A general Finite Element class. More...

#include <elements.h>

Inheritance diagram for oomph::FiniteElement:

Public Types
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...

Public Member Functions
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 &)
	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...

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)
	Set pointer to macro element – can be overloaded in derived elements to perform additional tasks. 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	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for Data stored at the nodes Virtual so that it can be overloaded by RefineableFiniteElements. If the boolean is true then the pointers to the degrees of freedom associated with each equation number are stored in Dof_pt. More...

virtual void	describe_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...

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...

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)
	Overloaded version of the calculation of the local equation numbers. If the boolean argument is true then pointers to the degrees of freedom associated with each equation number are stored locally in the array Dof_pt. 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	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}. 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...

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. Broken virtual function in "pure" finite elements. More...

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

virtual Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n)
	Construct the local node n as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. 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...

unsigned	ngeom_data () const
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...

Data *	geom_data_pt (const unsigned &j)
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. 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...

virtual double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
	Specify the values of the "global" intrinsic coordinate, zeta, of a compound geometric object (a mesh of elements) when the element is viewied as a sub-geometric object. The default assumption is that the element will be treated as a sub-geometric object in a bulk Mesh of other elements (geometric objects). The "global" coordinate of the compound geometric object is simply the Eulerian coordinate, x. The second default assumption is that the coordinate zeta will be stored at the nodes and interpolated using the shape functions of the element. This function returns the value of zeta stored at local node n, where k is the type of coordinate and i is the coordinate direction. The function is virtual so that it can be overloaded by different types of element: FaceElements and SolidFiniteElements. 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(). 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 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. The information will typically be used in interaction problems in which the FiniteElement provides a forcing term for an ElementWithExternalElement. The Data must be provided as `paired_load` data containing. More...

virtual void	identify_geometric_data (std::set< Data *> &geometric_data_pt)
	The purpose of this function is to identify all `Data` objects that affect the elements' geometry. This function is implemented as an empty virtual function since it can only be implemented in conjunction with a node-update strategy. A specific implementation is provided in the ElementWithMovingNodes class. 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

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 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 (std::ostream &outfile)
	Output the element data — typically the values at the nodes in a format suitable for post-processing. More...

virtual void	output (std::ostream &outfile, const unsigned &n_plot)
	Output the element data — pass (some measure of) the number of plot points per element. 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 (FILE *file_pt)
	Output the element data — typically the values at the nodes in a format suitable for post-processing. (C style output) More...

virtual void	output (FILE *file_pt, const unsigned &n_plot)
	Output the element data — pass (some measure of) the number of plot points per element (C style output) 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 (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. 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. 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

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

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

void	operator= (const GeneralisedElement &)
	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)

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 (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...

virtual unsigned	ndof_types () const
	The number of types of degrees of freedom in this element are sub-divided into. More...

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned > > &dof_lookup_list) const
	Create a list of pairs for the unknowns that this element is "in charge of" – ignore any unknowns associated with external `Data`. The first entry in each pair must contain the global equation number of the unknown, while the second one contains the number of the DOF type that this unknown is associated with. (The function can obviously only be called if the equation numbering scheme has been set up.) 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)
	Broken copy constructor. More...

void	operator= (const GeomObject &)
	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	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...

Static Public Attributes
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 =false
	Static boolean to suppress output while checking for inverted elements. More...

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data =false
	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
virtual 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. More...

virtual 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. More...

virtual 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. More...

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 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 function returns the determinant of the jacobian, the jacobian and the inverse jacobian. 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 $\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right).$ To do this it requires 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) = $\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right)$ By default the function will use the dimension of the element to call the correct d_dshape_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	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...

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 of the function assumes that the residuals vector has already been calculated. 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 slaved 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 slaved 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...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Add the elemental contribution to the jacobian matrix. and the residuals vector. Note that this function will NOT initialise the residuals vector or the jacobian matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is to use finite differences to calculate the jacobian. 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

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

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

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

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

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

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

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...

virtual void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Add the elemental contribution to the residuals vector. Note that this function will NOT initialise the residuals vector. It must be called after the residuals vector has been initialised to zero. 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 slaved 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 slaved 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 slaved 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 slaved 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 Attributes
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...

Static Protected Attributes
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...

Private Attributes
Integral *	Integral_pt
	Pointer to the spatial integration scheme. More...

Node **	Node_pt
	Storage for pointers to the nodes in the element. More...

int **	Nodal_local_eqn
	Storage for the local equation numbers associated with the values stored at the nodes. More...

unsigned	Nnode
	Number of nodes in the element. More...

unsigned	Elemental_dimension
	The spatial dimension of the element, i.e. the number of local coordinates used to parametrize it. More...

unsigned	Nodal_dimension
	The spatial dimension of the nodes in the element. We assume that nodes have the same spatial dimension, because we cannot think of any "real" problems for which that would not be the case. More...

unsigned	Nnodal_position_type
	The number of coordinate types required to interpolate the element's geometry between the nodes. For Lagrange elements it is 1 (the default). It must be over-ridden by using the set_nposition_type() function in the constructors of elements that use generalised coordinate, e.g. for 1D Hermite elements Nnodal_position_types =2. More...

Detailed Description

A general Finite Element class.

The main components of a FiniteElement are:

pointers to its Nodes
pointers to its internal Data (inherited from GeneralisedElement)
pointers to its external Data (inherited from GeneralisedElement)
a pointer to a spatial integration scheme
a pointer to the global Time object (inherited from GeneralisedElement)
a lookup table which establishes the relation between local and global equation numbers (inherited from GeneralisedElement)

We also provide interfaces for functions that compute the element's Jacobian matrix and/or the Vector of residuals (inherited from GeneralisedElement) plus various output routines.

Definition at line 1274 of file elements.h.

Member Typedef Documentation

◆ SteadyExactSolutionFctPt

typedef void(* oomph::FiniteElement::SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)

Function pointer for function that computes vector-valued steady "exact solution" ${\bf f}({\bf x})$ as $\mbox{\tt fct}({\bf x}, {\bf f})$ .

Definition at line 1723 of file elements.h.

◆ UnsteadyExactSolutionFctPt

typedef void(* oomph::FiniteElement::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 $\mbox{\tt fct}(t, {\bf x}, {\bf f})$ .

Definition at line 1729 of file elements.h.

Constructor & Destructor Documentation

◆ FiniteElement() [1/2]

oomph::FiniteElement::FiniteElement ( )

inline

Constructor.

Definition at line 1746 of file elements.h.

◆ ~FiniteElement()

oomph::FiniteElement::~FiniteElement ( )

virtual

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.

The destructor cleans up the memory allocated for storage of pointers to nodes. Internal and external data get wiped by the GeneralisedElement destructor; nodes get killed in mesh destructor.

Definition at line 3113 of file elements.cc.

◆ FiniteElement() [2/2]

oomph::FiniteElement::FiniteElement ( const FiniteElement & )

inline

Broken copy constructor.

Definition at line 1758 of file elements.h.

References oomph::BrokenCopy::broken_copy().

Member Function Documentation

◆ assemble_eulerian_base_vectors()

void oomph::FiniteElement::assemble_eulerian_base_vectors	(	const DShape &	dpsids,
		DenseMatrix< double > &	interpolated_G
	)		const

protectedvirtual

Assemble the covariant Eulerian base vectors, assuming that the derivatives of the shape functions with respect to the local coordinates have already been constructed.

Assemble the covariant Eulerian base vectors and return them in the matrix interpolated_G. The derivatives of the shape functions with respect to the local coordinate should already have been calculated before calling this function

Reimplemented in oomph::RefineableElement.

Definition at line 1989 of file elements.cc.

References i.

◆ assemble_local_to_eulerian_jacobian()

void oomph::FiniteElement::assemble_local_to_eulerian_jacobian	(	const DShape &	dpsids,
		DenseMatrix< double > &	jacobian
	)		const

protectedvirtual

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.

Internal function that is used to assemble the jacobian of the mapping from local coordinates (s) to the eulerian coordinates (x), given the derivatives of the shape functions. The entire jacobian matrix is constructed and this function will only work if there are the same number of local coordinates as global coordinates (i.e. for "bulk" elements).

Reimplemented in oomph::RefineableElement.

Definition at line 1883 of file elements.cc.

References assemble_local_to_eulerian_jacobian2(), and i.

Referenced by check_jacobian().

◆ assemble_local_to_eulerian_jacobian2()

void oomph::FiniteElement::assemble_local_to_eulerian_jacobian2	(	const DShape &	d2psids,
		DenseMatrix< double > &	jacobian2
	)		const

protectedvirtual

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.

Internal function that is used to assemble the jacobian of second derivatives of the mapping from local coordinates (s) to the eulerian coordinates (x), given the second derivatives of the shape functions.

Reimplemented in oomph::RefineableElement.

Definition at line 1944 of file elements.cc.

References i.

Referenced by assemble_local_to_eulerian_jacobian().

◆ assign_all_generic_local_eqn_numbers()

virtual void oomph::FiniteElement::assign_all_generic_local_eqn_numbers ( const bool & store_local_dof_pt )

inlinevirtual

Overloaded version of the calculation of the local equation numbers. If the boolean argument is true then pointers to the degrees of freedom associated with each equation number are stored locally in the array Dof_pt.

Reimplemented from oomph::GeneralisedElement.

Reimplemented in oomph::SolidFiniteElement, oomph::ElementWithSpecificMovingNodes< ELEMENT, NODE_TYPE >, oomph::ElementWithSpecificMovingNodes< ELEMENT, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< ELEMENT >, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< FaceGeometry< ELEMENT > >, SpineNode >, oomph::ElementWithSpecificMovingNodes< ELEMENT, AlgebraicNode >, oomph::ElementWithSpecificMovingNodes< ELEMENT, MacroElementNodeUpdateNode >, oomph::ElementWithMovingNodes, oomph::SpectralElement, oomph::FaceElementAsGeomObject< ELEMENT >, and oomph::RefineableQSpectralPoissonElement< DIM, NNODE_1D >.

Definition at line 2099 of file elements.h.

References oomph::GeneralisedElement::assign_all_generic_local_eqn_numbers().

Referenced by oomph::RefineableQSpectralPoissonElement< DIM, NNODE_1D >::assign_all_generic_local_eqn_numbers(), oomph::FaceElementAsGeomObject< ELEMENT >::assign_all_generic_local_eqn_numbers(), oomph::SpectralElement::assign_all_generic_local_eqn_numbers(), and oomph::SolidFiniteElement::assign_all_generic_local_eqn_numbers().

◆ assign_nodal_local_eqn_numbers()

void oomph::FiniteElement::assign_nodal_local_eqn_numbers ( const bool & store_local_dof_pt )

virtual

Assign the local equation numbers for Data stored at the nodes Virtual so that it can be overloaded by RefineableFiniteElements. If the boolean is true then the pointers to the degrees of freedom associated with each equation number are stored in Dof_pt.

This function loops over the nodal data of the element, adds the GLOBAL equation numbers to the local-to-global look-up scheme and fills in the Nodal_local_eqn look-up scheme for the local equation numbers If the boolean argument is true then pointers to the dofs will be stored in Dof_pt

Reimplemented in oomph::RefineableElement.

Definition at line 3475 of file elements.cc.

References oomph::GeneralisedElement::add_global_eqn_numbers(), oomph::Data::eqn_number(), oomph::GeneralisedElement::eqn_number(), fill_in_jacobian_from_nodal_by_fd(), i, oomph::Data::Is_pinned, oomph::Data::Is_unclassified, oomph::GeneralisedElement::local_eqn_number(), oomph::GeneralisedElement::ndof(), oomph::Data::nvalue(), and oomph::Data::value_pt().

Referenced by oomph::RefineableElement::assign_nodal_local_eqn_numbers().

◆ build_face_element()

void oomph::FiniteElement::build_face_element	(	const int &	face_index,
		FaceElement *	face_element_pt
	)

virtual

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.

Definition at line 5002 of file elements.cc.

References oomph::FaceElement::bulk_coordinate_derivatives_fct_pt(), oomph::FaceElement::bulk_element_pt(), oomph::FaceElement::bulk_node_number(), oomph::FaceElement::bulk_node_number_resize(), oomph::FaceElement::face_index(), oomph::FaceElement::face_to_bulk_coordinate_fct_pt(), i, oomph::FaceElement::Ignore_discontinuous_tangent_warning, oomph::FaceElement::nbulk_value(), oomph::FaceElement::nbulk_value_resize(), node_pt(), oomph::GeneralisedElement::Non_halo_proc_ID, oomph::FaceElement::normal_sign(), oomph::GeneralisedElement::set_halo(), and set_nodal_dimension().

◆ bulk_coordinate_derivatives_fct_pt()

virtual BulkCoordinateDerivativesFctPt oomph::FiniteElement::bulk_coordinate_derivatives_fct_pt ( const int & face_index ) const

inlinevirtual

Get a pointer to the derivative of the mapping from face to bulk coordinates.

Reimplemented in oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 3196 of file elements.h.

References oomph::Global_string_for_annotation::string().

Referenced by oomph::QElement< 1, NNODE_1D >::face_to_bulk_coordinate_fct_pt(), oomph::QElement< 2, NNODE_1D >::face_to_bulk_coordinate_fct_pt(), and oomph::QElement< 3, NNODE_1D >::face_to_bulk_coordinate_fct_pt().

◆ check_J_eulerian_at_knots()

void oomph::FiniteElement::check_J_eulerian_at_knots ( bool & passed ) const

Check that Jacobian of mapping between local and Eulerian coordinates at all integration points is positive.

Definition at line 4155 of file elements.cc.

References Accept_negative_jacobian.

Referenced by oomph::TetMeshBase::snap_nodes_onto_geometric_objects().

◆ check_jacobian()

void oomph::FiniteElement::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.

Internal function used to check for singular or negative values of the determinant of the Jacobian of the mapping between local and global or lagrangian coordinates. Negative jacobians are allowed if the Accept_negative_jacobian flag is set to true.

Definition at line 1724 of file elements.cc.

References assemble_local_to_eulerian_jacobian(), i, and Suppress_output_while_checking_for_inverted_elements.

Referenced by oomph::Mesh::check_inverted_elements(), oomph::RefineableElement::local_to_eulerian_mapping_diagonal(), and oomph::RefineableSolidElement::local_to_lagrangian_mapping_diagonal().

◆ compute_abs_error()

virtual void oomph::FiniteElement::compute_abs_error	(	std::ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		double &	error
	)

inlinevirtual

Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the maximum absolute error.

Definition at line 3107 of file elements.h.

References oomph::GeneralisedElement::self_test(), and oomph::Global_string_for_annotation::string().

◆ compute_error() [1/4]

virtual void oomph::FiniteElement::compute_error	(	std::ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		double &	error,
		double &	norm
	)

inlinevirtual

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.

Definition at line 3033 of file elements.h.

References oomph::Global_string_for_annotation::string().

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::compute_error(), oomph::BiharmonicEquations< DIM >::compute_error(), oomph::Mesh::compute_error(), oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::compute_error(), oomph::GeneralisedNewtonianNavierStokesEquations< DIM >::full_output(), oomph::NavierStokesEquations< DIM >::full_output(), oomph::UnsteadyHeatEquations< DIM >::output(), oomph::TimeHarmonicFourierDecomposedLinearElasticityEquations::output(), oomph::PMLTimeHarmonicLinearElasticityEquations< DIM, PML_ELEMENT >::output(), oomph::LinearElasticityEquations< DIM >::output(), and oomph::AxisymmetricLinearElasticityEquations::output().

◆ compute_error() [2/4]

virtual void oomph::FiniteElement::compute_error	(	std::ostream &	outfile,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt,
		const double &	time,
		double &	error,
		double &	norm
	)

inlinevirtual

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.

Definition at line 3049 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ compute_error() [3/4]

virtual void oomph::FiniteElement::compute_error	(	std::ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		Vector< double > &	error,
		Vector< double > &	norm
	)

inlinevirtual

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. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually.

Reimplemented in oomph::AxisymmetricPoroelasticityEquations, oomph::PoroelasticityEquations< DIM >, oomph::PoroelasticityEquations< 2 >, oomph::DarcyEquations< DIM >, and oomph::DarcyEquations< 2 >.

Definition at line 3068 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ compute_error() [4/4]

virtual void oomph::FiniteElement::compute_error	(	std::ostream &	outfile,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt,
		const double &	time,
		Vector< double > &	error,
		Vector< double > &	norm
	)

inlinevirtual

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. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually.

Reimplemented in oomph::AxisymmetricPoroelasticityEquations, oomph::PoroelasticityEquations< DIM >, oomph::PoroelasticityEquations< 2 >, oomph::EulerEquations< DIM >, and oomph::ScalarAdvectionEquations< DIM >.

Definition at line 3087 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ compute_physical_size()

virtual double oomph::FiniteElement::compute_physical_size ( ) const

inlinevirtual

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.

Reimplemented in oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesEquations, oomph::AxisymmetricPVDEquationsWithPressure, and oomph::AxisymmetricPVDEquations.

Definition at line 2677 of file elements.h.

◆ construct_boundary_node() [1/2]

virtual Node* oomph::FiniteElement::construct_boundary_node ( const unsigned & n )

inlinevirtual

Construct the local node n as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object.

Reimplemented in oomph::SolidFiniteElement, oomph::ElementWithSpecificMovingNodes< ELEMENT, NODE_TYPE >, oomph::ElementWithSpecificMovingNodes< ELEMENT, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< ELEMENT >, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< FaceGeometry< ELEMENT > >, SpineNode >, oomph::ElementWithSpecificMovingNodes< ELEMENT, AlgebraicNode >, and oomph::ElementWithSpecificMovingNodes< ELEMENT, MacroElementNodeUpdateNode >.

Definition at line 2420 of file elements.h.

Referenced by oomph::TetgenMesh< ELEMENT >::build_from_scaffold(), oomph::TriangleMesh< ELEMENT >::build_from_scaffold(), oomph::GmshTetMesh< ELEMENT >::build_from_scaffold(), oomph::BrickFromTetMesh< ELEMENT >::build_mesh(), oomph::DGElement::construct_boundary_nodes_and_faces(), oomph::Missing_masters_functions::construct_new_external_halo_node_helper(), oomph::Multi_domain_functions::construct_new_external_halo_node_helper(), oomph::RefineableTriangleMesh< ELEMENT >::construct_new_halo_node_helper(), oomph::RefineableTriangleMesh< ELEMENT >::construct_new_node_load_balance_helper(), oomph::GeompackQuadScaffoldMesh::GeompackQuadScaffoldMesh(), oomph::TetMeshBase::split_elements_in_corners(), oomph::TetgenScaffoldMesh::TetgenScaffoldMesh(), and oomph::TriangleScaffoldMesh::TriangleScaffoldMesh().

◆ construct_boundary_node() [2/2]

virtual Node* oomph::FiniteElement::construct_boundary_node	(	const unsigned &	n,
		TimeStepper *const &	time_stepper_pt
	)

inlinevirtual

Construct the local node n, including storage for history values required by timestepper, as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object.

Reimplemented in oomph::SolidFiniteElement, oomph::ElementWithSpecificMovingNodes< ELEMENT, NODE_TYPE >, oomph::ElementWithSpecificMovingNodes< ELEMENT, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< ELEMENT >, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< FaceGeometry< ELEMENT > >, SpineNode >, oomph::ElementWithSpecificMovingNodes< ELEMENT, AlgebraicNode >, and oomph::ElementWithSpecificMovingNodes< ELEMENT, MacroElementNodeUpdateNode >.

Definition at line 2435 of file elements.h.

◆ construct_node() [1/2]

virtual Node* oomph::FiniteElement::construct_node ( const unsigned & n )

inlinevirtual

Construct the local node n and return a pointer to the newly created node object.

Reimplemented in oomph::SolidFiniteElement, oomph::ElementWithSpecificMovingNodes< ELEMENT, NODE_TYPE >, oomph::ElementWithSpecificMovingNodes< ELEMENT, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< ELEMENT >, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< FaceGeometry< ELEMENT > >, SpineNode >, oomph::ElementWithSpecificMovingNodes< ELEMENT, AlgebraicNode >, and oomph::ElementWithSpecificMovingNodes< ELEMENT, MacroElementNodeUpdateNode >.

Definition at line 2392 of file elements.h.

Referenced by oomph::TetgenMesh< ELEMENT >::build_from_scaffold(), oomph::TriangleMesh< ELEMENT >::build_from_scaffold(), oomph::GmshTetMesh< ELEMENT >::build_from_scaffold(), oomph::BrickFromTetMesh< ELEMENT >::build_mesh(), oomph::DGElement::construct_boundary_nodes_and_faces(), oomph::Missing_masters_functions::construct_new_external_halo_node_helper(), oomph::Multi_domain_functions::construct_new_external_halo_node_helper(), oomph::RefineableTriangleMesh< ELEMENT >::construct_new_halo_node_helper(), oomph::RefineableTriangleMesh< ELEMENT >::construct_new_node_load_balance_helper(), oomph::DGElement::construct_nodes_and_faces(), oomph::GeompackQuadScaffoldMesh::GeompackQuadScaffoldMesh(), oomph::SimpleRectangularTriMesh< ELEMENT >::SimpleRectangularTriMesh(), oomph::TetMeshBase::split_elements_in_corners(), oomph::TetgenScaffoldMesh::TetgenScaffoldMesh(), and oomph::TriangleScaffoldMesh::TriangleScaffoldMesh().

◆ construct_node() [2/2]

virtual Node* oomph::FiniteElement::construct_node	(	const unsigned &	n,
		TimeStepper *const &	time_stepper_pt
	)

inlinevirtual

Construct the local node n, including storage for history values required by timestepper, and return a pointer to the newly created node object.

Reimplemented in oomph::SolidFiniteElement, oomph::ElementWithSpecificMovingNodes< ELEMENT, NODE_TYPE >, oomph::ElementWithSpecificMovingNodes< ELEMENT, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< ELEMENT >, SpineNode >, oomph::ElementWithSpecificMovingNodes< FaceGeometry< FaceGeometry< ELEMENT > >, SpineNode >, oomph::ElementWithSpecificMovingNodes< ELEMENT, AlgebraicNode >, and oomph::ElementWithSpecificMovingNodes< ELEMENT, MacroElementNodeUpdateNode >.

Definition at line 2405 of file elements.h.

◆ d2shape_eulerian()

double oomph::FiniteElement::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) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ .

Compute the geometric shape functions and also first and second derivatives w.r.t. global coordinates at local coordinate s; Also 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) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ .

Definition at line 3378 of file elements.cc.

◆ d2shape_eulerian_at_knot()

double oomph::FiniteElement::d2shape_eulerian_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		DShape &	d2psidx
	)		const

virtual

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) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ .

Compute the geometric shape functions and also first and second derivatives w.r.t. global coordinates at ipt-th integration point Returns Jacobian of mapping from global to local coordinates. This is the most general version, may be overloaded, if desired. 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) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ .

Reimplemented in oomph::StorableShapeElementBase.

Definition at line 3432 of file elements.cc.

Referenced by oomph::StorableShapeElementBase::d2shape_eulerian_at_knot(), and oomph::StorableShapeElementBase::pre_compute_d2shape_eulerian_at_knots().

◆ d2shape_local()

virtual void oomph::FiniteElement::d2shape_local	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsids,
		DShape &	d2psids
	)		const

inlinevirtual

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) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ .

Reimplemented in oomph::BellElement< DIM, NNODE_1D >, oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, and oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >.

Definition at line 1955 of file elements.h.

References oomph::GeneralisedElement::describe_local_dofs(), and oomph::Global_string_for_annotation::string().

Referenced by oomph::QHermiteElement< DIM-1 >::move_local_coord_back_into_element(), oomph::QElement< 1, NNODE_1D >::QElement(), oomph::QElement< 2, NNODE_1D >::QElement(), and oomph::QElement< 3, NNODE_1D >::QElement().

◆ d2shape_local_at_knot()

void oomph::FiniteElement::d2shape_local_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsids,
		DShape &	d2psids
	)		const

virtual

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) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ .

Calculate the shape function and its first and second derivatives w.r.t. local coordinates at the ipt-th integration point. Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / d s^2$ 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) = $\partial^2 \psi_j / \partial s_1 \partial s_2$

Reimplemented in oomph::StorableShapeElementBase.

Definition at line 3207 of file elements.cc.

References i, and s.

Referenced by oomph::StorableShapeElementBase::d2shape_local_at_knot(), and oomph::StorableShapeElementBase::pre_compute_d2shape_local_at_knots().

◆ d_dshape_eulerian_dnodal_coordinates()

void oomph::FiniteElement::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

protectedvirtual

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 $ x_i $ . I.e. this function calculates

$\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right).$

To do this it requires 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) = $\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right)$ By default the function will use the dimension of the element to call the correct d_dshape_eulerian_dnodal_coordinates_templated_helper(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements.

Template-free interface calculating 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 $ x_i $ . I.e. this function calculates

$\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right).$

To do this it requires 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 slightly inefficient, given that it uses a switch statement. It can always be overloaded in specific geometric elements, for efficiency reasons.

Definition at line 2697 of file elements.cc.

References oomph::RankFourTensor< T >::nindex1(), oomph::RankFourTensor< T >::nindex2(), oomph::RankFourTensor< T >::nindex3(), and oomph::RankFourTensor< T >::nindex4().

Referenced by oomph::AxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst(), and oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst().

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [1/5]

template<unsigned DIM>

void oomph::FiniteElement::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

protected

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 $ x_i $ , 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.

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [2/5]

template<>

void oomph::FiniteElement::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

protected

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 $ x_i $ .

Definition at line 2284 of file elements.cc.

References oomph::oomph_info.

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [3/5]

template<>

void oomph::FiniteElement::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

protected

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 $ x_i $ .

Definition at line 2306 of file elements.cc.

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [4/5]

template<>

void oomph::FiniteElement::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

protected

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 $ x_i $ .

Definition at line 2338 of file elements.cc.

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [5/5]

template<>

void oomph::FiniteElement::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

protected

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 $ x_i $ .

Definition at line 2395 of file elements.cc.

References Accept_negative_jacobian, Default_Initial_Nvalue, i, local_to_eulerian_mapping_diagonal(), N2deriv, Node_location_tolerance, Suppress_output_while_checking_for_inverted_elements, and Tolerance_for_singular_jacobian.

◆ describe_local_dofs()

void oomph::FiniteElement::describe_local_dofs	(	std::ostream &	out,
		const std::string &	current_string
	)		const

virtual

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(...)

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(...)

Reimplemented from oomph::GeneralisedElement.

Definition at line 1682 of file elements.cc.

References oomph::GeneralisedElement::describe_local_dofs(), and describe_nodal_local_dofs().

Referenced by oomph::RefineableQSpectralPoissonElement< DIM, NNODE_1D >::describe_local_dofs(), oomph::ElementWithMovingNodes::describe_local_dofs(), oomph::SpectralElement::describe_local_dofs(), oomph::FSIWallElement::describe_local_dofs(), and oomph::SolidFiniteElement::describe_local_dofs().

◆ describe_nodal_local_dofs()

void oomph::FiniteElement::describe_nodal_local_dofs	(	std::ostream &	out,
		const std::string &	current_string
	)		const

virtual

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(...)

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(...)

Definition at line 1701 of file elements.cc.

References oomph::Data::describe_dofs(), and oomph::Global_string_for_annotation::string().

Referenced by describe_local_dofs().

◆ dim()

unsigned oomph::FiniteElement::dim ( ) const

inline

Return the spatial dimension of the element, i.e. the number of local coordinates required to parametrise its geometry.

Definition at line 2482 of file elements.h.

◆ disable_ALE()

virtual void oomph::FiniteElement::disable_ALE ( )

inlinevirtual

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.

Reimplemented in oomph::NavierStokesEquations< DIM >, oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >, oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesEquations, oomph::GeneralisedNewtonianNavierStokesEquations< DIM >, oomph::LinearisedNavierStokesEquations, oomph::SphericalNavierStokesEquations, oomph::LinearisedAxisymmetricNavierStokesEquations, oomph::AdvectionDiffusionReactionEquations< NREAGENT, DIM >, oomph::UnsteadyHeatEquations< DIM >, oomph::AxisymAdvectionDiffusionEquations, oomph::SphericalAdvectionDiffusionEquations, oomph::GeneralisedAdvectionDiffusionEquations< DIM >, oomph::AdvectionDiffusionEquations< DIM >, and oomph::BuoyantQCrouzeixRaviartElement< DIM >.

Definition at line 2297 of file elements.h.

◆ dJ_eulerian_at_knot()

double oomph::FiniteElement::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.

Definition at line 3283 of file elements.cc.

◆ dJ_eulerian_dnodal_coordinates()

void oomph::FiniteElement::dJ_eulerian_dnodal_coordinates	(	const DenseMatrix< double > &	jacobian,
		const DShape &	dpsids,
		DenseMatrix< double > &	djacobian_dX
	)		const

protectedvirtual

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.

Template-free interface calculating the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. This is slightly inefficient, given that it uses a switch statement. It can always be overloaded in specific geometric elements, for efficiency reasons.

Definition at line 2611 of file elements.cc.

References oomph::DenseMatrix< T >::ncol(), and oomph::DenseMatrix< T >::nrow().

Referenced by oomph::AxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst(), and oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst().

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [1/5]

template<unsigned DIM>

void oomph::FiniteElement::dJ_eulerian_dnodal_coordinates_templated_helper	(	const DenseMatrix< double > &	jacobian,
		const DShape &	dpsids,
		DenseMatrix< double > &	djacobian_dX
	)		const

protected

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.

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [2/5]

template<>

void oomph::FiniteElement::dJ_eulerian_dnodal_coordinates_templated_helper	(	const DenseMatrix< double > &	jacobian,
		const DShape &	dpsids,
		DenseMatrix< double > &	djacobian_dX
	)		const

protected

Zero-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij.

Definition at line 2180 of file elements.cc.

References oomph::oomph_info.

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [3/5]

template<>

void oomph::FiniteElement::dJ_eulerian_dnodal_coordinates_templated_helper	(	const DenseMatrix< double > &	jacobian,
		const DShape &	dpsids,
		DenseMatrix< double > &	djacobian_dX
	)		const

protected

One-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij.

Definition at line 2197 of file elements.cc.

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [4/5]

template<>

void oomph::FiniteElement::dJ_eulerian_dnodal_coordinates_templated_helper	(	const DenseMatrix< double > &	jacobian,
		const DShape &	dpsids,
		DenseMatrix< double > &	djacobian_dX
	)		const

protected

Two-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij.

Definition at line 2216 of file elements.cc.

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [5/5]

template<>

void oomph::FiniteElement::dJ_eulerian_dnodal_coordinates_templated_helper	(	const DenseMatrix< double > &	jacobian,
		const DShape &	dpsids,
		DenseMatrix< double > &	djacobian_dX
	)		const

protected

Three-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij.

Definition at line 2239 of file elements.cc.

◆ dnodal_position_dt() [1/2]

double oomph::FiniteElement::dnodal_position_dt	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

Return the i-th component of nodal velocity: dx/dt at local node n.

Definition at line 2238 of file elements.h.

◆ dnodal_position_dt() [2/2]

double oomph::FiniteElement::dnodal_position_dt	(	const unsigned &	n,
		const unsigned &	j,
		const unsigned &	i
	)		const

inline

Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n.

Definition at line 2243 of file elements.h.

◆ dnodal_position_gen_dt() [1/2]

double oomph::FiniteElement::dnodal_position_gen_dt	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. `Type': k; Coordinate direction: i.

Definition at line 2262 of file elements.h.

Referenced by oomph::KirchhoffLoveShellEquations::get_energy(), and oomph::KirchhoffLoveShellEquations::load_rate_of_work().

◆ dnodal_position_gen_dt() [2/2]

double oomph::FiniteElement::dnodal_position_gen_dt	(	const unsigned &	j,
		const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2270 of file elements.h.

◆ dposition_dt()

void oomph::FiniteElement::dposition_dt	(	const Vector< double > &	zeta,
		const unsigned &	t,
		Vector< double > &	drdt
	)

inlinevirtual

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.

Reimplemented from oomph::GeomObject.

Definition at line 2555 of file elements.h.

Referenced by oomph::FSIAxisymFoepplvonKarmanElement< NNODE_1D, FLUID_ELEMENT >::output().

◆ dshape_eulerian()

double oomph::FiniteElement::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.

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. Most general form of the function, but may be over-loaded, if desired.

Definition at line 3227 of file elements.cc.

◆ dshape_eulerian_at_knot() [1/2]

double oomph::FiniteElement::dshape_eulerian_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx
	)		const

virtual

Return the geometric shape functions and also first derivatives w.r.t. global coordinates at the ipt-th integration point.

Compute the geometric shape functions and also first derivatives w.r.t. global coordinates at integration point ipt. Most general form of function, but may be over-loaded if desired.

Reimplemented in oomph::StorableShapeElementBase.

Definition at line 3254 of file elements.cc.

◆ dshape_eulerian_at_knot() [2/2]

double oomph::FiniteElement::dshape_eulerian_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsi,
		DenseMatrix< double > &	djacobian_dX,
		RankFourTensor< double > &	d_dpsidx_dX
	)		const

virtual

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.

Compute the geometric shape functions (psi) and first derivatives w.r.t. global coordinates (dpsidx) at integration point ipt. 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. Most general form of function, but may be over-loaded if desired.

Definition at line 3320 of file elements.cc.

◆ dshape_local()

virtual void oomph::FiniteElement::dshape_local	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsids
	)		const

inlinevirtual

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)

Reimplemented in oomph::BellElement< DIM, NNODE_1D >, oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::ClampedHermiteShellBoundaryConditionElement, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >, oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, and oomph::QHermiteElement< DIM-1 >.

Definition at line 1922 of file elements.h.

Referenced by oomph::FourierDecomposedHelmholtzDtNBoundaryElement< ELEMENT >::compute_gamma_contribution(), oomph::FourierDecomposedHelmholtzBCElementBase< ELEMENT >::d_shape_and_test_local(), oomph::PMLFourierDecomposedHelmholtzPowerMonitorElement< ELEMENT >::d_shape_and_test_local(), oomph::AxisymmetricTCrouzeixRaviartElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricTCrouzeixRaviartElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricTTaylorHoodElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::AxisymmetricTTaylorHoodElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::GeneralisedNewtonianQCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::QCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianQTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::QTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::BiharmonicFluxElement< DIM >::fill_in_generic_residual_contribution_biharmonic_flux(), oomph::LineFluidInterfaceBoundingElement::fill_in_generic_residual_contribution_interface_boundary(), oomph::KirchhoffLoveBeamEquations::get_non_unit_tangent(), oomph::AxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst(), oomph::DarcyEquations< 2 >::interpolated_div_q(), oomph::PoroelasticityEquations< 2 >::interpolated_div_q(), oomph::AxisymmetricPoroelasticityEquations::interpolated_div_q(), oomph::AxisymmetricNavierStokesEquations::interpolated_duds_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::interpolated_duds_axi_nst(), oomph::BiharmonicFluxElement< DIM >::J_eulerian(), oomph::QHermiteElement< DIM-1 >::move_local_coord_back_into_element(), oomph::QElement< 1, NNODE_1D >::QElement(), oomph::QElement< 2, NNODE_1D >::QElement(), oomph::QElement< 3, NNODE_1D >::QElement(), and oomph::AxisymmetricPoroelasticityEquations::transform_basis().

◆ dshape_local_at_knot()

void oomph::FiniteElement::dshape_local_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsids
	)		const

virtual

Return the geometric shape function and its derivative w.r.t. the local coordinates at the ipt-th integration point.

Return the shape function and its derivatives w.r.t. the local coordinates at the ipt-th integration point.

Reimplemented in oomph::StorableShapeElementBase.

Definition at line 3176 of file elements.cc.

References i, and s.

Referenced by oomph::StorableShapeElementBase::dshape_local_at_knot(), oomph::AxisymmetricSolidTractionElement< ELEMENT >::fill_in_contribution_to_residuals(), oomph::TimeHarmonicLinElastLoadedByHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::fill_in_contribution_to_residuals_helmholtz_traction(), oomph::TimeHarmonicLinElastLoadedByPMLHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::fill_in_contribution_to_residuals_helmholtz_traction(), oomph::FourierDecomposedTimeHarmonicLinElastLoadedByHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::fill_in_contribution_to_residuals_helmholtz_traction(), oomph::FluidInterfaceElement::fill_in_generic_residual_contribution_interface(), oomph::SurfactantTransportInterfaceElement::integrate_c(), and oomph::StorableShapeElementBase::pre_compute_dshape_local_at_knots().

◆ element_geometry()

virtual ElementGeometry::ElementGeometry oomph::FiniteElement::element_geometry ( ) const

inlinevirtual

Return the geometry type of the element (either Q or T usually).

Reimplemented in oomph::TElementBase, and oomph::QElementBase.

Definition at line 2485 of file elements.h.

References oomph::Global_string_for_annotation::string(), and t.

◆ enable_ALE()

virtual void oomph::FiniteElement::enable_ALE ( )

inlinevirtual

(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.

Reimplemented in oomph::NavierStokesEquations< DIM >, oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >, oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesEquations, oomph::GeneralisedNewtonianNavierStokesEquations< DIM >, oomph::LinearisedNavierStokesEquations, oomph::SphericalNavierStokesEquations, oomph::LinearisedAxisymmetricNavierStokesEquations, oomph::AdvectionDiffusionReactionEquations< NREAGENT, DIM >, oomph::UnsteadyHeatEquations< DIM >, oomph::AxisymAdvectionDiffusionEquations, oomph::GeneralisedAdvectionDiffusionEquations< DIM >, oomph::AdvectionDiffusionEquations< DIM >, and oomph::BuoyantQCrouzeixRaviartElement< DIM >.

Definition at line 2320 of file elements.h.

◆ face_node_number_error_check()

void oomph::FiniteElement::face_node_number_error_check ( const unsigned & i ) const

inline

Range check for face node numbers.

Definition at line 3172 of file elements.h.

References oomph::Global_string_for_annotation::string().

Referenced by oomph::QElement< 1, NNODE_1D >::get_bulk_node_number(), oomph::QElement< 2, NNODE_1D >::get_bulk_node_number(), and oomph::QElement< 3, NNODE_1D >::get_bulk_node_number().

◆ face_outer_unit_normal_sign()

virtual int oomph::FiniteElement::face_outer_unit_normal_sign ( const int & face_index ) const

inlinevirtual

Get the sign of the outer unit normal on the face given by face_index.

Reimplemented in oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 3157 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ face_to_bulk_coordinate_fct_pt()

virtual CoordinateMappingFctPt oomph::FiniteElement::face_to_bulk_coordinate_fct_pt ( const int & face_index ) const

inlinevirtual

Get a pointer to the function mapping face coordinates to bulk coordinates.

Reimplemented in oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 3186 of file elements.h.

References oomph::Global_string_for_annotation::string().

Referenced by oomph::QElement< 1, NNODE_1D >::face_outer_unit_normal_sign(), oomph::QElement< 2, NNODE_1D >::face_outer_unit_normal_sign(), and oomph::QElement< 3, NNODE_1D >::face_outer_unit_normal_sign().

◆ fill_in_contribution_to_jacobian()

void oomph::FiniteElement::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlineprotectedvirtual

Add the elemental contribution to the jacobian matrix. and the residuals vector. Note that this function will NOT initialise the residuals vector or the jacobian matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is to use finite differences to calculate the jacobian.

Reimplemented from oomph::GeneralisedElement.

Definition at line 1697 of file elements.h.

References oomph::GeneralisedElement::fill_in_contribution_to_residuals(), oomph::GeneralisedElement::fill_in_jacobian_from_external_by_fd(), oomph::GeneralisedElement::fill_in_jacobian_from_internal_by_fd(), oomph::GeneralisedElement::get_residuals(), and oomph::GeneralisedElement::ndof().

◆ fill_in_jacobian_from_nodal_by_fd() [1/2]

void oomph::FiniteElement::fill_in_jacobian_from_nodal_by_fd	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

protectedvirtual

Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated.

This function calculates the entries of Jacobian matrix, used in the Newton method, associated with the nodal degrees of freedom. It does this using finite differences, rather than an analytical formulation, so can be done in total generality.

Reimplemented in oomph::RefineableElement.

Definition at line 3583 of file elements.cc.

References oomph::GeneralisedElement::Default_fd_jacobian_step, oomph::GeneralisedElement::get_residuals(), i, and oomph::GeneralisedElement::ndof().

Referenced by assign_nodal_local_eqn_numbers(), oomph::FSIWallElement::fill_in_contribution_to_jacobian(), and oomph::ElementWithExternalElement::fill_in_contribution_to_jacobian().

◆ fill_in_jacobian_from_nodal_by_fd() [2/2]

void oomph::FiniteElement::fill_in_jacobian_from_nodal_by_fd ( DenseMatrix< double > & jacobian )

inlineprotected

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.

Definition at line 1659 of file elements.h.

References oomph::GeneralisedElement::get_residuals(), and oomph::GeneralisedElement::ndof().

◆ geom_data_pt()

Data* oomph::FiniteElement::geom_data_pt ( const unsigned & j )

inlinevirtual

A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation.

Reimplemented from oomph::GeomObject.

Reimplemented in oomph::SolidFiniteElement, oomph::RefineableSolidElement, and oomph::FaceElementAsGeomObject< ELEMENT >.

Definition at line 2529 of file elements.h.

Referenced by oomph::ElementWithExternalElement::assign_external_interaction_data_local_eqn_numbers(), and oomph::RefineableSolidElement::assign_solid_local_eqn_numbers().

◆ get_bulk_node_number()

virtual unsigned oomph::FiniteElement::get_bulk_node_number	(	const int &	face_index,
		const unsigned &	i
	)		const

inlinevirtual

Get the number of the ith node on face face_index (in the bulk node vector).

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 3148 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ get_centre_of_gravity_and_max_radius_in_terms_of_zeta()

void oomph::FiniteElement::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.

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. NOTE: All computed in terms of zeta!

Definition at line 3844 of file elements.cc.

References i.

◆ get_dresidual_dnodal_coordinates()

void oomph::FiniteElement::get_dresidual_dnodal_coordinates ( RankThreeTensor< double > & dresidual_dnodal_coordinates )

virtual

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}.

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}

Reimplemented in oomph::NavierStokesEquations< DIM >, oomph::GeneralisedNewtonianNavierStokesEquations< DIM >, oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesEquations, oomph::RefineableNavierStokesEquations< DIM >, oomph::RefineableElement, oomph::PoissonEquations< DIM >, oomph::RefineableGeneralisedNewtonianNavierStokesEquations< DIM >, oomph::RefineableGeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::RefineableAxisymmetricNavierStokesEquations, and oomph::RefineablePoissonEquations< DIM >.

Definition at line 3666 of file elements.cc.

References oomph::GeneralisedElement::Default_fd_jacobian_step, oomph::GeneralisedElement::get_residuals(), i, oomph::GeneralisedElement::ndof(), oomph::Node::perform_auxiliary_node_update_fct(), and oomph::Node::x().

Referenced by oomph::NavierStokesEquations< DIM >::delete_pressure_advection_diffusion_robin_elements(), oomph::RefineableNavierStokesEquations< DIM >::dinterpolated_u_nst_ddata(), oomph::ElementWithMovingNodes::fill_in_jacobian_from_geometric_data(), and oomph::GeneralisedNewtonianNavierStokesEquations< DIM >::pin_all_non_pressure_dofs().

◆ get_node_at_local_coordinate()

Node * oomph::FiniteElement::get_node_at_local_coordinate ( const Vector< double > & s ) const

virtual

If there is a node at this local coordinate, return the pointer to the node.

If there is a node at the local coordinate, s, return the pointer to the node. If not return 0. Note that this is a default, brute force implementation, can almost certainly be made more efficient for specific elements.

Reimplemented in oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >, oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >, and oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >.

Definition at line 3806 of file elements.cc.

References i.

◆ get_node_number()

int oomph::FiniteElement::get_node_number ( Node *const & global_node_pt ) const

Return the number of the node *node_pt if this node is in the element, else return -1;.

Return the number of the node located at *node_pt if this node is in the element, else return $ -1 $

Definition at line 3737 of file elements.cc.

References i.

Referenced by oomph::RefineableElement::unbuild().

◆ get_s_plot()

virtual void oomph::FiniteElement::get_s_plot	(	const unsigned &	i,
		const unsigned &	nplot,
		Vector< double > &	s,
		const bool &	shifted_to_interior = `false`
	)		const

inlinevirtual

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.

Definition at line 2978 of file elements.h.

◆ get_x() [1/2]

void oomph::FiniteElement::get_x	(	const Vector< double > &	s,
		Vector< double > &	x
	)		const

inline

Global coordinates as function of local coordinates. Either via FE representation or via macro-element (if Macro_elem_pt!=0)

Definition at line 1841 of file elements.h.

Referenced by oomph::TreeBasedRefineableMeshBase::adapt_mesh(), oomph::RefineableQElement< 3 >::build(), oomph::RefineableQElement< 1 >::build(), oomph::RefineableQElement< 2 >::build(), oomph::OcTree::doc_face_neighbours(), oomph::BinaryTree::doc_neighbours(), oomph::QuadTree::doc_neighbours(), oomph::OcTree::doc_true_edge_neighbours(), oomph::MacroElementNodeUpdateNode::node_update(), oomph::Mesh::node_update(), oomph::TreeBasedRefineableMeshBase::p_adapt_mesh(), oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::p_refine(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::p_refine(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::p_refine(), oomph::RefineableQSpectralElement< 2 >::rebuild_from_sons(), oomph::RefineableQSpectralElement< 3 >::rebuild_from_sons(), oomph::RefineableQSpectralElement< 1 >::rebuild_from_sons(), oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::rebuild_from_sons(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::rebuild_from_sons(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::rebuild_from_sons(), and oomph::TreeBasedRefineableMeshBase::synchronise_nonhanging_nodes().

◆ get_x() [2/2]

void oomph::FiniteElement::get_x	(	const unsigned &	t,
		const Vector< double > &	s,
		Vector< double > &	x
	)

inline

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).

Definition at line 1854 of file elements.h.

References oomph::TimeStepper::nprev_values().

◆ get_x_from_macro_element() [1/2]

virtual void oomph::FiniteElement::get_x_from_macro_element	(	const Vector< double > &	s,
		Vector< double > &	x
	)		const

inlinevirtual

Global coordinates as function of local coordinates using macro element representation. (Broken virtual — this must be overloaded in specific geometric element classes)

Reimplemented in oomph::QElementBase.

Definition at line 1879 of file elements.h.

◆ get_x_from_macro_element() [2/2]

virtual void oomph::FiniteElement::get_x_from_macro_element	(	const unsigned &	t,
		const Vector< double > &	s,
		Vector< double > &	x
	)

inlinevirtual

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.)

Reimplemented in oomph::QElementBase.

Definition at line 1893 of file elements.h.

◆ has_hanging_nodes()

bool oomph::FiniteElement::has_hanging_nodes ( ) const

inline

Return boolean to indicate if any of the element's nodes are geometrically hanging.

Definition at line 2356 of file elements.h.

◆ identify_field_data_for_interactions()

void oomph::FiniteElement::identify_field_data_for_interactions ( std::set< std::pair< Data *, unsigned > > & paired_field_data )

virtual

The purpose of this function is to identify all possible Data that can affect the fields interpolated by the FiniteElement. The information will typically be used in interaction problems in which the FiniteElement provides a forcing term for an ElementWithExternalElement. The Data must be provided as paired_load data containing.

the pointer to a Data object and

the index of the value in that Data objectThe generic implementation (should be overloaded in more specific applications) is to include all nodal and internal Data stored in the FiniteElement. The geometric data, which includes the positions of SolidNodes, is treated separately by the function identify_geometric_data()

The purpose of this function is to identify all possible Data that can affect the fields interpolated by the FiniteElement. The information will typically be used in interaction problems in which the FiniteElement provides a forcing term for an ElementWithExternalElement. The Data must be provided as paired_load data containing (a) the pointer to a Data object and (b) the index of the value in that Data object. The generic implementation (should be overloaded in more specific applications) is to include all nodal and internal Data stored in the FiniteElement. Note that the geometric data, which includes the positions of SolidNodes, is treated separately by the function identify_geometric_data()

Reimplemented in oomph::RefineableElement.

Definition at line 4966 of file elements.cc.

References i, oomph::GeneralisedElement::internal_data_pt(), oomph::GeneralisedElement::ninternal_data(), and oomph::Data::nvalue().

◆ identify_geometric_data()

virtual void oomph::FiniteElement::identify_geometric_data ( std::set< Data *> & geometric_data_pt )

inlinevirtual

The purpose of this function is to identify all Data objects that affect the elements' geometry. This function is implemented as an empty virtual function since it can only be implemented in conjunction with a node-update strategy. A specific implementation is provided in the ElementWithMovingNodes class.

Reimplemented in oomph::SolidFiniteElement, oomph::RefineableSolidElement, and oomph::ElementWithMovingNodes.

Definition at line 2639 of file elements.h.

Referenced by oomph::RefineableSolidElement::assign_solid_local_eqn_numbers(), and oomph::ImmersedRigidBodyElement::set_drag_mesh().

◆ integral_pt()

Integral* const& oomph::FiniteElement::integral_pt ( ) const

inline

Return the pointer to the integration scheme (const version)

Definition at line 1908 of file elements.h.

References oomph::OneDimLagrange::shape().

◆ integrate_fct() [1/2]

void oomph::FiniteElement::integrate_fct	(	FiniteElement::SteadyExactSolutionFctPt	integrand_fct_pt,
		Vector< double > &	integral
	)

Evaluate integral of a Vector-valued function ${\bf f}({\bf x})$ over the element.

Integrate Vector-valued function over element.

Definition at line 4283 of file elements.cc.

References i, and s.

Referenced by integrate_fct(), and size().

◆ integrate_fct() [2/2]

void oomph::FiniteElement::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.

Integrate Vector-valued time-dep function over element.

Definition at line 4233 of file elements.cc.

References i, integrate_fct(), and s.

◆ interpolated_dxdt() [1/2]

double oomph::FiniteElement::interpolated_dxdt	(	const Vector< double > &	s,
		const unsigned &	i,
		const unsigned &	t_deriv
	)

virtual

Return t-th time-derivative of the i-th FE-interpolated Eulerian coordinate at local coordinate s.

Return the t-th time-derivative of the i-th FE-interpolated Eulerian coordinate at local coordinate s.

Reimplemented in oomph::FaceElement.

Definition at line 4484 of file elements.cc.

References oomph::OneDimLagrange::shape().

Referenced by oomph::HermiteShellElement::output_with_time_dep_quantities().

◆ interpolated_dxdt() [2/2]

void oomph::FiniteElement::interpolated_dxdt	(	const Vector< double > &	s,
		const unsigned &	t_deriv,
		Vector< double > &	dxdt
	)

virtual

Compte t-th time-derivative of the FE-interpolated Eulerian coordinate vector at local coordinate s.

Compute t-th time-derivative of the FE-interpolated Eulerian coordinate vector at local coordinate s.

Reimplemented in oomph::FaceElement.

Definition at line 4518 of file elements.cc.

References i, and oomph::OneDimLagrange::shape().

◆ interpolated_x() [1/4]

double oomph::FiniteElement::interpolated_x	(	const Vector< double > &	s,
		const unsigned &	i
	)		const

virtual

Return FE interpolated coordinate x[i] at local coordinate s.

Reimplemented in oomph::FaceElement.

Definition at line 3881 of file elements.cc.

References oomph::OneDimLagrange::shape().

◆ interpolated_x() [2/4]

double oomph::FiniteElement::interpolated_x	(	const unsigned &	t,
		const Vector< double > &	s,
		const unsigned &	i
	)		const

virtual

Return FE interpolated coordinate x[i] at local coordinate s at previous timestep t (t=0: present; t>0: previous timestep)

Reimplemented in oomph::FaceElement.

Definition at line 3912 of file elements.cc.

References oomph::OneDimLagrange::shape().

◆ interpolated_x() [3/4]

void oomph::FiniteElement::interpolated_x	(	const Vector< double > &	s,
		Vector< double > &	x
	)		const

virtual

Return FE interpolated position x[] at local coordinate s as Vector.

Reimplemented in oomph::FaceElement.

Definition at line 3944 of file elements.cc.

References i, and oomph::OneDimLagrange::shape().

◆ interpolated_x() [4/4]

void oomph::FiniteElement::interpolated_x	(	const unsigned &	t,
		const Vector< double > &	s,
		Vector< double > &	x
	)		const

virtual

Return FE interpolated position x[] at local coordinate s at previous timestep t as Vector (t=0: present; t>0: previous timestep)

Reimplemented in oomph::FaceElement.

Definition at line 3980 of file elements.cc.

References i, and oomph::OneDimLagrange::shape().

◆ interpolated_zeta()

void oomph::FiniteElement::interpolated_zeta	(	const Vector< double > &	s,
		Vector< double > &	zeta
	)		const

virtual

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.

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.

Reimplemented from oomph::GeomObject.

Definition at line 4564 of file elements.cc.

References i, and oomph::OneDimLagrange::shape().

Referenced by oomph::BrickFromTetMesh< ELEMENT >::build_mesh(), oomph::YoungLaplaceContactAngleElement< ELEMENT >::contact_line_vectors(), oomph::Mesh::doc_boundary_coordinates(), oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), oomph::YoungLaplaceEquations::fill_in_contribution_to_residuals(), oomph::Multi_domain_functions::first_closer_than_second(), oomph::FSIHermiteBeamElement::locate_zeta(), oomph::Multi_domain_functions::locate_zeta_for_local_coordinates(), oomph::TimeHarmonicLinElastLoadedByHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::output(), oomph::TimeHarmonicLinElastLoadedByPMLHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::output(), oomph::FourierDecomposedTimeHarmonicLinElastLoadedByHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::output(), oomph::HelmholtzFluxFromNormalDisplacementBCElement< HELMHOLTZ_BULK_ELEMENT, ELASTICITY_BULK_ELEMENT >::output(), oomph::FourierDecomposedHelmholtzFluxFromNormalDisplacementBCElement< HELMHOLTZ_BULK_ELEMENT, ELASTICITY_BULK_ELEMENT >::output(), oomph::PMLHelmholtzFluxFromNormalDisplacementBCElement< HELMHOLTZ_BULK_ELEMENT, ELASTICITY_BULK_ELEMENT >::output(), oomph::Multi_domain_functions::setup_bulk_elements_adjacent_to_face_mesh(), and oomph::ThinLayerBrickOnTetMesh< ELEMENT >::ThinLayerBrickOnTetMesh().

◆ invert_jacobian() [1/5]

template<unsigned DIM>

double oomph::FiniteElement::invert_jacobian	(	const DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

protected

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.

◆ invert_jacobian() [2/5]

template<>

double oomph::FiniteElement::invert_jacobian	(	const DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

protected

Zero-d specialisation of function to calculate inverse of jacobian mapping.

Definition at line 2024 of file elements.cc.

References oomph::oomph_info.

◆ invert_jacobian() [3/5]

template<>

double oomph::FiniteElement::invert_jacobian	(	const DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

protected

One-d specialisation of function to calculate inverse of jacobian mapping.

Definition at line 2043 of file elements.cc.

◆ invert_jacobian() [4/5]

template<>

double oomph::FiniteElement::invert_jacobian	(	const DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

protected

Two-d specialisation of function to calculate inverse of jacobian mapping.

Definition at line 2066 of file elements.cc.

◆ invert_jacobian() [5/5]

template<>

double oomph::FiniteElement::invert_jacobian	(	const DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

protected

Three-d specialisation of function to calculate inverse of jacobian mapping.

Definition at line 2092 of file elements.cc.

References invert_jacobian_mapping().

◆ invert_jacobian_mapping()

double oomph::FiniteElement::invert_jacobian_mapping	(	const DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

protectedvirtual

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.

Template-free interface for inversion of the jacobian of a mapping. This is slightly inefficient, given that it uses a switch statement. It can always be overloaded in specific geometric elements, for efficiency reasons.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::DiagQHermiteElement< DIM >, oomph::QHermiteElement< DIM >, and oomph::QHermiteElement< DIM-1 >.

Definition at line 2139 of file elements.cc.

Referenced by invert_jacobian().

◆ J_eulerian()

double oomph::FiniteElement::J_eulerian ( const Vector< double > & s ) const

virtual

Return the Jacobian of mapping from local to global coordinates at local position s.

Calculate the determinant of the Jacobian of the mapping between local and global coordinates at the position. Works directly from the base vectors without assuming that coordinates match spatial dimension. Will be overloaded in FaceElements, in which the elemental dimension does not match the spatial dimension. WARNING: this is always positive and cannot be used to check if the element is inverted, say!

Reimplemented in oomph::FaceElement, oomph::BiharmonicFluxElement< DIM >, and oomph::BiharmonicFluxElement< DIM >.

Definition at line 4022 of file elements.cc.

References i, and oomph::oomph_info.

◆ J_eulerian_at_knot()

double oomph::FiniteElement::J_eulerian_at_knot ( const unsigned & ipt ) const

virtual

Return the Jacobian of the mapping from local to global coordinates at the ipt-th integration point.

Compute the Jacobian of the mapping between the local and global coordinates at the ipt-th integration point.

Reimplemented in oomph::FaceElement, and oomph::StorableShapeElementBase.

Definition at line 4086 of file elements.cc.

References i, and oomph::oomph_info.

Referenced by oomph::SphericalNavierStokesEquations::get_pressure_and_velocity_mass_matrix_diagonal(), oomph::AxisymmetricNavierStokesEquations::get_pressure_and_velocity_mass_matrix_diagonal(), oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::get_pressure_and_velocity_mass_matrix_diagonal(), oomph::StorableShapeElementBase::J_eulerian_at_knot(), oomph::StorableShapeElementBase::pre_compute_J_eulerian_at_knots(), oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::shape_and_test_at_knot(), oomph::SphericalAdvectionDiffusionFluxElement< ELEMENT >::shape_and_test_at_knot(), and oomph::AxisymAdvectionDiffusionFluxElement< ELEMENT >::shape_and_test_at_knot().

◆ local_coord_is_valid()

virtual bool oomph::FiniteElement::local_coord_is_valid ( const Vector< double > & s )

inlinevirtual

Broken assignment operator.

Check whether the local coordinate are valid or not

Reimplemented in oomph::TElementBase, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, and oomph::QElementBase.

Definition at line 1774 of file elements.h.

◆ local_coordinate_of_node()

virtual void oomph::FiniteElement::local_coordinate_of_node	(	const unsigned &	j,
		Vector< double > &	s
	)		const

inlinevirtual

Get local coordinates of node j in the element; vector sets its own size (broken virtual)

Definition at line 1803 of file elements.h.

Referenced by oomph::TreeBasedRefineableMeshBase::adapt_mesh(), oomph::TetgenMesh< ELEMENT >::build_from_scaffold(), oomph::TriangleMesh< ELEMENT >::build_from_scaffold(), oomph::GmshTetMesh< ELEMENT >::build_from_scaffold(), oomph::BrickFromTetMesh< ELEMENT >::build_mesh(), oomph::Missing_masters_functions::construct_new_external_halo_master_node_helper(), oomph::Multi_domain_functions::construct_new_external_halo_master_node_helper(), oomph::Missing_masters_functions::construct_new_external_halo_node_helper(), oomph::Multi_domain_functions::construct_new_external_halo_node_helper(), oomph::RefineableTriangleMesh< ELEMENT >::construct_new_halo_node_helper(), oomph::RefineableTriangleMesh< ELEMENT >::construct_new_node_load_balance_helper(), oomph::Mesh::node_update(), oomph::TreeBasedRefineableMeshBase::p_adapt_mesh(), oomph::AlgebraicCylinderWithFlagMesh< ELEMENT >::setup_algebraic_node_update(), oomph::RefineableTriangleMesh< ELEMENT >::snap_nodes_onto_boundary(), and oomph::TreeBasedRefineableMeshBase::synchronise_nonhanging_nodes().

◆ local_fraction_of_node()

void oomph::FiniteElement::local_fraction_of_node	(	const unsigned &	j,
		Vector< double > &	s_fraction
	)

virtual

Get the local fraction of the node j in the element A dumb, but correct default implementation is provided.

Get the local fraction of the node j in the element; vector sets its own size

Reimplemented in oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >, and oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >.

Definition at line 3131 of file elements.cc.

References i.

Referenced by oomph::FishMesh< ELEMENT >::build_mesh(), and oomph::EighthSphereMesh< ELEMENT >::EighthSphereMesh().

◆ local_one_d_fraction_of_node()

virtual double oomph::FiniteElement::local_one_d_fraction_of_node	(	const unsigned &	n1d,
		const unsigned &	i
	)

inlinevirtual

Get the local fraction of any node in the n-th position in a one dimensional expansion along the i-th local coordinate.

Reimplemented in oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >, and oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >.

Definition at line 1818 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ local_to_eulerian_mapping() [1/2]

virtual double oomph::FiniteElement::local_to_eulerian_mapping	(	const DShape &	dpsids,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

inlineprotectedvirtual

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.

Reimplemented in oomph::DiagQHermiteElement< DIM >.

Definition at line 1464 of file elements.h.

Referenced by oomph::AxisymmetricTCrouzeixRaviartElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricTCrouzeixRaviartElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricTTaylorHoodElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::AxisymmetricTTaylorHoodElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::TCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianTCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::TTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianTTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianQCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::QCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianQTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::QTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::AxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::interpolated_d_dudx_dX_axi_nst(), oomph::DarcyEquations< 2 >::interpolated_div_q(), oomph::PoroelasticityEquations< 2 >::interpolated_div_q(), oomph::AxisymmetricPoroelasticityEquations::interpolated_div_q(), and oomph::AxisymmetricPoroelasticityEquations::transform_basis().

◆ local_to_eulerian_mapping() [2/2]

double oomph::FiniteElement::local_to_eulerian_mapping	(	const DShape &	dpsids,
		DenseMatrix< double > &	inverse_jacobian
	)		const

inlineprotected

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).

Definition at line 1479 of file elements.h.

◆ local_to_eulerian_mapping_diagonal()

double oomph::FiniteElement::local_to_eulerian_mapping_diagonal	(	const DShape &	dpsids,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

protectedvirtual

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 function returns the determinant of the jacobian, the jacobian and the inverse jacobian.

Calculate the mapping from local to eulerian 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. The local derivatives are passed as dpsids and the jacobian and inverse jacobian are returned.

Reimplemented in oomph::RefineableElement.

Definition at line 2536 of file elements.cc.

References i.

Referenced by d_dshape_eulerian_dnodal_coordinates_templated_helper(), and oomph::DiagQHermiteElement< DIM >::local_to_eulerian_mapping().

◆ locate_zeta()

void oomph::FiniteElement::locate_zeta	(	const Vector< double > &	zeta,
		GeomObject *&	geom_object_pt,
		Vector< double > &	s,
		const bool &	use_coordinate_as_initial_guess = `false`
	)

virtual

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.

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. This is achieved in generality by using Newton's method to find the value of the local coordinate, s, such that interpolated_zeta(s) is equal 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. Setting the optional bool argument to true means that the coordinate argument "s" is used as the initial guess. (Default is false).

Reimplemented from oomph::GeomObject.

Definition at line 4617 of file elements.cc.

References oomph::GeneralisedElement::Default_fd_jacobian_step, oomph::OomphLibException::disable_error_message(), i, oomph::Locate_zeta_helpers::Max_newton_iterations, oomph::Locate_zeta_helpers::N_local_points, oomph::Locate_zeta_helpers::Newton_tolerance, oomph::oomph_info, oomph::Locate_zeta_helpers::Radius_multiplier_for_fast_exit_from_locate_zeta, s, and oomph::DoubleMatrixBase::solve().

Referenced by oomph::FSIHermiteBeamElement::fill_in_contribution_to_jacobian().

◆ macro_elem_pt()

MacroElement* oomph::FiniteElement::macro_elem_pt ( )

inline

Access function to pointer to macro element.

Definition at line 1837 of file elements.h.

Referenced by oomph::TreeBasedRefineableMeshBase::adapt_mesh(), oomph::RefineableQElement< 3 >::build(), oomph::Missing_masters_functions::get_required_master_nodal_information_helper(), oomph::Multi_domain_functions::get_required_master_nodal_information_helper(), oomph::Multi_domain_functions::locate_zeta_for_missing_coordinates(), oomph::TreeBasedRefineableMeshBase::p_adapt_mesh(), and oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::pre_build().

◆ move_local_coord_back_into_element()

virtual void oomph::FiniteElement::move_local_coord_back_into_element ( Vector< double > & s ) const

inlinevirtual

Adjust local coordinates so that they're located inside the element.

Reimplemented in oomph::TElementBase, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, and oomph::QElementBase.

Definition at line 1785 of file elements.h.

◆ ngeom_data()

unsigned oomph::FiniteElement::ngeom_data ( ) const

inlinevirtual

A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation.

Reimplemented from oomph::GeomObject.

Reimplemented in oomph::SolidFiniteElement, oomph::RefineableSolidElement, and oomph::FaceElementAsGeomObject< ELEMENT >.

Definition at line 2525 of file elements.h.

Referenced by oomph::ElementWithExternalElement::assign_external_interaction_data_local_eqn_numbers(), and oomph::RefineableSolidElement::assign_solid_local_eqn_numbers().

◆ nnodal_position_type()

unsigned oomph::FiniteElement::nnodal_position_type ( ) const

inline

Return the number of coordinate types that the element requires to interpolate the geometry between the nodes. For Lagrange elements it is 1.

Definition at line 2352 of file elements.h.

Referenced by oomph::RefineableElement::assemble_eulerian_base_vectors(), oomph::RefineableElement::assemble_local_to_eulerian_jacobian(), oomph::RefineableElement::assemble_local_to_eulerian_jacobian2(), oomph::RefineableSolidElement::assign_solid_hanging_local_eqn_numbers(), oomph::SolidICProblem::backup_original_state(), oomph::ElementWithSpecificMovingNodes< ELEMENT, MacroElementNodeUpdateNode >::construct_boundary_node(), oomph::ElementWithSpecificMovingNodes< ELEMENT, MacroElementNodeUpdateNode >::construct_node(), oomph::FSIHermiteBeamElement::dposition_dlagrangian_at_local_coordinate(), oomph::FSIDiagHermiteShellElement::dposition_dlagrangian_at_local_coordinate(), oomph::AxisymmetricSolidTractionElement< ELEMENT >::fill_in_contribution_to_residuals(), oomph::ClampedSlidingHermiteBeamBoundaryConditionElement::fill_in_contribution_to_residuals(), oomph::AxisymmetricPVDEquations::fill_in_contribution_to_residuals_axisym_pvd(), oomph::KirchhoffLoveBeamEquations::fill_in_contribution_to_residuals_beam(), oomph::TimeHarmonicLinElastLoadedByHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::fill_in_contribution_to_residuals_helmholtz_traction(), oomph::TimeHarmonicLinElastLoadedByPMLHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::fill_in_contribution_to_residuals_helmholtz_traction(), oomph::FourierDecomposedTimeHarmonicLinElastLoadedByHelmholtzPressureBCElement< ELASTICITY_BULK_ELEMENT, HELMHOLTZ_BULK_ELEMENT >::fill_in_contribution_to_residuals_helmholtz_traction(), oomph::KirchhoffLoveShellEquations::fill_in_contribution_to_residuals_shell(), oomph::AxisymmetricLinearElasticityEquations::fill_in_generic_contribution_to_residuals_axisymmetric_linear_elasticity(), oomph::TimeHarmonicFourierDecomposedLinearElasticityEquations::fill_in_generic_contribution_to_residuals_fourier_decomp_time_harmonic_linear_elasticity(), oomph::AxisymmetricPVDEquationsWithPressure::fill_in_generic_residual_contribution_axisym_pvd_with_pressure(), oomph::RefineableSolidElement::fill_in_jacobian_from_solid_position_by_fd(), oomph::FSIImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::FSIImposeDisplacementByLagrangeMultiplierElement(), oomph::PVDEquationsBase< DIM >::get_dof_numbers_for_unknowns(), oomph::FSIHermiteBeamElement::get_dof_numbers_for_unknowns(), oomph::FSIDiagHermiteShellElement::get_dof_numbers_for_unknowns(), oomph::ClampedHermiteShellBoundaryConditionElement::get_dof_numbers_for_unknowns(), oomph::PVDEquationsWithPressure< DIM >::get_dof_numbers_for_unknowns(), oomph::KirchhoffLoveShellEquations::get_energy(), oomph::KirchhoffLoveBeamEquations::get_energy(), oomph::KirchhoffLoveBeamEquations::get_non_unit_tangent(), oomph::KirchhoffLoveShellEquations::get_normal(), oomph::KirchhoffLoveBeamEquations::get_normal(), oomph::TimeHarmonicFourierDecomposedLinearElasticityEquations::get_strain(), oomph::AxisymmetricLinearElasticityEquations::get_strain(), oomph::KirchhoffLoveShellEquations::get_strain_and_bend(), oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::ImposeDisplacementByLagrangeMultiplierElement(), oomph::KirchhoffLoveShellEquations::load_rate_of_work(), oomph::RefineableElement::local_to_eulerian_mapping_diagonal(), oomph::HermiteBeamElement::output(), oomph::StorableShapeElementBase::pre_compute_d2shape_eulerian_at_knots(), oomph::StorableShapeElementBase::pre_compute_d2shape_local_at_knots(), oomph::StorableShapeElementBase::pre_compute_dshape_eulerian_at_knots(), oomph::StorableShapeElementBase::pre_compute_dshape_local_at_knots(), oomph::StorableShapeElementBase::pre_compute_shape_at_knots(), oomph::SolidICProblem::reset_original_state(), oomph::ProjectableDarcyElement< DARCY_ELEMENT >::residual_for_projection(), oomph::ProjectableAxisymmetricPoroelasticityElement< AXISYMMETRIC_POROELASTICITY_ELEMENT >::residual_for_projection(), and oomph::SolidICProblem::setup_problem().

◆ nnode()

unsigned oomph::FiniteElement::nnode ( ) const

inline

Return the number of nodes.

Definition at line 2146 of file elements.h.

◆ nnode_1d()

virtual unsigned oomph::FiniteElement::nnode_1d ( ) const

inlinevirtual

Return the number of nodes along one edge of the element Default is to return zero — must be overloaded by geometric elements.

Reimplemented in oomph::C1CurvedElement< 2, NNODE_1D >, oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >, and oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >.

Definition at line 2151 of file elements.h.

References i.

◆ nnode_on_face()

virtual unsigned oomph::FiniteElement::nnode_on_face ( ) const

inlinevirtual

Reimplemented in oomph::QElementBase.

Definition at line 3164 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ nodal_dimension()

unsigned oomph::FiniteElement::nodal_dimension ( ) const

inline

Return the required Eulerian dimension of the nodes in this element.

Definition at line 2370 of file elements.h.

◆ nodal_local_eqn()

int oomph::FiniteElement::nodal_local_eqn	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

Return the local equation number corresponding to the i-th value at the n-th local node.

Definition at line 1386 of file elements.h.

References i.

◆ nodal_position() [1/2]

double oomph::FiniteElement::nodal_position	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2227 of file elements.h.

◆ nodal_position() [2/2]

double oomph::FiniteElement::nodal_position	(	const unsigned &	t,
		const unsigned &	n,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2233 of file elements.h.

◆ nodal_position_gen() [1/2]

double oomph::FiniteElement::nodal_position_gen	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

Return the value of the k-th type of the i-th positional variable at the local node n.

Definition at line 2249 of file elements.h.

Referenced by oomph::RefineableElement::assemble_eulerian_base_vectors(), oomph::RefineableElement::assemble_local_to_eulerian_jacobian(), oomph::RefineableElement::assemble_local_to_eulerian_jacobian2(), oomph::AxisymmetricPVDEquations::compute_physical_size(), oomph::AxisymmetricPVDEquationsWithPressure::compute_physical_size(), oomph::FSIHermiteBeamElement::dposition_dlagrangian_at_local_coordinate(), oomph::FSIDiagHermiteShellElement::dposition_dlagrangian_at_local_coordinate(), oomph::AxisymmetricSolidTractionElement< ELEMENT >::fill_in_contribution_to_residuals(), oomph::AxisymmetricPVDEquations::fill_in_contribution_to_residuals_axisym_pvd(), oomph::AxisymmetricPVDEquationsWithPressure::fill_in_generic_residual_contribution_axisym_pvd_with_pressure(), oomph::KirchhoffLoveShellEquations::get_energy(), oomph::KirchhoffLoveShellEquations::load_rate_of_work(), and oomph::RefineableElement::local_to_eulerian_mapping_diagonal().

◆ nodal_position_gen() [2/2]

double oomph::FiniteElement::nodal_position_gen	(	const unsigned &	t,
		const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n.

Definition at line 2255 of file elements.h.

◆ nodal_value() [1/2]

double oomph::FiniteElement::nodal_value	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

Return the i-th value stored at local node n. Produces suitably interpolated values for hanging nodes.

Definition at line 2470 of file elements.h.

References oomph::Node::value().

◆ nodal_value() [2/2]

double oomph::FiniteElement::nodal_value	(	const unsigned &	t,
		const unsigned &	n,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2476 of file elements.h.

References oomph::Node::value().

◆ node_pt() [1/2]

Node* & oomph::FiniteElement::node_pt ( const unsigned & n )

inline

Return a pointer to the local node n.

Definition at line 2109 of file elements.h.

◆ node_pt() [2/2]

Node* const& oomph::FiniteElement::node_pt ( const unsigned & n ) const

inline

Return a pointer to the local node n (const version)

Definition at line 2127 of file elements.h.

◆ node_update()

void oomph::FiniteElement::node_update ( )

virtual

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.

Loop over all nodes in the element and update their positions using each node's (algebraic) update function

Definition at line 4945 of file elements.cc.

Referenced by oomph::ElementWithMovingNodes::fill_in_jacobian_from_geometric_data(), oomph::ElementWithMovingNodes::get_dnodal_coordinates_dgeom_dofs(), oomph::ImmersedRigidBodyElement::node_update_adjacent_fluid_elements(), oomph::FSIWallElement::node_update_adjacent_fluid_elements(), oomph::FluidInterfaceBoundingElement::reset_after_external_fd(), and oomph::FluidInterfaceBoundingElement::update_in_external_fd().

◆ nplot_points()

virtual unsigned oomph::FiniteElement::nplot_points ( const unsigned & nplot ) const

inlinevirtual

Return total number of plot points (when plotting nplot points in each "coordinate direction")

Definition at line 3017 of file elements.h.

◆ nplot_points_paraview()

virtual unsigned oomph::FiniteElement::nplot_points_paraview ( const unsigned & nplot ) const

inlinevirtual

Return the number of actual plot points for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 2712 of file elements.h.

◆ nscalar_paraview()

virtual unsigned oomph::FiniteElement::nscalar_paraview ( ) const

inlinevirtual

Number of scalars/fields output by this element. Broken virtual. Needs to be implemented for each new specific element type.

Reimplemented in oomph::AxisymmetricPoroelasticityEquations, oomph::NavierStokesEquations< DIM >, oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >, oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::GeneralisedNewtonianNavierStokesEquations< DIM >, oomph::AxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesTractionElement< ELEMENT >, oomph::AxisymAdvectionDiffusionEquations, oomph::AdvectionDiffusionEquations< DIM >, oomph::BuoyantQCrouzeixRaviartElement< DIM >, oomph::PMLHelmholtzEquationsBase< DIM >, oomph::HelmholtzEquations< DIM >, and oomph::PoissonEquations< DIM >.

Definition at line 2838 of file elements.h.

Referenced by oomph::Mesh::output_fct_paraview(), and oomph::Mesh::output_paraview().

◆ nsub_elements_paraview()

virtual unsigned oomph::FiniteElement::nsub_elements_paraview ( const unsigned & nplot ) const

inlinevirtual

Return the number of local sub-elements for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 2726 of file elements.h.

Referenced by oomph::Mesh::output_fct_paraview(), oomph::Mesh::output_paraview(), oomph::QElement< 1, NNODE_1D >::write_paraview_offsets(), oomph::QElement< 2, NNODE_1D >::write_paraview_offsets(), oomph::QElement< 3, NNODE_1D >::write_paraview_offsets(), oomph::QElement< 1, NNODE_1D >::write_paraview_output_offset_information(), oomph::QElement< 2, NNODE_1D >::write_paraview_output_offset_information(), oomph::QElement< 3, NNODE_1D >::write_paraview_output_offset_information(), oomph::QElement< 1, NNODE_1D >::write_paraview_type(), oomph::QElement< 2, NNODE_1D >::write_paraview_type(), and oomph::QElement< 3, NNODE_1D >::write_paraview_type().

◆ nvertex_node()

virtual unsigned oomph::FiniteElement::nvertex_node ( ) const

inlinevirtual

Return the number of vertex nodes in this element. Broken virtual function in "pure" finite elements.

Definition at line 2374 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ output() [1/5]

virtual void oomph::FiniteElement::output ( std::ostream & outfile )

inlinevirtual

Output the element data — typically the values at the nodes in a format suitable for post-processing.

Definition at line 2884 of file elements.h.

◆ output() [2/5]

virtual void oomph::FiniteElement::output	(	std::ostream &	outfile,
		const unsigned &	n_plot
	)

inlinevirtual

Output the element data — pass (some measure of) the number of plot points per element.

Definition at line 2894 of file elements.h.

◆ output() [3/5]

virtual void oomph::FiniteElement::output	(	const unsigned &	t,
		std::ostream &	outfile,
		const unsigned &	n_plot
	)		const

inlinevirtual

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!

Reimplemented in oomph::HermiteBeamElement.

Definition at line 2905 of file elements.h.

◆ output() [4/5]

virtual void oomph::FiniteElement::output ( FILE * file_pt )

inlinevirtual

Output the element data — typically the values at the nodes in a format suitable for post-processing. (C style output)

Definition at line 2918 of file elements.h.

◆ output() [5/5]

virtual void oomph::FiniteElement::output	(	FILE *	file_pt,
		const unsigned &	n_plot
	)

inlinevirtual

Output the element data — pass (some measure of) the number of plot points per element (C style output)

Definition at line 2929 of file elements.h.

◆ output_fct() [1/3]

virtual void oomph::FiniteElement::output_fct	(	std::ostream &	outfile,
		const unsigned &	n_plot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

Output an exact solution over the element.

Definition at line 2938 of file elements.h.

Referenced by oomph::TimeHarmonicLinearElasticityEquations< DIM >::fill_in_contribution_to_jacobian(), oomph::TimeHarmonicFourierDecomposedLinearElasticityEquations::fill_in_contribution_to_jacobian(), oomph::PMLTimeHarmonicLinearElasticityEquations< DIM, PML_ELEMENT >::fill_in_contribution_to_jacobian(), oomph::LinearElasticityEquations< DIM >::fill_in_contribution_to_jacobian(), oomph::AxisymmetricLinearElasticityEquations::fill_in_contribution_to_jacobian(), oomph::GeneralisedNewtonianNavierStokesEquations< DIM >::full_output(), oomph::NavierStokesEquations< DIM >::full_output(), oomph::UnsteadyHeatEquations< DIM >::output(), oomph::TPMLHelmholtzElement< DIM, NNODE_1D, PML_ELEMENT >::output_fct(), oomph::TPMLFourierDecomposedHelmholtzElement< NNODE_1D, PML_ELEMENT >::output_fct(), oomph::BuoyantQCrouzeixRaviartElement< DIM >::output_fct(), oomph::BiharmonicEquations< DIM >::output_fct(), oomph::QPMLFourierDecomposedHelmholtzElement< NNODE_1D, PML_ELEMENT >::output_fct(), oomph::QPMLHelmholtzElement< 2, NNODE_1D, PML_ELEMENT >::output_fct(), oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::output_fct(), and oomph::Mesh::output_fct().

◆ output_fct() [2/3]

virtual void oomph::FiniteElement::output_fct	(	std::ostream &	outfile,
		const unsigned &	n_plot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

Output a time-dependent exact solution over the element.

Definition at line 2949 of file elements.h.

◆ output_fct() [3/3]

virtual void oomph::FiniteElement::output_fct	(	std::ostream &	outfile,
		const unsigned &	n_plot,
		const double &	time,
		const SolutionFunctorBase &	exact_soln
	)		const

inlinevirtual

Output a time-dependent exact solution over the element.

Definition at line 2960 of file elements.h.

◆ output_paraview()

void oomph::FiniteElement::output_paraview	(	std::ofstream &	file_out,
		const unsigned &	nplot
	)		const

inline

Paraview output – this outputs the coordinates at the plot points (for parameter nplot) to specified output file.

Definition at line 2739 of file elements.h.

References i, oomph::Node::ndim(), and s.

Referenced by oomph::Mesh::output_fct_paraview(), and oomph::Mesh::output_paraview().

◆ point_output()

void oomph::FiniteElement::point_output	(	std::ostream &	outfile,
		const Vector< double > &	s
	)

inline

Output solution (as defined by point_output_data()) at local cordinates s.

Definition at line 2695 of file elements.h.

References i.

◆ point_output_data()

virtual void oomph::FiniteElement::point_output_data	(	const Vector< double > &	s,
		Vector< double > &	data
	)

inlinevirtual

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.

Reimplemented in oomph::NavierStokesEquations< DIM >, oomph::GeneralisedNewtonianNavierStokesEquations< DIM >, oomph::AxisymmetricPoroelasticityEquations, oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesEquations, and oomph::PoissonEquations< DIM >.

Definition at line 2690 of file elements.h.

◆ position() [1/2]

void oomph::FiniteElement::position	(	const Vector< double > &	zeta,
		Vector< double > &	r
	)		const

inlinevirtual

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).

Implements oomph::GeomObject.

Reimplemented in oomph::YoungLaplaceEquations.

Definition at line 2535 of file elements.h.

Referenced by oomph::FSIAxisymFoepplvonKarmanElement< NNODE_1D, FLUID_ELEMENT >::position().

◆ position() [2/2]

void oomph::FiniteElement::position	(	const unsigned &	t,
		const Vector< double > &	zeta,
		Vector< double > &	r
	)		const

inlinevirtual

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.

Reimplemented from oomph::GeomObject.

Definition at line 2546 of file elements.h.

◆ raw_dnodal_position_dt() [1/2]

double oomph::FiniteElement::raw_dnodal_position_dt	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

Return the i-th component of nodal velocity: dx/dt at local node n. Do not use the hanging node representation.

Definition at line 2182 of file elements.h.

Referenced by oomph::AxisymmetricNavierStokesEquations::fill_in_generic_dresidual_contribution_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::fill_in_generic_dresidual_contribution_axi_nst(), oomph::AxisymAdvectionDiffusionEquations::fill_in_generic_residual_contribution_axi_adv_diff(), oomph::AxisymmetricNavierStokesEquations::fill_in_generic_residual_contribution_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::fill_in_generic_residual_contribution_axi_nst(), oomph::LinearisedAxisymmetricNavierStokesEquations::fill_in_generic_residual_contribution_linearised_axi_nst(), oomph::SphericalNavierStokesEquations::fill_in_generic_residual_contribution_spherical_nst(), oomph::AxisymmetricNavierStokesEquations::get_dresidual_dnodal_coordinates(), and oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::get_dresidual_dnodal_coordinates().

◆ raw_dnodal_position_dt() [2/2]

double oomph::FiniteElement::raw_dnodal_position_dt	(	const unsigned &	n,
		const unsigned &	j,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2187 of file elements.h.

◆ raw_dnodal_position_gen_dt() [1/2]

double oomph::FiniteElement::raw_dnodal_position_gen_dt	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2208 of file elements.h.

Referenced by oomph::KirchhoffLoveBeamEquations::fill_in_contribution_to_residuals_beam(), oomph::KirchhoffLoveShellEquations::fill_in_contribution_to_residuals_shell(), oomph::KirchhoffLoveBeamEquations::get_energy(), oomph::KirchhoffLoveShellEquations::get_strain_and_bend(), and oomph::HermiteBeamElement::output().

◆ raw_dnodal_position_gen_dt() [2/2]

double oomph::FiniteElement::raw_dnodal_position_gen_dt	(	const unsigned &	j,
		const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2217 of file elements.h.

◆ raw_nodal_position() [1/2]

double oomph::FiniteElement::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...

Definition at line 1659 of file elements.cc.

◆ raw_nodal_position() [2/2]

double oomph::FiniteElement::raw_nodal_position	(	const unsigned &	t,
		const unsigned &	n,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2176 of file elements.h.

◆ raw_nodal_position_gen() [1/2]

double oomph::FiniteElement::raw_nodal_position_gen	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2193 of file elements.h.

Referenced by oomph::KirchhoffLoveBeamEquations::fill_in_contribution_to_residuals_beam(), oomph::KirchhoffLoveShellEquations::fill_in_contribution_to_residuals_shell(), oomph::KirchhoffLoveBeamEquations::get_energy(), oomph::KirchhoffLoveBeamEquations::get_non_unit_tangent(), oomph::KirchhoffLoveShellEquations::get_normal(), oomph::KirchhoffLoveBeamEquations::get_normal(), and oomph::KirchhoffLoveShellEquations::get_strain_and_bend().

◆ raw_nodal_position_gen() [2/2]

double oomph::FiniteElement::raw_nodal_position_gen	(	const unsigned &	t,
		const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inline

Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. Do not use the hanging node representation.

Definition at line 2200 of file elements.h.

◆ raw_nodal_value() [1/2]

double oomph::FiniteElement::raw_nodal_value	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

Return the i-th value stored at local node n but do NOT take hanging nodes into account.

Definition at line 2458 of file elements.h.

References oomph::Node::raw_value().

◆ raw_nodal_value() [2/2]

double oomph::FiniteElement::raw_nodal_value	(	const unsigned &	t,
		const unsigned &	n,
		const unsigned &	i
	)		const

inline

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.

Definition at line 2464 of file elements.h.

References oomph::Node::raw_value().

◆ required_nvalue()

virtual unsigned oomph::FiniteElement::required_nvalue ( const unsigned & n ) const

inlinevirtual

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).

Definition at line 2346 of file elements.h.

◆ reset_after_nodal_fd()

virtual void oomph::FiniteElement::reset_after_nodal_fd ( )

inlineprotectedvirtual

Function that is call after the finite differencing of the nodal data. This may be overloaded to reset any slaved variables that may have changed during the finite differencing.

Reimplemented in oomph::FSIWallElement.

Definition at line 1678 of file elements.h.

Referenced by oomph::RefineableElement::fill_in_jacobian_from_nodal_by_fd().

◆ reset_in_nodal_fd()

virtual void oomph::FiniteElement::reset_in_nodal_fd ( const unsigned & i )

inlineprotectedvirtual

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.

Reimplemented in oomph::FSIWallElement.

Definition at line 1687 of file elements.h.

Referenced by oomph::RefineableElement::fill_in_jacobian_from_nodal_by_fd().

◆ s_max()

virtual double oomph::FiniteElement::s_max ( ) const

inlinevirtual

Max. value of local coordinate.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::QHermiteElement< DIM >, and oomph::QHermiteElement< DIM-1 >.

Definition at line 2654 of file elements.h.

Referenced by oomph::FSI_functions::doc_fsi(), oomph::QElementBase::local_coord_is_valid(), oomph::QHermiteElement< DIM-1 >::local_coord_is_valid(), oomph::QHermiteElement< DIM-1 >::local_coordinate_of_node(), oomph::QElement< 1, NNODE_1D >::local_coordinate_of_node(), oomph::QElement< 2, NNODE_1D >::local_coordinate_of_node(), oomph::QElement< 3, NNODE_1D >::local_coordinate_of_node(), oomph::QElementBase::move_local_coord_back_into_element(), oomph::QHermiteElement< DIM-1 >::move_local_coord_back_into_element(), and oomph::RefineableQElement< 2 >::quad_hang_helper().

◆ s_min()

virtual double oomph::FiniteElement::s_min ( ) const

inlinevirtual

Min value of local coordinate.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::QHermiteElement< DIM >, and oomph::QHermiteElement< DIM-1 >.

Definition at line 2643 of file elements.h.

Referenced by oomph::FSI_functions::doc_fsi(), oomph::QElementBase::local_coord_is_valid(), oomph::QHermiteElement< DIM-1 >::local_coord_is_valid(), oomph::QHermiteElement< DIM-1 >::local_coordinate_of_node(), oomph::QElement< 1, NNODE_1D >::local_coordinate_of_node(), oomph::QElement< 2, NNODE_1D >::local_coordinate_of_node(), oomph::QElement< 3, NNODE_1D >::local_coordinate_of_node(), oomph::QElementBase::move_local_coord_back_into_element(), oomph::QHermiteElement< DIM-1 >::move_local_coord_back_into_element(), and oomph::RefineableQElement< 2 >::quad_hang_helper().

◆ scalar_name_paraview()

virtual std::string oomph::FiniteElement::scalar_name_paraview ( const unsigned & i ) const

inlinevirtual

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.

Reimplemented in oomph::AxisymmetricPoroelasticityEquations, oomph::NavierStokesEquations< DIM >, oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >, oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::GeneralisedNewtonianNavierStokesEquations< DIM >, oomph::AxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesTractionElement< ELEMENT >, oomph::PMLHelmholtzEquationsBase< DIM >, oomph::AxisymAdvectionDiffusionEquations, oomph::AdvectionDiffusionEquations< DIM >, oomph::HelmholtzEquations< DIM >, oomph::PoissonEquations< DIM >, and oomph::BuoyantQCrouzeixRaviartElement< DIM >.

Definition at line 2877 of file elements.h.

References oomph::StringConversion::to_string().

Referenced by oomph::Mesh::output_fct_paraview(), and oomph::Mesh::output_paraview().

◆ scalar_value_fct_paraview()

virtual void oomph::FiniteElement::scalar_value_fct_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type.

Reimplemented in oomph::PMLHelmholtzEquationsBase< DIM >, and oomph::PoissonEquations< DIM >.

Definition at line 2863 of file elements.h.

Referenced by oomph::Mesh::output_fct_paraview().

◆ scalar_value_paraview()

virtual void oomph::FiniteElement::scalar_value_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type.

Reimplemented in oomph::AxisymmetricPoroelasticityEquations, oomph::NavierStokesEquations< DIM >, oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >, oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations, oomph::GeneralisedNewtonianNavierStokesEquations< DIM >, oomph::AxisymmetricNavierStokesEquations, oomph::AxisymmetricNavierStokesTractionElement< ELEMENT >, oomph::AxisymAdvectionDiffusionEquations, oomph::AdvectionDiffusionEquations< DIM >, oomph::BuoyantQCrouzeixRaviartElement< DIM >, oomph::PMLHelmholtzEquationsBase< DIM >, oomph::HelmholtzEquations< DIM >, and oomph::PoissonEquations< DIM >.

Definition at line 2851 of file elements.h.

Referenced by oomph::Mesh::output_paraview().

◆ self_test()

unsigned oomph::FiniteElement::self_test ( )

virtual

Self-test: Check inversion of element & do self-test for GeneralisedElement. Return 0 if OK.

Self-test: Have all internal values been classified as pinned/unpinned? Has pointer to spatial integration scheme been set? Return 0 if OK.

Reimplemented from oomph::GeneralisedElement.

Definition at line 4333 of file elements.cc.

References e, i, s, and oomph::GeneralisedElement::self_test().

◆ set_dimension()

void oomph::FiniteElement::set_dimension ( const unsigned & dim )

inline

Set the dimension of the element and initially set the dimension of the nodes to be the same as the dimension of the element.

Definition at line 1344 of file elements.h.

Referenced by oomph::QElement< 1, NNODE_1D >::QElement(), oomph::QElement< 2, NNODE_1D >::QElement(), oomph::QElement< 3, NNODE_1D >::QElement(), and oomph::QHermiteElement< DIM-1 >::QHermiteElement().

◆ set_integration_scheme()

void oomph::FiniteElement::set_integration_scheme ( Integral *const & integral_pt )

virtual

Set the spatial integration scheme.

Set the spatial integration scheme and also calculate the values of the shape functions and their derivatives w.r.t. the local coordinates, placing the values into storage so that they may be re-used, without recalculation

Reimplemented in oomph::StorableShapeSolidElementBase, and oomph::StorableShapeElementBase.

Definition at line 3150 of file elements.cc.

Referenced by oomph::DGEulerFaceElement< ELEMENT >::DGEulerFaceElement(), oomph::DGSpectralEulerElement< 1, NNODE_1D >::DGSpectralEulerElement(), oomph::DGSpectralEulerElement< 2, NNODE_1D >::DGSpectralEulerElement(), oomph::PRefineableGeneralisedNewtonianQCrouzeixRaviartElement< DIM >::PRefineableGeneralisedNewtonianQCrouzeixRaviartElement(), oomph::PRefineableQCrouzeixRaviartElement< DIM >::PRefineableQCrouzeixRaviartElement(), oomph::PRefineableQLinearElasticityElement< DIM >::PRefineableQLinearElasticityElement(), oomph::PRefineableQPoissonElement< DIM >::PRefineableQPoissonElement(), oomph::QElement< 1, NNODE_1D >::QElement(), oomph::QElement< 2, NNODE_1D >::QElement(), oomph::QElement< 3, NNODE_1D >::QElement(), oomph::QHermiteElement< DIM-1 >::QHermiteElement(), and oomph::StorableShapeElementBase::set_integration_scheme().

◆ set_macro_elem_pt()

virtual void oomph::FiniteElement::set_macro_elem_pt ( MacroElement * macro_elem_pt )

inlinevirtual

Set pointer to macro element – can be overloaded in derived elements to perform additional tasks.

Reimplemented in oomph::SolidFiniteElement, oomph::QSolidElementBase, oomph::RefineableSolidQElement< 3 >, oomph::RefineableSolidQElement< 2 >, oomph::RefineableSolidQElement< 1 >, and oomph::QElementBase.

Definition at line 1833 of file elements.h.

Referenced by oomph::FishMesh< ELEMENT >::build_mesh(), oomph::ChannelWithLeafletMesh< ELEMENT >::ChannelWithLeafletMesh(), oomph::CollapsibleChannelMesh< ELEMENT >::CollapsibleChannelMesh(), oomph::Missing_masters_functions::construct_new_external_halo_master_node_helper(), oomph::Multi_domain_functions::construct_new_external_halo_master_node_helper(), oomph::Multi_domain_functions::create_external_halo_elements(), oomph::QuarterPipeMesh< ELEMENT >::QuarterPipeMesh(), and oomph::QElementBase::set_macro_elem_pt().

◆ set_n_node()

void oomph::FiniteElement::set_n_node ( const unsigned & n )

inline

Set the number of nodes in the element to n, by resizing the storage for pointers to the Node objects.

Definition at line 1361 of file elements.h.

References i.

Referenced by oomph::QElement< 1, NNODE_1D >::QElement(), oomph::QElement< 2, NNODE_1D >::QElement(), oomph::QElement< 3, NNODE_1D >::QElement(), and oomph::QHermiteElement< DIM-1 >::QHermiteElement().

◆ set_nnodal_position_type()

void oomph::FiniteElement::set_nnodal_position_type ( const unsigned & nposition_type )

inline

Set the number of types required to interpolate the coordinate.

Definition at line 1355 of file elements.h.

Referenced by oomph::ClampedHermiteShellBoundaryConditionElement::ClampedHermiteShellBoundaryConditionElement(), oomph::ClampedSlidingHermiteBeamBoundaryConditionElement::ClampedSlidingHermiteBeamBoundaryConditionElement(), and oomph::QHermiteElement< DIM-1 >::QHermiteElement().

◆ set_nodal_dimension()

void oomph::FiniteElement::set_nodal_dimension ( const unsigned & nodal_dim )

inline

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.

Definition at line 1351 of file elements.h.

Referenced by oomph::QHermiteElement< DIM-1 >::build_face_element(), oomph::QSpectralElement< 1, NNODE_1D >::build_face_element(), oomph::QSpectralElement< 2, NNODE_1D >::build_face_element(), oomph::QSpectralElement< 3, NNODE_1D >::build_face_element(), oomph::TElement< 1, NNODE_1D >::build_face_element(), oomph::TElement< 2, NNODE_1D >::build_face_element(), build_face_element(), oomph::TElement< 3, NNODE_1D >::build_face_element(), oomph::HermiteBeamElement::HermiteBeamElement(), and oomph::HermiteShellElement::HermiteShellElement().

◆ shape()

virtual void oomph::FiniteElement::shape	(	const Vector< double > &	s,
		Shape &	psi
	)		const

pure virtual

Calculate the geometric shape functions at local coordinate s. This function must be overloaded for each specific geometric element.

Implemented in oomph::BellElement< DIM, NNODE_1D >, oomph::PointElement, oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QSpectralElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, oomph::QSpectralElement< 2, NNODE_1D >, oomph::ClampedHermiteShellBoundaryConditionElement, oomph::QElement< 1, NNODE_1D >, oomph::QSpectralElement< 1, NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, oomph::QHermiteElement< DIM-1 >, oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >, oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >, oomph::QHermiteElement< DIM >, and oomph::QHermiteElement< DIM-1 >.

◆ shape_at_knot()

void oomph::FiniteElement::shape_at_knot	(	const unsigned &	ipt,
		Shape &	psi
	)		const

virtual

Return the geometric shape function at the ipt-th integration point.

Return the shape function stored at the ipt-th integration point.

Reimplemented in oomph::StorableShapeElementBase.

Definition at line 3160 of file elements.cc.

References i, s, and oomph::OneDimLagrange::shape().

◆ size()

double oomph::FiniteElement::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.

Calculate the size of the element (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.

Definition at line 4207 of file elements.cc.

References integrate_fct().

◆ tecplot_zone_string()

virtual std::string oomph::FiniteElement::tecplot_zone_string ( const unsigned & nplot ) const

inlinevirtual

Return string for tecplot zone header (when plotting nplot points in each "coordinate direction")

Definition at line 2990 of file elements.h.

◆ transform_derivatives()

void oomph::FiniteElement::transform_derivatives	(	const DenseMatrix< double > &	inverse_jacobian,
		DShape &	dbasis
	)		const

protectedvirtual

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.

Convert derivatives w.r.t local coordinates to derivatives w.r.t the coordinates used to assemble the inverse jacobian mapping passed as inverse_jacobian. The derivatives passed in dbasis will be modified in this function from dbasisds to dbasisdX.

Reimplemented in oomph::DiagQHermiteElement< DIM >.

Definition at line 2764 of file elements.cc.

References i, oomph::DShape::nindex1(), and oomph::DShape::nindex2().

Referenced by oomph::AxisymmetricTCrouzeixRaviartElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricTCrouzeixRaviartElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::GeneralisedNewtonianAxisymmetricTTaylorHoodElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::AxisymmetricTTaylorHoodElement::dpshape_and_dptest_eulerian_axi_nst(), oomph::TCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianTCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::TTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianTTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianQCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::QCrouzeixRaviartElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::GeneralisedNewtonianQTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), oomph::QTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst(), and oomph::AxisymmetricPoroelasticityEquations::transform_basis().

◆ transform_derivatives_diagonal()

void oomph::FiniteElement::transform_derivatives_diagonal	(	const DenseMatrix< double > &	inverse_jacobian,
		DShape &	dbasis
	)		const

protected

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.

Convert derivatives w.r.t local coordinates to derivatives w.r.t the coordinates used to assemble the inverse jacobian mapping passed as inverse_jacobian, assuming that the mapping is diagonal. This merely saves a few loops, but is probably worth it.

Definition at line 2806 of file elements.cc.

References oomph::DShape::nindex1(), and oomph::DShape::nindex2().

Referenced by oomph::DiagQHermiteElement< DIM >::transform_derivatives().

◆ transform_second_derivatives()

void oomph::FiniteElement::transform_second_derivatives	(	const DenseMatrix< double > &	jacobian,
		const DenseMatrix< double > &	inverse_jacobian,
		const DenseMatrix< double > &	jacobian2,
		DShape &	dbasis,
		DShape &	d2basis
	)		const

protectedvirtual

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.

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. This is a template-free general interface, that should be overloaded for efficiency.

Reimplemented in oomph::DiagQHermiteElement< DIM >, oomph::QHermiteElement< DIM >, and oomph::QHermiteElement< DIM-1 >.

Definition at line 3059 of file elements.cc.

◆ transform_second_derivatives_diagonal() [1/3]

template<unsigned DIM>

void oomph::FiniteElement::transform_second_derivatives_diagonal	(	const DenseMatrix< double > &	jacobian,
		const DenseMatrix< double > &	inverse_jacobian,
		const DenseMatrix< double > &	jacobian2,
		DShape &	dbasis,
		DShape &	d2basis
	)		const

protected

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.

◆ transform_second_derivatives_diagonal() [2/3]

template<>

void oomph::FiniteElement::transform_second_derivatives_diagonal	(	const DenseMatrix< double > &	jacobian,
		const DenseMatrix< double > &	inverse_jacobian,
		const DenseMatrix< double > &	jacobian2,
		DShape &	dbasis,
		DShape &	d2basis
	)		const

protected

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.

Definition at line 2989 of file elements.cc.

◆ transform_second_derivatives_diagonal() [3/3]

template<>

void oomph::FiniteElement::transform_second_derivatives_diagonal	(	const DenseMatrix< double > &	jacobian,
		const DenseMatrix< double > &	inverse_jacobian,
		const DenseMatrix< double > &	jacobian2,
		DShape &	dbasis,
		DShape &	d2basis
	)		const

protected

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

Definition at line 3012 of file elements.cc.

◆ transform_second_derivatives_template() [1/3]

template<unsigned DIM>

void oomph::FiniteElement::transform_second_derivatives_template	(	const DenseMatrix< double > &	jacobian,
		const DenseMatrix< double > &	inverse_jacobian,
		const DenseMatrix< double > &	jacobian2,
		DShape &	dbasis,
		DShape &	d2basis
	)		const

protected

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.

◆ transform_second_derivatives_template() [2/3]

template<>

void oomph::FiniteElement::transform_second_derivatives_template	(	const DenseMatrix< double > &	jacobian,
		const DenseMatrix< double > &	inverse_jacobian,
		const DenseMatrix< double > &	jacobian2,
		DShape &	dbasis,
		DShape &	d2basis
	)		const

protected

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.

Definition at line 2840 of file elements.cc.

◆ transform_second_derivatives_template() [3/3]

template<>

void oomph::FiniteElement::transform_second_derivatives_template	(	const DenseMatrix< double > &	jacobian,
		const DenseMatrix< double > &	inverse_jacobian,
		const DenseMatrix< double > &	jacobian2,
		DShape &	dbasis,
		DShape &	d2basis
	)		const

protected

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

Definition at line 2882 of file elements.cc.

References i.

◆ update_before_nodal_fd()

virtual void oomph::FiniteElement::update_before_nodal_fd ( )

inlineprotectedvirtual

Function that is called before the finite differencing of any nodal data. This may be overloaded to update any slaved data before finite differencing takes place.

Definition at line 1673 of file elements.h.

Referenced by oomph::RefineableElement::fill_in_jacobian_from_nodal_by_fd().

◆ update_in_nodal_fd()

virtual void oomph::FiniteElement::update_in_nodal_fd ( const unsigned & i )

inlineprotectedvirtual

Function called within the finite difference loop for nodal data after a change in the i-th nodal value.

Reimplemented in oomph::FSIWallElement.

Definition at line 1682 of file elements.h.

Referenced by oomph::RefineableElement::fill_in_jacobian_from_nodal_by_fd().

◆ vertex_node_pt()

virtual Node* oomph::FiniteElement::vertex_node_pt ( const unsigned & j ) const

inlinevirtual

Pointer to the j-th vertex node in the element. Broken virtual function in "pure" finite elements.

Definition at line 2383 of file elements.h.

References oomph::Global_string_for_annotation::string().

◆ write_paraview_offsets()

virtual void oomph::FiniteElement::write_paraview_offsets	(	std::ofstream &	file_out,
		const unsigned &	nplot,
		unsigned &	offset_sum
	)		const

inlinevirtual

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.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 2826 of file elements.h.

Referenced by oomph::Mesh::output_fct_paraview(), and oomph::Mesh::output_paraview().

◆ write_paraview_output_offset_information()

virtual void oomph::FiniteElement::write_paraview_output_offset_information	(	std::ofstream &	file_out,
		const unsigned &	nplot,
		unsigned &	counter
	)		const

inlinevirtual

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.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 2801 of file elements.h.

Referenced by oomph::Mesh::output_fct_paraview(), and oomph::Mesh::output_paraview().

◆ write_paraview_type()

virtual void oomph::FiniteElement::write_paraview_type	(	std::ofstream &	file_out,
		const unsigned &	nplot
	)		const

inlinevirtual

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.

Reimplemented in oomph::TElement< 3, NNODE_1D >, oomph::TElement< 2, NNODE_1D >, oomph::TElement< 1, NNODE_1D >, oomph::QElement< 3, NNODE_1D >, oomph::QElement< 2, NNODE_1D >, and oomph::QElement< 1, NNODE_1D >.

Definition at line 2814 of file elements.h.

Referenced by oomph::Mesh::output_fct_paraview(), and oomph::Mesh::output_paraview().

◆ write_tecplot_zone_footer() [1/2]

virtual void oomph::FiniteElement::write_tecplot_zone_footer	(	std::ostream &	outfile,
		const unsigned &	nplot
	)		const

inlinevirtual

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.

Reimplemented in oomph::TElement< 3, NNODE_1D >, and oomph::TElement< 2, NNODE_1D >.

Definition at line 3003 of file elements.h.

◆ write_tecplot_zone_footer() [2/2]

virtual void oomph::FiniteElement::write_tecplot_zone_footer	(	FILE *	file_pt,
		const unsigned &	nplot
	)		const

inlinevirtual

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.

Reimplemented in oomph::TElement< 3, NNODE_1D >, and oomph::TElement< 2, NNODE_1D >.

Definition at line 3011 of file elements.h.

◆ zeta_nodal()

virtual double oomph::FiniteElement::zeta_nodal	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inlinevirtual

Specify the values of the "global" intrinsic coordinate, zeta, of a compound geometric object (a mesh of elements) when the element is viewied as a sub-geometric object. The default assumption is that the element will be treated as a sub-geometric object in a bulk Mesh of other elements (geometric objects). The "global" coordinate of the compound geometric object is simply the Eulerian coordinate, x. The second default assumption is that the coordinate zeta will be stored at the nodes and interpolated using the shape functions of the element. This function returns the value of zeta stored at local node n, where k is the type of coordinate and i is the coordinate direction. The function is virtual so that it can be overloaded by different types of element: FaceElements and SolidFiniteElements.

Definition at line 2573 of file elements.h.

Member Data Documentation

◆ Accept_negative_jacobian

bool oomph::FiniteElement::Accept_negative_jacobian = false

static

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).

Set the default value of the Accept_negative_jacobian flag to be false

Definition at line 1739 of file elements.h.

Referenced by check_J_eulerian_at_knots(), and d_dshape_eulerian_dnodal_coordinates_templated_helper().

◆ Default_Initial_Nvalue

const unsigned oomph::FiniteElement::Default_Initial_Nvalue = 0

staticprotected

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.

Default value for the number of values at a node.

Definition at line 1333 of file elements.h.

Referenced by d_dshape_eulerian_dnodal_coordinates_templated_helper().

◆ Elemental_dimension

unsigned oomph::FiniteElement::Elemental_dimension

private

The spatial dimension of the element, i.e. the number of local coordinates used to parametrize it.

Definition at line 1293 of file elements.h.

◆ Integral_pt

Integral* oomph::FiniteElement::Integral_pt

private

Pointer to the spatial integration scheme.

Definition at line 1279 of file elements.h.

◆ Macro_elem_pt

MacroElement* oomph::FiniteElement::Macro_elem_pt

protected

Pointer to the element's macro element (NULL by default)

Definition at line 1647 of file elements.h.

Referenced by oomph::RefineableQElement< 1 >::build(), oomph::RefineableQElement< 2 >::build(), oomph::QSolidElementBase::get_x_and_xi(), and oomph::QElementBase::get_x_from_macro_element().

◆ N2deriv

const unsigned oomph::FiniteElement::N2deriv ={0,1,3,6}

staticprotected

Static array that holds the number of second derivatives as a function of the dimension of the element.

Static array that holds the number of rows in the second derivative matrix as a function of spatial dimension. In one-dimension, there is only one possible second derivative. In two-dimensions, there are three, the two second derivatives and the mixed derivatives. In three dimensions there are six.

Definition at line 1440 of file elements.h.

Referenced by oomph::RefineableElement::assemble_local_to_eulerian_jacobian2(), oomph::RefineableSolidElement::assemble_local_to_lagrangian_jacobian2(), and d_dshape_eulerian_dnodal_coordinates_templated_helper().

◆ Nnodal_position_type

unsigned oomph::FiniteElement::Nnodal_position_type

private

The number of coordinate types required to interpolate the element's geometry between the nodes. For Lagrange elements it is 1 (the default). It must be over-ridden by using the set_nposition_type() function in the constructors of elements that use generalised coordinate, e.g. for 1D Hermite elements Nnodal_position_types =2.

Definition at line 1307 of file elements.h.

◆ Nnode

unsigned oomph::FiniteElement::Nnode

private

Number of nodes in the element.

Definition at line 1289 of file elements.h.

◆ Nodal_dimension

unsigned oomph::FiniteElement::Nodal_dimension

private

The spatial dimension of the nodes in the element. We assume that nodes have the same spatial dimension, because we cannot think of any "real" problems for which that would not be the case.

Definition at line 1299 of file elements.h.

◆ Nodal_local_eqn

int** oomph::FiniteElement::Nodal_local_eqn

private

Storage for the local equation numbers associated with the values stored at the nodes.

Definition at line 1286 of file elements.h.

◆ Node_location_tolerance

const double oomph::FiniteElement::Node_location_tolerance = 1.0e-14

staticprotected

Default value for the tolerance to be used when locating nodes via local coordinates.

Default value that is used for the tolerance required when locating nodes via local coordinates.

Definition at line 1337 of file elements.h.

◆ Node_pt

Node** oomph::FiniteElement::Node_pt

private

Storage for pointers to the nodes in the element.

Definition at line 1282 of file elements.h.

Referenced by oomph::BackupMeshForProjection< GEOMETRIC_ELEMENT >::BackupMeshForProjection().

◆ Suppress_output_while_checking_for_inverted_elements

bool oomph::FiniteElement::Suppress_output_while_checking_for_inverted_elements =false

static

Static boolean to suppress output while checking for inverted elements.

Set default for static boolean to suppress output while checking for inverted elements

Definition at line 1743 of file elements.h.

Referenced by oomph::Mesh::check_inverted_elements(), check_jacobian(), and d_dshape_eulerian_dnodal_coordinates_templated_helper().

◆ Tolerance_for_singular_jacobian

double oomph::FiniteElement::Tolerance_for_singular_jacobian = 1.0e-16

static

Tolerance below which the jacobian is considered singular.

Set the default tolerance for a singular jacobian.

Definition at line 1734 of file elements.h.

Referenced by d_dshape_eulerian_dnodal_coordinates_templated_helper().

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Attributes

Detailed Description

Member Typedef Documentation

◆ SteadyExactSolutionFctPt

◆ UnsteadyExactSolutionFctPt

Constructor & Destructor Documentation

◆ FiniteElement() [1/2]

◆ ~FiniteElement()

◆ FiniteElement() [2/2]

Member Function Documentation

◆ assemble_eulerian_base_vectors()

◆ assemble_local_to_eulerian_jacobian()

◆ assemble_local_to_eulerian_jacobian2()

◆ assign_all_generic_local_eqn_numbers()

◆ assign_nodal_local_eqn_numbers()

◆ build_face_element()

◆ bulk_coordinate_derivatives_fct_pt()

◆ check_J_eulerian_at_knots()

◆ check_jacobian()

◆ compute_abs_error()

◆ compute_error() [1/4]

◆ compute_error() [2/4]

◆ compute_error() [3/4]

◆ compute_error() [4/4]

◆ compute_physical_size()

◆ construct_boundary_node() [1/2]

◆ construct_boundary_node() [2/2]

◆ construct_node() [1/2]

◆ construct_node() [2/2]

◆ d2shape_eulerian()

◆ d2shape_eulerian_at_knot()

◆ d2shape_local()

◆ d2shape_local_at_knot()

◆ d_dshape_eulerian_dnodal_coordinates()

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [1/5]

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [2/5]

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [3/5]

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [4/5]

◆ d_dshape_eulerian_dnodal_coordinates_templated_helper() [5/5]

◆ describe_local_dofs()

◆ describe_nodal_local_dofs()

◆ dim()

◆ disable_ALE()

◆ dJ_eulerian_at_knot()

◆ dJ_eulerian_dnodal_coordinates()

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [1/5]

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [2/5]

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [3/5]

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [4/5]

◆ dJ_eulerian_dnodal_coordinates_templated_helper() [5/5]

◆ dnodal_position_dt() [1/2]

◆ dnodal_position_dt() [2/2]

◆ dnodal_position_gen_dt() [1/2]

◆ dnodal_position_gen_dt() [2/2]

◆ dposition_dt()

◆ dshape_eulerian()

◆ dshape_eulerian_at_knot() [1/2]

◆ dshape_eulerian_at_knot() [2/2]

◆ dshape_local()

◆ dshape_local_at_knot()

◆ element_geometry()

◆ enable_ALE()

◆ face_node_number_error_check()

◆ face_outer_unit_normal_sign()

◆ face_to_bulk_coordinate_fct_pt()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_jacobian_from_nodal_by_fd() [1/2]

◆ fill_in_jacobian_from_nodal_by_fd() [2/2]

◆ geom_data_pt()

◆ get_bulk_node_number()

◆ get_centre_of_gravity_and_max_radius_in_terms_of_zeta()

◆ get_dresidual_dnodal_coordinates()

◆ get_node_at_local_coordinate()

◆ get_node_number()