#include <pml_time_harmonic_linear_elasticity_elements.h>

Inheritance diagram for oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >:

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

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

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

Public Member Functions
	PMLTimeHarmonicLinearElasticityEquationsBase ()

virtual std::complex< unsigned >	u_index_time_harmonic_linear_elasticity (const unsigned i) const

void	interpolated_u_time_harmonic_linear_elasticity (const Vector< double > &s, Vector< std::complex< double >> &disp) const
	Compute vector of FE interpolated displacement u at local coordinate s. More...

std::complex< double >	interpolated_u_time_harmonic_linear_elasticity (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated displacement u[i] at local coordinate s. More...

PMLTimeHarmonicIsotropicElasticityTensor *&	elasticity_tensor_pt ()
	Return the pointer to the elasticity_tensor. More...

std::complex< double >	E (const unsigned &i, const unsigned &j, const unsigned &k, const unsigned &l) const
	Access function to the entries in the elasticity tensor. More...

double	nu () const
	Access function to nu in the elasticity tensor. More...

const double &	omega_sq () const
	Access function for square of non-dim frequency. More...

double *&	omega_sq_pt ()
	Access function for square of non-dim frequency. More...

BodyForceFctPt &	body_force_fct_pt ()
	Access function: Pointer to body force function. More...

BodyForceFctPt	body_force_fct_pt () const
	Access function: Pointer to body force function (const version) More...

virtual void	get_stress (const Vector< double > &s, DenseMatrix< std::complex< double >> &sigma) const =0

void	get_strain (const Vector< double > &s, DenseMatrix< std::complex< double >> &strain) const
	Return the strain tensor. More...

void	body_force (const Vector< double > &x, Vector< std::complex< double >> &b) const

void	values_to_be_pinned_on_outer_pml_boundary (Vector< unsigned > &values_to_pin)

unsigned	ndof_types () const

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

void	compute_pml_coefficients (const unsigned &ipt, const Vector< double > &x, Vector< std::complex< double >> &pml_inverse_jacobian_diagonal, std::complex< double > &pml_jacobian_det)

PMLMapping *&	pml_mapping_pt ()
	Return a pointer to the PML Mapping object. More...

PMLMapping *const &	pml_mapping_pt () const
	Return a pointer to the PML Mapping object (const version) More...

Public Member Functions inherited from oomph::PMLElementBase< DIM >
	PMLElementBase ()
	Constructor. More...

virtual	~PMLElementBase ()
	Virtual destructor. More...

void	disable_pml ()

void	enable_pml (const int &direction, const double &interface_border_value, const double &outer_domain_border_value)

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

virtual void	output (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)

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

Static Public Attributes
static ContinuousBermudezPMLMapping	Default_pml_mapping

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 Attributes
PMLTimeHarmonicIsotropicElasticityTensor *	Elasticity_tensor_pt
	Pointer to the elasticity tensor. More...

double *	Omega_sq_pt
	Square of nondim frequency. More...

BodyForceFctPt	Body_force_fct_pt
	Pointer to body force function. More...

PMLMapping *	Pml_mapping_pt

Protected Attributes inherited from oomph::PMLElementBase< DIM >
bool	Pml_is_enabled
	Boolean indicating if element is used in pml mode. More...

std::vector< bool >	Pml_direction_active

Vector< double >	Pml_inner_boundary

Vector< double >	Pml_outer_boundary

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
static double	Default_omega_sq_value
	Static default value for square of frequency. More...

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

Additional Inherited Members
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)

Detailed Description

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

A base class for elements that solve the equations of time-harmonic linear elasticity in Cartesian coordinates. Combines a few generic functions that are shared by PMLTimeHarmonicLinearElasticityEquations and PMLTimeHarmonicLinearElasticityEquationsWithPressure (Note: The latter don't exist yet but will be written as soon as somebody needs them...)

Member Typedef Documentation

◆ BodyForceFctPt

template<unsigned DIM>

typedef void(* oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::BodyForceFctPt) (const Vector< double > &x, Vector< std::complex< double >> &b)

Function pointer to function that specifies the body force as a function of the Cartesian coordinates FCT(x,b) – x and b are Vectors!

Constructor & Destructor Documentation

◆ PMLTimeHarmonicLinearElasticityEquationsBase()

template<unsigned DIM>

oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::PMLTimeHarmonicLinearElasticityEquationsBase ( )

inline

Constructor: Set null pointers for constitutive law and for isotropic growth function. Set physical parameter values to default values, and set body force to zero.

       : Elasticity_tensor_pt(0),
         Omega_sq_pt(&Default_omega_sq_value),
         Body_force_fct_pt(0)
     {
       Pml_mapping_pt =
         &PMLTimeHarmonicLinearElasticityEquationsBase::Default_pml_mapping;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Default_pml_mapping, and oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Pml_mapping_pt.

Member Function Documentation

◆ body_force()

template<unsigned DIM>

void oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::body_force	(	const Vector< double > &	x,
		Vector< std::complex< double >> &	b
	)		const

inline

Evaluate body force at Eulerian coordinate x (returns zero vector if no body force function pointer has been set)

     {
       // If no function has been set, return zero vector
       if (Body_force_fct_pt == 0)
       {
         // Get spatial dimension of element
         unsigned n = dim();
         for (unsigned i = 0; i < n; i++)
         {
           b[i] = std::complex<double>(0.0, 0.0);
         }
       }
       else
       {
         // Get body force
         (*Body_force_fct_pt)(x, b);
       }
     }

References b, oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Body_force_fct_pt, oomph::FiniteElement::dim(), i, n, and plotDoE::x.

◆ body_force_fct_pt() [1/2]

template<unsigned DIM>

BodyForceFctPt& oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::body_force_fct_pt ( )

inline

Access function: Pointer to body force function.

     {
       return Body_force_fct_pt;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Body_force_fct_pt.

◆ body_force_fct_pt() [2/2]

template<unsigned DIM>

BodyForceFctPt oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::body_force_fct_pt ( ) const

inline

Access function: Pointer to body force function (const version)

     {
       return Body_force_fct_pt;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Body_force_fct_pt.

◆ compute_pml_coefficients()

template<unsigned DIM>

void oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::compute_pml_coefficients	(	const unsigned &	ipt,
		const Vector< double > &	x,
		Vector< std::complex< double >> &	pml_inverse_jacobian_diagonal,
		std::complex< double > &	pml_jacobian_det
	)

inline

Compute pml coefficients at position x and integration point ipt. pml_inverse_jacobian_diagonal contains the diagonal terms from the inverse of the Jacobian of the PML transformation. These are used to transform derivatives in real x to derivatives in transformed space \(\tilde x \). This can be interpreted as an anisotropic stiffness. pml_jacobian_det is the determinant of the Jacobian of the PML transformation, this allows us to transform volume integrals in transformed space to real space. This can be interpreted as a mass factor If the PML is not enabled via enable_pml, both default to 1.0.

The factors all default to 1.0 if the propagation medium is the physical domain (no PML transformation)

Vector which points from the inner boundary to x

Vector which points from the inner boundary to the edge of the boundary

Calculate the square of the non-dimensional wavenumber

     {
       for (unsigned k = 0; k < DIM; k++)
       {
         pml_inverse_jacobian_diagonal[k] = std::complex<double>(1.0, 0.0);
       }
       pml_jacobian_det = std::complex<double>(1.0, 0.0);
  
       // Only calculate PML factors if PML is enabled
       if (this->Pml_is_enabled)
       {
         Vector<double> nu(DIM);
         for (unsigned k = 0; k < DIM; k++)
         {
           nu[k] = x[k] - this->Pml_inner_boundary[k];
         }
  
         Vector<double> pml_width(DIM);
         for (unsigned k = 0; k < DIM; k++)
         {
           pml_width[k] =
             this->Pml_outer_boundary[k] - this->Pml_inner_boundary[k];
         }
  
 #ifdef PARANOID
         // Check if the Pml_mapping_pt is set
         if (this->Pml_mapping_pt == 0)
         {
           std::ostringstream error_message_stream;
           error_message_stream << "Pml_mapping_pt needs to be set "
                                << std::endl;
  
           throw OomphLibError(error_message_stream.str(),
                               OOMPH_CURRENT_FUNCTION,
                               OOMPH_EXCEPTION_LOCATION);
         }
 #endif
         // Declare gamma_i vectors of complex numbers for PML weights
         Vector<std::complex<double>> pml_gamma(DIM);
  
         double wavenumber_squared = 2.0 * (1.0 + this->nu()) * this->omega_sq();
  
         for (unsigned k = 0; k < DIM; k++)
         {
           // If PML is enabled in the respective direction
           if (this->Pml_direction_active[k])
           {
             std::complex<double> pml_gamma =
               Pml_mapping_pt->gamma(nu[k], pml_width[k], wavenumber_squared);
  
             // The diagonals of the INVERSE of the PML transformation jacobian
             // are 1/gamma
             pml_inverse_jacobian_diagonal[k] = 1.0 / pml_gamma;
             // To get the determinant, multiply all the diagonals together
             pml_jacobian_det *= pml_gamma;
           }
         }
       }
     }

References DIM, oomph::PMLMapping::gamma(), k, oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::nu(), oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::omega_sq(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::PMLElementBase< DIM >::Pml_direction_active, oomph::PMLElementBase< DIM >::Pml_inner_boundary, oomph::PMLElementBase< DIM >::Pml_is_enabled, oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Pml_mapping_pt, oomph::PMLElementBase< DIM >::Pml_outer_boundary, and plotDoE::x.

◆ E()

template<unsigned DIM>

std::complex<double> oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::E	(	const unsigned &	i,
		const unsigned &	j,
		const unsigned &	k,
		const unsigned &	l
	)		const

inline

Access function to the entries in the elasticity tensor.

     {
       return (*Elasticity_tensor_pt)(i, j, k, l);
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Elasticity_tensor_pt, i, j, and k.

◆ elasticity_tensor_pt()

template<unsigned DIM>

PMLTimeHarmonicIsotropicElasticityTensor*& oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::elasticity_tensor_pt ( )

inline

Return the pointer to the elasticity_tensor.

     {
       return Elasticity_tensor_pt;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Elasticity_tensor_pt.

Referenced by ElasticAnnulusProblem< ELASTICITY_ELEMENT >::complete_problem_setup().

◆ get_dof_numbers_for_unknowns()

template<unsigned DIM>

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

inlinevirtual

Create a list of pairs for all unknowns in this element, so that the first entry in each pair contains the global equation number of the unknown, while the second one contains the number of the "DOF types" that this unknown is associated with. (Function can obviously only be called if the equation numbering scheme has been set up.)

Reimplemented from oomph::GeneralisedElement.

     {
       // temporary pair (used to store dof lookup prior to being added
       // to list)
       std::pair<unsigned long, unsigned> dof_lookup;
  
       // number of nodes
       const unsigned n_node = this->nnode();
  
       // Integer storage for local unknown
       int local_unknown = 0;
  
       // Loop over the nodes
       for (unsigned n = 0; n < n_node; n++)
       {
         // Loop over dimension (real and imag)
         for (unsigned i = 0; i < 2 * DIM; i++)
         {
           // If the variable is free
           local_unknown = nodal_local_eqn(n, i);
  
           // ignore pinned values
           if (local_unknown >= 0)
           {
             // store dof lookup in temporary pair: First entry in pair
             // is global equation number; second entry is dof type
             dof_lookup.first = this->eqn_number(local_unknown);
             dof_lookup.second = 0;
  
             // add to list
             dof_lookup_list.push_front(dof_lookup);
           }
         }
       }
     }

References DIM, oomph::GeneralisedElement::eqn_number(), i, n, oomph::FiniteElement::nnode(), and oomph::FiniteElement::nodal_local_eqn().

◆ get_strain()

template<unsigned DIM>

void oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::get_strain	(	const Vector< double > &	s,
		DenseMatrix< std::complex< double >> &	strain
	)		const

Return the strain tensor.

Compute the strain tensor at local coordinate s.

/////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////

Now fill in the entries of the strain tensor

   {
 #ifdef PARANOID
     if ((strain.ncol() != DIM) || (strain.nrow() != DIM))
     {
       std::ostringstream error_message;
       error_message << "Strain matrix is " << strain.ncol() << " x "
                     << strain.nrow() << ", but dimension of the equations is "
                     << DIM << std::endl;
       throw OomphLibError(
         error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
     }
  
     // Find out how many position types there are
     unsigned n_position_type = this->nnodal_position_type();
  
     if (n_position_type != 1)
     {
       std::ostringstream error_message;
       error_message << "PMLTimeHarmonicLinearElasticity is not yet "
                     << "implemented for more than one position type"
                     << std::endl;
       throw OomphLibError(
         error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
     }
 #endif
  
  
     // Find out how many nodes there are in the element
     unsigned n_node = nnode();
  
     // Find the indices at which the local velocities are stored
     std::complex<unsigned> u_nodal_index[DIM];
     for (unsigned i = 0; i < DIM; i++)
     {
       u_nodal_index[i] = u_index_time_harmonic_linear_elasticity(i);
     }
  
     // Set up memory for the shape and derivative functions
     Shape psi(n_node);
     DShape dpsidx(n_node, DIM);
  
     // Call the derivatives of the shape functions
     (void)dshape_eulerian(s, psi, dpsidx);
  
     // Calculate interpolated values of the derivative of global position
     DenseMatrix<std::complex<double>> interpolated_dudx(
       DIM, DIM, std::complex<double>(0.0, 0.0));
  
     // Loop over nodes
     for (unsigned l = 0; l < n_node; l++)
     {
       // Loop over velocity components
       for (unsigned i = 0; i < DIM; i++)
       {
         // Get the nodal value
         const std::complex<double> u_value =
           std::complex<double>(this->nodal_value(l, u_nodal_index[i].real()),
                                this->nodal_value(l, u_nodal_index[i].imag()));
  
         // Loop over derivative directions
         for (unsigned j = 0; j < DIM; j++)
         {
           interpolated_dudx(i, j) += u_value * dpsidx(l, j);
         }
       }
     }
  
     for (unsigned i = 0; i < DIM; i++)
     {
       // Do upper half of matrix
       // Note that j must be signed here for the comparison test to work
       // Also i must be cast to an int
       for (int j = (DIM - 1); j >= static_cast<int>(i); j--)
       {
         // Off diagonal terms
         if (static_cast<int>(i) != j)
         {
           strain(i, j) =
             0.5 * (interpolated_dudx(i, j) + interpolated_dudx(j, i));
         }
         // Diagonal terms will including growth factor when it comes back in
         else
         {
           strain(i, i) = interpolated_dudx(i, i);
         }
       }
       // Matrix is symmetric so just copy lower half
       for (int j = (i - 1); j >= 0; j--)
       {
         strain(i, j) = strain(j, i);
       }
     }
   }

References DIM, i, imag(), j, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

Referenced by oomph::TPMLTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >::get_Z2_flux().

◆ get_stress()

template<unsigned DIM>

virtual void oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::get_stress	(	const Vector< double > &	s,
		DenseMatrix< std::complex< double >> &	sigma
	)		const

pure virtual

Return the Cauchy stress tensor, as calculated from the elasticity tensor at specified local coordinate Virtual so separaete versions can (and must!) be provided for displacement and pressure-displacement formulations.

Implemented in oomph::PMLTimeHarmonicLinearElasticityEquations< DIM >.

◆ interpolated_u_time_harmonic_linear_elasticity() [1/2]

template<unsigned DIM>

std::complex<double> oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::interpolated_u_time_harmonic_linear_elasticity	(	const Vector< double > &	s,
		const unsigned &	i
	)		const

inline

Return FE interpolated displacement u[i] at local coordinate s.

     {
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       // Get nodal index at which i-th velocity is stored
       std::complex<unsigned> u_nodal_index =
         u_index_time_harmonic_linear_elasticity(i);
  
       // Initialise value of u
       std::complex<double> interpolated_u(0.0, 0.0);
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         const std::complex<double> u_value(
           nodal_value(l, u_nodal_index.real()),
           nodal_value(l, u_nodal_index.imag()));
  
         interpolated_u += u_value * psi[l];
       }
  
       return (interpolated_u);
     }

References i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::u_index_time_harmonic_linear_elasticity().

◆ interpolated_u_time_harmonic_linear_elasticity() [2/2]

template<unsigned DIM>

void oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::interpolated_u_time_harmonic_linear_elasticity	(	const Vector< double > &	s,
		Vector< std::complex< double >> &	disp
	)		const

inline

Compute vector of FE interpolated displacement u at local coordinate s.

     {
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       for (unsigned i = 0; i < DIM; i++)
       {
         // Index at which the nodal value is stored
         std::complex<unsigned> u_nodal_index =
           u_index_time_harmonic_linear_elasticity(i);
  
         // Initialise value of u
         disp[i] = std::complex<double>(0.0, 0.0);
  
         // Loop over the local nodes and sum
         for (unsigned l = 0; l < n_node; l++)
         {
           const std::complex<double> u_value(
             nodal_value(l, u_nodal_index.real()),
             nodal_value(l, u_nodal_index.imag()));
  
           disp[i] += u_value * psi[l];
         }
       }
     }

References DIM, i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::u_index_time_harmonic_linear_elasticity().

◆ ndof_types()

template<unsigned DIM>

unsigned oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::ndof_types ( ) const

inlinevirtual

The number of "DOF types" that degrees of freedom in this element are sub-divided into: for now lump them all into one DOF type. Can be adjusted later

Reimplemented from oomph::GeneralisedElement.

     {
       return 1;
     }

◆ nu()

template<unsigned DIM>

double oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::nu ( ) const

inline

Access function to nu in the elasticity tensor.

     {
       return Elasticity_tensor_pt->nu();
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Elasticity_tensor_pt, and oomph::PMLTimeHarmonicIsotropicElasticityTensor::nu().

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::compute_pml_coefficients().

◆ omega_sq()

template<unsigned DIM>

const double& oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::omega_sq ( ) const

inline

Access function for square of non-dim frequency.

     {
       return *Omega_sq_pt;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Omega_sq_pt.

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::compute_pml_coefficients().

◆ omega_sq_pt()

template<unsigned DIM>

double*& oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::omega_sq_pt ( )

inline

Access function for square of non-dim frequency.

     {
       return Omega_sq_pt;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Omega_sq_pt.

Referenced by ElasticAnnulusProblem< ELASTICITY_ELEMENT >::complete_problem_setup().

◆ pml_mapping_pt() [1/2]

template<unsigned DIM>

PMLMapping*& oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::pml_mapping_pt ( )

inline

Return a pointer to the PML Mapping object.

     {
       return Pml_mapping_pt;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Pml_mapping_pt.

◆ pml_mapping_pt() [2/2]

template<unsigned DIM>

PMLMapping* const& oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::pml_mapping_pt ( ) const

inline

Return a pointer to the PML Mapping object (const version)

     {
       return Pml_mapping_pt;
     }

References oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Pml_mapping_pt.

◆ u_index_time_harmonic_linear_elasticity()

template<unsigned DIM>

virtual std::complex<unsigned> oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::u_index_time_harmonic_linear_elasticity ( const unsigned i ) const

inlinevirtual

Return the index at which the i-th real or imag unknown displacement component is stored. The default value is appropriate for single-physics problems:

     {
       return std::complex<unsigned>(i, i + DIM);
     }

References DIM, and i.

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::interpolated_u_time_harmonic_linear_elasticity().

◆ values_to_be_pinned_on_outer_pml_boundary()

template<unsigned DIM>

void oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::values_to_be_pinned_on_outer_pml_boundary ( Vector< unsigned > & values_to_pin )

inlinevirtual

Pure virtual function in which we specify the values to be pinned (and set to zero) on the outer edge of the pml layer. All of them! Vector is resized internally.

Implements oomph::PMLElementBase< DIM >.

     {
       values_to_pin.resize(DIM * 2);
       for (unsigned j = 0; j < DIM * 2; j++)
       {
         values_to_pin[j] = j;
       }
     }

References DIM, and j.

Member Data Documentation

◆ Body_force_fct_pt

template<unsigned DIM>

BodyForceFctPt oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Body_force_fct_pt

protected

Pointer to body force function.

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::body_force(), and oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::body_force_fct_pt().

◆ Default_omega_sq_value

template<unsigned DIM>

double oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Default_omega_sq_value

staticprotected

Initial value:

=

1.0

Static default value for square of frequency.

◆ Default_pml_mapping

template<unsigned DIM>

ContinuousBermudezPMLMapping oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Default_pml_mapping

static

Static so that the class doesn't need to instantiate a new default everytime it uses it

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::PMLTimeHarmonicLinearElasticityEquationsBase().

◆ Elasticity_tensor_pt

template<unsigned DIM>

PMLTimeHarmonicIsotropicElasticityTensor* oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Elasticity_tensor_pt

protected

Pointer to the elasticity tensor.

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::E(), oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::elasticity_tensor_pt(), and oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::nu().

◆ Omega_sq_pt

template<unsigned DIM>

double* oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Omega_sq_pt

protected

Square of nondim frequency.

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::omega_sq(), and oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::omega_sq_pt().

◆ Pml_mapping_pt

template<unsigned DIM>

PMLMapping* oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::Pml_mapping_pt

protected

Pointer to class which holds the pml mapping function, also known as gamma

Referenced by oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::compute_pml_coefficients(), oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::pml_mapping_pt(), and oomph::PMLTimeHarmonicLinearElasticityEquationsBase< DIM >::PMLTimeHarmonicLinearElasticityEquationsBase().

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

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Static Protected Attributes

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

◆ BodyForceFctPt

Constructor & Destructor Documentation

◆ PMLTimeHarmonicLinearElasticityEquationsBase()

Member Function Documentation

◆ body_force()

◆ body_force_fct_pt() [1/2]

◆ body_force_fct_pt() [2/2]

◆ compute_pml_coefficients()

◆ E()

◆ elasticity_tensor_pt()

◆ get_dof_numbers_for_unknowns()

◆ get_strain()

◆ get_stress()

◆ interpolated_u_time_harmonic_linear_elasticity() [1/2]

◆ interpolated_u_time_harmonic_linear_elasticity() [2/2]

◆ ndof_types()

◆ nu()

◆ omega_sq()

◆ omega_sq_pt()

◆ pml_mapping_pt() [1/2]

◆ pml_mapping_pt() [2/2]

◆ u_index_time_harmonic_linear_elasticity()

◆ values_to_be_pinned_on_outer_pml_boundary()

Member Data Documentation

◆ Body_force_fct_pt

◆ Default_omega_sq_value

◆ Default_pml_mapping

◆ Elasticity_tensor_pt

◆ Omega_sq_pt

◆ Pml_mapping_pt

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