FE-discretization of the time-harmonic E-based formulation of the eddy current model. More...

#include <eddy_current_e_nedelec.h>

Inheritance diagram for ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >:

Classes
struct	RegisterLocalDiscr

struct	tGeneratorCurrent
	class for a generator current (source) in a subdomain More...

Public Member Functions
	EddyCurrent_E_Nedelec (const char *functions, ConstSmartPtr< EMaterial< domain_type > > spSubsetData, number frequency)
	class constructor

void	set_generator_current (SmartPtr< TGridFunction > spgfJG, const char *cmp)
	adds a generator current item \( \mathbf{J}_{G,h} \) to the discretization

void	set_generator_current (SmartPtr< TGridFunction > spgfJG, const char cmp, const char ss_names=NULL)
	adds a generator current item \( \mathbf{J}_{G,h} \) to the discretization

Public Member Functions inherited from ug::IElemDisc< TDomain >
void	add_elem_modifier (SmartPtr< IElemDiscModifier< TDomain > > elemModifier)

std::vector< SmartPtr< IElemDiscModifier< TDomain > > > &	get_elem_modifier ()

	IElemDisc (const char functions, const char subsets)

	IElemDisc (const std::vector< std::string > &vFct, const std::vector< std::string > &vSubset)

Public Member Functions inherited from ug::IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
virtual void	add_def_A_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

virtual void	add_def_A_expl_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

virtual void	add_def_M_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

virtual void	add_jac_A_elem (LocalMatrix &J, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

virtual void	add_jac_M_elem (LocalMatrix &J, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

virtual void	add_rhs_elem (LocalVector &rhs, GridObject *elem, const MathVector< dim > vCornerCoords[])

TLeaf &	asLeaf ()

void	check_roid (ReferenceObjectID roid, int discType)

void	do_add_def_A_elem (LocalVector &d, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_add_def_A_expl_elem (LocalVector &d, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_add_def_M_elem (LocalVector &d, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_add_jac_A_elem (LocalMatrix &J, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_add_jac_M_elem (LocalMatrix &J, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_add_rhs_elem (LocalVector &rhs, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_fsh_elem_loop ()

void	do_fsh_timestep (const number time, VectorProxyBase *u, size_t algebra_id)

void	do_fsh_timestep_elem (const number time, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_prep_elem (LocalVector &u, GridObject *elem, const ReferenceObjectID roid, const MathVector< dim > vCornerCoords[])

void	do_prep_elem_loop (const ReferenceObjectID roid, const int si)

void	do_prep_timestep (number future_time, const number time, VectorProxyBase *u, size_t algebra_id)

void	do_prep_timestep_elem (const number time, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

virtual void	fsh_elem_loop ()

virtual void	fsh_timestep (number time, VectorProxyBase *u)

virtual void	fsh_timestep_elem (const number time, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

	IElemAssembleFuncs ()

virtual void	post_assemble_loop ()

virtual void	prep_assemble_loop ()

virtual void	prep_elem (const LocalVector &u, GridObject *elem, const ReferenceObjectID roid, const MathVector< dim > vCornerCoords[])

virtual void	prep_elem_loop (const ReferenceObjectID roid, const int si)

virtual void	prep_timestep (number future_time, number time, VectorProxyBase *u)

virtual void	prep_timestep_elem (const number time, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	set_roid (ReferenceObjectID id, int discType)

virtual	~IElemAssembleFuncs ()

Public Member Functions inherited from ug::IElemError< typename TDomain >
	IElemError (const char functions, const char subsets)

	IElemError (const std::vector< std::string > &vFct, const std::vector< std::string > &vSubset)

Public Member Functions inherited from ug::IElemDiscBase< typename TDomain >
SmartPtr< ApproximationSpace< TDomain > >	approx_space ()

ConstSmartPtr< ApproximationSpace< TDomain > >	approx_space () const

void	check_setup (bool bNonRegularGrid)

void	clear_imports ()

SmartPtr< TDomain >	domain ()

ConstSmartPtr< TDomain >	domain () const

const FunctionGroup &	function_group () const

ConstSmartPtr< FunctionPattern >	function_pattern () const

IDataImport< dim > &	get_import (size_t i)

	IElemDiscBase (const char functions="", const char subsets="")

	IElemDiscBase (const std::vector< std::string > &vFct, const std::vector< std::string > &vSubset)

bool	is_time_dependent () const

bool	local_time_series_needed ()

const LocalVectorTimeSeries *	local_time_solutions () const

const FunctionIndexMapping &	map () const

number	mass_scale () const

number	mass_scale () const

number	mass_scale (const size_t timePoint) const

number	mass_scale (const size_t timePoint) const

const std::vector< number > &	mass_scales () const

const std::vector< number > &	mass_scales () const

size_t	num_fct () const

size_t	num_imports () const

size_t	num_subsets () const

void	register_import (IDataImport< dim > &Imp)

virtual bool	requests_local_time_series ()

void	set_approximation_space (SmartPtr< ApproximationSpace< TDomain > > approxSpace)

void	set_functions (const std::string &functions)

void	set_functions (const std::vector< std::string > &functions)

void	set_stationary ()

void	set_stationary (bool bStationaryForced=true)

void	set_subsets (const std::string &subsets)

void	set_subsets (const std::vector< std::string > &subsets)

void	set_time_dependent (LocalVectorTimeSeries &locTimeSeries, const std::vector< number > &vScaleMass, const std::vector< number > &vScaleStiff)

void	set_time_independent ()

void	set_time_point (const size_t timePoint)

number	stiff_scale () const

number	stiff_scale () const

number	stiff_scale (const size_t timePoint) const

number	stiff_scale (const size_t timePoint) const

const std::vector< number > &	stiff_scales () const

const std::vector< number > &	stiff_scales () const

TDomain::subset_handler_type &	subset_handler ()

const TDomain::subset_handler_type &	subset_handler () const

const std::vector< std::string > &	symb_fcts () const

const std::vector< std::string > &	symb_subsets () const

number	time () const

size_t	time_point () const

virtual int	type () const

virtual bool	use_hanging () const

virtual	~IElemDiscBase ()

Public Member Functions inherited from ug::IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
TLeaf &	asLeaf ()

void	check_roid (ReferenceObjectID roid, int discType)

virtual void	compute_err_est_A_elem (const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)

virtual void	compute_err_est_M_elem (const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)

virtual void	compute_err_est_rhs_elem (GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)

void	do_compute_err_est_A_elem (LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)

void	do_compute_err_est_M_elem (LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)

void	do_compute_err_est_rhs_elem (GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)

void	do_fsh_err_est_elem_loop ()

void	do_prep_err_est_elem (LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

void	do_prep_err_est_elem_loop (const ReferenceObjectID roid, const int si)

virtual SmartPtr< IErrEstData< TDomain > >	err_est_data ()

bool	err_est_enabled () const

virtual void	fsh_err_est_elem_loop ()

	IElemEstimatorFuncs ()

virtual void	prep_err_est_elem (const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])

virtual void	prep_err_est_elem_loop (const ReferenceObjectID roid, const int si)

void	set_error_estimator (SmartPtr< IErrEstData< TDomain > > ee)

void	set_roid (ReferenceObjectID id, int discType)

virtual	~IElemEstimatorFuncs ()

Private Types
typedef IElemDisc< TDomain >	base_type
	base class type

typedef base_type::domain_type	domain_type
	domain type

typedef base_type::position_type	position_type
	position type

typedef GridFunction< TDomain, TAlgebra >	TGridFunction
	type of grid functions (used for the sources)

typedef EddyCurrent_E_Nedelec< TDomain, TAlgebra >	this_type
	own type

Private Member Functions
template<typename TElem >
void	ass_dA_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const position_type vCornerCoords[])
	computes the local defect and transfers it to the global discretization

template<typename TElem >
void	ass_dM_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const position_type vCornerCoords[])
	computes the mass part of the defect of a time-dependent problem

template<size_t numEdges>
void	ass_elem_stiffness (number perm, number cond, number S[2][numEdges][2][numEdges])
	composes the stiffness matrix of the stationary problem

template<typename TElem >
void	ass_JA_elem (LocalMatrix &J, const LocalVector &u, GridObject *elem, const position_type vCornerCoords[])
	transfers the precomputed local stiffness matrix to the global discretization

template<typename TElem >
void	ass_JM_elem (LocalMatrix &J, const LocalVector &u, GridObject *elem, const position_type vCornerCoords[])
	computes the mass matrix of a time-dependent problem

template<typename TElem >
void	ass_rhs_elem (LocalVector &d, GridObject *elem, const position_type vCornerCoords[])
	computes the right-hand side due to the generator currents

template<typename TElem >
void	finish_element_loop ()
	finalizes the loop over the elements: clear the source

template<typename TElem >
void	prepare_element (const LocalVector &u, GridObject *elem, ReferenceObjectID roid, const position_type vCornerCoords[])
	prepares a given element for assembling: computes the discretization of the rot-rot operator

template<typename TElem >
void	prepare_element_loop (ReferenceObjectID roid, int si)
	prepares the loop over the elements: checks whether the parameters are set, ...

virtual void	prepare_setting (const std::vector< LFEID > &vLfeID, bool bNonRegular)
	check type of the grid and the trial space

void	register_all_loc_discr_funcs ()
	registers the local assembler functions for all the elements and dimensions

template<typename TElem >
void	register_loc_discr_func ()
	registers the local assembler functions for a given element

Private Attributes
number	m_conductivity
	the electric conductivity in the subdomain

number	m_omega
	frequency \(\omega\) for the discretization

number	m_permeability
	the magnetic permeability in the subdomain

tGeneratorCurrent *	m_pSsJG
	the source active in the current (assembled) subset

number	m_rot_rot_M [maxNumEdges][maxNumEdges]
	local mass matrix of the rot-rot operator

number	m_rot_rot_S [maxNumEdges][maxNumEdges]
	local stiffness matrix of the rot-rot operator

ConstSmartPtr< EMaterial< domain_type > >	m_spSubsetData
	parameters of the materials in the domain

std::vector< tGeneratorCurrent >	m_vJG
	array of all the sources (generator currents)

Static Private Attributes
static const int	dim = base_type::dim
	world dimension

static const size_t	maxNumEdges = element_list_traits<typename domain_traits<dim>::DimElemList>::maxEdges
	max. number of the edges of the full-dimensional elements in the domain

Additional Inherited Members
Public Types inherited from ug::IElemDisc< TDomain >
typedef IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >	assemble_base_type

typedef IElemError< TDomain >	base_type

typedef TDomain	domain_type

typedef IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >	estimator_base_type

Public Types inherited from ug::IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
typedef TDomain	domain_type

typedef TLeaf	leaf_type

Public Types inherited from ug::IElemError< typename TDomain >
typedef TDomain	domain_type

typedef IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >	estimator_base_type

Public Types inherited from ug::IElemDiscBase< typename TDomain >
typedef TDomain	domain_type

typedef TDomain::position_type	position_type

Public Types inherited from ug::IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
typedef TDomain	domain_type

typedef TLeaf	leaf_type

Static Public Attributes inherited from ug::IElemDisc< TDomain >
static const int	dim

Static Public Attributes inherited from ug::IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
static const int	dim

Static Public Attributes inherited from ug::IElemError< typename TDomain >
static const int	dim

Static Public Attributes inherited from ug::IElemDiscBase< typename TDomain >
static const int	dim

Static Public Attributes inherited from ug::IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
static const int	dim

Static Public Attributes inherited from ug::Electromagnetism::EddyCurrentTraits
static const size_t	_Im_ = 1
	index of the imaginary part in the grid functions

static const size_t	_Re_ = 0
	index of the real part in the grid functions

Protected Member Functions inherited from ug::IElemDisc< TDomain >
void	clear_add_fct ()

void	clear_add_fct (ReferenceObjectID id)

void	set_default_add_fct ()

Protected Member Functions inherited from ug::IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
void	clear_add_fct ()

void	clear_add_fct (ReferenceObjectID id)

void	remove_add_def_A_elem_fct (ReferenceObjectID id)

void	remove_add_def_A_expl_elem_fct (ReferenceObjectID id)

void	remove_add_def_M_elem_fct (ReferenceObjectID id)

void	remove_add_jac_A_elem_fct (ReferenceObjectID id)

void	remove_add_jac_M_elem_fct (ReferenceObjectID id)

void	remove_add_rhs_elem_fct (ReferenceObjectID id)

void	remove_fsh_elem_loop_fct (ReferenceObjectID id)

void	remove_fsh_timestep_elem_fct (ReferenceObjectID id)

void	remove_fsh_timestep_fct (size_t algebra_id)

void	remove_prep_elem_fct (ReferenceObjectID id)

void	remove_prep_elem_loop_fct (ReferenceObjectID id)

void	remove_prep_timestep_elem_fct (ReferenceObjectID id)

void	remove_prep_timestep_fct (size_t algebra_id)

void	set_add_def_A_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_add_def_A_expl_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_add_def_M_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_add_jac_A_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_add_jac_M_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_add_rhs_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_default_add_fct ()

void	set_fsh_elem_loop_fct (ReferenceObjectID id, TAssFunc func)

void	set_fsh_timestep_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_fsh_timestep_fct (size_t algebra_id, TAssFunc func)

void	set_prep_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_prep_elem_loop_fct (ReferenceObjectID id, TAssFunc func)

void	set_prep_timestep_elem_fct (ReferenceObjectID id, TAssFunc func)

void	set_prep_timestep_fct (size_t algebra_id, TAssFunc func)

Protected Member Functions inherited from ug::IElemError< typename TDomain >
void	clear_add_fct ()

void	clear_add_fct (ReferenceObjectID id)

Protected Member Functions inherited from ug::IElemDiscBase< typename TDomain >
virtual void	approximation_space_changed ()

void	set_function_pattern (ConstSmartPtr< FunctionPattern > fctPatt)

void	update_function_index_mapping ()

Protected Member Functions inherited from ug::IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
void	clear_add_fct ()

void	clear_add_fct (ReferenceObjectID id)

void	remove_compute_err_est_A_elem (ReferenceObjectID id)

void	remove_compute_err_est_M_elem (ReferenceObjectID id)

void	remove_compute_err_est_rhs_elem (ReferenceObjectID id)

void	remove_fsh_err_est_elem_loop (ReferenceObjectID id)

void	remove_prep_err_est_elem (ReferenceObjectID id)

void	remove_prep_err_est_elem_loop (ReferenceObjectID id)

void	set_compute_err_est_A_elem (ReferenceObjectID id, TAssFunc func)

void	set_compute_err_est_M_elem (ReferenceObjectID id, TAssFunc func)

void	set_compute_err_est_rhs_elem (ReferenceObjectID id, TAssFunc func)

void	set_default_add_fct ()

void	set_fsh_err_est_elem_loop (ReferenceObjectID id, TAssFunc func)

void	set_prep_err_est_elem (ReferenceObjectID id, TAssFunc func)

void	set_prep_err_est_elem_loop (ReferenceObjectID id, TAssFunc func)

Protected Attributes inherited from ug::IElemDisc< TDomain >
std::vector< SmartPtr< IElemDiscModifier< TDomain > > >	m_spElemModifier

Protected Attributes inherited from ug::IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
ReferenceObjectID	m_roid

Protected Attributes inherited from ug::IElemDiscBase< typename TDomain >
bool	m_bStationaryForced

FunctionGroup	m_fctGrp

FunctionIndexMapping	m_fctIndexMap

LocalVectorTimeSeries *	m_pLocalVectorTimeSeries

SmartPtr< ApproximationSpace< TDomain > >	m_spApproxSpace

ConstSmartPtr< FunctionPattern >	m_spFctPattern

size_t	m_timePoint

std::vector< std::string >	m_vFct

std::vector< IDataImport< dim > * >	m_vIImport

std::vector< number >	m_vScaleMass

std::vector< number >	m_vScaleStiff

std::vector< std::string >	m_vSubset

Protected Attributes inherited from ug::IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
ReferenceObjectID	m_roid

SmartPtr< IErrEstData< TDomain > >	m_spErrEstData

Detailed Description

template<typename TDomain, typename TAlgebra>
class ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >

FE-discretization of the time-harmonic E-based formulation of the eddy current model.

This class implements the local FE-discretization of the time-harmonic E-based formulation of the eddy current model using the linear Nedelec-Type-1 (Whitney-1) elements. The model is formulated as follows:

\begin{eqnarray*} \mathbf{rot} \mu^{-1} \mathbf{rot} \mathbf{E} + i \omega \sigma \mathbf{E} = - i \omega \mathbf{J}_G, \end{eqnarray*}

where

\( \mathbf{E} \) (unknown, complex-valued scalar) electric field
\( \mu \) (given) magnetic permeability (a real number)
\( \sigma \) (given) conductivity (a real number)
\( \omega \) (given) frequency (a real number)
\( \mathbf{J}_G \) (given) generator current (non-zero only in the subdomain with \( \sigma = 0 \))
\( i = \sqrt{-1} \)

Remarks: Note that every Nedelec shape function requires a scalar (complex) dof value. These functions are thus vector-valued for the scalar dofs, each dof storing two doubles (one for the real and one for the imaginary part of the value).

References:

O. Sterz. Modellierung und Numerik zeitharmonischer Wirbelstromprobleme in 3D. PhD thesis, Heidelberg University, 2003.
A. Bossavit. Computational Electromagnetism. Academic Press (Boston), 1998

Template Parameters

TDomain	Domain type
TAlgebra	Algebra type

Member Typedef Documentation

◆ base_type

template<typename TDomain , typename TAlgebra >

typedef IElemDisc<TDomain> ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::base_type

private

base class type

◆ domain_type

template<typename TDomain , typename TAlgebra >

typedef base_type::domain_type ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::domain_type

private

domain type

◆ position_type

template<typename TDomain , typename TAlgebra >

typedef base_type::position_type ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::position_type

private

position type

◆ TGridFunction

template<typename TDomain , typename TAlgebra >

typedef GridFunction<TDomain, TAlgebra> ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::TGridFunction

private

type of grid functions (used for the sources)

◆ this_type

template<typename TDomain , typename TAlgebra >

typedef EddyCurrent_E_Nedelec<TDomain,TAlgebra> ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::this_type

private

own type

Constructor & Destructor Documentation

◆ EddyCurrent_E_Nedelec()

template<typename TDomain , typename TAlgebra >

ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::EddyCurrent_E_Nedelec	(	const char *	functions,
		ConstSmartPtr< EMaterial< domain_type > >	spSubsetData,
		number	frequency
	)

class constructor

Parameters

functions	grid function names
spSubsetData	material data object
frequency	frequency \(\omega\)

References ug::IElemDiscBase< typename TDomain >::num_fct(), ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::register_all_loc_discr_funcs(), and UG_THROW.

Member Function Documentation

◆ ass_dA_elem()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::ass_dA_elem	(	LocalVector &	d,
		const LocalVector &	u,
		GridObject *	elem,
		const position_type	vCornerCoords[]
	)

private

computes the local defect and transfers it to the global discretization

◆ ass_dM_elem()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::ass_dM_elem	(	LocalVector &	d,
		const LocalVector &	u,
		GridObject *	elem,
		const position_type	vCornerCoords[]
	)

private

computes the mass part of the defect of a time-dependent problem

This is a stationary problem, so there is no mass matrix in this sence. For this, the following function does nothing.

◆ ass_elem_stiffness()

template<typename TDomain , typename TAlgebra >

template<size_t numEdges>

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::ass_elem_stiffness	(	number	perm,
		number	cond,
		number	S[2][numEdges][2][numEdges]
	)

private

composes the stiffness matrix of the stationary problem

composes the local stiffness matrix

This function composes the local stiffness matrix of the stationary problem by combining the stiffness and the mass matrix of the discretization of the rot-rot operator. Following O. Sterz, the system has the following block form:

\begin{eqnarray*} \left ( \begin{array} {cc} - S_h (\mu^{-1}) & \omega M^{(1)}_h (\sigma) \\ \omega M^{(1)}_h (\sigma) & S_h (\mu^{-1}) \end{array} \right ) \left ( \begin{array} {c} \mathbf{Re} \mathbf{E}_h \\ \mathbf{Im} \mathbf{E}_h \end{array} \right ) = \left ( \begin{array} {c} - \omega M^{(1)}_h (1) \mathbf{Im} \mathbf{J}_{Gh} \\ - \omega M^{(1)}_h (1) \mathbf{Re} \mathbf{J}_{Gh} \end{array} \right ), \end{eqnarray*}

where

\(S_h (\mu^{-1})\) the stiffness matrix of the \(\mathbf{rot}\mu^{-1}\mathbf{rot}\),
\( M^{(1)}_h (\sigma)\) the mass matrix of the \(\sigma I\) operator,
\(\mathbf{E}_h\) the unknown electric field grid function (represented using the Nedelec element),
\(\mathbf{J}_{Gh}\) the generator current (represented using the Nedelec element).

Remarks: For the solvability of the problem, the generator current must be numerically weakly divergence free (cf. the documentation for the class NedelecLoopCurrent for details).

Parameters

perm	the magnetic permeability
cond	the electric conductivity
S	for the composed matrix

◆ ass_JA_elem()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::ass_JA_elem	(	LocalMatrix &	J,
		const LocalVector &	u,
		GridObject *	elem,
		const position_type	vCornerCoords[]
	)

private

transfers the precomputed local stiffness matrix to the global discretization

◆ ass_JM_elem()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::ass_JM_elem	(	LocalMatrix &	J,
		const LocalVector &	u,
		GridObject *	elem,
		const position_type	vCornerCoords[]
	)

private

computes the mass matrix of a time-dependent problem

This is a stationary problem, so there is no mass matrix in this sence. For this, the following function does nothing.

◆ ass_rhs_elem()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::ass_rhs_elem	(	LocalVector &	b,
		GridObject *	elem,
		const position_type	vCornerCoords[]
	)

private

computes the right-hand side due to the generator currents

The right-hand side has the form

\begin{eqnarray*} \left ( \begin{array} {c} - \omega M^{(1)}_h \mathbf{Im} \mathbf{J}_{Gh} \\ - \omega M^{(1)}_h \mathbf{Re} \mathbf{J}_{Gh} \end{array} \right ), \end{eqnarray*}

where

\( M^{(1)}_h\) the mass matrix of the \(I\) (identity) operator,
\(\mathbf{J}_{Gh}\) the generator current (represented using the Nedelec element).

Remarks: For the solvability of the problem, the generator current must be numerically weakly divergence free.

References ug::DoFRef().

◆ finish_element_loop()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::finish_element_loop ( )

private

finalizes the loop over the elements: clear the source

◆ prepare_element()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::prepare_element	(	const LocalVector &	u,
		GridObject *	elem,
		ReferenceObjectID	roid,
		const position_type	vCornerCoords[]
	)

private

prepares a given element for assembling: computes the discretization of the rot-rot operator

Parameters

u	local solution at the dofs associated with elem
elem	element to prepare
vCornerCoords	coordinates of the corners of the element

References ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::local_stiffness_and_mass().

◆ prepare_element_loop()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::prepare_element_loop	(	ReferenceObjectID	roid,
		int	si
	)

private

prepares the loop over the elements: checks whether the parameters are set, ...

Parameters

roid	only elements with this roid are looped over
si	and only in this subdomain

References UG_THROW.

◆ prepare_setting()

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::prepare_setting	(	const std::vector< LFEID > &	vLfeID,
		bool	bNonRegular
	)

privatevirtual

check type of the grid and the trial space

Implements ug::IElemDiscBase< typename TDomain >.

References ug::LFEID::NEDELEC, type(), and UG_THROW.

◆ register_all_loc_discr_funcs()

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::register_all_loc_discr_funcs ( )

private

registers the local assembler functions for all the elements and dimensions

Referenced by ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::EddyCurrent_E_Nedelec().

◆ register_loc_discr_func()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::register_loc_discr_func ( )

private

registers the local assembler functions for a given element

Referenced by ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::RegisterLocalDiscr::operator()().

◆ set_generator_current() [1/2]

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::set_generator_current	(	SmartPtr< TGridFunction >	spgfJG,
		const char *	cmp
	)

inline

adds a generator current item \( \mathbf{J}_{G,h} \) to the discretization

Parameters

spgfJG	grid function with the data
cmp	grid function components

References ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::set_generator_current().

◆ set_generator_current() [2/2]

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::set_generator_current	(	SmartPtr< TGridFunction >	spgfJG,
		const char *	cmp,
		const char *	ss_names = `NULL`
	)

adds a generator current item \( \mathbf{J}_{G,h} \) to the discretization

Adds a generator current item \( \mathbf{J}_{G,h} \) to the discretization.

Remarks: Note that for the solvability of the problem, the correct specification of the subsets is important.

See also: NedelecLoopCurrent

Parameters

spgfJG	grid function with the data
cmp	grid function components
ss_names	names of the subsets where the current is defined (NULL for "everywhere")

References ug::SubsetGroup::add(), SmartPtr< typename T, template< class TT > class FreePolicy >::invalid(), ug::LFEID::NEDELEC, ug::RemoveWhitespaceFromString(), ug::TokenizeString(), UG_CATCH_THROW, and UG_THROW.

Referenced by ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::set_generator_current().

Member Data Documentation

◆ dim

template<typename TDomain , typename TAlgebra >

const int ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::dim = base_type::dim

staticprivate

world dimension

◆ m_conductivity

template<typename TDomain , typename TAlgebra >

number ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_conductivity

private

the electric conductivity in the subdomain

◆ m_omega

template<typename TDomain , typename TAlgebra >

number ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_omega

private

frequency \(\omega\) for the discretization

◆ m_permeability

template<typename TDomain , typename TAlgebra >

number ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_permeability

private

the magnetic permeability in the subdomain

◆ m_pSsJG

template<typename TDomain , typename TAlgebra >

tGeneratorCurrent* ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_pSsJG

private

the source active in the current (assembled) subset

◆ m_rot_rot_M

template<typename TDomain , typename TAlgebra >

number ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_rot_rot_M[maxNumEdges][maxNumEdges]

private

local mass matrix of the rot-rot operator

◆ m_rot_rot_S

template<typename TDomain , typename TAlgebra >

number ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_rot_rot_S[maxNumEdges][maxNumEdges]

private

local stiffness matrix of the rot-rot operator

◆ m_spSubsetData

template<typename TDomain , typename TAlgebra >

ConstSmartPtr<EMaterial<domain_type> > ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_spSubsetData

private

parameters of the materials in the domain

◆ m_vJG

template<typename TDomain , typename TAlgebra >

std::vector<tGeneratorCurrent> ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::m_vJG

private

array of all the sources (generator currents)

◆ maxNumEdges

template<typename TDomain , typename TAlgebra >

const size_t ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::maxNumEdges = element_list_traits<typename domain_traits<dim>::DimElemList>::maxEdges

staticprivate

max. number of the edges of the full-dimensional elements in the domain

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

/home/runner/work/docs/docs/ug4/plugins/Electromagnetism/EddyCurrent_E_Nedelec/eddy_current_e_nedelec.h
/home/runner/work/docs/docs/ug4/plugins/Electromagnetism/EddyCurrent_E_Nedelec/eddy_current_e_nedelec_impl.h

Classes

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

◆ domain_type

◆ position_type

◆ TGridFunction

◆ this_type

Constructor & Destructor Documentation

◆ EddyCurrent_E_Nedelec()

Member Function Documentation

◆ ass_dA_elem()

◆ ass_dM_elem()

◆ ass_elem_stiffness()

◆ ass_JA_elem()

◆ ass_JM_elem()

◆ ass_rhs_elem()

◆ finish_element_loop()

◆ prepare_element()

◆ prepare_element_loop()

◆ prepare_setting()

◆ register_all_loc_discr_funcs()

◆ register_loc_discr_func()

◆ set_generator_current() [1/2]

◆ set_generator_current() [2/2]

Member Data Documentation

◆ dim

◆ m_conductivity

◆ m_omega

◆ m_permeability

◆ m_pSsJG

◆ m_rot_rot_M

◆ m_rot_rot_S

◆ m_spSubsetData

◆ m_vJG

◆ maxNumEdges