#include <fourier_decomposed_helmholtz_elements.h>

Inheritance diagram for oomph::FourierDecomposedHelmholtzEquations:

Public Types
typedef void(*	FourierDecomposedHelmholtzSourceFctPt) (const Vector< double > &x, std::complex< double > &f)

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
	FourierDecomposedHelmholtzEquations ()
	Constructor. More...

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

virtual std::complex< unsigned >	u_index_fourier_decomposed_helmholtz () const
	Broken assignment operator. More...

double *&	k_squared_pt ()
	Get pointer to square of wavenumber. More...

double	k_squared ()
	Get the square of wavenumber. More...

int *&	fourier_wavenumber_pt ()
	Get pointer to Fourier wavenumber. More...

int	fourier_wavenumber ()
	Get the Fourier wavenumber. More...

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

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

void	output_real (std::ostream &outfile, const double &phi, 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	output_real_fct (std::ostream &outfile, const double &phi, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)

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

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

void	compute_norm (double &norm)
	Compute norm of fe solution. More...

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

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

virtual void	get_source_fourier_decomposed_helmholtz (const unsigned &ipt, const Vector< double > &x, std::complex< double > &source) const

void	get_flux (const Vector< double > &s, Vector< std::complex< double >> &flux) const
	Get flux: flux[i] = du/dx_i for real and imag part. 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)

std::complex< double >	interpolated_u_fourier_decomposed_helmholtz (const Vector< double > &s) const

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_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_fourier_decomposed_helmholtz (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

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

virtual void	fill_in_generic_residual_contribution_fourier_decomposed_helmholtz (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)

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
FourierDecomposedHelmholtzSourceFctPt	Source_fct_pt
	Pointer to source function: More...

double *	K_squared_pt
	Pointer to square of wavenumber. More...

int *	N_fourier_pt
	Pointer to Fourier wave number. 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

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// A class for all isoparametric elements that solve the Helmholtz equations.

\[ \nabla^2 U + k^2 U = f \]

in Fourier decomposed form (cylindrical polars):

\[ U(r,\varphi,z) = \Re( u^{(n)}(r,z) \exp(-i n \varphi)) \]

We are solving for \( u^{(n)}(r,z)\) for given parameters \( k^2 \) and \( n \) . This contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class.

Member Typedef Documentation

◆ FourierDecomposedHelmholtzSourceFctPt

typedef void(* oomph::FourierDecomposedHelmholtzEquations::FourierDecomposedHelmholtzSourceFctPt) (const Vector< double > &x, std::complex< double > &f)

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

Constructor & Destructor Documentation

◆ FourierDecomposedHelmholtzEquations() [1/2]

oomph::FourierDecomposedHelmholtzEquations::FourierDecomposedHelmholtzEquations ( )

inline

Constructor.

       : Source_fct_pt(0), K_squared_pt(0), N_fourier_pt(0)
     {
     }

◆ FourierDecomposedHelmholtzEquations() [2/2]

oomph::FourierDecomposedHelmholtzEquations::FourierDecomposedHelmholtzEquations ( const FourierDecomposedHelmholtzEquations & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ compute_error() [1/2]

void oomph::FourierDecomposedHelmholtzEquations::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(2);
  
     // Vector for coordintes
     Vector<double> x(2);
  
     // 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
     Vector<double> exact_soln(2);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < 2; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get x position as Vector
       interpolated_x(s, x);
  
       // Get FE function value
       std::complex<double> u_fe =
         interpolated_u_fourier_decomposed_helmholtz(s);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Output r,z,error
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << x[i] << " ";
       }
       outfile << exact_soln[0] << " " << exact_soln[1] << " "
               << exact_soln[0] - u_fe.real() << " "
               << exact_soln[1] - u_fe.imag() << std::endl;
  
       // Add to error and norm
       norm +=
         (exact_soln[0] * exact_soln[0] + exact_soln[1] * exact_soln[1]) * W;
       error += ((exact_soln[0] - u_fe.real()) * (exact_soln[0] - u_fe.real()) +
                 (exact_soln[1] - u_fe.imag()) * (exact_soln[1] - u_fe.imag())) *
                W;
     }
   }

References calibrate::error, ProblemParameters::exact_soln(), i, oomph::FiniteElement::integral_pt(), interpolated_u_fourier_decomposed_helmholtz(), oomph::FiniteElement::interpolated_x(), J, oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::FiniteElement::nnode(), oomph::Integral::nweight(), s, w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and plotDoE::x.

◆ compute_error() [2/2]

void oomph::FourierDecomposedHelmholtzEquations::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 "
                           "FourierDecomposedHelmholtz elements",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ compute_norm()

void oomph::FourierDecomposedHelmholtzEquations::compute_norm ( double & norm )

virtual

Compute norm of fe solution.

Reimplemented from oomph::GeneralisedElement.

   {
     // Initialise
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Vector for coordintes
     Vector<double> x(2);
  
     // 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();
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < 2; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get FE function value
       std::complex<double> u_fe =
         interpolated_u_fourier_decomposed_helmholtz(s);
  
       // Add to  norm
       norm += (u_fe.real() * u_fe.real() + u_fe.imag() * u_fe.imag()) * W;
     }
   }

References i, oomph::FiniteElement::integral_pt(), interpolated_u_fourier_decomposed_helmholtz(), J, oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::FiniteElement::nnode(), oomph::Integral::nweight(), s, w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and plotDoE::x.

◆ dshape_and_dtest_eulerian_at_knot_fourier_decomposed_helmholtz()

virtual double oomph::FourierDecomposedHelmholtzEquations::dshape_and_dtest_eulerian_at_knot_fourier_decomposed_helmholtz	(	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::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

Referenced by fill_in_generic_residual_contribution_fourier_decomposed_helmholtz().

◆ dshape_and_dtest_eulerian_fourier_decomposed_helmholtz()

virtual double oomph::FourierDecomposedHelmholtzEquations::dshape_and_dtest_eulerian_fourier_decomposed_helmholtz	(	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::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

◆ fill_in_contribution_to_jacobian()

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

inlinevirtual

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

Reimplemented from oomph::GeneralisedElement.

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

References fill_in_generic_residual_contribution_fourier_decomposed_helmholtz().

◆ fill_in_contribution_to_residuals()

void oomph::FourierDecomposedHelmholtzEquations::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_fourier_decomposed_helmholtz(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution_fourier_decomposed_helmholtz().

◆ fill_in_generic_residual_contribution_fourier_decomposed_helmholtz()

void oomph::FourierDecomposedHelmholtzEquations::fill_in_generic_residual_contribution_fourier_decomposed_helmholtz	(	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

   {
     // 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, 2), dtestdx(n_node, 2);
  
     // 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_real = 0, local_unknown_real = 0;
     int local_eqn_imag = 0, local_unknown_imag = 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_fourier_decomposed_helmholtz(
         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
       std::complex<double> interpolated_u(0.0, 0.0);
       Vector<double> interpolated_x(2, 0.0);
       Vector<std::complex<double>> interpolated_dudx(2);
  
       // Calculate function value and derivatives:
       //-----------------------------------------
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over directions
         for (unsigned j = 0; j < 2; j++)
         {
           interpolated_x[j] += raw_nodal_position(l, j) * psi(l);
         }
  
         // Get the nodal value of the helmholtz unknown
         const std::complex<double> u_value(
           raw_nodal_value(l, u_index_fourier_decomposed_helmholtz().real()),
           raw_nodal_value(l, u_index_fourier_decomposed_helmholtz().imag()));
  
         // Add to the interpolated value
         interpolated_u += u_value * psi(l);
  
         // Loop over directions
         for (unsigned j = 0; j < 2; j++)
         {
           interpolated_dudx[j] += u_value * dpsidx(l, j);
         }
       }
  
       // Get source function
       //-------------------
       std::complex<double> source(0.0, 0.0);
       get_source_fourier_decomposed_helmholtz(ipt, interpolated_x, source);
  
       double r = interpolated_x[0];
       double rr = r * r;
       double n = (double)fourier_wavenumber();
       double n_squared = n * n;
  
       // Assemble residuals and Jacobian
       //--------------------------------
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // first, compute the real part contribution
         //-------------------------------------------
  
         // Get the local equation
         local_eqn_real =
           nodal_local_eqn(l, u_index_fourier_decomposed_helmholtz().real());
  
         /*IF it's not a boundary condition*/
         if (local_eqn_real >= 0)
         {
           // Add body force/source term and Helmholtz bit
  
           residuals[local_eqn_real] +=
             (source.real() -
              ((-n_squared / rr) + k_squared()) * interpolated_u.real()) *
             test(l) * r * W;
  
           // The Helmholtz bit itself
           for (unsigned k = 0; k < 2; k++)
           {
             residuals[local_eqn_real] +=
               interpolated_dudx[k].real() * dtestdx(l, k) * r * W;
           }
  
           // Calculate the jacobian
           //-----------------------
           if (flag)
           {
             // Loop over the velocity shape functions again
             for (unsigned l2 = 0; l2 < n_node; l2++)
             {
               local_unknown_real = nodal_local_eqn(
                 l2, u_index_fourier_decomposed_helmholtz().real());
  
               // If at a non-zero degree of freedom add in the entry
               if (local_unknown_real >= 0)
               {
                 // Add contribution to elemental Matrix
                 for (unsigned i = 0; i < 2; i++)
                 {
                   jacobian(local_eqn_real, local_unknown_real) +=
                     dpsidx(l2, i) * dtestdx(l, i) * r * W;
                 }
  
                 // Add the helmholtz contribution
                 jacobian(local_eqn_real, local_unknown_real) -=
                   ((-n_squared / rr) + k_squared()) * psi(l2) * test(l) * r * W;
  
               } // end of local_unknown
             }
           }
         }
  
         // Second, compute the imaginary part contribution
         //------------------------------------------------
  
         // Get the local equation
         local_eqn_imag =
           nodal_local_eqn(l, u_index_fourier_decomposed_helmholtz().imag());
  
         /*IF it's not a boundary condition*/
         if (local_eqn_imag >= 0)
         {
           // Add body force/source term and Helmholtz bit
           residuals[local_eqn_imag] +=
             (source.imag() -
              ((-n_squared / rr) + k_squared()) * interpolated_u.imag()) *
             test(l) * r * W;
  
           // The Helmholtz bit itself
           for (unsigned k = 0; k < 2; k++)
           {
             residuals[local_eqn_imag] +=
               interpolated_dudx[k].imag() * dtestdx(l, k) * r * W;
           }
  
           // Calculate the jacobian
           //-----------------------
           if (flag)
           {
             // Loop over the velocity shape functions again
             for (unsigned l2 = 0; l2 < n_node; l2++)
             {
               local_unknown_imag = nodal_local_eqn(
                 l2, u_index_fourier_decomposed_helmholtz().imag());
  
               // If at a non-zero degree of freedom add in the entry
               if (local_unknown_imag >= 0)
               {
                 // Add contribution to Elemental Matrix
                 for (unsigned i = 0; i < 2; i++)
                 {
                   jacobian(local_eqn_imag, local_unknown_imag) +=
                     dpsidx(l2, i) * dtestdx(l, i) * r * W;
                 }
                 // Add the helmholtz contribution
                 jacobian(local_eqn_imag, local_unknown_imag) -=
                   ((-n_squared / rr) + k_squared()) * psi(l2) * test(l) * r * W;
               }
             }
           }
         }
       }
     } // End of loop over integration points
   }

References dshape_and_dtest_eulerian_at_knot_fourier_decomposed_helmholtz(), fourier_wavenumber(), get_source_fourier_decomposed_helmholtz(), i, imag(), oomph::FiniteElement::integral_pt(), oomph::FiniteElement::interpolated_x(), J, j, k, k_squared(), n, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::Integral::nweight(), UniformPSDSelfTest::r, oomph::FiniteElement::raw_nodal_position(), oomph::FiniteElement::raw_nodal_value(), TestProblem::source(), Eigen::test, u_index_fourier_decomposed_helmholtz(), w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by fill_in_contribution_to_jacobian(), and fill_in_contribution_to_residuals().

◆ fourier_wavenumber()

int oomph::FourierDecomposedHelmholtzEquations::fourier_wavenumber ( )

inline

Get the Fourier wavenumber.

     {
       if (N_fourier_pt == 0)
       {
         return 0;
       }
       else
       {
         return *N_fourier_pt;
       }
     }

References N_fourier_pt.

Referenced by fill_in_generic_residual_contribution_fourier_decomposed_helmholtz().

◆ fourier_wavenumber_pt()

int*& oomph::FourierDecomposedHelmholtzEquations::fourier_wavenumber_pt ( )

inline

Get pointer to Fourier wavenumber.

     {
       return N_fourier_pt;
     }

References N_fourier_pt.

◆ get_flux()

void oomph::FourierDecomposedHelmholtzEquations::get_flux	(	const Vector< double > &	s,
		Vector< std::complex< double >> &	flux
	)		const

inline

Get flux: flux[i] = du/dx_i for real and imag part.

     {
       // 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, 2);
  
       // Call the derivatives of the shape and test functions
       dshape_eulerian(s, psi, dpsidx);
  
       // Initialise to zero
       const std::complex<double> zero(0.0, 0.0);
       for (unsigned j = 0; j < 2; j++)
       {
         flux[j] = zero;
       }
  
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Cache the complex value of the unknown
         const std::complex<double> u_value(
           this->nodal_value(l, u_index_fourier_decomposed_helmholtz().real()),
           this->nodal_value(l, u_index_fourier_decomposed_helmholtz().imag()));
  
         // Loop over derivative directions
         for (unsigned j = 0; j < 2; j++)
         {
           flux[j] += u_value * dpsidx(l, j);
         }
       }
     }

References oomph::FiniteElement::dshape_eulerian(), ProblemParameters::flux(), imag(), j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, u_index_fourier_decomposed_helmholtz(), and zero().

Referenced by oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >::get_Z2_flux().

◆ get_source_fourier_decomposed_helmholtz()

virtual void oomph::FourierDecomposedHelmholtzEquations::get_source_fourier_decomposed_helmholtz	(	const unsigned &	ipt,
		const Vector< double > &	x,
		std::complex< 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 = std::complex<double>(0.0, 0.0);
       }
       else
       {
         // Get source strength
         (*Source_fct_pt)(x, source);
       }
     }

References TestProblem::source(), Source_fct_pt, and plotDoE::x.

Referenced by fill_in_generic_residual_contribution_fourier_decomposed_helmholtz().

◆ interpolated_u_fourier_decomposed_helmholtz()

std::complex<double> oomph::FourierDecomposedHelmholtzEquations::interpolated_u_fourier_decomposed_helmholtz ( const Vector< double > & s ) const

inline

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

     {
       // Find number of nodes
       const unsigned n_node = nnode();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       // Initialise value of u
       std::complex<double> interpolated_u(0.0, 0.0);
  
       // Get the index at which the helmholtz unknown is stored
       const unsigned u_nodal_index_real =
         u_index_fourier_decomposed_helmholtz().real();
       const unsigned u_nodal_index_imag =
         u_index_fourier_decomposed_helmholtz().imag();
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         // Make a temporary complex number from the stored data
         const std::complex<double> u_value(
           this->nodal_value(l, u_nodal_index_real),
           this->nodal_value(l, u_nodal_index_imag));
         // Add to the interpolated value
         interpolated_u += u_value * psi[l];
       }
       return interpolated_u;
     }

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

Referenced by compute_error(), compute_norm(), output(), and output_real().

◆ k_squared()

double oomph::FourierDecomposedHelmholtzEquations::k_squared ( )

inline

Get the square of wavenumber.

     {
       if (K_squared_pt == 0)
       {
         return 0.0;
       }
       else
       {
         return *K_squared_pt;
       }
     }

References K_squared_pt.

Referenced by fill_in_generic_residual_contribution_fourier_decomposed_helmholtz().

◆ k_squared_pt()

double*& oomph::FourierDecomposedHelmholtzEquations::k_squared_pt ( )

inline

Get pointer to square of wavenumber.

     {
       return K_squared_pt;
     }

References K_squared_pt.

◆ output() [1/4]

void oomph::FourierDecomposedHelmholtzEquations::output ( FILE * file_pt )

inlinevirtual

C_style output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

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

References output().

◆ output() [2/4]

void oomph::FourierDecomposedHelmholtzEquations::output	(	FILE *	file_pt,
		const unsigned &	nplot
	)

virtual

C-style output FE representation of soln: r,z,u_re,u_im or at n_plot^2 plot points

C-style output function:

r,z,u

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // 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);
       std::complex<double> u(interpolated_u_fourier_decomposed_helmholtz(s));
  
       for (unsigned i = 0; i < 2; i++)
       {
         fprintf(file_pt, "%g ", interpolated_x(s, i));
       }
  
       for (unsigned i = 0; i < 2; i++)
       {
         fprintf(file_pt, "%g ", interpolated_x(s, i));
       }
       fprintf(file_pt, "%g ", u.real());
       fprintf(file_pt, "%g \n", u.imag());
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(file_pt, nplot);
   }

References oomph::FiniteElement::get_s_plot(), i, interpolated_u_fourier_decomposed_helmholtz(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output() [3/4]

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

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

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

Referenced by output(), oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >::output(), and oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >::output().

◆ output() [4/4]

void oomph::FourierDecomposedHelmholtzEquations::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

virtual

Output FE representation of soln: x,y,u_re,u_im or x,y,z,u_re,u_im at n_plot^2 plot points

Output function:

r,z,u_re,u_imag

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
       std::complex<double> u(interpolated_u_fourier_decomposed_helmholtz(s));
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << interpolated_x(s, i) << " ";
       }
       outfile << u.real() << " " << u.imag() << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References oomph::FiniteElement::get_s_plot(), i, interpolated_u_fourier_decomposed_helmholtz(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output_fct() [1/2]

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

inlinevirtual

Output exact soln: (dummy time-dependent version to keep intel compiler happy)

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

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

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ output_fct() [2/2]

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

virtual

Output exact soln: r,z,u_re_exact,u_im_exact at n_plot^2 plot points

Output exact solution

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

r,z,u_exact

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >, and oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Vector for coordintes
     Vector<double> x(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Exact solution Vector
     Vector<double> exact_soln(2);
  
     // 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 r,z,u_exact
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << x[i] << " ";
       }
       outfile << exact_soln[0] << " " << exact_soln[1] << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

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

Referenced by oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >::output_fct(), and oomph::TFourierDecomposedHelmholtzElement< NNODE_1D >::output_fct().

◆ output_real()

void oomph::FourierDecomposedHelmholtzEquations::output_real	(	std::ostream &	outfile,
		const double &	phi,
		const unsigned &	nplot
	)

Output function for real part of full time-dependent solution u = Re( (u_r +i u_i) exp(-i omega t) at phase angle omega t = phi. r,z,u at n_plot plot points in each coordinate direction

Output function for real part of full time-dependent solution

u = Re( (u_r +i u_i) exp(-i omega t)

at phase angle omega t = phi.

r,z,u

Output at nplot points in each coordinate direction

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
       std::complex<double> u(interpolated_u_fourier_decomposed_helmholtz(s));
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << interpolated_x(s, i) << " ";
       }
       outfile << u.real() * cos(phi) + u.imag() * sin(phi) << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References cos(), oomph::FiniteElement::get_s_plot(), i, interpolated_u_fourier_decomposed_helmholtz(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, sin(), oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

Referenced by oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >::output_real().

◆ output_real_fct()

void oomph::FourierDecomposedHelmholtzEquations::output_real_fct	(	std::ostream &	outfile,
		const double &	phi,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

Output function for real part of full time-dependent fct u = Re( (u_r +i u_i) exp(-i omega t) at phase angle omega t = phi. r,z,u at n_plot plot points in each coordinate direction

Output function for real part of full time-dependent fct

u = Re( (u_r +i u_i) exp(-i omega t)

at phase angle omega t = phi.

r,z,u

Output at nplot points in each coordinate direction

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Vector for coordintes
     Vector<double> x(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Exact solution Vector
     Vector<double> exact_soln(2);
  
     // 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 < 2; i++)
       {
         outfile << x[i] << " ";
       }
       outfile << exact_soln[0] * cos(phi) + exact_soln[1] * sin(phi)
               << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

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

Referenced by oomph::QFourierDecomposedHelmholtzElement< NNODE_1D >::output_real_fct().

◆ self_test()

unsigned oomph::FourierDecomposedHelmholtzEquations::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_pt() [1/2]

FourierDecomposedHelmholtzSourceFctPt& oomph::FourierDecomposedHelmholtzEquations::source_fct_pt ( )

inline

Access function: Pointer to source function.

     {
       return Source_fct_pt;
     }

References Source_fct_pt.

◆ source_fct_pt() [2/2]

FourierDecomposedHelmholtzSourceFctPt oomph::FourierDecomposedHelmholtzEquations::source_fct_pt ( ) const

inline

Access function: Pointer to source function. Const version.

     {
       return Source_fct_pt;
     }

References Source_fct_pt.

◆ u_index_fourier_decomposed_helmholtz()

virtual std::complex<unsigned> oomph::FourierDecomposedHelmholtzEquations::u_index_fourier_decomposed_helmholtz ( ) const

inlinevirtual

Broken assignment operator.

Return the index at which the unknown value is stored: Real/imag part of index contains (real) index of real/imag part.

     {
       return std::complex<unsigned>(0, 1);
     }

Referenced by fill_in_generic_residual_contribution_fourier_decomposed_helmholtz(), oomph::FourierDecomposedHelmholtzBCElementBase< ELEMENT >::FourierDecomposedHelmholtzBCElementBase(), oomph::FourierDecomposedHelmholtzFluxElement< ELEMENT >::FourierDecomposedHelmholtzFluxElement(), oomph::FourierDecomposedHelmholtzFluxFromNormalDisplacementBCElement< HELMHOLTZ_BULK_ELEMENT, ELASTICITY_BULK_ELEMENT >::FourierDecomposedHelmholtzFluxFromNormalDisplacementBCElement(), get_flux(), and interpolated_u_fourier_decomposed_helmholtz().

Member Data Documentation

◆ K_squared_pt

double* oomph::FourierDecomposedHelmholtzEquations::K_squared_pt

protected

Pointer to square of wavenumber.

Referenced by k_squared(), and k_squared_pt().

◆ N_fourier_pt

int* oomph::FourierDecomposedHelmholtzEquations::N_fourier_pt

protected

Pointer to Fourier wave number.

Referenced by fourier_wavenumber(), and fourier_wavenumber_pt().

◆ Source_fct_pt

FourierDecomposedHelmholtzSourceFctPt oomph::FourierDecomposedHelmholtzEquations::Source_fct_pt

protected

Pointer to source function:

Referenced by get_source_fourier_decomposed_helmholtz(), and 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

Member Typedef Documentation

◆ FourierDecomposedHelmholtzSourceFctPt

Constructor & Destructor Documentation

◆ FourierDecomposedHelmholtzEquations() [1/2]

◆ FourierDecomposedHelmholtzEquations() [2/2]

Member Function Documentation

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ compute_norm()

◆ dshape_and_dtest_eulerian_at_knot_fourier_decomposed_helmholtz()

◆ dshape_and_dtest_eulerian_fourier_decomposed_helmholtz()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_fourier_decomposed_helmholtz()

◆ fourier_wavenumber()

◆ fourier_wavenumber_pt()

◆ get_flux()

◆ get_source_fourier_decomposed_helmholtz()

◆ interpolated_u_fourier_decomposed_helmholtz()

◆ k_squared()

◆ k_squared_pt()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ output_real()

◆ output_real_fct()

◆ self_test()

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ u_index_fourier_decomposed_helmholtz()

Member Data Documentation

◆ K_squared_pt

◆ N_fourier_pt

◆ Source_fct_pt