#include <coordinate_transformation_utilities.h>

Inheritance diagram for Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >:

Collaboration diagram for Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >:

Public Member Functions
Life Cycle
	CoordinateTransformationUtils (const unsigned int DomainSize, const unsigned int NumRowsPerNode, const Kratos::Flags &rSelectionFlag=SLIP)
	Constructor. More...

virtual	~CoordinateTransformationUtils ()
	Destructor. More...

Operations
virtual void	CalculateRotationOperatorPure (TLocalMatrixType &rRotationMatrix, const GeometryType::PointType &rThisPoint) const
	Calculates rotation operator for given point. More...

void	LocalRotationOperatorPure (BoundedMatrix< double, 3, 3 > &rRot, const GeometryType::PointType &rThisPoint) const

void	LocalRotationOperatorPure (BoundedMatrix< double, 2, 2 > &rRot, const GeometryType::PointType &rThisPoint) const

virtual void	CalculateRotationOperatorPureShapeSensitivities (TLocalMatrixType &rRotationMatrixShapeDerivative, const std::size_t DerivativeNodeIndex, const std::size_t DerivativeDirectionIndex, const GeometryType::PointType &rThisPoint) const
	Calculates rotation nodal matrix shape sensitivities. More...

virtual void	CalculateRotationOperatorPureShapeSensitivities (BoundedMatrix< double, 2, 2 > &rOutput, const std::size_t DerivativeNodeIndex, const std::size_t DerivativeDirectionIndex, const GeometryType::PointType &rThisPoint) const
	Calculate 2d rotation nodal matrix shape sensitivities. More...

virtual void	CalculateRotationOperatorPureShapeSensitivities (BoundedMatrix< double, 3, 3 > &rOutput, const std::size_t DerivativeNodeIndex, const std::size_t DerivativeDirectionIndex, const GeometryType::PointType &rThisPoint) const
	Calculate 3d rotation nodal matrix shape sensitivities. More...

virtual void	Rotate (TLocalMatrixType &rLocalMatrix, TLocalVectorType &rLocalVector, GeometryType &rGeometry) const
	Rotate the local system contributions so that they are oriented with each node's normal. More...

virtual void	Rotate (TLocalVectorType &rLocalVector, GeometryType &rGeometry) const
	RHS only version of Rotate. More...

virtual void	ApplySlipCondition (TLocalMatrixType &rLocalMatrix, TLocalVectorType &rLocalVector, GeometryType &rGeometry) const
	Apply slip boundary conditions to the rotated local contributions. More...

virtual void	ApplySlipCondition (TLocalVectorType &rLocalVector, GeometryType &rGeometry) const
	RHS only version of ApplySlipCondition. More...

virtual void	RotateVelocities (ModelPart &rModelPart) const
	Transform nodal velocities to the rotated coordinates (aligned with each node's normal) More...

virtual void	RecoverVelocities (ModelPart &rModelPart) const
	Transform nodal velocities from the rotated system to the original one. More...

Input and output
virtual std::string	Info () const
	Turn back information as a string. More...

virtual void	PrintInfo (std::ostream &rOStream) const
	Print information about this object. More...

virtual void	PrintData (std::ostream &rOStream) const
	Print object's data. More...

Protected Member Functions
Protected Operations
template<unsigned int TDim, unsigned int TBlockSize, unsigned int TSkip = 0>
void	RotateAux (TLocalMatrixType &rLocalMatrix, TLocalVectorType &rLocalVector, GeometryType &rGeometry) const

template<unsigned int TDim>
void	RotateAuxPure (TLocalMatrixType &rLocalMatrix, TLocalVectorType &rLocalVector, GeometryType &rGeometry) const

template<unsigned int TBlockSize, unsigned int TSkip = 0>
void	LocalRotationOperator2D (BoundedMatrix< double, TBlockSize, TBlockSize > &rRot, GeometryType::PointType &rThisPoint) const

template<unsigned int TBlockSize, unsigned int TSkip = 0>
void	LocalRotationOperator3D (BoundedMatrix< double, TBlockSize, TBlockSize > &rRot, GeometryType::PointType &rThisPoint) const

bool	IsSlip (const Node &rNode) const

template<class TVectorType >
double	Normalize (TVectorType &rThis) const
	Normalize a vector. More...

Protected Access
unsigned int	GetDomainSize () const

unsigned int	GetBlockSize () const

Type Definitions
typedef Node	NodeType

typedef Geometry< Node >	GeometryType

	KRATOS_CLASS_POINTER_DEFINITION (CoordinateTransformationUtils)
	Pointer definition of CoordinateTransformationUtils. More...

Detailed Description

template<class TLocalMatrixType, class TLocalVectorType, class TValueType>
class Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >

A utility to rotate the local contributions of certain nodes to the system matrix, which is required to apply slip conditions in arbitrary directions. TODO: Move code to source file. Use explicit template instantiation (this way the compilation is faster).

Member Typedef Documentation

◆ GeometryType

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

typedef Geometry< Node > Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::GeometryType

◆ NodeType

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

typedef Node Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::NodeType

Constructor & Destructor Documentation

◆ CoordinateTransformationUtils()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::CoordinateTransformationUtils	(	const unsigned int	DomainSize,
		const unsigned int	NumRowsPerNode,
		const Kratos::Flags &	rSelectionFlag = `SLIP`
	)

inline

Constructor.

Parameters

DomainSize	Number of space dimensions (2 or 3)
NumRowsPerNode	Number of matrix or vector rows associated to each node. Velocity DOFs are assumed to be the first mDomainSize rows in each block of rows.
rSelectionFlag	All nodes where the flag given by this argument is set to true will be transformed to a rotated coordinate system.

◆ ~CoordinateTransformationUtils()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::~CoordinateTransformationUtils ( )

inlinevirtual

Destructor.

Member Function Documentation

◆ ApplySlipCondition() [1/2]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::ApplySlipCondition	(	TLocalMatrixType &	rLocalMatrix,
		TLocalVectorType &	rLocalVector,
		GeometryType &	rGeometry
	)		const

inlinevirtual

Apply slip boundary conditions to the rotated local contributions.

This function takes the local system contributions rotated so each node's velocities are expressed using a base oriented with its normal and imposes that the normal velocity is equal to the mesh velocity in the normal direction.

Reimplemented in Kratos::FlowRateSlipUtility< TLocalMatrixType, TLocalVectorType, TValueType >, Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::FlowRateSlipUtility< LocalSystemMatrixType, LocalSystemVectorType, double >, and Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >.

◆ ApplySlipCondition() [2/2]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::ApplySlipCondition	(	TLocalVectorType &	rLocalVector,
		GeometryType &	rGeometry
	)		const

inlinevirtual

RHS only version of ApplySlipCondition.

Reimplemented in Kratos::FlowRateSlipUtility< TLocalMatrixType, TLocalVectorType, TValueType >, Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::FlowRateSlipUtility< LocalSystemMatrixType, LocalSystemVectorType, double >, and Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >.

◆ CalculateRotationOperatorPure()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::CalculateRotationOperatorPure	(	TLocalMatrixType &	rRotationMatrix,
		const GeometryType::PointType &	rThisPoint
	)		const

inlinevirtual

Calculates rotation operator for given point.

This metod calculates rotation matrix for a given point. Nodal NORMAL variable should be assigned properly since rotation is calculated based on it.

Parameters

rRotationMatrix	Output rotation matrix
rThisPoint	Current node

◆ CalculateRotationOperatorPureShapeSensitivities() [1/3]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::CalculateRotationOperatorPureShapeSensitivities	(	BoundedMatrix< double, 2, 2 > &	rOutput,
		const std::size_t	DerivativeNodeIndex,
		const std::size_t	DerivativeDirectionIndex,
		const GeometryType::PointType &	rThisPoint
	)		const

inlinevirtual

Calculate 2d rotation nodal matrix shape sensitivities.

This method calculates shape sensitivities of 2D rotation matrix for given node. Nodal NORMAL(historical data container) and NORMAL_SHAPE_SENSITIVITY(non-historical data contaienr) variables should be properly initialized.

NORMAL_SHAPE_SENSITIVITY matrix should be properly sized and initialized with proper shape sensitivity values rows: (number_of_neighbour_nodes + 1) * 2 cols: 2

Parameters

rOutput	Output shape sensitivities matrix w.r.t. NodeIndex and DerivativeIndex
DerivativeNodeIndex	NodeIndex for which shape sensitivity matrix is computed
DerivativeDirectionIndex	Direction index of the node for which shape sensitivity matrix is computed
rThisPoint	Current node where rotation matrix shape sensitivities are required

◆ CalculateRotationOperatorPureShapeSensitivities() [2/3]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::CalculateRotationOperatorPureShapeSensitivities	(	BoundedMatrix< double, 3, 3 > &	rOutput,
		const std::size_t	DerivativeNodeIndex,
		const std::size_t	DerivativeDirectionIndex,
		const GeometryType::PointType &	rThisPoint
	)		const

inlinevirtual

Calculate 3d rotation nodal matrix shape sensitivities.

This method calculates shape sensitivities of 3D rotation matrix for given node. Nodal NORMAL(historical data container) and NORMAL_SHAPE_SENSITIVITY(non-historical data contaienr) variables should be properly initialized.

NORMAL_SHAPE_SENSITIVITY matrix should be properly sized and initialized with proper shape sensitivity values rows: (number_of_neighbour_nodes + 1) * 3 cols: 3

Parameters

rOutput	Output shape sensitivities matrix w.r.t. NodeIndex and DerivativeIndex
DerivativeNodeIndex	NodeIndex for which shape sensitivity matrix is computed
DerivativeDirectionIndex	Direction index of the node for which shape sensitivity matrix is computed
rThisPoint	Current node where rotation matrix shape sensitivities are required

◆ CalculateRotationOperatorPureShapeSensitivities() [3/3]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::CalculateRotationOperatorPureShapeSensitivities	(	TLocalMatrixType &	rRotationMatrixShapeDerivative,
		const std::size_t	DerivativeNodeIndex,
		const std::size_t	DerivativeDirectionIndex,
		const GeometryType::PointType &	rThisPoint
	)		const

inlinevirtual

Calculates rotation nodal matrix shape sensitivities.

This method calculates shape sensitivities of rotation matrix for given node. Nodal NORMAL(historical data container) and NORMAL_SHAPE_SENSITIVITY(non-historical data contaienr) variables should be properly initialized.

NORMAL_SHAPE_SENSITIVITY matrix should be properly sized and initialized with proper shape sensitivity values rows: number_of_nodes contributing to NORMAL * DOMAIN_SIZE, columns: DOMAIN_SIZE

Parameters

rRotationMatrixShapeDerivative	Output shape sensitivities matrix w.r.t. NodeIndex and DerivativeIndex
DerivativeNodeIndex	NodeIndex for which shape sensitivity matrix is computed
DerivativeDirectionIndex	Direction index of the node for which shape sensitivity matrix is computed
rThisPoint	Current node where rotation matrix shape sensitivities are required

◆ GetBlockSize()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

unsigned int Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::GetBlockSize ( ) const

inlineprotected

◆ GetDomainSize()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

unsigned int Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::GetDomainSize ( ) const

inlineprotected

◆ Info()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual std::string Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::Info ( ) const

inlinevirtual

Turn back information as a string.

Reimplemented in Kratos::FlowRateSlipUtility< TLocalMatrixType, TLocalVectorType, TValueType >, Kratos::FlowRateSlipUtility< LocalSystemMatrixType, LocalSystemVectorType, double >, Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >, and Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >.

◆ IsSlip()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

bool Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::IsSlip ( const Node & rNode ) const

inlineprotected

◆ KRATOS_CLASS_POINTER_DEFINITION()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::KRATOS_CLASS_POINTER_DEFINITION ( CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType > )

Pointer definition of CoordinateTransformationUtils.

◆ LocalRotationOperator2D()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

template<unsigned int TBlockSize, unsigned int TSkip = 0>

void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::LocalRotationOperator2D	(	BoundedMatrix< double, TBlockSize, TBlockSize > &	rRot,
		GeometryType::PointType &	rThisPoint
	)		const

inlineprotected

◆ LocalRotationOperator3D()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

template<unsigned int TBlockSize, unsigned int TSkip = 0>

void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::LocalRotationOperator3D	(	BoundedMatrix< double, TBlockSize, TBlockSize > &	rRot,
		GeometryType::PointType &	rThisPoint
	)		const

inlineprotected

◆ LocalRotationOperatorPure() [1/2]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::LocalRotationOperatorPure	(	BoundedMatrix< double, 2, 2 > &	rRot,
		const GeometryType::PointType &	rThisPoint
	)		const

inline

◆ LocalRotationOperatorPure() [2/2]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::LocalRotationOperatorPure	(	BoundedMatrix< double, 3, 3 > &	rRot,
		const GeometryType::PointType &	rThisPoint
	)		const

inline

◆ Normalize()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

template<class TVectorType >

double Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::Normalize ( TVectorType & rThis ) const

inlineprotected

Normalize a vector.

Parameters

rThis the vector

Returns: Original norm of the input vector

◆ PrintData()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::PrintData ( std::ostream & rOStream ) const

inlinevirtual

Print object's data.

Reimplemented in Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >, and Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >.

◆ PrintInfo()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::PrintInfo ( std::ostream & rOStream ) const

inlinevirtual

Print information about this object.

Reimplemented in Kratos::FlowRateSlipUtility< TLocalMatrixType, TLocalVectorType, TValueType >, Kratos::FlowRateSlipUtility< LocalSystemMatrixType, LocalSystemVectorType, double >, Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >, and Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >.

◆ RecoverVelocities()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::RecoverVelocities ( ModelPart & rModelPart ) const

inlinevirtual

Transform nodal velocities from the rotated system to the original one.

Reimplemented in Kratos::FlowRateSlipUtility< TLocalMatrixType, TLocalVectorType, TValueType >, Kratos::FlowRateSlipUtility< LocalSystemMatrixType, LocalSystemVectorType, double >, Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >, and Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >.

◆ Rotate() [1/2]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::Rotate	(	TLocalMatrixType &	rLocalMatrix,
		TLocalVectorType &	rLocalVector,
		GeometryType &	rGeometry
	)		const

inlinevirtual

Rotate the local system contributions so that they are oriented with each node's normal.

Parameters

rLocalMatrix	Local system matrix
rLocalVector	Local RHS vector
rGeometry	A reference to the element's (or condition's) geometry

Reimplemented in Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >, and Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >.

◆ Rotate() [2/2]

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::Rotate	(	TLocalVectorType &	rLocalVector,
		GeometryType &	rGeometry
	)		const

inlinevirtual

RHS only version of Rotate.

Reimplemented in Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >.

◆ RotateAux()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

template<unsigned int TDim, unsigned int TBlockSize, unsigned int TSkip = 0>

void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::RotateAux	(	TLocalMatrixType &	rLocalMatrix,
		TLocalVectorType &	rLocalVector,
		GeometryType &	rGeometry
	)		const

inlineprotected

◆ RotateAuxPure()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

template<unsigned int TDim>

void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::RotateAuxPure	(	TLocalMatrixType &	rLocalMatrix,
		TLocalVectorType &	rLocalVector,
		GeometryType &	rGeometry
	)		const

inlineprotected

◆ RotateVelocities()

template<class TLocalMatrixType , class TLocalVectorType , class TValueType >

virtual void Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >::RotateVelocities ( ModelPart & rModelPart ) const

inlinevirtual

Transform nodal velocities to the rotated coordinates (aligned with each node's normal)

Reimplemented in Kratos::FlowRateSlipUtility< TLocalMatrixType, TLocalVectorType, TValueType >, Kratos::FlowRateSlipUtility< LocalSystemMatrixType, LocalSystemVectorType, double >, Kratos::MPMBoundaryRotationUtility< TLocalMatrixType, TLocalVectorType >, Kratos::MPMBoundaryRotationUtility< LocalSystemMatrixType, LocalSystemVectorType >, and Kratos::CompressibleElementRotationUtility< TLocalMatrixType, TLocalVectorType >.

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

/home/runner/work/Documentation/Documentation/master/kratos/utilities/coordinate_transformation_utilities.h

Public Member Functions

Protected Member Functions

Type Definitions

Detailed Description

template<class TLocalMatrixType, class TLocalVectorType, class TValueType> class Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >

Member Typedef Documentation

◆ GeometryType

◆ NodeType

Constructor & Destructor Documentation

◆ CoordinateTransformationUtils()

◆ ~CoordinateTransformationUtils()

Member Function Documentation

◆ ApplySlipCondition() [1/2]

◆ ApplySlipCondition() [2/2]

◆ CalculateRotationOperatorPure()

◆ CalculateRotationOperatorPureShapeSensitivities() [1/3]

◆ CalculateRotationOperatorPureShapeSensitivities() [2/3]

◆ CalculateRotationOperatorPureShapeSensitivities() [3/3]

◆ GetBlockSize()

◆ GetDomainSize()

◆ Info()

◆ IsSlip()

◆ KRATOS_CLASS_POINTER_DEFINITION()

◆ LocalRotationOperator2D()

◆ LocalRotationOperator3D()

◆ LocalRotationOperatorPure() [1/2]

◆ LocalRotationOperatorPure() [2/2]

◆ Normalize()

◆ PrintData()

◆ PrintInfo()

◆ RecoverVelocities()

◆ Rotate() [1/2]

◆ Rotate() [2/2]

◆ RotateAux()

◆ RotateAuxPure()

◆ RotateVelocities()

template<class TLocalMatrixType, class TLocalVectorType, class TValueType>
class Kratos::CoordinateTransformationUtils< TLocalMatrixType, TLocalVectorType, TValueType >