Biharmonic Flux Element. More...

#include <biharmonic_flux_elements.h>

Inheritance diagram for oomph::BiharmonicFluxElement< DIM >:

Public Types
typedef void(*	FluxFctPt) (const double &s, double &flux)

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

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

Public Member Functions
	BiharmonicFluxElement (FiniteElement *const &bulk_el_pt, const int &face_index, const unsigned &b)
	constructor More...

	BiharmonicFluxElement ()
	Broken empty constructor. More...

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

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

FluxFctPt &	flux0_fct_pt ()
	Access function for the flux0 function pointer. More...

FluxFctPt &	flux1_fct_pt ()
	Access function for the flux1 function pointer. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Add the element's contribution to its residual vector. More...

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

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

void	output (std::ostream &outfile)
	Output function – does nothing. More...

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output function – does nothing. More...

void	output (FILE *file_pt)
	C-style output function – does nothing. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	C-style output function – does nothing. More...

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	compute_error – does nothing More...

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

	BiharmonicFluxElement (FiniteElement *const &bulk_el_pt, const int &face_index, const unsigned &b)

Public Member Functions inherited from oomph::FaceElement
	FaceElement ()
	Constructor: Initialise all appropriate member data. More...

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

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

const unsigned &	boundary_number_in_bulk_mesh () const
	Broken assignment operator. More...

void	set_boundary_number_in_bulk_mesh (const unsigned &b)
	Set function for the boundary number in bulk mesh. More...

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

double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

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

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

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

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

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

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

int &	normal_sign ()

int	normal_sign () const

int &	face_index ()

int	face_index () const

const Vector< double > *	tangent_direction_pt () const
	Public access function for the tangent direction pointer. More...

void	set_tangent_direction (Vector< double > *tangent_direction_pt)
	Set the tangent direction vector. More...

void	turn_on_warning_for_discontinuous_tangent ()

void	turn_off_warning_for_discontinuous_tangent ()

void	continuous_tangent_and_outer_unit_normal (const Vector< double > &s, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	continuous_tangent_and_outer_unit_normal (const unsigned &ipt, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	outer_unit_normal (const Vector< double > &s, Vector< double > &unit_normal) const
	Compute outer unit normal at the specified local coordinate. More...

void	outer_unit_normal (const unsigned &ipt, Vector< double > &unit_normal) const
	Compute outer unit normal at ipt-th integration point. More...

FiniteElement *&	bulk_element_pt ()
	Pointer to higher-dimensional "bulk" element. More...

FiniteElement *	bulk_element_pt () const
	Pointer to higher-dimensional "bulk" element (const version) More...

CoordinateMappingFctPt &	face_to_bulk_coordinate_fct_pt ()

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt () const

BulkCoordinateDerivativesFctPt &	bulk_coordinate_derivatives_fct_pt ()

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt () const

Vector< double >	local_coordinate_in_bulk (const Vector< double > &s) const

void	get_local_coordinate_in_bulk (const Vector< double > &s, Vector< double > &s_bulk) const

void	get_ds_bulk_ds_face (const Vector< double > &s, DenseMatrix< double > &dsbulk_dsface, unsigned &interior_direction) const

unsigned &	bulk_position_type (const unsigned &i)

const unsigned &	bulk_position_type (const unsigned &i) const

void	bulk_node_number_resize (const unsigned &i)
	Resize the storage for the bulk node numbers. More...

unsigned &	bulk_node_number (const unsigned &n)

const unsigned &	bulk_node_number (const unsigned &n) const

void	bulk_position_type_resize (const unsigned &i)
	Resize the storage for bulk_position_type to i entries. More...

unsigned &	nbulk_value (const unsigned &n)

unsigned	nbulk_value (const unsigned &n) const

void	nbulk_value_resize (const unsigned &i)

void	resize_nodes (Vector< unsigned > &nadditional_data_values)

void	output_zeta (std::ostream &outfile, const unsigned &nplot)
	Output boundary coordinate zeta. 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...

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

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

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

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

virtual void	get_x_from_macro_element (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 (const Vector< double > &s, Shape &psi) const =0

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const

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

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

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

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

virtual unsigned	nnode_1d () const

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 unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

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

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) 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 ElementGeometry::ElementGeometry	element_geometry () const
	Return the geometry type of the element (either Q or T usually). More...

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)

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)

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

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

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

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 unsigned	nplot_points (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::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 ()

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

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

Private Member Functions
void	get_flux0 (const double &s, double &flux)

void	get_flux1 (const double &s, double &flux)

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

void	fill_in_generic_residual_contribution_biharmonic_flux (Vector< double > &residuals)

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

void	fill_in_generic_residual_contribution_biharmonic_flux (Vector< double > &residual)

Private Attributes
FluxFctPt	Flux0_fct_pt
	Function pointer to the prescribed flux. More...

FluxFctPt	Flux1_fct_pt
	Function pointer to the prescribed flux. More...

unsigned	Nface_nodal_dof

unsigned	Boundary
	Boundary ID. More...

Additional Inherited Members
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::FaceElement
void	add_additional_values (const Vector< unsigned > &nadditional_values, const unsigned &id)

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	invert_jacobian_mapping (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)

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::FaceElement
unsigned	Boundary_number_in_bulk_mesh
	The boundary number in the bulk mesh to which this element is attached. More...

FiniteElement *	Bulk_element_pt
	Pointer to the associated higher-dimensional "bulk" element. More...

Vector< unsigned >	Bulk_node_number

Vector< unsigned >	Nbulk_value

Vector< double > *	Tangent_direction_pt

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 DIM>
class oomph::BiharmonicFluxElement< DIM >

Biharmonic Flux Element.

Member Typedef Documentation

◆ FluxFctPt

template<unsigned DIM>

typedef void(* oomph::BiharmonicFluxElement< DIM >::FluxFctPt) (const double &s, double &flux)

definition of flux function pointer, flux must be parametised in terms of the macro element coordinate position (s) along the problem edge

Constructor & Destructor Documentation

◆ BiharmonicFluxElement() [1/4]

template<unsigned DIM>

oomph::BiharmonicFluxElement< DIM >::BiharmonicFluxElement	(	FiniteElement *const &	bulk_el_pt,
		const int &	face_index,
		const unsigned &	b
	)

constructor

◆ BiharmonicFluxElement() [2/4]

template<unsigned DIM>

oomph::BiharmonicFluxElement< DIM >::BiharmonicFluxElement ( )

inline

Broken empty constructor.

     {
       throw OomphLibError("Don't call empty constructor for PoissonFluxElement",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ BiharmonicFluxElement() [3/4]

template<unsigned DIM>

oomph::BiharmonicFluxElement< DIM >::BiharmonicFluxElement ( const BiharmonicFluxElement< DIM > & dummy )

delete

Broken copy constructor.

◆ BiharmonicFluxElement() [4/4]

oomph::BiharmonicFluxElement< 2 >::BiharmonicFluxElement	(	FiniteElement *const &	bulk_el_pt,
		const int &	face_index,
		const unsigned &	b
	)

Constructor, takes the pointer to the "bulk" element, the index of the fixed local coordinate and its value represented by an integer (+/- 1), indicating that the face is located at the max. or min. value of the "fixed" local coordinate in the bulk element. And the macro element position of the flux element along the edge of the problem

     : FaceGeometry<BiharmonicElement<2>>(), FaceElement()
   {
     // Let the bulk element build the FaceElement, i.e. setup the pointers
     // to its nodes (by referring to the appropriate nodes in the bulk
     // element), etc.
     bulk_el_pt->build_face_element(face_index, this);
  
     // Initialise the prescribed-flux function pointer to zero
     Flux0_fct_pt = 0;
     Flux1_fct_pt = 0;
  
     // set the number of nodal degrees of freedom for the face element
     Nface_nodal_dof = 2;
  
     //
     Boundary = b;
   }

References b, oomph::BiharmonicFluxElement< DIM >::Boundary, oomph::FiniteElement::build_face_element(), oomph::FaceElement::face_index(), oomph::BiharmonicFluxElement< DIM >::Flux0_fct_pt, oomph::BiharmonicFluxElement< DIM >::Flux1_fct_pt, and oomph::BiharmonicFluxElement< DIM >::Nface_nodal_dof.

Member Function Documentation

◆ compute_error()

template<unsigned DIM>

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

inlinevirtual

compute_error – does nothing

Reimplemented from oomph::FiniteElement.

176 {

177 }

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

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

inlinevirtual

Add the element's contribution to its residual vector and its Jacobian matrix (note - no contributions are made to the jacobian)

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic residuals routine
       fill_in_generic_residual_contribution_biharmonic_flux(residuals);
     }

References oomph::BiharmonicFluxElement< DIM >::fill_in_generic_residual_contribution_biharmonic_flux().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

Add the element's contribution to its residual vector.

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic residuals function
       fill_in_generic_residual_contribution_biharmonic_flux(residuals);
     }

References oomph::BiharmonicFluxElement< DIM >::fill_in_generic_residual_contribution_biharmonic_flux().

◆ fill_in_generic_residual_contribution_biharmonic_flux() [1/2]

void oomph::BiharmonicFluxElement< 2 >::fill_in_generic_residual_contribution_biharmonic_flux ( Vector< double > & residual )

private

Compute the elemental contribution to the residual vector for 2D problem type 0 biharmonic flux elements

   {
     // Find out how many nodes there are in the face element
     unsigned n_node = this->nnode();
  
     // set up memory for shape functions
     Shape psi(n_node, Nface_nodal_dof);
  
     // setup memory for derivative of shape functions
     DShape dpsi(n_node, Nface_nodal_dof, 1);
  
     // Set the value of Nintpt
     unsigned n_intpt = this->integral_pt()->nweight();
  
     // local coordinate position of integration point in face element
     Vector<double> s(1);
  
     // edge sign adjust
     int edge_sign = //-int(this->s_fixed_value())*int((s_fixed_index-0.5)*2);
       -this->normal_sign();
  
     // Flip for the different normal conventions (TIDY THIS UP)
     if ((this->face_index() == 2) || (this->face_index() == -2))
     {
       edge_sign *= -1;
     }
  
     // Get the bulk position type corresponding to the slope
     const unsigned slope_index = this->bulk_position_type(1);
  
     // Ge the position type corresponding to the outer slope
     const unsigned outer_slope_index = 3 - slope_index;
  
     // Loop over the integration points
     //--------------------------------
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Get the integral weight
       double w = this->integral_pt()->weight(ipt);
  
       // value of local coordinate s at integration point
       s[0] = this->integral_pt()->knot(ipt, 0);
  
       // get the (1D) shape fn
       this->dshape_local(s, psi, dpsi);
  
       // compute dx_i/ds_t and dx_i/ds_n at ipt
       Vector<double> dxds_t(2, 0.0);
       Vector<double> dxds_n(2, 0.0);
       for (unsigned n = 0; n < n_node; n++)
       {
         for (unsigned d = 0; d < 2; d++)
         {
           for (unsigned k = 0; k < Nface_nodal_dof; k++)
           {
             dxds_t[d] += dpsi(n, k, 0) * node_pt(n)->x_gen(slope_index * k, d);
             dxds_n[d] += psi(n, k) * node_pt(n)->x_gen(
                                        outer_slope_index + slope_index * k, d);
           }
         }
       }
  
       // compute ds_n/dn
       double ds_ndn = -edge_sign *
                       sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]) /
                       (-dxds_n[0] * dxds_t[1] + dxds_t[0] * dxds_n[1]);
  
       // compute ds_t/dn
       double ds_tdn = edge_sign *
                       (dxds_t[1] * dxds_n[1] + dxds_t[0] * dxds_n[0]) /
                       (sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]) *
                        (-dxds_n[0] * dxds_t[1] + dxds_t[0] * dxds_n[1]));
  
       // compute interpolated_m at s
       double interpolated_m = 0.0;
       Vector<double> m(2);
       for (unsigned n = 0; n < n_node; n++)
       {
         this->node_pt(n)->get_coordinates_on_boundary(Boundary, m);
         for (unsigned k = 0; k < Nface_nodal_dof; k++)
         {
           interpolated_m += psi(n, k) * m[k];
         }
       }
  
       // get the fluxes
       double flux0 = 0.0;
       get_flux0(interpolated_m, flux0);
       double flux1 = 0.0;
       get_flux1(interpolated_m, flux1);
  
       // get J
       double J = J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Now add to the appropriate equations
  
  
       // Loop over the test function nodes
       for (unsigned n = 0; n < n_node; n++)
       {
         // loop over the face element position types
         for (unsigned k = 0; k < Nface_nodal_dof; k++)
         {
           // apply contribution for flux0
  
           // determine bulk position type
           unsigned bulk_p_type = slope_index * k;
  
           // local equation number
           int local_eqn = this->nodal_local_eqn(n, bulk_p_type);
  
           // if node not pinned
           if (local_eqn >= 0)
           {
             // add contribution to residual
             residual[local_eqn] += flux1 * psi(n, k) * W;
           }
  
           // apply first contribution for flux1
  
           // if node not pinned
           if (local_eqn >= 0)
           {
             // add contribution to residual
             residual[local_eqn] -= flux0 * dpsi(n, k, 0) * ds_tdn * W;
           }
  
           // apply second contribution for flux1
  
           // determine bulk position type
           bulk_p_type = outer_slope_index + slope_index * k;
  
           // local equation number
           local_eqn = this->nodal_local_eqn(n, bulk_p_type);
  
           // if node not pinned
           if (local_eqn >= 0)
           {
             // add contribution to residual
             residual[local_eqn] -= flux0 * psi(n, k) * ds_ndn * W;
           }
         }
       }
     }
   }

References J, k, m, n, s, sqrt(), w, and oomph::QuadTreeNames::W.

◆ fill_in_generic_residual_contribution_biharmonic_flux() [2/2]

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::fill_in_generic_residual_contribution_biharmonic_flux ( Vector< double > & residuals )

private

Add the element's contribution to its residual vector. Flux elements only make contribution to the residual vector

Referenced by oomph::BiharmonicFluxElement< DIM >::fill_in_contribution_to_jacobian(), and oomph::BiharmonicFluxElement< DIM >::fill_in_contribution_to_residuals().

◆ flux0_fct_pt()

template<unsigned DIM>

FluxFctPt& oomph::BiharmonicFluxElement< DIM >::flux0_fct_pt ( )

inline

Access function for the flux0 function pointer.

     {
       return Flux0_fct_pt;
     }

References oomph::BiharmonicFluxElement< DIM >::Flux0_fct_pt.

Referenced by oomph::BiharmonicProblem< DIM >::set_neumann_boundary_condition().

◆ flux1_fct_pt()

template<unsigned DIM>

FluxFctPt& oomph::BiharmonicFluxElement< DIM >::flux1_fct_pt ( )

inline

Access function for the flux1 function pointer.

     {
       return Flux1_fct_pt;
     }

References oomph::BiharmonicFluxElement< DIM >::Flux1_fct_pt.

Referenced by oomph::BiharmonicProblem< DIM >::set_neumann_boundary_condition().

◆ get_flux0()

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::get_flux0	(	const double &	s,
		double &	flux
	)

inlineprivate

Function to return the prescribed flux at a given macro element coordinate position

     {
       // If the function pointer is zero return zero
       if (Flux0_fct_pt == 0)
       {
         flux = 0.0;
       }
       // Otherwise call the function
       else
       {
         (*Flux0_fct_pt)(s, flux);
       }
     }

References ProblemParameters::flux(), oomph::BiharmonicFluxElement< DIM >::Flux0_fct_pt, and s.

◆ get_flux1()

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::get_flux1	(	const double &	s,
		double &	flux
	)

inlineprivate

Function to return the prescribed flux at a given macro element coordinate position

     {
       // If the function pointer is zero return zero
       if (Flux1_fct_pt == 0)
       {
         flux = 0.0;
       }
       // Otherwise call the function
       else
       {
         (*Flux1_fct_pt)(s, flux);
       }
     }

References ProblemParameters::flux(), oomph::BiharmonicFluxElement< DIM >::Flux1_fct_pt, and s.

◆ J_eulerian() [1/2]

double oomph::BiharmonicFluxElement< 2 >::J_eulerian ( const Vector< double > & s ) const

privatevirtual

Calculate the Jacobian of the mapping between local and global coordinates at the position s for face elements for two dimensional problems The jacobian of the 1D face element is computed which is dt/ds_t

Reimplemented from oomph::FaceElement.

   {
     // Find the number of nodes
     unsigned n_node = this->nnode();
  
     // Set up dummy memory for the shape functions
     Shape psi(n_node, Nface_nodal_dof);
     DShape dpsids(n_node, Nface_nodal_dof, 1);
  
     // Get the shape functions and local derivatives
     this->dshape_local(s, psi, dpsids);
  
     // computed dx_i/ds_t along edge element
     Vector<double> interpolated_dxds_t(2);
  
     // Get the bulk position type corresponding to the slope
     const unsigned slope_index = this->bulk_position_type(1);
     for (unsigned l = 0; l < n_node; l++)
     {
       for (unsigned d = 0; d < 2; d++)
       {
         interpolated_dxds_t[d] +=
           this->node_pt(l)->x_gen(0, d) * dpsids(l, 0, 0) +
           this->node_pt(l)->x_gen(slope_index, d) * dpsids(l, 1, 0);
       }
     }
  
     // dt/ds_t = dx_0/ds_t*t_0 + dx_1/ds_t*t_1
     //
     // given : t_0 = dx_0/ds_t / ( (dx_0/ds_t)^2 + (dx_1/ds_t)^2 )^0.5
     //         t_1 = dx_1/ds_t / ( (dx_0/ds_t)^2 + (dx_1/ds_t)^2 )^0.5
     //
     // then : dt/ds_t = ( (dx_0/ds_t)^2 + (dx_1/ds_t)^2 )^0.5
     //
     // (note : it is gaurantee that dt/ds_t is +ve, therefore do not need
     // PARANOID
     //         check of jacobian)
     double dtds_t = sqrt(interpolated_dxds_t[0] * interpolated_dxds_t[0] +
                          interpolated_dxds_t[1] * interpolated_dxds_t[1]);
  
     // Return the Jacobian
     return dtds_t;
   }

References s, and sqrt().

◆ J_eulerian() [2/2]

template<unsigned DIM>

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

privatevirtual

Calculate the Jacobian of the mapping between local and global coordinates at the position s for face elements

Reimplemented from oomph::FiniteElement.

◆ operator=()

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::operator= ( const BiharmonicFluxElement< DIM > & )

delete

Broken assignment operator.

◆ output() [1/4]

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::output ( FILE * file_pt )

inlinevirtual

C-style output function – does nothing.

Reimplemented from oomph::FiniteElement.

164 {}

◆ output() [2/4]

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::output	(	FILE *	file_pt,
		const unsigned &	n_plot
	)

inlinevirtual

C-style output function – does nothing.

Reimplemented from oomph::FiniteElement.

168 {}

◆ output() [3/4]

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::output ( std::ostream & outfile )

inlinevirtual

Output function – does nothing.

Reimplemented from oomph::FiniteElement.

156 {}

◆ output() [4/4]

template<unsigned DIM>

void oomph::BiharmonicFluxElement< DIM >::output	(	std::ostream &	outfile,
		const unsigned &	n_plot
	)

inlinevirtual

Output function – does nothing.

Reimplemented from oomph::FiniteElement.

160 {}

◆ output_fct()

template<unsigned DIM>

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

inlinevirtual

Output an exact solution over the element.

Reimplemented from oomph::FiniteElement.

184 {

185 }

◆ zeta_nodal()

template<unsigned DIM>

double oomph::BiharmonicFluxElement< DIM >::zeta_nodal	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inlinevirtual

Specify the value of nodal zeta from the face geometry The "global" intrinsic coordinate of the element when viewed as part of a geometric object should be given by the FaceElement representation, by default (needed to break indeterminacy if bulk element is SolidElement)

Reimplemented from oomph::FiniteElement.

     {
       return FaceElement::zeta_nodal(n, k, i);
     }

References i, k, n, and oomph::FaceElement::zeta_nodal().

Member Data Documentation

◆ Boundary

template<unsigned DIM>

unsigned oomph::BiharmonicFluxElement< DIM >::Boundary

private

Boundary ID.

Referenced by oomph::BiharmonicFluxElement< DIM >::BiharmonicFluxElement().

◆ Flux0_fct_pt

template<unsigned DIM>

FluxFctPt oomph::BiharmonicFluxElement< DIM >::Flux0_fct_pt

private

Function pointer to the prescribed flux.

Referenced by oomph::BiharmonicFluxElement< DIM >::BiharmonicFluxElement(), oomph::BiharmonicFluxElement< DIM >::flux0_fct_pt(), and oomph::BiharmonicFluxElement< DIM >::get_flux0().

◆ Flux1_fct_pt

template<unsigned DIM>

FluxFctPt oomph::BiharmonicFluxElement< DIM >::Flux1_fct_pt

private

Function pointer to the prescribed flux.

Referenced by oomph::BiharmonicFluxElement< DIM >::BiharmonicFluxElement(), oomph::BiharmonicFluxElement< DIM >::flux1_fct_pt(), and oomph::BiharmonicFluxElement< DIM >::get_flux1().

◆ Nface_nodal_dof

template<unsigned DIM>

unsigned oomph::BiharmonicFluxElement< DIM >::Nface_nodal_dof

private

the number of nodal degrees of freedom for the face element basis functions

Referenced by oomph::BiharmonicFluxElement< DIM >::BiharmonicFluxElement().

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

biharmonic_flux_elements.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<unsigned DIM> class oomph::BiharmonicFluxElement< DIM >

Member Typedef Documentation

◆ FluxFctPt

Constructor & Destructor Documentation

◆ BiharmonicFluxElement() [1/4]

◆ BiharmonicFluxElement() [2/4]

◆ BiharmonicFluxElement() [3/4]

◆ BiharmonicFluxElement() [4/4]

Member Function Documentation

◆ compute_error()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_biharmonic_flux() [1/2]

◆ fill_in_generic_residual_contribution_biharmonic_flux() [2/2]

◆ flux0_fct_pt()

◆ flux1_fct_pt()

◆ get_flux0()

◆ get_flux1()

◆ J_eulerian() [1/2]

◆ J_eulerian() [2/2]

◆ operator=()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct()

◆ zeta_nodal()

Member Data Documentation

◆ Boundary

◆ Flux0_fct_pt

◆ Flux1_fct_pt

◆ Nface_nodal_dof

template<unsigned DIM>
class oomph::BiharmonicFluxElement< DIM >