_rad[node_idx // 3]

shape_rad_coarse()

integrands.shape_rad_coarse	(		coarse_node_idx,
			fine_radial_wedge_idx,
			zeta_fine
	)

Matches the switch/case logic in C++.
coarse_node_idx // 3 selects bottom (0) or top (1).
fine_radial_wedge_idx selects which fine wedge (0 or 1).

shape_rad_vec()

integrands.shape_rad_vec	(		node_idx,
			xi_eta_zeta
	)

Overload that accepts a 3-vector like in C++: xi_eta_zeta(2) is zeta.

shape_vec()

integrands.shape_vec	(		node_idx,
			xi_eta_zeta
	)

symmetric_grad()

integrands.symmetric_grad	(		J_inv_transposed,
			quad_point,
			dof,
			dim
	)

J_inv_transposed: 3x3 Matrix (inverse-transposed Jacobian mapping to physical element)
quad_point: 3x1 vector of coordinates on reference element
dof: local index of shape function
dim: which column (0..2) of the vector-valued shape function we're computing the gradient for
Returns the symmetric gradient: 0.5*(grad + grad.T), where grad = J_inv_transposed * E
and E is a 3x3 matrix with grad_shape(dof, quad_point) as column 'dim' and zeros elsewhere.

vec3()

integrands.vec3	(		x,
			y,
			z
	)

zero3()

integrands.zero3

(

)

zero3x3()

integrands.zero3x3

(

)