#include <time_harmonic_linear_elasticity_elements.h>

Inheritance diagram for oomph::TimeHarmonicLinearElasticityEquations< DIM >:

Public Member Functions
	TimeHarmonicLinearElasticityEquations ()
	Constructor. More...

unsigned	required_nvalue (const unsigned &n) const
	Number of values required at node n. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)

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

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

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output exact solution x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]. More...

void	output (std::ostream &outfile)
	Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]. More...

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]. More...

void	output (FILE *file_pt)
	C-style output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i]. More...

void	compute_norm (double &norm)
	Compute norm of solution: square of the L2 norm. More...

Public Member Functions inherited from oomph::TimeHarmonicLinearElasticityEquationsBase< DIM >
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...

	TimeHarmonicLinearElasticityEquationsBase ()

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

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...

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...

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

unsigned	ndof_types () const

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

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 ()

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, 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)

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

	GeomObject (const unsigned &ndim)

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

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

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

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

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

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

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

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

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

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

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

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

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

Additional Inherited Members
Public Types inherited from oomph::TimeHarmonicLinearElasticityEquationsBase< DIM >
typedef void(*	BodyForceFctPt) (const double &t, 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 > &)

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::FiniteElement
virtual void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

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

Protected Attributes inherited from oomph::TimeHarmonicLinearElasticityEquationsBase< DIM >
TimeHarmonicElasticityTensor *	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...

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Static Protected Attributes inherited from oomph::TimeHarmonicLinearElasticityEquationsBase< DIM >
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

Detailed Description

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

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// A class for elements that solve the equations of linear elasticity in cartesian coordinates.

Constructor & Destructor Documentation

◆ TimeHarmonicLinearElasticityEquations()

template<unsigned DIM>

oomph::TimeHarmonicLinearElasticityEquations< DIM >::TimeHarmonicLinearElasticityEquations ( )

inline

Constructor.

319 {}

Member Function Documentation

◆ compute_norm()

template<unsigned DIM>

void oomph::TimeHarmonicLinearElasticityEquations< DIM >::compute_norm ( double & norm )

virtual

Compute norm of solution: square of the L2 norm.

Compute norm of the solution.

Reimplemented from oomph::GeneralisedElement.

   {
     // Initialise
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Vector for coordintes
     Vector<double> x(DIM);
  
     // Displacement vector
     Vector<std::complex<double>> disp(DIM);
  
     // Find out how many nodes there are in the element
     unsigned n_node = this->nnode();
  
     Shape psi(n_node);
  
     // Set the value of n_intpt
     unsigned n_intpt = this->integral_pt()->nweight();
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < DIM; i++)
       {
         s[i] = this->integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = this->integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = this->J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get FE function value
       this->interpolated_u_time_harmonic_linear_elasticity(s, disp);
  
       // Add to  norm
       for (unsigned ii = 0; ii < DIM; ii++)
       {
         norm += (disp[ii].real() * disp[ii].real() +
                  disp[ii].imag() * disp[ii].imag()) *
                 W;
       }
     }
   }

References DIM, i, J, s, w, oomph::QuadTreeNames::W, and plotDoE::x.

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

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

inlinevirtual

The jacobian is calculated by finite differences by default, We need only to take finite differences w.r.t. positional variables For this element

Reimplemented from oomph::FiniteElement.

     {
       // Add the contribution to the residuals
       this
         ->fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity(
           residuals, jacobian, 1);
     }

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

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

inlinevirtual

Return the residuals for the solid equations (the discretised principle of virtual displacements)

Reimplemented from oomph::GeneralisedElement.

     {
       fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::TimeHarmonicLinearElasticityEquations< DIM >::fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity().

◆ fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity()

template<unsigned DIM>

void oomph::TimeHarmonicLinearElasticityEquations< DIM >::fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		unsigned	flag
	)

privatevirtual

Private helper function to compute residuals and (if requested via flag) also the Jacobian matrix.

Compute the residuals for the linear elasticity equations in cartesian coordinates. Flag indicates if we want Jacobian too.

Reimplemented in oomph::RefineableTimeHarmonicLinearElasticityEquations< DIM >.

   {
     // Find out how many nodes there are
     unsigned n_node = this->nnode();
  
 #ifdef PARANOID
     // Find out how many positional dofs there are
     unsigned n_position_type = this->nnodal_position_type();
  
     if (n_position_type != 1)
     {
       throw OomphLibError("TimeHarmonicLinearElasticity is not yet implemented "
                           "for more than one position type",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }
  
     // Throw and error if an elasticity tensor has not been set
     if (this->Elasticity_tensor_pt == 0)
     {
       throw OomphLibError("No elasticity tensor set.",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }
 #endif
  
     // 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] = this->u_index_time_harmonic_linear_elasticity(i);
     }
  
  
     // Square of non-dimensional frequency
     const double omega_sq_local = this->omega_sq();
  
     // Set up memory for the shape functions
     Shape psi(n_node);
     DShape dpsidx(n_node, DIM);
  
     // Set the value of Nintpt -- the number of integration points
     unsigned n_intpt = this->integral_pt()->nweight();
  
     // Set the vector to hold the local coordinates in the element
     Vector<double> s(DIM);
  
     // Integer to store the local equation number
     int local_eqn = 0, local_unknown = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign the values of s
       for (unsigned i = 0; i < DIM; ++i)
       {
         s[i] = this->integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = this->integral_pt()->weight(ipt);
  
       // Call the derivatives of the shape functions (and get Jacobian)
       double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
  
       // Storage for Eulerian coordinates (initialised to zero)
       Vector<double> interpolated_x(DIM, 0.0);
  
       // Displacement
       Vector<std::complex<double>> interpolated_u(
         DIM, std::complex<double>(0.0, 0.0));
  
       // Calculate interpolated values of the derivative of global position
       // wrt lagrangian coordinates
       DenseMatrix<std::complex<double>> interpolated_dudx(
         DIM, DIM, std::complex<double>(0.0, 0.0));
  
       // Calculate displacements and derivatives
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over displacement components (deformed position)
         for (unsigned i = 0; i < DIM; i++)
         {
           // Calculate the Lagrangian coordinates and the accelerations
           interpolated_x[i] += this->raw_nodal_position(l, i) * psi(l);
  
  
           // Get the nodal displacements
           const std::complex<double> u_value = std::complex<double>(
             this->raw_nodal_value(l, u_nodal_index[i].real()),
             this->raw_nodal_value(l, u_nodal_index[i].imag()));
  
           interpolated_u[i] += u_value * psi(l);
  
           // Loop over derivative directions
           for (unsigned j = 0; j < DIM; j++)
           {
             interpolated_dudx(i, j) += u_value * dpsidx(l, j);
           }
         }
       }
  
       // Get body force at current time
       Vector<std::complex<double>> b(DIM);
       this->body_force(interpolated_x, b);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       //=====EQUATIONS OF LINEAR ELASTICITY ========
  
       // Loop over the test functions, nodes of the element
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over the displacement components
         for (unsigned a = 0; a < DIM; a++)
         {
           // Get the REAL equation number
           local_eqn = this->nodal_local_eqn(l, u_nodal_index[a].real());
  
           /*IF it's not a boundary condition*/
           if (local_eqn >= 0)
           {
             // Acceleration and body force
             residuals[local_eqn] +=
               (-omega_sq_local * interpolated_u[a].real() - b[a].real()) *
               psi(l) * W;
  
             // Stress term
             for (unsigned b = 0; b < DIM; b++)
             {
               for (unsigned c = 0; c < DIM; c++)
               {
                 for (unsigned d = 0; d < DIM; d++)
                 {
                   // Add the stress terms to the residuals
                   residuals[local_eqn] += this->E(a, b, c, d) *
                                           interpolated_dudx(c, d).real() *
                                           dpsidx(l, b) * W;
                 }
               }
             }
  
             // Jacobian entries
             if (flag)
             {
               // Loop over the displacement basis functions again
               for (unsigned l2 = 0; l2 < n_node; l2++)
               {
                 // Loop over the displacement components again
                 for (unsigned c = 0; c < DIM; c++)
                 {
                   local_unknown =
                     this->nodal_local_eqn(l2, u_nodal_index[c].real());
                   // If it's not pinned
                   if (local_unknown >= 0)
                   {
                     // Inertial term
                     if (a == c)
                     {
                       jacobian(local_eqn, local_unknown) -=
                         omega_sq_local * psi(l) * psi(l2) * W;
                     }
  
                     // Stress term
                     for (unsigned b = 0; b < DIM; b++)
                     {
                       for (unsigned d = 0; d < DIM; d++)
                       {
                         // Add the contribution to the Jacobian matrix
                         jacobian(local_eqn, local_unknown) +=
                           this->E(a, b, c, d) * dpsidx(l2, d) * dpsidx(l, b) *
                           W;
                       }
                     }
                   } // End of if not boundary condition
                 }
               }
             } // End of jacobian calculation
  
           } // End of if not boundary condition for real eqn
  
  
           // Get the IMAG equation number
           local_eqn = this->nodal_local_eqn(l, u_nodal_index[a].imag());
  
           /*IF it's not a boundary condition*/
           if (local_eqn >= 0)
           {
             // Acceleration and body force
             residuals[local_eqn] +=
               (-omega_sq_local * interpolated_u[a].imag() - b[a].imag()) *
               psi(l) * W;
  
             // Stress term
             for (unsigned b = 0; b < DIM; b++)
             {
               for (unsigned c = 0; c < DIM; c++)
               {
                 for (unsigned d = 0; d < DIM; d++)
                 {
                   // Add the stress terms to the residuals
                   residuals[local_eqn] += this->E(a, b, c, d) *
                                           interpolated_dudx(c, d).imag() *
                                           dpsidx(l, b) * W;
                 }
               }
             }
  
             // Jacobian entries
             if (flag)
             {
               // Loop over the displacement basis functions again
               for (unsigned l2 = 0; l2 < n_node; l2++)
               {
                 // Loop over the displacement components again
                 for (unsigned c = 0; c < DIM; c++)
                 {
                   local_unknown =
                     this->nodal_local_eqn(l2, u_nodal_index[c].imag());
                   // If it's not pinned
                   if (local_unknown >= 0)
                   {
                     // Inertial term
                     if (a == c)
                     {
                       jacobian(local_eqn, local_unknown) -=
                         omega_sq_local * psi(l) * psi(l2) * W;
                     }
  
                     // Stress term
                     for (unsigned b = 0; b < DIM; b++)
                     {
                       for (unsigned d = 0; d < DIM; d++)
                       {
                         // Add the contribution to the Jacobian matrix
                         jacobian(local_eqn, local_unknown) +=
                           this->E(a, b, c, d) * dpsidx(l2, d) * dpsidx(l, b) *
                           W;
                       }
                     }
                   } // End of if not boundary condition
                 }
               }
             } // End of jacobian calculation
  
           } // End of if not boundary condition for imag eqn
  
         } // End of loop over coordinate directions
       } // End of loop over shape functions
     } // End of loop over integration points
   }

References a, b, Global_Parameters::body_force(), calibrate::c, DIM, Global_Physical_Variables::E, i, imag(), J, j, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, s, w, and oomph::QuadTreeNames::W.

Referenced by oomph::TimeHarmonicLinearElasticityEquations< DIM >::fill_in_contribution_to_residuals().

◆ get_stress()

template<unsigned DIM>

void oomph::TimeHarmonicLinearElasticityEquations< DIM >::get_stress	(	const Vector< double > &	s,
		DenseMatrix< std::complex< double >> &	stress
	)		const

virtual

Return the Cauchy stress tensor, as calculated from the elasticity tensor at specified local coordinate

Compute the Cauchy stress tensor at local coordinate s for displacement formulation.

Implements oomph::TimeHarmonicLinearElasticityEquationsBase< DIM >.

   {
 #ifdef PARANOID
     if ((stress.ncol() != DIM) || (stress.nrow() != DIM))
     {
       std::ostringstream error_message;
       error_message << "Stress matrix is " << stress.ncol() << " x "
                     << stress.nrow() << ", but dimension of the equations is "
                     << DIM << std::endl;
       throw OomphLibError(
         error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
     }
 #endif
  
     // Get strain
     DenseMatrix<std::complex<double>> strain(DIM, DIM);
     this->get_strain(s, strain);
  
     // Now fill in the entries of the stress tensor without exploiting
     // symmetry -- sorry too lazy. This fct is only used for
     // postprocessing anyway...
     for (unsigned i = 0; i < DIM; i++)
     {
       for (unsigned j = 0; j < DIM; j++)
       {
         stress(i, j) = 0.0;
         for (unsigned k = 0; k < DIM; k++)
         {
           for (unsigned l = 0; l < DIM; l++)
           {
             stress(i, j) += this->E(i, j, k, l) * strain(k, l);
           }
         }
       }
     }
   }

References DIM, Global_Physical_Variables::E, i, j, k, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

◆ output() [1/4]

template<unsigned DIM>

void oomph::TimeHarmonicLinearElasticityEquations< DIM >::output ( FILE * file_pt )

inlinevirtual

C-style output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >, and oomph::QTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >.

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

References oomph::TimeHarmonicLinearElasticityEquations< DIM >::output().

◆ output() [2/4]

template<unsigned DIM>

void oomph::TimeHarmonicLinearElasticityEquations< DIM >::output	(	FILE *	file_pt,
		const unsigned &	n_plot
	)

virtual

Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i].

C-style output: x,y,[z],u,v,[w].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >, and oomph::QTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Tecplot header info
     fprintf(file_pt, "%s", this->tecplot_zone_string(nplot).c_str());
  
     // Loop over plot points
     unsigned num_plot_points = this->nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       this->get_s_plot(iplot, nplot, s);
  
       // Coordinates
       for (unsigned i = 0; i < DIM; i++)
       {
         fprintf(file_pt, "%g ", this->interpolated_x(s, i));
       }
  
       // Displacement
       for (unsigned i = 0; i < DIM; i++)
       {
         fprintf(
           file_pt,
           "%g ",
           this->interpolated_u_time_harmonic_linear_elasticity(s, i).real());
       }
       for (unsigned i = 0; i < DIM; i++)
       {
         fprintf(
           file_pt,
           "%g ",
           this->interpolated_u_time_harmonic_linear_elasticity(s, i).imag());
       }
     }
     fprintf(file_pt, "\n");
  
     // Write tecplot footer (e.g. FE connectivity lists)
     this->write_tecplot_zone_footer(file_pt, nplot);
   }

References DIM, i, imag(), and s.

◆ output() [3/4]

template<unsigned DIM>

void oomph::TimeHarmonicLinearElasticityEquations< DIM >::output ( std::ostream & outfile )

inlinevirtual

Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >, and oomph::QTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >.

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

Referenced by oomph::TimeHarmonicLinearElasticityEquations< DIM >::output(), oomph::QTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >::output(), and oomph::TTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >::output().

◆ output() [4/4]

template<unsigned DIM>

void oomph::TimeHarmonicLinearElasticityEquations< DIM >::output	(	std::ostream &	outfile,
		const unsigned &	n_plot
	)

virtual

Output: x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i].

Output: x,y,[z],u,v,[w].

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >, and oomph::QTimeHarmonicLinearElasticityElement< DIM, NNODE_1D >.

   {
     // Set output Vector
     Vector<double> s(DIM);
     Vector<double> x(DIM);
     Vector<std::complex<double>> u(DIM);
  
     // Tecplot header info
     outfile << this->tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = this->nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       this->get_s_plot(iplot, nplot, s);
  
       // Get Eulerian coordinates and displacements
       this->interpolated_x(s, x);
       this->interpolated_u_time_harmonic_linear_elasticity(s, u);
  
       // Output the x,y,..
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << x[i] << " ";
       }
  
       // Output u,v,..
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << u[i].real() << " ";
       }
  
       // Output u,v,..
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << u[i].imag() << " ";
       }
  
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     this->write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, i, s, and plotDoE::x.

◆ output_fct()

template<unsigned DIM>

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

virtual

Output exact solution x,y,[z],u_r,v_r,[w_r],u_i,v_i,[w_i].

Reimplemented from oomph::FiniteElement.

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Vector for coordintes
     Vector<double> x(DIM);
  
     // Tecplot header info
     outfile << this->tecplot_zone_string(nplot);
  
     // Exact solution Vector
     Vector<double> exact_soln(2 * DIM);
  
     // Loop over plot points
     unsigned num_plot_points = this->nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       this->get_s_plot(iplot, nplot, s);
  
       // Get x position as Vector
       this->interpolated_x(s, x);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Output x,y,...,u_exact,...
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << x[i] << " ";
       }
       for (unsigned i = 0; i < 2 * DIM; i++)
       {
         outfile << exact_soln[i] << " ";
       }
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     this->write_tecplot_zone_footer(outfile, nplot);
   }

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

◆ required_nvalue()

template<unsigned DIM>

unsigned oomph::TimeHarmonicLinearElasticityEquations< DIM >::required_nvalue ( const unsigned & n ) const

inlinevirtual

Number of values required at node n.

Reimplemented from oomph::FiniteElement.

     {
       return 2 * DIM;
     }

References DIM.

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

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ TimeHarmonicLinearElasticityEquations()

Member Function Documentation

◆ compute_norm()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_contribution_to_residuals_time_harmonic_linear_elasticity()

◆ get_stress()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct()

◆ required_nvalue()

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