#include <pml_helmholtz_flux_elements.h>

Inheritance diagram for oomph::PMLHelmholtzPowerElement< ELEMENT >:

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

	PMLHelmholtzPowerElement ()
	Broken empty constructor. More...

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

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

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

double	global_power_contribution ()

double	global_power_contribution (std::ofstream &outfile)

std::complex< double >	global_flux_contribution ()

std::complex< double >	global_flux_contribution (std::ofstream &outfile)

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 (std::ostream &outfile)

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

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

virtual void	output (FILE *file_pt)

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	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

Protected Attributes
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

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::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)

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)

virtual void	fill_in_contribution_to_residuals (Vector< double > &residuals)

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)

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::PMLHelmholtzPowerElement< ELEMENT >

A class for elements that allow the post-processing of radiated power and flux on the boundaries of PMLHelmholtz elements. The element geometry is obtained from the FaceGeometry<ELEMENT> policy class.

Constructor & Destructor Documentation

◆ PMLHelmholtzPowerElement() [1/3]

template<class ELEMENT >

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

Constructor, takes the pointer to the "bulk" element and the index of the face to which the element is attached.

/////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////// Constructor, takes the pointer to the "bulk" element, the index of the fixed local coordinate and its value represented by an integer (+/- 1), indicating that the face is located at the max. or min. value of the "fixed" local coordinate in the bulk element.

     : FaceGeometry<ELEMENT>(), FaceElement()
   {
 #ifdef PARANOID
     {
       // Check that the element is not a refineable 3d element
       ELEMENT* elem_pt = dynamic_cast<ELEMENT*>(bulk_el_pt);
       // If it's three-d
       if (elem_pt->dim() == 3)
       {
         // Is it refineable
         RefineableElement* ref_el_pt =
           dynamic_cast<RefineableElement*>(elem_pt);
         if (ref_el_pt != 0)
         {
           if (this->has_hanging_nodes())
           {
             throw OomphLibError("This flux element will not work correctly if "
                                 "nodes are hanging\n",
                                 OOMPH_CURRENT_FUNCTION,
                                 OOMPH_EXCEPTION_LOCATION);
           }
         }
       }
     }
 #endif
  
     // Let the bulk element build the FaceElement, i.e. setup the pointers
     // to its nodes (by referring to the appropriate nodes in the bulk
     // element), etc.
     bulk_el_pt->build_face_element(face_index, this);
  
     // Extract the dimension of the problem from the dimension of
     // the first node
     Dim = this->node_pt(0)->ndim();
  
     // Set up U_index_helmholtz. Initialise to zero, which probably won't change
     // in most cases, oh well, the price we pay for generality
     U_index_helmholtz = std::complex<unsigned>(0, 1);
  
     // Cast to the appropriate PMLHelmholtzEquation so that we can
     // find the index at which the variable is stored
     // We assume that the dimension of the full problem is the same
     // as the dimension of the node, if this is not the case you will have
     // to write custom elements, sorry
     switch (Dim)
     {
         // One dimensional problem
       case 1:
       {
         PMLHelmholtzEquations<1>* eqn_pt =
           dynamic_cast<PMLHelmholtzEquations<1>*>(bulk_el_pt);
         // If the cast has failed die
         if (eqn_pt == 0)
         {
           std::string error_string =
             "Bulk element must inherit from PMLHelmholtzEquations.";
           error_string +=
             "Nodes are one dimensional, but cannot cast the bulk element to\n";
           error_string += "PMLHelmholtzEquations<1>\n.";
           error_string += "If you desire this functionality, you must "
                           "implement it yourself\n";
  
           throw OomphLibError(
             error_string, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
         }
         // Otherwise read out the value
         else
         {
           // Read the index from the (cast) bulk element
           U_index_helmholtz = eqn_pt->u_index_helmholtz();
         }
       }
       break;
  
       // Two dimensional problem
       case 2:
       {
         PMLHelmholtzEquations<2>* eqn_pt =
           dynamic_cast<PMLHelmholtzEquations<2>*>(bulk_el_pt);
         // If the cast has failed die
         if (eqn_pt == 0)
         {
           std::string error_string =
             "Bulk element must inherit from PMLHelmholtzEquations.";
           error_string +=
             "Nodes are two dimensional, but cannot cast the bulk element to\n";
           error_string += "PMLHelmholtzEquations<2>\n.";
           error_string += "If you desire this functionality, you must "
                           "implement it yourself\n";
  
           throw OomphLibError(
             error_string, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
         }
         else
         {
           // Read the index from the (cast) bulk element
           U_index_helmholtz = eqn_pt->u_index_helmholtz();
         }
       }
  
       break;
  
       // Three dimensional problem
       case 3:
       {
         PMLHelmholtzEquations<3>* eqn_pt =
           dynamic_cast<PMLHelmholtzEquations<3>*>(bulk_el_pt);
         // If the cast has failed die
         if (eqn_pt == 0)
         {
           std::string error_string =
             "Bulk element must inherit from PMLHelmholtzEquations.";
           error_string += "Nodes are three dimensional, but cannot cast the "
                           "bulk element to\n";
           error_string += "PMLHelmholtzEquations<3>\n.";
           error_string += "If you desire this functionality, you must "
                           "implement it yourself\n";
  
           throw OomphLibError(
             error_string, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
         }
         else
         {
           // Read the index from the (cast) bulk element
           U_index_helmholtz = eqn_pt->u_index_helmholtz();
         }
       }
       break;
  
       // Any other case is an error
       default:
         std::ostringstream error_stream;
         error_stream << "Dimension of node is " << Dim
                      << ". It should be 1,2, or 3!" << std::endl;
  
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
         break;
     }
   }

References oomph::FiniteElement::build_face_element(), oomph::PMLHelmholtzPowerElement< ELEMENT >::Dim, oomph::FaceElement::face_index(), oomph::FiniteElement::has_hanging_nodes(), oomph::Node::ndim(), oomph::FiniteElement::node_pt(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::Global_string_for_annotation::string(), oomph::PMLHelmholtzEquations< DIM >::u_index_helmholtz(), and oomph::PMLHelmholtzPowerElement< ELEMENT >::U_index_helmholtz.

◆ PMLHelmholtzPowerElement() [2/3]

template<class ELEMENT >

oomph::PMLHelmholtzPowerElement< ELEMENT >::PMLHelmholtzPowerElement ( )

inline

Broken empty constructor.

     {
       throw OomphLibError(
         "Don't call empty constructor for PMLHelmholtzPowerElement",
         OOMPH_CURRENT_FUNCTION,
         OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ PMLHelmholtzPowerElement() [3/3]

template<class ELEMENT >

oomph::PMLHelmholtzPowerElement< ELEMENT >::PMLHelmholtzPowerElement ( const PMLHelmholtzPowerElement< ELEMENT > & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ global_flux_contribution() [1/2]

template<class ELEMENT >

std::complex<double> oomph::PMLHelmholtzPowerElement< ELEMENT >::global_flux_contribution ( )

inline

Compute the element's contribution to the time-averaged flux

     {
       // Dummy output file
       std::ofstream outfile;
       return global_flux_contribution(outfile);
     }

◆ global_flux_contribution() [2/2]

template<class ELEMENT >

std::complex<double> oomph::PMLHelmholtzPowerElement< ELEMENT >::global_flux_contribution ( std::ofstream & outfile )

inline

Compute the element's contribution to the integral of the flux over the artificial boundary. Also output the flux in the specified output file if it's open.

     {
       // pointer to the corresponding bulk element
       ELEMENT* bulk_elem_pt = dynamic_cast<ELEMENT*>(this->bulk_element_pt());
  
       // Number of nodes in bulk element
       unsigned nnode_bulk = bulk_elem_pt->nnode();
       const unsigned n_node_local = nnode();
  
       // get the dim of the bulk and local nodes
       const unsigned bulk_dim = bulk_elem_pt->dim();
       const unsigned local_dim = this->dim();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node_local);
  
       // Set up memory for the shape functions
       Shape psi_bulk(nnode_bulk);
       DShape dpsi_bulk_dx(nnode_bulk, bulk_dim);
  
       // Set up memory for the outer unit normal
       Vector<double> unit_normal(bulk_dim);
  
       // Set the value of n_intpt
       const unsigned n_intpt = integral_pt()->nweight();
  
       // Set the Vector to hold local coordinates
       Vector<double> s(local_dim);
       std::complex<double> flux(0.0, 0.0);
  
       // Output?
       if (outfile.is_open())
       {
         outfile << "ZONE\n";
       }
  
       // Loop over the integration points
       //--------------------------------
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Assign values of s
         for (unsigned i = 0; i < local_dim; i++)
         {
           s[i] = integral_pt()->knot(ipt, i);
         }
         // get the outer_unit_ext vector
         this->outer_unit_normal(s, unit_normal);
  
         // 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 local coordinates in bulk element by copy construction
         Vector<double> s_bulk(local_coordinate_in_bulk(s));
  
         // Call the derivatives of the shape  functions
         // in the bulk -- must do this via s because this point
         // is not an integration point the bulk element!
         (void)bulk_elem_pt->dshape_eulerian(s_bulk, psi_bulk, dpsi_bulk_dx);
         this->shape(s, psi);
  
         // Derivs of Eulerian coordinates w.r.t. local coordinates
         std::complex<double> dphi_dn(0.0, 0.0);
         Vector<std::complex<double>> interpolated_dphidx(
           bulk_dim, std::complex<double>(0.0, 0.0));
         Vector<double> x(bulk_dim);
  
         // Calculate function value and derivatives:
         //-----------------------------------------
         // Loop over nodes
         for (unsigned l = 0; l < nnode_bulk; l++)
         {
           // Get the nodal value of the helmholtz unknown
           const std::complex<double> phi_value(
             bulk_elem_pt->nodal_value(l,
                                       bulk_elem_pt->u_index_helmholtz().real()),
             bulk_elem_pt->nodal_value(
               l, bulk_elem_pt->u_index_helmholtz().imag()));
  
           // Loop over directions
           for (unsigned i = 0; i < bulk_dim; i++)
           {
             interpolated_dphidx[i] += phi_value * dpsi_bulk_dx(l, i);
           }
         } // End of loop over the bulk_nodes
  
  
         // define dphi_dn
         for (unsigned i = 0; i < bulk_dim; i++)
         {
           dphi_dn += interpolated_dphidx[i] * unit_normal[i];
         }
  
         // Output?
         if (outfile.is_open())
         {
           interpolated_x(s, x);
           outfile << x[0] << " " << x[1] << " " << dphi_dn.real() << " "
                   << dphi_dn.imag() << "\n";
         }
  
         // ...add to integral
         flux += dphi_dn * W;
       }
  
       return flux;
     }

References oomph::FaceElement::bulk_element_pt(), oomph::FiniteElement::dim(), ProblemParameters::flux(), i, oomph::FiniteElement::integral_pt(), oomph::FaceElement::interpolated_x(), J, oomph::FaceElement::J_eulerian(), oomph::Integral::knot(), oomph::FaceElement::local_coordinate_in_bulk(), oomph::FiniteElement::nnode(), oomph::Integral::nweight(), oomph::FaceElement::outer_unit_normal(), s, oomph::FiniteElement::shape(), w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and plotDoE::x.

◆ global_power_contribution() [1/2]

template<class ELEMENT >

double oomph::PMLHelmholtzPowerElement< ELEMENT >::global_power_contribution ( )

inline

Compute the element's contribution to the time-averaged radiated power over the artificial boundary

     {
       // Dummy output file
       std::ofstream outfile;
       return global_power_contribution(outfile);
     }

◆ global_power_contribution() [2/2]

template<class ELEMENT >

double oomph::PMLHelmholtzPowerElement< ELEMENT >::global_power_contribution ( std::ofstream & outfile )

inline

Compute the element's contribution to the time-averaged radiated power over the artificial boundary. Also output the power density in the specified output file if it's open.

     {
       // pointer to the corresponding bulk element
       ELEMENT* bulk_elem_pt = dynamic_cast<ELEMENT*>(this->bulk_element_pt());
  
       // Number of nodes in bulk element
       unsigned nnode_bulk = bulk_elem_pt->nnode();
       const unsigned n_node_local = nnode();
  
       // get the dim of the bulk and local nodes
       const unsigned bulk_dim = bulk_elem_pt->dim();
       const unsigned local_dim = this->dim();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node_local);
  
       // Set up memory for the shape functions
       Shape psi_bulk(nnode_bulk);
       DShape dpsi_bulk_dx(nnode_bulk, bulk_dim);
  
       // Set up memory for the outer unit normal
       Vector<double> unit_normal(bulk_dim);
  
       // Set the value of n_intpt
       const unsigned n_intpt = integral_pt()->nweight();
  
       // Set the Vector to hold local coordinates
       Vector<double> s(local_dim);
       double power = 0.0;
  
       // Output?
       if (outfile.is_open())
       {
         outfile << "ZONE\n";
       }
  
       // Loop over the integration points
       //--------------------------------
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Assign values of s
         for (unsigned i = 0; i < local_dim; i++)
         {
           s[i] = integral_pt()->knot(ipt, i);
         }
         // get the outer_unit_ext vector
         this->outer_unit_normal(s, unit_normal);
  
         // 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 local coordinates in bulk element by copy construction
         Vector<double> s_bulk(local_coordinate_in_bulk(s));
  
         // Call the derivatives of the shape  functions
         // in the bulk -- must do this via s because this point
         // is not an integration point the bulk element!
         (void)bulk_elem_pt->dshape_eulerian(s_bulk, psi_bulk, dpsi_bulk_dx);
         this->shape(s, psi);
  
         // Derivs of Eulerian coordinates w.r.t. local coordinates
         std::complex<double> dphi_dn(0.0, 0.0);
         Vector<std::complex<double>> interpolated_dphidx(
           bulk_dim, std::complex<double>(0.0, 0.0));
         std::complex<double> interpolated_phi(0.0, 0.0);
         Vector<double> x(bulk_dim);
  
         // Calculate function value and derivatives:
         //-----------------------------------------
         // Loop over nodes
         for (unsigned l = 0; l < nnode_bulk; l++)
         {
           // Get the nodal value of the helmholtz unknown
           const std::complex<double> phi_value(
             bulk_elem_pt->nodal_value(l,
                                       bulk_elem_pt->u_index_helmholtz().real()),
             bulk_elem_pt->nodal_value(
               l, bulk_elem_pt->u_index_helmholtz().imag()));
  
           // Loop over directions
           for (unsigned i = 0; i < bulk_dim; i++)
           {
             interpolated_dphidx[i] += phi_value * dpsi_bulk_dx(l, i);
           }
         } // End of loop over the bulk_nodes
  
         for (unsigned l = 0; l < n_node_local; l++)
         {
           // Get the nodal value of the helmholtz unknown
           const std::complex<double> phi_value(
             nodal_value(l, u_index_helmholtz().real()),
             nodal_value(l, u_index_helmholtz().imag()));
  
           interpolated_phi += phi_value * psi(l);
         }
  
         // define dphi_dn
         for (unsigned i = 0; i < bulk_dim; i++)
         {
           dphi_dn += interpolated_dphidx[i] * unit_normal[i];
         }
  
         // Power density
         double integrand = 0.5 * (interpolated_phi.real() * dphi_dn.imag() -
                                   interpolated_phi.imag() * dphi_dn.real());
  
         // Output?
         if (outfile.is_open())
         {
           interpolated_x(s, x);
           double phi = atan2(x[1], x[0]);
           outfile << x[0] << " " << x[1] << " " << phi << " " << integrand
                   << "\n";
         }
  
         // ...add to integral
         power += integrand * W;
       }
  
       return power;
     }

References atan2(), oomph::FaceElement::bulk_element_pt(), oomph::FiniteElement::dim(), i, imag(), oomph::FiniteElement::integral_pt(), oomph::FaceElement::interpolated_x(), J, oomph::FaceElement::J_eulerian(), oomph::Integral::knot(), oomph::FaceElement::local_coordinate_in_bulk(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), oomph::Integral::nweight(), oomph::FaceElement::outer_unit_normal(), s, oomph::FiniteElement::shape(), oomph::PMLHelmholtzPowerElement< ELEMENT >::u_index_helmholtz(), w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and plotDoE::x.

◆ u_index_helmholtz()

template<class ELEMENT >

virtual std::complex<unsigned> oomph::PMLHelmholtzPowerElement< ELEMENT >::u_index_helmholtz ( ) const

inlinevirtual

Return the index at which the unknown value is stored.

     {
       return std::complex<unsigned>(U_index_helmholtz.real(),
                                     U_index_helmholtz.imag());
     }

References oomph::PMLHelmholtzPowerElement< ELEMENT >::U_index_helmholtz.

Referenced by oomph::PMLHelmholtzPowerElement< ELEMENT >::global_power_contribution().

◆ zeta_nodal()

template<class ELEMENT >

double oomph::PMLHelmholtzPowerElement< ELEMENT >::zeta_nodal	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inlinevirtual

Broken assignment operator.

Specify the value of nodal zeta from the face geometry The "global" intrinsic coordinate of the element when viewed as part of a geometric object should be given by the FaceElement representation, by default (needed to break indeterminacy if bulk element is SolidElement)

Reimplemented from oomph::FaceElement.

     {
       return FaceElement::zeta_nodal(n, k, i);
     }

References i, k, n, and oomph::FaceElement::zeta_nodal().

Member Data Documentation

◆ Dim

template<class ELEMENT >

unsigned oomph::PMLHelmholtzPowerElement< ELEMENT >::Dim

protected

The spatial dimension of the problem.

Referenced by oomph::PMLHelmholtzPowerElement< ELEMENT >::PMLHelmholtzPowerElement().

◆ U_index_helmholtz

template<class ELEMENT >

std::complex<unsigned> oomph::PMLHelmholtzPowerElement< ELEMENT >::U_index_helmholtz

protected

The index at which the real and imag part of the unknown is stored at the nodes

Referenced by oomph::PMLHelmholtzPowerElement< ELEMENT >::PMLHelmholtzPowerElement(), and oomph::PMLHelmholtzPowerElement< ELEMENT >::u_index_helmholtz().

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

pml_helmholtz_flux_elements.h

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::PMLHelmholtzPowerElement< ELEMENT >

Constructor & Destructor Documentation

◆ PMLHelmholtzPowerElement() [1/3]

◆ PMLHelmholtzPowerElement() [2/3]

◆ PMLHelmholtzPowerElement() [3/3]

Member Function Documentation

◆ global_flux_contribution() [1/2]

◆ global_flux_contribution() [2/2]

◆ global_power_contribution() [1/2]

◆ global_power_contribution() [2/2]

◆ u_index_helmholtz()

◆ zeta_nodal()

Member Data Documentation

◆ Dim

◆ U_index_helmholtz

template<class ELEMENT>
class oomph::PMLHelmholtzPowerElement< ELEMENT >