Refineable version of Poisson equations. More...

Inheritance diagram for RefineableModalPoissonEquations< DIM >:

Public Member Functions
	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)

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

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

virtual double	u (const unsigned &n) const =0

virtual unsigned	nbasis () const =0
	Number of basis functions. More...

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

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

virtual 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)
	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...

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

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...

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	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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 (FILE *file_pt)

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	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

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 unsigned	ncont_interpolated_values () const =0

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 unsigned	nvertex_node () const =0
	Number of vertex nodes in the element. More...

virtual Node *	vertex_node_pt (const unsigned &j) const =0

virtual unsigned	nrecovery_order ()=0
	Order of recovery shape functions. More...

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

Private Member Functions
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	get_source_gradient (unsigned int &, oomph::Vector< double > &, oomph::Vector< double > &)

Additional Inherited Members
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 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 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 ModalPoissonEquations< DIM >
virtual double	dshape_dbasis_and_dtest_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &basis, DShape &dbasisdx, Shape &test, DShape &dtestdx) const =0

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 =0

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

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 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 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::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 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...

Detailed Description

template<unsigned DIM>
class RefineableModalPoissonEquations< DIM >

Refineable version of Poisson equations.

Constructor & Destructor Documentation

◆ RefineableModalPoissonEquations() [1/2]

template<unsigned DIM>

RefineableModalPoissonEquations< DIM >::RefineableModalPoissonEquations ( )

inline

Constructor, simply call other constructors.

                                    : ModalPoissonEquations<DIM>(),
   RefineableElement(), ElementWithZ2ErrorEstimator() 
   { } 

◆ RefineableModalPoissonEquations() [2/2]

template<unsigned DIM>

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

inline

Broken copy constructor.

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

References oomph::BrokenCopy::broken_copy().

Member Function Documentation

◆ fill_in_generic_residual_contribution()

template<unsigned DIM>

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

private

Add element's contribution to elemental residual vector and/or Jacobian matrix flag=1: compute both flag=0: compute only residual vector

Referenced by ModalPRefineableQPoissonElement< DIM >::fill_in_generic_residual_contribution().

◆ further_build()

template<unsigned DIM>

void RefineableModalPoissonEquations< DIM >::further_build ( )

inlinevirtual

Further build: Copy source function pointer from father element.

Reimplemented from oomph::RefineableElement.

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

   {
    this->Source_fct_pt=dynamic_cast<RefineableModalPoissonEquations<DIM>*>
                                 (this->father_element_pt())->source_fct_pt();
   }

References oomph::source_fct_pt(), and oomph::Source_fct_pt.

Referenced by ModalPRefineableQPoissonElement< DIM >::further_build().

◆ get_dresidual_dnodal_coordinates()

template<unsigned DIM>

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

privatevirtual

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 oomph::FiniteElement.

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

 {
  
  //Find out how many nodes there are
  unsigned n_node = nnode();
  //Find out the total number of basis and test functions there are
  unsigned n_basis = this->nbasis();
  
  //Set up memory for the shape and test functions
  Shape psi(n_node), basis(n_basis), test(n_basis);
  DShape dpsidx(n_node,DIM), dbasisdx(n_basis,DIM), dtestdx(n_basis,DIM);
  DShape dpsidx_pls(n_node,DIM), dbasisdx_pls(n_basis,DIM), dtestdx_pls(n_basis,DIM);
  
  // Get number of shape controlling nodes 
  unsigned n_shape_controlling_node=nshape_controlling_nodes();
  
  // Deriatives of shape fct derivatives w.r.t. nodal coords
  RankFourTensor<double> d_dpsidx_dX(DIM,n_shape_controlling_node,n_node,DIM);
  RankFourTensor<double> d_dtestdx_dX(DIM,n_shape_controlling_node,n_node,DIM);
  
  // Derivative of Jacobian of mapping w.r.t. to nodal coords
  DenseMatrix<double> dJ_dX(DIM,n_shape_controlling_node);
  
  // Derivatives of derivative of u w.r.t. nodal coords
  RankThreeTensor<double> d_dudx_dX(DIM,n_shape_controlling_node,DIM);
  
  // Gradient of source fct
  Vector<double> d_source_dx(DIM);
  
  //Index at which the poisson unknown is stored
  const unsigned u_nodal_index = this->u_index_poisson();
  
  //Set the value of n_intpt
  const unsigned n_intpt = integral_pt()->nweight();
  
  //Integers to store the local equation number
  int local_eqn=0;
  
  // Local storage for pointers to hang_info object
  HangInfo *hang_info_pt=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 = this->dshape_dbasis_and_dtest_eulerian_at_knot(ipt, 
                                                              psi, 
                                                              dpsidx,
                                                              basis,
                                                              dbasisdx,
                                                              test, 
                                                              dtestdx);
        
    //Calculate local values 
    //Allocate and initialise to zero
    Vector<double> interpolated_x(DIM,0.0);
    Vector<double> interpolated_dudx(DIM,0.0);
    
    //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 u_value = nodal_value(l,u_nodal_index);
      // Loop over directions
      for(unsigned j=0;j<DIM;j++)
       {
        interpolated_x[j] += nodal_position(l,j)*psi(l);
        interpolated_dudx[j] += u_value*dpsidx(l,j);
       }
     }
  
    //Get source function
    //-------------------
    double source;
    //this->get_source(ipt,interpolated_x,source);
    this->get_source_poisson(interpolated_x,source);
  
    // FD step 
    double eps_fd=GeneralisedElement::Default_fd_jacobian_step;
    
    std::map<Node*,unsigned> local_shape_controlling_node_lookup= 
     shape_controlling_node_lookup();
  
    // FD loop over shape-controlling nodes
    for (std::map<Node*,unsigned>::iterator it=
         local_shape_controlling_node_lookup.begin();
         it!=local_shape_controlling_node_lookup.end();
         it++)
     {  
      // Get node
      Node* nod_pt=it->first;
      
      // Get its number
      unsigned jj=it->second;
           
      // Loop over coordinate directions
      for (unsigned ii=0;ii<DIM;ii++)
       {
        // Make backup
        double backup=nod_pt->x(ii);
        
        // Do FD step. No node update required as we're
        // attacking the coordinate directly...
        nod_pt->x(ii)+=eps_fd;
        
        //Call the derivatives of the shape and test functions
        //at advanced level
        double J_pls =
         this->dshape_dbasis_and_dtest_eulerian_at_knot(ipt, 
                                                        psi, 
                                                        dpsidx_pls,
                                                        basis,
                                                        dbasisdx_pls,
                                                        test, 
                                                        dtestdx_pls);
        
        // Assign
        dJ_dX(ii,jj)=(J_pls-J)/eps_fd;
        for (unsigned i=0;i<DIM;i++)
         {
          for (unsigned j=0;j<n_node;j++)
           {
            d_dpsidx_dX(ii,jj,j,i)=(dpsidx_pls(j,i)-dpsidx(j,i))/eps_fd;
            d_dtestdx_dX(ii,jj,j,i)=(dtestdx_pls(j,i)-dtestdx(j,i))/eps_fd;
           }
         }
  
        // Shape deriv of du/dx_i
        for (unsigned i=0;i<DIM;i++)
         {
          double aux=0.0;
          for (unsigned j_nod=0;j_nod<n_node;j_nod++)
           {
            aux+=nodal_value(j_nod,u_nodal_index)*
             d_dpsidx_dX(ii,jj,j_nod,i);
           }
          d_dudx_dX(ii,jj,i)=aux;
         }
   
        // Reset coordinate. No node update required as we're
        // attacking the coordinate directly...
        nod_pt->x(ii)=backup;
       }
     }
    
    // Get gradient of source function
    this->get_source_gradient(ipt, interpolated_x, d_source_dx);
  
    
    // Assemble shape derivatives
    //---------------------------
        
    // Loop over the nodes for the test functions 
    for(unsigned l=0;l<n_node;l++)
     {
      //Local variables used to store the number of master nodes and the
      //weight associated with the shape function if the node is hanging
      unsigned n_master=1; 
      double hang_weight=1.0;
      
      //Local bool (is the node hanging)
      bool is_node_hanging = this->node_pt(l)->is_hanging();
      
      //If the node is hanging, get the number of master nodes
      if(is_node_hanging)
       {
        hang_info_pt = this->node_pt(l)->hanging_pt();
        n_master = hang_info_pt->nmaster();
       }
      //Otherwise there is just one master node, the node itself
      else
       {
        n_master = 1;
       }
      
      //Loop over the master nodes
      for(unsigned m=0;m<n_master;m++)
       {
        //Get the local equation number and hang_weight
        //If the node is hanging
        if(is_node_hanging)
         {
          //Read out the local equation number from the m-th master node
          local_eqn =  this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                            u_nodal_index);
          
          //Read out the weight from the master node
          hang_weight = hang_info_pt->master_weight(m);
         }
        //If the node is not hanging
        else
         {
          //The local equation number comes from the node itself
          local_eqn = this->nodal_local_eqn(l,u_nodal_index);
          //The hang weight is one
          hang_weight = 1.0;
         }
        
        //If the nodal equation is not a boundary condition
        if(local_eqn >= 0)
         {
          // Loop over coordinate directions
          for (unsigned ii=0;ii<DIM;ii++)
           {              
            // Loop over shape controlling nodes
            for (unsigned jj=0;jj<n_shape_controlling_node;jj++)
             {       
              double sum=source*psi(l)*dJ_dX(ii,jj)+
               d_source_dx[ii]*psi(l)*psi(jj)*J;
              
              for (unsigned k=0;k<DIM;k++)
               {
                sum+=interpolated_dudx[k]*(dtestdx(l,k)*dJ_dX(ii,jj)+
                                           d_dtestdx_dX(ii,jj,l,k)*J)
                 + d_dudx_dX(ii,jj,k)*dtestdx(l,k)*J;
               }
              
              // Multiply through by integration weight
              dresidual_dnodal_coordinates(local_eqn,ii,jj)+=sum*w*hang_weight;
             }
           }
         }
       }
     }
    
   } // End of loop over integration points
  
 }

References DIM, i, J, j, k, m, oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), TestProblem::source(), Eigen::test, w, and oomph::Node::x().

◆ get_interpolated_values() [1/2]

template<unsigned DIM>

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

inlinevirtual

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Implements oomph::RefineableElement.

   {
    if (t!=0)
     {
      std::string error_message =
       "Time-dependent version of get_interpolated_values() ";
      error_message += "not implemented for this element \n";
      throw 
       OomphLibError(error_message,
                     "RefineablePoissonEquations::get_interpolated_values()",
                     OOMPH_EXCEPTION_LOCATION);
     }
    else
     {
      //Make sure that we call this particular object's steady 
      //get_interpolated_values (it could get overloaded lower down)
      this->get_interpolated_values(s,values);
     }
   }

References OOMPH_EXCEPTION_LOCATION, s, oomph::Global_string_for_annotation::string(), and plotPSD::t.

◆ get_interpolated_values() [2/2]

template<unsigned DIM>

void RefineableModalPoissonEquations< DIM >::get_interpolated_values	(	const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get error against and norm of exact flux.

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Reimplemented from oomph::RefineableElement.

  {
   // Set size of Vector: u
   values.resize(1);
   
   //Find number of nodes
   unsigned n_node = nnode();
   
   //Local shape function
   Shape psi(n_node);
   
   //Find values of shape function
   shape(s,psi);
   
   //Initialise value of u
   values[0] = 0.0;
  
   //Find the index at which the poisson unknown is stored
   unsigned u_nodal_index = this->u_index_poisson();
   
   //Loop over the local nodes and sum up the values
   for(unsigned l=0;l<n_node;l++)
    {
     values[0] += this->nodal_value(l,u_nodal_index)*psi[l];
    }
  }

References s, and oomph::OneDimLagrange::shape().

◆ get_source_gradient()

template<unsigned DIM>

void RefineableModalPoissonEquations< DIM >::get_source_gradient	(	unsigned int &	,
		oomph::Vector< double > &	,
		oomph::Vector< double > &
	)

inlineprivate

   {
    std::string error_message = "get_source_gradient() is ";
    error_message += "not implemented for this element \n";
    throw 
     OomphLibError(error_message,
                   "RefineablePoissonEquations::get_source_gradient()",
                   OOMPH_EXCEPTION_LOCATION);
   }

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

◆ get_Z2_flux()

template<unsigned DIM>

void RefineableModalPoissonEquations< DIM >::get_Z2_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)

inlinevirtual

Get 'flux' for Z2 error recovery: Standard flux.from Poisson equations.

Implements oomph::ElementWithZ2ErrorEstimator.

724 {this->get_flux(s,flux,2);}

ModalPoissonEquations::get_flux

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

Get flux: flux[i] = du/dx_i.

Definition: one_d_poisson_hp_adapt.cc:448

ProblemParameters::flux

void flux(const double &time, const Vector< double > &x, double &flux)

Get flux applied along boundary x=0.

Definition: pretend_melt.cc:59

References ProblemParameters::flux(), and oomph::get_flux().

◆ num_Z2_flux_terms()

template<unsigned DIM>

unsigned RefineableModalPoissonEquations< DIM >::num_Z2_flux_terms ( )

inlinevirtual

Number of 'flux' terms for Z2 error estimation.

Implements oomph::ElementWithZ2ErrorEstimator.

720 {return DIM;}

References DIM.

◆ u_index_poisson()

template<unsigned DIM>

virtual unsigned RefineableModalPoissonEquations< DIM >::u_index_poisson ( ) const

inlinevirtual

717 {return 0;}

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

one_d_poisson_hp_adapt.cc

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

template<unsigned DIM> class RefineableModalPoissonEquations< DIM >

Constructor & Destructor Documentation

◆ RefineableModalPoissonEquations() [1/2]

◆ RefineableModalPoissonEquations() [2/2]

Member Function Documentation

◆ fill_in_generic_residual_contribution()

◆ further_build()

◆ get_dresidual_dnodal_coordinates()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ get_source_gradient()

◆ get_Z2_flux()

◆ num_Z2_flux_terms()

◆ u_index_poisson()

template<unsigned DIM>
class RefineableModalPoissonEquations< DIM >