#include <tetra_element_linear.h>

Data Structures
struct	tetrahedron_gauss_point

Public Member Functions
	tetra_element_linear ()

scalar *	get_K_alpha_element_mem_loc (int ni, int nj)
	Get the memory location of the specified element of K_alpha. More...

void	calculate_K_alpha ()
	Calc the diffusion matrix for this element. More...

void	construct_element_mass_matrix (MassMatrixQuadratic *M_alpha)

void	construct_element_mass_matrix (MassMatrixLinear *M_alpha)

void	add_K_alpha (scalar *K, int num_nodes)

void	get_grad_phi_at_stu (vector3 &grad_phi, scalar s, scalar t, scalar u)
	Returns the gradient of the potential at the given (s,t,u) position in the element. More...

void	calculate_electrostatic_forces ()
	Calculates the force on each node of the element due to the electrostatic potential gradient there. More...

void	calculate_jacobian (matrix3 J)
	Calculates the Jacobian matrix for this element. More...

void	calc_deformation (matrix3 J)
	Calculates Deformation Gradient. More...

void	calc_elastic_force_vector (vector12 F)
	Calculate the elastic contribution to the force. More...

int	calc_shape_function_derivatives_and_volume (matrix3 J)
	Inverts the given jacobian matrix J, using this to calculate the derivatives of the shape functions which are stored in dpsi. This is an array of all 12 derivatives, in the following order: dpsi = [ d(psi)_1/dx ] [ d(psi)_2/dx ] [ d(psi)_3/dx ] [ d(psi)_4/dx ] [ d(psi)_1/dy ] [ d(psi)_2/dy ] [ ... ] [ d(psi)_4/dz ]. More...

void	print_structural_details ()
	Prints a variety of structural details about the element to analyse it's configuration. More...

scalar	calc_volume ()
	Uses above functions to get volume. Easy. More...

void	create_viscosity_matrix ()
	Builds the viscosity matrix from the shape function derivatives, the shear and bulk viscosity constants, and the element volume. More...

void	add_shear_elastic_stress (matrix3 J, matrix3 stress)

void	add_bulk_elastic_stress (matrix3 stress)

void	add_bulk_elastic_stress_OLD (matrix3 stress)

void	add_fluctuating_stress (SimulationParams *params, RngStream rng[], matrix3 stress, int thread_id)
	Given the shape function derivatives, the element volume and a random number generator, this function calculates the fluctuating stress tensor, generating a stochastic change in the nodal velocities for the element under consideration. This function will add its contribution to the given 12-vector du. More...

void	apply_stress_tensor (matrix3 stress, vector12 du)
	Applies the given stress tensor to the shape function derivatives to get the contribution to du. More...

void	get_element_velocity_vector (vector12 v)
	Sets the given 12-vector to the velocities of this element's four nodes,. More...

void	add_element_force_vector (vector12 force)
	Add this element's nodal forces to those given in the force 12-vector. More...

void	add_force_to_node (int i, vector3 *f)
	Add given force to the specified node of this element. More...

int	what_node_is_this (int index)
	A roundabout and inefficient way of working out what node (from 0 to 9) this index corresponds to. More...

void	print ()

void	print_viscosity_matrix ()

void	apply_element_mass_matrix (vector12 du)
	Applies the mass matrix (for a linear tetrahedral element of density rho and equilibrium volume vol_0) to the force vector du to get the correct distribution of force between nodes. More...

void	volume_coord_to_xyz (scalar eta0, scalar eta1, scalar eta2, scalar eta3, vector3 *r)

void	zero_force ()

void	linearise_element ()

void	calc_centroid ()

int	get_opposite_node (int n1, int n2, int n3)

scalar	length_of_longest_edge ()

Data Fields
scalar	rho
	density More...

scalar	A
	shear viscosity More...

scalar	B
	second coefficient of viscosity More...

scalar	G
	shear modulus More...

scalar	E
	bulk modulus More...

scalar	dielectric

scalar	mass

mesh_node *	n [NUM_NODES_QUADRATIC_TET]
	A quadratic tetrahedron has 10 nodes. Keep pointers to the actual memory location of the nodes. More...

vector12	dpsi
	The 12-vector containing the shape function derivatives for this element. More...

upper_triangular_matrix4	del2
	The del2 matrix for this element (in upper triangular form, since it's symmetric). Used in constructing the diffusion matrix and the poisson matrix. More...

PoissonMatrixQuadratic	K_alpha

vector3	node_force [NUM_NODES_QUADRATIC_TET]
	Store the contribution from this element to the force on each of its four nodes. More...

scalar	vol_0
	The rest volume of this element. More...

scalar	vol
	The current volume of this element. More...

matrix3	F_ij
	The gradient deformation tensor for this element (needed for potential energy calculation) More...

scalar	internal_stress_mag
	The double contraction of the internal stress tensor, including elastic and thermal stresses. More...

matrix3	J_inv_0
	The inverse jacobian of this element at rest. More...

matrix12	viscosity_matrix
	Viscosity Matrix for the internal forces of this element. More...

Blob *	daddy_blob

int	index
	Index of this element in the parent Blob. More...

vector3	centroid

Private Member Functions
void	calc_del2_matrix ()
	Creates del2 matrix from the shape function derivatives. More...

void	add_diffusion_matrix (matrix12 V)

Private Attributes
scalar	last_det
	The last determinant of this element's transformation (used to work out whether it has inverted itself) More...

Detailed Description

A 10-point "quadratic" tetrahedron

Constructor & Destructor Documentation

◆ tetra_element_linear()

tetra_element_linear::tetra_element_linear ( )

Member Function Documentation

◆ add_bulk_elastic_stress()

void tetra_element_linear::add_bulk_elastic_stress ( matrix3 stress )

Referenced by calc_elastic_force_vector(), and Blob::update_internal_forces().

◆ add_bulk_elastic_stress_OLD()

void tetra_element_linear::add_bulk_elastic_stress_OLD ( matrix3 stress )

◆ add_diffusion_matrix()

void tetra_element_linear::add_diffusion_matrix ( matrix12 V )

private

Referenced by create_viscosity_matrix().

◆ add_element_force_vector()

void tetra_element_linear::add_element_force_vector ( vector12 force )

Add this element's nodal forces to those given in the force 12-vector.

Referenced by Blob::update_internal_forces().

◆ add_fluctuating_stress()

void tetra_element_linear::add_fluctuating_stress	(	SimulationParams *	params,
		RngStream	rng[],
		matrix3	stress,
		int	thread_id
	)

Given the shape function derivatives, the element volume and a random number generator, this function calculates the fluctuating stress tensor, generating a stochastic change in the nodal velocities for the element under consideration. This function will add its contribution to the given 12-vector du.

Referenced by Blob::update_internal_forces().

◆ add_force_to_node()

void tetra_element_linear::add_force_to_node	(	int	i,
		vector3 *	f
	)

Add given force to the specified node of this element.

Referenced by calculate_electrostatic_forces(), PreComp_solver::solve(), PreComp_solver::solve_using_neighbours(), and PreComp_solver::solve_using_neighbours_non_critical().

◆ add_K_alpha()

void tetra_element_linear::add_K_alpha	(	scalar *	K,
		int	num_nodes
	)

◆ add_shear_elastic_stress()

void tetra_element_linear::add_shear_elastic_stress	(	matrix3	J,
		matrix3	stress
	)

Referenced by calc_elastic_force_vector(), and Blob::update_internal_forces().

◆ apply_element_mass_matrix()

void tetra_element_linear::apply_element_mass_matrix ( vector12 du )

Applies the mass matrix (for a linear tetrahedral element of density rho and equilibrium volume vol_0) to the force vector du to get the correct distribution of force between nodes.

Referenced by Blob::make_measurements().

◆ apply_stress_tensor()

void tetra_element_linear::apply_stress_tensor	(	matrix3	stress,
		vector12	du
	)

Applies the given stress tensor to the shape function derivatives to get the contribution to du.

Referenced by calc_elastic_force_vector(), and Blob::update_internal_forces().

◆ calc_centroid()

void tetra_element_linear::calc_centroid ( )

Referenced by Blob::calc_all_centroids(), and PreComp_solver::init().

◆ calc_deformation()

void tetra_element_linear::calc_deformation ( matrix3 J )

Calculates Deformation Gradient.

Referenced by Blob::calculate_deformation().

◆ calc_del2_matrix()

void tetra_element_linear::calc_del2_matrix ( )

private

Creates del2 matrix from the shape function derivatives.

Referenced by create_viscosity_matrix().

◆ calc_elastic_force_vector()

void tetra_element_linear::calc_elastic_force_vector ( vector12 F )

Calculate the elastic contribution to the force.

Referenced by Blob::build_linear_node_elasticity_matrix().

◆ calc_shape_function_derivatives_and_volume()

int tetra_element_linear::calc_shape_function_derivatives_and_volume ( matrix3 J )

Inverts the given jacobian matrix J, using this to calculate the derivatives of the shape functions which are stored in dpsi. This is an array of all 12 derivatives, in the following order: dpsi = [ d(psi)_1/dx ] [ d(psi)_2/dx ] [ d(psi)_3/dx ] [ d(psi)_4/dx ] [ d(psi)_1/dy ] [ d(psi)_2/dy ] [ ... ] [ d(psi)_4/dz ].

Function also (as a by-product of the inversion) calculates the volume of the element whose jacobian this is, which is stored in 'vol'.

Referenced by Blob::build_linear_node_viscosity_matrix(), calc_elastic_force_vector(), Blob::calc_rest_state_info(), calc_volume(), and NoMassCGSolver::init().

◆ calc_volume()

scalar tetra_element_linear::calc_volume ( )

Uses above functions to get volume. Easy.

Referenced by Blob::calc_volume(), and print_structural_details().

◆ calculate_electrostatic_forces()

void tetra_element_linear::calculate_electrostatic_forces ( )

Calculates the force on each node of the element due to the electrostatic potential gradient there.

Referenced by Blob::update_internal_forces().

◆ calculate_jacobian()

void tetra_element_linear::calculate_jacobian ( matrix3 J )

Calculates the Jacobian matrix for this element.

Referenced by Blob::build_linear_node_viscosity_matrix(), calc_elastic_force_vector(), Blob::calc_rest_state_info(), calc_volume(), Blob::calculate_deformation(), Blob::check_inversion(), PreComp_solver::compute_bead_positions(), NoMassCGSolver::init(), PreComp_solver::init(), and Blob::update_internal_forces().

◆ calculate_K_alpha()

void tetra_element_linear::calculate_K_alpha ( )

Calc the diffusion matrix for this element.

Referenced by Blob::build_poisson_matrices().

◆ construct_element_mass_matrix() [1/2]

void tetra_element_linear::construct_element_mass_matrix ( MassMatrixQuadratic * M_alpha )

Referenced by Blob::build_linear_node_mass_matrix(), and Blob::build_mass_matrix().

◆ construct_element_mass_matrix() [2/2]

void tetra_element_linear::construct_element_mass_matrix ( MassMatrixLinear * M_alpha )

◆ create_viscosity_matrix()

void tetra_element_linear::create_viscosity_matrix ( )

Builds the viscosity matrix from the shape function derivatives, the shear and bulk viscosity constants, and the element volume.

Referenced by Blob::build_linear_node_viscosity_matrix(), NoMassCGSolver::init(), and Blob::update_internal_forces().

◆ get_element_velocity_vector()

void tetra_element_linear::get_element_velocity_vector ( vector12 v )

Sets the given 12-vector to the velocities of this element's four nodes,.

Referenced by Blob::make_measurements(), and Blob::update_internal_forces().

◆ get_grad_phi_at_stu()

void tetra_element_linear::get_grad_phi_at_stu	(	vector3 &	grad_phi,
		scalar	s,
		scalar	t,
		scalar	u
	)

Returns the gradient of the potential at the given (s,t,u) position in the element.

Referenced by Face::get_normal_flux().

◆ get_K_alpha_element_mem_loc()

scalar * tetra_element_linear::get_K_alpha_element_mem_loc	(	int	ni,
		int	nj
	)

Get the memory location of the specified element of K_alpha.

Referenced by Blob::init().

◆ get_opposite_node()

int tetra_element_linear::get_opposite_node	(	int	n1,
		int	n2,
		int	n3
	)

Returns the opposite node for a 2nd order face, e. g., returns 3 for face [0,4,5]. The 2nd order nodes were created at setup time, in: FFEA_initialise/FFEA_convert_from_volume/convert_tetrahedra_linear_to_quadratic.py

Referenced by Blob::load_surface().