Inheritance diagram for ModalPRefineableQPoissonElement< DIM >:

Public Types
typedef void(*	PoissonSourceFctPt) (const Vector< double > &x, double &f)

Public Types inherited from oomph::PoissonEquations< DIM >
typedef void(*	PoissonSourceFctPt) (const Vector< double > &x, double &f)

typedef void(*	PoissonSourceFctGradientPt) (const Vector< double > &x, Vector< double > &gradient)

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

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

Public Types inherited from ModalPoissonEquations< DIM >
typedef void(*	PoissonSourceFctPt) (const Vector< double > &x, double &f)

typedef void(*	PoissonDiffFctPt) (const Vector< double > &x, double &f)
	Function pointer to a diffusion function fxt(x,f(x)) More...

Public Member Functions
	ModalPRefineableQPoissonElement ()
	Constructor, simply call the other constructors. More...

	ModalPRefineableQPoissonElement (const ModalPRefineableQPoissonElement< DIM > &dummy)
	Broken copy constructor. More...

unsigned	nnode_1d () const

virtual void	further_build ()
	Further build: Copy source function pointer from father element. More...

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 1. More...

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

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

unsigned	nrecovery_order ()

void	basis (const Vector< double > &s, Shape &basis) const

void	dbasis_local (const Vector< double > &s, Shape &basis, DShape &dbasis) const

void	d2basis_local (const Vector< double > &s, Shape &basis, DShape &dbasisds, DShape &d2basisds) const

double	u (const unsigned &n) const

virtual unsigned	nbasis () const
	Number of basis functions. More...

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

void	output (ostream &outfile, const unsigned &nplot)

void	output_fct (ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)

void	output_fct (ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)

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

void	compute_energy_error (ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_grad_pt, double &error, double &norm)
	Get error against and norm of exact solution. More...

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

PoissonSourceFctPt &	source_fct_pt ()

PoissonSourceFctPt	source_fct_pt () const

unsigned	self_test ()
	Self-test: Return 0 for OK. More...

virtual double	dbasis_eulerian (const Vector< double > &s, Shape &basis, DShape &dbasis) const

virtual double	dbasis_eulerian_at_knot (const unsigned &ipt, Shape &basis, DShape &dbasis) const

virtual void	dbasis_local_at_knot (const unsigned &ipt, Shape &basis, DShape &dbasisds) const

virtual double	dshape_dbasis_and_dtest_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &basis, DShape &dbasisdx, Shape &test, DShape &dtestdx) const

virtual double	dshape_dbasis_and_dtest_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &basis, DShape &dbasisdx, Shape &test, DShape &dtestdx) 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)

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

void	assign_additional_local_eqn_numbers ()

Public Member Functions inherited from oomph::QPoissonElement< DIM, 2 >
	QPoissonElement ()

	QPoissonElement (const QPoissonElement< DIM, NNODE_1D > &dummy)=delete
	Broken copy constructor. More...

void	operator= (const QPoissonElement< DIM, NNODE_1D > &)=delete
	Broken assignment operator. More...

unsigned	required_nvalue (const unsigned &n) const

void	output (std::ostream &outfile)

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

void	output (FILE *file_pt)

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

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

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

Public Member Functions inherited from oomph::PoissonEquations< DIM >
	PoissonEquations ()
	Constructor (must initialise the Source_fct_pt to null) More...

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

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

virtual unsigned	u_index_poisson () const

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

unsigned	nscalar_paraview () const

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

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

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

void	compute_norm (double &norm)
	Compute norm of solution: square of the L2 norm. More...

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Get error against and norm of exact solution. More...

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Dummy, time dependent error checker. More...

PoissonSourceFctPt &	source_fct_pt ()
	Access function: Pointer to source function. More...

PoissonSourceFctPt	source_fct_pt () const
	Access function: Pointer to source function. Const version. More...

PoissonSourceFctGradientPt &	source_fct_gradient_pt ()
	Access function: Pointer to gradient of source function. More...

PoissonSourceFctGradientPt	source_fct_gradient_pt () const
	Access function: Pointer to gradient source function. Const version. More...

virtual void	get_source_poisson (const unsigned &ipt, const Vector< double > &x, double &source) const

virtual void	get_source_gradient_poisson (const unsigned &ipt, const Vector< double > &x, Vector< double > &gradient) const

void	get_flux (const Vector< double > &s, Vector< double > &flux) const
	Get flux: flux[i] = du/dx_i. More...

void	get_dflux_dnodal_u (const Vector< double > &s, Vector< Vector< double >> &dflux_dnodal_u) 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)

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

unsigned	self_test ()
	Self-test: Return 0 for OK. 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

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

double	dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. More...

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

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

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

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

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

virtual void	disable_ALE ()

virtual void	enable_ALE ()

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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_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

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

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, 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, 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	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 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

Public Member Functions inherited from RefineableModalPoissonEquations< DIM >
	RefineableModalPoissonEquations ()
	Constructor, simply call other constructors. More...

	RefineableModalPoissonEquations (const RefineableModalPoissonEquations< DIM > &dummy)
	Broken copy constructor. More...

virtual unsigned	u_index_poisson () const

unsigned	num_Z2_flux_terms ()
	Number of 'flux' terms for Z2 error estimation. More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)
	Get 'flux' for Z2 error recovery: Standard flux.from Poisson equations. More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)
	Get error against and norm of exact flux. More...

void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)

Public Member Functions inherited from ModalPoissonEquations< DIM >
	ModalPoissonEquations ()
	Constructor (must initialise the Source_fct_pt to null) More...

void	output_fct (ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output exact soln: x,y,u_exact or x,y,z,u_exact at nplot^DIM plot points. More...

void	compute_error (ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Get error against and norm of exact solution. More...

void	compute_error (ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Dummy, time dependent error checker. More...

PoissonSourceFctPt &	source_fct_pt ()
	Access function: Pointer to source function. More...

PoissonSourceFctPt	source_fct_pt () const
	Access function: Pointer to source function. Const version. More...

virtual void	get_source_poisson (const Vector< double > &x, double &source) const

PoissonDiffFctPt &	diff_fct_pt ()
	Access function: Pointer to diffusivity function. More...

PoissonDiffFctPt	diff_fct_pt () const
	Access function: Pointer to source function. Const version. More...

virtual void	get_diff (const Vector< double > &x, double &diff) const

void	get_flux (const Vector< double > &s, Vector< double > &flux, unsigned p_order) const
	Get flux: flux[i] = du/dx_i. More...

double	interpolated_u (const Vector< double > &s) const
	Return FE representation of function value u(s) at local coordinate s. More...

Public Member Functions inherited from oomph::RefineableElement
	RefineableElement ()

virtual	~RefineableElement ()
	Destructor, delete the allocated storage for the hanging equations. More...

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

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

Tree *	tree_pt ()
	Access function: Pointer to quadtree representation of this element. More...

void	set_tree_pt (Tree *my_tree_pt)
	Set pointer to quadtree representation of this element. More...

virtual unsigned	required_nsons () const

bool	refinement_is_enabled ()
	Flag to indicate suppression of any refinement. More...

void	disable_refinement ()
	Suppress of any refinement for this element. More...

void	enable_refinement ()
	Emnable refinement for this element. More...

template<class ELEMENT >
void	split (Vector< ELEMENT * > &son_pt) const

int	local_hang_eqn (Node *const &node_pt, const unsigned &i)

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)=0

void	set_refinement_level (const int &refine_level)
	Set the refinement level. More...

unsigned	refinement_level () const
	Return the Refinement level. More...

void	select_for_refinement ()
	Select the element for refinement. More...

void	deselect_for_refinement ()
	Deselect the element for refinement. More...

void	select_sons_for_unrefinement ()
	Unrefinement will be performed by merging the four sons of this element. More...

void	deselect_sons_for_unrefinement ()

bool	to_be_refined ()
	Has the element been selected for refinement? More...

bool	sons_to_be_unrefined ()
	Has the element been selected for unrefinement? More...

virtual void	rebuild_from_sons (Mesh *&mesh_pt)=0

virtual void	unbuild ()

virtual void	deactivate_element ()

virtual bool	nodes_built ()
	Return true if all the nodes have been built, false if not. More...

long	number () const
	Element number (for debugging/plotting) More...

void	set_number (const long &mynumber)
	Set element number (for debugging/plotting) More...

virtual Node *	interpolating_node_pt (const unsigned &n, const int &value_id)

virtual double	local_one_d_fraction_of_interpolating_node (const unsigned &n1d, const unsigned &i, const int &value_id)

virtual Node *	get_interpolating_node_at_local_coordinate (const Vector< double > &s, const int &value_id)

virtual unsigned	ninterpolating_node (const int &value_id)

virtual unsigned	ninterpolating_node_1d (const int &value_id)

virtual void	interpolating_basis (const Vector< double > &s, Shape &psi, const int &value_id) const

virtual void	check_integrity (double &max_error)=0

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

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual RefineableElement *	root_element_pt ()

virtual RefineableElement *	father_element_pt () const
	Return a pointer to the father element. More...

void	get_father_at_refinement_level (unsigned &refinement_level, RefineableElement *&father_at_reflevel_pt)

virtual void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)

virtual void	pre_build (Mesh &mesh_pt, Vector< Node > &new_node_pt)
	Pre-build the element. More...

virtual void	setup_hanging_nodes (Vector< std::ofstream * > &output_stream)

virtual void	further_setup_hanging_nodes ()

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

unsigned	nshape_controlling_nodes ()

std::map< Node *, unsigned >	shape_controlling_node_lookup ()

Public Member Functions inherited from oomph::ElementWithZ2ErrorEstimator
	ElementWithZ2ErrorEstimator ()
	Default empty constructor. More...

	ElementWithZ2ErrorEstimator (const ElementWithZ2ErrorEstimator &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithZ2ErrorEstimator &)=delete
	Broken assignment operator. More...

virtual unsigned	ncompound_fluxes ()

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)

virtual double	geometric_jacobian (const Vector< double > &x)

Public Member Functions inherited from ModalPRefineableQElement< DIM >
	ModalPRefineableQElement ()

void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)

void	pre_build (Mesh &, Vector< Node > &)

void	further_build ()

void	p_refine (const int &inc, Mesh const &mesh_pt, GeneralisedElement const &clone_pt)

void	shape (const Vector< double > &s, Shape &psi) const

void	basis (const Vector< double > &s, Shape &basis) const

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

void	dbasis_local (const Vector< double > &s, Shape &basis, DShape &dbasis) const

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

void	d2basis_local (const Vector< double > &s, Shape &basis, DShape &dbasisds, DShape &d2basisds) const

void	initial_setup (Tree *const &adopted_father_pt, const unsigned &initial_p_order)

void	pre_build (Mesh &, Vector< Node > &)

void	p_refine (const int &inc, Mesh const &mesh_pt, GeneralisedElement const &clone_pt)

Public Member Functions inherited from oomph::PRefineableQElement< DIM, 2 >
	PRefineableQElement ()
	Empty constuctor. More...

Additional Inherited Members
Static Public Member Functions inherited from oomph::RefineableElement
static double &	max_integrity_tolerance ()
	Max. allowed discrepancy in element integrity check. More...

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

Protected Member Functions inherited from oomph::QPoissonElement< DIM, 2 >
double	dshape_and_dtest_eulerian_poisson (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

double	dshape_and_dtest_eulerian_at_knot_poisson (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const

Protected Member Functions inherited from oomph::PoissonEquations< DIM >
virtual void	fill_in_generic_residual_contribution_poisson (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

Protected Member Functions inherited from oomph::FiniteElement
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 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

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)

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)

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 Member Functions inherited from ModalPoissonEquations< DIM >
virtual void	add_generic_residual_contribution (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)

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

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

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

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

void	assign_hanging_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for hanging node variables. More...

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

Static Protected Member Functions inherited from oomph::RefineableElement
static void	check_value_id (const int &n_continuously_interpolated_values, const int &value_id)

Protected Attributes inherited from oomph::PoissonEquations< DIM >
PoissonSourceFctPt	Source_fct_pt
	Pointer to source function: More...

PoissonSourceFctGradientPt	Source_fct_gradient_pt
	Pointer to gradient of source function. 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

Protected Attributes inherited from ModalPoissonEquations< DIM >
PoissonSourceFctPt	Source_fct_pt
	Pointer to source function: More...

PoissonDiffFctPt	Diff_fct_pt
	Pointer to the diffusivity function. More...

Vector< int >	Local_eqn
	Array to hold local eqn numbers: Local_eqn[n] (=-1 for BC) More...

Protected Attributes inherited from oomph::RefineableElement
Tree *	Tree_pt
	A pointer to a general tree object. More...

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

bool	Refinement_is_enabled
	Flag to indicate suppression of any refinement. More...

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

long	Number
	Global element number – for plotting/validation purposes. More...

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

Static Protected Attributes inherited from oomph::RefineableElement
static double	Max_integrity_tolerance = 1.0e-8
	Max. allowed discrepancy in element integrity check. More...

Member Typedef Documentation

◆ PoissonSourceFctPt

template<unsigned DIM>

typedef void(* ModalPRefineableQPoissonElement< DIM >::PoissonSourceFctPt) (const Vector< double > &x, double &f)

Function pointer to source function fct(x,f(x)) – x is a Vector!

Constructor & Destructor Documentation

◆ ModalPRefineableQPoissonElement() [1/2]

template<unsigned DIM>

ModalPRefineableQPoissonElement< DIM >::ModalPRefineableQPoissonElement ( )

inline

Constructor, simply call the other constructors.

                                    : 
   RefineableElement(),
   RefineableModalPoissonEquations<DIM>(),
   ModalPRefineableQElement<DIM>(),
   QPoissonElement<DIM,2>()
    {
     // Set integration scheme
     // (To avoid memory leaks in pre-build and p-refine where new integration schemes are created)
     this->set_integration_scheme(new GaussLobattoLegendre<DIM,2>);
    }

◆ ModalPRefineableQPoissonElement() [2/2]

template<unsigned DIM>

ModalPRefineableQPoissonElement< DIM >::ModalPRefineableQPoissonElement ( const ModalPRefineableQPoissonElement< DIM > & dummy )

inline

Broken copy constructor.

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

References oomph::BrokenCopy::broken_copy().

Member Function Documentation

◆ assign_additional_local_eqn_numbers()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::assign_additional_local_eqn_numbers

virtual

Setup the local equation numbering schemes:

                /  local equation number.

Local_eqn[n] = | \ -1 if boundary condition.

Pure version without hanging nodes

Reimplemented from oomph::GeneralisedElement.

 {
  //Resize the equation counters
  this->Local_eqn.resize(this->p_order());
  
  //Loop over the nodes
  for(unsigned i=0;i<this->nnode_1d();i++)
   {
    //Set the local equation number to be the first value stored at the node
    this->Local_eqn[i] = this->nodal_local_eqn(i,0);
   }
  //Continue over the internal data
  for(unsigned i=this->nnode_1d();i<this->p_order();i++)
   {
    //Set the local equation number to be the ith value of the internal data
    this->Local_eqn[i] = this->internal_local_eqn(0,i-this->nnode_1d());
   }
 }

References i.

◆ basis()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::basis	(	const Vector< double > &	s,
		Shape &	basis
	)		const

inlinevirtual

Implements ModalPoissonEquations< DIM >.

1401 {ModalPRefineableQElement<DIM>::basis(s, basis);}

ModalPRefineableQElement::basis

void basis(const Vector< double > &s, Shape &basis) const

Definition: one_d_poisson_hp_adapt.cc:1273

ModalPRefineableQPoissonElement::basis

void basis(const Vector< double > &s, Shape &basis) const

Definition: one_d_poisson_hp_adapt.cc:1400

s

RealScalar s

Definition: level1_cplx_impl.h:130

References ModalPRefineableQElement< DIM >::basis(), and s.

◆ compute_energy_error()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::compute_energy_error	(	ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_grad_pt,
		double &	error,
		double &	norm
	)

inline

Get error against and norm of exact solution.

   {
  
    // Initialise
    error=0.0;
    norm=0.0;
  
    //Vector of local coordinates
    Vector<double> s(DIM);
  
    // Vector for coordintes
    Vector<double> x(DIM);
    
    //Set the value of n_intpt
    unsigned n_intpt = this->integral_pt()->nweight();
    
    // Setup output structure: Conversion is fishy but it's only output...
    unsigned nplot;
    if (DIM==1)
     {
      nplot=n_intpt;
     }
    else 
     {
      nplot=unsigned(pow(n_intpt,1.0/double(DIM)));
     }
    
    // Tecplot header info
    outfile << this->tecplot_zone_string(nplot);
    
    // Exact solution Vector (here a scalar)
    Vector<double> exact_grad(1);
    
    //Loop over the integration points
    for(unsigned ipt=0;ipt<n_intpt;ipt++)
     {
      
      //Assign values of s
      for(unsigned i=0;i<DIM;i++)
       {
        s[i] = this->integral_pt()->knot(ipt,i);
       }
      
      //Get the integral weight
      double w = this->integral_pt()->weight(ipt);
      
      // Get jacobian of mapping
      double J=this->J_eulerian(s);
      
      //Premultiply the weights and the Jacobian
      double W = w*J;
      
      // Get x position as Vector
      this->interpolated_x(s,x);
      
      // Get FE du/dx
      Vector<double> dudx_fe(1);
      ModalPoissonEquations<1>::get_flux(s,dudx_fe,this->p_order());
      
      // Get exact solution at this point
      (*exact_grad_pt)(x,exact_grad);
      
      //Output x,y,...,error
      for(unsigned i=0;i<DIM;i++)
       {
        outfile << x[i] << " ";
       }
      outfile << exact_grad[0] << " " << exact_grad[0]-dudx_fe[0] << std::endl;
      
      // Add to error and norm
      norm+=exact_grad[0]*exact_grad[0]*W;
      error+=(exact_grad[0]-dudx_fe[0])*(exact_grad[0]-dudx_fe[0])*W;
      
     }
   }

References DIM, calibrate::error, ModalPoissonEquations< DIM >::get_flux(), i, J, Eigen::bfloat16_impl::pow(), s, w, oomph::QuadTreeNames::W, and plotDoE::x.

◆ compute_error() [1/2]

template<unsigned DIM>

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

inline

1452 {RefineableModalPoissonEquations<DIM>::compute_error(outfile,

1453 exact_soln_pt, error, norm);}

ModalPoissonEquations::compute_error

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

Get error against and norm of exact solution.

Definition: one_d_poisson_hp_adapt.cc:219

References ModalPoissonEquations< DIM >::compute_error(), and calibrate::error.

◆ compute_error() [2/2]

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::compute_error	(	ostream &	outfile,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt,
		const double &	time,
		double &	error,
		double &	norm
	)

inline

1537 {RefineableModalPoissonEquations<DIM>::compute_error(outfile,

1538 exact_soln_pt, time, error, norm);}

References ModalPoissonEquations< DIM >::compute_error(), and calibrate::error.

◆ d2basis_local()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::d2basis_local	(	const Vector< double > &	s,
		Shape &	basis,
		DShape &	dbasisds,
		DShape &	d2basisds
	)		const

inline

1408 {ModalPRefineableQElement<DIM>::d2basis_local(s, basis, dbasisds, d2basisds);}

ModalPRefineableQElement::d2basis_local

void d2basis_local(const Vector< double > &s, Shape &basis, DShape &dbasisds, DShape &d2basisds) const

Definition: one_d_poisson_hp_adapt.cc:1331

References ModalPRefineableQElement< DIM >::d2basis_local(), and s.

◆ dbasis_eulerian()

template<unsigned DIM>

double ModalPRefineableQPoissonElement< DIM >::dbasis_eulerian	(	const Vector< double > &	s,
		Shape &	basis,
		DShape &	dbasis
	)		const

virtual

Compute the geometric basis functions and also first derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. Most general form of the function, but may be over-loaded, if desired

 {
  //Find the element dimension
  const unsigned el_dim = this->dim();
  
  //Get the values of the shape functions and their local derivatives
  //Temporarily stored in dpsi
  this->dbasis_local(s,basis,dbasis);
  
  //Allocate memory for the inverse jacobian
  DenseMatrix<double> inverse_jacobian(el_dim);
  //Now calculate the inverse jacobian
  const double det = this->local_to_eulerian_mapping(dbasis,inverse_jacobian);
  
  //Now set the values of the derivatives to be dpsidx
  this->transform_derivatives(inverse_jacobian,dbasis);
  //Return the determinant of the jacobian
  
  return det;
 }

References el_dim, and s.

◆ dbasis_eulerian_at_knot()

template<unsigned DIM>

double ModalPRefineableQPoissonElement< DIM >::dbasis_eulerian_at_knot	(	const unsigned &	ipt,
		Shape &	basis,
		DShape &	dbasis
	)		const

virtual

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

 {
  //Find the element dimension
  const unsigned el_dim = this->dim();
  
  //Get the values of the shape function and local derivatives
  //Temporarily store it in dpsi
  this->dbasis_local_at_knot(ipt,basis,dbasis);
  
  //Allocate memory for the inverse jacobian
  DenseMatrix<double> inverse_jacobian(el_dim);
  //Now calculate the inverse jacobian
  const double det = this->local_to_eulerian_mapping(dbasis,inverse_jacobian);
  
  //Now set the values of the derivatives to dpsidx
  this->transform_derivatives(inverse_jacobian,dbasis);
  //Return the determinant of the jacobian
  
  return det;
 }

References el_dim.

◆ dbasis_local()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::dbasis_local	(	const Vector< double > &	s,
		Shape &	basis,
		DShape &	dbasis
	)		const

inline

1404 {ModalPRefineableQElement<DIM>::dbasis_local(s, basis, dbasis);}

ModalPRefineableQElement::dbasis_local

void dbasis_local(const Vector< double > &s, Shape &basis, DShape &dbasis) const

Definition: one_d_poisson_hp_adapt.cc:1301

References ModalPRefineableQElement< DIM >::dbasis_local(), and s.

◆ dbasis_local_at_knot()

template<unsigned DIM>

virtual void ModalPRefineableQPoissonElement< DIM >::dbasis_local_at_knot	(	const unsigned &	ipt,
		Shape &	basis,
		DShape &	dbasisds
	)		const

inlinevirtual

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

  {
   //Find the dimension of the element
   const unsigned el_dim = this->dim();
   //Storage for the local coordinates of the integration point
   Vector<double> s(el_dim); 
   //Set the local coordinate
   for(unsigned i=0;i<el_dim;i++) {s[i] = this->integral_pt()->knot(ipt,i);}
   //Get the shape function and derivatives
   this->dbasis_local(s,basis,dbasisds);
  }

References el_dim, i, and s.

◆ dshape_dbasis_and_dtest_eulerian()

template<unsigned DIM>

virtual double ModalPRefineableQPoissonElement< DIM >::dshape_dbasis_and_dtest_eulerian	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	basis,
		DShape &	dbasisdx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

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

Implements ModalPoissonEquations< DIM >.

   {
    //Call the geometrical basis functions and derivatives
    double J = dbasis_eulerian(s,basis,dbasisdx);
    
    //Loop over the nodes and set the first nodal shapes equal to the basis functions
    for(unsigned i=0;i<this->nnode_1d();i++)
     {
      psi[i] = basis[i];
      dpsidx(i,0) = dbasisdx(i,0);
     }
    
    //Loop over the test functions and derivatives and set them equal to the
    //basis functions
    for(unsigned i=0;i<this->p_order();i++)
     {
      test[i] = basis[i]; 
      dtestdx(i,0) = dbasisdx(i,0);
     }
   
    //Return the jacobian
    return J;
   }

References i, J, and s.

◆ dshape_dbasis_and_dtest_eulerian_at_knot()

template<unsigned DIM>

virtual double ModalPRefineableQPoissonElement< DIM >::dshape_dbasis_and_dtest_eulerian_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	basis,
		DShape &	dbasisdx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

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

Implements ModalPoissonEquations< DIM >.

  {
   //Call the geometrical shape functions and derivatives  
   double J = dbasis_eulerian_at_knot(ipt,basis,dbasisdx);
   
   Vector<double> s(1);
   s[0] = this->integral_pt()->knot(ipt,0);
   
   //Loop over the nodes and set the first nodal shapes equal to the basis functions
   for(unsigned i=0;i<this->nnode_1d();i++)
    {
     psi[i] = basis[i];
     dpsidx(i,0) = dbasisdx(i,0);
    }
   
   //Loop over the test functions and derivatives and set them equal to the
   //basis functions
   for(unsigned i=0;i<this->p_order();i++)
    {
     test[i] = basis[i]; 
     dtestdx(i,0) = dbasisdx(i,0);
    }
   
   //Return the jacobian
   return J;
  }

References i, J, and s.

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::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 ModalPoissonEquations< DIM >.

1654 {RefineableModalPoissonEquations<DIM>::

1655 fill_in_contribution_to_jacobian(residuals, jacobian);}

ModalPoissonEquations::fill_in_contribution_to_jacobian

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

Definition: one_d_poisson_hp_adapt.cc:495

References ModalPoissonEquations< DIM >::fill_in_contribution_to_jacobian().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from ModalPoissonEquations< DIM >.

1649 {RefineableModalPoissonEquations<DIM>::

1650 fill_in_contribution_to_residuals(residuals);}

ModalPoissonEquations::fill_in_contribution_to_residuals

void fill_in_contribution_to_residuals(Vector< double > &residuals)

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

Definition: one_d_poisson_hp_adapt.cc:483

References ModalPoissonEquations< DIM >::fill_in_contribution_to_residuals().

◆ fill_in_generic_residual_contribution()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::fill_in_generic_residual_contribution	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

inline

1660 {RefineableModalPoissonEquations<DIM>::

1661 fill_in_generic_residual_contribution(residuals, jacobian, flag);}

RefineableModalPoissonEquations::fill_in_generic_residual_contribution

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

References RefineableModalPoissonEquations< DIM >::fill_in_generic_residual_contribution().

◆ further_build()

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::further_build

virtual

Further build: Copy source function pointer from father element.

Reimplemented from RefineableModalPoissonEquations< DIM >.

 {
  // Do the ModalPRefineableQElement further build
  ModalPRefineableQElement<DIM>::further_build();
  // Needed to set the source function pointer
  RefineableModalPoissonEquations<DIM>::further_build();
 }

References RefineableModalPoissonEquations< DIM >::further_build(), and ModalPRefineableQElement< DIM >::further_build().

◆ get_dresidual_dnodal_coordinates()

template<unsigned DIM>

virtual void ModalPRefineableQPoissonElement< DIM >::get_dresidual_dnodal_coordinates ( RankThreeTensor< double > & dresidual_dnodal_coordinates )

inlinevirtual

Compute derivatives of elemental residual vector with respect to nodal coordinates. Overwrites default implementation in FiniteElement base class. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij}

Compute derivatives of elemental residual vector with respect to nodal coordinates. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij} Overloads the FD-based version in the FE base class.

Reimplemented from RefineableModalPoissonEquations< DIM >.

1665 {ModalPoissonEquations<DIM>::

1666 get_dresidual_dnodal_coordinates(dresidual_dnodal_coordinates);}

oomph::FiniteElement::get_dresidual_dnodal_coordinates

virtual void get_dresidual_dnodal_coordinates(RankThreeTensor< double > &dresidual_dnodal_coordinates)

Definition: elements.cc:3744

References oomph::FiniteElement::get_dresidual_dnodal_coordinates().

◆ nbasis()

template<unsigned DIM>

virtual unsigned ModalPRefineableQPoissonElement< DIM >::nbasis ( ) const

inlinevirtual

Number of basis functions.

Implements ModalPoissonEquations< DIM >.

1429 {return this->p_order();}

◆ ncont_interpolated_values()

template<unsigned DIM>

unsigned ModalPRefineableQPoissonElement< DIM >::ncont_interpolated_values ( ) const

inlinevirtual

Number of continuously interpolated values: 1.

Implements oomph::RefineableElement.

1379 {return 1;}

◆ nnode_1d()

template<unsigned DIM>

unsigned ModalPRefineableQPoissonElement< DIM >::nnode_1d ( ) const

inlinevirtual

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

Reimplemented from oomph::FiniteElement.

1374 {return 2;}

◆ nrecovery_order()

template<unsigned DIM>

unsigned ModalPRefineableQPoissonElement< DIM >::nrecovery_order ( )

inlinevirtual

Order of recovery shape functions for Z2 error estimation:

Same order as shape functions.
Constant recovery order, since recovery order of the first element is used for the whole mesh.

Implements oomph::ElementWithZ2ErrorEstimator.

1398 {return 3;}

◆ nvertex_node()

template<unsigned DIM>

unsigned ModalPRefineableQPoissonElement< DIM >::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element.

Implements oomph::ElementWithZ2ErrorEstimator.

1383 {return QPoissonElement<DIM,2>::nvertex_node();}

◆ output() [1/2]

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::output ( ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from ModalPoissonEquations< DIM >.

1432 {RefineableModalPoissonEquations<DIM>::output(outfile);}

ModalPoissonEquations::output

void output(ostream &outfile)

Output with default number of plot points.

Definition: one_d_poisson_hp_adapt.cc:114

References ModalPoissonEquations< DIM >::output().

◆ output() [2/2]

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::output	(	ostream &	outfile,
		const unsigned &	nplot
	)

inlinevirtual

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

Reimplemented from ModalPoissonEquations< DIM >.

1435 {RefineableModalPoissonEquations<DIM>::output(outfile, nplot);}

References ModalPoissonEquations< DIM >::output().

◆ output_fct() [1/2]

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::output_fct	(	ostream &	outfile,
		const unsigned &	nplot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

Output exact soln: x,y,u_exact or x,y,z,u_exact at nplot^DIM plot points (dummy time-dependent version to keep intel compiler happy)

Reimplemented from ModalPoissonEquations< DIM >.

1446 {RefineableModalPoissonEquations<DIM>::output_fct(outfile, nplot, time,

1447 exact_soln_pt);}

ModalPoissonEquations::output_fct

void output_fct(ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)

Output exact soln: x,y,u_exact or x,y,z,u_exact at nplot^DIM plot points.

Definition: one_d_poisson_hp_adapt.cc:162

References ModalPoissonEquations< DIM >::output_fct().

◆ output_fct() [2/2]

template<unsigned DIM>

void ModalPRefineableQPoissonElement< DIM >::output_fct	(	ostream &	outfile,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

inline

1439 {RefineableModalPoissonEquations<DIM>::output_fct(outfile, nplot,

1440 exact_soln_pt);}

References ModalPoissonEquations< DIM >::output_fct().

◆ self_test()

template<unsigned DIM>

unsigned ModalPRefineableQPoissonElement< DIM >::self_test ( )

inlinevirtual

Self-test: Return 0 for OK.

Reimplemented from ModalPoissonEquations< DIM >.

1547 {return RefineableModalPoissonEquations<DIM>::self_test();}

ModalPoissonEquations::self_test

unsigned self_test()

Self-test: Return 0 for OK.

Definition: one_d_poisson_hp_adapt.cc:529

References ModalPoissonEquations< DIM >::self_test().

◆ source_fct_pt() [1/2]

template<unsigned DIM>

PoissonSourceFctPt& ModalPRefineableQPoissonElement< DIM >::source_fct_pt ( )

inline

1541 {return RefineableModalPoissonEquations<DIM>::source_fct_pt();}

ModalPoissonEquations::source_fct_pt

PoissonSourceFctPt & source_fct_pt()

Access function: Pointer to source function.

Definition: one_d_poisson_hp_adapt.cc:388

References ModalPoissonEquations< DIM >::source_fct_pt().

◆ source_fct_pt() [2/2]

template<unsigned DIM>

PoissonSourceFctPt ModalPRefineableQPoissonElement< DIM >::source_fct_pt ( ) const

inline

1544 {return RefineableModalPoissonEquations<DIM>::source_fct_pt();}

References ModalPoissonEquations< DIM >::source_fct_pt().

◆ u()

template<unsigned DIM>

double ModalPRefineableQPoissonElement< DIM >::u ( const unsigned & n ) const

inlinevirtual

Access function: Nodal function value at local node n Uses suitably interpolated value for hanging nodes.

Implements ModalPoissonEquations< DIM >.

   {
    if(n < this->nnode())
     {
      return this->nodal_value(n,0);
     }
    else
     {
      return this->internal_data_pt(0)->value(n-this->nnode());
     }
   }

References n.

◆ vertex_node_pt()

template<unsigned DIM>

Node* ModalPRefineableQPoissonElement< DIM >::vertex_node_pt ( const unsigned & j ) const

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

1387 {return QPoissonElement<DIM,2>::vertex_node_pt(j);}

j

std::ptrdiff_t j

Definition: tut_arithmetic_redux_minmax.cpp:2

References j.

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

one_d_poisson_hp_adapt.cc

Public Types

Public Member Functions

Additional Inherited Members

Member Typedef Documentation

◆ PoissonSourceFctPt

Constructor & Destructor Documentation

◆ ModalPRefineableQPoissonElement() [1/2]

◆ ModalPRefineableQPoissonElement() [2/2]

Member Function Documentation

◆ assign_additional_local_eqn_numbers()

◆ basis()

◆ compute_energy_error()

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ d2basis_local()

◆ dbasis_eulerian()

◆ dbasis_eulerian_at_knot()

◆ dbasis_local()

◆ dbasis_local_at_knot()

◆ dshape_dbasis_and_dtest_eulerian()

◆ dshape_dbasis_and_dtest_eulerian_at_knot()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution()

◆ further_build()

◆ get_dresidual_dnodal_coordinates()

◆ nbasis()

◆ ncont_interpolated_values()

◆ nnode_1d()

◆ nrecovery_order()

◆ nvertex_node()

◆ output() [1/2]

◆ output() [2/2]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ self_test()

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ u()

◆ vertex_node_pt()