Inheritance diagram for GelfandBratuElement< NNODE_1D >:

Public Member Functions
	GelfandBratuElement ()

const double &	lambda () const

const double &	mu () const

double *&	lambda_pt ()

double *&	mu_pt ()

unsigned	required_nvalue (const unsigned &n) const
	For the Equation, only one value is stored at each node. More...

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

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

void	fill_in_generic_residual_contribution (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)

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

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

void	fill_in_generic_dresidual_contribution (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, unsigned flag)

void	output (ostream &output)

Public Member Functions inherited from oomph::QElement< 1, NNODE_1D >
	QElement ()
	Constructor. More...

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

void	shape (const Vector< double > &s, Shape &psi) const
	Broken assignment operator. More...

void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Derivatives of shape functions for specific QElement<1,..> More...

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

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

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

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

unsigned	nvertex_node () const
	Number of vertex nodes in the element. More...

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
	Get local coordinates of node j in the element; vector sets its own size. More...

void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
	Get the local fraction of node j in the element. More...

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

Node *	get_node_at_local_coordinate (const Vector< double > &s) const
	Get the node at the specified local coordinate. More...

unsigned	nnode_1d () const
	Number of nodes along each element edge. More...

unsigned	nplot_points_paraview (const unsigned &nplot) const

unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

unsigned	nplot_points (const unsigned &nplot) const

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

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...

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

Public Member Functions inherited from oomph::QElementBase
	QElementBase ()
	Constructor: Initialise pointers to macro element reference coords. More...

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

virtual	~QElementBase ()
	Broken assignment operator. More...

bool	local_coord_is_valid (const Vector< double > &s)
	Check whether the local coordinate are valid or not. More...

void	move_local_coord_back_into_element (Vector< double > &s) const

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

double &	s_macro_ll (const unsigned &i)

double &	s_macro_ur (const unsigned &i)

double	s_macro_ll (const unsigned &i) const

double	s_macro_ur (const unsigned &i) const

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

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

unsigned	nnode_on_face () const

ElementGeometry::ElementGeometry	element_geometry () const
	It's a Q element! More...

Public Member Functions inherited from oomph::QElementGeometricBase
	QElementGeometricBase ()
	Empty default constructor. More...

	QElementGeometricBase (const QElementGeometricBase &)=delete
	Broken copy constructor. 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...

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

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	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_at_knot (const unsigned &ipt, Shape &psi) const

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

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 ()

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 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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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)

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

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

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

Private Attributes
double *	Lambda_pt

double *	Mu_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

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

Constructor & Destructor Documentation

◆ GelfandBratuElement()

template<unsigned NNODE_1D>

GelfandBratuElement< NNODE_1D >::GelfandBratuElement ( )

inline

62 {}

Member Function Documentation

◆ fill_in_contribution_to_djacobian_dparameter()

template<unsigned NNODE_1D>

void GelfandBratuElement< NNODE_1D >::fill_in_contribution_to_djacobian_dparameter	(	double *const &	parameter_pt,
		Vector< double > &	dres_dparam,
		DenseMatrix< double > &	djac_dparam
	)

inlinevirtual

Add the element's contribution to the derivaives of its residual vector and element Jacobian matrix with respect to a parameter (wrapper)

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the generic routine with the flag set to 1
    fill_in_generic_dresidual_contribution(parameter_pt,
                                           dres_dparam,djac_dparam,1);
   }

◆ fill_in_contribution_to_dresiduals_dparameter()

template<unsigned NNODE_1D>

void GelfandBratuElement< NNODE_1D >::fill_in_contribution_to_dresiduals_dparameter	(	double *const &	parameter_pt,
		Vector< double > &	dres_dparam
	)

inlinevirtual

Add the element's contribution to the derivatives of its residual vector with respect to a parameter (wrapper)

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the generic residuals function with flag set to 0
    //using a dummy matrix argument
    fill_in_generic_dresidual_contribution(
     parameter_pt,dres_dparam,GeneralisedElement::Dummy_matrix,0);
   }

◆ fill_in_contribution_to_jacobian()

template<unsigned NNODE_1D>

void GelfandBratuElement< NNODE_1D >::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

Add the element's contribution to its residual vector and element Jacobian matrix (wrapper)

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the generic routine with the flag set to 1
    fill_in_generic_residual_contribution(residuals,jacobian,1);
   }

◆ fill_in_contribution_to_residuals()

template<unsigned NNODE_1D>

void GelfandBratuElement< NNODE_1D >::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

Add the element's contribution to its residual vector (wrapper)

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the generic residuals function with flag set to 0
    //using a dummy matrix argument
    fill_in_generic_residual_contribution(
     residuals,GeneralisedElement::Dummy_matrix,0);
   }

◆ fill_in_generic_dresidual_contribution()

template<unsigned NNODE_1D>

void GelfandBratuElement< NNODE_1D >::fill_in_generic_dresidual_contribution	(	double *const &	parameter_pt,
		Vector< double > &	dres_dparam,
		DenseMatrix< double > &	djac_dparam,
		unsigned	flag
	)

inline

Calculate the elemental contributions to the derivatives of the global residual vector and jacobian for the weak form of the Gelfand-Bratu equation with respect to the passed parameter.

   {
    //There are only two parameters, if it's not either of them, then
    //die
    if((parameter_pt!=Lambda_pt) && (parameter_pt!=Mu_pt))
     {
      std::ostringstream error_stream;
      error_stream << 
       "Cannot compute analytic jacobian for parameter addressed by " 
                   << parameter_pt << "\n";
      error_stream << "Can only compute derivatives wrt lambda ("
                   << Lambda_pt << ") or mu (" << Mu_pt << ")\n";
      throw OomphLibError(
       error_stream.str(),
       OOMPH_CURRENT_FUNCTION,
       OOMPH_EXCEPTION_LOCATION);
     }
  
    //Find the number of nodes in the element
    unsigned n_node = this->nnode();
    
    //Allocate memory for shape functions and their derivatives:
    // There's one shape function for each node:
    Shape psi(n_node);
    // Each of the n_node shape functions has one derivative with 
    // respect to the single local coordinate:
    DShape dpsidx(n_node,1);
    
    //Get the value of the parameter
    double lam = lambda();
    double m = mu();
  
     //Find the number of integration points in the underlying 
     //geometric element's integration scheme 
     unsigned n_intpt = this->integral_pt()->nweight();
     //Loop over the integration points
     for(unsigned ipt=0;ipt<n_intpt;ipt++)
      {
       //Set the value of the local coordinate to be the integration 
       //scheme's knot point
       //Find the weight of the integration scheme at this knot point
       double w = this->integral_pt()->weight(ipt);
       //Find the shape functions and their derivatives at the knot point. 
       //This function is implemented in FiniteElement.
       //It also returns the Jacobian of the mapping from local to 
       //global coordinates.
       double J = this->dshape_eulerian_at_knot(ipt,psi,dpsidx);
       //Premultiply the weight and the Jacobian
       double W = w*J;
       
       //Allocate storage for the value of the field variable u,
       //its derivative and the global position at the knot point.
       //Initialise them all to zero.
       double interpolated_u=0.0, interpolated_dudx=0.0;
       //Calculate the interpolated values by  looping over the shape 
       //functions and summing the appropriate contributions
       for(unsigned n=0;n<n_node;n++) 
        {
         double value = this->nodal_value(n,0);
         interpolated_u += value*psi[n];
         interpolated_dudx += value*dpsidx(n,0);
        }
    
       //Get the derivative of the source function with respect to the 
       //parameter
       double source = exp(interpolated_u);
  
       //If the parameter is lambda
       if(parameter_pt==Lambda_pt) {source *= 2.0*lam;} 
       //Only other possibility is mu 
       else {source *= 2.0*m;}
    
       //ASSEMBLE THE DERIVATIVE OF THE RESIDUALS
       
       //Loop over the test functions (same as the shape functions
       //since we're implementing an isoparametric element)
       for(unsigned l=0;l<n_node;l++)
        {
         //Get the local equation number
         //The variable is the first (only) value stored at the nodes
         int local_eqn_number = this->nodal_local_eqn(l,0);
         //If the equation is not a Dirichlet boundary condition
         if(local_eqn_number >= 0)
          {
           //Add body force/source term here 
           dres_dparam[local_eqn_number] -= source*psi[l]*W;
  
           //If we are doing the jacobian terms
           if(flag)
            {
             for(unsigned l2=0;l2<n_node;l2++)
              {
               int local_unknown = this->nodal_local_eqn(l2,0);
               if(local_unknown >= 0)
                {
                 djac_dparam(local_eqn_number,local_unknown) -=
                  source*psi[l2]*psi[l]*W;
                }
              }
            }
          }
        }
      } //End of loop over the integration points
    } //End of function

References Eigen::bfloat16_impl::exp(), J, lambda, Global_Physical_Variables::Lambda_pt, m, Global_Parameters::mu, Global_Physical_Variables::Mu_pt, n, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, TestProblem::source(), Eigen::value, w, and oomph::QuadTreeNames::W.

◆ fill_in_generic_residual_contribution()

template<unsigned NNODE_1D>

void GelfandBratuElement< NNODE_1D >::fill_in_generic_residual_contribution	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		unsigned	flag
	)

inline

Calculate the elemental contributions to the global residual vector for the weak form of the Gelfand-Bratu equation

   {
     //Find the number of nodes in the element
     unsigned n_node = this->nnode();
  
     //Allocate memory for shape functions and their derivatives:
     // There's one shape function for each node:
     Shape psi(n_node);
     // Each of the n_node shape functions has one derivative with 
     // respect to the single local coordinate:
     DShape dpsidx(n_node,1);
  
     //Get the value of the parameter
     double lam = lambda();
     double m = mu();
  
     //Find the number of integration points in the underlying 
     //geometric element's integration scheme 
     unsigned n_intpt = this->integral_pt()->nweight();
     //Loop over the integration points
     for(unsigned ipt=0;ipt<n_intpt;ipt++)
      {
       //Set the value of the local coordinate to be the integration 
       //scheme's knot point
       //Find the weight of the integration scheme at this knot point
       double w = this->integral_pt()->weight(ipt);
       //Find the shape functions and their derivatives at the knot point. 
       //This function is implemented in FiniteElement.
       //It also returns the Jacobian of the mapping from local to 
       //global coordinates.
       double J = this->dshape_eulerian_at_knot(ipt,psi,dpsidx);
       //Premultiply the weight and the Jacobian
       double W = w*J;
       
       //Allocate storage for the value of the field variable u,
       //its derivative and the global position at the knot point.
       //Initialise them all to zero.
       double interpolated_u=0.0, interpolated_dudx=0.0;
       //Calculate the interpolated values by  looping over the shape 
       //functions and summing the appropriate contributions
       for(unsigned n=0;n<n_node;n++) 
        {
         double value = this->nodal_value(n,0);
         interpolated_u += value*psi[n];
         interpolated_dudx += value*dpsidx(n,0);
        }
    
       //Get the source function
       double source = (lam*lam + m*m)*exp(interpolated_u);
    
       //ASSEMBLE THE RESIDUALS
       
       //Loop over the test functions (same as the shape functions
       //since we're implementing an isoparametric element)
       for(unsigned l=0;l<n_node;l++)
        {
         //Get the local equation number
         //The variable is the first (only) value stored at the nodes
         int local_eqn_number = this->nodal_local_eqn(l,0);
         //If the equation is not a Dirichlet boundary condition
         if(local_eqn_number >= 0)
          {
           //Add body force/source term here 
           residuals[local_eqn_number] -= source*psi[l]*W;
           //Add the Poisson bit itself
           residuals[local_eqn_number] += interpolated_dudx*dpsidx(l,0)*W;
  
           //If we are doing the jacobian terms
           if(flag)
            {
             for(unsigned l2=0;l2<n_node;l2++)
              {
               int local_unknown = this->nodal_local_eqn(l2,0);
               if(local_unknown >= 0)
                {
                 jacobian(local_eqn_number,local_unknown) -=
                  source*psi[l2]*psi[l]*W;
                 jacobian(local_eqn_number,local_unknown) +=
                  dpsidx(l2,0)*dpsidx(l,0)*W;
                }
              }
            }
          }
        }
      } //End of loop over the integration points
    } //End of function

References Eigen::bfloat16_impl::exp(), J, lambda, m, Global_Parameters::mu, n, TestProblem::source(), Eigen::value, w, and oomph::QuadTreeNames::W.

◆ lambda()

template<unsigned NNODE_1D>

const double& GelfandBratuElement< NNODE_1D >::lambda ( ) const

inline

65 {return *Lambda_pt;}

References Global_Physical_Variables::Lambda_pt.

◆ lambda_pt()

template<unsigned NNODE_1D>

double* & GelfandBratuElement< NNODE_1D >::lambda_pt ( )

inline

70 {return Lambda_pt;}

References Global_Physical_Variables::Lambda_pt.

◆ mu()

template<unsigned NNODE_1D>

const double& GelfandBratuElement< NNODE_1D >::mu ( ) const

inline

67 {return *Mu_pt;}

References Global_Physical_Variables::Mu_pt.

◆ mu_pt()

template<unsigned NNODE_1D>

double* & GelfandBratuElement< NNODE_1D >::mu_pt ( )

inline

72 {return Mu_pt;}

References Global_Physical_Variables::Mu_pt.

◆ output()

template<unsigned NNODE_1D>

void GelfandBratuElement< NNODE_1D >::output ( ostream & outfile )

inlinevirtual

Output the element data — typically the values at the nodes in a format suitable for post-processing.

Reimplemented from oomph::FiniteElement.

    {
     //Read out the number of nodes in the element   
     unsigned n_node = this->nnode();
     //Loop over the nodes and print out the global coordinate 
     //and value of the field variable, u, at each node
     for(unsigned n=0;n<n_node;n++)
      {
       output << this->nodal_position(n,0) << " " 
              << this->nodal_value(n,0) << std::endl;
      }
    } //End of function

References n, and output().

◆ required_nvalue()

template<unsigned NNODE_1D>

unsigned GelfandBratuElement< NNODE_1D >::required_nvalue ( const unsigned & n ) const

inlinevirtual

For the Equation, only one value is stored at each node.

Reimplemented from oomph::FiniteElement.

75 {return 1;}

Member Data Documentation

◆ Lambda_pt

template<unsigned NNODE_1D>

double* GelfandBratuElement< NNODE_1D >::Lambda_pt

private

◆ Mu_pt

template<unsigned NNODE_1D>

double* GelfandBratuElement< NNODE_1D >::Mu_pt

private

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

fold.cc

Public Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ GelfandBratuElement()

Member Function Documentation

◆ fill_in_contribution_to_djacobian_dparameter()

◆ fill_in_contribution_to_dresiduals_dparameter()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_dresidual_contribution()

◆ fill_in_generic_residual_contribution()

◆ lambda()

◆ lambda_pt()

◆ mu()

◆ mu_pt()

◆ output()

◆ required_nvalue()

Member Data Documentation

◆ Lambda_pt

◆ Mu_pt