Class for computation of loop currents. More...

#include <nedelec_source.h>

Classes
class	AuxLaplaceLocAss
	Class for local assembling of the auxiliary Laplace operator. More...

struct	GetFluxOfPotential
	Helper class for computation of the flux of potential over the cut. More...

class	LocLaplaceA
	Helper class for assembling the local stiffness matrix of Laplacian in various routines. More...

struct	MarkSourceEdges
	Helper class for marking the edges in the source. More...

class	OutOfSource
	Constraint that sets the problem to 0-identity out of the source. More...

struct	TSrcData
	Structure for keeping electric current data. More...

class	ZeroAverage
	Postprocessor to eliminate the kernel parts in the solution. More...

Public Types
typedef TAlgebra	algebra_type
	Type of algebra (for the Nedelec-element-based grid functions) More...

typedef TDomain	domain_type
	Type of Domain. More...

typedef TDomain::grid_type	grid_type
	Type of Grid: More...

typedef TAlgebra::matrix_type	matrix_type
	Type of Vector (for the Nedelec-element-based grid functions) More...

typedef TDomain::position_type	position_type
	position type More...

typedef GridFunction< TDomain, TPotAlgebra >	pot_gf_type
	Grid function type for the potential space. More...

typedef TPotAlgebra::matrix_type	pot_matrix_type
	Matrix type for the potential space. More...

typedef TPotAlgebra::vector_type	pot_vector_type
	Vector type for the potential space. More...

typedef domain_type::subset_handler_type	subset_handler_type
	Type of subset handler. More...

typedef CPUAlgebra	TPotAlgebra
	The auxiliary algebra type for the space of the potential. (Note: It should be scalar.) More...

typedef TAlgebra::vector_type	vector_type
	Type of Vector (for the Nedelec-element-based grid functions) More...

Public Member Functions
void	compute (SmartPtr< GridFunction< TDomain, TAlgebra > > sp_u)
	Computation of the source (only if 'init'ialized): distributes the potential. More...

	NedelecLoopCurrent (const char ssNames, const char posSsNames, const char *cutSsNames, SmartPtr< ApproximationSpace< TDomain > > vertApproxSpace, SmartPtr< ILinearOperatorInverse< pot_vector_type > > potSolver)
	Constructor. More...

void	set (const char *fctNames, number I)
	Setting the electric current value. More...

std::string	subsets ()
	Returns the subsets where the source is defined. More...

SmartPtr< ITransferPostProcess< TDomain, TPotAlgebra > >	zero_average ()
	Returns the postprocess routine to eliminate the kernel part of the potential. More...

Static Public Attributes
static const int	WDim = TDomain::dim
	world dimention More...

Private Types
typedef AChar	a_edge_flag_type
	Type of the attachment and its accessor for flags. More...

typedef ABool	a_vert_flag_type

typedef Grid::EdgeAttachmentAccessor< a_edge_flag_type >	aa_edge_flag_type

typedef Grid::VertexAttachmentAccessor< a_vert_flag_type >	aa_vert_flag_type

typedef NedelecLoopCurrent< TDomain, TAlgebra >	this_type
	This type. More...

Private Member Functions
void	compute_potential (pot_gf_type &pot_u)
	Computes the potential of the source. More...

void	distribute_source_potential (const DoFDistribution &vertDD, pot_vector_type &src_pot, DoFDistribution &edgeDD, size_t func, number value, vector_type &src_field)
	Computes the gradient of the potential. More...

template<typename TElem >
void	get_flux_of_pot (const TDomain &domain, const pot_vector_type &pot, const DoFDistribution &vertDD, number &flux)
	Computes the flux of of the gradient of the potential over the cut (for one type of elements) More...

template<typename TElem >
void	mark_source_edges (const DoFDistribution &edgeDD, aa_edge_flag_type &in_source)
	Marks edges that belong to the loop source domain (for one type of elements) More...

Private Attributes
SubsetGroup	m_allSsGrp
	Group of all the subsets of the source. More...

std::string	m_allSsNames
	Names of all the subsets of the source. More...

SmartPtr< DomainDiscretization< TDomain, TPotAlgebra > >	m_auxLaplaceAss
	Global discretization of the auxiliary equations. More...

SmartPtr< AssembledLinearOperator< TPotAlgebra > >	m_auxLaplaceOp
	Matrix of the discretization. More...

SmartPtr< AuxLaplaceLocAss >	m_auxLocLaplace
	Local discretization of the auxiliary equations. More...

SubsetGroup	m_cutSsGrp
	Group of the surfaces of the cut of the loop. More...

std::string	m_cutSsNames
	Names of the surfaces of the cut of the loop. More...

SmartPtr< OutOfSource >	m_outOfSource
	Extension of the matrices and vectors to the whole domain. More...

SubsetGroup	m_posSsGrp
	Group of the subsets of the positive direction. More...

std::string	m_posSsNames
	Names of the subsets of the positive direction. More...

SmartPtr< ILinearOperatorInverse< pot_vector_type > >	m_potSolver
	Solver for the auxliliary equations. More...

SmartPtr< ApproximationSpace< TDomain > >	m_spVertApproxSpace
	Vertex-centered approximation space. More...

std::vector< TSrcData >	m_vSrcData
	Array of the electric current data. More...

SmartPtr< ZeroAverage >	m_zeroAverage
	Elimination of the kernal parts in the solution. More...

Detailed Description

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

Class for computation of loop currents.

Class for computation of weakly divergence-free loop currents that are non-zero only in a given subdomain \(T\) (i.e. in a coil).

The range (image) of the stiffness matrix of the discrete \(\mathbf{rot} \, \mathbf{rot}\) operator is the subspace of all functions othrogonal to all the gradients \( \mathbf{G} \psi \), where \( \mathbf{G} \) is the incidence matrix between the vertices and the edges, and \( \psi \) is any vertex-centered grid function. Thus, for the solvability of the discretized system (for ex. of the E-based formulation of the eddy-current model), its right-hand side \(M^{(1)} J \) ( \(M^{(1)}\) being the mass matrix of the Whitney-1 shapes) must satisfy

\begin{eqnarray*} ( \mathbf{G}^T M^{(1)} J, \psi ) = ( M^{(1)} J, \mathbf{G} \psi ) = 0 \end{eqnarray*}

This is really true only in insulators. In conductors, a mass matrix is added to the \(\mathbf{rot} \, \mathbf{rot}\) operator, so that the kernel is trivial. We assume that a coil is modelled as a zero-conductivity medium with the source, so that \(T\) is completely contained in insulators. Thus the former condition implies

\begin{eqnarray*} \mathbf{G}_{i}^T M^{(1)} J = 0, \end{eqnarray*}

(with \( J = 0 \) out of \( T \)) i.e. the weak divergence of the rhs must be zero.

This class implements a computation of such a weakly divergence-free current \(J\) in a given set of insulators \(T\) constituting (topologically) a ring (torus) by specifying a cut with the jump of the potential and a part adjacent to this cut that specifies the positive direction of the current. The current is represented as \(J = \hat{\mathbf{G}} \phi\) and the potential \(\phi\) is computed as the solution of a discretized Laplace equation with the special boundary conditions. Here, \(\hat{\mathbf{G}}\) is the matrix obtained from \(\mathbf{G}\) by replacing the rows

The computed \(J\) is rescaled so that the current over the cut is equal to the given value. Different values of the currents can be used for different function names: cf. the 'set' functions of this class.

Note that the mass matrix \(M^{(1)}\) is not the same as the mass matrix at the off-diagonal positions of the stiffness matrix of the time-harmonic problem. The matrix \(M^{(1)}\) mentioned here for the computation of the right-hand side is assembled only of the local mass matrices for the grid elements from \(T\). The resulting discretized system for \(\phi\) consists the discrete Laplace operator on \(T\), the discrete Neumann-0 (natural) boundary condition on \(\partial{T}\) and the identity matrix for all other DoFs. Note furthermore that the same \(M^{(1)}\) should be used in the assembling of the right-hand side of the discretized Maxwell equations.

References:

O. Sterz. Modellierung und Numerik zeitharmonischer Wirbelstromprobleme in 3D. PhD thesis, 2003.

Template Parameters

TDomain	Domain type
TAlgebra	Algebra type

Member Typedef Documentation

◆ a_edge_flag_type

template<typename TDomain , typename TAlgebra >

typedef AChar ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::a_edge_flag_type

private

Type of the attachment and its accessor for flags.

◆ a_vert_flag_type

template<typename TDomain , typename TAlgebra >

typedef ABool ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::a_vert_flag_type

private

◆ aa_edge_flag_type

template<typename TDomain , typename TAlgebra >

typedef Grid::EdgeAttachmentAccessor<a_edge_flag_type> ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::aa_edge_flag_type

private

◆ aa_vert_flag_type

template<typename TDomain , typename TAlgebra >

typedef Grid::VertexAttachmentAccessor<a_vert_flag_type> ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::aa_vert_flag_type

private

◆ algebra_type

template<typename TDomain , typename TAlgebra >

typedef TAlgebra ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::algebra_type

Type of algebra (for the Nedelec-element-based grid functions)

◆ domain_type

template<typename TDomain , typename TAlgebra >

typedef TDomain ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::domain_type

Type of Domain.

◆ grid_type

template<typename TDomain , typename TAlgebra >

typedef TDomain::grid_type ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::grid_type

Type of Grid:

◆ matrix_type

template<typename TDomain , typename TAlgebra >

typedef TAlgebra::matrix_type ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::matrix_type

Type of Vector (for the Nedelec-element-based grid functions)

◆ position_type

template<typename TDomain , typename TAlgebra >

typedef TDomain::position_type ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::position_type

position type

◆ pot_gf_type

template<typename TDomain , typename TAlgebra >

typedef GridFunction<TDomain, TPotAlgebra> ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::pot_gf_type

Grid function type for the potential space.

◆ pot_matrix_type

template<typename TDomain , typename TAlgebra >

typedef TPotAlgebra::matrix_type ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::pot_matrix_type

Matrix type for the potential space.

◆ pot_vector_type

template<typename TDomain , typename TAlgebra >

typedef TPotAlgebra::vector_type ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::pot_vector_type

Vector type for the potential space.

◆ subset_handler_type

template<typename TDomain , typename TAlgebra >

typedef domain_type::subset_handler_type ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::subset_handler_type

Type of subset handler.

◆ this_type

template<typename TDomain , typename TAlgebra >

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

private

This type.

◆ TPotAlgebra

template<typename TDomain , typename TAlgebra >

typedef CPUAlgebra ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::TPotAlgebra

The auxiliary algebra type for the space of the potential. (Note: It should be scalar.)

◆ vector_type

template<typename TDomain , typename TAlgebra >

typedef TAlgebra::vector_type ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::vector_type

Type of Vector (for the Nedelec-element-based grid functions)

Constructor & Destructor Documentation

◆ NedelecLoopCurrent()

template<typename TDomain , typename TAlgebra >

ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::NedelecLoopCurrent	(	const char *	ssNames,
		const char *	posSsNames,
		const char *	cutSsNames,
		SmartPtr< ApproximationSpace< TDomain > >	vertApproxSpace,
		SmartPtr< ILinearOperatorInverse< pot_vector_type > >	potSolver
	)

Constructor.

Class constructor:

Parameters

ssNames	names of the subsets of the source (up to the subset of the pos. dir.)
posSsNames	names of the subsets of the positive direction
cutSsNames	names of the surfaces on the cut of the loop
vertApproxSpace	vertex-centered approx. space
potSolver	linear solver for the potential

Member Function Documentation

◆ compute()

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::compute ( SmartPtr< GridFunction< TDomain, TAlgebra > > sp_u )

Computation of the source (only if 'init'ialized): distributes the potential.

Computation of the source by updating a given grid function

Parameters

sp_u	the grid function for the source

References pcl::ProcessCommunicator::allreduce(), ug::GridFunction< class, class >::dof_distribution(), ug::DoFDistributionInfoProvider::fct_grp_by_name(), SmartPtr< class, FreePolicy >::get(), ug::GridFunction< class, class >::grid_level(), ug::DoFDistributionInfoProvider::local_finite_element_id(), ug::LFEID::NEDELEC, PCL_RO_SUM, ug::PST_CONSISTENT, ug::FunctionGroup::size(), ug::LFEID::type(), UG_CATCH_THROW, and UG_THROW.

◆ compute_potential()

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::compute_potential ( pot_gf_type & pot_u )

private

Computes the potential of the source.

Computes the potential of the source

Parameters

pot_u a grid function for the potential

References ug::GridFunction< class, class >::approx_space(), ug::Grid::attach_to_vertices(), ug::GridFunction< class, class >::dd(), ug::Grid::detach_from_vertices(), ug::GridFunction< class, class >::dof_distribution(), ug::GridFunction< class, class >::domain(), SmartPtr< TDomain >::get(), ug::GridFunction< class, class >::grid_level(), and ug::GridFunction< class, class >::init().

◆ distribute_source_potential()

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::distribute_source_potential	(	const DoFDistribution &	vertDD,
		pot_vector_type &	src_pot,
		DoFDistribution &	edgeDD,
		size_t	func,
		number	value,
		vector_type &	src_field
	)

private

Computes the gradient of the potential.

Computes the gradient of the potential for one function.

Remark: The potential is considered to be properly scaled. Otherwise, the scaling should be included into the value of the source

Parameters

[in]	vertDD	the vertex DD
[in]	src_pot	potential to distribute
[in]	edgeDD	the edge DD
[in]	func	index of the function
[in]	value	value of the source
[out]	src_field	the computed source field

References ug::DoFDistribution::begin(), ug::DoFRef(), ug::DoFDistribution::end(), ug::DoFDistribution::inner_algebra_indices(), ug::DoFDistribution::inner_dof_indices(), ug::DoFDistribution::multi_grid(), PCL_RO_BOR, ug::SetAttachmentValues(), UG_THROW, and ug::EdgeVertices::vertex().

◆ get_flux_of_pot()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::get_flux_of_pot	(	const TDomain &	domain,
		const pot_vector_type &	pot,
		const DoFDistribution &	vertDD,
		number &	flux
	)

private

Computes the flux of of the gradient of the potential over the cut (for one type of elements)

Computes the flux of the gradient of the potential over the cut (for one type of elements)

Parameters

[in]	domain	the domain
[in]	pot	the potential field
[in]	vertDD	the vertex DD
[out]	flux	the flux to update

References ug::DoFDistribution::inner_algebra_indices(), ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_allSsGrp, ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_cutSsGrp, ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_posSsGrp, ug::SubsetGroup::remove(), ug::SubsetGroup::size(), ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::LocLaplaceA< TElem >::stiffness(), and UG_THROW.

◆ mark_source_edges()

template<typename TDomain , typename TAlgebra >

template<typename TElem >

void ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::mark_source_edges	(	const DoFDistribution &	edgeDD,
		aa_edge_flag_type &	in_source
	)

private

Marks edges that belong to the loop source domain (for one type of elements)

Marks edges that belong to the loop source domain (for one type of elements). For edges of elements belonging to the source domain, the entries of 'in_source' are set to non-zero. (Other entries are not set.) For those entries that correspond to edges belonging to elements in the 'positive direction' subdomain and having one of the ends at the cut surface, the 1st and the 2nd bits of the entry is set to 1 (depending whether the beginning or the end lyies at the cut). For all other edges in the source, these bits are set to zero (so that only the 0th bit is 1).

Parameters

[in]	edgeDD	the edge DD
[out]	in_source	the flags to update

References ug::Grid::associated_elements(), ug::ISubsetHandler::get_subset_index(), ug::ISubsetHandler::grid(), ug::PointerConstArray< class >::size(), ug::DoFDistributionInfoProvider::subset_handler(), UG_ASSERT, and ug::EdgeVertices::vertex().

◆ set()

template<typename TDomain , typename TAlgebra >

void ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::set	(	const char *	fctNames,
		number	I
	)

Setting the electric current value.

Setting the electric current value

Parameters

fctNames	names of the components
I	electric current for the functions

◆ subsets()

template<typename TDomain , typename TAlgebra >

std::string ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::subsets ( )

inline

Returns the subsets where the source is defined.

References ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_allSsNames.

◆ zero_average()

template<typename TDomain , typename TAlgebra >

SmartPtr<ITransferPostProcess<TDomain, TPotAlgebra> > ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::zero_average ( )

inline

Returns the postprocess routine to eliminate the kernel part of the potential.

References ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_zeroAverage.

Member Data Documentation

◆ m_allSsGrp

template<typename TDomain , typename TAlgebra >

SubsetGroup ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_allSsGrp

private

Group of all the subsets of the source.

Referenced by ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::get_flux_of_pot(), and ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::NedelecLoopCurrent().

◆ m_allSsNames

template<typename TDomain , typename TAlgebra >

std::string ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_allSsNames

private

Names of all the subsets of the source.

Referenced by ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::NedelecLoopCurrent(), and ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::subsets().

◆ m_auxLaplaceAss

template<typename TDomain , typename TAlgebra >

SmartPtr<DomainDiscretization<TDomain, TPotAlgebra> > ug::Electromagnetism::NedelecLoopCurrent< TDomain, TAlgebra >::m_auxLaplaceAss

private

Global discretization of the auxiliary equations.

This discretization object uses m_auxLocLaplace and m_outOfSource to assemble the Laplace equation and the jump right-hand side in the subsets of the source, as well as the identity equations in the other parts of the domain.

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