Inheritance diagram for ModalPoissonEquations< DIM >:

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

typedef void(*	PoissonDiffFctPt) (const Vector< double > &x, double &f)
	Function pointer to a diffusion function fxt(x,f(x)) More...

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

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

Public Member Functions
	ModalPoissonEquations ()
	Constructor (must initialise the Source_fct_pt to null) More...

virtual double	u (const unsigned &n) const =0

virtual unsigned	nbasis () const =0
	Number of basis functions. More...

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

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

void	output (ostream &outfile, const unsigned &nplot)

void	output_fct (ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output exact soln: x,y,u_exact or x,y,z,u_exact at nplot^DIM plot points. More...

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

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

void	compute_error (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...

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

PoissonDiffFctPt &	diff_fct_pt ()
	Access function: Pointer to diffusivity function. More...

PoissonDiffFctPt	diff_fct_pt () const
	Access function: Pointer to source function. Const version. More...

virtual void	get_diff (const Vector< double > &x, double &diff) const

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

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

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

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

void	position (const 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

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

virtual void	output (FILE *file_pt)

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

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

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

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

	GeomObject (const unsigned &ndim)

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

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

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

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

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

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

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

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

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

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

Protected Attributes
PoissonSourceFctPt	Source_fct_pt
	Pointer to source function: More...

PoissonDiffFctPt	Diff_fct_pt
	Pointer to the diffusivity function. More...

Vector< int >	Local_eqn
	Array to hold local eqn numbers: Local_eqn[n] (=-1 for BC) 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 ModalPoissonEquations< DIM >

A class for all 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

◆ PoissonDiffFctPt

template<unsigned DIM>

typedef void(* ModalPoissonEquations< DIM >::PoissonDiffFctPt) (const Vector< double > &x, double &f)

Function pointer to a diffusion function fxt(x,f(x))

◆ PoissonSourceFctPt

template<unsigned DIM>

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

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

Constructor & Destructor Documentation

◆ ModalPoissonEquations()

template<unsigned DIM>

ModalPoissonEquations< DIM >::ModalPoissonEquations ( )

inline

Constructor (must initialise the Source_fct_pt to null)

101 : Source_fct_pt(0), Diff_fct_pt(0) {}

ModalPoissonEquations::Source_fct_pt

PoissonSourceFctPt Source_fct_pt

Pointer to source function:

Definition: one_d_poisson_hp_adapt.cc:680

ModalPoissonEquations::Diff_fct_pt

PoissonDiffFctPt Diff_fct_pt

Pointer to the diffusivity function.

Definition: one_d_poisson_hp_adapt.cc:683

Member Function Documentation

◆ add_generic_residual_contribution()

template<unsigned DIM>

virtual void ModalPoissonEquations< DIM >::add_generic_residual_contribution	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		unsigned	flag
	)

inlineprotectedvirtual

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

   {
    //Find out how many nodes there are
    unsigned n_node = nnode();
    //Find out the total number of basis and test functions there are
    unsigned n_basis = nbasis();
    
    //Set up memory for the shape and test functions
    Shape psi(n_node), basis(n_basis), test(n_basis);
    DShape dpsidx(n_node,DIM), dbasisdx(n_basis,DIM), dtestdx(n_basis,DIM);
  
    //Set the value of n_intpt
    unsigned n_intpt = integral_pt()->nweight();
    
    //Set the Vector to hold local coordinates
    Vector<double> s(DIM);
    
    //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++)
     {
      //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);
      
      //Call the derivatives of the shape and test functions
      double J = dshape_dbasis_and_dtest_eulerian_at_knot(ipt,
                                                          psi,dpsidx,
                                                          basis,dbasisdx,
                                                          test,dtestdx);
      
      //Premultiply the weights and the Jacobian
      double W = w*J;
  
      //Calculate local values of the pressure and velocity components
      //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++) 
       {
        // Loop over directions
        for(unsigned j=0;j<DIM;j++)
         {
          interpolated_x[j] += nodal_position(l,j)*psi[l];
         }
       }
  
  
      for(unsigned l=0;l<n_basis;l++)
       {
        interpolated_u += u(l)*basis[l];
        for(unsigned j=0;j<DIM;j++)
         {
          interpolated_dudx[j] += u(l)*dbasisdx(l,j);
         }
       }
  
      //Get source function
      //-------------------
      double source;
      get_source_poisson(interpolated_x,source);
  
      //Get the diffusivity
      double diff;
      get_diff(interpolated_x,diff);
      
      // Assemble residuals and Jacobian
      //--------------------------------
        
      // Loop over the test functions
      for(unsigned l=0;l<n_basis;l++)
       {
        //Get the local equation
        local_eqn = Local_eqn[l];
        //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] += diff*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_basis;l2++)
             { 
              local_unknown = Local_eqn[l2];
              //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) 
                   += diff*dbasisdx(l2,i)*dtestdx(l,i)*W;
                 }
               }
             }
           }
         }
       }
      
     } // End of loop over integration points
    
   }

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

◆ basis()

template<unsigned DIM>

virtual void ModalPoissonEquations< DIM >::basis	(	const Vector< double > &	s,
		Shape &	basis
	)		const

pure virtual

Implemented in ModalPRefineableQPoissonElement< DIM >.

◆ compute_error() [1/2]

template<unsigned DIM>

void ModalPoissonEquations< DIM >::compute_error	(	ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		double &	error,
		double &	norm
	)

inline

Get error against and norm of exact solution.

   {
  
    // Initialise
    error=0.0;
    norm=0.0;
  
    //Vector of local coordinates
    Vector<double> s(DIM);
  
    // Vector for coordintes
    Vector<double> x(DIM);
    
    //Set the value of n_intpt
    unsigned n_intpt = integral_pt()->nweight();
    
    // Setup output structure: Conversion is fishy but it's only output...
    unsigned nplot;
    if (DIM==1)
     {
      nplot=n_intpt;
     }
    else 
     {
      nplot=unsigned(pow(n_intpt,1.0/double(DIM)));
     }
    
    // Tecplot header info
    outfile << tecplot_zone_string(nplot);
    
    // 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(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, ProblemParameters::exact_soln(), i, J, Eigen::bfloat16_impl::pow(), s, w, oomph::QuadTreeNames::W, and plotDoE::x.

Referenced by ModalPRefineableQPoissonElement< DIM >::compute_error().

◆ compute_error() [2/2]

template<unsigned DIM>

void ModalPoissonEquations< DIM >::compute_error	(	ostream &	outfile,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt,
		const double &	time,
		double &	error,
		double &	norm
	)

inline

Dummy, time dependent error checker.

   {
    oomph_info << "No time-dep. compute_error() for Poisson elements " << std::endl;
    exit(1);
   }

References oomph::oomph_info.

◆ diff_fct_pt() [1/2]

template<unsigned DIM>

PoissonDiffFctPt& ModalPoissonEquations< DIM >::diff_fct_pt ( )

inline

Access function: Pointer to diffusivity function.

   {
    return Diff_fct_pt;
   }

References oomph::Diff_fct_pt.

◆ diff_fct_pt() [2/2]

template<unsigned DIM>

PoissonDiffFctPt ModalPoissonEquations< DIM >::diff_fct_pt ( ) const

inline

Access function: Pointer to source function. Const version.

   {
    return Diff_fct_pt;
   }

References oomph::Diff_fct_pt.

◆ dshape_dbasis_and_dtest_eulerian()

template<unsigned DIM>

virtual double ModalPoissonEquations< DIM >::dshape_dbasis_and_dtest_eulerian	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	basis,
		DShape &	dbasisdx,
		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 ModalPRefineableQPoissonElement< DIM >.

◆ dshape_dbasis_and_dtest_eulerian_at_knot()

template<unsigned DIM>

virtual double ModalPoissonEquations< DIM >::dshape_dbasis_and_dtest_eulerian_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	basis,
		DShape &	dbasisdx,
		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 ModalPRefineableQPoissonElement< DIM >.

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

void ModalPoissonEquations< 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::GeneralisedElement.

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

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

Referenced by ModalPRefineableQPoissonElement< DIM >::fill_in_contribution_to_jacobian().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

void ModalPoissonEquations< DIM >::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

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

Reimplemented from oomph::GeneralisedElement.

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

   {
    //Create a dummy matrix
    DenseMatrix<double> dummy(1);
  
    //Call the generic residuals function with flag set to 0
    add_generic_residual_contribution(residuals,dummy,0);
   }

Referenced by ModalPRefineableQPoissonElement< DIM >::fill_in_contribution_to_residuals().

◆ get_diff()

template<unsigned DIM>

virtual void ModalPoissonEquations< DIM >::get_diff	(	const Vector< double > &	x,
		double &	diff
	)		const

inlinevirtual

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

   {
    //If no source function has been set, return one
    if(Diff_fct_pt==0) {diff = 1.0;}
    else
     {
      // Get source strength
      (*Diff_fct_pt)(x,diff);
     }
   }

References oomph::Diff_fct_pt, and plotDoE::x.

◆ get_flux()

template<unsigned DIM>

void ModalPoissonEquations< DIM >::get_flux	(	const Vector< double > &	s,
		Vector< double > &	flux,
		unsigned	p_order
	)		const

inline

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

   {
    //Find out how many nodes there are
    unsigned n_node = nnode();
    //Find out the total number of basis and test functions there are
    unsigned n_basis = nbasis();
    
    //Set up memory for the shape and test functions
    Shape psi(n_node), basis(n_basis), test(n_basis);
    DShape dpsidx(n_node,DIM), dbasisdx(n_basis,DIM), dtestdx(n_basis,DIM);
    
    //Call the derivatives of the shape and test functions
    //dshape_eulerian(s,psi,dpsidx);
    dshape_dbasis_and_dtest_eulerian(s, psi, dpsidx, basis, dbasisdx, test, dtestdx);
      
    //Initialise to zero
    for(unsigned j=0;j<DIM;j++)
     {
      flux[j] = 0.0;
     }
    
    // Loop over modes
    for(unsigned l=0;l<p_order;l++) 
     {
      //Loop over derivative directions
      for(unsigned j=0;j<DIM;j++)
       {
        //flux[j] += u(l)*dpsidx(l,j);
        flux[j] += u(l)*dbasisdx(l,j);
       }
     }
   }

References DIM, ProblemParameters::flux(), j, s, and Eigen::test.

Referenced by ModalPRefineableQPoissonElement< DIM >::compute_energy_error().

◆ get_source_poisson()

template<unsigned DIM>

virtual void ModalPoissonEquations< DIM >::get_source_poisson	(	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::Source_fct_pt, and plotDoE::x.

◆ interpolated_u()

template<unsigned DIM>

double ModalPoissonEquations< DIM >::interpolated_u ( const Vector< double > & s ) const

inline

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

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

References s.

◆ nbasis()

template<unsigned DIM>

virtual unsigned ModalPoissonEquations< DIM >::nbasis ( ) const

pure virtual

Number of basis functions.

Implemented in ModalPRefineableQPoissonElement< DIM >.

◆ output() [1/2]

template<unsigned DIM>

void ModalPoissonEquations< DIM >::output ( ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

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

References output().

Referenced by ModalPRefineableQPoissonElement< DIM >::output().

◆ output() [2/2]

template<unsigned DIM>

void ModalPoissonEquations< DIM >::output	(	ostream &	outfile,
		const unsigned &	nplot
	)

inlinevirtual

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

Reimplemented from oomph::FiniteElement.

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

   {
    //Vector of local coordinates
    Vector<double> s(DIM);
    
    //Find out how many nodes there are
    unsigned n_node = nnode();
    //Find out the total number of basis and test functions there are
    unsigned n_basis = nbasis();
    
    //Set up memory for the shape and test functions
    Shape psi(n_node), basis(n_basis), test(n_basis);
    DShape dpsidx(n_node,DIM), dbasisdx(n_basis,DIM), dtestdx(n_basis,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);
  
      //get_basis(s,basis);
      dshape_dbasis_and_dtest_eulerian(s,psi,dpsidx,basis,
                                       dbasisdx,test,dtestdx);
  
      for(unsigned i=0;i<DIM;i++) 
       {outfile << interpolated_x(s,i) << " ";}
      
      outfile << interpolated_u(s) << std::endl;   
     }
  
   }

References DIM, i, s, and Eigen::test.

◆ output_fct() [1/2]

template<unsigned DIM>

virtual void ModalPoissonEquations< DIM >::output_fct	(	ostream &	outfile,
		const unsigned &	nplot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

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

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

   {
  
    oomph_info << "No time-dep. output_fct() for Poisson elements " << std::endl;
    exit(1);
   }

References oomph::oomph_info.

◆ output_fct() [2/2]

template<unsigned DIM>

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

inline

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

   {
  
    //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;  
     
     }
   }

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

Referenced by ModalPRefineableQPoissonElement< DIM >::output_fct().

◆ self_test()

template<unsigned DIM>

unsigned ModalPoissonEquations< DIM >::self_test ( )

inlinevirtual

Self-test: Return 0 for OK.

Reimplemented from oomph::FiniteElement.

Reimplemented in ModalPRefineableQPoissonElement< DIM >.

529 {return 0;}

Referenced by ModalPRefineableQPoissonElement< DIM >::self_test().

◆ source_fct_pt() [1/2]

template<unsigned DIM>

PoissonSourceFctPt& ModalPoissonEquations< DIM >::source_fct_pt ( )

inline

Access function: Pointer to source function.

   {
    return Source_fct_pt;
   }

References oomph::Source_fct_pt.

Referenced by ModalPRefineableQPoissonElement< DIM >::source_fct_pt().

◆ source_fct_pt() [2/2]

template<unsigned DIM>

PoissonSourceFctPt ModalPoissonEquations< DIM >::source_fct_pt ( ) const

inline

Access function: Pointer to source function. Const version.

   {
    return Source_fct_pt;
   }

References oomph::Source_fct_pt.

◆ u()

template<unsigned DIM>

virtual double ModalPoissonEquations< DIM >::u ( const unsigned & n ) const

pure virtual

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

Implemented in ModalPRefineableQPoissonElement< DIM >.

Member Data Documentation

◆ Diff_fct_pt

template<unsigned DIM>

PoissonDiffFctPt ModalPoissonEquations< DIM >::Diff_fct_pt

protected

Pointer to the diffusivity function.

◆ Local_eqn

template<unsigned DIM>

Vector<int> ModalPoissonEquations< DIM >::Local_eqn

protected

Array to hold local eqn numbers: Local_eqn[n] (=-1 for BC)

◆ Source_fct_pt

template<unsigned DIM>

PoissonSourceFctPt ModalPoissonEquations< DIM >::Source_fct_pt

protected

Pointer to source function:

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

one_d_poisson_hp_adapt.cc

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

template<unsigned DIM> class ModalPoissonEquations< DIM >

Member Typedef Documentation

◆ PoissonDiffFctPt

◆ PoissonSourceFctPt

Constructor & Destructor Documentation

◆ ModalPoissonEquations()

Member Function Documentation

◆ add_generic_residual_contribution()

◆ basis()

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ diff_fct_pt() [1/2]

◆ diff_fct_pt() [2/2]

◆ dshape_dbasis_and_dtest_eulerian()

◆ dshape_dbasis_and_dtest_eulerian_at_knot()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ get_diff()

◆ get_flux()

◆ get_source_poisson()

◆ interpolated_u()

◆ nbasis()

◆ output() [1/2]

◆ output() [2/2]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ self_test()

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ u()

Member Data Documentation

◆ Diff_fct_pt

◆ Local_eqn

◆ Source_fct_pt

template<unsigned DIM>
class ModalPoissonEquations< DIM >