Inheritance diagram for HarmonicEquations:

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

virtual double	u (const unsigned &n) const

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

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

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

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

	HarmonicEquations ()
	Empty Constructor. More...

virtual double	u (const unsigned &n) const

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

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

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

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::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 &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const

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

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

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

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

unsigned	dim () const

virtual ElementGeometry::ElementGeometry	element_geometry () const
	Return the geometry type of the element (either Q or T usually). More...

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const

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

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

virtual void	output (FILE *file_pt)

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	self_test ()

virtual unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const

virtual int	face_outer_unit_normal_sign (const int &face_index) const
	Get the sign of the outer unit normal on the face given by face_index. More...

virtual unsigned	nnode_on_face () const

void	face_node_number_error_check (const unsigned &i) const
	Range check for face node numbers. More...

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

Public Member Functions inherited from oomph::GeneralisedElement
	GeneralisedElement ()
	Constructor: Initialise all pointers and all values to zero. More...

virtual	~GeneralisedElement ()
	Virtual destructor to clean up any memory allocated by the object. More...

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

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

Data *&	internal_data_pt (const unsigned &i)
	Return a pointer to i-th internal data object. More...

Data *const &	internal_data_pt (const unsigned &i) const
	Return a pointer to i-th internal data object (const version) More...

Data *&	external_data_pt (const unsigned &i)
	Return a pointer to i-th external data object. More...

Data *const &	external_data_pt (const unsigned &i) const
	Return a pointer to i-th external data object (const version) More...

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

void	flush_external_data ()
	Flush all external data. More...

void	flush_external_data (Data *const &data_pt)
	Flush the object addressed by data_pt from the external data array. More...

unsigned	ninternal_data () const
	Return the number of internal data objects. More...

unsigned	nexternal_data () const
	Return the number of external data objects. More...

unsigned	ndof () const
	Return the number of equations/dofs in the element. More...

void	dof_vector (const unsigned &t, Vector< double > &dof)
	Return the vector of dof values at time level t. More...

void	dof_pt_vector (Vector< double * > &dof_pt)
	Return the vector of pointers to dof values. More...

void	set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)

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

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

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

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const

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

	GeomObject (const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)

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

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

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

unsigned	nlagrangian () const
	Access function to # of Lagrangian coordinates. More...

unsigned	ndim () const
	Access function to # of Eulerian coordinates. More...

void	set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
	Set # of Lagrangian and Eulerian coordinates. More...

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const

Protected Member Functions
virtual double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const =0

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const =0

virtual int	u_local_eqn (const unsigned &n)

virtual double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const =0

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const =0

virtual int	u_local_eqn (const unsigned &n)

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

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

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

template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

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

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

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

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<unsigned DIM>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

virtual void	d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<unsigned DIM>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

virtual void	transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<unsigned DIM>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<unsigned DIM>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Zero-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	One-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Two-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

int	internal_local_eqn (const unsigned &i, const unsigned &j) const

int	external_local_eqn (const unsigned &i, const unsigned &j)

virtual void	fill_in_contribution_to_residuals (Vector< double > &residuals)

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_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)

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

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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default value for the number of values at a node. More...

static const double	Node_location_tolerance = 1.0e-14

static const unsigned	N2deriv [] = {0, 1, 3, 6}

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix

static std::deque< double * >	Dof_pt_deque

Detailed Description

A class for all elements that solve the simple one-dimensional eigenvalue problem

\[ \frac{\partial^2 u}{\partial x_i^2} + \lambda u = 0 \]

These elements are very closely related to the Poisson elements and could inherit from them. They are here developed from scratch for pedagogical purposes. This class contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class.

Constructor & Destructor Documentation

◆ HarmonicEquations() [1/2]

HarmonicEquations::HarmonicEquations ( )

inline

Empty Constructor.

75 {}

◆ HarmonicEquations() [2/2]

HarmonicEquations::HarmonicEquations ( )

inline

Empty Constructor.

74 {}

Member Function Documentation

◆ dshape_eulerian() [1/2]

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

protectedpure virtual

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

Implemented in QHarmonicElement< NNODE_1D >, and QHarmonicElement< NNODE_1D >.

◆ dshape_eulerian() [2/2]

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

protectedpure virtual

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

Implemented in QHarmonicElement< NNODE_1D >, and QHarmonicElement< NNODE_1D >.

◆ dshape_eulerian_at_knot() [1/2]

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

protectedpure virtual

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

Reimplemented from oomph::FiniteElement.

Implemented in QHarmonicElement< NNODE_1D >, and QHarmonicElement< NNODE_1D >.

◆ dshape_eulerian_at_knot() [2/2]

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

protectedpure virtual

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

Reimplemented from oomph::FiniteElement.

Implemented in QHarmonicElement< NNODE_1D >, and QHarmonicElement< NNODE_1D >.

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [1/2]

void HarmonicEquations::fill_in_contribution_to_jacobian_and_mass_matrix	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	mass_matrix
	)

inlinevirtual

Assemble the contributions to the jacobian and mass matrices

Reimplemented from oomph::GeneralisedElement.

   {
    //Find out how many nodes there are
    unsigned n_node = nnode();
    
    //Set up memory for the shape functions and their derivatives
    Shape psi(n_node);
    DShape dpsidx(n_node,1);
  
    //Set the number of integration points
    unsigned n_intpt = integral_pt()->nweight();
    
    //Integers to store the local equation and unknown numbers
    int local_eqn=0, local_unknown=0;
    
    //Loop over the integration points
    for(unsigned ipt=0;ipt<n_intpt;ipt++)
     {
      //Get the integral weight
      double w = integral_pt()->weight(ipt);
      
      //Call the derivatives of the shape and test functions
      double J = dshape_eulerian_at_knot(ipt,psi,dpsidx);
      
      //Premultiply the weights and the Jacobian
      double W = w*J;
  
      //Assemble the contributions to the mass matrix
      //Loop over the test functions
      for(unsigned l=0;l<n_node;l++)
       {
        //Get the local equation number
        local_eqn = u_local_eqn(l);
        /*IF it's not a boundary condition*/
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           { 
            local_unknown = u_local_eqn(l2);
            //If at a non-zero degree of freedom add in the entry
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += dpsidx(l,0)*dpsidx(l2,0)*W;
              mass_matrix(local_eqn, local_unknown) += psi(l)*psi(l2)*W;
             }
           }
         }
       }
     }
   } //end_of_fill_in_contribution_to_jacobian_and_mass_matrix

References J, w, and oomph::QuadTreeNames::W.

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [2/2]

void HarmonicEquations::fill_in_contribution_to_jacobian_and_mass_matrix	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	mass_matrix
	)

inlinevirtual

Assemble the contributions to the jacobian and mass matrices

Reimplemented from oomph::GeneralisedElement.

   {
    //Find out how many nodes there are
    unsigned n_node = nnode();
    
    //Set up memory for the shape functions and their derivatives
    Shape psi(n_node);
    DShape dpsidx(n_node,1);
  
    //Set the number of integration points
    unsigned n_intpt = integral_pt()->nweight();
    
    //Integers to store the local equation and unknown numbers
    int local_eqn=0, local_unknown=0;
    
    //Loop over the integration points
    for(unsigned ipt=0;ipt<n_intpt;ipt++)
     {
      //Get the integral weight
      double w = integral_pt()->weight(ipt);
      
      //Call the derivatives of the shape and test functions
      double J = dshape_eulerian_at_knot(ipt,psi,dpsidx);
      
      //Premultiply the weights and the Jacobian
      double W = w*J;
  
      //Assemble the contributions to the mass matrix
      //Loop over the test functions
      for(unsigned l=0;l<n_node;l++)
       {
        //Get the local equation number
        local_eqn = u_local_eqn(l);
        /*IF it's not a boundary condition*/
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           { 
            local_unknown = u_local_eqn(l2);
            //If at a non-zero degree of freedom add in the entry
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += dpsidx(l,0)*dpsidx(l2,0)*W;
              mass_matrix(local_eqn, local_unknown) += psi(l)*psi(l2)*W;
             }
           }
         }
       }
     }
   }

References J, w, and oomph::QuadTreeNames::W.

◆ interpolated_u() [1/2]

double HarmonicEquations::interpolated_u ( const Vector< double > & s ) const

inline

Return FE representation of function value u(s) at local coordinate s.

   {
    unsigned n_node = nnode();
  
    //Local shape functions
    Shape psi(n_node);
  
    //Find values of basis function
    this->shape(s,psi);
  
    //Initialise value of u
    double interpolated_u = 0.0;
  
    //Loop over the local nodes and sum
    for(unsigned l=0;l<n_node;l++)  {interpolated_u+=u(l)*psi[l];}
  
    //Return the interpolated value of the eigenfunction
    return(interpolated_u);
   }

References oomph::OneDimLagrange::shape().

◆ interpolated_u() [2/2]

double HarmonicEquations::interpolated_u ( const Vector< double > & s ) const

inline

Return FE representation of function value u(s) at local coordinate s.

   {
    unsigned n_node = nnode();
  
    //Local shape functions
    Shape psi(n_node);
  
    //Find values of basis function
    this->shape(s,psi);
  
    //Initialise value of u
    double interpolated_u = 0.0;
  
    //Loop over the local nodes and sum
    for(unsigned l=0;l<n_node;l++)  {interpolated_u+=u(l)*psi[l];}
  
    //Return the interpolated value of the eigenfunction
    return(interpolated_u);
   }

References oomph::OneDimLagrange::shape().

◆ output() [1/4]

void HarmonicEquations::output ( ostream & outfile )

inlinevirtual

Output the eigenfunction with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in QHarmonicElement< NNODE_1D >, and QHarmonicElement< NNODE_1D >.

   {
    unsigned nplot=5;
    output(outfile,nplot);
   }

References output().

Referenced by QHarmonicElement< NNODE_1D >::output().

◆ output() [2/4]

void HarmonicEquations::output ( ostream & outfile )

inlinevirtual

Output the eigenfunction with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in QHarmonicElement< NNODE_1D >.

   {
    unsigned nplot=5;
    output(outfile,nplot);
   }

References output().

◆ output() [3/4]

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

inlinevirtual

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

Reimplemented from oomph::FiniteElement.

Reimplemented in QHarmonicElement< NNODE_1D >, and QHarmonicElement< NNODE_1D >.

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

References s.

◆ output() [4/4]

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

inlinevirtual

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

Reimplemented from oomph::FiniteElement.

Reimplemented in QHarmonicElement< NNODE_1D >.

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

References s.

◆ u() [1/2]

virtual double HarmonicEquations::u ( const unsigned & n ) const

inlinevirtual

Access function: Eigenfunction value at local node n Note that solving the eigenproblem does not assign values to this storage space. It is used for output purposes only.

81 {return nodal_value(n,0);}

n

const unsigned n

Definition: CG3DPackingUnitTest.cpp:11

oomph::FiniteElement::nodal_value

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

Definition: elements.h:2593

References n.

◆ u() [2/2]

virtual double HarmonicEquations::u ( const unsigned & n ) const

inlinevirtual

Access function: Eigenfunction value at local node n Note that solving the eigenproblem does not assign values to this storage space. It is used for output purposes only.

80 {return nodal_value(n,0);}

References n.

◆ u_local_eqn() [1/2]

virtual int HarmonicEquations::u_local_eqn ( const unsigned & n )

inlineprotectedvirtual

Access function that returns the local equation number of the unknown in the problem. Default is to assume that it is the first (only) value stored at the node.

208 {return nodal_local_eqn(n,0);}

oomph::FiniteElement::nodal_local_eqn

int nodal_local_eqn(const unsigned &n, const unsigned &i) const

Definition: elements.h:1432

References n.

◆ u_local_eqn() [2/2]

virtual int HarmonicEquations::u_local_eqn ( const unsigned & n )

inlineprotectedvirtual

Access function that returns the local equation number of the unknown in the problem. Default is to assume that it is the first (only) value stored at the node.

207 {return nodal_local_eqn(n,0);}

References n.

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

eigenproblems/harmonic/harmonic.cc

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ HarmonicEquations() [1/2]

◆ HarmonicEquations() [2/2]

Member Function Documentation

◆ dshape_eulerian() [1/2]

◆ dshape_eulerian() [2/2]

◆ dshape_eulerian_at_knot() [1/2]

◆ dshape_eulerian_at_knot() [2/2]

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [1/2]

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [2/2]

◆ interpolated_u() [1/2]

◆ interpolated_u() [2/2]

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ u() [1/2]

◆ u() [2/2]

◆ u_local_eqn() [1/2]

◆ u_local_eqn() [2/2]