Class for refineable QPVDElement elements. More...

#include <refineable_solid_elements.h>

Inheritance diagram for oomph::RefineableQPVDElement< DIM, NNODE_1D >:

Public Member Functions
	RefineableQPVDElement ()
	Constructor: More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Empty rebuild from sons, no need to reconstruct anything here. More...

unsigned	nvertex_node () const
	Number of vertex nodes in the element. More...

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

unsigned	nrecovery_order ()
	Order of recovery shape functions for Z2 error estimation: Same order as shape functions. More...

void	further_setup_hanging_nodes ()
	No additional hanging node procedures are required for the solid elements. More...

Public Member Functions inherited from oomph::QPVDElement< DIM, NNODE_1D >
	QPVDElement ()
	Constructor, there are no internal data points. More...

void	output (std::ostream &outfile)
	Output function. More...

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output function. More...

void	output (FILE *file_pt)
	C-style output function. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	C-style output function. More...

Public Member Functions inherited from oomph::PVDEquations< DIM >
	PVDEquations ()
	Constructor. More...

void	get_stress (const Vector< double > &s, DenseMatrix< double > &sigma)
	Return the 2nd Piola Kirchoff stress tensor, as calculated from the constitutive law at specified local coordinate. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Fill in the residuals for the solid equations (the discretised principle of virtual displacements) More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Fill in contribution to Jacobian (either by FD or analytically, control this via evaluate_jacobian_by_fd() More...

void	extended_output (std::ostream &outfile, const unsigned &n_plot)
	Output: x,y,[z],xi0,xi1,[xi2],gamma and the strain and stress components. More...

Public Member Functions inherited from oomph::PVDEquationsBase< DIM >
	PVDEquationsBase ()
	Constructor: Set null pointers for constitutive law and for isotropic growth function. Set physical parameter values to default values, enable inertia and set body force to zero. Default evaluation of Jacobian: analytically rather than by FD. More...

ConstitutiveLaw *&	constitutive_law_pt ()
	Return the constitutive law pointer. More...

const double &	lambda_sq () const
	Access function for timescale ratio (nondim density) More...

double *&	lambda_sq_pt ()
	Access function for pointer to timescale ratio (nondim density) More...

IsotropicGrowthFctPt &	isotropic_growth_fct_pt ()
	Access function: Pointer to isotropic growth function. More...

PrestressFctPt &	prestress_fct_pt ()
	Access function: Pointer to pre-stress function. More...

IsotropicGrowthFctPt	isotropic_growth_fct_pt () const
	Access function: Pointer to isotropic growth function (const version) More...

BodyForceFctPt &	body_force_fct_pt ()
	Access function: Pointer to body force function. More...

BodyForceFctPt	body_force_fct_pt () const
	Access function: Pointer to body force function (const version) More...

void	enable_inertia ()
	Switch on solid inertia. More...

void	disable_inertia ()
	Switch off solid inertia. More...

bool	is_inertia_enabled () const
	Access function to flag that switches inertia on/off (const version) More...

virtual unsigned	npres_solid () const
	Return the number of solid pressure degrees of freedom Default is that there are no solid pressures. More...

virtual int	solid_p_local_eqn (const unsigned &i) const
	Return the local degree of freedom associated with the i-th solid pressure. Default is that there are none. More...

virtual int	solid_p_nodal_index () const
	Return the index at which the solid pressure is stored if it is stored at the nodes. If not stored at the nodes this will return a negative number. More...

virtual void	pin_elemental_redundant_nodal_solid_pressures ()
	Pin the element's redundant solid pressures (needed for refinement) More...

void	get_strain (const Vector< double > &s, DenseMatrix< double > &strain) const
	Return the strain tensor. More...

void	get_energy (double &pot_en, double &kin_en)
	Get potential (strain) and kinetic energy. More...

void	get_deformed_covariant_basis_vectors (const Vector< double > &s, DenseMatrix< double > &def_covariant_basis)
	Return the deformed covariant basis vectors at specified local coordinate: `def_covariant_basis(i,j)` is the j-th component of the i-th basis vector. More...

void	get_principal_stress (const Vector< double > &s, DenseMatrix< double > &principal_stress_vector, Vector< double > &principal_stress)
	Compute principal stress vectors and (scalar) principal stresses at specified local coordinate. `principal_stress_vector(i,j)` is the j-th component of the i-th principal stress vector. More...

virtual void	get_isotropic_growth (const unsigned &ipt, const Vector< double > &s, const Vector< double > &xi, double &gamma) const
	Evaluate isotropic growth function at Lagrangian coordinate xi and/or local coordinate s. (returns 1, i.e. no growth, if no function pointer has been set) This function is virtual to allow overloading in multi-physics problems where the growth function might be determined by another system of equations. More...

void	body_force (const Vector< double > &xi, Vector< double > &b) const
	Evaluate body force at Lagrangian coordinate xi at present time (returns zero vector if no body force function pointer has been set) More...

unsigned	ndof_types () const
	returns the number of DOF types associated with this element. More...

void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const
	Create a list of pairs for all unknowns in this element, so that the first entry in each pair contains the global equation number of the unknown, while the second one contains the number of the "DOF" that this unknown is associated with. (Function can obviously only be called if the equation numbering scheme has been set up.) E.g. in a 3D problem there are 3 types of DOF: 0 - x displacement 1 - y displacement 2 - z displacement. More...

void	enable_evaluate_jacobian_by_fd ()
	Set Jacobian to be evaluated by FD? Else: Analytically. More...

void	disable_evaluate_jacobian_by_fd ()
	Set Jacobian to be evaluated analytically Else: by FD. More...

bool	is_jacobian_evaluated_by_fd () const
	Return the flag indicating whether the jacobian is evaluated by fd. More...

double	prestress (const unsigned &i, const unsigned &j, const Vector< double > xi)
	Return (i,j)-th component of second Piola Kirchhoff membrane prestress at Lagrangian coordinate xi. More...

Public Member Functions inherited from oomph::SolidFiniteElement
void	set_lagrangian_dimension (const unsigned &lagrangian_dimension)
	Set the lagrangian dimension of the element — the number of lagrangian coordinates stored at the nodes in the element. More...

virtual bool	has_internal_solid_data ()
	Return whether there is internal solid data (e.g. discontinuous solid pressure). At present, this is used to report an error in setting initial conditions for ElasticProblems which can't handle such cases. The default is false. More...

	SolidFiniteElement ()
	Constructor: Set defaults. More...

virtual	~SolidFiniteElement ()
	Destructor to clean up any allocated memory. More...

	SolidFiniteElement (const SolidFiniteElement &)=delete
	Broken copy constructor. More...

double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
	In a SolidFiniteElement, the "global" intrinsic coordinate of the element when viewed as part of a compound geometric object (a Mesh) is, by default, the Lagrangian coordinate Note the assumption here is that we are always using isoparameteric elements in which the lagrangian coordinate is interpolated by the same shape functions as the eulerian coordinate. More...

virtual void	get_x_and_xi (const Vector< double > &s, Vector< double > &x_fe, Vector< double > &x, Vector< double > &xi_fe, Vector< double > &xi) const
	Eulerian and Lagrangian coordinates as function of the local coordinates: The Eulerian position is returned in FE-interpolated form (`x_fe`) and then in the form obtained from the "current" MacroElement representation (if it exists – if not, `x` is the same as `x_fe`). This allows the Domain/MacroElement- based representation to be used to apply displacement boundary conditions exactly. Ditto for the Lagrangian coordinates returned in xi_fe and xi. (Broken virtual – overload in specific geometric element class if you want to use this functionality.) More...

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)
	Set pointer to MacroElement – overloads generic version and uses the MacroElement also as the default for the "undeformed" configuration. This assignment must be overwritten with set_undeformed_macro_elem_pt(...) if the deformation of the solid body is driven by a deformation of the "current" Domain/MacroElement representation of it's boundary. Can be overloaded in derived classes to perform additional tasks. More...

virtual void	set_macro_elem_pt (MacroElement macro_elem_pt, MacroElement undeformed_macro_elem_pt)
	Set pointers to "current" and "undeformed" MacroElements. Can be overloaded in derived classes to perform additional tasks. More...

void	set_undeformed_macro_elem_pt (MacroElement *undeformed_macro_elem_pt)
	Set pointer to "undeformed" macro element. Can be overloaded in derived classes to perform additional tasks. More...

MacroElement *	undeformed_macro_elem_pt ()
	Access function to pointer to "undeformed" macro element. More...

double	dshape_lagrangian (const Vector< double > &s, Shape &psi, DShape &dpsidxi) const
	Calculate shape functions and derivatives w.r.t. Lagrangian coordinates at local coordinate s. Returns the Jacobian of the mapping from Lagrangian to local coordinates. More...

virtual double	dshape_lagrangian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidxi) const
	Return the geometric shape functions and also first derivatives w.r.t. Lagrangian coordinates at ipt-th integration point. More...

double	d2shape_lagrangian (const Vector< double > &s, Shape &psi, DShape &dpsidxi, DShape &d2psidxi) const
	Compute the geometric shape functions and also first and second derivatives w.r.t. Lagrangian coordinates at local coordinate s; Returns Jacobian of mapping from Lagrangian to local coordinates. Numbering: 1D: d2pidxi(i,0) = $d^2 \psi_j / d \xi^2$ 2D: d2psidxi(i,0) = $\partial^2 \psi_j / \partial \xi_0^2$ d2psidxi(i,1) = $\partial^2 \psi_j / \partial \xi_1^2$ d2psidxi(i,2) = $\partial^2 \psi_j / \partial \xi_0 \partial \xi_1$ 3D: d2psidxi(i,0) = $\partial^2 \psi_j / \partial \xi_0^2$ d2psidxi(i,1) = $\partial^2 \psi_j / \partial \xi_1^2$ d2psidxi(i,2) = $\partial^2 \psi_j / \partial \xi_2^2$ d2psidxi(i,3) = $\partial^2 \psi_j/\partial \xi_0 \partial \xi_1$ d2psidxi(i,4) = $\partial^2 \psi_j/\partial \xi_0 \partial \xi_2$ d2psidxi(i,5) = $\partial^2 \psi_j/\partial \xi_1 \partial \xi_2$ . More...

virtual double	d2shape_lagrangian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidxi, DShape &d2psidxi) const
	Return the geometric shape functions and also first and second derivatives w.r.t. Lagrangian coordinates at the ipt-th integration point. Returns Jacobian of mapping from Lagrangian to local coordinates. Numbering: 1D: d2pidxi(i,0) = $d^2 \psi_j / d^2 \xi^2$ 2D: d2psidxi(i,0) = $\partial^2 \psi_j/\partial^2 \xi_0^2$ d2psidxi(i,1) = $\partial^2 \psi_j/\partial^2 \xi_1^2$ d2psidxi(i,2) = $\partial^2 \psi_j/\partial \xi_0 \partial \xi_1$ 3D: d2psidxi(i,0) = $\partial^2 \psi_j / \partial^2 \xi_0^2$ d2psidxi(i,1) = $\partial^2 \psi_j / \partial^2 \xi_1^2$ d2psidxi(i,2) = $\partial^2 \psi_j / \partial^2 \xi_2^2$ d2psidxi(i,3) = $\partial^2 \psi_j / \partial \xi_0 \partial \xi_1$ d2psidxi(i,4) = $\partial^2 \psi_j / \partial \xi_0 \partial \xi_2$ d2psidxi(i,5) = $\partial^2 \psi_j / \partial \xi_1 \partial \xi_2$ . More...

unsigned	lagrangian_dimension () const
	Return the number of Lagrangian coordinates that the element requires at all nodes. This is by default the elemental dimension. If we ever need any other case, it can be implemented. More...

unsigned	nnodal_lagrangian_type () const
	Return the number of types of (generalised) nodal Lagrangian coordinates required to interpolate the Lagrangian coordinates in the element. (E.g. 1 for Lagrange-type elements; 2 for Hermite beam elements; 4 for Hermite shell elements). Default value is 1. Needs to be overloaded for any other element. More...

Node *	construct_node (const unsigned &n)
	Construct the local node n and return a pointer to it. More...

Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n and return a pointer to it. Additionally, create storage for ‘history’ values as required by timestepper. More...

Node *	construct_boundary_node (const unsigned &n)
	Construct the local node n and return a pointer to it. in the case when it is a boundary node; that is it MAY be located on a Mesh boundary. More...

Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n and return a pointer to it, in the case when the node MAY be located on a boundary. Additionally, create storage for ‘history’ values as required by timestepper. More...

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)
	Overload assign_all_generic_local_equation numbers to include the data associated with solid dofs. It remains virtual so that it can be overloaded by RefineableSolidElements. If the boolean argument is true then the degrees of freedom are stored in Dof_pt. More...

void	describe_local_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the local dofs of the element. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

double	raw_lagrangian_position (const unsigned &n, const unsigned &i) const
	Return i-th Lagrangian coordinate at local node n without using the hanging representation. More...

double	raw_lagrangian_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return Generalised Lagrangian coordinate at local node n. ‘Direction’ i, ‘Type’ k. Does not use the hanging node representation. More...

double	lagrangian_position (const unsigned &n, const unsigned &i) const
	Return i-th Lagrangian coordinate at local node n. More...

double	lagrangian_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return Generalised Lagrangian coordinate at local node n. ‘Direction’ i, ‘Type’ k. More...

virtual double	interpolated_xi (const Vector< double > &s, const unsigned &i) const
	Return i-th FE-interpolated Lagrangian coordinate xi[i] at local coordinate s. More...

virtual void	interpolated_xi (const Vector< double > &s, Vector< double > &xi) const
	Compute FE interpolated Lagrangian coordinate vector xi[] at local coordinate s as Vector. More...

virtual void	interpolated_dxids (const Vector< double > &s, DenseMatrix< double > &dxids) const
	Compute derivatives of FE-interpolated Lagrangian coordinates xi with respect to local coordinates: dxids[i][j]=dxi_i/ds_j. More...

virtual void	J_lagrangian (const Vector< double > &s) const
	Return the Jacobian of mapping from local to Lagrangian coordinates at local position s. NOT YET IMPLEMENTED. More...

virtual double	J_lagrangian_at_knot (const unsigned &ipt) const
	Return the Jacobian of the mapping from local to Lagrangian coordinates at the ipt-th integration point. NOT YET IMPLEMENTED. More...

SolidInitialCondition *&	solid_ic_pt ()
	Pointer to object that describes the initial condition. More...

void	enable_solve_for_consistent_newmark_accel ()
	Set to alter the problem being solved when assigning the initial conditions for time-dependent problems: solve for the history value that corresponds to the acceleration in the Newmark scheme by demanding that the PDE is satisifed at the initial time. In this case the Jacobian is replaced by the mass matrix. More...

void	disable_solve_for_consistent_newmark_accel ()
	Set to reset the problem being solved to be the standard problem. More...

MultiplierFctPt &	multiplier_fct_pt ()
	Access function: Pointer to multiplicator function for assignment of consistent assignement of initial conditions for Newmark scheme. More...

MultiplierFctPt	multiplier_fct_pt () const
	Access function: Pointer to multiplicator function for assignment of consistent assignement of initial conditions for Newmark scheme (const version) More...

virtual void	get_residuals_for_solid_ic (Vector< double > &residuals)
	Compute the residuals for the setup of an initial condition. The global equations are: More...

void	fill_in_residuals_for_solid_ic (Vector< double > &residuals)
	Fill in the residuals for the setup of an initial condition. The global equations are: More...

void	fill_in_jacobian_for_solid_ic (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Fill in the residuals and Jacobian for the setup of an initial condition. The global equations are: More...

void	fill_in_jacobian_for_newmark_accel (DenseMatrix< double > &jacobian)
	Fill in the contributions of the Jacobian matrix for the consistent assignment of the initial "accelerations" in Newmark scheme. In this case the Jacobian is the mass matrix. More...

void	compute_norm (double &el_norm)
	Calculate the L2 norm of the displacement u=R-r to overload the compute_norm function in the GeneralisedElement base class. More...

int	position_local_eqn (const unsigned &n, const unsigned &k, const unsigned &j) const
	Access function that returns the local equation number that corresponds to the j-th coordinate of the k-th position-type at the n-th local node. More...

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)
	Set the dimension of the element and initially set the dimension of the nodes to be the same as the dimension of the element. More...

void	set_nodal_dimension (const unsigned &nodal_dim)
	Set the dimension of the nodes in the element. This will typically only be required when constructing FaceElements or in beam and shell type elements where a lower dimensional surface is embedded in a higher dimensional space. More...

void	set_nnodal_position_type (const unsigned &nposition_type)
	Set the number of types required to interpolate the coordinate. More...

void	set_n_node (const unsigned &n)
	Set the number of nodes in the element to n, by resizing the storage for pointers to the Node objects. More...

int	nodal_local_eqn (const unsigned &n, const unsigned &i) const
	Return the local equation number corresponding to the i-th value at the n-th local node. More...

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const
	Compute the geometric shape functions (psi) at integration point ipt. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of "detJ" w.r.t. the nodal coordinates. More...

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()
	The destructor cleans up the static memory allocated for shape function storage. Internal and external data get wiped by the GeneralisedElement destructor; nodes get killed in mesh destructor. More...

	FiniteElement (const FiniteElement &)=delete
	Broken copy constructor. More...

virtual bool	local_coord_is_valid (const Vector< double > &s)
	Broken assignment operator. More...

virtual void	move_local_coord_back_into_element (Vector< double > &s) const
	Adjust local coordinates so that they're located inside the element. More...

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const
	Compute centre of gravity of all nodes and radius of node that is furthest from it. Used to assess approximately if a point is likely to be contained with an element in locate_zeta-like operations. More...

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
	Get local coordinates of node j in the element; vector sets its own size (broken virtual) More...

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
	Get the local fraction of the node j in the element A dumb, but correct default implementation is provided. More...

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)
	Get the local fraction of any node in the n-th position in a one dimensional expansion along the i-th local coordinate. More...

MacroElement *	macro_elem_pt ()
	Access function to pointer to macro element. More...

void	get_x (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates. Either via FE representation or via macro-element (if Macro_elem_pt!=0) More...

void	get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). Either via FE representation of QElement or via macro-element (if Macro_elem_pt!=0). More...

virtual void	get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates using macro element representation. (Broken virtual — this must be overloaded in specific geometric element classes) More...

virtual void	get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). using macro element representation (Broken virtual – overload in specific geometric element class if you want to use this functionality.) More...

virtual void	set_integration_scheme (Integral *const &integral_pt)
	Set the spatial integration scheme. More...

Integral *const &	integral_pt () const
	Return the pointer to the integration scheme (const version) More...

virtual void	shape (const Vector< double > &s, Shape &psi) const =0
	Calculate the geometric shape functions at local coordinate s. This function must be overloaded for each specific geometric element. More...

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const
	Return the geometric shape function at the ipt-th integration point. More...

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Function to compute the geometric shape functions and derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element. (Broken virtual function — specifies the interface) More...

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const
	Return the geometric shape function and its derivative w.r.t. the local coordinates at the ipt-th integration point. More...

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Function to compute the geometric shape functions and also first and second derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element (if required). (Broken virtual function — specifies the interface). Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Return the geometric shape function and its first and second derivatives w.r.t. the local coordinates at the ipt-th integration point. Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual double	J_eulerian (const Vector< double > &s) const
	Return the Jacobian of mapping from local to global coordinates at local position s. More...

virtual double	J_eulerian_at_knot (const unsigned &ipt) const
	Return the Jacobian of the mapping from local to global coordinates at the ipt-th integration point. More...

void	check_J_eulerian_at_knots (bool &passed) const
	Check that Jacobian of mapping between local and Eulerian coordinates at all integration points is positive. More...

void	check_jacobian (const double &jacobian) const
	Helper function used to check for singular or negative Jacobians in the transform from local to global or Lagrangian coordinates. More...

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const
	Compute the geometric shape functions and also first derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const
	Return the geometric shape functions and also first derivatives w.r.t. global coordinates at the ipt-th integration point. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const
	Compute the geometric shape functions (psi) and first derivatives w.r.t. global coordinates (dpsidx) at the ipt-th integration point. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of both "detJ" and "dpsidx" w.r.t. the nodal coordinates. More...

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Compute the geometric shape functions and also first and second derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d x^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Return the geometric shape functions and also first and second derivatives w.r.t. global coordinates at ipt-th integration point. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d s^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual void	describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

Node *&	node_pt (const unsigned &n)
	Return a pointer to the local node n. More...

Node *const &	node_pt (const unsigned &n) const
	Return a pointer to the local node n (const version) More...

unsigned	nnode () const
	Return the number of nodes. More...

virtual unsigned	nnode_1d () const
	Return the number of nodes along one edge of the element Default is to return zero — must be overloaded by geometric elements. More...

double	raw_nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. Do not use the hanging node representation. NOTE: Moved to cc file because of a possible compiler bug in gcc (yes, really!). The move to the cc file avoids inlining which appears to cause problems (only) when compiled with gcc and -O3; offensive "illegal read" is in optimised-out section of code and data that is allegedly illegal is readily readable (by other means) just before this function is called so I can't really see how we could possibly be responsible for this... More...

double	raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level). Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. If the node is hanging, the appropriate interpolation is handled by the position function in the Node class. More...

double	nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level) Returns suitably interpolated version for hanging nodes. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. More...

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. More...

double	nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. More...

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

double	dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

virtual void	disable_ALE ()
	This is an empty function that establishes a uniform interface for all (derived) elements that involve time-derivatives. Such elements are/should be implemented in ALE form to allow mesh motions. The additional expense associated with the computation of the mesh velocities is, of course, superfluous if the elements are used in problems in which the mesh is stationary. This function should therefore be overloaded in all derived elements that are formulated in ALE form to suppress the computation of the mesh velocities. The user disables the ALE functionality at his/her own risk! If the mesh does move after all, then the results will be wrong. Here we simply issue a warning message stating that the empty function has been called. More...

virtual void	enable_ALE ()
	(Re-)enable ALE, i.e. take possible mesh motion into account when evaluating the time-derivative. This function is empty and simply establishes a common interface for all derived elements that are formulated in ALE form. More...

virtual unsigned	required_nvalue (const unsigned &n) const
	Number of values that must be stored at local node n by the element. The default is 0, until over-ridden by a particular element. For example, a Poisson equation requires only one value to be stored at each node; 2D Navier–Stokes equations require two values (velocity components) to be stored at each Node (provided that the pressure interpolation is discontinuous). More...

unsigned	nnodal_position_type () const
	Return the number of coordinate types that the element requires to interpolate the geometry between the nodes. For Lagrange elements it is 1. More...

bool	has_hanging_nodes () const
	Return boolean to indicate if any of the element's nodes are geometrically hanging. More...

unsigned	nodal_dimension () const
	Return the required Eulerian dimension of the nodes in this element. More...

int	get_node_number (Node *const &node_pt) const
	Return the number of the node *node_pt if this node is in the element, else return -1;. More...

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const
	If there is a node at this local coordinate, return the pointer to the node. More...

double	raw_nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n but do NOT take hanging nodes into account. More...

double	raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps), but do NOT take hanging nodes into account. More...

double	nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n. Produces suitably interpolated values for hanging nodes. More...

double	nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps). Produces suitably interpolated values for hanging nodes. More...

unsigned	dim () const
	Return the spatial dimension of the element, i.e. the number of local coordinates required to parametrise its geometry. More...

virtual ElementGeometry::ElementGeometry	element_geometry () const
	Return the geometry type of the element (either Q or T usually). More...

virtual double	interpolated_x (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s. More...

virtual double	interpolated_x (const unsigned &t, const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s at previous timestep t (t=0: present; t>0: previous timestep) More...

virtual void	interpolated_x (const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s as Vector. More...

virtual void	interpolated_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s at previous timestep t as Vector (t=0: present; t>0: previous timestep) More...

virtual double	interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)
	Return t-th time-derivative of the i-th FE-interpolated Eulerian coordinate at local coordinate s. More...

virtual void	interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)
	Compte t-th time-derivative of the FE-interpolated Eulerian coordinate vector at local coordinate s. More...

void	position (const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its incarnation as a GeomObject, r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s). More...

void	position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its GeomObject incarnation: r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s) This version of the function returns the position as a function of time t=0: current time; t>0: previous timestep. Works for t=0 but needs to be overloaded if genuine time-dependence is required. More...

void	dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)
	Return the t-th time derivative of the parametrised position of the FiniteElement in its GeomObject incarnation: $\frac{d^{t} dr(zeta)}{d t^{t}}$ . Call the t-th time derivative of the FE-interpolated Eulerian coordinate. More...

void	interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const
	Calculate the interpolated value of zeta, the intrinsic coordinate of the element when viewed as a compound geometric object within a Mesh as a function of the local coordinate of the element, s. The default assumption is the zeta is interpolated using the shape functions of the element with the values given by zeta_nodal(). A MacroElement representation of the intrinsic coordinate parametrised by the local coordinate s is used if available. Choosing the MacroElement representation of zeta (Eulerian x by default) allows a correspondence to be established between elements on different Meshes covering the same curvilinear domain in cases where one element is much coarser than the other. More...

void	locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)
	For a given value of zeta, the "global" intrinsic coordinate of a mesh of FiniteElements represented as a compound geometric object, find the local coordinate in this element that corresponds to the requested value of zeta. If zeta cannot be located in this element, geom_object_pt is set to NULL. If zeta is located in this element, we return its "this" pointer. By default don't use any value passed in to the local coordinate s as the initial guess in the Newton method. More...

virtual void	node_update ()
	Update the positions of all nodes in the element using each node update function. The default implementation may be overloaded so that more efficient versions can be written. More...

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

double	size () const
	Calculate the size of the element (length, area, volume,...) in Eulerian computational coordinates. Use suitably overloaded compute_physical_size() function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

virtual double	compute_physical_size () const
	Broken virtual function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

virtual void	point_output_data (const Vector< double > &s, Vector< double > &data)
	Virtual function to write the double precision numbers that appear in a single line of output into the data vector. Empty virtual, can be overloaded for specific elements; used e.g. by LineVisualiser. More...

void	point_output (std::ostream &outfile, const Vector< double > &s)
	Output solution (as defined by point_output_data()) at local cordinates s. More...

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const
	Return the number of actual plot points for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const
	Return the number of local sub-elements for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) const
	Paraview output – this outputs the coordinates at the plot points (for parameter nplot) to specified output file. More...

virtual void	write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const
	Fill in the offset information for paraview plot. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const
	Return the paraview element type. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const
	Return the offsets for the paraview sub-elements. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual unsigned	nscalar_paraview () const
	Number of scalars/fields output by this element. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual std::string	scalar_name_paraview (const unsigned &i) const
	Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names in specific elements. More...

virtual void	output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const
	Output the element data at time step t. This is const because it is newly added and so can be done easily. Really all the output(...) functions should be const! More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output a time-dependent exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const
	Output a time-dependent exact solution over the element. More...

virtual void	get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const
	Get cector of local coordinates of plot point i (when plotting nplot points in each "coordinate direction"). Generally these plot points will be uniformly spaced across the element. The optional final boolean flag (default: false) allows them to be shifted inwards to avoid duplication of plot point points between elements – useful when they are used in locate_zeta, say. More...

virtual std::string	tecplot_zone_string (const unsigned &nplot) const
	Return string for tecplot zone header (when plotting nplot points in each "coordinate direction") More...

virtual void	write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const
	Add tecplot zone "footer" to output stream (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual void	write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const
	Add tecplot zone "footer" to C-style output. (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual unsigned	nplot_points (const unsigned &nplot) const
	Return total number of plot points (when plotting nplot points in each "coordinate direction") More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the norm of the error and that of the exact solution. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Plot the error when compared against a given time-dependent exact solution ${\bf f}(t,{\bf x})$ . Also calculates the norm of the error and that of the exact solution. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Plot the error when compared against a given time-dependent exact solution ${\bf f}(t,{\bf x})$ . Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the maximum absolute error. More...

void	integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
	Evaluate integral of a Vector-valued function ${\bf f}({\bf x})$ over the element. More...

void	integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
	Evaluate integral of a Vector-valued, time-dependent function ${\bf f}(t,{\bf x})$ over the element. More...

virtual void	build_face_element (const int &face_index, FaceElement *face_element_pt)
	Function for building a lower dimensional FaceElement on the specified face of the FiniteElement. The arguments are the index of the face, an integer whose value depends on the particular element type, and a pointer to the FaceElement. More...

virtual unsigned	self_test ()
	Self-test: Check inversion of element & do self-test for GeneralisedElement. Return 0 if OK. More...

virtual unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const
	Get the number of the ith node on face face_index (in the bulk node vector). More...

virtual int	face_outer_unit_normal_sign (const int &face_index) const
	Get the sign of the outer unit normal on the face given by face_index. More...

virtual unsigned	nnode_on_face () const

void	face_node_number_error_check (const unsigned &i) const
	Range check for face node numbers. More...

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const
	Get a pointer to the function mapping face coordinates to bulk coordinates. More...

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const
	Get a pointer to the derivative of the mapping from face to bulk coordinates. More...

Public Member Functions inherited from oomph::GeneralisedElement
GeneralisedElement()	GeneralisedElement (const GeneralisedElement &)=delete
	Constructor: Initialise all pointers and all values to zero. More...

void	operator= (const GeneralisedElement &)=delete
	Broken assignment operator. More...

Data *&	internal_data_pt (const unsigned &i)
	Return a pointer to i-th internal data object. More...

Data *const &	internal_data_pt (const unsigned &i) const
	Return a pointer to i-th internal data object (const version) More...

Data *&	external_data_pt (const unsigned &i)
	Return a pointer to i-th external data object. More...

Data *const &	external_data_pt (const unsigned &i) const
	Return a pointer to i-th external data object (const version) More...

unsigned long	eqn_number (const unsigned &ieqn_local) const
	Return the global equation number corresponding to the ieqn_local-th local equation number. More...

int	local_eqn_number (const unsigned long &ieqn_global) const
	Return the local equation number corresponding to the ieqn_global-th global equation number. Returns minus one (-1) if there is no local degree of freedom corresponding to the chosen global equation number. More...

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) external data object to the element and return its index (i.e. the index required to obtain it from the access function `external_data_pt(...)`. The optional boolean flag indicates whether the data should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite-differencing. More...

bool	external_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the external data is included in the finite difference loop. More...

void	exclude_external_data_fd (const unsigned &i)
	Set the boolean flag to exclude the external datum from the the finite difference loop when computing the jacobian matrix. More...

void	include_external_data_fd (const unsigned &i)
	Set the boolean flag to include the external datum in the the finite difference loop when computing the jacobian matrix. More...

void	flush_external_data ()
	Flush all external data. More...

void	flush_external_data (Data *const &data_pt)
	Flush the object addressed by data_pt from the external data array. More...

unsigned	ninternal_data () const
	Return the number of internal data objects. More...

unsigned	nexternal_data () const
	Return the number of external data objects. More...

unsigned	ndof () const
	Return the number of equations/dofs in the element. More...

void	dof_vector (const unsigned &t, Vector< double > &dof)
	Return the vector of dof values at time level t. More...

void	dof_pt_vector (Vector< double * > &dof_pt)
	Return the vector of pointers to dof values. More...

void	set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)
	Set the timestepper associated with the i-th internal data object. More...

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)
	Assign the global equation numbers to the internal Data. The arguments are the current highest global equation number (which will be incremented) and a Vector of pointers to the global variables (to which any unpinned values in the internal Data are added). More...

void	describe_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the dofs of the element. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)
	Add pointers to the internal data values to map indexed by the global equation number. More...

void	add_internal_data_values_to_vector (Vector< double > &vector_of_values)
	Add all internal data and time history values to the vector in the internal storage order. More...

void	read_internal_data_values_from_vector (const Vector< double > &vector_of_values, unsigned &index)
	Read all internal data and time history values from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

void	add_internal_eqn_numbers_to_vector (Vector< long > &vector_of_eqn_numbers)
	Add all equation numbers associated with internal data to the vector in the internal storage order. More...

void	read_internal_eqn_numbers_from_vector (const Vector< long > &vector_of_eqn_numbers, unsigned &index)
	Read all equation numbers associated with internal data from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)
	Setup the arrays of local equation numbers for the element. If the optional boolean argument is true, then pointers to the associated degrees of freedom are stored locally in the array Dof_pt. More...

virtual void	complete_setup_of_dependencies ()
	Complete the setup of any additional dependencies that the element may have. Empty virtual function that may be overloaded for specific derived elements. Used, e.g., for elements with algebraic node update functions to determine the "geometric Data", i.e. the Data that affects the element's shape. This function is called (for all elements) at the very beginning of the equation numbering procedure to ensure that all dependencies are accounted for. More...

virtual void	get_residuals (Vector< double > &residuals)
	Calculate the vector of residuals of the equations in the element. By default initialise the vector to zero and then call the fill_in_contribution_to_residuals() function. Note that this entire function can be overloaded if desired. More...

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the elemental Jacobian matrix "d equation / d variable". More...

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and the elemental "mass" matrix, the matrix that multiplies the time derivative terms in a problem. More...

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and jacobian and elemental "mass" matrix, the matrix that multiplies the time derivative terms. More...

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Calculate the derivatives of the residuals with respect to a parameter. More...

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Calculate the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. More...

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
	Calculate the derivatives of the elemental Jacobian matrix mass matrix and residuals with respect to a parameter. More...

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Calculate the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Return the vector of inner product of the given pairs of history values. More...

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Compute the vectors that when taken as a dot product with other history values give the inner product over the element. More...

virtual void	compute_norm (Vector< double > &norm)
	Compute norm of solution – broken virtual can be overloaded by element writer to implement whatever norm is desired for the specific element. More...

void	set_halo (const unsigned &non_halo_proc_ID)
	Label the element as halo and specify processor that holds non-halo counterpart. More...

void	set_nonhalo ()
	Label the element as not being a halo. More...

bool	is_halo () const
	Is this element a halo? More...

int	non_halo_proc_ID ()
	ID of processor ID that holds non-halo counterpart of halo element; negative if not a halo. More...

void	set_must_be_kept_as_halo ()
	Insist that this element be kept as a halo element during a distribute? More...

void	unset_must_be_kept_as_halo ()
	Do not insist that this element be kept as a halo element during distribution. More...

bool	must_be_kept_as_halo () const
	Test whether the element must be kept as a halo element. More...

Public Member Functions inherited from oomph::GeomObject
	GeomObject ()
	Default constructor. More...

	GeomObject (const unsigned &ndim)
	Constructor: Pass dimension of geometric object (# of Eulerian coords = # of Lagrangian coords; no time history available/needed) More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)
	Constructor: pass # of Eulerian and Lagrangian coordinates. No time history available/needed. More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)
	Constructor: pass # of Eulerian and Lagrangian coordinates and pointer to time-stepper which is used to handle the position at previous timesteps and allows the evaluation of veloc/acceleration etc. in cases where the GeomData varies with time. More...

	GeomObject (const GeomObject &dummy)=delete
	Broken copy constructor. More...

void	operator= (const GeomObject &)=delete
	Broken assignment operator. More...

virtual	~GeomObject ()
	(Empty) destructor More...

unsigned	nlagrangian () const
	Access function to # of Lagrangian coordinates. More...

unsigned	ndim () const
	Access function to # of Eulerian coordinates. More...

void	set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
	Set # of Lagrangian and Eulerian coordinates. More...

TimeStepper *&	time_stepper_pt ()
	Access function for pointer to time stepper: Null if object is not time-dependent. More...

TimeStepper *	time_stepper_pt () const
	Access function for pointer to time stepper: Null if object is not time-dependent. Const version. More...

virtual void	position (const double &t, const Vector< double > &zeta, Vector< double > &r) const
	Parametrised position on object: r(zeta). Evaluated at the continuous time value, t. More...

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const
	Derivative of position Vector w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const
	2nd derivative of position Vector w.r.t. to coordinates: $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const
	Posn Vector and its 1st & 2nd derivatives w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

Public Member Functions inherited from oomph::RefineablePVDEquations< DIM >
	RefineablePVDEquations ()
	Constructor. More...

void	fill_in_generic_contribution_to_residuals_pvd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)
	Call the residuals including hanging node cases. More...

void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)
	No values are interpolated in this element (pure solid) More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)
	No values are interpolated in this element (pure solid) More...

unsigned	num_Z2_flux_terms ()
	Number of 'flux' terms for Z2 error estimation. More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)
	Get 'flux' for Z2 error recovery: Upper triangular entries in strain tensor. More...

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 0 (pure solid problem) More...

virtual Node *	solid_pressure_node_pt (const unsigned &l)

void	further_build ()
	Further build function, pass the pointers down to the sons. More...

Public Member Functions inherited from oomph::RefineableSolidElement
	RefineableSolidElement ()
	Constructor. More...

virtual	~RefineableSolidElement ()
	Virtual Destructor, delete any allocated storage. More...

void	assign_solid_local_eqn_numbers (const bool &store_local_dof_pt)
	Overload the local equation numbers for Data stored as part of solid nodes to include hanging node data. More...

unsigned	ngeom_data () const
	The number of geometric data affecting a RefineableSolidFiniteElement is the positional Data of all non-hanging nodes plus the geometric Data of all distinct master nodes. Recomputed on the fly. More...

Data *	geom_data_pt (const unsigned &j)
	Return pointer to the j-th Data item that the object's shape depends on: Positional data of non-hanging nodes and positional data of master nodes. Recomputed on the fly. More...

void	identify_geometric_data (std::set< Data * > &geometric_data_pt)
	Specify Data that affects the geometry of the element by adding the position Data to the set that's passed in. (This functionality is required in FSI problems; set is used to avoid double counting). Refineable version includes hanging nodes. More...

void	fill_in_jacobian_from_solid_position_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Compute element residual Vector and element Jacobian matrix corresponding to the solid positions. Overloaded version to take the hanging nodes into account. More...

bool	is_undeformed_macro_element_used_for_new_lagrangian_coords () const
	Return the flag deciding if the Lagrangian coordinates of newly-created interior SolidNodes are to be determined by the father element's undeformed MacroElement representation (if it has one). Default: False as it means that, following a refinement an element is no longer in equilbrium (as the Lagrangian coordinate is determined differently from the Eulerian one). However, basing the Lagrangian coordinates on the undeformed MacroElement can be more stable numerically and for steady problems it's not a big deal either way as the difference between the two formulations only matters at finite resolution so we have no right to say that one is "more correct" than the other... More...

void	enable_use_of_undeformed_macro_element_for_new_lagrangian_coords ()
	Set the flag deciding if the Lagrangian coordinates of newly-created interior SolidNodes are to be determined by the father element's undeformed MacroElement representation (if it has one). More...

void	disable_use_of_undeformed_macro_element_for_new_lagrangian_coords ()
	Unset the flag deciding if the Lagrangian coordinates of newly-created interior SolidNodes are to be determined by the father element's undeformed MacroElement representation (if it has one). More...

DenseMatrix< int > &	local_position_hang_eqn (Node *const &node_pt)
	Access the local equation number of of hanging node variables associated with nodal positions. The function returns a dense matrix that contains all the local equation numbers corresponding to the positional degrees of freedom. More...

Public Member Functions inherited from oomph::RefineableElement
	RefineableElement ()
	Constructor, calls the FiniteElement constructor and initialises the member data. More...

virtual	~RefineableElement ()
	Destructor, delete the allocated storage for the hanging equations. More...

	RefineableElement (const RefineableElement &)=delete
	Broken copy constructor. More...

void	operator= (const RefineableElement &)=delete
	Broken assignment operator. More...

Tree *	tree_pt ()
	Access function: Pointer to quadtree representation of this element. More...

void	set_tree_pt (Tree *my_tree_pt)
	Set pointer to quadtree representation of this element. More...

virtual unsigned	required_nsons () const
	Set the number of sons that can be constructed by the element The default is none. More...

bool	refinement_is_enabled ()
	Flag to indicate suppression of any refinement. More...

void	disable_refinement ()
	Suppress of any refinement for this element. More...

void	enable_refinement ()
	Emnable refinement for this element. More...

template<class ELEMENT >
void	split (Vector< ELEMENT * > &son_pt) const
	Split the element into the number of sons to be constructed and return a vector of pointers to the sons. Elements are allocated, but they are not given any properties. The refinement level of the sons is one higher than that of the father elemern. More...

int	local_hang_eqn (Node *const &node_pt, const unsigned &i)
	Access function that returns the local equation number for the hanging node variables (values stored at master nodes). The local equation number corresponds to the i-th unknown stored at the node addressed by node_pt. More...

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)=0
	Interface to function that builds the element: i.e. construct the nodes, assign their positions, apply boundary conditions, etc. The required procedures depend on the geometrical type of the element and must be implemented in specific refineable elements. Any new nodes created during the build process are returned in the vector new_node_pt. More...

void	set_refinement_level (const int &refine_level)
	Set the refinement level. More...

unsigned	refinement_level () const
	Return the Refinement level. More...

void	select_for_refinement ()
	Select the element for refinement. More...

void	deselect_for_refinement ()
	Deselect the element for refinement. More...

void	select_sons_for_unrefinement ()
	Unrefinement will be performed by merging the four sons of this element. More...

void	deselect_sons_for_unrefinement ()
	No unrefinement will be performed by merging the four sons of this element. More...

bool	to_be_refined ()
	Has the element been selected for refinement? More...

bool	sons_to_be_unrefined ()
	Has the element been selected for unrefinement? More...

virtual void	unbuild ()
	Unbuild the element, i.e. mark the nodes that were created during its creation for possible deletion. More...

virtual void	deactivate_element ()
	Final operations that must be performed when the element is no longer active in the mesh, but still resident in the QuadTree. More...

virtual bool	nodes_built ()
	Return true if all the nodes have been built, false if not. More...

long	number () const
	Element number (for debugging/plotting) More...

void	set_number (const long &mynumber)
	Set element number (for debugging/plotting) More...

virtual Node *	interpolating_node_pt (const unsigned &n, const int &value_id)
	In mixed elements, different sets of nodes are used to interpolate different unknowns. This function returns the n-th node that interpolates the value_id-th unknown. Default implementation is that all variables use the positional nodes, i.e. isoparametric elements. Note that any overloaded versions of this function MUST provide a set of nodes for the position, which always has the value_id -1. More...

virtual double	local_one_d_fraction_of_interpolating_node (const unsigned &n1d, const unsigned &i, const int &value_id)
	Return the local one dimensional fraction of the n1d-th node in the direction of the local coordinate s[i] that is used to interpolate the value_id-th continuously interpolated unknown. Default assumes isoparametric interpolation for all unknowns. More...

virtual Node *	get_interpolating_node_at_local_coordinate (const Vector< double > &s, const int &value_id)
	Return a pointer to the node that interpolates the value-id-th unknown at local coordinate s. If there is not a node at that position, then return 0. More...

virtual unsigned	ninterpolating_node (const int &value_id)
	Return the number of nodes that are used to interpolate the value_id-th unknown. Default is to assume isoparametric elements. More...

virtual unsigned	ninterpolating_node_1d (const int &value_id)
	Return the number of nodes in a one_d direction that are used to interpolate the value_id-th unknown. Default is to assume an isoparametric mapping. More...

virtual void	interpolating_basis (const Vector< double > &s, Shape &psi, const int &value_id) const
	Return the basis functions that are used to interpolate the value_id-th unknown. By default assume isoparameteric interpolation. More...

virtual void	check_integrity (double &max_error)=0
	Check the integrity of the element: Continuity of positions values, etc. Essentially, check that the approximation of the functions is consistent when viewed from both sides of the element boundaries Must be overloaded for each different geometric element. More...

void	identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data)
	The purpose of this function is to identify all possible Data that can affect the fields interpolated by the FiniteElement. This must be overloaded to include data from any hanging nodes correctly. More...

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)
	Overload the function that assigns local equation numbers for the Data stored at the nodes so that hanging data is taken into account. More...

virtual RefineableElement *	root_element_pt ()
	Pointer to the root element in refinement hierarchy (must be implemented in specific elements that do refinement via tree-like refinement structure. Here we provide a default implementation that is appropriate for cases where tree-like refinement doesn't exist or if the element doesn't have root in that tree (i.e. if it's a root itself): We return "this". More...

virtual RefineableElement *	father_element_pt () const
	Return a pointer to the father element. More...

void	get_father_at_refinement_level (unsigned &refinement_level, RefineableElement *&father_at_reflevel_pt)
	Return a pointer to the "father" element at the specified refinement level. More...

virtual void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)
	Initial setup of the element: e.g. set the appropriate internal p-order. If an adopted father is specified, information from this is used instead of using the father found from the tree. More...

virtual void	pre_build (Mesh &mesh_pt, Vector< Node > &new_node_pt)
	Pre-build the element. More...

virtual void	setup_hanging_nodes (Vector< std::ofstream * > &output_stream)
	Mark up any hanging nodes that arise as a result of non-uniform refinement. Any hanging nodes will be documented in files addressed by the streams in the vector output_stream, if the streams are open. More...

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)
	Compute derivatives of elemental residual vector with respect to nodal coordinates. Default implementation by FD can be overwritten for specific elements. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij} This version is overloaded from the version in FiniteElement and takes hanging nodes into account – j in the above loop loops over all the nodes that actively control the shape of the element (i.e. they are non-hanging or master nodes of hanging nodes in this element). More...

unsigned	nshape_controlling_nodes ()
	Number of shape-controlling nodes = the number of non-hanging nodes plus the number of master nodes associated with hanging nodes. More...

std::map< Node *, unsigned >	shape_controlling_node_lookup ()
	Return lookup scheme for unique number associated with any of the nodes that actively control the shape of the element (i.e. they are either non-hanging nodes of this element or master nodes of hanging nodes. More...

Public Member Functions inherited from oomph::ElementWithZ2ErrorEstimator
	ElementWithZ2ErrorEstimator ()
	Default empty constructor. More...

	ElementWithZ2ErrorEstimator (const ElementWithZ2ErrorEstimator &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithZ2ErrorEstimator &)=delete
	Broken assignment operator. More...

virtual unsigned	ncompound_fluxes ()
	A stuitable error estimator for a multi-physics elements may require one Z2 error estimate for each field (e.g. velocity and temperature in a fluid convection problem). It is assumed that these error estimates will each use selected flux terms. The number of compound fluxes returns the number of such combinations of the flux terms. Default value is one and all flux terms are combined with equal weight. More...

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)
	Plot the error when compared against a given exact flux. Also calculates the norm of the error and that of the exact flux. More...

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)
	Return the compound flux index of each flux component The default (do nothing behaviour) will mean that all indices remain at the default value zero. More...

virtual double	geometric_jacobian (const Vector< double > &x)
	Return the geometric jacobian (should be overloaded in cylindrical and spherical geometries). Default value one is suitable for Cartesian coordinates. More...

Public Member Functions inherited from oomph::RefineableSolidQElement< DIM >
	RefineableSolidQElement ()
	Empty constuctor. More...

Additional Inherited Members
Public Types inherited from oomph::PVDEquationsBase< DIM >
typedef void(*	IsotropicGrowthFctPt) (const Vector< double > &xi, double &gamma)
	Function pointer to function that specifies the isotropic growth as a function of the Lagrangian coordinates FCT(xi,gamma(xi)) – xi is a Vector! More...

typedef double(*	PrestressFctPt) (const unsigned &i, const unsigned &j, const Vector< double > &xi)
	Function pointer to function that specifies the pre-stress sigma_0(i,j) as a function of the Lagrangian coordinates FCT(i,j,xi) – xi is a Vector! More...

typedef void(*	BodyForceFctPt) (const double &t, const Vector< double > &xi, Vector< double > &b)
	Function pointer to function that specifies the body force as a function of the Lagrangian coordinates and time FCT(t,xi,b) – xi and b are Vectors! More...

Public Types inherited from oomph::SolidFiniteElement
typedef double(*	MultiplierFctPt) (const Vector< double > &xi)
	Pointer to function that computes the "multiplier" for the inertia terms in the consistent determination of the initial conditions for Newmark timestepping. More...

Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)
	Function pointer for function that computes vector-valued steady "exact solution" ${\bf f}({\bf x})$ as $\mbox{\tt fct}({\bf x}, {\bf f})$ . More...

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)
	Function pointer for function that computes Vector-valued time-dependent function ${\bf f}(t,{\bf x})$ as $\mbox{\tt fct}(t, {\bf x}, {\bf f})$ . More...

Static Public Member Functions inherited from oomph::PVDEquationsBase< DIM >
static void	pin_redundant_nodal_solid_pressures (const Vector< GeneralisedElement * > &element_pt)
	Loop over all elements in Vector (which typically contains all the elements in a refineable solid mesh) and pin the nodal solid pressure degrees of freedom that are not being used. Function uses the member function. More...

static void	unpin_all_solid_pressure_dofs (const Vector< GeneralisedElement * > &element_pt)
	Unpin all pressure dofs in elements listed in vector. More...

Static Public Member Functions inherited from oomph::RefineableElement
static double &	max_integrity_tolerance ()
	Max. allowed discrepancy in element integrity check. More...

Static Public Attributes inherited from oomph::FiniteElement
static double	Tolerance_for_singular_jacobian = 1.0e-16
	Tolerance below which the jacobian is considered singular. More...

static bool	Accept_negative_jacobian = false
	Boolean that if set to true allows a negative jacobian in the transform between global and local coordinates (negative surface area = left-handed coordinate system). More...

static bool	Suppress_output_while_checking_for_inverted_elements
	Static boolean to suppress output while checking for inverted elements. More...

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_any_repeated_data = false
	Static boolean to suppress warnings about repeated data. Defaults to false. More...

static bool	Suppress_warning_about_repeated_internal_data
	Static boolean to suppress warnings about repeated internal data. Defaults to false. More...

static bool	Suppress_warning_about_repeated_external_data = true
	Static boolean to suppress warnings about repeated external data. Defaults to true. More...

static double	Default_fd_jacobian_step = 1.0e-8
	Double used for the default finite difference step in elemental jacobian calculations. More...

Protected Member Functions inherited from oomph::PVDEquations< DIM >
void	get_stress (const DenseMatrix< double > &g, const DenseMatrix< double > &G, DenseMatrix< double > &sigma)
	Return the 2nd Piola Kirchhoff stress tensor, as calculated from the constitutive law: Pass metric tensors in the stress free and current configurations. More...

void	get_d_stress_dG_upper (const DenseMatrix< double > &g, const DenseMatrix< double > &G, const DenseMatrix< double > &sigma, RankFourTensor< double > &d_sigma_dG)
	Return the derivatives of the 2nd Piola Kirchhoff stress tensor, as calculated from the constitutive law: Pass metric tensors in the stress free and current configurations and the current value of the the stress tensor. More...

Protected Member Functions inherited from oomph::SolidFiniteElement
void	fill_in_generic_jacobian_for_solid_ic (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)
	Helper function to fill in the residuals and (if flag==1) the Jacobian for the setup of an initial condition. The global equations are: More...

void	set_nnodal_lagrangian_type (const unsigned &nlagrangian_type)
	Set the number of types required to interpolate the Lagrangian coordinates. More...

virtual double	local_to_lagrangian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to lagrangian coordinates, given the derivatives of the shape functions w.r.t. local coorindates. Return the determinant of the jacobian, the jacobian and inverse jacobian. More...

double	local_to_lagrangian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to lagrangian coordinates, given the derivatives of the shape functions w.r.t. local coordinates, Return only the determinant of the jacobian and the inverse of the mapping (ds/dx) More...

void	describe_solid_local_dofs (std::ostream &out, const std::string &current_string) const
	Classifies dofs locally for solid specific aspects. More...

void	fill_in_jacobian_from_solid_position_by_fd (DenseMatrix< double > &jacobian)
	Use finite differences to calculate the Jacobian entries corresponding to the solid positions. More...

virtual void	update_before_solid_position_fd ()
	Function that is called before the finite differencing of any solid position data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_solid_position_fd ()
	Function that is call after the finite differencing of the solid position data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_solid_position_fd (const unsigned &i)
	Function called within the finite difference loop for the solid position dat after a change in any values in the n-th node. More...

virtual void	reset_in_solid_position_fd (const unsigned &i)
	Function called within the finite difference loop for solid position data after the values in the i-th node are reset. The default behaviour is to call the update function. More...

Protected Member Functions inherited from oomph::FiniteElement
template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Take the matrix passed as jacobian and return its inverse in inverse_jacobian. This function is templated by the dimension of the element because matrix inversion cannot be written efficiently in a generic manner. More...

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	A template-free interface that takes the matrix passed as jacobian and return its inverse in inverse_jacobian. By default the function will use the dimension of the element to call the correct invert_jacobian(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

virtual double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates. Returns the determinant of the jacobian, the jacobian and inverse jacobian. More...

double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates, Return only the determinant of the jacobian and the inverse of the mapping (ds/dx). More...

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	A template-free interface that calculates the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. To do this it requires the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. By default the function will use the dimension of the element to call the correct dJ_eulerian_dnodal_coordinates_templated_helper(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

template<unsigned DIM>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij using the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. This function is templated by the dimension of the element. More...

virtual void	d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	A template-free interface that calculates the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions $\psi_j$ w.r.t. the global eulerian coordinates . I.e. this function calculates. More...

template<unsigned DIM>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates , using the determinant of the jacobian mapping, its derivative w.r.t. the nodal coordinates $X_{pq}$ , the inverse jacobian and the derivatives of the shape functions w.r.t. the local coordinates. The result is returned as a tensor of rank four. Numbering: d_dpsidx_dX(p,q,j,i) = $\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right)$ This function is templated by the dimension of the element. More...

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t.local coordinates to derivatives w.r.t the coordinates used to assemble the inverse_jacobian passed in the mapping. On entry, dbasis must contain the basis function derivatives w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates on exit. This is virtual so that it may be overloaded if desired for efficiency reasons. More...

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t local coordinates to derivatives w.r.t the coordinates used to assemble the inverse jacobian passed in the mapping, assuming that the coordinates are aligned in the direction of the local coordinates. On entry dbasis must contain the derivatives of the basis functions w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates. are converted into the new using the mapping inverse_jacobian. More...

virtual void	transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordiantes to derivatives and second derivatives w.r.t. the coordinates used to assemble the jacobian, inverse jacobian and jacobian2 passed to the function. By default this function will call transform_second_derivatives_template<>(...) using the dimension of the element as the template parameter. It is virtual so that it can be overloaded by a specific element to save using a switch statement. Optionally, the element writer may wish to use the transform_second_derivatives_diagonal<>(...) function On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

template<unsigned DIM>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This is templated by dimension because the method of calculation varies significantly with the dimension. On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

template<unsigned DIM>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This version of the function assumes that the local coordinates are aligned with the global coordinates, i.e. the jacobians are diagonal On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. More...

virtual void	update_before_nodal_fd ()
	Function that is called before the finite differencing of any nodal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_nodal_fd ()
	Function that is call after the finite differencing of the nodal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after a change in the i-th nodal value. More...

virtual void	reset_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after the i-th nodal values is reset. The default behaviour is to call the update function. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Zero-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	One-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Two-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Three-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Zero-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	One-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Two-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Three-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Zero-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	One-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Two-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Three-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly. Specialisation to two spatial dimensions. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert second derivatives w.r.t. local coordinates to second derivatives w.r.t. the coordinates passed in the tensor coordinate. Specialised to two spatial dimension. More...

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) internal data object to the element and return the index required to obtain it from the access function `internal_data_pt()`. The boolean indicates whether the datum should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite differencing. More...

bool	internal_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the internal data is included in the finite difference loop. More...

void	exclude_internal_data_fd (const unsigned &i)
	Set the boolean flag to exclude the internal datum from the finite difference loop when computing the jacobian matrix. More...

void	include_internal_data_fd (const unsigned &i)
	Set the boolean flag to include the internal datum in the finite difference loop when computing the jacobian matrix. More...

void	clear_global_eqn_numbers ()
	Clear the storage for the global equation numbers and pointers to dofs (if stored) More...

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)
	Add the contents of the queue global_eqn_numbers to the local storage for the local-to-global translation scheme. It is essential that the entries in the queue are added IN ORDER i.e. from the front. More...

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for the internal and external Data This must be called after the global equation numbers have all been assigned. It is virtual so that it can be overloaded by ElementWithExternalElements so that any external data from the external elements in included in the numbering scheme. If the boolean argument is true then pointers to the dofs will be stored in Dof_pt. More...

virtual void	assign_additional_local_eqn_numbers ()
	Setup any additional look-up schemes for local equation numbers. Examples of use include using local storage to refer to explicit degrees of freedom. The additional memory cost of such storage may or may not be offset by fast local access. More...

int	internal_local_eqn (const unsigned &i, const unsigned &j) const
	Return the local equation number corresponding to the j-th value stored at the i-th internal data. More...

int	external_local_eqn (const unsigned &i, const unsigned &j)
	Return the local equation number corresponding to the j-th value stored at the i-th external data. More...

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all external data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

virtual void	update_before_internal_fd ()
	Function that is called before the finite differencing of any internal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_internal_fd ()
	Function that is call after the finite differencing of the internal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after a change in any values in the i-th internal data object. More...

virtual void	reset_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	update_before_external_fd ()
	Function that is called before the finite differencing of any external data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_external_fd ()
	Function that is call after the finite differencing of the external data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after a change in any values in the i-th external data object. More...

virtual void	reset_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Add the elemental contribution to the mass matrix matrix. and the residuals vector. Note that this function should NOT initialise the residuals vector or the mass matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is deliberately broken. More...

virtual void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Add the elemental contribution to the jacobian matrix, mass matrix and the residuals vector. Note that this function should NOT initialise any entries. It must be called after the residuals vector and matrices have been initialised to zero. More...

virtual void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Add the elemental contribution to the derivatives of the residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More...

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Add the elemental contribution to the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More...

virtual void	fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
	Add the elemental contribution to the derivative of the jacobian matrix, mass matrix and the residuals vector with respect to the passed parameter. Note that this function should NOT initialise any entries. It must be called after the residuals vector and matrices have been initialised to zero. More...

virtual void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Fill in contribution to the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Fill in the contribution to the inner products between given pairs of history values. More...

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Fill in the contributions to the vectors that when taken as dot product with other history values give the inner product over the element. More...

Protected Member Functions inherited from oomph::RefineableSolidElement
void	assemble_local_to_lagrangian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const
	Assemble the jacobian matrix for the mapping from local to lagrangian coordinates, given the derivatives of the shape function Overload the standard version to use the hanging information for the lagrangian coordinates. More...

void	assemble_local_to_lagrangian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const
	Assemble the the "jacobian" matrix of second derivatives, given the second derivatives of the shape functions w.r.t. local coordinates Overload the standard version to use the hanging information for the lagrangian coordinates. More...

double	local_to_lagrangian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Lagrangian coordinates given the derivatives of the shape functions w.r.t the local coorindates. assuming that the coordinates are aligned in the direction of the local coordinates, i.e. there are no cross terms and the jacobian is diagonal. This function returns the determinant of the jacobian, the jacobian and the inverse jacobian. More...

Protected Member Functions inherited from oomph::RefineableElement
void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const
	Assemble the jacobian matrix for the mapping from local to Eulerian coordinates, given the derivatives of the shape function w.r.t the local coordinates. Overload the standard version to use the hanging information for the Eulerian coordinates. More...

void	assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const
	Assemble the the "jacobian" matrix of second derivatives of the mapping from local to Eulerian coordinates, given the second derivatives of the shape functions w.r.t. local coordinates. Overload the standard version to use the hanging information for the Eulerian coordinates. More...

void	assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const
	Assemble the covariant Eulerian base vectors, assuming that the derivatives of the shape functions with respect to the local coordinates have already been constructed. Overload the standard version to account for hanging nodes. More...

double	local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates given the derivatives of the shape functions w.r.t the local coordinates. assuming that the coordinates are aligned in the direction of the local coordinates, i.e. there are no cross terms and the jacobian is diagonal. This funciton returns the determinant of the jacobian, the jacobian and the inverse jacobian. Overload the standard version to take hanging info into account. More...

void	assign_hanging_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for hanging node variables. More...

virtual void	fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version is overloaded to take hanging node information into account. More...

Static Protected Member Functions inherited from oomph::RefineableElement
static void	check_value_id (const int &n_continuously_interpolated_values, const int &value_id)
	Static helper function that is used to check that the value_id is in range. More...

Protected Attributes inherited from oomph::PVDEquationsBase< DIM >
IsotropicGrowthFctPt	Isotropic_growth_fct_pt
	Pointer to isotropic growth function. More...

PrestressFctPt	Prestress_fct_pt
	Pointer to prestress function. More...

ConstitutiveLaw *	Constitutive_law_pt
	Pointer to the constitutive law. More...

double *	Lambda_sq_pt
	Timescale ratio (non-dim. density) More...

bool	Unsteady
	Flag that switches inertia on/off. More...

BodyForceFctPt	Body_force_fct_pt
	Pointer to body force function. More...

bool	Evaluate_jacobian_by_fd
	Use FD to evaluate Jacobian. More...

Protected Attributes inherited from oomph::SolidFiniteElement
MacroElement *	Undeformed_macro_elem_pt
	Pointer to the element's "undeformed" macro element (NULL by default) More...

SolidInitialCondition *	Solid_ic_pt
	Pointer to object that specifies the initial condition. More...

bool	Solve_for_consistent_newmark_accel_flag
	Flag to indicate which system of equations to solve when assigning initial conditions for time-dependent problems. If true, solve for the history value that corresponds to the acceleration in the Newmark scheme by demanding that the PDE is satisifed at the initial time. In this case the Jacobian is replaced by the mass matrix. More...

Protected Attributes inherited from oomph::FiniteElement
MacroElement *	Macro_elem_pt
	Pointer to the element's macro element (NULL by default) More...

Protected Attributes inherited from oomph::GeneralisedElement
int	Non_halo_proc_ID
	Non-halo processor ID for Data; -1 if it's not a halo. More...

bool	Must_be_kept_as_halo
	Does this element need to be kept as a halo element during a distribute? More...

Protected Attributes inherited from oomph::GeomObject
unsigned	NLagrangian
	Number of Lagrangian (intrinsic) coordinates. More...

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt
	Timestepper (used to handle access to geometry at previous timesteps) More...

Protected Attributes inherited from oomph::RefineableSolidElement
bool	Use_undeformed_macro_element_for_new_lagrangian_coords
	Flag deciding if the Lagrangian coordinates of newly-created interior SolidNodes are to be determined by the father element's undeformed MacroElement representation (if it has one). Default: False as it means that, following a refinement an element is no longer in equilbrium (as the Lagrangian coordinate is determined differently from the Eulerian one). However, basing the Lagrangian coordinates on the undeformed MacroElement can be more stable numerically and for steady problems it's not a big deal either way as the difference between the two formulations only matters at finite resolution so we have no right to say that one is "more correct" than the other... More...

Protected Attributes inherited from oomph::RefineableElement
Tree *	Tree_pt
	A pointer to a general tree object. More...

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

bool	Refinement_is_enabled
	Flag to indicate suppression of any refinement. More...

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

long	Number
	Global element number – for plotting/validation purposes. More...

Static Protected Attributes inherited from oomph::PVDEquationsBase< DIM >
static double	Default_lambda_sq_value = 1.0
	Static default value for timescale ratio (1.0 – for natural scaling) More...

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default return value for required_nvalue(n) which gives the number of "data" values required by the element at node n; for example, solving a Poisson equation would required only one "data" value at each node. The defaults is set to zero, because a general element is problem-less. More...

static const double	Node_location_tolerance = 1.0e-14
	Default value for the tolerance to be used when locating nodes via local coordinates. More...

static const unsigned	N2deriv [] = {0, 1, 3, 6}
	Static array that holds the number of second derivatives as a function of the dimension of the element. More...

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix
	Empty dense matrix used as a dummy argument to combined residual and jacobian functions in the case when only the residuals are being assembled. More...

static std::deque< double * >	Dof_pt_deque
	Static storage for deque used to add_global_equation_numbers when pointers to the dofs in each element are not required. More...

Static Protected Attributes inherited from oomph::RefineableElement
static double	Max_integrity_tolerance = 1.0e-8
	Max. allowed discrepancy in element integrity check. More...