#include <young_laplace_elements.h>

Inheritance diagram for oomph::YoungLaplaceEquations:

Public Types
typedef void(*	SpineBaseFctPt) (const Vector< double > &x, Vector< double > &spine_base, Vector< Vector< double >> &dspine_base)
	Function pointer to "spine base" function. More...

typedef void(*	SpineFctPt) (const Vector< double > &x, Vector< double > &spine, Vector< Vector< double >> &dspine)
	Function pointer to "spine" function. More...

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

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

Public Member Functions
	YoungLaplaceEquations ()

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

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

virtual double	u (const unsigned &n) const

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

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output solution at nplot points in each coordinate direction. More...

void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output exact soln at n_plot^2 plot points. More...

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

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Get error against and norm of exact solution. More...

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Dummy, time dependent error checker. More...

Data *	kappa_pt ()

bool	use_spines () const

SpineBaseFctPt &	spine_base_fct_pt ()

SpineFctPt &	spine_fct_pt ()

void	set_kappa (Data *kappa_pt)
	Set curvature data (and add it to the element's external Data) More...

double	get_kappa () const
	Get curvature. More...

void	get_flux (const Vector< double > &s, Vector< double > &flux) const
	Get flux: flux[i] = du/dx_i: Mainly used for error estimation. More...

virtual void	get_spine_base (const Vector< double > &x, Vector< double > &spine_base, Vector< Vector< double >> &dspine_base) const

void	get_spine (const Vector< double > &x, Vector< double > &spine, Vector< Vector< double >> &dspine) const

void	position (const Vector< double > &s, Vector< double > &r) const
	Get position vector to meniscus at local coordinate s. More...

void	exact_position (const Vector< double > &s, Vector< double > &r, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Get exact position vector to meniscus at local coordinate s. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Add the element's contribution to its residual vector. More...

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

unsigned	self_test ()
	Self-test: Return 0 for OK. More...

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)

void	set_nodal_dimension (const unsigned &nodal_dim)

void	set_nnodal_position_type (const unsigned &nposition_type)
	Set the number of types required to interpolate the coordinate. More...

void	set_n_node (const unsigned &n)

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

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

virtual bool	local_coord_is_valid (const Vector< double > &s)
	Broken assignment operator. More...

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

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

MacroElement *	macro_elem_pt ()
	Access function to pointer to macro element. More...

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

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

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

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

virtual void	set_integration_scheme (Integral *const &integral_pt)
	Set the spatial integration scheme. More...

Integral *const &	integral_pt () const
	Return the pointer to the integration scheme (const version) More...

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

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

virtual void	node_update ()

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

virtual void	output (FILE *file_pt)

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

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

Static Public Member Functions
static void	allocate_vector_of_vectors (unsigned n_rows, unsigned n_cols, Vector< Vector< double >> &v)

static void	scalar_times_vector (const double &lambda, const Vector< double > &v, Vector< double > &lambda_times_v)
	Multiply a vector by a scalar. More...

static double	two_norm (const Vector< double > &v)
	2-norm of a vector More...

static double	scalar_product (const Vector< double > &v1, const Vector< double > &v2)
	Scalar product between two vectors. More...

static void	cross_product (const Vector< double > &v1, const Vector< double > &v2, Vector< double > &v_cross)
	Cross-product: v_cross= v1 x v2. More...

static void	vector_sum (const Vector< double > &v1, const Vector< double > &v2, Vector< double > &vs)
	Vectorial sum of two vectors. More...

Protected Member Functions
virtual int	u_local_eqn (const unsigned &n)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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
unsigned	Kappa_index
	Index of Kappa_pt in the element's storage of external Data. More...

SpineBaseFctPt	Spine_base_fct_pt
	Pointer to spine base function: More...

SpineFctPt	Spine_fct_pt
	Pointer to spine function: More...

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Private Attributes
Data *	Kappa_pt

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

Detailed Description

A class for all isoparametric elements that solve the YoungLaplace equations.

\[ div (\frac{1}{W} \nabla u) = \kappa \]

with

\[ W^2=1+\|\nabla u\|^2 \]

These equations can either be solved in the above (cartesian) form, or in a parametric representation using the method of spines. See the theory write-up in the documentation for details. This class contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class.

Member Typedef Documentation

◆ SpineBaseFctPt

typedef void(* oomph::YoungLaplaceEquations::SpineBaseFctPt) (const Vector< double > &x, Vector< double > &spine_base, Vector< Vector< double >> &dspine_base)

Function pointer to "spine base" function.

◆ SpineFctPt

typedef void(* oomph::YoungLaplaceEquations::SpineFctPt) (const Vector< double > &x, Vector< double > &spine, Vector< Vector< double >> &dspine)

Function pointer to "spine" function.

Constructor & Destructor Documentation

◆ YoungLaplaceEquations() [1/2]

oomph::YoungLaplaceEquations::YoungLaplaceEquations ( )

inline

Constructor: Initialise pointers to NULL, so by default prescribed kappa evaluates to zero, and no spines are used.

                             : Spine_base_fct_pt(0), Spine_fct_pt(0), Kappa_pt(0)
     {
     }

◆ YoungLaplaceEquations() [2/2]

oomph::YoungLaplaceEquations::YoungLaplaceEquations ( const YoungLaplaceEquations & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ allocate_vector_of_vectors()

static void oomph::YoungLaplaceEquations::allocate_vector_of_vectors	(	unsigned	n_rows,
		unsigned	n_cols,
		Vector< Vector< double >> &	v
	)

inlinestatic

Helper fct: Allocate storage for a vector of vectors of doubles to v(n_rows,n_cols) and initialise each component to 0.0.

     {
       v.resize(n_rows);
       for (unsigned i = 0; i < n_rows; i++)
       {
         v[i].resize(n_cols);
         for (unsigned j = 0; j < n_cols; j++)
         {
           v[i][j] = 0.0;
         }
       }
     }

References i, j, and v.

Referenced by exact_position(), oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), fill_in_contribution_to_residuals(), output(), and position().

◆ compute_error() [1/2]

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

virtual

Get error against and norm of exact solution.

Validate against exact solution

Solution is provided via function pointer. Plot error at a given number of plot points.

Calculate the cartesian coordinates of point on meniscus

Calculate the exact position

Reimplemented from oomph::FiniteElement.

   {
     // Initialise
     error = 0.0;
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Vector for coordinates
     Vector<double> x(2);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Tecplot
     outfile << "ZONE" << std::endl;
  
     // Exact solution Vector (here a scalar)
     Vector<double> exact_soln(1);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < 2; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       Vector<double> r(3, 0.0);
       position(s, r);
  
       Vector<double> r_exact(3, 0.0);
       exact_position(s, r_exact, exact_soln_pt);
  
       // Output x,y,...,error
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << r[i] << " ";
       }
  
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << r_exact[i] << " ";
       }
  
       outfile << std::endl;
  
       // Add to error and norm
       norm += 0.0;
       for (unsigned i = 0; i < 2; i++)
       {
         error += (r[i] - r_exact[i]) * (r[i] - r_exact[i]) * W;
       }
     }
   }

References calibrate::error, exact_position(), ProblemParameters::exact_soln(), i, oomph::FiniteElement::integral_pt(), J, oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), position(), UniformPSDSelfTest::r, s, w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and plotDoE::x.

◆ compute_error() [2/2]

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

inlinevirtual

Dummy, time dependent error checker.

Reimplemented from oomph::FiniteElement.

     {
       throw OomphLibError("These equations are steady => no time dependence",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ cross_product()

static void oomph::YoungLaplaceEquations::cross_product	(	const Vector< double > &	v1,
		const Vector< double > &	v2,
		Vector< double > &	v_cross
	)

inlinestatic

Cross-product: v_cross= v1 x v2.

     {
 #ifdef PARANOID
       if ((v1.size() != v2.size()) || (v1.size() != 3))
       {
         throw OomphLibError("Vectors must be of dimension 3 for cross-product!",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
       }
 #endif
       v_cross[0] = v1[1] * v2[2] - v1[2] * v2[1];
       v_cross[1] = v1[2] * v2[0] - v1[0] * v2[2];
       v_cross[2] = v1[0] * v2[1] - v1[1] * v2[0];
     }

References OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, v1(), and v2().

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), and fill_in_contribution_to_residuals().

◆ exact_position()

void oomph::YoungLaplaceEquations::exact_position	(	const Vector< double > &	s,
		Vector< double > &	r,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

Get exact position vector to meniscus at local coordinate s.

Get exact position vector to meniscus.

Get spines values

Global Eulerian cooordinates

   {
     // Get global coordinates
     Vector<double> x(2);
     interpolated_x(s, x);
  
     // Exact solution Vector (here a scalar)
     Vector<double> exact_soln(1);
  
     // Get exact solution at this point
     (*exact_soln_pt)(x, exact_soln);
  
     if (!use_spines())
     {
       r[0] = x[0];
       r[1] = x[1];
       r[2] = exact_soln[0];
     }
     else
     {
       Vector<double> spine_base(3, 0.0);
       Vector<double> spine(3, 0.0);
       Vector<Vector<double>> dspine_base;
       allocate_vector_of_vectors(2, 3, dspine_base);
       Vector<Vector<double>> dspine;
       allocate_vector_of_vectors(2, 3, dspine);
  
       get_spine_base(x, spine_base, dspine_base);
       get_spine(x, spine, dspine);
  
       for (unsigned j = 0; j < 3; j++)
       {
         r[j] = spine_base[j] + exact_soln[0] * spine[j];
       }
     }
   }

References allocate_vector_of_vectors(), ProblemParameters::exact_soln(), get_spine(), get_spine_base(), oomph::FiniteElement::interpolated_x(), j, UniformPSDSelfTest::r, s, use_spines(), and plotDoE::x.

Referenced by compute_error(), and output_fct().

◆ fill_in_contribution_to_residuals()

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

virtual

Add the element's contribution to its residual vector.

Compute element residual vector. Pure version without hanging nodes.

"Simple" case

Spine case

Get the unnormalized normal

Reimplemented from oomph::GeneralisedElement.

   {
     // Find out how many nodes there are
     unsigned n_node = nnode();
  
     // Set up memory for the shape functions
     Shape psi(n_node);
     DShape dpsidzeta(n_node, 2);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Integers to store the local equation numbers
     int local_eqn = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Call the derivatives of the shape and test functions
       double J = dshape_eulerian_at_knot(ipt, psi, dpsidzeta);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Calculate local values of displacement along spine and its derivatives
       // Allocate and initialise to zero
       double interpolated_u = 0.0;
       Vector<double> interpolated_zeta(2, 0.0);
       Vector<double> interpolated_dudzeta(2, 0.0);
  
       // Calculate function value and derivatives:
       //-----------------------------------------
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         interpolated_u += u(l) * psi(l);
         // Loop over directions
         for (unsigned j = 0; j < 2; j++)
         {
           interpolated_zeta[j] += nodal_position(l, j) * psi(l);
           interpolated_dudzeta[j] += u(l) * dpsidzeta(l, j);
         }
       }
  
  
       // Allocation and definition of variables necessary for
       // further calculations
  
       double nonlinearterm = 1.0;
       double sqnorm = 0.0;
  
  
       // Derivs of position vector w.r.t. global intrinsic coords
       Vector<Vector<double>> dRdzeta;
       allocate_vector_of_vectors(2, 3, dRdzeta);
  
       // Unnormalised normal
       Vector<double> N_unnormalised(3, 0.0);
  
       // Spine and spine basis vectors, entries initialised to zero
       Vector<double> spine_base(3, 0.0), spine(3, 0.0);
  
       // Derivative of spine basis vector w.r.t to the intrinsic
       // coordinates: dspine_base[i,j] = j-th component of the deriv.
       // of the spine basis vector w.r.t. to the i-th global intrinsic
       // coordinate
       Vector<Vector<double>> dspine_base;
       allocate_vector_of_vectors(2, 3, dspine_base);
  
       // Derivative of spine vector w.r.t to the intrinsic
       // coordinates: dspine[i,j] = j-th component of the deriv.
       // of the spine vector w.r.t. to the i-th global intrinsic
       // coordinate
       Vector<Vector<double>> dspine;
       allocate_vector_of_vectors(2, 3, dspine);
  
       // Vector v_\alpha contains the numerator of the variations of the
       // area element {\cal A}^{1/2} w.r.t. the components of dR/d\zeta_\alpha
       Vector<double> area_variation_numerator_0(3, 0.0);
       Vector<double> area_variation_numerator_1(3, 0.0);
  
       // Vector position
       Vector<double> r(3, 0.0);
  
       // No spines
       //---------
       if (!use_spines())
       {
         for (unsigned j = 0; j < 2; j++)
         {
           sqnorm += interpolated_dudzeta[j] * interpolated_dudzeta[j];
         }
         nonlinearterm = 1.0 / sqrt(1.0 + sqnorm);
       }
  
       // Spines
       //------
       else
       {
         // Get the spines
         get_spine_base(interpolated_zeta, spine_base, dspine_base);
         get_spine(interpolated_zeta, spine, dspine);
  
         // calculation of dR/d\zeta_\alpha
         for (unsigned alpha = 0; alpha < 2; alpha++)
         {
           // Product rule for d(u {\bf S} ) / d \zeta_\alpha
           Vector<double> dudzeta_times_spine(3, 0.0);
           scalar_times_vector(
             interpolated_dudzeta[alpha], spine, dudzeta_times_spine);
  
           Vector<double> u_times_dspinedzeta(3, 0.0);
           scalar_times_vector(
             interpolated_u, dspine[alpha], u_times_dspinedzeta);
  
           Vector<double> d_u_times_spine_dzeta(3, 0.0);
           vector_sum(
             dudzeta_times_spine, u_times_dspinedzeta, d_u_times_spine_dzeta);
  
           // Add derivative of spine base
           vector_sum(d_u_times_spine_dzeta, dspine_base[alpha], dRdzeta[alpha]);
         }
  
         cross_product(dRdzeta[0], dRdzeta[1], N_unnormalised);
  
         // Tmp storage
         Vector<double> v_tmp_1(3, 0.0);
         Vector<double> v_tmp_2(3, 0.0);
  
         // Calculation of
         // |dR/d\zeta_1|^2 dR/d\zeta_0 - <dR/d\zeta_0,dR/d\zeta_1>dR/d\zeta_1
         scalar_times_vector(pow(two_norm(dRdzeta[1]), 2), dRdzeta[0], v_tmp_1);
         scalar_times_vector(
           -1 * scalar_product(dRdzeta[0], dRdzeta[1]), dRdzeta[1], v_tmp_2);
         vector_sum(v_tmp_1, v_tmp_2, area_variation_numerator_0);
  
         // Calculation of
         // |dR/d\zeta_0|^2 dR/d\zeta_1 - <dR/d\zeta_0,dR/d\zeta_1>dR/d\zeta_0
         scalar_times_vector(pow(two_norm(dRdzeta[0]), 2), dRdzeta[1], v_tmp_1);
         scalar_times_vector(
           -1 * scalar_product(dRdzeta[0], dRdzeta[1]), dRdzeta[0], v_tmp_2);
         vector_sum(v_tmp_1, v_tmp_2, area_variation_numerator_1);
  
         // Global Eulerian cooordinates
         for (unsigned j = 0; j < 3; j++)
         {
           r[j] = spine_base[j] + interpolated_u * spine[j];
         }
       }
  
  
       // Assemble residuals
       //-------------------
  
       // Loop over the test (shape) functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the local equation
         local_eqn = u_local_eqn(l);
  
         /*IF it's not a boundary condition*/
         if (local_eqn >= 0)
         {
           // "simple" calculation case
           if (!use_spines())
           {
             // Add source term: The curvature
             residuals[local_eqn] += get_kappa() * psi(l) * W;
  
             // The YoungLaplace bit itself
             for (unsigned k = 0; k < 2; k++)
             {
               residuals[local_eqn] +=
                 nonlinearterm * interpolated_dudzeta[k] * dpsidzeta(l, k) * W;
             }
           }
  
           // Spine calculation case
           else
           {
             // Calculation of d(u S)/d\zeta_0
             //-------------------------------
             Vector<double> v_tmp_1(3, 0.0);
             scalar_times_vector(dpsidzeta(l, 0), spine, v_tmp_1);
  
             Vector<double> v_tmp_2(3, 0.0);
             scalar_times_vector(psi(l), dspine[0], v_tmp_2);
  
             Vector<double> d_uS_dzeta0(3, 0.0);
             vector_sum(v_tmp_1, v_tmp_2, d_uS_dzeta0);
  
             // Add contribution to residual
             residuals[local_eqn] +=
               W * scalar_product(area_variation_numerator_0, d_uS_dzeta0) /
               two_norm(N_unnormalised);
  
             // Calculation of d(u S)/d\zeta_1
             scalar_times_vector(dpsidzeta(l, 1), spine, v_tmp_1);
             scalar_times_vector(psi(l), dspine[1], v_tmp_2);
             Vector<double> d_uS_dzeta1(3, 0.0);
             vector_sum(v_tmp_1, v_tmp_2, d_uS_dzeta1);
  
             // Add contribution to residual
             residuals[local_eqn] +=
               W * scalar_product(area_variation_numerator_1, d_uS_dzeta1) /
               two_norm(N_unnormalised);
  
             // Curvature contribution to the residual : kappa N S test
             residuals[local_eqn] += W * (get_kappa()) *
                                     scalar_product(N_unnormalised, spine) *
                                     psi(l);
           }
         }
       }
  
     } // End of loop over integration points
   }

References allocate_vector_of_vectors(), alpha, cross_product(), oomph::FiniteElement::dshape_eulerian_at_knot(), get_kappa(), get_spine(), get_spine_base(), oomph::FiniteElement::integral_pt(), interpolated_u(), oomph::FiniteElement::interpolated_zeta(), J, j, k, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), oomph::Integral::nweight(), Eigen::bfloat16_impl::pow(), UniformPSDSelfTest::r, scalar_product(), scalar_times_vector(), sqrt(), two_norm(), u(), u_local_eqn(), use_spines(), vector_sum(), w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

◆ get_flux()

void oomph::YoungLaplaceEquations::get_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)		const

inline

Get flux: flux[i] = du/dx_i: Mainly used for error estimation.

     {
       // Find out how many nodes there are in the element
       unsigned n_node = nnode();
  
       // Set up memory for the shape (same as test functions)
       Shape psi(n_node);
       DShape dpsidx(n_node, 2);
  
       // Call the derivatives of the shape (same as test functions)
       dshape_eulerian(s, psi, dpsidx);
  
       // Initialise to zero
       for (unsigned j = 0; j < 2; j++)
       {
         flux[j] = 0.0;
       }
  
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over derivative directions
         for (unsigned j = 0; j < 2; j++)
         {
           flux[j] += u(l) * dpsidx(l, j);
         }
       }
     }

References oomph::FiniteElement::dshape_eulerian(), ProblemParameters::flux(), j, oomph::FiniteElement::nnode(), s, and u().

Referenced by oomph::RefineableYoungLaplaceEquations::get_Z2_flux().

◆ get_kappa()

double oomph::YoungLaplaceEquations::get_kappa ( ) const

inline

Get curvature.

No kappa has been set: return zero (the default)

     {
       if (Kappa_pt == 0)
       {
         return 0.0;
       }
       else
       {
         // Get prescribed kappa value
         return Kappa_pt->value(0);
       }
     }

References Kappa_pt, and oomph::Data::value().

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), and fill_in_contribution_to_residuals().

◆ get_spine()

void oomph::YoungLaplaceEquations::get_spine	(	const Vector< double > &	x,
		Vector< double > &	spine,
		Vector< Vector< double >> &	dspine
	)		const

inline

Get spine vector field: Defaults to standard cartesian representation if no spine base fct pointers have been set. dspine[i][j] = d spine[j] / dx_i

     {
       // If no spine function has been set, default to vertical spines
       // emanating from x[0](,x[1])
       if (Spine_fct_pt == 0)
       {
         // Initialise all to zero
         for (unsigned i = 0; i < 3; i++)
         {
           spine[i] = 0.0;
           for (unsigned j = 0; j < 2; j++)
           {
             dspine[i][j] = 0.0;
           }
         }
         // Overwrite vertical component
         spine[2] = 1.0;
       }
       else
       {
         // Get spine
         (*Spine_fct_pt)(x, spine, dspine);
       }
     }

References i, j, Spine_fct_pt, and plotDoE::x.

Referenced by exact_position(), oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), fill_in_contribution_to_residuals(), output(), and position().

◆ get_spine_base()

virtual void oomph::YoungLaplaceEquations::get_spine_base	(	const Vector< double > &	x,
		Vector< double > &	spine_base,
		Vector< Vector< double >> &	dspine_base
	)		const

inlinevirtual

Get spine base vector field: Defaults to standard cartesian representation if no spine base fct pointers have been set. dspine_B[i][j] = d spine_B[j] / dx_i

     {
       // If no spine function has been set, default to vertical spines
       // emanating from x[0](,x[1])
       if (Spine_base_fct_pt == 0)
       {
         for (unsigned i = 0; i < 3; i++)
         {
           spine_base[i] = x[i];
           for (unsigned j = 0; j < 2; j++)
           {
             dspine_base[i][j] = 0.0;
           }
         }
       }
       else
       {
         // Get spine
         (*Spine_base_fct_pt)(x, spine_base, dspine_base);
       }
     }

References i, j, Spine_base_fct_pt, and plotDoE::x.

Referenced by exact_position(), oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), fill_in_contribution_to_residuals(), output(), and position().

◆ interpolated_u()

double oomph::YoungLaplaceEquations::interpolated_u ( const Vector< double > & s ) const

inline

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

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

References oomph::FiniteElement::nnode(), s, oomph::FiniteElement::shape(), and u().

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), fill_in_contribution_to_residuals(), output(), and position().

◆ kappa_pt()

Data* oomph::YoungLaplaceEquations::kappa_pt ( )

inline

Access function: Pointer Data object that stores kappa (const version – kappa must be set with set_kappa() which also ensures that the Data object is added to the element's external Data.

     {
       return Kappa_pt;
     }

References Kappa_pt.

Referenced by oomph::RefineableYoungLaplaceEquations::further_build(), and set_kappa().

◆ operator=()

void oomph::YoungLaplaceEquations::operator= ( const YoungLaplaceEquations & )

delete

Broken assignment operator.

◆ output() [1/2]

void oomph::YoungLaplaceEquations::output ( std::ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QYoungLaplaceElement< NNODE_1D >.

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

Referenced by oomph::QYoungLaplaceElement< NNODE_1D >::output().

◆ output() [2/2]

void oomph::YoungLaplaceEquations::output	(	std::ostream &	outfile,
		const unsigned &	n_plot
	)

virtual

Output solution at nplot points in each coordinate direction.

Output FE representation of soln at n_plot^2 plot points

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QYoungLaplaceElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Compute intrinsic coordinates
       Vector<double> xx(2, 0.0);
       for (unsigned i = 0; i < 2; i++)
       {
         xx[i] = interpolated_x(s, i);
       }
  
       // Calculate the cartesian coordinates of point on meniscus
       Vector<double> r(3, 0.0);
  
       // Position
       if (use_spines())
       {
         position(s, r);
       }
       else
       {
         r[0] = xx[0];
         r[1] = xx[1];
         r[2] = interpolated_u(s);
       }
  
       // Output positon on meniscus
       for (unsigned i = 0; i < 3; i++)
       {
         outfile << r[i] << " ";
       }
  
       // Get spine stuff
       Vector<double> spine_base(3, 0.0), spine(3, 0.0);
       Vector<Vector<double>> dspine_base;
       allocate_vector_of_vectors(2, 3, dspine_base);
       Vector<Vector<double>> dspine;
       allocate_vector_of_vectors(2, 3, dspine);
  
       // Get the spines
       if (use_spines())
       {
         get_spine_base(xx, spine_base, dspine_base);
         get_spine(xx, spine, dspine);
       }
  
  
       // Output spine base
       for (unsigned i = 0; i < 3; i++)
       {
         outfile << spine_base[i] << " ";
       }
  
       // Output spines
       for (unsigned i = 0; i < 3; i++)
       {
         outfile << spine[i] << " ";
       }
  
  
       // Output intrinsic coordinates
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << xx[i] << " ";
       }
  
       // Output unknown
       outfile << interpolated_u(s) << " ";
  
  
       // Done
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References allocate_vector_of_vectors(), oomph::FiniteElement::get_s_plot(), get_spine(), get_spine_base(), i, interpolated_u(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), position(), UniformPSDSelfTest::r, s, oomph::FiniteElement::tecplot_zone_string(), use_spines(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output_fct() [1/2]

virtual void oomph::YoungLaplaceEquations::output_fct	(	std::ostream &	outfile,
		const unsigned &	n_plot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

Output exact soln at n_plot^2 plot points (dummy time-dependent version to keep intel compiler happy)

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QYoungLaplaceElement< NNODE_1D >.

     {
       throw OomphLibError("These equations are steady => no time dependence",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ output_fct() [2/2]

void oomph::YoungLaplaceEquations::output_fct	(	std::ostream &	outfile,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

virtual

Output exact soln at n_plot^2 plot points.

Output exact solution

Solution is provided via function pointer. Plot at a given number of plot points.

Calculate the cartesian coordinates of point on meniscus

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QYoungLaplaceElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Vector for coordinates
     Vector<double> x(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Exact solution Vector (here a scalar)
     Vector<double> exact_soln(1);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Get x position as Vector
       interpolated_x(s, x);
  
       Vector<double> r_exact(3, 0.0);
       exact_position(s, r_exact, exact_soln_pt);
  
       // Output x_exact,y_exact,z_exact
       for (unsigned i = 0; i < 3; i++)
       {
         outfile << r_exact[i] << " ";
       }
  
       // Done
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

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

Referenced by oomph::QYoungLaplaceElement< NNODE_1D >::output_fct().

◆ position()

void oomph::YoungLaplaceEquations::position	(	const Vector< double > &	s,
		Vector< double > &	r
	)		const

virtual

Get position vector to meniscus at local coordinate s.

Get position vector to meniscus.

Get spines values

Global Eulerian cooordinates

Reimplemented from oomph::FiniteElement.

   {
     // Get global coordinates
     Vector<double> x(2);
     interpolated_x(s, x);
  
     // Displacement along spine (or cartesian displacement)
     double u = interpolated_u(s);
  
     // cartesian calculation case
     if (!use_spines())
     {
       r[0] = x[0];
       r[1] = x[1];
       r[2] = u;
     }
     // spine case
     else
     {
       Vector<double> spine_base(3, 0.0);
       Vector<double> spine(3, 0.0);
       Vector<Vector<double>> dspine_base;
       allocate_vector_of_vectors(2, 3, dspine_base);
       Vector<Vector<double>> dspine;
       allocate_vector_of_vectors(2, 3, dspine);
  
       get_spine_base(x, spine_base, dspine_base);
       get_spine(x, spine, dspine);
  
       for (unsigned j = 0; j < 3; j++)
       {
         r[j] = spine_base[j] + u * spine[j];
       }
     }
   }

References allocate_vector_of_vectors(), get_spine(), get_spine_base(), interpolated_u(), oomph::FiniteElement::interpolated_x(), j, UniformPSDSelfTest::r, s, u(), use_spines(), and plotDoE::x.

Referenced by compute_error(), and output().

◆ scalar_product()

static double oomph::YoungLaplaceEquations::scalar_product	(	const Vector< double > &	v1,
		const Vector< double > &	v2
	)

inlinestatic

Scalar product between two vectors.

     {
       double scalar = 0.0;
       unsigned n = v1.size();
       for (unsigned i = 0; i < n; i++)
       {
         scalar += v1[i] * v2[i];
       }
       return scalar;
     }

References i, n, v1(), and v2().

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), and fill_in_contribution_to_residuals().

◆ scalar_times_vector()

static void oomph::YoungLaplaceEquations::scalar_times_vector	(	const double &	lambda,
		const Vector< double > &	v,
		Vector< double > &	lambda_times_v
	)

inlinestatic

Multiply a vector by a scalar.

     {
       unsigned n = v.size();
       for (unsigned i = 0; i < n; i++)
       {
         lambda_times_v[i] = lambda * v[i];
       }
     }

References i, lambda, n, and v.

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), and fill_in_contribution_to_residuals().

◆ self_test()

unsigned oomph::YoungLaplaceEquations::self_test ( )

virtual

Self-test: Return 0 for OK.

Reimplemented from oomph::FiniteElement.

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

References oomph::FiniteElement::self_test().

◆ set_kappa()

void oomph::YoungLaplaceEquations::set_kappa ( Data * kappa_pt )

inline

Set curvature data (and add it to the element's external Data)

     {
 #ifdef PARANOID
       if (kappa_pt->nvalue() != 1)
       {
         throw OomphLibError("kappa must only store a single value!",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Make a local copy
       Kappa_pt = kappa_pt;
  
       // Add to external data and store index in this storage scheme
       Kappa_index = add_external_data(kappa_pt);
     }

References oomph::GeneralisedElement::add_external_data(), Kappa_index, kappa_pt(), Kappa_pt, oomph::Data::nvalue(), OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

Referenced by oomph::RefineableYoungLaplaceEquations::further_build().

◆ spine_base_fct_pt()

SpineBaseFctPt& oomph::YoungLaplaceEquations::spine_base_fct_pt ( )

inline

Access function to function pointer that specifies spine base vector field

     {
       return Spine_base_fct_pt;
     }

References Spine_base_fct_pt.

Referenced by oomph::RefineableYoungLaplaceEquations::further_build().

◆ spine_fct_pt()

SpineFctPt& oomph::YoungLaplaceEquations::spine_fct_pt ( )

inline

Access function to function pointer that specifies spine vector field

     {
       return Spine_fct_pt;
     }

References Spine_fct_pt.

Referenced by oomph::RefineableYoungLaplaceEquations::further_build().

◆ two_norm()

static double oomph::YoungLaplaceEquations::two_norm ( const Vector< double > & v )

inlinestatic

2-norm of a vector

     {
       double norm = 0.0;
       unsigned n = v.size();
       for (unsigned i = 0; i < n; i++)
       {
         norm += v[i] * v[i];
       }
       return sqrt(norm);
     }

References i, n, sqrt(), and v.

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), and fill_in_contribution_to_residuals().

◆ u()

virtual double oomph::YoungLaplaceEquations::u ( const unsigned & n ) const

inlinevirtual

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

     {
       return nodal_value(n, 0);
     }

References n, and oomph::FiniteElement::nodal_value().

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), fill_in_contribution_to_residuals(), get_flux(), oomph::RefineableYoungLaplaceEquations::get_interpolated_values(), interpolated_u(), and position().

◆ u_local_eqn()

virtual int oomph::YoungLaplaceEquations::u_local_eqn ( const unsigned & n )

inlineprotectedvirtual

Get the local equation number of the (one and only) unknown stored at local node n (returns -1 if value is pinned). Can be overloaded in derived multiphysics elements.

     {
       return nodal_local_eqn(n, 0);
     }

References n, and oomph::FiniteElement::nodal_local_eqn().

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), and fill_in_contribution_to_residuals().

◆ use_spines()

bool oomph::YoungLaplaceEquations::use_spines ( ) const

inline

Use spines or not? (Based on availability of function pointers to to spine and spine base vector fields)

     {
       return (Spine_fct_pt != 0);
     }

References Spine_fct_pt.

Referenced by exact_position(), oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), fill_in_contribution_to_residuals(), output(), and position().

◆ vector_sum()

static void oomph::YoungLaplaceEquations::vector_sum	(	const Vector< double > &	v1,
		const Vector< double > &	v2,
		Vector< double > &	vs
	)

inlinestatic

Vectorial sum of two vectors.

     {
       unsigned n = v1.size();
       for (unsigned i = 0; i < n; i++)
       {
         vs[i] = v1[i] + v2[i];
       }
     }

References i, n, v1(), and v2().

Referenced by oomph::RefineableYoungLaplaceEquations::fill_in_contribution_to_residuals(), and fill_in_contribution_to_residuals().

Member Data Documentation

◆ Kappa_index

unsigned oomph::YoungLaplaceEquations::Kappa_index

protected

Index of Kappa_pt in the element's storage of external Data.

Referenced by set_kappa().

◆ Kappa_pt

Data* oomph::YoungLaplaceEquations::Kappa_pt

private

Pointer to Data item that stores kappa as its first value – private to ensure that it must be set with set_kappa(...) which adds the Data to the element's internal Data!

Referenced by get_kappa(), kappa_pt(), and set_kappa().

◆ Spine_base_fct_pt

SpineBaseFctPt oomph::YoungLaplaceEquations::Spine_base_fct_pt

protected

Pointer to spine base function:

Referenced by oomph::RefineableYoungLaplaceEquations::further_build(), get_spine_base(), and spine_base_fct_pt().

◆ Spine_fct_pt

SpineFctPt oomph::YoungLaplaceEquations::Spine_fct_pt

protected

Pointer to spine function:

Referenced by oomph::RefineableYoungLaplaceEquations::further_build(), get_spine(), spine_fct_pt(), and use_spines().

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ SpineBaseFctPt

◆ SpineFctPt

Constructor & Destructor Documentation

◆ YoungLaplaceEquations() [1/2]

◆ YoungLaplaceEquations() [2/2]

Member Function Documentation

◆ allocate_vector_of_vectors()

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ cross_product()

◆ exact_position()

◆ fill_in_contribution_to_residuals()

"Simple" case

Spine case

◆ get_flux()

◆ get_kappa()

◆ get_spine()

◆ get_spine_base()

◆ interpolated_u()

◆ kappa_pt()

◆ operator=()

◆ output() [1/2]

◆ output() [2/2]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ position()

◆ scalar_product()

◆ scalar_times_vector()

◆ self_test()

◆ set_kappa()

◆ spine_base_fct_pt()

◆ spine_fct_pt()

◆ two_norm()

◆ u()

◆ u_local_eqn()

◆ use_spines()

◆ vector_sum()

Member Data Documentation

◆ Kappa_index

◆ Kappa_pt

◆ Spine_base_fct_pt

◆ Spine_fct_pt