#include <poisson_elements.h>

Inheritance diagram for oomph::PoissonEquations< DIM >:

Public Types
typedef void(*	PoissonSourceFctPt) (const Vector< double > &x, double &f)

typedef void(*	PoissonSourceFctGradientPt) (const Vector< double > &x, Vector< double > &gradient)

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
	PoissonEquations ()
	Constructor (must initialise the Source_fct_pt to null) More...

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

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

virtual unsigned	u_index_poisson () const

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

unsigned	nscalar_paraview () const

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

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

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

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

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

void	output (FILE *file_pt)
	C_style output with default number of plot points. More...

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

void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)

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

void	compute_norm (double &norm)
	Compute norm of solution: square of the L2 norm. More...

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...

PoissonSourceFctPt &	source_fct_pt ()
	Access function: Pointer to source function. More...

PoissonSourceFctPt	source_fct_pt () const
	Access function: Pointer to source function. Const version. More...

PoissonSourceFctGradientPt &	source_fct_gradient_pt ()
	Access function: Pointer to gradient of source function. More...

PoissonSourceFctGradientPt	source_fct_gradient_pt () const
	Access function: Pointer to gradient source function. Const version. More...

virtual void	get_source_poisson (const unsigned &ipt, const Vector< double > &x, double &source) const

virtual void	get_source_gradient_poisson (const unsigned &ipt, const Vector< double > &x, Vector< double > &gradient) const

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

void	get_dflux_dnodal_u (const Vector< double > &s, Vector< Vector< double >> &dflux_dnodal_u) const

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)

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

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	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual 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

Protected Member Functions
virtual double	dshape_and_dtest_eulerian_poisson (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

virtual double	dshape_and_dtest_eulerian_at_knot_poisson (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

virtual double	dshape_and_dtest_eulerian_at_knot_poisson (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const =0

virtual void	fill_in_generic_residual_contribution_poisson (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

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)

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
PoissonSourceFctPt	Source_fct_pt
	Pointer to source function: More...

PoissonSourceFctGradientPt	Source_fct_gradient_pt
	Pointer to gradient of source 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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

Detailed Description

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

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

\[ \frac{\partial^2 u}{\partial x_i^2} = f(x_j) \]

This contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class.

Member Typedef Documentation

◆ PoissonSourceFctGradientPt

template<unsigned DIM>

typedef void(* oomph::PoissonEquations< DIM >::PoissonSourceFctGradientPt) (const Vector< double > &x, Vector< double > &gradient)

Function pointer to gradient of source function fct(x,g(x)) – x is a Vector!

◆ PoissonSourceFctPt

template<unsigned DIM>

typedef void(* oomph::PoissonEquations< DIM >::PoissonSourceFctPt) (const Vector< double > &x, double &f)

Function pointer to source function fct(x,f(x)) – x is a Vector!

Constructor & Destructor Documentation

◆ PoissonEquations() [1/2]

template<unsigned DIM>

oomph::PoissonEquations< DIM >::PoissonEquations ( )

inline

Constructor (must initialise the Source_fct_pt to null)

70 : Source_fct_pt(0), Source_fct_gradient_pt(0) {}

oomph::PoissonEquations::Source_fct_pt

PoissonSourceFctPt Source_fct_pt

Pointer to source function:

Definition: poisson_elements.h:523

oomph::PoissonEquations::Source_fct_gradient_pt

PoissonSourceFctGradientPt Source_fct_gradient_pt

Pointer to gradient of source function.

Definition: poisson_elements.h:526

◆ PoissonEquations() [2/2]

template<unsigned DIM>

oomph::PoissonEquations< DIM >::PoissonEquations ( const PoissonEquations< DIM > & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ compute_error() [1/2]

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::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.

Reimplemented from oomph::FiniteElement.

   {
     // Initialise
     error = 0.0;
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Vector for coordintes
     Vector<double> x(DIM);
  
     // Find out how many nodes there are in the element
     unsigned n_node = nnode();
  
     Shape psi(n_node);
  
     // 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 < DIM; 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;
  
       // Get x position as Vector
       interpolated_x(s, x);
  
       // Get FE function value
       double u_fe = interpolated_u_poisson(s);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Output x,y,...,error
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << x[i] << " ";
       }
       outfile << exact_soln[0] << " " << exact_soln[0] - u_fe << std::endl;
  
       // Add to error and norm
       norm += exact_soln[0] * exact_soln[0] * W;
       error += (exact_soln[0] - u_fe) * (exact_soln[0] - u_fe) * W;
     }
   }

References DIM, calibrate::error, s, and plotDoE::x.

◆ compute_error() [2/2]

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::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(
         "There is no time-dependent compute_error() for Poisson elements",
         OOMPH_CURRENT_FUNCTION,
         OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ compute_norm()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::compute_norm ( double & norm )

virtual

Compute norm of solution: square of the L2 norm.

Compute norm of the solution.

Reimplemented from oomph::GeneralisedElement.

   {
     // Initialise
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Solution
     double u = 0.0;
  
     // Find out how many nodes there are in the element
     unsigned n_node = this->nnode();
  
     Shape psi(n_node);
  
     // Set the value of n_intpt
     unsigned n_intpt = this->integral_pt()->nweight();
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < DIM; i++)
       {
         s[i] = this->integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = this->integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = this->J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get FE function value
       u = this->interpolated_u_poisson(s);
  
       // Add to  norm
       norm += u * u * W;
     }
   }

References DIM, i, and s.

◆ dshape_and_dtest_eulerian_at_knot_poisson() [1/2]

template<unsigned DIM>

virtual double oomph::PoissonEquations< DIM >::dshape_and_dtest_eulerian_at_knot_poisson	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		RankFourTensor< double > &	d_dpsidx_dX,
		Shape &	test,
		DShape &	dtestdx,
		RankFourTensor< double > &	d_dtestdx_dX,
		DenseMatrix< double > &	djacobian_dX
	)		const

protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping (J). Also compute derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.

Implemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

◆ dshape_and_dtest_eulerian_at_knot_poisson() [2/2]

template<unsigned DIM>

virtual double oomph::PoissonEquations< DIM >::dshape_and_dtest_eulerian_at_knot_poisson	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping

Implemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

◆ dshape_and_dtest_eulerian_poisson()

template<unsigned DIM>

virtual double oomph::PoissonEquations< DIM >::dshape_and_dtest_eulerian_poisson	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at local coord. s; return Jacobian of mapping

Implemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::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::FiniteElement.

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

References oomph::PoissonEquations< DIM >::fill_in_generic_residual_contribution_poisson().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::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_poisson(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::PoissonEquations< DIM >::fill_in_generic_residual_contribution_poisson().

◆ fill_in_generic_residual_contribution_poisson()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::fill_in_generic_residual_contribution_poisson	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

protectedvirtual

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

Compute element residual Vector and/or element Jacobian matrix

flag=1: compute both flag=0: compute only residual Vector

Pure version without hanging nodes

Reimplemented in oomph::RefineablePoissonEquations< DIM >.

   {
     // Find out how many nodes there are
     const unsigned n_node = nnode();
  
     // Set up memory for the shape and test functions
     Shape psi(n_node), test(n_node);
     DShape dpsidx(n_node, DIM), dtestdx(n_node, DIM);
  
     // Index at which the poisson unknown is stored
     const unsigned u_nodal_index = u_index_poisson();
  
     // Set the value of n_intpt
     const unsigned n_intpt = integral_pt()->nweight();
  
     // Integers to store the local equation and unknown numbers
     int local_eqn = 0, local_unknown = 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_and_dtest_eulerian_at_knot_poisson(
         ipt, psi, dpsidx, test, dtestdx);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Calculate local values of unknown
       // Allocate and initialise to zero
       double interpolated_u = 0.0;
       Vector<double> interpolated_x(DIM, 0.0);
       Vector<double> interpolated_dudx(DIM, 0.0);
  
       // Calculate function value and derivatives:
       //-----------------------------------------
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the nodal value of the poisson unknown
         double u_value = raw_nodal_value(l, u_nodal_index);
         interpolated_u += u_value * psi(l);
         // Loop over directions
         for (unsigned j = 0; j < DIM; j++)
         {
           interpolated_x[j] += raw_nodal_position(l, j) * psi(l);
           interpolated_dudx[j] += u_value * dpsidx(l, j);
         }
       }
  
  
       // Get source function
       //-------------------
       double source;
       get_source_poisson(ipt, interpolated_x, source);
  
       // Assemble residuals and Jacobian
       //--------------------------------
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the local equation
         local_eqn = nodal_local_eqn(l, u_nodal_index);
         // IF it's not a boundary condition
         if (local_eqn >= 0)
         {
           // Add body force/source term here
           residuals[local_eqn] += source * test(l) * W;
  
           // The Poisson bit itself
           for (unsigned k = 0; k < DIM; k++)
           {
             residuals[local_eqn] += interpolated_dudx[k] * dtestdx(l, k) * W;
           }
  
           // Calculate the jacobian
           //-----------------------
           if (flag)
           {
             // Loop over the velocity shape functions again
             for (unsigned l2 = 0; l2 < n_node; l2++)
             {
               local_unknown = nodal_local_eqn(l2, u_nodal_index);
               // If at a non-zero degree of freedom add in the entry
               if (local_unknown >= 0)
               {
                 // Add contribution to Elemental Matrix
                 for (unsigned i = 0; i < DIM; i++)
                 {
                   jacobian(local_eqn, local_unknown) +=
                     dpsidx(l2, i) * dtestdx(l, i) * W;
                 }
               }
             }
           }
         }
       }
  
     } // End of loop over integration points
   }

References DIM, i, J, j, k, TestProblem::source(), Eigen::test, w, and oomph::QuadTreeNames::W.

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

◆ get_dflux_dnodal_u()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::get_dflux_dnodal_u	(	const Vector< double > &	s,
		Vector< Vector< double >> &	dflux_dnodal_u
	)		const

inline

Get derivative of flux w.r.t. to nodal values: dflux_dnodal_u[i][j] = d ( du/dx_i ) / dU_j

     {
       // Find out how many nodes there are in the element
       const unsigned n_node = nnode();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node);
       DShape dpsidx(n_node, DIM);
  
       // Call the derivatives of the shape and test functions
       dshape_eulerian(s, psi, dpsidx);
  
       // And here it is...
       for (unsigned i = 0; i < DIM; i++)
       {
         for (unsigned j = 0; j < n_node; j++)
         {
           dflux_dnodal_u[i][j] = dpsidx(j, i);
         }
       }
     }

References DIM, oomph::FiniteElement::dshape_eulerian(), i, j, oomph::FiniteElement::nnode(), and s.

◆ get_dresidual_dnodal_coordinates()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::get_dresidual_dnodal_coordinates ( RankThreeTensor< double > & dresidual_dnodal_coordinates )

virtual

Compute derivatives of elemental residual vector with respect to nodal coordinates. Overwrites default implementation in FiniteElement base class. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij}

Compute derivatives of elemental residual vector with respect to nodal coordinates (fully analytical). dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij} Overloads the FD-based version in the FE base class.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::RefineablePoissonEquations< DIM >, and ModalPRefineableQPoissonElement< DIM >.

   {
     // Determine number of nodes in element
     const unsigned n_node = nnode();
  
     // Set up memory for the shape and test functions
     Shape psi(n_node), test(n_node);
     DShape dpsidx(n_node, DIM), dtestdx(n_node, DIM);
  
     // Deriatives of shape fct derivatives w.r.t. nodal coords
     RankFourTensor<double> d_dpsidx_dX(DIM, n_node, n_node, DIM);
     RankFourTensor<double> d_dtestdx_dX(DIM, n_node, n_node, DIM);
  
     // Derivative of Jacobian of mapping w.r.t. to nodal coords
     DenseMatrix<double> dJ_dX(DIM, n_node);
  
     // Derivatives of derivative of u w.r.t. nodal coords
     RankThreeTensor<double> d_dudx_dX(DIM, n_node, DIM);
  
     // Source function and its gradient
     double source;
     Vector<double> d_source_dx(DIM);
  
     // Index at which the poisson unknown is stored
     const unsigned u_nodal_index = u_index_poisson();
  
     // Determine the number of integration points
     const unsigned n_intpt = integral_pt()->nweight();
  
     // Integer to store the local equation number
     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/test functions, as well as the
       // derivatives of these w.r.t. nodal coordinates and the derivative
       // of the jacobian of the mapping w.r.t. nodal coordinates
       const double J = dshape_and_dtest_eulerian_at_knot_poisson(
         ipt, psi, dpsidx, d_dpsidx_dX, test, dtestdx, d_dtestdx_dX, dJ_dX);
  
       // Calculate local values
       // Allocate and initialise to zero
       Vector<double> interpolated_x(DIM, 0.0);
       Vector<double> interpolated_dudx(DIM, 0.0);
  
       // Calculate function value and derivatives:
       // -----------------------------------------
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the nodal value of the Poisson unknown
         double u_value = raw_nodal_value(l, u_nodal_index);
  
         // Loop over directions
         for (unsigned i = 0; i < DIM; i++)
         {
           interpolated_x[i] += raw_nodal_position(l, i) * psi(l);
           interpolated_dudx[i] += u_value * dpsidx(l, i);
         }
       }
  
       // Calculate derivative of du/dx_i w.r.t. nodal positions X_{pq}
       for (unsigned q = 0; q < n_node; q++)
       {
         // Loop over coordinate directions
         for (unsigned p = 0; p < DIM; p++)
         {
           for (unsigned i = 0; i < DIM; i++)
           {
             double aux = 0.0;
             for (unsigned j = 0; j < n_node; j++)
             {
               aux +=
                 raw_nodal_value(j, u_nodal_index) * d_dpsidx_dX(p, q, j, i);
             }
             d_dudx_dX(p, q, i) = aux;
           }
         }
       }
  
       // Get source function
       get_source_poisson(ipt, interpolated_x, source);
  
       // Get gradient of source function
       get_source_gradient_poisson(ipt, interpolated_x, d_source_dx);
  
       // Assemble d res_{local_eqn} / d X_{pq}
       // -------------------------------------
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the local equation
         local_eqn = nodal_local_eqn(l, u_nodal_index);
  
         // IF it's not a boundary condition
         if (local_eqn >= 0)
         {
           // Loop over coordinate directions
           for (unsigned p = 0; p < DIM; p++)
           {
             // Loop over nodes
             for (unsigned q = 0; q < n_node; q++)
             {
               double sum = source * test(l) * dJ_dX(p, q) +
                            d_source_dx[p] * test(l) * psi(q) * J;
  
               for (unsigned i = 0; i < DIM; i++)
               {
                 sum += interpolated_dudx[i] * (dtestdx(l, i) * dJ_dX(p, q) +
                                                d_dtestdx_dX(p, q, l, i) * J) +
                        d_dudx_dX(p, q, i) * dtestdx(l, i) * J;
               }
  
               // Multiply through by integration weight
               dresidual_dnodal_coordinates(local_eqn, p, q) += sum * w;
             }
           }
         }
       }
     } // End of loop over integration points
   }

References DIM, J, TestProblem::source(), Eigen::test, and w.

◆ get_flux()

template<unsigned DIM>

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

inline

Get flux: flux[i] = du/dx_i.

     {
       // Find out how many nodes there are in the element
       const unsigned n_node = nnode();
  
       // Get the index at which the unknown is stored
       const unsigned u_nodal_index = u_index_poisson();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node);
       DShape dpsidx(n_node, DIM);
  
       // Call the derivatives of the shape and test functions
       dshape_eulerian(s, psi, dpsidx);
  
       // Initialise to zero
       for (unsigned j = 0; j < DIM; 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 < DIM; j++)
         {
           flux[j] += this->nodal_value(l, u_nodal_index) * dpsidx(l, j);
         }
       }
     }

References DIM, oomph::FiniteElement::dshape_eulerian(), ProblemParameters::flux(), j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, and oomph::PoissonEquations< DIM >::u_index_poisson().

Referenced by oomph::PRefineableQPoissonElement< DIM >::compute_energy_error(), oomph::RefineablePoissonEquations< DIM >::get_Z2_flux(), and oomph::TPoissonElement< DIM, NNODE_1D >::get_Z2_flux().

◆ get_source_gradient_poisson()

template<unsigned DIM>

virtual void oomph::PoissonEquations< DIM >::get_source_gradient_poisson	(	const unsigned &	ipt,
		const Vector< double > &	x,
		Vector< double > &	gradient
	)		const

inlinevirtual

Get gradient of source term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. Computed via function pointer (if set) or by finite differencing (default)

     {
       // If no gradient function has been set, FD it
       if (Source_fct_gradient_pt == 0)
       {
         // Reference value
         double source = 0.0;
         get_source_poisson(ipt, x, source);
  
         // FD it
         double eps_fd = GeneralisedElement::Default_fd_jacobian_step;
         double source_pls = 0.0;
         Vector<double> x_pls(x);
         for (unsigned i = 0; i < DIM; i++)
         {
           x_pls[i] += eps_fd;
           get_source_poisson(ipt, x_pls, source_pls);
           gradient[i] = (source_pls - source) / eps_fd;
           x_pls[i] = x[i];
         }
       }
       else
       {
         // Get gradient
         (*Source_fct_gradient_pt)(x, gradient);
       }
     }

References oomph::GeneralisedElement::Default_fd_jacobian_step, DIM, oomph::PoissonEquations< DIM >::get_source_poisson(), i, TestProblem::source(), oomph::PoissonEquations< DIM >::Source_fct_gradient_pt, and plotDoE::x.

◆ get_source_poisson()

template<unsigned DIM>

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

inlinevirtual

Get source term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations.

     {
       // If no source function has been set, return zero
       if (Source_fct_pt == 0)
       {
         source = 0.0;
       }
       else
       {
         // Get source strength
         (*Source_fct_pt)(x, source);
       }
     }

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

Referenced by oomph::PoissonEquations< DIM >::get_source_gradient_poisson().

◆ interpolated_u_poisson()

template<unsigned DIM>

virtual double oomph::PoissonEquations< DIM >::interpolated_u_poisson ( const Vector< double > & s ) const

inlinevirtual

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

     {
       // Find number of nodes
       const unsigned n_node = nnode();
  
       // Get the index at which the poisson unknown is stored
       const unsigned u_nodal_index = u_index_poisson();
  
       // 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 += this->nodal_value(l, u_nodal_index) * psi[l];
       }
  
       return (interpolated_u);
     }

References oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and oomph::PoissonEquations< DIM >::u_index_poisson().

Referenced by oomph::PoissonEquations< DIM >::point_output_data(), and oomph::PoissonEquations< DIM >::scalar_value_paraview().

◆ nscalar_paraview()

template<unsigned DIM>

unsigned oomph::PoissonEquations< DIM >::nscalar_paraview ( ) const

inlinevirtual

Number of scalars/fields output by this element. Reimplements broken virtual function in base class.

Reimplemented from oomph::FiniteElement.

     {
       return 1;
     }

◆ operator=()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::operator= ( const PoissonEquations< DIM > & )

delete

Broken assignment operator.

◆ output() [1/4]

template<unsigned DIM>

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

inlinevirtual

C_style output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

     {
       const unsigned n_plot = 5;
       output(file_pt, n_plot);
     }

References oomph::PoissonEquations< DIM >::output().

◆ output() [2/4]

template<unsigned DIM>

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

virtual

C-style output FE representation of soln: x,y,u or x,y,z,u at n_plot^DIM plot points

C-style output function:

x,y,u or x,y,z,u

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Tecplot header info
     fprintf(file_pt, "%s", tecplot_zone_string(nplot).c_str());
  
     // 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);
  
       for (unsigned i = 0; i < DIM; i++)
       {
         fprintf(file_pt, "%g ", interpolated_x(s, i));
       }
       fprintf(file_pt, "%g \n", interpolated_u_poisson(s));
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(file_pt, nplot);
   }

References DIM, i, and s.

◆ output() [3/4]

template<unsigned DIM>

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

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

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

Referenced by oomph::PoissonEquations< DIM >::output(), oomph::QPoissonElement< DIM, NNODE_1D >::output(), oomph::QSpectralPoissonElement< DIM, NNODE_1D >::output(), and oomph::TPoissonElement< DIM, NNODE_1D >::output().

◆ output() [4/4]

template<unsigned DIM>

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

virtual

Output FE representation of soln: x,y,u or x,y,z,u at n_plot^DIM plot points

Output function:

x,y,u or x,y,z,u

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // 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);
  
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << interpolated_x(s, i) << " ";
       }
       outfile << interpolated_u_poisson(s) << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, i, and s.

◆ output_fct() [1/2]

template<unsigned DIM>

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

inlinevirtual

Output exact soln: x,y,u_exact or x,y,z,u_exact at n_plot^DIM plot points (dummy time-dependent version to keep intel compiler happy)

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

     {
       throw OomphLibError(
         "There is no time-dependent output_fct() for Poisson elements ",
         OOMPH_CURRENT_FUNCTION,
         OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ output_fct() [2/2]

template<unsigned DIM>

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

virtual

Output exact soln: x,y,u_exact or x,y,z,u_exact at n_plot^DIM plot points

Output exact solution

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

x,y,u_exact or x,y,z,u_exact

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TPoissonElement< DIM, NNODE_1D >, oomph::QSpectralPoissonElement< DIM, NNODE_1D >, oomph::QPoissonElement< DIM, NNODE_1D >, and oomph::QPoissonElement< DIM, 2 >.

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Vector for coordintes
     Vector<double> x(DIM);
  
     // 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);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Output x,y,...,u_exact
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << x[i] << " ";
       }
       outfile << exact_soln[0] << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, ProblemParameters::exact_soln(), i, s, and plotDoE::x.

Referenced by oomph::QPoissonElement< DIM, NNODE_1D >::output_fct(), oomph::QSpectralPoissonElement< DIM, NNODE_1D >::output_fct(), and oomph::TPoissonElement< DIM, NNODE_1D >::output_fct().

◆ point_output_data()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::point_output_data	(	const Vector< double > &	s,
		Vector< double > &	data
	)

inlinevirtual

Output solution in data vector at local cordinates s: x,y [,z], u

Reimplemented from oomph::FiniteElement.

     {
       // Dimension
       unsigned dim = s.size();
  
       // Resize data for values
       data.resize(dim + 1);
  
       // Write values in the vector
       for (unsigned i = 0; i < dim; i++)
       {
         data[i] = interpolated_x(s, i);
       }
       data[dim] = this->interpolated_u_poisson(s);
     }

References data, oomph::FiniteElement::dim(), i, oomph::PoissonEquations< DIM >::interpolated_u_poisson(), oomph::FiniteElement::interpolated_x(), and s.

◆ scalar_name_paraview()

template<unsigned DIM>

std::string oomph::PoissonEquations< DIM >::scalar_name_paraview ( const unsigned & i ) const

inlinevirtual

Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names in specific elements.

Reimplemented from oomph::FiniteElement.

     {
 #ifdef PARANOID
       if (i != 0)
       {
         std::stringstream error_stream;
         error_stream
           << "Poisson elements only store a single field so i must be 0 rather"
           << " than " << i << std::endl;
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       return "Poisson solution";
     }

References i, OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ scalar_value_fct_paraview()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::scalar_value_fct_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type.

Reimplemented from oomph::FiniteElement.

     {
 #ifdef PARANOID
       if (i != 0)
       {
         std::stringstream error_stream;
         error_stream << "Poisson equation has only one field. Can't call "
                      << "this function for value " << i << std::endl;
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Vector of local coordinates
       Vector<double> s(DIM);
  
       // Vector for coordinates
       Vector<double> x(DIM);
  
       // Exact solution Vector
       Vector<double> exact_soln(1);
  
       // Loop over plot points
       unsigned num_plot_points = nplot_points_paraview(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);
  
         // Get exact solution at this point
         (*exact_soln_pt)(x, exact_soln);
  
         // Write it
         file_out << exact_soln[0] << std::endl;
       }
     }

References DIM, ProblemParameters::exact_soln(), oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points_paraview(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, s, and plotDoE::x.

◆ scalar_value_paraview()

template<unsigned DIM>

void oomph::PoissonEquations< DIM >::scalar_value_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type.

Reimplemented from oomph::FiniteElement.

     {
 #ifdef PARANOID
       if (i != 0)
       {
         std::stringstream error_stream;
         error_stream
           << "Poisson elements only store a single field so i must be 0 rather"
           << " than " << i << std::endl;
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       unsigned local_loop = this->nplot_points_paraview(nplot);
       for (unsigned j = 0; j < local_loop; j++)
       {
         // Get the local coordinate of the required plot point
         Vector<double> s(DIM);
         this->get_s_plot(j, nplot, s);
  
         file_out << this->interpolated_u_poisson(s) << std::endl;
       }
     }

References DIM, oomph::FiniteElement::get_s_plot(), i, oomph::PoissonEquations< DIM >::interpolated_u_poisson(), j, oomph::FiniteElement::nplot_points_paraview(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

◆ self_test()

template<unsigned DIM>

unsigned oomph::PoissonEquations< DIM >::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().

◆ source_fct_gradient_pt() [1/2]

template<unsigned DIM>

PoissonSourceFctGradientPt& oomph::PoissonEquations< DIM >::source_fct_gradient_pt ( )

inline

Access function: Pointer to gradient of source function.

     {
       return Source_fct_gradient_pt;
     }

References oomph::PoissonEquations< DIM >::Source_fct_gradient_pt.

◆ source_fct_gradient_pt() [2/2]

template<unsigned DIM>

PoissonSourceFctGradientPt oomph::PoissonEquations< DIM >::source_fct_gradient_pt ( ) const

inline

Access function: Pointer to gradient source function. Const version.

     {
       return Source_fct_gradient_pt;
     }

References oomph::PoissonEquations< DIM >::Source_fct_gradient_pt.

◆ source_fct_pt() [1/2]

template<unsigned DIM>

PoissonSourceFctPt& oomph::PoissonEquations< DIM >::source_fct_pt ( )

inline

Access function: Pointer to source function.

     {
       return Source_fct_pt;
     }

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

Referenced by oomph::RefineablePoissonEquations< DIM >::further_build().

◆ source_fct_pt() [2/2]

template<unsigned DIM>

PoissonSourceFctPt oomph::PoissonEquations< DIM >::source_fct_pt ( ) const

inline

Access function: Pointer to source function. Const version.

     {
       return Source_fct_pt;
     }

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

◆ u_index_poisson()

template<unsigned DIM>

virtual unsigned oomph::PoissonEquations< DIM >::u_index_poisson ( ) const

inlinevirtual

Return the index at which the unknown value is stored. The default value, 0, is appropriate for single-physics problems, when there is only one variable, the value that satisfies the poisson equation. In derived multi-physics elements, this function should be overloaded to reflect the chosen storage scheme. Note that these equations require that the unknown is always stored at the same index at each node.

     {
       return 0;
     }

Referenced by oomph::PoissonEquations< DIM >::get_flux(), oomph::RefineablePoissonEquations< DIM >::get_interpolated_values(), oomph::PoissonEquations< DIM >::interpolated_u_poisson(), and oomph::PoissonFluxElement< ELEMENT >::PoissonFluxElement().

Member Data Documentation

◆ Source_fct_gradient_pt

template<unsigned DIM>

PoissonSourceFctGradientPt oomph::PoissonEquations< DIM >::Source_fct_gradient_pt

protected

Pointer to gradient of source function.

Referenced by oomph::PoissonEquations< DIM >::get_source_gradient_poisson(), and oomph::PoissonEquations< DIM >::source_fct_gradient_pt().

◆ Source_fct_pt

template<unsigned DIM>

PoissonSourceFctPt oomph::PoissonEquations< DIM >::Source_fct_pt

protected

Pointer to source function:

Referenced by oomph::RefineablePoissonEquations< DIM >::further_build(), oomph::PoissonEquations< DIM >::get_source_poisson(), and oomph::PoissonEquations< DIM >::source_fct_pt().

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

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

◆ PoissonSourceFctGradientPt

◆ PoissonSourceFctPt

Constructor & Destructor Documentation

◆ PoissonEquations() [1/2]

◆ PoissonEquations() [2/2]

Member Function Documentation

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ compute_norm()

◆ dshape_and_dtest_eulerian_at_knot_poisson() [1/2]

◆ dshape_and_dtest_eulerian_at_knot_poisson() [2/2]

◆ dshape_and_dtest_eulerian_poisson()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_poisson()

◆ get_dflux_dnodal_u()

◆ get_dresidual_dnodal_coordinates()

◆ get_flux()

◆ get_source_gradient_poisson()

◆ get_source_poisson()

◆ interpolated_u_poisson()

◆ nscalar_paraview()

◆ operator=()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ point_output_data()

◆ scalar_name_paraview()

◆ scalar_value_fct_paraview()

◆ scalar_value_paraview()

◆ self_test()

◆ source_fct_gradient_pt() [1/2]

◆ source_fct_gradient_pt() [2/2]

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ u_index_poisson()

Member Data Documentation

◆ Source_fct_gradient_pt

◆ Source_fct_pt

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