#include <dg_elements.h>

Inheritance diagram for oomph::DGFaceElement:

Public Member Functions
	DGFaceElement ()
	Empty Constructor. More...

virtual	~DGFaceElement ()
	Empty Destructor. More...

FaceElement *	neighbour_face_pt (const unsigned &i)
	Access function for neighbouring face information. More...

void	setup_neighbour_info (const bool &add_neighbour_data_to_bulk)

void	report_info ()
	Output information about the present element and its neighbour. More...

virtual void	interpolated_u (const Vector< double > &s, Vector< double > &f)
	Return the interpolated values of the unknown fluxes. More...

virtual void	get_interpolation_data (Vector< Data * > &interpolation_data)

virtual void	numerical_flux_at_knot (const unsigned &ipt, const Shape &psi, Vector< double > &flux, DenseMatrix< double > &dflux_du_int, DenseMatrix< double > &dflux_du_ext, unsigned flag)

virtual void	numerical_flux (const Vector< double > &n_out, const Vector< double > &u_int, const Vector< double > &u_ext, Vector< double > &flux)

virtual void	dnumerical_flux_du (const Vector< double > &n_out, const Vector< double > &u_int, const Vector< double > &u_ext, DenseMatrix< double > &dflux_du_int, DenseMatrix< double > &dflux_du_ext)

void	add_flux_contributions (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)
	Add the contribution from integrating the numerical flux. More...

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

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

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

virtual void	output (FILE *file_pt)

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

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

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

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

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

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::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 ()

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

Protected Member Functions
virtual unsigned	flux_index (const unsigned &i) const
	Return the index at which the i-th unknown flux is stored. More...

virtual unsigned	required_nflux ()
	Set the number of flux components. More...

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)

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)

Private Attributes
Vector< FaceElement * >	Neighbour_face_pt
	Vector of neighbouring face elements at the integration points. More...

Vector< Vector< double > >	Neighbour_local_coordinate
	Vector of neighbouring local coordinates at the integration points. More...

Vector< Vector< unsigned > >	Neighbour_external_data

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 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

Base class for Discontinuous Galerkin Faces. These are responsible for calculating the normal fluxes that provide the communication between the discontinuous elements.

Constructor & Destructor Documentation

◆ DGFaceElement()

oomph::DGFaceElement::DGFaceElement ( )

inline

Empty Constructor.

81 : FaceElement() {}

oomph::FaceElement::FaceElement

FaceElement()

Constructor: Initialise all appropriate member data.

Definition: elements.h:4446

◆ ~DGFaceElement()

virtual oomph::DGFaceElement::~DGFaceElement ( )

inlinevirtual

Empty Destructor.

84 {}

Member Function Documentation

◆ add_flux_contributions()

void oomph::DGFaceElement::add_flux_contributions	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		unsigned	flag
	)

Add the contribution from integrating the numerical flux.

Calculate the integrated (numerical) flux out of the face and add it to the residuals vector

   {
 // Check that we have set up the coupling data if we are computing the jacobin
 #ifdef PARANOID
     if (flag && (flag < 3))
     {
       if (Neighbour_external_data.size() == 0)
       {
         std::ostringstream error_stream;
         error_stream
           << "Coupling data between elements not included in jacobian\n"
           << "You should call DGMesh::setup_face_neighbour_info(true) to "
              "ensure\n"
           << "that this information is included in the jacobian\n";
  
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
     }
 #endif
  
  
     // Find the number of nodes
     const unsigned n_node = nnode();
     // Dimension of the face
     const unsigned el_dim = dim();
     // Storage for the shape functions
     Shape psi(n_node);
  
     // Number of integration points
     const unsigned n_intpt = this->integral_pt()->nweight();
     // Number of fluxes
     const unsigned n_flux = this->required_nflux();
     // Find the indices at which the local fluxes are stored
     Vector<unsigned> flux_nodal_index(n_flux);
     for (unsigned i = 0; i < n_flux; i++)
     {
       flux_nodal_index[i] = this->flux_index(i);
     }
  
     // Cache the bulk element
     DGElement* bulk_elem_pt = dynamic_cast<DGElement*>(this->bulk_element_pt());
  
     // Storage for the flux and its derivatives
     Vector<double> F(n_flux);
     DenseMatrix<double> dF_du_int(n_flux, n_flux);
     DenseMatrix<double> dF_du_ext(n_flux, n_flux);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Get the integral weight
       double W = this->integral_pt()->weight(ipt);
       // Get the shape functions at the knot
       this->shape_at_knot(ipt, psi);
  
       // Calculate the Jacobian
       // For a point element, it's one
       double J = W;
       // Otherwise calculate for the element
       if (el_dim != 0)
       {
         J *= this->J_eulerian_at_knot(ipt);
       }
  
       // Now calculate the numerical flux (and derivatives)
       this->numerical_flux_at_knot(ipt, psi, F, dF_du_int, dF_du_ext, flag);
  
       // Limit if desired here
  
       // Cache the pointer to the neighbour
       DGFaceElement* neighbour_element_pt =
         dynamic_cast<DGFaceElement*>(Neighbour_face_pt[ipt]);
  
       // Finally  we need to assemble the appropriate contributions
       // to the residuals
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over the fluxes
         for (unsigned i = 0; i < n_flux; i++)
         {
           // Get the local equation number in the bulk
           int local_eqn = bulk_elem_pt->nodal_local_eqn(bulk_node_number(l),
                                                         flux_nodal_index[i]);
  
           // If it's not a boundary condition
           if (local_eqn >= 0)
           {
             // Add the flux multiplied by the shape function and the jacobian
             residuals[local_eqn] -= psi(l) * F[i] * J;
  
             // Add the jacobian contributions
             if (flag)
             {
               // If we are assembling the jacobian
               if (flag < 3)
               {
                 // Loop over the internal nodes and fluxes again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   for (unsigned i2 = 0; i2 < n_flux; i2++)
                   {
                     // Get the local unknown equation number in the bulk
                     int local_unknown = bulk_elem_pt->nodal_local_eqn(
                       bulk_node_number(l2), flux_nodal_index[i2]);
  
                     // If it's not a boundary condition
                     if (local_unknown >= 0)
                     {
                       // Add the flux multiplied by the shape function a
                       // nd the jacobian
                       jacobian(local_eqn, local_unknown) -=
                         psi(l) * dF_du_int(i, i2) * psi(l2) * J;
                     }
                   }
                 }
  
                 // How many nodes does it have
                 unsigned neigh_n_node = neighbour_element_pt->nnode();
  
                 // Get the flux indices from the neighbour
                 Vector<unsigned> neigh_flux_index(n_flux);
                 for (unsigned i2 = 0; i2 < n_flux; i2++)
                 {
                   neigh_flux_index[i2] = neighbour_element_pt->flux_index(i2);
                 }
  
                 // Loop over the neighbours nodes
                 for (unsigned l2 = 0; l2 < neigh_n_node; l2++)
                 {
                   // Loop over the fluxed
                   for (unsigned i2 = 0; i2 < n_flux; i2++)
                   {
                     // Get the local unknown equation number in the bulk
                     int local_unknown =
                       dynamic_cast<DGElement*>(this->bulk_element_pt())
                         ->external_local_eqn(Neighbour_external_data[ipt][l2],
                                              flux_nodal_index[i2]);
  
                     // If it's not a boundary condition
                     if (local_unknown >= 0)
                     {
                       // Add the flux multiplied by the shape function
                       // and the jacobian
                       jacobian(local_eqn, local_unknown) -=
                         psi(l) * dF_du_ext(i, i2) * psi(l2) * J;
                     }
                   }
                 }
               }
             } // End of jacobian calculation
           }
         }
       }
     }
   }

References oomph::FaceElement::bulk_element_pt(), oomph::FaceElement::bulk_node_number(), oomph::FiniteElement::dim(), el_dim, oomph::GeneralisedElement::external_local_eqn(), oomph::OcTreeNames::F, flux_index(), i, oomph::FiniteElement::integral_pt(), J, oomph::FaceElement::J_eulerian_at_knot(), Neighbour_external_data, Neighbour_face_pt, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), numerical_flux_at_knot(), oomph::Integral::nweight(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, required_nflux(), oomph::FiniteElement::shape_at_knot(), oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by oomph::DGElement::add_flux_contributions_to_residuals().

◆ dnumerical_flux_du()

void oomph::DGFaceElement::dnumerical_flux_du	(	const Vector< double > &	n_out,
		const Vector< double > &	u_int,
		const Vector< double > &	u_ext,
		DenseMatrix< double > &	dflux_du_int,
		DenseMatrix< double > &	dflux_du_ext
	)

virtual

Calculate the derivative of the normal flux, which is the dot product of our approximation to the flux with the outer unit normal, with respect to the interior and exterior variables Default is to use finite differences

   {
     // Find the number of fluxes
     const unsigned n_flux = this->required_nflux();
  
     // Get a local copy of the unknowns
     Vector<double> u_int_local = u_int;
     Vector<double> u_ext_local = u_ext;
  
     // Storage for incremented and decremented fluxes
     Vector<double> flux_plus(n_flux), flux_minus(n_flux);
  
     const double fd_step = GeneralisedElement::Default_fd_jacobian_step;
  
     // Now loop over all the fluxes
     for (unsigned n = 0; n < n_flux; n++)
     {
       // Increase internal value
  
       // Store the old value
       double old_var = u_int_local[n];
       // Increment the value
       u_int_local[n] += fd_step;
       // Get the new values
       this->numerical_flux(n_out, u_int_local, u_ext_local, flux_plus);
  
       // Reset the value
       u_int_local[n] = old_var;
       // Decrement the value
       u_int_local[n] -= fd_step;
       // Get the new values
       this->numerical_flux(n_out, u_int_local, u_ext_local, flux_minus);
  
       // Assemble the column of the jacobian
       for (unsigned m = 0; m < n_flux; m++)
       {
         dflux_du_int(m, n) = (flux_plus[m] - flux_minus[m]) / (2.0 * fd_step);
       }
  
       // Reset the value
       u_int_local[n] = old_var;
  
       // Increase external value
  
       // Store the old value
       old_var = u_ext_local[n];
       // Increment the value
       u_ext_local[n] += fd_step;
       // Get the new values
       this->numerical_flux(n_out, u_int_local, u_ext_local, flux_plus);
  
       // Reset the value
       u_ext_local[n] = old_var;
       // Decrement the value
       u_ext_local[n] -= fd_step;
       // Get the new values
       this->numerical_flux(n_out, u_int_local, u_ext_local, flux_minus);
  
       // Assemble the column of the jacobian
       for (unsigned m = 0; m < n_flux; m++)
       {
         dflux_du_ext(m, n) = (flux_plus[m] - flux_minus[m]) / (2.0 * fd_step);
       }
  
       // Reset the value
       u_ext_local[n] = old_var;
     }
   }

References oomph::GeneralisedElement::Default_fd_jacobian_step, m, n, numerical_flux(), and required_nflux().

Referenced by numerical_flux_at_knot().

◆ flux_index()

virtual unsigned oomph::DGFaceElement::flux_index ( const unsigned & i ) const

inlineprotectedvirtual

Return the index at which the i-th unknown flux is stored.

     {
       return i;
     }

References i.

Referenced by add_flux_contributions(), interpolated_u(), and numerical_flux_at_knot().

◆ get_interpolation_data()

void oomph::DGFaceElement::get_interpolation_data ( Vector< Data * > & interpolation_data )

virtual

Get the data that are used to interpolate the unkowns in the element. These must be returned in order.

Add all the data that are used to interpolate the unknowns. This must be consistent with the interpolated_u function above and the default implementation assumes pure nodal interpolaton.

   {
     // Find the number of nodes
     const unsigned n_node = nnode();
     // Now resize the vector
     interpolation_data.resize(n_node);
  
     // If there are no nodes then return immediately
     if (n_node == 0)
     {
       return;
     }
  
     // Otherwise loop over the nodes and add to the vector in order
     for (unsigned n = 0; n < n_node; n++)
     {
       interpolation_data[n] = this->node_pt(n);
     }
   }

References n, oomph::FiniteElement::nnode(), and oomph::FiniteElement::node_pt().

Referenced by setup_neighbour_info().

◆ interpolated_u()

void oomph::DGFaceElement::interpolated_u	(	const Vector< double > &	s,
		Vector< double > &	f
	)

virtual

Return the interpolated values of the unknown fluxes.

Reimplemented in oomph::DGEulerFaceReflectionElement< ELEMENT >.

   {
     // Find the number of nodes
     const unsigned n_node = nnode();
     // If there are no nodes then return immediately
     if (n_node == 0)
     {
       return;
     }
  
     // Get the shape functions at the local coordinate
     Shape psi(n_node);
     this->shape(s, psi);
  
     // Find the number of fluxes
     const unsigned n_flux = this->required_nflux();
  
     // Find the indices at which the local fluxes are stored
     Vector<unsigned> flux_nodal_index(n_flux);
     for (unsigned i = 0; i < n_flux; i++)
     {
       flux_nodal_index[i] = this->flux_index(i);
     }
     // Initialise the fluxes to zero
     for (unsigned i = 0; i < n_flux; i++)
     {
       u[i] = 0.0;
     }
  
     // Loop over the nodes
     for (unsigned n = 0; n < n_node; n++)
     {
       const double psi_ = psi[n];
       for (unsigned i = 0; i < n_flux; i++)
       {
         u[i] += this->node_pt(n)->value(flux_nodal_index[i]) * psi_;
       }
     }
   }

References flux_index(), i, n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), required_nflux(), oomph::FiniteElement::shape(), and oomph::Node::value().

Referenced by TwoDDGProblem< ELEMENT >::limit(), and numerical_flux_at_knot().

◆ neighbour_face_pt()

FaceElement* oomph::DGFaceElement::neighbour_face_pt ( const unsigned & i )

inline

Access function for neighbouring face information.

     {
       return Neighbour_face_pt[i];
     }

References i, and Neighbour_face_pt.

◆ numerical_flux()

virtual void oomph::DGFaceElement::numerical_flux	(	const Vector< double > &	n_out,
		const Vector< double > &	u_int,
		const Vector< double > &	u_ext,
		Vector< double > &	flux
	)

inlinevirtual

Calculate the normal flux, which is the dot product of our approximation to the flux with the outer unit normal

Reimplemented in oomph::DGScalarAdvectionFaceElement< ELEMENT >, and oomph::DGEulerFaceElement< ELEMENT >.

     {
       std::ostringstream error_stream;
       error_stream
         << "Empty numerical flux function called\n"
         << "This function should be overloaded with a specific flux\n"
         << "that is appropriate to the equations being solved.\n";
       throw OomphLibError(
         error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

Referenced by dnumerical_flux_du(), and numerical_flux_at_knot().

◆ numerical_flux_at_knot()

void oomph::DGFaceElement::numerical_flux_at_knot	(	const unsigned &	ipt,
		const Shape &	psi,
		Vector< double > &	flux,
		DenseMatrix< double > &	dflux_du_int,
		DenseMatrix< double > &	dflux_du_ext,
		unsigned	flag
	)

virtual

Calculate the normal numerical flux at the integration point. This is the most general interface that can be overloaded if desired

Calculate the numerical flux at the knot point ipt. This is the most general interface than can be overloaded if desired. The shape functions at the knot point will be passed into this function.

   {
     // Find the number of nodes
     const unsigned n_node = this->nnode();
     // Find the nodal dimension
     const unsigned nodal_dim = this->nodal_dimension();
     // Number of fluxes
     const unsigned n_flux = this->required_nflux();
     // Find the indices at which the local fluxes are stored
     Vector<unsigned> flux_nodal_index(n_flux);
     for (unsigned i = 0; i < n_flux; i++)
     {
       flux_nodal_index[i] = this->flux_index(i);
     }
  
     // Calculate the local unknowns
     Vector<double> interpolated_u(n_flux, 0.0);
  
     // Loop over the shape functions
     for (unsigned l = 0; l < n_node; l++)
     {
       // Cache the shape functions
       const double psi_ = psi(l);
       // Loop over the fluxes
       for (unsigned i = 0; i < n_flux; i++)
       {
         // Calculate the velocity from the most recent nodal values
         interpolated_u[i] += this->nodal_value(l, flux_nodal_index[i]) * psi_;
       }
     }
  
     // Now calculate the outer unit normal Vector
     Vector<double> interpolated_n(nodal_dim);
     this->outer_unit_normal(ipt, interpolated_n);
  
     // Get the pointer to the neighbour
     DGFaceElement* neighbour_element_pt =
       dynamic_cast<DGFaceElement*>(Neighbour_face_pt[ipt]);
  
     // Get the neighbour's fluxes
     Vector<double> interpolated_u_neigh(n_flux);
  
     neighbour_element_pt->interpolated_u(Neighbour_local_coordinate[ipt],
                                          interpolated_u_neigh);
  
     // Call the "standard" numerical flux function
     this->numerical_flux(
       interpolated_n, interpolated_u, interpolated_u_neigh, flux);
  
     // If we are calculating the jacobian add this term
     if (flag && (flag < 3))
     {
       this->dnumerical_flux_du(interpolated_n,
                                interpolated_u,
                                interpolated_u_neigh,
                                dflux_du_int,
                                dflux_du_ext);
     }
   }

References dnumerical_flux_du(), ProblemParameters::flux(), flux_index(), i, interpolated_u(), Neighbour_face_pt, Neighbour_local_coordinate, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_dimension(), oomph::FiniteElement::nodal_value(), numerical_flux(), oomph::FaceElement::outer_unit_normal(), and required_nflux().

Referenced by add_flux_contributions().

◆ report_info()

void oomph::DGFaceElement::report_info ( )

Output information about the present element and its neighbour.

   {
     // Find the number of nodes
     const unsigned n_node = this->nnode();
     // Allocate storage for the shape functions
     Shape psi(n_node);
  
     // Find the dimension of the problem
     const unsigned dim = this->nodal_dimension();
     // Storage for local coordinates in this face and its neighbour
     Vector<double> x(dim), face_x(dim);
  
     // Find the dimension of the element
     const unsigned el_dim = this->dim();
     // Storage for local coordinate
     Vector<double> s(el_dim);
  
     // Calculate the number of integration points from the array
     const unsigned n_intpt = this->integral_pt()->nweight();
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Find the local coordinate at the knot point
       for (unsigned i = 0; i < el_dim; i++)
       {
         s[i] = this->integral_pt()->knot(ipt, i);
       }
       // Get the value of the global coordinate in the present face
       this->interpolated_x(s, x);
  
       // Get the value of x in the neighbouring face
       Neighbour_face_pt[ipt]->interpolated_x(Neighbour_local_coordinate[ipt],
                                              face_x);
  
       // Let's compare
       oomph_info << "In Face                   In Neighbour\n";
       for (unsigned i = 0; i < dim; i++)
       {
         if (i == 0)
         {
           oomph_info << "(";
         }
         else
         {
           oomph_info << ", ";
         }
         oomph_info << std::setw(5) << std::left << x[i];
       }
       oomph_info << ")";
  
       oomph_info << "                   ";
  
       for (unsigned i = 0; i < dim; i++)
       {
         if (i == 0)
         {
           oomph_info << "(";
         }
         else
         {
           oomph_info << ", ";
         }
         oomph_info << std::setw(5) << std::left << face_x[i];
       }
       oomph_info << ")";
       oomph_info << std::endl;
     }
   }

References oomph::FiniteElement::dim(), el_dim, i, oomph::FiniteElement::integral_pt(), oomph::FaceElement::interpolated_x(), oomph::Integral::knot(), Neighbour_face_pt, Neighbour_local_coordinate, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_dimension(), oomph::Integral::nweight(), oomph::oomph_info, s, and plotDoE::x.

Referenced by oomph::DGElement::setup_face_neighbour_info().

◆ required_nflux()

virtual unsigned oomph::DGFaceElement::required_nflux ( )

inlineprotectedvirtual

Set the number of flux components.

Reimplemented in oomph::DGScalarAdvectionFaceElement< ELEMENT >, oomph::DGEulerFaceReflectionElement< ELEMENT >, and oomph::DGEulerFaceElement< ELEMENT >.

     {
       return 0;
     }

Referenced by add_flux_contributions(), dnumerical_flux_du(), interpolated_u(), and numerical_flux_at_knot().

◆ setup_neighbour_info()

void oomph::DGFaceElement::setup_neighbour_info ( const bool & add_neighbour_data_to_bulk )

Setup information from the neighbouring face, return a set of nodes (as data) in the neighour. The boolean flag is used to determine whether the data in the neighbour are added as external data to the bulk element — required when computing the jacobian of the system

Find pointers to neighbouring faces and the local coordinates in those faces that correspond to the integration points in the present face. This is achieved by moving up to the bulk element and thence the mesh which MUST have implemented a neighbour finding scheme

   {
     // Cache the pointer to the bulk element
     DGElement* const bulk_element_pt =
       dynamic_cast<DGElement*>(this->bulk_element_pt());
  
     // Find the number of points in the integration scheme
     const unsigned n_intpt = integral_pt()->nweight();
     // Resize the storage in the element
     Neighbour_face_pt.resize(n_intpt);
     Neighbour_local_coordinate.resize(n_intpt);
  
     // If we are adding the neighbour data to the bulk element
     // then resize this storage
     if (add_neighbour_data_to_bulk)
     {
       Neighbour_external_data.resize(n_intpt);
     }
  
  
     // Get the dimension of the present element
     const unsigned el_dim = this->dim();
     // Local coordinate in the face element
     Vector<double> s(el_dim);
  
     // Get the dimension of the bulk element
     const unsigned n_dim = bulk_element_pt->dim();
     // Local coordinate in the bulk element
     Vector<double> s_bulk(n_dim);
  
     // Storage for the interpolation data in the neighbour
     Vector<Data*> neighbour_data;
  
     // Now loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Get the local coordinate of the integration points
       for (unsigned i = 0; i < el_dim; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Now get the bulk coordinate
       this->get_local_coordinate_in_bulk(s, s_bulk);
  
       // Now we find the neighbouring face via the bulk element's member
       // function which calls the Mesh's member function
       bulk_element_pt->get_neighbouring_face_and_local_coordinate(
         this->face_index(),
         s_bulk,
         Neighbour_face_pt[ipt],
         Neighbour_local_coordinate[ipt]);
  
       // If we are adding the external data to the bulk
       if (add_neighbour_data_to_bulk)
       {
         // Throw the appropriate data from the neighbour face to the set
         dynamic_cast<DGFaceElement*>(Neighbour_face_pt[ipt])
           ->get_interpolation_data(neighbour_data);
  
         // Find the number of data
         unsigned n_neighbour_data = neighbour_data.size();
         // Resize the storage accordingly
         Neighbour_external_data.resize(n_neighbour_data);
  
         // Add the data to the external data of the bulk element
         for (unsigned n = 0; n < n_neighbour_data; n++)
         {
           Neighbour_external_data[ipt][n] =
             bulk_element_pt->add_external_data(neighbour_data[n]);
         }
       }
     }
   }

References oomph::GeneralisedElement::add_external_data(), oomph::FaceElement::bulk_element_pt(), oomph::FiniteElement::dim(), el_dim, oomph::FaceElement::face_index(), get_interpolation_data(), oomph::FaceElement::get_local_coordinate_in_bulk(), i, oomph::FiniteElement::integral_pt(), oomph::Integral::knot(), n, Neighbour_external_data, Neighbour_face_pt, Neighbour_local_coordinate, oomph::Integral::nweight(), and s.

Referenced by oomph::DGElement::setup_face_neighbour_info().

Member Data Documentation

◆ Neighbour_external_data

Vector<Vector<unsigned> > oomph::DGFaceElement::Neighbour_external_data

private

Vector of the vectors that will store the number of the bulk external data that correspond to the dofs in the neighbouring face This is only used if we are using implict timestepping and wish to assemble the jacobian matrix. In order that the data be correctly set up DGMesh::setup_face_neighbour_info() must be called with the boolean flag set to true.

Referenced by add_flux_contributions(), and setup_neighbour_info().

◆ Neighbour_face_pt

Vector<FaceElement*> oomph::DGFaceElement::Neighbour_face_pt

private

Vector of neighbouring face elements at the integration points.

Referenced by add_flux_contributions(), neighbour_face_pt(), numerical_flux_at_knot(), report_info(), and setup_neighbour_info().

◆ Neighbour_local_coordinate

Vector<Vector<double> > oomph::DGFaceElement::Neighbour_local_coordinate

private

Vector of neighbouring local coordinates at the integration points.

Referenced by numerical_flux_at_knot(), report_info(), and setup_neighbour_info().

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

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DGFaceElement()

◆ ~DGFaceElement()

Member Function Documentation

◆ add_flux_contributions()

◆ dnumerical_flux_du()

◆ flux_index()

◆ get_interpolation_data()

◆ interpolated_u()

◆ neighbour_face_pt()

◆ numerical_flux()

◆ numerical_flux_at_knot()

◆ report_info()

◆ required_nflux()

◆ setup_neighbour_info()

Member Data Documentation

◆ Neighbour_external_data

◆ Neighbour_face_pt

◆ Neighbour_local_coordinate