#include <solid_traction_elements.h>

Inheritance diagram for oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >:

Public Member Functions
	RefineableImposeDisplacementByLagrangeMultiplierElement (FiniteElement *const &element_pt, const int &face_index, const unsigned &id=0)

unsigned	ncont_interpolated_values () const

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Fill in the residuals. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Fill in contribution from Jacobian. More...

Public Member Functions inherited from oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >
	ImposeDisplacementByLagrangeMultiplierElement (FiniteElement *const &element_pt, const int &face_index, const unsigned &id=0, const bool &called_from_refineable_constructor=false)

GeomObject *	boundary_shape_geom_object_pt () const

void	set_boundary_shape_geom_object_pt (GeomObject *boundary_shape_geom_object_pt, const unsigned &boundary_number_in_bulk_mesh)

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

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output function. More...

void	output (std::ostream &outfile)
	Output function. More...

double	square_of_l2_norm_of_error ()

Public Member Functions inherited from oomph::SolidFaceElement
double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const

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

void	interpolated_xi (const Vector< double > &s, Vector< double > &xi) const

Public Member Functions inherited from oomph::FaceElement
	FaceElement ()
	Constructor: Initialise all appropriate member data. More...

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

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

const unsigned &	boundary_number_in_bulk_mesh () const
	Broken assignment operator. More...

void	set_boundary_number_in_bulk_mesh (const unsigned &b)
	Set function for the boundary number in bulk mesh. More...

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

double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

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

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

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

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

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

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

int &	normal_sign ()

int	normal_sign () const

int &	face_index ()

int	face_index () const

const Vector< double > *	tangent_direction_pt () const
	Public access function for the tangent direction pointer. More...

void	set_tangent_direction (Vector< double > *tangent_direction_pt)
	Set the tangent direction vector. More...

void	turn_on_warning_for_discontinuous_tangent ()

void	turn_off_warning_for_discontinuous_tangent ()

void	continuous_tangent_and_outer_unit_normal (const Vector< double > &s, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	continuous_tangent_and_outer_unit_normal (const unsigned &ipt, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	outer_unit_normal (const Vector< double > &s, Vector< double > &unit_normal) const
	Compute outer unit normal at the specified local coordinate. More...

void	outer_unit_normal (const unsigned &ipt, Vector< double > &unit_normal) const
	Compute outer unit normal at ipt-th integration point. More...

FiniteElement *&	bulk_element_pt ()
	Pointer to higher-dimensional "bulk" element. More...

FiniteElement *	bulk_element_pt () const
	Pointer to higher-dimensional "bulk" element (const version) More...

CoordinateMappingFctPt &	face_to_bulk_coordinate_fct_pt ()

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt () const

BulkCoordinateDerivativesFctPt &	bulk_coordinate_derivatives_fct_pt ()

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt () const

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

void	get_local_coordinate_in_bulk (const Vector< double > &s, Vector< double > &s_bulk) const

void	get_ds_bulk_ds_face (const Vector< double > &s, DenseMatrix< double > &dsbulk_dsface, unsigned &interior_direction) const

unsigned &	bulk_position_type (const unsigned &i)

const unsigned &	bulk_position_type (const unsigned &i) const

void	bulk_node_number_resize (const unsigned &i)
	Resize the storage for the bulk node numbers. More...

unsigned &	bulk_node_number (const unsigned &n)

const unsigned &	bulk_node_number (const unsigned &n) const

void	bulk_position_type_resize (const unsigned &i)
	Resize the storage for bulk_position_type to i entries. More...

unsigned &	nbulk_value (const unsigned &n)

unsigned	nbulk_value (const unsigned &n) const

void	nbulk_value_resize (const unsigned &i)

void	resize_nodes (Vector< unsigned > &nadditional_data_values)

void	output_zeta (std::ostream &outfile, const unsigned &nplot)
	Output boundary coordinate zeta. 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)

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

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

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

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

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...

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)

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 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)

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

	GeomObject (const unsigned &ndim)

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

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

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

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

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

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

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

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

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

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

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

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

Public Member Functions inherited from oomph::SolidFiniteElement
void	set_lagrangian_dimension (const unsigned &lagrangian_dimension)

virtual bool	has_internal_solid_data ()

	SolidFiniteElement ()
	Constructor: Set defaults. More...

virtual	~SolidFiniteElement ()
	Destructor to clean up any allocated memory. More...

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

virtual void	get_x_and_xi (const Vector< double > &s, Vector< double > &x_fe, Vector< double > &x, Vector< double > &xi_fe, Vector< double > &xi) const

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

virtual void	set_macro_elem_pt (MacroElement macro_elem_pt, MacroElement undeformed_macro_elem_pt)

void	set_undeformed_macro_elem_pt (MacroElement *undeformed_macro_elem_pt)

MacroElement *	undeformed_macro_elem_pt ()
	Access function to pointer to "undeformed" macro element. More...

double	dshape_lagrangian (const Vector< double > &s, Shape &psi, DShape &dpsidxi) const

virtual double	dshape_lagrangian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidxi) const

double	d2shape_lagrangian (const Vector< double > &s, Shape &psi, DShape &dpsidxi, DShape &d2psidxi) const

virtual double	d2shape_lagrangian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidxi, DShape &d2psidxi) const

unsigned	lagrangian_dimension () const

unsigned	nnodal_lagrangian_type () const

Node *	construct_node (const unsigned &n)
	Construct the local node n and return a pointer to it. More...

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

Node *	construct_boundary_node (const unsigned &n)

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

double	lagrangian_position (const unsigned &n, const unsigned &i) const
	Return i-th Lagrangian coordinate at local node n. More...

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

virtual void	interpolated_dxids (const Vector< double > &s, DenseMatrix< double > &dxids) const

virtual void	J_lagrangian (const Vector< double > &s) const

virtual double	J_lagrangian_at_knot (const unsigned &ipt) const

SolidInitialCondition *&	solid_ic_pt ()
	Pointer to object that describes the initial condition. More...

void	enable_solve_for_consistent_newmark_accel ()

void	disable_solve_for_consistent_newmark_accel ()
	Set to reset the problem being solved to be the standard problem. More...

MultiplierFctPt &	multiplier_fct_pt ()

MultiplierFctPt	multiplier_fct_pt () const

virtual void	get_residuals_for_solid_ic (Vector< double > &residuals)

void	fill_in_residuals_for_solid_ic (Vector< double > &residuals)

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

void	fill_in_jacobian_for_newmark_accel (DenseMatrix< double > &jacobian)

void	compute_norm (double &el_norm)

int	position_local_eqn (const unsigned &n, const unsigned &k, const unsigned &j) const

Public Member Functions inherited from oomph::NonRefineableElementWithHangingNodes
void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)
	Broken build function – shouldn't really be needed. More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)
	Broken function – this shouldn't really be needed. More...

virtual void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)
	Broken function – this shouldn't really be needed. More...

void	check_integrity (double &max_error)
	Broken function – this shouldn't really be needed. More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Broken function – this shouldn't really be needed. More...

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

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

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

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

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

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

virtual unsigned	required_nsons () const

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

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

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

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

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

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

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

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

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

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

void	deselect_sons_for_unrefinement ()

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

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

virtual void	unbuild ()

virtual void	deactivate_element ()

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

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

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

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

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

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

virtual unsigned	ninterpolating_node (const int &value_id)

virtual unsigned	ninterpolating_node_1d (const int &value_id)

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

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

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual RefineableElement *	root_element_pt ()

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

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

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

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

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

virtual void	further_setup_hanging_nodes ()

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

unsigned	nshape_controlling_nodes ()

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

Public Member Functions inherited from oomph::RefineableSolidElement
	RefineableSolidElement ()
	Constructor. More...

virtual	~RefineableSolidElement ()
	Virtual Destructor, delete any allocated storage. More...

void	assign_solid_local_eqn_numbers (const bool &store_local_dof_pt)

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

bool	is_undeformed_macro_element_used_for_new_lagrangian_coords () const

void	enable_use_of_undeformed_macro_element_for_new_lagrangian_coords ()

void	disable_use_of_undeformed_macro_element_for_new_lagrangian_coords ()

DenseMatrix< int > &	local_position_hang_eqn (Node *const &node_pt)

virtual void	further_build ()

Protected Member Functions
void	refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

Protected Member Functions inherited from oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >
void	fill_in_generic_contribution_to_residuals_displ_lagr_multiplier (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

unsigned	ndof_types () const

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

Protected Member Functions inherited from oomph::FaceElement
void	add_additional_values (const Vector< unsigned > &nadditional_values, const unsigned &id)

Protected Member Functions inherited from oomph::FiniteElement
template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

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_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

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

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

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

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

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

Protected Member Functions inherited from oomph::SolidFiniteElement
void	fill_in_generic_jacobian_for_solid_ic (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

void	set_nnodal_lagrangian_type (const unsigned &nlagrangian_type)

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

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

void	describe_solid_local_dofs (std::ostream &out, const std::string &current_string) const
	Classifies dofs locally for solid specific aspects. More...

void	fill_in_jacobian_from_solid_position_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_solid_position_fd ()

virtual void	reset_after_solid_position_fd ()

virtual void	update_in_solid_position_fd (const unsigned &i)

virtual void	reset_in_solid_position_fd (const unsigned &i)

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

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

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

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

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

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

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

void	assemble_local_to_lagrangian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const

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

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 > &)

Public Types inherited from oomph::SolidFiniteElement
typedef double(*	MultiplierFctPt) (const Vector< double > &xi)

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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

Protected Attributes inherited from oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >
unsigned	Id
	Lagrange Id. More...

GeomObject *	Boundary_shape_geom_object_pt

Vector< GeomObject * >	Sub_geom_object_pt
	Storage for sub-GeomObject at the integration points. More...

Vector< Vector< double > >	Zeta_sub_geom_object

bool	Sparsify

Protected Attributes inherited from oomph::FaceElement
unsigned	Boundary_number_in_bulk_mesh
	The boundary number in the bulk mesh to which this element is attached. More...

FiniteElement *	Bulk_element_pt
	Pointer to the associated higher-dimensional "bulk" element. More...

Vector< unsigned >	Bulk_node_number

Vector< unsigned >	Nbulk_value

Vector< double > *	Tangent_direction_pt

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Protected Attributes inherited from oomph::SolidFiniteElement
MacroElement *	Undeformed_macro_elem_pt
	Pointer to the element's "undeformed" macro element (NULL by default) More...

SolidInitialCondition *	Solid_ic_pt
	Pointer to object that specifies the initial condition. More...

bool	Solve_for_consistent_newmark_accel_flag

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

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

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

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

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

Protected Attributes inherited from oomph::RefineableSolidElement
bool	Use_undeformed_macro_element_for_new_lagrangian_coords

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

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

Detailed Description

template<class ELEMENT>
class oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >

///////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////// A class for elements that allow the imposition of a displacement constraint for "bulk" solid elements via a Lagrange multiplier. The geometrical information can be read from the FaceGeometry<ELEMENT> class and and thus, we can be generic enough without the need to have a separate equations class. NOTE: Currently (and for the foreseeable future) this element only works with bulk elements that do not have generalised degrees of freedom (so it won't work with Hermite-type elements, say). The additional functionality to deal with such elements could easily be added (once a a suitable test case is written). For now we simply throw errors if an attempt is made to use the element with an unsuitable bulk element.

REFINEABLE VERSION

Constructor & Destructor Documentation

◆ RefineableImposeDisplacementByLagrangeMultiplierElement()

template<class ELEMENT >

oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::RefineableImposeDisplacementByLagrangeMultiplierElement	(	FiniteElement *const &	element_pt,
		const int &	face_index,
		const unsigned &	id = `0`
	)

inline

Constructor takes a "bulk" element and the index that identifies which face the FaceElement is supposed to be attached to. The optional identifier can be used to distinguish the additional nodal values created by this element from thos created by other FaceElements.

       : ImposeDisplacementByLagrangeMultiplierElement<ELEMENT>(
           element_pt, face_index, id, true)
     {
     }

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

template<class ELEMENT >

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

inlinevirtual

Fill in contribution from Jacobian.

Reimplemented from oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >.

     {
       // Call the generic routine with the flag set to 1
       refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier(
         residuals, jacobian, 1);
  
       // Fill in the derivatives w.r.t. external data by FD, re-using
       // the pre-computed residual vector
       this->fill_in_jacobian_from_external_by_fd(residuals, jacobian);
     }

References oomph::GeneralisedElement::fill_in_jacobian_from_external_by_fd(), and oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier().

◆ fill_in_contribution_to_residuals()

template<class ELEMENT >

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

inlinevirtual

Fill in the residuals.

Reimplemented from oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >.

     {
       // Call the generic routine with the flag set to 0
       refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier().

◆ ncont_interpolated_values()

template<class ELEMENT >

unsigned oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::ncont_interpolated_values ( ) const

inlinevirtual

Number of continuously interpolated values: Same for all nodes since it's a refineable element

Implements oomph::RefineableElement.

     {
       return node_pt(0)->nvalue();
     }

References oomph::FiniteElement::node_pt(), and oomph::Data::nvalue().

◆ refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier()

template<class ELEMENT >

void oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

inlineprotected

Helper function to compute the residuals and, if flag==1, the Jacobian

     {
       // Find out how many positional dofs there are
       unsigned n_position_type = this->nnodal_position_type();
  
 #ifdef PARANOID
       if (n_position_type != 1)
       {
         throw OomphLibError(
           "RefineableImposeDisplacementByLagrangeMultiplierElement \n cannot "
           "(currently) be used with elements that have generalised\n "
           "positional dofs. Upgrade should be straightforward though the code "
           "is in a \n bit of state, with generalised degrees of freedom "
           "sometimes half taken into \n account, sometimes completely "
           "ignored...",
           OOMPH_CURRENT_FUNCTION,
           OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Find out how many nodes there are
       unsigned n_node = this->nnode();
  
       // Dimension of element
       unsigned dim_el = this->dim();
  
       // Set up memory for the shape functions
       Shape psi(n_node);
       DShape dpsids(n_node, dim_el);
  
       // Set the value of n_intpt
       unsigned n_intpt = this->integral_pt()->nweight();
  
  
       // Integers to store local equation number
       int local_eqn = 0;
       int local_unknown = 0;
  
       // Loop over the integration points
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Get the integral weight
         double w = this->integral_pt()->weight(ipt);
  
         // Only need to call the local derivatives
         this->dshape_local_at_knot(ipt, psi, dpsids);
  
         // Calculate the Eulerian coordinates and Lagrange multiplier
         Vector<double> x(dim_el + 1, 0.0);
         Vector<double> lambda(dim_el + 1, 0.0);
         Vector<double> zeta(dim_el, 0.0);
         DenseMatrix<double> interpolated_a(dim_el, dim_el + 1, 0.0);
  
         // Loop over nodes -- note in these calculations hang-ness is
         // automatically taken into account because of calls to position(...)
         // etc
         for (unsigned j = 0; j < n_node; j++)
         {
           Node* nod_pt = this->node_pt(j);
  
           // Cast to a boundary node
           BoundaryNodeBase* bnod_pt = dynamic_cast<BoundaryNodeBase*>(nod_pt);
  
           // Get the index of the first nodal value associated with
           // this FaceElement
           unsigned first_index =
             bnod_pt->index_of_first_value_assigned_by_face_element(this->Id);
  
           // Assemble higher-dimensional quantities
           for (unsigned i = 0; i < dim_el + 1; i++)
           {
             x[i] += this->nodal_position(j, i) * psi(j);
             lambda[i] += nod_pt->value(first_index + i) * psi(j);
             for (unsigned ii = 0; ii < dim_el; ii++)
             {
               interpolated_a(ii, i) +=
                 this->lagrangian_position(j, i) * dpsids(j, ii);
             }
           }
           if (!this->Sparsify)
           {
             for (unsigned k = 0; k < n_position_type; k++)
             {
               // Assemble in-element quantities: boundary coordinate
               for (unsigned i = 0; i < dim_el; i++)
               {
                 zeta[i] += this->zeta_nodal(j, k, i) * psi(j, k);
               }
             }
           }
         }
  
         if (this->Sparsify) zeta = this->Zeta_sub_geom_object[ipt];
  
  
         // Now find the local undeformed metric tensor from the tangent Vectors
         DenseMatrix<double> a(dim_el);
         for (unsigned i = 0; i < dim_el; i++)
         {
           for (unsigned j = 0; j < dim_el; j++)
           {
             // Initialise surface metric tensor to zero
             a(i, j) = 0.0;
             // Take the dot product
             for (unsigned k = 0; k < dim_el + 1; k++)
             {
               a(i, j) += interpolated_a(i, k) * interpolated_a(j, k);
             }
           }
         }
  
  
         // Find the determinant of the metric tensor
         double adet = 0.0;
         switch (dim_el + 1)
         {
           case 2:
             adet = a(0, 0);
             break;
  
           case 3:
             adet = a(0, 0) * a(1, 1) - a(0, 1) * a(1, 0);
             break;
  
           default:
             throw OomphLibError(
               "Wrong dimension "
               "refineable_fill_in_generic_contribution_to_residuals_displ_lagr_"
               "multiplier",
               "RefineableImposeDisplacementByLagrangeMultiplierElement::"
               "refineablefill_in_generic_contribution_to_residuals_displ_lagr_"
               "multiplier()",
               OOMPH_EXCEPTION_LOCATION);
         }
  
         // Get prescribed wall shape
         Vector<double> r_prescribed(dim_el + 1);
         if (!this->Sparsify)
         {
           this->Boundary_shape_geom_object_pt->position(zeta, r_prescribed);
         }
         else
         {
           this->Sub_geom_object_pt[ipt]->position(zeta, r_prescribed);
         }
  
         // Premultiply the weights and the square-root of the determinant of
         // the metric tensor
         double W = w * sqrt(adet);
  
         // Assemble residuals and jacobian
  
  
         // Number of master nodes and storage for the weight of the shape
         // function
         unsigned n_master = 1;
         unsigned n_master2 = 1;
         double hang_weight = 1.0;
         double hang_weight2 = 1.0;
  
         // Pointer to hang info object
         HangInfo* hang_info_pt = 0;
         HangInfo* hang_info2_pt = 0;
  
  
         // Loop over nodes
         for (unsigned j = 0; j < n_node; j++)
         {
           // Local node itself (hanging or not)
           Node* local_node_pt = this->node_pt(j);
  
           // Local boolean to indicate whether the node is hanging
           bool is_node_hanging = local_node_pt->is_hanging();
  
           // If the node is hanging
           if (is_node_hanging)
           {
             hang_info_pt = local_node_pt->hanging_pt();
  
             // Read out number of master nodes from hanging data
             n_master = hang_info_pt->nmaster();
           }
           // Otherwise the node is its own master
           else
           {
             n_master = 1;
           }
  
           // Loop over the master nodes
           for (unsigned m = 0; m < n_master; m++)
           {
             // Loop over velocity components for equations
             for (unsigned i = 0; i < dim_el + 1; i++)
             {
               // Get the equation number for Lagrange multiplier eqn
  
               // If the node is hanging
               if (is_node_hanging)
               {
                 // Cast to a boundary node
                 BoundaryNodeBase* bnod_pt = dynamic_cast<BoundaryNodeBase*>(
                   hang_info_pt->master_node_pt(m));
  
                 // Get the equation number from the master node
                 local_eqn = this->local_hang_eqn(
                   hang_info_pt->master_node_pt(m),
                   bnod_pt->index_of_first_value_assigned_by_face_element(
                     this->Id) +
                     i);
  
                 // Get the hang weight from the master node
                 hang_weight = hang_info_pt->master_weight(m);
               }
               // If the node is not hanging
               else
               {
                 // Cast to a boundary node
                 BoundaryNodeBase* bnod_pt =
                   dynamic_cast<BoundaryNodeBase*>(local_node_pt);
  
                 // Local equation number
                 local_eqn = this->nodal_local_eqn(
                   j,
                   bnod_pt->index_of_first_value_assigned_by_face_element(
                     this->Id) +
                     i);
  
                 // Node contributes with full weight
                 hang_weight = 1.0;
               }
  
               // If it's not a boundary condition...
               if (local_eqn >= 0)
               {
                 residuals[local_eqn] +=
                   (x[i] - r_prescribed[i]) * psi(j) * W * hang_weight;
  
                 // Do Jacobian too?
                 if (flag == 1)
                 {
                   // Loop over the nodes again for unknowns (only diagonal
                   // contribution to direction!).
                   for (unsigned jj = 0; jj < n_node; jj++)
                   {
                     // Local node itself (hanging or not)
                     Node* local_node2_pt = this->node_pt(jj);
  
                     // Local boolean to indicate whether the node is hanging
                     bool is_node_hanging2 = local_node2_pt->is_hanging();
  
                     // If the node is hanging
                     if (is_node_hanging2)
                     {
                       hang_info2_pt = local_node2_pt->hanging_pt();
  
                       // Read out number of master nodes from hanging data
                       n_master2 = hang_info2_pt->nmaster();
                     }
                     // Otherwise the node is its own master
                     else
                     {
                       n_master2 = 1;
                     }
  
                     // Loop over the master nodes
                     for (unsigned m2 = 0; m2 < n_master2; m2++)
                     {
                       // Storage for local equation numbers at node indexed by
                       // type and direction
                       DenseMatrix<int> position_local_eqn_at_node2(
                         n_position_type, dim_el + 1);
  
                       if (is_node_hanging2)
                       {
                         // Find the equation numbers
                         position_local_eqn_at_node2 = local_position_hang_eqn(
                           local_node2_pt->hanging_pt()->master_node_pt(m2));
  
                         // Find the hanging node weight
                         hang_weight2 =
                           local_node2_pt->hanging_pt()->master_weight(m2);
                       }
                       else
                       {
                         // Non-loop of types of dofs
                         // for(unsigned k2=0;k2<n_position_type;k2++)
                         // {
                         unsigned k2 = 0;
  
                         // Loop over the displacement components
                         // for(unsigned i2=0;i2<dim_el+1;i2++)
                         unsigned i2 =
                           i; // only need that one, but need to store
                              // information in this container because
                              // it's required for hanging case.
                         {
                           position_local_eqn_at_node2(k2, i2) =
                             this->position_local_eqn(jj, k2, i2);
                         }
  
                         // Hang weight is one
                         hang_weight2 = 1.0;
                       }
  
                       unsigned k2 = 0;
                       local_unknown = position_local_eqn_at_node2(k2, i);
                       if (local_unknown >= 0)
                       {
                         jacobian(local_eqn, local_unknown) +=
                           psi(jj) * psi(j) * W * hang_weight * hang_weight2;
                       }
                     }
                   }
                 }
  
  
                 // Add Lagrange multiplier contribution to bulk equations
  
  
                 // Storage for local equation numbers at node indexed by
                 // type and direction
                 DenseMatrix<int> position_local_eqn_at_node(n_position_type,
                                                             dim_el + 1);
  
                 if (is_node_hanging)
                 {
                   // Find the equation numbers
                   position_local_eqn_at_node = local_position_hang_eqn(
                     local_node_pt->hanging_pt()->master_node_pt(m));
                 }
                 else
                 {
                   // Non-loop of types of dofs
                   // for(unsigned k2=0;k2<n_position_type;k2++)
                   // {
                   unsigned k2 = 0;
  
                   // Loop over the displacement components
                   // for(unsigned i2=0;i2<dim_el+1;i2++)
                   unsigned i2 = i; // only need that one, but need to store
                                    // information in this container because
                                    // it's required for hanging case.
                   {
                     position_local_eqn_at_node(k2, i2) =
                       this->position_local_eqn(j, k2, i2);
                   }
                 }
                 unsigned k = 0;
                 local_eqn = position_local_eqn_at_node(k, i);
  
                 /*IF it's not a boundary condition*/
                 if (local_eqn >= 0)
                 {
                   // Add to residual
                   residuals[local_eqn] += lambda[i] * psi(j) * W * hang_weight;
  
                   // Do Jacobian too?
                   if (flag == 1)
                   {
                     // Loop over the nodes again for unknowns (only diagonal
                     // contribution to direction!).
                     for (unsigned jj = 0; jj < n_node; jj++)
                     {
                       // Local node itself (hanging or not)
                       Node* local_node2_pt = this->node_pt(jj);
  
                       // Local boolean to indicate whether the node is hanging
                       bool is_node_hanging2 = local_node2_pt->is_hanging();
  
                       // If the node is hanging
                       if (is_node_hanging2)
                       {
                         hang_info2_pt = local_node2_pt->hanging_pt();
  
                         // Read out number of master nodes from hanging data
                         n_master2 = hang_info2_pt->nmaster();
                       }
                       // Otherwise the node is its own master
                       else
                       {
                         n_master2 = 1;
                       }
  
                       // Loop over the master nodes
                       for (unsigned m2 = 0; m2 < n_master2; m2++)
                       {
                         // Get the equation number for Lagrange multiplier eqn
  
                         // If the node is hanging
                         if (is_node_hanging2)
                         {
                           // Cast to a boundary node
                           BoundaryNodeBase* bnod2_pt =
                             dynamic_cast<BoundaryNodeBase*>(
                               hang_info2_pt->master_node_pt(m2));
  
                           // Get the equation number from the master node
                           local_unknown = this->local_hang_eqn(
                             hang_info2_pt->master_node_pt(m2),
                             bnod2_pt
                                 ->index_of_first_value_assigned_by_face_element(
                                   this->Id) +
                               i);
  
                           // Get the hang weight from the master node
                           hang_weight2 = hang_info2_pt->master_weight(m2);
                         }
                         // If the node is not hanging
                         else
                         {
                           // Cast to a boundary node
                           BoundaryNodeBase* bnod2_pt =
                             dynamic_cast<BoundaryNodeBase*>(local_node2_pt);
  
                           // Local equation number
                           local_unknown = this->nodal_local_eqn(
                             jj,
                             bnod2_pt
                                 ->index_of_first_value_assigned_by_face_element(
                                   this->Id) +
                               i);
  
                           // Node contributes with full weight
                           hang_weight2 = 1.0;
                         }
  
                         if (local_unknown >= 0)
                         {
                           jacobian(local_eqn, local_unknown) +=
                             psi(jj) * psi(j) * W * hang_weight * hang_weight2;
                         }
                       }
                     }
                   }
                 }
               }
             }
           }
         }
  
       } // End of loop over the integration points
     }

References a, oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::Boundary_shape_geom_object_pt, oomph::FiniteElement::dim(), oomph::FiniteElement::dshape_local_at_knot(), oomph::Node::hanging_pt(), i, oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::Id, oomph::BoundaryNodeBase::index_of_first_value_assigned_by_face_element(), oomph::FiniteElement::integral_pt(), oomph::Node::is_hanging(), j, k, oomph::SolidFiniteElement::lagrangian_position(), lambda, oomph::RefineableElement::local_hang_eqn(), oomph::RefineableSolidElement::local_position_hang_eqn(), m, m2(), oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), oomph::FiniteElement::nnodal_position_type(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::node_pt(), oomph::Integral::nweight(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::GeomObject::position(), oomph::SolidFiniteElement::position_local_eqn(), oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::Sparsify, sqrt(), oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::Sub_geom_object_pt, oomph::Node::value(), w, oomph::QuadTreeNames::W, oomph::Integral::weight(), plotDoE::x, Eigen::zeta(), oomph::SolidFaceElement::zeta_nodal(), and oomph::ImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::Zeta_sub_geom_object.

Referenced by oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::fill_in_contribution_to_jacobian(), and oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >::fill_in_contribution_to_residuals().

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

solid_traction_elements.h

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >

Constructor & Destructor Documentation

◆ RefineableImposeDisplacementByLagrangeMultiplierElement()

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ ncont_interpolated_values()

◆ refineable_fill_in_generic_contribution_to_residuals_displ_lagr_multiplier()

template<class ELEMENT>
class oomph::RefineableImposeDisplacementByLagrangeMultiplierElement< ELEMENT >