A class for solving my poisson like streamfunction problem. More...

#include <streamfunction_elements.h>

Inheritance diagram for oomph::PolarStreamfunctionEquations:

Public Member Functions
const double &	alpha () const
	Alpha. More...

double *&	alpha_pt ()
	Pointer to Alpha. More...

	PolarStreamfunctionEquations ()
	Constructor (must initialise the Source_fct_pt to null) More...

	PolarStreamfunctionEquations (const PolarStreamfunctionEquations &dummy)
	Broken copy constructor. More...

virtual unsigned	u_index_streamfunction () const
	Return the indicies at which the unknown values are stored. More...

virtual unsigned	u_index_velocity (const unsigned &i) const
	Return the indicies at which the (known) velocities are stored. More...

void	output (std::ostream &outfile)
	Output with default number of plot points. More...

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

void	output (FILE *file_pt)
	C_style output with default number of plot points. More...

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

void	get_flux (const Vector< double > &s, Vector< double > &flux) const

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

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

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

double	interpolated_velocity (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated velocity u[i] at local coordinate s. More...

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

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...

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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, 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 double	dshape_and_dtest_eulerian_poisson (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

virtual double	dshape_and_dtest_eulerian_at_knot_poisson (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

virtual void	fill_in_generic_residual_contribution (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)

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
double *	Alpha_pt
	Pointer to the angle alpha. More...

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

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

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

A class for solving my poisson like streamfunction problem.

Constructor & Destructor Documentation

◆ PolarStreamfunctionEquations() [1/2]

oomph::PolarStreamfunctionEquations::PolarStreamfunctionEquations ( )

inline

Constructor (must initialise the Source_fct_pt to null)

52 {}

◆ PolarStreamfunctionEquations() [2/2]

oomph::PolarStreamfunctionEquations::PolarStreamfunctionEquations ( const PolarStreamfunctionEquations & dummy )

inline

Broken copy constructor.

   { 
    BrokenCopy::broken_copy("PolarStreamfunctionEquations");
   } 

References oomph::BrokenCopy::broken_copy().

Member Function Documentation

◆ alpha()

const double& oomph::PolarStreamfunctionEquations::alpha ( ) const

inline

Alpha.

46 {return *Alpha_pt;}

oomph::PolarStreamfunctionEquations::Alpha_pt

double * Alpha_pt

Pointer to the angle alpha.

Definition: streamfunction_elements.h:41

References Alpha_pt.

Referenced by oomph::RefineablePolarStreamfunctionEquations::fill_in_generic_residual_contribution(), fill_in_generic_residual_contribution(), and interpolated_vorticity().

◆ alpha_pt()

double* & oomph::PolarStreamfunctionEquations::alpha_pt ( )

inline

Pointer to Alpha.

49 {return Alpha_pt;}

References Alpha_pt.

Referenced by oomph::RefineablePolarStreamfunctionEquations::further_build(), and oomph::StreamfunctionProblem::StreamfunctionProblem().

◆ dshape_and_dtest_eulerian_at_knot_poisson()

virtual double oomph::PolarStreamfunctionEquations::dshape_and_dtest_eulerian_at_knot_poisson	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping

Implemented in oomph::PolarStreamfunctionElement.

Referenced by oomph::RefineablePolarStreamfunctionEquations::fill_in_generic_residual_contribution(), and fill_in_generic_residual_contribution().

◆ dshape_and_dtest_eulerian_poisson()

virtual double oomph::PolarStreamfunctionEquations::dshape_and_dtest_eulerian_poisson	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at local coord. s; return Jacobian of mapping

Implemented in oomph::PolarStreamfunctionElement.

◆ fill_in_contribution_to_jacobian()

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

inlinevirtual

Add the element's contribution to its residual vector and element Jacobian matrix (wrapper)

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the generic routine with the flag set to 1
    fill_in_generic_residual_contribution(residuals,jacobian,1);
   }

References fill_in_generic_residual_contribution().

◆ fill_in_contribution_to_residuals()

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

inlinevirtual

Add the element's contribution to its residual vector (wrapper)

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the generic residuals function with flag set to 0
    //using a dummy matrix argument
    fill_in_generic_residual_contribution(
     residuals,GeneralisedElement::Dummy_matrix,0);
   }

References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution().

◆ fill_in_generic_residual_contribution()

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

protectedvirtual

Compute element residual Vector only (if flag=and/or element Jacobian matrix

Compute element residual Vector and/or element Jacobian matrix

flag=1: compute both flag=0: compute only residual Vector

Pure version without hanging nodes

Reimplemented in oomph::RefineablePolarStreamfunctionEquations.

 {
  //Find out how many nodes there are
  const unsigned n_node = nnode();
  
  //Get Alpha
  const double Alpha = alpha();
  
  //Set up memory for the shape and test functions
  Shape psi(n_node), test(n_node);
  DShape dpsidx(n_node,2), dtestdx(n_node,2);
  
  //Indicies at which the unknowns are stored
  const unsigned s_nodal_index = u_index_streamfunction();
  
  //Find the indices at which the local velocities are stored
  unsigned u_nodal_index[2];
  for(unsigned i=0;i<2;i++) {u_nodal_index[i] = u_index_velocity(i);}
  
  //Set the value of n_intpt
  const unsigned n_intpt = integral_pt()->nweight();
  
  //Integers to store the local equation and unknown numbers
  int local_eqn=0, local_unknown=0;
  
  //Loop over the integration points
  for(unsigned ipt=0;ipt<n_intpt;ipt++)
   {
    //Get the integral weight
    double w = integral_pt()->weight(ipt);
  
    //Call the derivatives of the shape and test functions
    double J = dshape_and_dtest_eulerian_at_knot_poisson(ipt,psi,dpsidx,
                                                         test,dtestdx);
        
    //Premultiply the weights and the Jacobian
    double W = w*J;
  
    //Allocate and initialise to zero
    Vector<double> interpolated_x(2,0.0);
    double interpolated_s=0.0;
    Vector<double> interpolated_dsdx(2,0.0);
    Vector<double> interpolated_u(2);
    DenseMatrix<double> interpolated_dudx(2,2);
    
    //Calculate function value and derivatives:
    //-----------------------------------------
    // Loop over nodes
    for(unsigned l=0;l<n_node;l++) 
     {
      //Get the nodal value of the poisson unknown
      double s_value = raw_nodal_value(l,s_nodal_index);
      interpolated_s += s_value*psi(l);
      // Loop over directions1
      for(unsigned i=0;i<2;i++)
       {
        interpolated_x[i] += raw_nodal_position(l,i)*psi(l);
        interpolated_dsdx[i] += s_value*dpsidx(l,i);
        double u_value = this->nodal_value(l,u_nodal_index[i]);
        interpolated_u[i] += u_value*psi(l);
        // Loop over directions2
        for(unsigned j=0;j<2;j++)
         {                               
          interpolated_dudx(i,j) += u_value*dpsidx(l,j);
         }
       }
     }
  
    // Assemble residuals and Jacobian
    //--------------------------------
        
    // Loop over the test functions
    for(unsigned l=0;l<n_node;l++)
     {
       //Get the local equation
       local_eqn = nodal_local_eqn(l,s_nodal_index);
       /*IF it's not a boundary condition*/
       if(local_eqn >= 0)
        {
     // Laplacian of the streamfunction (integrated by parts)
     residuals[local_eqn] += interpolated_dsdx[0]*dtestdx(l,0)*interpolated_x[0]*Alpha*W;
     residuals[local_eqn] += (1./(interpolated_x[0]*Alpha))*interpolated_dsdx[1]
                            *(1./(interpolated_x[0]*Alpha))*dtestdx(l,1)
       *interpolated_x[0]*Alpha*W;
  
     // Should equal the vorticity
     residuals[local_eqn] -= (interpolated_dudx(1,0)+(interpolated_u[1]/interpolated_x[0]))*test(l)*interpolated_x[0]*Alpha*W;
     residuals[local_eqn] += (1./(interpolated_x[0]*Alpha))*interpolated_dudx(0,1)*test(l)*interpolated_x[0]*Alpha*W;
  
     // Calculate the jacobian
     //-----------------------
     if(flag)
      {
           //Loop over the velocity shape functions again
           for(unsigned l2=0;l2<n_node;l2++)
            {
          local_unknown = nodal_local_eqn(l2,s_nodal_index);
          //If at a non-zero degree of freedom add in the entry
          if(local_unknown >= 0)
               {
                //Add contribution to Elemental Matrix
                  jacobian(local_eqn,local_unknown) 
            += dpsidx(l2,0)*dtestdx(l,0)*interpolated_x[0]*Alpha*W;
                  jacobian(local_eqn,local_unknown) 
            += (1./(interpolated_x[0]*Alpha))*dpsidx(l2,1)*(1./(interpolated_x[0]*Alpha))*dtestdx(l,1)
             *interpolated_x[0]*Alpha*W;
           } 
  
        } // End of loop over l2
      } // End of if Jacobian flag statement
        } // End of Residual if not boundary condition statement
       
     } // End of loop over test functions (l)
  
   } // End of loop over integration points
 }   

References TanhSolnForAdvectionDiffusion::Alpha, alpha(), dshape_and_dtest_eulerian_at_knot_poisson(), i, oomph::FiniteElement::integral_pt(), interpolated_dudx(), oomph::FiniteElement::interpolated_x(), J, j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::nodal_value(), oomph::Integral::nweight(), oomph::FiniteElement::raw_nodal_position(), oomph::FiniteElement::raw_nodal_value(), Eigen::test, u_index_streamfunction(), u_index_velocity(), w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by fill_in_contribution_to_jacobian(), and fill_in_contribution_to_residuals().

◆ get_flux()

void oomph::PolarStreamfunctionEquations::get_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)		const

inline

Get flux: Necessary for Z2 error estimator in refineable version Doesn't matter what it is though as we're NEVER? going to refine

   {
    //Find out how many nodes there are in the element
    const unsigned n_node = nnode();
  
    //Get the index at which the unknown is stored
    const unsigned u_nodal_index = u_index_streamfunction();
  
    //Set up memory for the shape and test functions
    Shape psi(n_node);
    DShape dpsidx(n_node,2);
  
    //Call the derivatives of the shape and test functions
    dshape_eulerian(s,psi,dpsidx);
      
    //Initialise to zero
    for(unsigned j=0;j<2;j++)
     {
      flux[j] = 0.0;
     }
    
    // Loop over nodes
    for(unsigned l=0;l<n_node;l++) 
     {
      //Loop over derivative directions
      for(unsigned j=0;j<2;j++)
       {                               
        flux[j] += this->nodal_value(l,u_nodal_index)*dpsidx(l,j);
       }
     }
   }

References oomph::FiniteElement::dshape_eulerian(), ProblemParameters::flux(), j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, and u_index_streamfunction().

Referenced by oomph::RefineablePolarStreamfunctionEquations::get_Z2_flux().

◆ interpolated_dudx()

double oomph::PolarStreamfunctionEquations::interpolated_dudx	(	const Vector< double > &	s,
		const unsigned &	i,
		const unsigned &	j
	)		const

inline

Return FE interpolated velocity derivative du[i]/dx[j]
at local coordinate s

   {
    //Find number of nodes
    unsigned n_node = nnode(); 
  
    //Get the index at which the poisson unknown is stored
    const unsigned u_nodal_index = u_index_velocity(i);
  
    //Set up memory for the shape and test functions
    Shape psi(n_node);
    DShape dpsidx(n_node,2);
  
    //double J = 
    dshape_eulerian(s,psi,dpsidx);
  
    //Initialise to zero
    double interpolated_dudx = 0.0;
    
    //Calculate velocity derivative:
  
    // Loop over nodes
    for(unsigned l=0;l<n_node;l++) 
     {                              
      interpolated_dudx += this->nodal_value(l,u_nodal_index)*dpsidx(l,j);
     }
   
    return(interpolated_dudx);
   }

References oomph::FiniteElement::dshape_eulerian(), i, j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, and u_index_velocity().

Referenced by oomph::RefineablePolarStreamfunctionEquations::fill_in_generic_residual_contribution(), fill_in_generic_residual_contribution(), and interpolated_vorticity().

◆ interpolated_streamfunction()

double oomph::PolarStreamfunctionEquations::interpolated_streamfunction ( const Vector< double > & s ) const

inline

Return FE representation of streamfunction at local coordinate s

   {
    //Find number of nodes
    const unsigned n_node = nnode();
  
    //Get the index at which the poisson unknown is stored
    const unsigned u_nodal_index = u_index_streamfunction();
    
    //Local shape function
    Shape psi(n_node);
  
    //Find values of shape function
    shape(s,psi);
  
    //Initialise value of u
    double interpolated_u = 0.0;
  
    //Loop over the local nodes and sum
    for(unsigned l=0;l<n_node;l++) 
     {
      interpolated_u += this->nodal_value(l,u_nodal_index)*psi[l];
     }
  
    return(interpolated_u);
   }

References oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and u_index_streamfunction().

Referenced by output().

◆ interpolated_velocity()

double oomph::PolarStreamfunctionEquations::interpolated_velocity	(	const Vector< double > &	s,
		const unsigned &	i
	)		const

inline

Return FE interpolated velocity u[i] at local coordinate s.

   {
    //Find number of nodes
    unsigned n_node = nnode();
  
    //Get the index at which the poisson unknown is stored
    const unsigned u_nodal_index = u_index_velocity(i);
  
    //Local shape function
    Shape psi(n_node);
    //Find values of shape function
    shape(s,psi);
    
    //Initialise value of u
    double interpolated_u = 0.0;
    //Loop over the local nodes and sum
    for(unsigned l=0;l<n_node;l++) 
     {
      interpolated_u += this->nodal_value(l,u_nodal_index)*psi[l];
     }
    
    return(interpolated_u);
   }

References i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and u_index_velocity().

Referenced by interpolated_vorticity(), and output().

◆ interpolated_vorticity()

double oomph::PolarStreamfunctionEquations::interpolated_vorticity ( const Vector< double > & s ) const

inline

Construct and Return FE representation of vorticity at local coordinate s

   {
    //Find number of nodes
    unsigned n_node = nnode(); 
  
    //Get Alpha
    const double Alpha = alpha();
  
    //Local shape function
    Shape psi(n_node);
    //Find values of shape function
    shape(s,psi);
  
    //Allocate and initialise to zero
    double r = 0.0;
  
    // Loop over nodes to calculate r
    for(unsigned l=0;l<n_node;l++) 
     {
        r += nodal_position(l,0)*psi(l);
     }
  
    //Initialise value of u
    double interpolated_u = 0.0;
  
    interpolated_u += interpolated_dudx(s,1,0);
    interpolated_u += (1./r)*interpolated_velocity(s,1);
    interpolated_u -= (1./(r*Alpha))*interpolated_dudx(s,0,1);
  
    return(interpolated_u);
   }

References TanhSolnForAdvectionDiffusion::Alpha, alpha(), interpolated_dudx(), interpolated_velocity(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), UniformPSDSelfTest::r, s, and oomph::FiniteElement::shape().

Referenced by output().

◆ output() [1/4]

void oomph::PolarStreamfunctionEquations::output ( FILE * file_pt )

inlinevirtual

C_style output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::PolarStreamfunctionElement.

   {
    const unsigned n_plot=5;
    output(file_pt,n_plot);
   }

References output().

◆ output() [2/4]

void oomph::PolarStreamfunctionEquations::output	(	FILE *	file_pt,
		const unsigned &	nplot
	)

virtual

C-style output FE representation of soln: x,y,u or x,y,z,u at n_plot^DIM plot points

C-style output function:

x,y,u or x,y,z,u

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::PolarStreamfunctionElement.

 {
  //Vector of local coordinates
  Vector<double> s(2);
  
  // Tecplot header info
  fprintf(file_pt,"%s",tecplot_zone_string(nplot).c_str());
  
  // Loop over plot points
  unsigned num_plot_points=nplot_points(nplot);
  for (unsigned iplot=0;iplot<num_plot_points;iplot++)
   {
    // Get local coordinates of plot point
    get_s_plot(iplot,nplot,s);
    
    for(unsigned i=0;i<2;i++) 
     {
      fprintf(file_pt,"%g ",interpolated_x(s,i));
     }
    fprintf(file_pt,"%g ",interpolated_streamfunction(s));
    fprintf(file_pt,"%g \n",interpolated_vorticity(s));
   }
  
  // Write tecplot footer (e.g. FE connectivity lists)
  write_tecplot_zone_footer(file_pt,nplot);
 }

References oomph::FiniteElement::get_s_plot(), i, interpolated_streamfunction(), interpolated_vorticity(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output() [3/4]

void oomph::PolarStreamfunctionEquations::output ( std::ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::PolarStreamfunctionElement.

   {
    const unsigned n_plot=5;
    output(outfile,n_plot);
   }

Referenced by output(), and oomph::PolarStreamfunctionElement::output().

◆ output() [4/4]

void oomph::PolarStreamfunctionEquations::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

virtual

Output FE representation of soln: x,y,u or x,y,z,u at n_plot^DIM plot points

Output function:

x,y,u or x,y,z,u

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::PolarStreamfunctionElement.

 {
  
  //Vector of local coordinates
  Vector<double> s(2);
  
  // Tecplot header info
  outfile << tecplot_zone_string(nplot);
  
  // Loop over plot points
  unsigned num_plot_points=nplot_points(nplot);
  for (unsigned iplot=0;iplot<num_plot_points;iplot++)
   {
    
    // Get local coordinates of plot point
    get_s_plot(iplot,nplot,s);
    
    for(unsigned i=0;i<2;i++) 
     {
      outfile << interpolated_x(s,i) << " ";
     }
    outfile << interpolated_streamfunction(s) << " "
        << interpolated_vorticity(s) << " " 
        << interpolated_velocity(s,0) << " "
        << interpolated_velocity(s,1) << std::endl;   
    
   }
  
  // Write tecplot footer (e.g. FE connectivity lists)
  write_tecplot_zone_footer(outfile,nplot);
  
 }

References oomph::FiniteElement::get_s_plot(), i, interpolated_streamfunction(), interpolated_velocity(), interpolated_vorticity(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ u_index_streamfunction()

virtual unsigned oomph::PolarStreamfunctionEquations::u_index_streamfunction ( ) const

inlinevirtual

Return the indicies at which the unknown values are stored.

62 {return 0;}

Referenced by oomph::RefineablePolarStreamfunctionEquations::fill_in_generic_residual_contribution(), fill_in_generic_residual_contribution(), get_flux(), oomph::RefineablePolarStreamfunctionEquations::get_interpolated_values(), and interpolated_streamfunction().

◆ u_index_velocity()

virtual unsigned oomph::PolarStreamfunctionEquations::u_index_velocity ( const unsigned & i ) const

inlinevirtual

Return the indicies at which the (known) velocities are stored.

65 {return i+1;}

References i.

Referenced by oomph::RefineablePolarStreamfunctionEquations::fill_in_generic_residual_contribution(), fill_in_generic_residual_contribution(), oomph::RefineablePolarStreamfunctionEquations::get_interpolated_values(), interpolated_dudx(), and interpolated_velocity().

Member Data Documentation

◆ Alpha_pt

double* oomph::PolarStreamfunctionEquations::Alpha_pt

protected

Pointer to the angle alpha.

Referenced by alpha(), alpha_pt(), and oomph::RefineablePolarStreamfunctionEquations::further_build().

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

streamfunction_elements.h

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PolarStreamfunctionEquations() [1/2]

◆ PolarStreamfunctionEquations() [2/2]

Member Function Documentation

◆ alpha()

◆ alpha_pt()

◆ dshape_and_dtest_eulerian_at_knot_poisson()

◆ dshape_and_dtest_eulerian_poisson()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution()

◆ get_flux()

◆ interpolated_dudx()

◆ interpolated_streamfunction()

◆ interpolated_velocity()

◆ interpolated_vorticity()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ u_index_streamfunction()

◆ u_index_velocity()

Member Data Documentation

◆ Alpha_pt