#include <helmholtz_bc_elements.h>

Inheritance diagram for oomph::HelmholtzAbsorbingBCElement< ELEMENT >:

Public Member Functions
	HelmholtzAbsorbingBCElement (FiniteElement *const &bulk_el_pt, const int &face_index)

unsigned *&	abc_order_pt ()
	Pointer to order of absorbing boundary condition. More...

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

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

double *&	outer_radius_pt ()
	Get pointer to radius of outer boundary (must be a cirle) More...

Public Member Functions inherited from oomph::HelmholtzBCElementBase< ELEMENT >
	HelmholtzBCElementBase (FiniteElement *const &bulk_el_pt, const int &face_index)
	Constructor, takes the pointer to the "bulk" element and the face index. More...

	HelmholtzBCElementBase ()
	Broken empty constructor. More...

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

double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
	Broken assignment operator. More...

void	output (std::ostream &outfile)

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

void	output (FILE *file_pt)

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

virtual std::complex< unsigned >	u_index_helmholtz () const

double	global_power_contribution ()

double	global_power_contribution (std::ofstream &outfile)

void	compute_contribution_to_fourier_components (Vector< std::complex< double >> &a_coeff_pos, Vector< std::complex< double >> &a_coeff_neg)

Public Member Functions inherited from oomph::FaceElement
	FaceElement ()
	Constructor: Initialise all appropriate member data. More...

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

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

const unsigned &	boundary_number_in_bulk_mesh () const
	Broken assignment operator. More...

void	set_boundary_number_in_bulk_mesh (const unsigned &b)
	Set function for the boundary number in bulk mesh. More...

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

double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

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

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

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

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

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

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

int &	normal_sign ()

int	normal_sign () const

int &	face_index ()

int	face_index () const

const Vector< double > *	tangent_direction_pt () const
	Public access function for the tangent direction pointer. More...

void	set_tangent_direction (Vector< double > *tangent_direction_pt)
	Set the tangent direction vector. More...

void	turn_on_warning_for_discontinuous_tangent ()

void	turn_off_warning_for_discontinuous_tangent ()

void	continuous_tangent_and_outer_unit_normal (const Vector< double > &s, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	continuous_tangent_and_outer_unit_normal (const unsigned &ipt, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	outer_unit_normal (const Vector< double > &s, Vector< double > &unit_normal) const
	Compute outer unit normal at the specified local coordinate. More...

void	outer_unit_normal (const unsigned &ipt, Vector< double > &unit_normal) const
	Compute outer unit normal at ipt-th integration point. More...

FiniteElement *&	bulk_element_pt ()
	Pointer to higher-dimensional "bulk" element. More...

FiniteElement *	bulk_element_pt () const
	Pointer to higher-dimensional "bulk" element (const version) More...

CoordinateMappingFctPt &	face_to_bulk_coordinate_fct_pt ()

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt () const

BulkCoordinateDerivativesFctPt &	bulk_coordinate_derivatives_fct_pt ()

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt () const

Vector< double >	local_coordinate_in_bulk (const Vector< double > &s) const

void	get_local_coordinate_in_bulk (const Vector< double > &s, Vector< double > &s_bulk) const

void	get_ds_bulk_ds_face (const Vector< double > &s, DenseMatrix< double > &dsbulk_dsface, unsigned &interior_direction) const

unsigned &	bulk_position_type (const unsigned &i)

const unsigned &	bulk_position_type (const unsigned &i) const

void	bulk_node_number_resize (const unsigned &i)
	Resize the storage for the bulk node numbers. More...

unsigned &	bulk_node_number (const unsigned &n)

const unsigned &	bulk_node_number (const unsigned &n) const

void	bulk_position_type_resize (const unsigned &i)
	Resize the storage for bulk_position_type to i entries. More...

unsigned &	nbulk_value (const unsigned &n)

unsigned	nbulk_value (const unsigned &n) const

void	nbulk_value_resize (const unsigned &i)

void	resize_nodes (Vector< unsigned > &nadditional_data_values)

void	output_zeta (std::ostream &outfile, const unsigned &nplot)
	Output boundary coordinate zeta. 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

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...

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)

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, 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	self_test ()

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

Private Member Functions
void	fill_in_generic_residual_contribution_helmholtz_abc (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

Private Attributes
double *	Outer_radius_pt
	Pointer to radius of outer boundary (must be a circle!) More...

unsigned *	ABC_order_pt
	Pointer to order of absorbing boundary condition. More...

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

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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

Protected Member Functions inherited from oomph::HelmholtzBCElementBase< ELEMENT >
double	test_only (const Vector< double > &s, Shape &test) const

double	d_shape_and_test_local (const Vector< double > &s, Shape &psi, Shape &test, DShape &dpsi_ds, DShape &dtest_ds) const

Protected Member Functions inherited from oomph::FaceElement
void	add_additional_values (const Vector< unsigned > &nadditional_values, const unsigned &id)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

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

Protected Attributes inherited from oomph::HelmholtzBCElementBase< ELEMENT >
std::complex< unsigned >	U_index_helmholtz

unsigned	Dim
	The spatial dimension of the problem. More...

Protected Attributes inherited from oomph::FaceElement
unsigned	Boundary_number_in_bulk_mesh
	The boundary number in the bulk mesh to which this element is attached. More...

FiniteElement *	Bulk_element_pt
	Pointer to the associated higher-dimensional "bulk" element. More...

Vector< unsigned >	Bulk_node_number

Vector< unsigned >	Nbulk_value

Vector< double > *	Tangent_direction_pt

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

Detailed Description

template<class ELEMENT>
class oomph::HelmholtzAbsorbingBCElement< ELEMENT >

////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////// Absorbing BC element for approximation imposition of Sommerfeld radiation condition

Constructor & Destructor Documentation

◆ HelmholtzAbsorbingBCElement()

template<class ELEMENT >

oomph::HelmholtzAbsorbingBCElement< ELEMENT >::HelmholtzAbsorbingBCElement	(	FiniteElement *const &	bulk_el_pt,
		const int &	face_index
	)

inline

Construct element from specification of bulk element and face index.

       : HelmholtzBCElementBase<ELEMENT>(bulk_el_pt, face_index)
     {
       // Initialise pointers
       Outer_radius_pt = 0;
  
       // Initialise order of absorbing boundary condition
       ABC_order_pt = 0;
     }

References oomph::HelmholtzAbsorbingBCElement< ELEMENT >::ABC_order_pt, and oomph::HelmholtzAbsorbingBCElement< ELEMENT >::Outer_radius_pt.

Member Function Documentation

◆ abc_order_pt()

template<class ELEMENT >

unsigned*& oomph::HelmholtzAbsorbingBCElement< ELEMENT >::abc_order_pt ( )

inline

Pointer to order of absorbing boundary condition.

     {
       return ABC_order_pt;
     }

References oomph::HelmholtzAbsorbingBCElement< ELEMENT >::ABC_order_pt.

Referenced by CoatedDiskProblem< ELASTICITY_ELEMENT, HELMHOLTZ_ELEMENT >::create_helmholtz_ABC_elements(), HelmholtzPointSourceProblem< ELEMENT >::setup_outer_boundary(), and ScatteringProblem< ELEMENT >::setup_outer_boundary().

◆ fill_in_contribution_to_jacobian()

template<class ELEMENT >

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

inlinevirtual

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

Reimplemented from oomph::FiniteElement.

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

References oomph::HelmholtzAbsorbingBCElement< ELEMENT >::fill_in_generic_residual_contribution_helmholtz_abc().

◆ fill_in_contribution_to_residuals()

template<class ELEMENT >

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

inlinevirtual

Add the element's contribution to its residual vector.

Reimplemented from oomph::GeneralisedElement.

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

References oomph::GeneralisedElement::Dummy_matrix, and oomph::HelmholtzAbsorbingBCElement< ELEMENT >::fill_in_generic_residual_contribution_helmholtz_abc().

◆ fill_in_generic_residual_contribution_helmholtz_abc()

template<class ELEMENT >

void oomph::HelmholtzAbsorbingBCElement< ELEMENT >::fill_in_generic_residual_contribution_helmholtz_abc	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

inlineprivate

Compute the element's residual vector and the ( Jacobian matrix. Overloaded version, using the abc approximation

     {
 #ifdef PARANOID
  
       if (ABC_order_pt == 0)
       {
         throw OomphLibError("Order of ABC hasn't been set!",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
       }
  
       if (this->Outer_radius_pt == 0)
       {
         throw OomphLibError("Pointer to outer radius hasn't been set!",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
       }
  
 #endif
  
       // Find out how many nodes there are
       const unsigned n_node = this->nnode();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node), test(n_node);
       DShape dpsi_ds(n_node, this->Dim - 1), dtest_ds(n_node, this->Dim - 1),
         dtest_dS(n_node, this->Dim - 1), dpsi_dS(n_node, this->Dim - 1);
  
       // Set the value of Nintpt
       const unsigned n_intpt = this->integral_pt()->nweight();
  
       // Set the Vector to hold local coordinates
       Vector<double> s(this->Dim - 1);
  
       // Integers to hold the local equation and unknown numbers
       int local_eqn_real = 0, local_unknown_real = 0;
       int local_eqn_imag = 0, local_unknown_imag = 0;
  
       // Define the problem parameters
       double R = *Outer_radius_pt;
       double k =
         sqrt(dynamic_cast<ELEMENT*>(this->bulk_element_pt())->k_squared());
  
       // Loop over the integration points
       //--------------------------------
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Assign values of s
         for (unsigned i = 0; i < (this->Dim - 1); i++)
         {
           s[i] = this->integral_pt()->knot(ipt, i);
         }
  
         // Get the integral weight
         double w = this->integral_pt()->weight(ipt);
  
         // Find the shape test functions and derivates; return the Jacobian
         // of the mapping between local and global (Eulerian)
         // coordinates
         double J =
           this->d_shape_and_test_local(s, psi, test, dpsi_ds, dtest_ds);
  
         // Premultiply the weights and the Jacobian
         double W = w * J;
         // get the inverse of jacibian
         double inv_J = 1 / J;
  
         // Need to find position to feed into flux function,
         // initialise to zero
         std::complex<double> interpolated_u(0.0, 0.0);
         std::complex<double> du_dS(0.0, 0.0);
  
         // Calculate velocities and derivatives:loop over the nodes
         for (unsigned l = 0; l < n_node; l++)
         {
           // Loop over real and imag part
           // Get the nodal value of the helmholtz unknown
           const std::complex<double> u_value(
             this->nodal_value(l, this->U_index_helmholtz.real()),
             this->nodal_value(l, this->U_index_helmholtz.imag()));
  
           interpolated_u += u_value * psi[l];
  
           du_dS += u_value * dpsi_ds(l, 0) * inv_J;
  
           // Get the value of dtest_dS
           dtest_dS(l, 0) = dtest_ds(l, 0) * inv_J;
           // Get the value of dpsif_dS
           dpsi_dS(l, 0) = dpsi_ds(l, 0) * inv_J;
         }
  
         // use ABC first order approximation
         if (*ABC_order_pt == 1)
         {
           // Now add to the appropriate equations:use second order approximation
           // Loop over the test functions
           for (unsigned l = 0; l < n_node; l++)
           {
             local_eqn_real =
               this->nodal_local_eqn(l, this->U_index_helmholtz.real());
             local_eqn_imag =
               this->nodal_local_eqn(l, this->U_index_helmholtz.imag());
  
             // first, calculate the real part contrubution
             //-----------------------
             // IF it's not a boundary condition
             if (local_eqn_real >= 0)
             {
               // Add the second order terms:compute manually real and imag part
  
               residuals[local_eqn_real] += (k * interpolated_u.imag() +
                                             (0.5 / R) * interpolated_u.real()) *
                                            test[l] * W;
  
               // Calculate the jacobian
               //-----------------------
               if (flag)
               {
                 // Loop over the shape functions again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   local_unknown_real =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.real());
                   local_unknown_imag =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.imag());
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_real >= 0)
                   {
                     jacobian(local_eqn_real, local_unknown_real) +=
                       (0.5 / R) * psi[l2] * test[l] * W;
                   }
  
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_imag >= 0)
                   {
                     jacobian(local_eqn_real, local_unknown_imag) +=
                       k * psi[l2] * test[l] * W;
                   }
                 }
               }
             } // end of local_eqn_real
  
             // second, calculate the imag part contrubution
             //-----------------------
             // IF it's not a boundary condition
             if (local_eqn_imag >= 0)
             {
               // Add the second order terms contibution to the residual
               residuals[local_eqn_imag] += (-k * interpolated_u.real() +
                                             (0.5 / R) * interpolated_u.imag()) *
                                            test[l] * W;
  
  
               // Calculate the jacobian
               //-----------------------
               if (flag)
               {
                 // Loop over the shape functions again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   local_unknown_real =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.real());
                   local_unknown_imag =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.imag());
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_real >= 0)
                   {
                     jacobian(local_eqn_imag, local_unknown_real) +=
                       (-k) * psi[l2] * test[l] * W;
                   }
  
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_imag >= 0)
                   {
                     jacobian(local_eqn_imag, local_unknown_imag) +=
                       (0.5 / R) * psi[l2] * test[l] * W;
                   }
                 }
               }
             }
           } // End of loop over the nodes
         }
  
         //:use second order approximation
         if (*ABC_order_pt == 2)
         {
           // Now add to the appropriate equations:use second order approximation
           // Loop over the test functions
           for (unsigned l = 0; l < n_node; l++)
           {
             local_eqn_real =
               this->nodal_local_eqn(l, this->U_index_helmholtz.real());
             local_eqn_imag =
               this->nodal_local_eqn(l, this->U_index_helmholtz.imag());
  
             // first, calculate the real part contrubution
             //-----------------------
             // IF it's not a boundary condition
             if (local_eqn_real >= 0)
             {
               // Add the second order terms:compute manually real and imag part
  
               residuals[local_eqn_real] +=
                 (k * interpolated_u.imag() +
                  (0.5 / R) * interpolated_u.real()) *
                   test[l] * W +
                 ((0.125 / (k * R * R)) * interpolated_u.imag()) * test[l] * W;
  
               residuals[local_eqn_real] +=
                 (-0.5 / k) * du_dS.imag() * dtest_dS(l, 0) * W;
  
               // Calculate the jacobian
               //-----------------------
               if (flag)
               {
                 // Loop over the shape functions again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   local_unknown_real =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.real());
                   local_unknown_imag =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.imag());
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_real >= 0)
                   {
                     jacobian(local_eqn_real, local_unknown_real) +=
                       (0.5 / R) * psi[l2] * test[l] * W;
                   }
  
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_imag >= 0)
                   {
                     jacobian(local_eqn_real, local_unknown_imag) +=
                       k * psi[l2] * test[l] * W +
                       (0.125 / (k * R * R)) * psi[l2] * test[l] * W;
  
                     jacobian(local_eqn_real, local_unknown_imag) +=
                       (-0.5 / k) * dpsi_dS(l2, 0) * dtest_dS(l, 0) * W;
                   }
                 }
               }
             } // end of local_eqn_real
  
             // second, calculate the imag part contrubution
             //-----------------------
             // IF it's not a boundary condition
             if (local_eqn_imag >= 0)
             {
               // Add the second order terms contibution to the residual
               residuals[local_eqn_imag] +=
                 (-k * interpolated_u.real() +
                  (0.5 / R) * interpolated_u.imag()) *
                   test[l] * W +
                 ((-0.125 / (k * R * R)) * interpolated_u.real()) * test[l] * W;
  
               residuals[local_eqn_imag] +=
                 (0.5 / k) * du_dS.real() * dtest_dS(l, 0) * W;
  
               // Calculate the jacobian
               //-----------------------
               if (flag)
               {
                 // Loop over the shape functions again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   local_unknown_real =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.real());
                   local_unknown_imag =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.imag());
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_real >= 0)
                   {
                     jacobian(local_eqn_imag, local_unknown_real) +=
                       (-k) * psi[l2] * test[l] * W -
                       (0.125 / (k * R * R)) * psi[l2] * test[l] * W;
  
                     jacobian(local_eqn_imag, local_unknown_real) +=
                       (0.5 / k) * dpsi_dS(l2, 0) * dtest_dS(l, 0) * W;
                   }
  
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_imag >= 0)
                   {
                     jacobian(local_eqn_imag, local_unknown_imag) +=
                       (0.5 / R) * psi[l2] * test[l] * W;
                   }
                 }
               }
             }
           } // End of loop over the nodes
         }
  
         if (*ABC_order_pt == 3)
         {
           // Now add to the appropriate equations:use second order approximation
           // Loop over the test functions
           for (unsigned l = 0; l < n_node; l++)
           {
             local_eqn_real =
               this->nodal_local_eqn(l, this->U_index_helmholtz.real());
             local_eqn_imag =
               this->nodal_local_eqn(l, this->U_index_helmholtz.imag());
  
             // first, calculate the real part contrubution
             //-----------------------
             // IF it's not a boundary condition
             if (local_eqn_real >= 0)
             {
               // Add the second order terms:compute manually real and imag part
               residuals[local_eqn_real] +=
                 ((k * (1 + 0.125 / (k * k * R * R))) * interpolated_u.imag() +
                  (0.5 / R - 0.125 / (k * k * R * R * R)) *
                    interpolated_u.real()) *
                 test[l] * W;
  
               residuals[local_eqn_real] +=
                 ((-0.5 / k) * du_dS.imag() +
                  (0.5 / (k * k * R)) * du_dS.real()) *
                 dtest_dS(l, 0) * W;
  
               // Calculate the jacobian
               //-----------------------
               if (flag)
               {
                 // Loop over the shape functions again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   local_unknown_real =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.real());
                   local_unknown_imag =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.imag());
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_real >= 0)
                   {
                     jacobian(local_eqn_real, local_unknown_real) +=
                       (0.5 / R - 0.125 / (k * k * R * R * R)) * psi[l2] *
                       test[l] * W;
  
                     jacobian(local_eqn_real, local_unknown_real) +=
                       (0.5 / (k * k * R)) * dpsi_dS(l2, 0) * dtest_dS(l, 0) * W;
                   }
  
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_imag >= 0)
                   {
                     jacobian(local_eqn_real, local_unknown_imag) +=
                       (k * (1 + 0.125 / (k * k * R * R))) * psi[l2] * test[l] *
                       W;
  
                     jacobian(local_eqn_real, local_unknown_imag) +=
                       (-0.5 / k) * dpsi_dS(l2, 0) * dtest_dS(l, 0) * W;
                   }
                 }
               }
             } // end of local_eqn_real
  
             // second, calculate the imag part contrubution
             //-----------------------
             // IF it's not a boundary condition
             if (local_eqn_imag >= 0)
             {
               // Add the second order terms contibution to the residual
               residuals[local_eqn_imag] +=
                 ((-k * (1 + 0.125 / (k * k * R * R))) * interpolated_u.real() +
                  (0.5 / R - 0.125 / (k * k * R * R * R)) *
                    interpolated_u.imag()) *
                 test[l] * W;
  
               residuals[local_eqn_imag] +=
                 ((0.5 / k) * du_dS.real() +
                  (0.5 / (k * k * R)) * du_dS.imag()) *
                 dtest_dS(l, 0) * W;
  
               // Calculate the jacobian
               //-----------------------
               if (flag)
               {
                 // Loop over the shape functions again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   local_unknown_real =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.real());
                   local_unknown_imag =
                     this->nodal_local_eqn(l2, this->U_index_helmholtz.imag());
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_real >= 0)
                   {
                     jacobian(local_eqn_imag, local_unknown_real) +=
                       (-k * (1 + 0.125 / (k * k * R * R))) * psi[l2] * test[l] *
                       W;
  
                     jacobian(local_eqn_imag, local_unknown_real) +=
                       (0.5 / k) * dpsi_dS(l2, 0) * dtest_dS(l, 0) * W;
                   }
                   // If at a non-zero degree of freedom add in the entry
                   if (local_unknown_imag >= 0)
                   {
                     jacobian(local_eqn_imag, local_unknown_imag) +=
                       (0.5 / R - 0.125 / (k * k * R * R * R)) * psi[l2] *
                       test[l] * W;
  
                     jacobian(local_eqn_imag, local_unknown_imag) +=
                       (0.5 / (k * k * R)) * dpsi_dS(l2, 0) * dtest_dS(l, 0) * W;
                   }
                 }
               }
             }
           } // End of loop over the nodes
         }
       } // End of loop over int_pt
  
     } // End of fill_in_generic_residual_contribution_helmholtz_flux

References oomph::HelmholtzAbsorbingBCElement< ELEMENT >::ABC_order_pt, oomph::FaceElement::bulk_element_pt(), oomph::HelmholtzBCElementBase< ELEMENT >::d_shape_and_test_local(), oomph::HelmholtzBCElementBase< ELEMENT >::Dim, i, oomph::FiniteElement::integral_pt(), J, k, oomph::Integral::knot(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::nodal_value(), oomph::Integral::nweight(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::HelmholtzAbsorbingBCElement< ELEMENT >::Outer_radius_pt, R, s, sqrt(), Eigen::test, oomph::HelmholtzBCElementBase< ELEMENT >::U_index_helmholtz, w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by oomph::HelmholtzAbsorbingBCElement< ELEMENT >::fill_in_contribution_to_jacobian(), and oomph::HelmholtzAbsorbingBCElement< ELEMENT >::fill_in_contribution_to_residuals().

◆ outer_radius_pt()

template<class ELEMENT >

double*& oomph::HelmholtzAbsorbingBCElement< ELEMENT >::outer_radius_pt ( )

inline

Get pointer to radius of outer boundary (must be a cirle)

     {
       return Outer_radius_pt;
     }

References oomph::HelmholtzAbsorbingBCElement< ELEMENT >::Outer_radius_pt.

Referenced by CoatedDiskProblem< ELASTICITY_ELEMENT, HELMHOLTZ_ELEMENT >::create_helmholtz_ABC_elements(), HelmholtzPointSourceProblem< ELEMENT >::setup_outer_boundary(), and ScatteringProblem< ELEMENT >::setup_outer_boundary().

Member Data Documentation

◆ ABC_order_pt

template<class ELEMENT >

unsigned* oomph::HelmholtzAbsorbingBCElement< ELEMENT >::ABC_order_pt

private

Pointer to order of absorbing boundary condition.

Referenced by oomph::HelmholtzAbsorbingBCElement< ELEMENT >::abc_order_pt(), oomph::HelmholtzAbsorbingBCElement< ELEMENT >::fill_in_generic_residual_contribution_helmholtz_abc(), and oomph::HelmholtzAbsorbingBCElement< ELEMENT >::HelmholtzAbsorbingBCElement().

◆ Outer_radius_pt

template<class ELEMENT >

double* oomph::HelmholtzAbsorbingBCElement< ELEMENT >::Outer_radius_pt

private

Pointer to radius of outer boundary (must be a circle!)

Referenced by oomph::HelmholtzAbsorbingBCElement< ELEMENT >::fill_in_generic_residual_contribution_helmholtz_abc(), oomph::HelmholtzAbsorbingBCElement< ELEMENT >::HelmholtzAbsorbingBCElement(), and oomph::HelmholtzAbsorbingBCElement< ELEMENT >::outer_radius_pt().

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

helmholtz_bc_elements.h

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::HelmholtzAbsorbingBCElement< ELEMENT >

Constructor & Destructor Documentation

◆ HelmholtzAbsorbingBCElement()

Member Function Documentation

◆ abc_order_pt()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_helmholtz_abc()

◆ outer_radius_pt()

Member Data Documentation

◆ ABC_order_pt

◆ Outer_radius_pt

template<class ELEMENT>
class oomph::HelmholtzAbsorbingBCElement< ELEMENT >