#include <axisym_poroelasticity_face_elements.h>

Inheritance diagram for oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >:

Public Member Functions
	AxisymmetricPoroelasticityTractionElement (FiniteElement *const &element_pt, const int &face_index)

	AxisymmetricPoroelasticityTractionElement ()
	Default constructor. More...

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

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

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

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

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

void	output (FILE *file_pt)
	C_style output function. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	C-style output function. More...

double	lagrangian_eulerian_translation_factor (const Vector< double > &s)

void	traction (const double &time, const Vector< double > &s, Vector< double > &traction)

void	pressure (const double &time, const Vector< double > &s, double &pressure)

void	contribution_to_total_porous_flux (double &skeleton_flux_contrib, double &seepage_flux_contrib)

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

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)

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

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...

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)

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, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	self_test ()

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

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

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

	GeomObject (const unsigned &ndim)

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

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

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

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

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

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

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

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

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

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

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

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

Public Attributes
void(*&)(const double &time, const Vector< double > &x, const Vector< double > &n, Vector< double > &traction)	traction_fct_pt ()
	Reference to the traction function pointer. More...

void(*&)(const double &time, const Vector< double > &x, const Vector< double > &n, double &pressure)	pressure_fct_pt ()
	Reference to the pressure function pointer. More...

Protected Member Functions
virtual void	get_traction (const double &time, const unsigned &intpt, const Vector< double > &x, const Vector< double > &n, Vector< double > &traction)

virtual void	get_pressure (const double &time, const unsigned &intpt, const Vector< double > &x, const Vector< double > &n, double &pressure)

void	fill_in_contribution_to_residuals_axisym_poroelasticity_face (Vector< double > &residuals)
	Helper function that actually calculates the residuals. More...

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
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
void(*	Traction_fct_pt )(const double &time, const Vector< double > &x, const Vector< double > &n, Vector< double > &result)

void(*	Pressure_fct_pt )(const double &time, const Vector< double > &x, const Vector< double > &n, double &result)

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

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

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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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<class ELEMENT>
class oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >

A class for elements that allow the imposition of an applied combined traction and pore fluid pressure in the axisym poroelasticity equations. The geometrical information can be read from the FaceGeometry<ELEMENT> class and thus, we can be generic enough without the need to have a separate equations class.

Constructor & Destructor Documentation

◆ AxisymmetricPoroelasticityTractionElement() [1/2]

template<class ELEMENT >

oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::AxisymmetricPoroelasticityTractionElement	(	FiniteElement *const &	element_pt,
		const int &	face_index
	)

inline

Constructor, which takes a "bulk" element and the value of the index and its limit

       : FaceGeometry<ELEMENT>(), FaceElement()
     {
 #ifdef PARANOID
       {
         // Check that the element is not a refineable 3d element
         ELEMENT* elem_pt = dynamic_cast<ELEMENT*>(element_pt);
         // If it's three-d
         if (elem_pt->dim() == 3)
         {
           // Is it refineable
           RefineableElement* ref_el_pt =
             dynamic_cast<RefineableElement*>(elem_pt);
           if (ref_el_pt != 0)
           {
             if (this->has_hanging_nodes())
             {
               throw OomphLibError("This flux element will not work correctly "
                                   "if nodes are hanging\n",
                                   OOMPH_CURRENT_FUNCTION,
                                   OOMPH_EXCEPTION_LOCATION);
             }
           }
         }
       }
 #endif
  
       // Attach the geometrical information to the element. N.B. This function
       // also assigns nbulk_value from the required_nvalue of the bulk element
       element_pt->build_face_element(face_index, this);
  
       // Zero traction
       Traction_fct_pt =
         &AxisymmetricPoroelasticityTractionElementHelper::Zero_traction_fct;
  
       // Zero pressure
       Pressure_fct_pt =
         &AxisymmetricPoroelasticityTractionElementHelper::Zero_pressure_fct;
     }

References oomph::FiniteElement::build_face_element(), oomph::FaceElement::face_index(), oomph::FiniteElement::has_hanging_nodes(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::Pressure_fct_pt, oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::Traction_fct_pt, oomph::AxisymmetricPoroelasticityTractionElementHelper::Zero_pressure_fct(), and oomph::AxisymmetricPoroelasticityTractionElementHelper::Zero_traction_fct().

◆ AxisymmetricPoroelasticityTractionElement() [2/2]

template<class ELEMENT >

oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::AxisymmetricPoroelasticityTractionElement ( )

inline

Default constructor.

199 {}

Member Function Documentation

◆ contribution_to_total_porous_flux()

template<class ELEMENT >

void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::contribution_to_total_porous_flux	(	double &	skeleton_flux_contrib,
		double &	seepage_flux_contrib
	)

inline

Compute contributions to integrated porous flux over boundary: q_skeleton = \int \partial u_displ / \partial t \cdot n ds q_seepage = \int k q \cdot n ds

Calculate the FE representation of q

     {
       // Get pointer to bulk element
       ELEMENT* bulk_el_pt = dynamic_cast<ELEMENT*>(bulk_element_pt());
  
       // Get permeability from the bulk poroelasticity element
       const double permeability = bulk_el_pt->permeability();
  
       // Find out how many nodes there are
       const unsigned n_node = this->nnode();
  
       // Set up memeory for the shape functions
       Shape psi(n_node);
       DShape dpsids(n_node, 1);
  
       // Get the value of Nintpt
       const unsigned n_intpt = integral_pt()->nweight();
  
       // Set the Vector to hold local coordinates
       Vector<double> s(1);
       Vector<double> s_bulk(2);
  
       // Loop over the integration points
       skeleton_flux_contrib = 0.0;
       seepage_flux_contrib = 0.0;
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Assign values of s
         s[0] = integral_pt()->knot(ipt, 0);
  
         // Get the integral weight
         double W = this->integral_pt()->weight(ipt);
  
         // Call the derivatives of the shape function at the knot point
         this->dshape_local_at_knot(ipt, psi, dpsids);
  
         // Get position and tangent vector
         Vector<double> interpolated_t1(2, 0.0);
         Vector<double> interpolated_x(2, 0.0);
         for (unsigned l = 0; l < n_node; l++)
         {
           // Loop over directional components
           for (unsigned i = 0; i < 2; i++)
           {
             interpolated_x[i] += this->nodal_position(l, i) * psi(l);
             interpolated_t1[i] += this->nodal_position(l, i) * dpsids(l, 0);
           }
         }
  
         // Calculate the length of the tangent Vector
         double tlength = interpolated_t1[0] * interpolated_t1[0] +
                          interpolated_t1[1] * interpolated_t1[1];
  
         // Set the Jacobian of the line element
         double J = sqrt(tlength) * interpolated_x[0];
  
         // Get the outer unit normal
         Vector<double> interpolated_normal(2);
         outer_unit_normal(s, interpolated_normal);
  
         // Get coordinate in bulk element
         s_bulk = this->local_coordinate_in_bulk(s);
  
         Vector<double> q(2);
         bulk_el_pt->interpolated_q(s_bulk, q);
  
         // Skeleton velocity from bulk
         Vector<double> du_dt(2);
         bulk_el_pt->interpolated_du_dt(s_bulk, du_dt);
  
 #ifdef PARANOID
         Vector<double> x_bulk(2);
         x_bulk[0] = bulk_el_pt->interpolated_x(s_bulk, 0);
         x_bulk[1] = bulk_el_pt->interpolated_x(s_bulk, 1);
         double error = sqrt(
           (interpolated_x[0] - x_bulk[0]) * (interpolated_x[0] - x_bulk[0]) +
           (interpolated_x[1] - x_bulk[1]) * (interpolated_x[1] - x_bulk[1]));
         double tol = 1.0e-10;
         if (error > tol)
         {
           std::stringstream junk;
           junk << "Gap between bulk and face element coordinate\n"
                << "is suspiciously large: " << error
                << "\nBulk at: " << x_bulk[0] << " " << x_bulk[1] << "\n"
                << "Face at: " << interpolated_x[0] << " " << interpolated_x[1]
                << "\n";
           OomphLibWarning(
             junk.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
         }
 #endif
  
         // Get net flux through boundary
         double q_flux = 0.0;
         double dudt_flux = 0.0;
         for (unsigned i = 0; i < 2; i++)
         {
           q_flux += permeability * q[i] * interpolated_normal[i];
           dudt_flux += du_dt[i] * interpolated_normal[i];
         }
  
         // Add
         seepage_flux_contrib +=
           2.0 * MathematicalConstants::Pi * q_flux * W * J;
         skeleton_flux_contrib +=
           2.0 * MathematicalConstants::Pi * dudt_flux * W * J;
       }
     }

References oomph::FaceElement::bulk_element_pt(), oomph::FiniteElement::dshape_local_at_knot(), calibrate::error, i, oomph::FiniteElement::integral_pt(), oomph::FaceElement::interpolated_x(), J, oomph::Integral::knot(), oomph::FaceElement::local_coordinate_in_bulk(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), oomph::Integral::nweight(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::FaceElement::outer_unit_normal(), oomph::MathematicalConstants::Pi, Eigen::numext::q, s, sqrt(), oomph::QuadTreeNames::W, and oomph::Integral::weight().

◆ fill_in_contribution_to_jacobian()

template<class ELEMENT >

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

inlinevirtual

Fill in contribution from Jacobian.

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the residuals (element makes no contribution to Jacobian)
       fill_in_contribution_to_residuals_axisym_poroelasticity_face(residuals);
     }

References oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::fill_in_contribution_to_residuals_axisym_poroelasticity_face().

◆ fill_in_contribution_to_residuals()

template<class ELEMENT >

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

inlinevirtual

Return the residuals.

Reimplemented from oomph::GeneralisedElement.

     {
       fill_in_contribution_to_residuals_axisym_poroelasticity_face(residuals);
     }

References oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::fill_in_contribution_to_residuals_axisym_poroelasticity_face().

◆ fill_in_contribution_to_residuals_axisym_poroelasticity_face()

template<class ELEMENT >

void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::fill_in_contribution_to_residuals_axisym_poroelasticity_face ( Vector< double > & residuals )

protected

Helper function that actually calculates the residuals.

Return the residuals for the AxisymmetricPoroelasticityTractionElement equations

   {
     // Find out how many nodes there are
     unsigned n_node = nnode();
  
     // Get continuous time from timestepper of first node
     double time = node_pt(0)->time_stepper_pt()->time_pt()->time();
  
 #ifdef PARANOID
     // Find out how many positional dofs there are
     unsigned n_position_type = this->nnodal_position_type();
     if (n_position_type != 1)
     {
       throw OomphLibError("Poroelasticity equations are not yet implemented "
                           "for more than one position type",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }
 #endif
  
     // Find out the dimension of the node
     unsigned n_dim = this->nodal_dimension();
  
  
     // Get bulk element
     ELEMENT* bulk_el_pt = dynamic_cast<ELEMENT*>(bulk_element_pt());
  
     unsigned n_q_basis = bulk_el_pt->nq_basis();
     unsigned n_q_basis_edge = bulk_el_pt->nq_basis_edge();
  
     // Integer to hold the local equation number
     int local_eqn = 0;
  
     // Set up memory for the shape functions
     // Note that in this case, the number of lagrangian coordinates is always
     // equal to the dimension of the nodes
     Shape psi(n_node);
     DShape dpsids(n_node, n_dim - 1);
     Shape q_basis(n_q_basis, n_dim);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Storage for the local coordinates
     Vector<double> s_face(n_dim - 1, 0.0), s_bulk(n_dim, 0.0);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Only need to call the local derivatives
       dshape_local_at_knot(ipt, psi, dpsids);
  
       // Assign values of s in FaceElement and local coordinates in bulk element
       for (unsigned i = 0; i < n_dim - 1; i++)
       {
         s_face[i] = integral_pt()->knot(ipt, i);
       }
       s_bulk = local_coordinate_in_bulk(s_face);
  
       // Get bulk element
       ELEMENT* bulk_el_pt = dynamic_cast<ELEMENT*>(bulk_element_pt());
  
       // Get the q basis at bulk local coordinate s_bulk,
       // corresponding to face local
       // coordinate s_face
       bulk_el_pt->get_q_basis(s_bulk, q_basis);
  
       // Calculate the Eulerian and Lagrangian coordinates
       Vector<double> interpolated_x(n_dim, 0.0);
  
       // Also calculate the surface Vectors (derivatives wrt local coordinates)
       DenseMatrix<double> interpolated_A(n_dim - 1, n_dim, 0.0);
  
       // Calculate displacements and derivatives
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over directions
         for (unsigned i = 0; i < n_dim; i++)
         {
           // Calculate the Eulerian coords
           const double x_local = nodal_position(l, i);
           interpolated_x[i] += x_local * psi(l);
  
           // Loop over LOCAL derivative directions, to calculate the tangent(s)
           for (unsigned j = 0; j < n_dim - 1; j++)
           {
             interpolated_A(j, i) += x_local * dpsids(l, j);
           }
         }
       }
  
       // Now find the local metric tensor from the tangent vectors
       DenseMatrix<double> A(n_dim - 1);
       for (unsigned i = 0; i < n_dim - 1; i++)
       {
         for (unsigned j = 0; j < n_dim - 1; j++)
         {
           // Initialise surface metric tensor to zero
           A(i, j) = 0.0;
  
           // Take the dot product
           for (unsigned k = 0; k < n_dim; k++)
           {
             A(i, j) += interpolated_A(i, k) * interpolated_A(j, k);
           }
         }
       }
  
       // Get the outer unit normal
       Vector<double> interpolated_normal(n_dim);
       outer_unit_normal(ipt, interpolated_normal);
  
       // Find the determinant of the metric tensor
       double Adet = 0.0;
       switch (n_dim)
       {
         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 in AxisymmetricPoroelasticityTractionElement",
             OOMPH_CURRENT_FUNCTION,
             OOMPH_EXCEPTION_LOCATION);
       }
  
       // Premultiply the weights and the square-root of the determinant of
       // the metric tensor
       double W = w * sqrt(Adet);
  
       // Now calculate the traction load
       Vector<double> traction(n_dim);
       get_traction(time, ipt, interpolated_x, interpolated_normal, traction);
  
       // Now calculate the load
       double pressure;
       get_pressure(time, ipt, interpolated_x, interpolated_normal, pressure);
  
       // Loop over the test functions, nodes of the element
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over the displacement components
         for (unsigned i = 0; i < n_dim; i++)
         {
           local_eqn = this->nodal_local_eqn(
             l, bulk_el_pt->u_index_axisym_poroelasticity(i));
           /*IF it's not a boundary condition*/
           if (local_eqn >= 0)
           {
             // Add the traction loading terms to the residuals
             residuals[local_eqn] -=
               traction[i] * psi(l) * interpolated_x[0] * W;
           } // End of if not boundary condition
         }
       } // End of loop over shape functions
  
       // Loop over the q edge test functions only (internal basis functions
       // have zero normal component on the boundary)
       for (unsigned l = 0; l < n_q_basis_edge; l++)
       {
         local_eqn = this->nodal_local_eqn(1, bulk_el_pt->q_edge_index(l));
  
         /*IF it's not a boundary condition*/
         if (local_eqn >= 0)
         {
           // Loop over the displacement components
           for (unsigned i = 0; i < n_dim; i++)
           {
             // Add the loading terms to the residuals
             residuals[local_eqn] += pressure * q_basis(l, i) *
                                     interpolated_normal[i] * interpolated_x[0] *
                                     W;
           }
         } // End of if not boundary condition
       } // End of loop over shape functions
     } // End of loop over integration points
   }

References GlobalParameters::get_pressure(), i, j, k, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, sqrt(), w, and oomph::QuadTreeNames::W.

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

◆ get_pressure()

template<class ELEMENT >

virtual void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::get_pressure	(	const double &	time,
		const unsigned &	intpt,
		const Vector< double > &	x,
		const Vector< double > &	n,
		double &	pressure
	)

inlineprotectedvirtual

Get the pressure value: Pass number of integration point (dummy), Eulerrian coordinate and normal vector and return the pressure (not all of the input arguments will be required for all specific load functions but the list should cover all cases). This function is virtual so it can be overloaded for FSI.

Reimplemented in oomph::FSILinearisedAxisymPoroelasticTractionElement< POROELASTICITY_BULK_ELEMENT, NAVIER_STOKES_BULK_ELEMENT >.

     {
       Pressure_fct_pt(time, x, n, pressure);
     }

References n, oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::pressure(), oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::Pressure_fct_pt, and plotDoE::x.

Referenced by oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output().

◆ get_traction()

template<class ELEMENT >

virtual void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::get_traction	(	const double &	time,
		const unsigned &	intpt,
		const Vector< double > &	x,
		const Vector< double > &	n,
		Vector< double > &	traction
	)

inlineprotectedvirtual

Get the traction vector: Pass number of integration point (dummy), Eulerrian coordinate and normal vector and return the pressure (not all of the input arguments will be required for all specific load functions but the list should cover all cases). This function is virtual so it can be overloaded for FSI.

Reimplemented in oomph::FSILinearisedAxisymPoroelasticTractionElement< POROELASTICITY_BULK_ELEMENT, NAVIER_STOKES_BULK_ELEMENT >.

     {
       Traction_fct_pt(time, x, n, traction);
     }

References n, oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::traction(), oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::Traction_fct_pt, and plotDoE::x.

Referenced by oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output().

◆ lagrangian_eulerian_translation_factor()

template<class ELEMENT >

double oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::lagrangian_eulerian_translation_factor ( const Vector< double > & s )

inline

Ratio of lengths of line elements (or annular surface areas) in the undeformed and deformed configuration (needed to translate normal flux correctly between small displacement formulation used here and the possibly large displacement NSt formulation used in FSI problems. Maths is as follows: Surface area: A = 2 \pi \int r \sqrt((dr/ds)^2+(dz/ds)^2) ds = 2 \pi \int J ds This function returns the ratio of J in the undeformed configuration (used here) to that in the deformed configuration where (r,z) = (r,z)_undef + (u_r,u_z).

Calculate the FE representation of u – the skeleton displacement

     {
       // Get continuous time from timestepper of first node
       unsigned n_dim = this->nodal_dimension();
  
       // Find out how many nodes there are
       unsigned n_node = nnode();
  
       Vector<double> x(n_dim);
       Vector<double> s_bulk(n_dim);
       Vector<double> disp(n_dim);
       Shape psi(n_node);
       DShape dpsids(n_node, n_dim - 1);
  
       // Call the derivatives of the shape function at the knot point
       this->dshape_local(s, psi, dpsids);
  
       // Get pointer to bulk element
       ELEMENT* bulk_pt = dynamic_cast<ELEMENT*>(bulk_element_pt());
       s_bulk = local_coordinate_in_bulk(s);
  
       // Get Eulerian coordinates
       this->interpolated_x(s, x);
  
       // Outer unit normal
       Vector<double> unit_normal(n_dim);
       outer_unit_normal(s, unit_normal);
  
       bulk_pt->interpolated_u(s_bulk, disp);
  
       // Get deformed and undeformed tangent vectors
       Vector<double> interpolated_t1(2, 0.0);
       Vector<double> interpolated_T1(2, 0.0);
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over directional components
         for (unsigned i = 0; i < 2; i++)
         {
           // Index at which the nodal value is stored
           unsigned u_nodal_index = bulk_pt->u_index_axisym_poroelasticity(i);
  
           interpolated_t1[i] += this->nodal_position(l, i) * dpsids(l, 0);
           interpolated_T1[i] +=
             (this->nodal_position(l, i) + nodal_value(l, u_nodal_index)) *
             dpsids(l, 0);
         }
       }
  
       // Set the Jacobian of the undeformed line element
       double J_undef = sqrt(interpolated_t1[0] * interpolated_t1[0] +
                             interpolated_t1[1] * interpolated_t1[1]) *
                        x[0];
  
  
       // Set the Jacobian of the deformed line element
       double J_def = sqrt(interpolated_T1[0] * interpolated_T1[0] +
                           interpolated_T1[1] * interpolated_T1[1]) *
                      (x[0] + disp[0]);
  
       double return_val = 1.0;
       if (J_def != 0.0) return_val = J_undef / J_def;
       return return_val;
     }

References oomph::FaceElement::bulk_element_pt(), oomph::FiniteElement::dshape_local(), i, oomph::FaceElement::interpolated_x(), oomph::FaceElement::local_coordinate_in_bulk(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_dimension(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nodal_value(), oomph::FaceElement::outer_unit_normal(), s, sqrt(), and plotDoE::x.

Referenced by oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output().

◆ output() [1/4]

template<class ELEMENT >

void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output ( FILE * file_pt )

inlinevirtual

C_style output function.

Reimplemented from oomph::FiniteElement.

     {
       FaceGeometry<ELEMENT>::output(file_pt);
     }

References output().

◆ output() [2/4]

template<class ELEMENT >

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

inlinevirtual

C-style output function.

Reimplemented from oomph::FiniteElement.

     {
       FaceGeometry<ELEMENT>::output(file_pt, n_plot);
     }

References output().

◆ output() [3/4]

template<class ELEMENT >

void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output ( std::ostream & outfile )

inlinevirtual

Output function.

Reimplemented from oomph::FiniteElement.

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

◆ output() [4/4]

template<class ELEMENT >

void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output	(	std::ostream &	outfile,
		const unsigned &	n_plot
	)

inlinevirtual

Output function.

Calculate the FE representation of u – the skeleton displacement

Skeleton velocity

Reimplemented from oomph::FiniteElement.

     {
       // Get continuous time from timestepper of first node
       double time = node_pt(0)->time_stepper_pt()->time_pt()->time();
       unsigned n_dim = this->nodal_dimension();
  
       // Find out how many nodes there are
       unsigned n_node = nnode();
  
       Vector<double> x(n_dim);
       Vector<double> s(n_dim - 1);
       Vector<double> s_bulk(n_dim);
       Vector<double> disp(n_dim);
       Shape psi(n_node);
       DShape dpsids(n_node, n_dim - 1);
  
       // Tecplot header info
       outfile << this->tecplot_zone_string(n_plot);
  
       // Loop over plot points
       unsigned num_plot_points = this->nplot_points(n_plot);
       for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
       {
         // Get local coordinates of plot point
         this->get_s_plot(iplot, n_plot, s);
  
         // Call the derivatives of the shape function at the knot point
         this->dshape_local(s, psi, dpsids);
  
         // Get pointer to bulk element
         ELEMENT* bulk_pt = dynamic_cast<ELEMENT*>(bulk_element_pt());
         s_bulk = local_coordinate_in_bulk(s);
  
  
         // Get Eulerian coordinates
         this->interpolated_x(s, x);
  
         // Outer unit normal
         Vector<double> unit_normal(n_dim);
         outer_unit_normal(s, unit_normal);
  
         bulk_pt->interpolated_u(s_bulk, disp);
  
         Vector<double> du_dt(2);
         bulk_pt->interpolated_du_dt(s_bulk, du_dt);
  
         // Porous seepage flux
         Vector<double> q(2);
         bulk_pt->interpolated_q(s_bulk, q);
  
         // Get permeability from the bulk poroelasticity element
         const double permeability = bulk_pt->permeability();
  
  
         // Surface area: S = 2 \pi \int r \sqrt((dr/ds)^2+(dz/ds)^2) ds
         //                 = 2 \pi \int r \sqrt( 1 + ( (dr/ds)/(dz/ds) )^2 )
         //                 dz/ds ds = 2 \pi \int J dz
         // where J is an objective measure of the length of the line element
         // (indep of local coordinates) so should be the same from fluid
         // and solid.
  
         // Get deformed and undeformed tangent vectors
         Vector<double> interpolated_t1(2, 0.0);
         Vector<double> interpolated_T1(2, 0.0);
         for (unsigned l = 0; l < n_node; l++)
         {
           // Loop over directional components
           for (unsigned i = 0; i < 2; i++)
           {
             // Index at which the nodal value is stored
             unsigned u_nodal_index = bulk_pt->u_index_axisym_poroelasticity(i);
  
             interpolated_t1[i] += this->nodal_position(l, i) * dpsids(l, 0);
             interpolated_T1[i] +=
               (this->nodal_position(l, i) + nodal_value(l, u_nodal_index)) *
               dpsids(l, 0);
           }
         }
  
         // Set the Jacobian of the undeformed line element
         double J_undef =
           sqrt(1.0 + (interpolated_t1[0] * interpolated_t1[0]) /
                        (interpolated_t1[1] * interpolated_t1[1])) *
           x[0];
  
  
         // Set the Jacobian of the deformed line element
         double J_def = sqrt(1.0 + (interpolated_T1[0] * interpolated_T1[0]) /
                                     (interpolated_T1[1] * interpolated_T1[1])) *
                        (x[0] + disp[0]);
  
         // Dummy
         unsigned ipt = 0;
  
         // Now calculate the traction load
         Vector<double> traction(n_dim);
         get_traction(time, ipt, x, unit_normal, traction);
  
         // Now calculate the load
         double pressure;
         get_pressure(time, ipt, x, unit_normal, pressure);
  
         // Get correction factor for geometry
         double lagr_euler_translation_factor =
           lagrangian_eulerian_translation_factor(s);
  
         // Output the x,y,..
         for (unsigned i = 0; i < n_dim; i++)
         {
           outfile << x[i] << " ";
         } // column 1,2
  
         // Output displacement
         for (unsigned i = 0; i < n_dim; i++)
         {
           outfile << disp[i] << " "; // column 3,4
         }
  
         // Output imposed traction
         for (unsigned i = 0; i < n_dim; i++)
         {
           outfile << traction[i] << " "; // column 5,6
         }
  
         // Output imposed pressure
         outfile << pressure << " "; // column 7
  
         // Output seepage flux
         outfile << permeability * q[0] << " " // column 8
                 << permeability * q[1] << " "; // column 9
  
         // Output skeleton velocity
         outfile << du_dt[0] << " " // column 10
                 << du_dt[1] << " "; // column 11
  
         // Total veloc
         outfile << du_dt[0] + permeability * q[0] << " " // column 12
                 << du_dt[1] + permeability * q[1] << " "; // column 13
  
         // Outer unit normal
         outfile << unit_normal[0] << " " // column 14
                 << unit_normal[1] << " "; // column 15
  
         // Output FE representation of div u at s_bulk
         outfile << bulk_pt->interpolated_div_q(s_bulk) << " "; // column 16
  
         // Output FE representation of p at s_bulk
         outfile << bulk_pt->interpolated_p(s_bulk) << " "; // column 17
  
         // Output undeformed jacobian
         outfile << J_undef << " "; // column 18
  
         // Output deformed jacobian
         outfile << J_def << " "; // column 19
  
         // Lagranian/Eulerian translation factor
         outfile << lagr_euler_translation_factor << " "; // column 20
  
         outfile << std::endl;
       }
  
       // Write tecplot footer (e.g. FE connectivity lists)
       this->write_tecplot_zone_footer(outfile, n_plot);
     }

◆ pressure()

template<class ELEMENT >

void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::pressure	(	const double &	time,
		const Vector< double > &	s,
		double &	pressure
	)

Compute pressure value at specified local coordinate Should only be used for post-processing; ignores dependence on integration point!

   {
     unsigned n_dim = this->nodal_dimension();
  
     // Position vector
     Vector<double> x(n_dim);
     interpolated_x(s, x);
  
     // Outer unit normal
     Vector<double> unit_normal(n_dim);
     outer_unit_normal(s, unit_normal);
  
     // Dummy
     unsigned ipt = 0;
  
     // Pressure value
     get_pressure(time, ipt, x, unit_normal, pressure);
   }

References GlobalParameters::get_pressure(), s, and plotDoE::x.

Referenced by oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::get_pressure(), and oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output().

◆ traction()

template<class ELEMENT >

void oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::traction	(	const double &	time,
		const Vector< double > &	s,
		Vector< double > &	traction
	)

Compute traction vector at specified local coordinate Should only be used for post-processing; ignores dependence on integration point!

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// Compute traction vector at specified local coordinate Should only be used for post-processing; ignores dependence on integration point!

   {
     unsigned n_dim = this->nodal_dimension();
  
     // Position vector
     Vector<double> x(n_dim);
     interpolated_x(s, x);
  
     // Outer unit normal
     Vector<double> unit_normal(n_dim);
     outer_unit_normal(s, unit_normal);
  
     // Dummy
     unsigned ipt = 0;
  
     // Pressure value
     get_traction(time, ipt, x, unit_normal, traction);
   }

References s, and plotDoE::x.

Referenced by oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::get_traction(), and oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::output().

◆ zeta_nodal()

template<class ELEMENT >

double oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::zeta_nodal	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inlinevirtual

Specify the value of nodal zeta from the face geometry The "global" intrinsic coordinate of the element when viewed as part of a geometric object should be given by the FaceElement representation, by default (needed to break indeterminacy if bulk element is SolidElement)

Reimplemented from oomph::FiniteElement.

     {
       return FaceElement::zeta_nodal(n, k, i);
     }

References i, k, n, and oomph::FaceElement::zeta_nodal().

Member Data Documentation

◆ pressure_fct_pt

template<class ELEMENT >

void(*&)(const double& time, const Vector<double>& x, const Vector<double>& n, double& pressure) oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::pressure_fct_pt()

inline

Reference to the pressure function pointer.

     {
       return Pressure_fct_pt;
     }

Referenced by AxiPoroProblem< ELEMENT, TIMESTEPPER >::create_pressure_elements().

◆ Pressure_fct_pt

template<class ELEMENT >

void(* oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::Pressure_fct_pt) (const double &time, const Vector< double > &x, const Vector< double > &n, double &result)

protected

Pointer to an imposed pressure function. Arguments: Eulerian coordinate; outer unit normal; applied pressure. (Not all of the input arguments will be required for all specific load functions but the list should cover all cases)

Referenced by oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::AxisymmetricPoroelasticityTractionElement(), and oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::get_pressure().

◆ traction_fct_pt

template<class ELEMENT >

void(*&)(const double& time, const Vector<double>& x, const Vector<double>& n, Vector<double>& traction) oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::traction_fct_pt()

inline

Reference to the traction function pointer.

     {
       return Traction_fct_pt;
     }

Referenced by AxiPoroProblem< ELEMENT, TIMESTEPPER >::create_pressure_elements().

◆ Traction_fct_pt

template<class ELEMENT >

void(* oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::Traction_fct_pt) (const double &time, const Vector< double > &x, const Vector< double > &n, Vector< double > &result)

protected

Pointer to an imposed traction function. Arguments: Eulerian coordinate; outer unit normal; applied traction. (Not all of the input arguments will be required for all specific load functions but the list should cover all cases)

Referenced by oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::AxisymmetricPoroelasticityTractionElement(), and oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >::get_traction().

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

axisym_poroelasticity_face_elements.h

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >

Constructor & Destructor Documentation

◆ AxisymmetricPoroelasticityTractionElement() [1/2]

◆ AxisymmetricPoroelasticityTractionElement() [2/2]

Member Function Documentation

◆ contribution_to_total_porous_flux()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_contribution_to_residuals_axisym_poroelasticity_face()

◆ get_pressure()

◆ get_traction()

◆ lagrangian_eulerian_translation_factor()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ pressure()

◆ traction()

◆ zeta_nodal()

Member Data Documentation

◆ pressure_fct_pt

◆ Pressure_fct_pt

◆ traction_fct_pt

◆ Traction_fct_pt

template<class ELEMENT>
class oomph::AxisymmetricPoroelasticityTractionElement< ELEMENT >