General QElement class specialised to two spatial dimensions. More...

#include <Qelements.h>

Inheritance diagram for oomph::QElement< 2, NNODE_1D >:

Public Member Functions
	QElement ()
	Constructor. More...

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

void	shape (const Vector< double > &s, Shape &psi) const
	Broken assignment operator. More...

void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Derivatives of shape functions for specific QElement<2,..> More...

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

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

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

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

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

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

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. More...

void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
	Get the local fraction of node j in the element. More...

double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)

Node *	get_node_at_local_coordinate (const Vector< double > &s) const
	Get the node at the specified local coordinate. More...

unsigned	nnode_1d () const
	Number of nodes along each element edge. More...

unsigned	nplot_points_paraview (const unsigned &nplot) const

unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

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

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

void	output (FILE *file_pt, const unsigned &n_plot)
	C_style output at n_plot points. More...

void	get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &use_equally_spaced_interior_sample_points=false) const

std::string	tecplot_zone_string (const unsigned &nplot) const

unsigned	nplot_points (const unsigned &nplot) const

unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const

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...

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

Public Member Functions inherited from oomph::QElementBase
	QElementBase ()
	Constructor: Initialise pointers to macro element reference coords. More...

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

virtual	~QElementBase ()
	Broken assignment operator. More...

bool	local_coord_is_valid (const Vector< double > &s)
	Check whether the local coordinate are valid or not. More...

void	move_local_coord_back_into_element (Vector< double > &s) const

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

double &	s_macro_ll (const unsigned &i)

double &	s_macro_ur (const unsigned &i)

double	s_macro_ll (const unsigned &i) const

double	s_macro_ur (const unsigned &i) const

void	get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const

void	get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)

unsigned	nnode_on_face () const

ElementGeometry::ElementGeometry	element_geometry () const
	It's a Q element! More...

Public Member Functions inherited from oomph::QElementGeometricBase
	QElementGeometricBase ()
	Empty default constructor. More...

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

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)

void	set_nodal_dimension (const unsigned &nodal_dim)

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)

int	nodal_local_eqn (const unsigned &n, const unsigned &i) const

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const

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

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

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

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_at_knot (const unsigned &ipt, Shape &psi) const

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const

virtual double	J_eulerian (const Vector< double > &s) const

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const

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

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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...

double	raw_nodal_position (const unsigned &n, const unsigned &i) const

double	raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

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

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

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

double	nodal_position (const unsigned &n, const unsigned &i) const

double	nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const

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

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

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

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

double	raw_nodal_value (const unsigned &n, const unsigned &i) const

double	raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const

double	nodal_value (const unsigned &n, const unsigned &i) const

double	nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const

unsigned	dim () const

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

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

virtual double	interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)

virtual void	interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const

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

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

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	write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

void	integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
	Integrate Vector-valued function over element. More...

void	integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
	Integrate Vector-valued time-dep function over element. More...

virtual void	build_face_element (const int &face_index, FaceElement *face_element_pt)

virtual unsigned	self_test ()

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

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

virtual	~GeneralisedElement ()
	Virtual destructor to clean up any memory allocated by the object. More...

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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)

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)

void	describe_dofs (std::ostream &out, const std::string &current_string) const

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

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)

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const

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

	GeomObject (const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)

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

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

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

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

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

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

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

virtual void	position (const double &t, const Vector< double > &zeta, Vector< double > &r) const

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const

Static Private Attributes
static Gauss< 2, NNODE_1D >	Default_integration_scheme
	Assign the spatial integration scheme. More...

Additional Inherited Members
Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

Protected Member Functions inherited from oomph::FiniteElement
virtual void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const

virtual void	assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const

virtual void	assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const

template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

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

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

virtual double	local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

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

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

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

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

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

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

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

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

virtual void	fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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)

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

int	internal_local_eqn (const unsigned &i, const unsigned &j) const

int	external_local_eqn (const unsigned &i, const unsigned &j)

virtual void	fill_in_contribution_to_residuals (Vector< double > &residuals)

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

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)

virtual void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default value for the number of values at a node. More...

static const double	Node_location_tolerance = 1.0e-14

static const unsigned	N2deriv [] = {0, 1, 3, 6}

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix

static std::deque< double * >	Dof_pt_deque

Detailed Description

template<unsigned NNODE_1D>
class oomph::QElement< 2, NNODE_1D >

General QElement class specialised to two spatial dimensions.

Constructor & Destructor Documentation

◆ QElement() [1/2]

template<unsigned NNODE_1D>

oomph::QElement< 2, NNODE_1D >::QElement ( )

inline

Constructor.

     {
       // There are NNODE_1D*NNODE_1D nodes in this element
       this->set_n_node(NNODE_1D * NNODE_1D);
       // Set the dimensions of the element and the nodes, by default, both 2D
       set_dimension(2);
       // Assign default (full) spatial integration scheme
       set_integration_scheme(&Default_integration_scheme);
     }

◆ QElement() [2/2]

template<unsigned NNODE_1D>

oomph::QElement< 2, NNODE_1D >::QElement ( const QElement< 2, NNODE_1D > & )

delete

Broken copy constructor.

Member Function Documentation

◆ bulk_coordinate_derivatives_fct_pt()

template<unsigned NNODE_1D>

BulkCoordinateDerivativesFctPt oomph::QElement< 2, NNODE_1D >::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 from oomph::FiniteElement.

     {
       if (face_index == 1)
       {
         return &QElement2BulkCoordinateDerivatives::faces0;
       }
       else if (face_index == -1)
       {
         return &QElement2BulkCoordinateDerivatives::faces0;
       }
       else if (face_index == -2)
       {
         return &QElement2BulkCoordinateDerivatives::faces1;
       }
       else if (face_index == 2)
       {
         return &QElement2BulkCoordinateDerivatives::faces1;
       }
       else
       {
         std::string err = "Face index should be in {-1, +1}.";
         throw OomphLibError(
           err, OOMPH_EXCEPTION_LOCATION, OOMPH_CURRENT_FUNCTION);
       }
     }

References oomph::QElement2BulkCoordinateDerivatives::faces0(), oomph::QElement2BulkCoordinateDerivatives::faces1(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and oomph::Global_string_for_annotation::string().

◆ d2shape_local()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::d2shape_local	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsids,
		DShape &	d2psids
	)		const

virtual

Compute the geometric shape functions, derivatives and second derivatives w.r.t. local coordinates at local coordinate s 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) = \( \partial^2 \psi_j / \partial s_0 \partial s_1 \)

Second derivatives of shape functions for specific QElement<2,..>: 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) = \( \partial^2 \psi_j / \partial s_0 \partial s_1 \)

Reimplemented from oomph::FiniteElement.

   {
     // Local storage
     double Psi[2][NNODE_1D];
     double DPsi[2][NNODE_1D];
     double D2Psi[2][NNODE_1D];
     // Index for the assembly process
     unsigned index = 0;
  
     // Call the shape functions and derivatives
     OneDimLagrange::shape<NNODE_1D>(s[0], Psi[0]);
     OneDimLagrange::shape<NNODE_1D>(s[1], Psi[1]);
     OneDimLagrange::dshape<NNODE_1D>(s[0], DPsi[0]);
     OneDimLagrange::dshape<NNODE_1D>(s[1], DPsi[1]);
     OneDimLagrange::d2shape<NNODE_1D>(s[0], D2Psi[0]);
     OneDimLagrange::d2shape<NNODE_1D>(s[1], D2Psi[1]);
  
     // Loop over shape functions in element
     for (unsigned i = 0; i < NNODE_1D; i++)
     {
       for (unsigned j = 0; j < NNODE_1D; j++)
       {
         // Assign the values
         psi[index] = Psi[1][i] * Psi[0][j];
         // First derivatives
         dpsids(index, 0) = Psi[1][i] * DPsi[0][j];
         dpsids(index, 1) = DPsi[1][i] * Psi[0][j];
         // Second derivatives
         // N.B. index 2 is the mixed derivative
         d2psids(index, 0) = Psi[1][i] * D2Psi[0][j];
         d2psids(index, 1) = D2Psi[1][i] * Psi[0][j];
         d2psids(index, 2) = DPsi[1][i] * DPsi[0][j];
         // Increment the index
         ++index;
       }
     }
   }

References i, j, and s.

◆ dshape_local()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::dshape_local	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsids
	)		const

virtual

Derivatives of shape functions for specific QElement<2,..>

Compute the geometric shape functions and derivatives w.r.t. local coordinates at local coordinate s

Reimplemented from oomph::FiniteElement.

   {
     // Local storage
     double Psi[2][NNODE_1D];
     double DPsi[2][NNODE_1D];
     unsigned index = 0;
  
     // Call the shape functions and derivatives
     OneDimLagrange::shape<NNODE_1D>(s[0], Psi[0]);
     OneDimLagrange::shape<NNODE_1D>(s[1], Psi[1]);
     OneDimLagrange::dshape<NNODE_1D>(s[0], DPsi[0]);
     OneDimLagrange::dshape<NNODE_1D>(s[1], DPsi[1]);
  
     // Loop over shape functions in element
     for (unsigned i = 0; i < NNODE_1D; i++)
     {
       for (unsigned j = 0; j < NNODE_1D; j++)
       {
         // Assign the values
         dpsids(index, 0) = Psi[1][i] * DPsi[0][j];
         dpsids(index, 1) = DPsi[1][i] * Psi[0][j];
         psi[index] = Psi[1][i] * Psi[0][j];
         // Increment the index
         ++index;
       }
     }
   }

References i, j, and s.

◆ face_outer_unit_normal_sign()

template<unsigned NNODE_1D>

int oomph::QElement< 2, NNODE_1D >::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 from oomph::FiniteElement.

     {
       if (face_index < 0)
       {
         return 1;
       }
       else if (face_index > 0)
       {
         return -1;
       }
       else
       {
         std::string err = "Face index should be one of {-1, +1, -2, +2}.";
         throw OomphLibError(
           err, OOMPH_EXCEPTION_LOCATION, OOMPH_CURRENT_FUNCTION);
       }
     }

References OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and oomph::Global_string_for_annotation::string().

◆ face_to_bulk_coordinate_fct_pt()

template<unsigned NNODE_1D>

CoordinateMappingFctPt oomph::QElement< 2, NNODE_1D >::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 from oomph::FiniteElement.

     {
       if (face_index == 1)
       {
         return &QElement2FaceToBulkCoordinates::face2;
       }
       else if (face_index == -1)
       {
         return &QElement2FaceToBulkCoordinates::face0;
       }
       else if (face_index == -2)
       {
         return &QElement2FaceToBulkCoordinates::face1;
       }
       else if (face_index == 2)
       {
         return &QElement2FaceToBulkCoordinates::face3;
       }
       else
       {
         std::string err = "Face index should be in {-1, +1}.";
         throw OomphLibError(
           err, OOMPH_EXCEPTION_LOCATION, OOMPH_CURRENT_FUNCTION);
       }
     }

References oomph::QElement2FaceToBulkCoordinates::face0(), oomph::QElement2FaceToBulkCoordinates::face1(), oomph::QElement2FaceToBulkCoordinates::face2(), oomph::QElement2FaceToBulkCoordinates::face3(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and oomph::Global_string_for_annotation::string().

◆ get_bulk_node_number()

template<unsigned NNODE_1D>

unsigned oomph::QElement< 2, NNODE_1D >::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 from oomph::FiniteElement.

     {
       face_node_number_error_check(i);
  
       const unsigned nn1d = nnode_1d();
  
       if (face_index == -1)
       {
         return i * nn1d;
       }
       else if (face_index == +1)
       {
         return nn1d * i + nn1d - 1;
       }
       else if (face_index == -2)
       {
         return i;
       }
       else if (face_index == +2)
       {
         return nn1d * (nn1d - 1) + i;
       }
       else
       {
         std::string err = "Face index should be in {-1, +1, -2, +2}.";
         throw OomphLibError(
           err, OOMPH_EXCEPTION_LOCATION, OOMPH_CURRENT_FUNCTION);
       }
     }

References i, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and oomph::Global_string_for_annotation::string().

◆ get_node_at_local_coordinate()

template<unsigned NNODE_1D>

Node * oomph::QElement< 2, NNODE_1D >::get_node_at_local_coordinate ( const Vector< double > & s ) const

virtual

Get the node at the specified local coordinate.

Return the node at the specified local coordinate.

Reimplemented from oomph::FiniteElement.

   {
     // Load the tolerance into a local variable
     double tol = FiniteElement::Node_location_tolerance;
     // There are two possible indices.
     Vector<int> index(2);
     // Loop over the coordinates and determine the indices
     for (unsigned i = 0; i < 2; i++)
     {
       // If we are at the lower limit, the index is zero
       if (std::fabs(s[i] + 1.0) < tol)
       {
         index[i] = 0;
       }
       // If we are at the upper limit, the index is the number of nodes minus 1
       else if (std::fabs(s[i] - 1.0) < tol)
       {
         index[i] = NNODE_1D - 1;
       }
       // Otherwise, we have to calculate the index in general
       else
       {
         // For uniformly spaced nodes the node number would be
         double float_index = 0.5 * (1.0 + s[i]) * (NNODE_1D - 1);
         // Convert to an integer by taking the floor (rounding down)
         index[i] = static_cast<int>(std::floor(float_index));
         // What is the excess. This should be safe because the
         // we have rounded down
         double excess = float_index - index[i];
         // If the excess is bigger than our tolerance there is no node,
         // return null
         // Note that we test at both lower and upper ends.
         if ((excess > tol) && ((1.0 - excess) > tol))
         {
           return 0;
         }
         // If we are at the upper end (i.e. the system has actually rounded up)
         // we need to add one to the index
         if ((1.0 - excess) <= tol)
         {
           index[i] += 1;
         }
       }
     }
     // If we've got here we have a node, so let's return a pointer to it
     return node_pt(index[0] + NNODE_1D * index[1]);
   }

References boost::multiprecision::fabs(), Eigen::bfloat16_impl::floor(), i, oomph::FiniteElement::Node_location_tolerance, and s.

◆ get_s_plot()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::get_s_plot	(	const unsigned &	i,
		const unsigned &	nplot,
		Vector< double > &	s,
		const bool &	use_equally_spaced_interior_sample_points = `false`
	)		const

inlinevirtual

Get cector of local coordinates of plot point i (when plotting nplot points in each "coordinate direction).

Reimplemented from oomph::FiniteElement.

     {
       if (nplot > 1)
       {
         unsigned i0 = i % nplot;
         unsigned i1 = (i - i0) / nplot;
  
         s[0] = -1.0 + 2.0 * double(i0) / double(nplot - 1);
         s[1] = -1.0 + 2.0 * double(i1) / double(nplot - 1);
         if (use_equally_spaced_interior_sample_points)
         {
           double range = 2.0;
           double dx_new = range / double(nplot);
           double range_new = double(nplot - 1) * dx_new;
           s[0] = -1.0 + 0.5 * dx_new + range_new * (1.0 + s[0]) / range;
           s[1] = -1.0 + 0.5 * dx_new + range_new * (1.0 + s[1]) / range;
         }
       }
       else
       {
         s[0] = 0.0;
         s[1] = 0.0;
       }
     }

References i, and s.

Referenced by oomph::RefineableBuoyantQAxisymCrouzeixRaviartElement::output(), oomph::AxisymmetricQAdvectionCrouzeixRaviartElement::output(), and oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output().

◆ invert_jacobian_mapping()

template<unsigned NNODE_1D>

double oomph::QElement< 2, NNODE_1D >::invert_jacobian_mapping	(	const DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	inverse_jacobian
	)		const

inlinevirtual

Overload the template-free interface for the calculation of inverse jacobian matrix. This is a two-dimensional element, so use the two-d version.

Reimplemented from oomph::FiniteElement.

     {
       return FiniteElement::invert_jacobian<2>(jacobian, inverse_jacobian);
     }

◆ local_coordinate_of_node()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::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.

Reimplemented from oomph::FiniteElement.

     {
       s.resize(2);
       unsigned j0 = j % NNODE_1D;
       unsigned j1 = j / NNODE_1D;
       const double S_min = this->s_min();
       const double S_range = this->s_max() - S_min;
       s[0] = S_min + double(j0) / double(NNODE_1D - 1) * S_range;
       s[1] = S_min + double(j1) / double(NNODE_1D - 1) * S_range;
     }

References j, and s.

◆ local_fraction_of_node()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::local_fraction_of_node	(	const unsigned &	j,
		Vector< double > &	s_fraction
	)

inlinevirtual

Get the local fraction of node j in the element.

Reimplemented from oomph::FiniteElement.

     {
       s_fraction.resize(2);
       unsigned j0 = j % NNODE_1D;
       unsigned j1 = j / NNODE_1D;
       s_fraction[0] = double(j0) / double(NNODE_1D - 1);
       s_fraction[1] = double(j1) / double(NNODE_1D - 1);
     }

References j.

◆ local_one_d_fraction_of_node()

template<unsigned NNODE_1D>

double oomph::QElement< 2, NNODE_1D >::local_one_d_fraction_of_node	(	const unsigned &	n1d,
		const unsigned &	i
	)

inlinevirtual

This function returns the local fraction of ant nodes in the n-th positoin in a one dimensional expansion along the i-th local coordinate

Reimplemented from oomph::FiniteElement.

     {
       // It's just the value of the node divided by the number of 1-D nodes
       return double(n1d) / double(NNODE_1D - 1);
     }

◆ nnode_1d()

template<unsigned NNODE_1D>

unsigned oomph::QElement< 2, NNODE_1D >::nnode_1d ( ) const

inlinevirtual

Number of nodes along each element edge.

Reimplemented from oomph::FiniteElement.

     {
       return NNODE_1D;
     }

◆ nplot_points()

template<unsigned NNODE_1D>

unsigned oomph::QElement< 2, NNODE_1D >::nplot_points ( const unsigned & nplot ) const

inlinevirtual

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

Reimplemented from oomph::FiniteElement.

     {
       unsigned DIM = 2;
       unsigned np = 1;
       for (unsigned i = 0; i < DIM; i++)
       {
         np *= nplot;
       }
       return np;
     };

References DIM, and i.

Referenced by oomph::RefineableBuoyantQAxisymCrouzeixRaviartElement::output(), oomph::AxisymmetricQAdvectionCrouzeixRaviartElement::output(), and oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output().

◆ nplot_points_paraview()

template<unsigned NNODE_1D>

unsigned oomph::QElement< 2, NNODE_1D >::nplot_points_paraview ( const unsigned & nplot ) const

inlinevirtual

Return the number of actual plot points for paraview plot with parameter nplot.

Reimplemented from oomph::FiniteElement.

     {
       return nplot * nplot;
     }

◆ nsub_elements_paraview()

template<unsigned NNODE_1D>

unsigned oomph::QElement< 2, NNODE_1D >::nsub_elements_paraview ( const unsigned & nplot ) const

inlinevirtual

Return the number of local sub-elements for paraview plot with parameter nplot.

Reimplemented from oomph::FiniteElement.

     {
       return (nplot - 1) * (nplot - 1);
     }

◆ nvertex_node()

template<unsigned NNODE_1D>

unsigned oomph::QElement< 2, NNODE_1D >::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element.

Implements oomph::QuadElementBase.

Reimplemented in oomph::RefineableQYoungLaplaceElement< NNODE_1D >, oomph::RefineableQSphericalAdvectionDiffusionElement< NNODE_1D >, oomph::RefineableQSphericalAdvectionDiffusionElement< 3 >, and oomph::RefineableQAxisymAdvectionDiffusionElement< 3 >.

     {
       return 4;
     }

Referenced by oomph::RefineableQAxisymAdvectionDiffusionElement< NNODE_1D >::nvertex_node(), oomph::RefineableQSphericalAdvectionDiffusionElement< NNODE_1D >::nvertex_node(), and oomph::RefineableQYoungLaplaceElement< NNODE_1D >::nvertex_node().

◆ output() [1/4]

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::output ( FILE * file_pt )

virtual

C-style output.

C-style output function for QElement<2,NNODE_1D>

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QTimeHarmonicFourierDecomposedLinearElasticityElement< NNODE_1D >, oomph::QSteadyAxisymAdvectionDiffusionElement< NNODE_1D >, oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >, oomph::QPMLFourierDecomposedHelmholtzElement< NNODE_1D >, oomph::SolidQElement< 2, NNODE_1D >, and oomph::QAxisymAdvectionDiffusionElement< 3 >.

   {
     output(file_pt, NNODE_1D);
   }

References oomph::output().

◆ output() [2/4]

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::output	(	FILE *	file_pt,
		const unsigned &	n_plot
	)

virtual

C_style output at n_plot points.

C-style output function for n_plot points in each coordinate direction.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QTimeHarmonicFourierDecomposedLinearElasticityElement< NNODE_1D >, oomph::QSteadyAxisymAdvectionDiffusionElement< NNODE_1D >, oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >, oomph::QPMLFourierDecomposedHelmholtzElement< NNODE_1D >, oomph::SolidQElement< 2, NNODE_1D >, and oomph::QAxisymAdvectionDiffusionElement< 3 >.

   {
     // Local variables
     Vector<double> s(2);
  
     // Find the dimension of the nodes
     unsigned n_dim = this->nodal_dimension();
  
     // Tecplot header info
     // outfile << "ZONE I=" << n_plot << ", J=" << n_plot << std::endl;
     fprintf(file_pt, "ZONE I=%i, J=%i\n", n_plot, n_plot);
  
     // Loop over element nodes
     for (unsigned l2 = 0; l2 < n_plot; l2++)
     {
       s[1] = -1.0 + l2 * 2.0 / (n_plot - 1);
       for (unsigned l1 = 0; l1 < n_plot; l1++)
       {
         s[0] = -1.0 + l1 * 2.0 / (n_plot - 1);
  
         // Output the coordinates
         for (unsigned i = 0; i < n_dim; i++)
         {
           // outfile << interpolated_x(s,i) << " " ;
           fprintf(file_pt, "%g ", interpolated_x(s, i));
         }
         // outfile << std::endl;
         fprintf(file_pt, "\n");
       }
     }
     // outfile << std::endl;
     fprintf(file_pt, "\n");
   }

References i, and s.

◆ output() [3/4]

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::output ( std::ostream & outfile )

virtual

Output.

The output function for QElement<2,NNODE_1D>

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QYoungLaplaceElement< NNODE_1D >, oomph::QTimeHarmonicFourierDecomposedLinearElasticityElement< NNODE_1D >, oomph::QSteadyAxisymAdvectionDiffusionElement< NNODE_1D >, oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >, oomph::QPMLFourierDecomposedHelmholtzElement< NNODE_1D >, oomph::SolidQElement< 2, NNODE_1D >, and oomph::QAxisymAdvectionDiffusionElement< 3 >.

   {
     output(outfile, NNODE_1D);
   }

References oomph::output().

◆ output() [4/4]

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::output	(	std::ostream &	outfile,
		const unsigned &	n_plot
	)

virtual

Output at n_plot points.

The output function for n_plot points in each coordinate direction.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QYoungLaplaceElement< NNODE_1D >, oomph::QTimeHarmonicFourierDecomposedLinearElasticityElement< NNODE_1D >, oomph::QSteadyAxisymAdvectionDiffusionElement< NNODE_1D >, oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >, oomph::QPMLFourierDecomposedHelmholtzElement< NNODE_1D >, oomph::SolidQElement< 2, NNODE_1D >, and oomph::QAxisymAdvectionDiffusionElement< 3 >.

   {
     // Local variables
     Vector<double> s(2);
  
     // Tecplot header info
     outfile << "ZONE I=" << n_plot << ", J=" << n_plot << std::endl;
  
     // Find the dimension of the nodes
     unsigned n_dim = this->nodal_dimension();
  
     // Loop over plot points
     for (unsigned l2 = 0; l2 < n_plot; l2++)
     {
       s[1] = -1.0 + l2 * 2.0 / (n_plot - 1);
       for (unsigned l1 = 0; l1 < n_plot; l1++)
       {
         s[0] = -1.0 + l1 * 2.0 / (n_plot - 1);
  
         // Output the coordinates
         for (unsigned i = 0; i < n_dim; i++)
         {
           outfile << interpolated_x(s, i) << " ";
         }
         outfile << std::endl;
       }
     }
     outfile << std::endl;
   }

References i, and s.

◆ s_max()

template<unsigned NNODE_1D>

double oomph::QElement< 2, NNODE_1D >::s_max ( ) const

inlinevirtual

Max. value of local coordinate.

Reimplemented from oomph::FiniteElement.

     {
       return 1.0;
     }

◆ s_min()

template<unsigned NNODE_1D>

double oomph::QElement< 2, NNODE_1D >::s_min ( ) const

inlinevirtual

Min. value of local coordinate.

Reimplemented from oomph::FiniteElement.

     {
       return -1.0;
     }

◆ shape()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::shape	(	const Vector< double > &	s,
		Shape &	psi
	)		const

virtual

Broken assignment operator.

Calculate the geometric shape functions at local coordinate s

Shape function for specific QElement<2,..>

Implements oomph::FiniteElement.

   {
     // Local storage
     double Psi[2][NNODE_1D];
     // Call the OneDimensional Shape functions
     OneDimLagrange::shape<NNODE_1D>(s[0], Psi[0]);
     OneDimLagrange::shape<NNODE_1D>(s[1], Psi[1]);
     // Index for the shape functions
     unsigned index = 0;
  
     // Now let's loop over the nodal points in the element
     // s1 is the "x" coordinate, s2 the "y"
     for (unsigned i = 0; i < NNODE_1D; i++)
     {
       for (unsigned j = 0; j < NNODE_1D; j++)
       {
         // Multiply the two 1D functions together to get the 2D function
         psi[index] = Psi[1][i] * Psi[0][j];
         // Incremenet the index
         ++index;
       }
     }
   }

References i, j, and s.

◆ tecplot_zone_string()

template<unsigned NNODE_1D>

std::string oomph::QElement< 2, NNODE_1D >::tecplot_zone_string ( const unsigned & nplot ) const

inlinevirtual

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

Reimplemented from oomph::FiniteElement.

     {
       std::ostringstream header;
       header << "ZONE I=" << nplot << ", J=" << nplot << "\n";
       return header.str();
     }

Referenced by oomph::RefineableBuoyantQAxisymCrouzeixRaviartElement::output(), oomph::AxisymmetricQAdvectionCrouzeixRaviartElement::output(), and oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output().

◆ vertex_node_pt()

template<unsigned NNODE_1D>

Node* oomph::QElement< 2, NNODE_1D >::vertex_node_pt ( const unsigned & j ) const

inlinevirtual

Pointer to the j-th vertex node in the element.

Implements oomph::QuadElementBase.

Reimplemented in oomph::RefineableQYoungLaplaceElement< NNODE_1D >, oomph::RefineableQSphericalAdvectionDiffusionElement< NNODE_1D >, oomph::RefineableQSphericalAdvectionDiffusionElement< 3 >, and oomph::RefineableQAxisymAdvectionDiffusionElement< 3 >.

     {
       unsigned n_node_1d = nnode_1d();
       Node* nod_pt;
       switch (j)
       {
         case 0:
           nod_pt = node_pt(0);
           break;
         case 1:
           nod_pt = node_pt(n_node_1d - 1);
           break;
         case 2:
           nod_pt = node_pt(n_node_1d * (n_node_1d - 1));
           break;
         case 3:
           nod_pt = node_pt(n_node_1d * n_node_1d - 1);
           break;
         default:
           std::ostringstream error_message;
           error_message << "Vertex node number is " << j
                         << " but must be from 0 to 3\n";
  
           throw OomphLibError(error_message.str(),
                               OOMPH_CURRENT_FUNCTION,
                               OOMPH_EXCEPTION_LOCATION);
       }
       return nod_pt;
     }

References j, OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

Referenced by oomph::RefineableQAxisymAdvectionDiffusionElement< NNODE_1D >::vertex_node_pt(), oomph::RefineableQSphericalAdvectionDiffusionElement< NNODE_1D >::vertex_node_pt(), and oomph::RefineableQYoungLaplaceElement< NNODE_1D >::vertex_node_pt().

◆ write_paraview_offsets()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::write_paraview_offsets	(	std::ofstream &	file_out,
		const unsigned &	nplot,
		unsigned &	offset_sum
	)		const

inlinevirtual

Return the offsets for the paraview sub-elements. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf

Reimplemented from oomph::FiniteElement.

     {
       // Loop over all local elements and add its offset to the overall
       // offset_sum
       unsigned local_loop = nsub_elements_paraview(nplot);
       for (unsigned i = 0; i < local_loop; i++)
       {
         offset_sum += 4;
         file_out << offset_sum << std::endl;
       }
     }

References i.

◆ write_paraview_output_offset_information()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::write_paraview_output_offset_information	(	std::ofstream &	file_out,
		const unsigned &	nplot,
		unsigned &	counter
	)		const

inlinevirtual

Fill in the offset information for paraview plot. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf

Reimplemented from oomph::FiniteElement.

     {
       // Number of local elements we want to plot over
       unsigned plot = nsub_elements_paraview(nplot);
  
       // loops over the i-th local element in parent element
       for (unsigned i = 0; i < plot; i++)
       {
         unsigned d = (i - (i % (nplot - 1))) / (nplot - 1);
  
         file_out << i % (nplot - 1) + d * nplot + counter << " "
                  << i % (nplot - 1) + 1 + d * nplot + counter << " "
                  << i % (nplot - 1) + 1 + (d + 1) * nplot + counter << " "
                  << i % (nplot - 1) + (d + 1) * nplot + counter << std::endl;
       }
       counter += nplot_points_paraview(nplot);
     }

References i, and PlanarWave::plot().

◆ write_paraview_type()

template<unsigned NNODE_1D>

void oomph::QElement< 2, NNODE_1D >::write_paraview_type	(	std::ofstream &	file_out,
		const unsigned &	nplot
	)		const

inlinevirtual

Return the paraview element type. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf Use type "VTK_QUAD" (== 9) for 2D quad elements

Reimplemented from oomph::FiniteElement.

     {
       unsigned local_loop = nsub_elements_paraview(nplot);
       for (unsigned i = 0; i < local_loop; i++)
       {
         file_out << "9" << std::endl;
       }
     }

References i.

Member Data Documentation

◆ Default_integration_scheme

template<unsigned NNODE_1D>

Gauss< 2, NNODE_1D > oomph::QElement< 2, NNODE_1D >::Default_integration_scheme

staticprivate

Assign the spatial integration scheme.

Default integration rule: Gaussian integration of same 'order' as the element

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

Public Member Functions

Static Private Attributes

Additional Inherited Members

Detailed Description

template<unsigned NNODE_1D> class oomph::QElement< 2, NNODE_1D >

Constructor & Destructor Documentation

◆ QElement() [1/2]

◆ QElement() [2/2]

Member Function Documentation

◆ bulk_coordinate_derivatives_fct_pt()

◆ d2shape_local()

◆ dshape_local()

◆ face_outer_unit_normal_sign()

◆ face_to_bulk_coordinate_fct_pt()

◆ get_bulk_node_number()

◆ get_node_at_local_coordinate()

◆ get_s_plot()

◆ invert_jacobian_mapping()

◆ local_coordinate_of_node()

◆ local_fraction_of_node()

◆ local_one_d_fraction_of_node()

◆ nnode_1d()

◆ nplot_points()

◆ nplot_points_paraview()

◆ nsub_elements_paraview()

◆ nvertex_node()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ s_max()

◆ s_min()

◆ shape()

◆ tecplot_zone_string()

◆ vertex_node_pt()

◆ write_paraview_offsets()

◆ write_paraview_output_offset_information()

◆ write_paraview_type()

Member Data Documentation

◆ Default_integration_scheme

template<unsigned NNODE_1D>
class oomph::QElement< 2, NNODE_1D >