Biharmonic Equation Class - contains the equations. More...

#include <biharmonic_elements.h>

Inheritance diagram for oomph::BiharmonicEquations< DIM >:

Public Types
typedef void(*	SourceFctPt) (const Vector< double > &x, double &u)
	source function type definition 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 > &)

Public Member Functions
	BiharmonicEquations ()
	Constructor (must initialise the Source_fct_pt to null) More...

	~BiharmonicEquations ()

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

virtual void	get_source (const unsigned &ipt, const Vector< double > &x, double &source) const
	gets source strength More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	wrapper function, adds contribution to residual More...

void	fill_in_contribution_to_jacobian (Vector< double > &residual, DenseMatrix< double > &jacobian)
	wrapper function, adds contribution to residual and generic More...

void	output (std::ostream &outfile, const unsigned &nplot)
	output with nplot points More...

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

void	output (FILE *file_pt)
	C-style output. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	C_style output at n_plot points. More...

void	output_fluid_velocity (std::ostream &outfile, const unsigned &nplot)
	output fluid velocity field More...

void	interpolated_dudx (const Vector< double > &s, Vector< double > &dudx)
	output with nplot points More...

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	output analytic solution More...

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

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	computes the error More...

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

double	interpolated_u_biharmonic (const Vector< double > &s)
	calculates interpolated u at s More...

unsigned	self_test ()
	self test wrapper More...

unsigned	get_d2_dof ()
	return number of second derivate degrees of freedom More...

unsigned	ndof_types () const

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

SourceFctPt &	source_fct_pt ()
	Access functions for the source function pointer. More...

SourceFctPt	source_fct_pt () const
	Access functions for the source function pointers (const version) 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	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

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 void	fill_in_generic_residual_contribution_biharmonic (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned JFLAG)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

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

Protected Attributes
SourceFctPt	Source_fct_pt
	Pointer to source 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

Static Private Attributes
static const unsigned	d2_dof [] = {1, 3, 6}

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

Detailed Description

template<unsigned DIM>
class oomph::BiharmonicEquations< DIM >

Biharmonic Equation Class - contains the equations.

Member Typedef Documentation

◆ SourceFctPt

template<unsigned DIM>

typedef void(* oomph::BiharmonicEquations< DIM >::SourceFctPt) (const Vector< double > &x, double &u)

source function type definition

Constructor & Destructor Documentation

◆ BiharmonicEquations()

template<unsigned DIM>

oomph::BiharmonicEquations< DIM >::BiharmonicEquations ( )

inline

Constructor (must initialise the Source_fct_pt to null)

63 : Source_fct_pt(0) {}

oomph::BiharmonicEquations::Source_fct_pt

SourceFctPt Source_fct_pt

Pointer to source function:

Definition: biharmonic_elements.h:504

◆ ~BiharmonicEquations()

template<unsigned DIM>

oomph::BiharmonicEquations< DIM >::~BiharmonicEquations ( )

inline

66 {};

Member Function Documentation

◆ compute_error() [1/2]

template<unsigned DIM>

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

inlinevirtual

computes the error

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

     {
       // Initialise
       error = 0.0;
       norm = 0.0;
  
       // Vector of local coordinates
       Vector<double> s(DIM);
  
       // Vector for coordintes
       Vector<double> x(DIM);
  
       // Find out how many nodes there are in the element
       unsigned n_node = this->nnode();
  
       Shape psi(n_node);
  
       // Set the value of n_intpt
       unsigned n_intpt = this->integral_pt()->nweight();
  
       // Tecplot header info
       outfile << this->tecplot_zone_string(3);
  
       // Tecplot
       // outfile << "ZONE" << std::endl;
  
       // Exact solution Vector (here a scalar)
       Vector<double> exact_soln(1);
  
       // Loop over the integration points
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Assign values of s
         for (unsigned i = 0; i < DIM; i++)
         {
           s[i] = this->integral_pt()->knot(ipt, i);
         }
  
         // Get the integral weight
         double w = this->integral_pt()->weight(ipt);
  
         // Get jacobian of mapping
         double J = this->J_eulerian(s);
  
         // Premultiply the weights and the Jacobian
         double W = w * J;
  
         // Get x position as Vector
         this->interpolated_x(s, x);
  
         // Get FE function value
         double u_fe = interpolated_u_biharmonic(s);
  
         // Get exact solution at this point
         (*exact_soln_pt)(x, exact_soln);
  
         // Output x,y,...,error
         for (unsigned i = 0; i < DIM; i++)
         {
           outfile << x[i] << " ";
         }
         outfile << exact_soln[0] << " " << fabs(exact_soln[0] - u_fe)
                 << std::endl;
  
         // Add to error and norm
         norm += exact_soln[0] * exact_soln[0] * W;
         error += (exact_soln[0] - u_fe) * (exact_soln[0] - u_fe) * W;
       }
  
       this->write_tecplot_zone_footer(outfile, 3);
     }

References DIM, calibrate::error, ProblemParameters::exact_soln(), boost::multiprecision::fabs(), i, oomph::FiniteElement::integral_pt(), oomph::BiharmonicEquations< DIM >::interpolated_u_biharmonic(), oomph::FiniteElement::interpolated_x(), J, oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::FiniteElement::nnode(), oomph::Integral::nweight(), s, oomph::FiniteElement::tecplot_zone_string(), w, oomph::QuadTreeNames::W, oomph::Integral::weight(), oomph::FiniteElement::write_tecplot_zone_footer(), and plotDoE::x.

Referenced by oomph::BiharmonicElement< DIM >::compute_error().

◆ compute_error() [2/2]

template<unsigned DIM>

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

inlinevirtual

Plot the error when compared against a given time-dependent exact solution \( {\bf f}(t,{\bf x}) \). Also calculates the norm of the error and that of the exact solution. Call broken base-class version.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

     {
       FiniteElement::compute_error(outfile, exact_soln_pt, time, error, norm);
     }

References oomph::FiniteElement::compute_error(), and calibrate::error.

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::fill_in_contribution_to_jacobian	(	Vector< double > &	residual,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

wrapper function, adds contribution to residual and generic

Reimplemented from oomph::GeneralisedElement.

     {
       // call generic routine with flag set to 1
       fill_in_generic_residual_contribution_biharmonic(residual, jacobian, 1);
     }

References oomph::BiharmonicEquations< DIM >::fill_in_generic_residual_contribution_biharmonic().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

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

inlinevirtual

wrapper function, adds contribution to residual

Reimplemented from oomph::GeneralisedElement.

     {
       // create a dummy matrix
       DenseDoubleMatrix dummy(1);
  
       // call the generic residuals functions with flag set to zero
       fill_in_generic_residual_contribution_biharmonic(residuals, dummy, 0);
     }

References oomph::BiharmonicEquations< DIM >::fill_in_generic_residual_contribution_biharmonic().

◆ fill_in_generic_residual_contribution_biharmonic()

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::fill_in_generic_residual_contribution_biharmonic	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		unsigned	JFLAG
	)

protectedvirtual

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

   {
     // Find out how many nodes there are
     unsigned n_node = this->nnode();
  
     // Find out how many values there
     unsigned n_value = this->node_pt(0)->nvalue();
  
     // Find out how many degrees of freedom are associated with 2nd derivative
     unsigned d2_dof = this->get_d2_dof();
  
     // set up memory for shape and test functions
     Shape psi(n_node, n_value);
     DShape dpsidx(n_node, n_value, DIM);
     DShape d2psidx(n_node, n_value, d2_dof);
     // Shape psi(n_node,n_value);
     DShape dpsids(n_node, n_value, DIM);
     DShape d2psids(n_node, n_value, d2_dof);
  
     // storage of single local coordinate
     Vector<double> s(DIM);
  
     // number of integration points
     unsigned n_intpt = this->integral_pt()->nweight();
  
     // loop over integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // set local coordinates to be intergration scheme knot
       for (unsigned i = 0; i < DIM; i++)
         s[i] = this->integral_pt()->knot(ipt, i);
  
       // find weight at knot
       double w = this->integral_pt()->weight(ipt);
  
       // find shape fn and derivate fns at knot point,
       // and Jacobian of local to global mapping
       double J = this->d2shape_eulerian(s, psi, dpsidx, d2psidx);
       this->d2shape_local(s, psi, dpsids, d2psids);
  
       // premultiply weight by jacobian
       double W = w * J;
  
       // initialise storage for d2u_interpolated
       Vector<double> d2u_interpolated(DIM);
       for (unsigned i = 0; i < DIM; i++)
       {
         d2u_interpolated[i] = 0.0;
       }
  
       // loop over nodes, degrees of freedom, and dimension to calculate
       // interpolated_d2u
       for (unsigned n = 0; n < n_node; n++)
       {
         for (unsigned k = 0; k < n_value; k++)
         {
           for (unsigned d = 0; d < DIM; d++)
           {
             d2u_interpolated[d] +=
               this->node_pt(n)->value(k) * d2psidx(n, k, d);
           }
         }
       }
  
       // create vector for interpolated position and calculate
       Vector<double> interpolated_position(DIM);
       this->interpolated_x(s, interpolated_position);
  
       // evaluate source function at knot position
       double source = 0.0;
       get_source(ipt, interpolated_position, source);
  
       // loop over nodes
       for (unsigned n1 = 0; n1 < n_node; n1++)
       {
         // loop over types of degrees of freedom
         for (unsigned k1 = 0; k1 < n_value; k1++)
         {
           // determine the local equation number
           int local_eqn_number = this->nodal_local_eqn(n1, k1);
  
           // if local equation number equal to -1 then its a boundary
           // node(pinned)
           if (local_eqn_number >= 0)
           {
             // add source contribution to residual
             residuals[local_eqn_number] -= source * psi(n1, k1) * W;
  
             // loop over dimension of d2u interpolated
             for (unsigned d1 = 0; d1 < DIM; d1++)
             {
               // loop over derivatives of d2psidx
               for (unsigned d2 = 0; d2 < DIM; d2++)
               {
                 // add residual contribution
                 residuals[local_eqn_number] +=
                   d2u_interpolated[d1] * d2psidx(n1, k1, d2) * W;
               }
  
               // calculate the jacobian
               if (JFLAG)
               {
                 // loop over nodes
                 for (unsigned n2 = 0; n2 < n_node; n2++)
                 {
                   // loop over types of degrees of freedom
                   for (unsigned k2 = 0; k2 < n_value; k2++)
                   {
                     // get local dof, -if -1 then node pinned
                     int local_dof_number = this->nodal_local_eqn(n2, k2);
  
                     // if local dof # = -1, then its pinned
                     if (local_dof_number >= 0)
                     {
                       // loop over derivatives
                       for (unsigned d2 = 0; d2 < DIM; d2++)
                       {
                         // add contribution to jacobian
                         jacobian(local_eqn_number, local_dof_number) +=
                           d2psidx(n1, k1, d1) * d2psidx(n2, k2, d2) * W;
                       }
                     }
                   }
                 }
               }
             }
           }
         }
       }
     }
   }

References DIM, TanhSolnForPoisson::get_source(), i, J, k, n, s, TestProblem::source(), w, and oomph::QuadTreeNames::W.

Referenced by oomph::BiharmonicEquations< DIM >::fill_in_contribution_to_jacobian(), and oomph::BiharmonicEquations< DIM >::fill_in_contribution_to_residuals().

◆ get_d2_dof()

template<unsigned DIM>

unsigned oomph::BiharmonicEquations< DIM >::get_d2_dof ( )

inline

return number of second derivate degrees of freedom

     {
       return d2_dof[DIM - 1];
     }

References oomph::BiharmonicEquations< DIM >::d2_dof, and DIM.

◆ get_dof_numbers_for_unknowns()

template<unsigned DIM>

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

inlinevirtual

Create a list of pairs for all unknowns in this element, so that the first entry in each pair contains the global equation number of the unknown, while the second one contains the number of the "DOF types" that this unknown is associated with. (Function can obviously only be called if the equation numbering scheme has been set up.) (for block preconditioning)

Reimplemented from oomph::GeneralisedElement.

     {
       // number of nodes
       int n_node = this->nnode();
  
       // number of degrees of freedom at each node
       int n_value = this->node_pt(0)->nvalue();
  
       // temporary pair (used to store dof lookup prior to being added to list
       std::pair<unsigned long, unsigned> dof_lookup;
  
       // loop over the nodes
       for (int n = 0; n < n_node; n++)
       {
         // loop over the degree of freedom
         for (int k = 0; k < n_value; k++)
         {
           // determine local eqn number
           int local_eqn_number = this->nodal_local_eqn(n, k);
  
           // if local equation number is less than zero then nodal dof pinned
           // then ignore
           if (local_eqn_number >= 0)
           {
             // store dof lookup in temporary pair
             dof_lookup.first = this->eqn_number(local_eqn_number);
             dof_lookup.second = k;
             dof_lookup_list.push_front(dof_lookup);
             // add to list
           }
         }
       }
     }

References oomph::GeneralisedElement::eqn_number(), k, oomph::GeneralisedElement::local_eqn_number(), n, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::node_pt(), and oomph::Data::nvalue().

◆ get_source()

template<unsigned DIM>

virtual void oomph::BiharmonicEquations< DIM >::get_source	(	const unsigned &	ipt,
		const Vector< double > &	x,
		double &	source
	)		const

inlinevirtual

gets source strength

     {
       // if source function is not provided, i.e. zero, then return zero
       if (Source_fct_pt == 0)
       {
         source = 0.0;
       }
  
       // else get source strength
       else
       {
         (*Source_fct_pt)(x, source);
       }
     }

References TestProblem::source(), oomph::BiharmonicEquations< DIM >::Source_fct_pt, and plotDoE::x.

◆ interpolated_dudx()

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::interpolated_dudx	(	const Vector< double > &	s,
		Vector< double > &	dudx
	)

inline

output with nplot points

     {
       // Find out how many nodes there are
       unsigned n_node = this->nnode();
  
       // Find out how many values there
       unsigned n_value = this->node_pt(0)->nvalue();
  
       // set up memory for shape functions
       Shape psi(n_node, n_value);
       DShape dpsidx(n_node, n_value, DIM);
  
       // evaluate dpsidx at local coordinate s
       dshape_eulerian(s, psi, dpsidx);
  
       // initialise storage for d2u_interpolated
       dudx[0] = 0.0;
       dudx[1] = 0.0;
  
       // loop over nodes, degrees of freedom, and dimension to calculate
       // interpolated_d2u
       for (unsigned n = 0; n < n_node; n++)
       {
         for (unsigned k = 0; k < n_value; k++)
         {
           for (unsigned d = 0; d < DIM; d++)
           {
             dudx[d] += this->node_pt(n)->value(k) * dpsidx(n, k, d);
           }
         }
       }
     }

References DIM, oomph::FiniteElement::dshape_eulerian(), k, n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::Data::nvalue(), s, and oomph::Node::value().

Referenced by oomph::BiharmonicEquations< DIM >::output_fluid_velocity().

◆ interpolated_u_biharmonic()

template<unsigned DIM>

double oomph::BiharmonicEquations< DIM >::interpolated_u_biharmonic ( const Vector< double > & s )

inline

calculates interpolated u at s

     {
       // initialise storage for u_interpolated
       double uu = 0;
  
       // number of nodes
       unsigned n_node = this->nnode();
  
       // number of degrees of freedom per node
       unsigned n_value = this->node_pt(0)->nvalue();
  
       // set up memory for shape functions
       Shape psi(n_node, n_value);
  
       // find shape fn at position s
       this->shape(s, psi);
  
       // calculate interpolated u
       for (unsigned n = 0; n < n_node; n++)
       {
         for (unsigned k = 0; k < n_value; k++)
         {
           uu += u(n, k) * psi(n, k);
         }
       }
  
       // return interpolated_u
       return uu;
     }

References k, n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::Data::nvalue(), oomph::FiniteElement::shape(), and oomph::BiharmonicEquations< DIM >::u().

Referenced by oomph::BiharmonicEquations< DIM >::compute_error(), and oomph::BiharmonicEquations< DIM >::output().

◆ ndof_types()

template<unsigned DIM>

unsigned oomph::BiharmonicEquations< DIM >::ndof_types ( ) const

inlinevirtual

The number of "DOF types" that degrees of freedom in this element are sub-divided into (for block preconditioning)

Reimplemented from oomph::GeneralisedElement.

     {
       return this->required_nvalue(1);
     }

References oomph::FiniteElement::required_nvalue().

◆ output() [1/4]

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::output ( FILE * file_pt )

inlinevirtual

C-style output.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

     {
       FiniteElement::output(file_pt);
     }

References oomph::FiniteElement::output().

◆ output() [2/4]

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::output	(	FILE *	file_pt,
		const unsigned &	n_plot
	)

inlinevirtual

C_style output at n_plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

     {
       FiniteElement::output(file_pt, n_plot);
     }

References oomph::FiniteElement::output().

◆ output() [3/4]

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::output ( std::ostream & outfile )

inlinevirtual

Output at default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

     {
       FiniteElement::output(outfile);
     }

References oomph::FiniteElement::output().

◆ output() [4/4]

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

inlinevirtual

output with nplot points

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

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

References DIM, oomph::FiniteElement::get_s_plot(), i, oomph::BiharmonicEquations< DIM >::interpolated_u_biharmonic(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

Referenced by oomph::BiharmonicElement< DIM >::output().

◆ output_fct() [1/2]

template<unsigned DIM>

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

inlinevirtual

Output exact solution specified via function pointer at a given time and at a given number of plot points. Function prints as many components as are returned in solution Vector. Implement broken FiniteElement base class version

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

     {
       FiniteElement::output_fct(outfile, nplot, time, exact_soln_pt);
     }

References oomph::FiniteElement::output_fct().

◆ output_fct() [2/2]

template<unsigned DIM>

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

inlinevirtual

output analytic solution

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::BiharmonicElement< DIM >.

     {
       // Vector of local coordinates
       Vector<double> s(DIM);
  
       // Vector for coordintes
       Vector<double> x(DIM);
  
       // Tecplot header info
       outfile << this->tecplot_zone_string(nplot);
  
       // Exact solution Vector (here a scalar)
       Vector<double> exact_soln(1);
  
       // Loop over plot points
       unsigned num_plot_points = this->nplot_points(nplot);
       for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
       {
         // Get local coordinates of plot point
         this->get_s_plot(iplot, nplot, s);
  
         // Get x position as Vector
         this->interpolated_x(s, x);
  
         // Get exact solution at this point
         (*exact_soln_pt)(x, exact_soln);
  
         // Output x,y,...,u_exact
         for (unsigned i = 0; i < DIM; i++)
         {
           outfile << x[i] << " ";
         }
         outfile << exact_soln[0] << std::endl;
       }
  
       // Write tecplot footer (e.g. FE connectivity lists)
       this->write_tecplot_zone_footer(outfile, nplot);
     }

References DIM, ProblemParameters::exact_soln(), oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), oomph::FiniteElement::write_tecplot_zone_footer(), and plotDoE::x.

Referenced by oomph::BiharmonicElement< DIM >::output_fct().

◆ output_fluid_velocity()

template<unsigned DIM>

void oomph::BiharmonicEquations< DIM >::output_fluid_velocity	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

inline

output fluid velocity field

     {
       // Vector of local coordinates
       Vector<double> s(DIM);
  
       // Tecplot header info
       outfile << this->tecplot_zone_string(nplot);
  
       // Loop over plot points
       unsigned num_plot_points = this->nplot_points(nplot);
       for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
       {
         // Get local coordinates of plot point
         this->get_s_plot(iplot, nplot, s);
  
         for (unsigned i = 0; i < DIM; i++)
         {
           outfile << this->interpolated_x(s, i) << " ";
         }
  
         Vector<double> dudx(2, 0.0);
         interpolated_dudx(s, dudx);
  
         outfile << dudx[1] << "  " << -dudx[0] << std::endl;
       }
  
       // Write tecplot footer (e.g. FE connectivity lists)
       this->write_tecplot_zone_footer(outfile, nplot);
     }

References DIM, oomph::FiniteElement::get_s_plot(), i, oomph::BiharmonicEquations< DIM >::interpolated_dudx(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

Referenced by oomph::BiharmonicFluidProblem< DIM >::doc_solution().

◆ self_test()

template<unsigned DIM>

unsigned oomph::BiharmonicEquations< DIM >::self_test ( )

inlinevirtual

self test wrapper

Reimplemented from oomph::FiniteElement.

     {
       bool passed = true;
  
       // Check lower-level stuff
       if (FiniteElement::self_test() != 0)
       {
         passed = false;
       }
  
       // Return verdict
       if (passed)
       {
         return 0;
       }
       else
       {
         return 1;
       }
     }

References oomph::FiniteElement::self_test().

◆ source_fct_pt() [1/2]

template<unsigned DIM>

SourceFctPt& oomph::BiharmonicEquations< DIM >::source_fct_pt ( )

inline

Access functions for the source function pointer.

     {
       return Source_fct_pt;
     }

References oomph::BiharmonicEquations< DIM >::Source_fct_pt.

Referenced by oomph::BiharmonicProblem< DIM >::set_source_function().

◆ source_fct_pt() [2/2]

template<unsigned DIM>

SourceFctPt oomph::BiharmonicEquations< DIM >::source_fct_pt ( ) const

inline

Access functions for the source function pointers (const version)

     {
       return Source_fct_pt;
     }

References oomph::BiharmonicEquations< DIM >::Source_fct_pt.

◆ u()

template<unsigned DIM>

virtual double oomph::BiharmonicEquations< DIM >::u	(	const unsigned &	n,
		const unsigned &	k
	)		const

pure virtual

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

Implemented in oomph::BiharmonicElement< DIM >.

Referenced by oomph::BiharmonicEquations< DIM >::interpolated_u_biharmonic().

Member Data Documentation

◆ d2_dof

template<unsigned DIM>

const unsigned oomph::BiharmonicEquations< DIM >::d2_dof = {1, 3, 6}

staticprivate

Referenced by oomph::BiharmonicEquations< DIM >::get_d2_dof().

◆ Local_eqn

template<unsigned DIM>

Vector<int> oomph::BiharmonicEquations< DIM >::Local_eqn

protected

Array to hold local eqn numbers: Local_eqn[n] (=-1 for BC)

◆ Source_fct_pt

template<unsigned DIM>

SourceFctPt oomph::BiharmonicEquations< DIM >::Source_fct_pt

protected

Pointer to source function:

Referenced by oomph::BiharmonicEquations< DIM >::get_source(), and oomph::BiharmonicEquations< DIM >::source_fct_pt().

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

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

template<unsigned DIM> class oomph::BiharmonicEquations< DIM >

Member Typedef Documentation

◆ SourceFctPt

Constructor & Destructor Documentation

◆ BiharmonicEquations()

◆ ~BiharmonicEquations()

Member Function Documentation

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_biharmonic()

◆ get_d2_dof()

◆ get_dof_numbers_for_unknowns()

◆ get_source()

◆ interpolated_dudx()

◆ interpolated_u_biharmonic()

◆ ndof_types()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ output_fluid_velocity()

◆ self_test()

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ u()

Member Data Documentation

◆ d2_dof

◆ Local_eqn

◆ Source_fct_pt

template<unsigned DIM>
class oomph::BiharmonicEquations< DIM >