#include <AbstractFeVolumeIntegralAssembler.hpp>

Inheritance diagram for AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >:

Collaboration diagram for AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >:

Public Member Functions
	AbstractFeVolumeIntegralAssembler (AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > *pMesh)

virtual	~AbstractFeVolumeIntegralAssembler ()

Public Member Functions inherited from AbstractFeAssemblerCommon< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >
	AbstractFeAssemblerCommon ()

void	SetCurrentSolution (Vec currentSolution)

virtual	~AbstractFeAssemblerCommon ()

Public Member Functions inherited from AbstractFeAssemblerInterface< CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >
	AbstractFeAssemblerInterface ()

void	SetMatrixToAssemble (Mat &rMatToAssemble, bool zeroMatrixBeforeAssembly=true)

void	SetVectorToAssemble (Vec &rVecToAssemble, bool zeroVectorBeforeAssembly)

void	Assemble ()

void	AssembleMatrix ()

void	AssembleVector ()

virtual	~AbstractFeAssemblerInterface ()

Protected Types
typedef LinearBasisFunction< ELEMENT_DIM >	BasisFunction

Protected Member Functions
void	ComputeTransformedBasisFunctionDerivatives (const ChastePoint< ELEMENT_DIM > &rPoint, const c_matrix< double, ELEMENT_DIM, SPACE_DIM > &rInverseJacobian, c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &rReturnValue)

void	DoAssemble ()

virtual c_matrix< double, PROBLEM_DIM (ELEMENT_DIM+1), PROBLEM_DIM (ELEMENT_DIM+1)>	ComputeMatrixTerm (c_vector< double, ELEMENT_DIM+1 > &rPhi, c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &rGradPhi, ChastePoint< SPACE_DIM > &rX, c_vector< double, PROBLEM_DIM > &rU, c_matrix< double, PROBLEM_DIM, SPACE_DIM > &rGradU, Element< ELEMENT_DIM, SPACE_DIM > *pElement)

virtual c_vector< double, PROBLEM_DIM *(ELEMENT_DIM+1)>	ComputeVectorTerm (c_vector< double, ELEMENT_DIM+1 > &rPhi, c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &rGradPhi, ChastePoint< SPACE_DIM > &rX, c_vector< double, PROBLEM_DIM > &rU, c_matrix< double, PROBLEM_DIM, SPACE_DIM > &rGradU, Element< ELEMENT_DIM, SPACE_DIM > *pElement)

virtual void	AssembleOnElement (Element< ELEMENT_DIM, SPACE_DIM > &rElement, c_matrix< double, PROBLEM_DIM (ELEMENT_DIM+1), PROBLEM_DIM (ELEMENT_DIM+1) > &rAElem, c_vector< double, PROBLEM_DIM *(ELEMENT_DIM+1)> &rBElem)

virtual bool	ElementAssemblyCriterion (Element< ELEMENT_DIM, SPACE_DIM > &rElement)

Protected Member Functions inherited from AbstractFeAssemblerCommon< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >
virtual double	GetCurrentSolutionOrGuessValue (unsigned nodeIndex, unsigned indexOfUnknown)

virtual void	ResetInterpolatedQuantities ()

virtual void	IncrementInterpolatedQuantities (double phiI, const Node< SPACE_DIM > *pNode)

virtual void	IncrementInterpolatedGradientQuantities (const c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &rGradPhi, unsigned phiIndex, const Node< SPACE_DIM > *pNode)

Protected Attributes
AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > *	mpMesh

GaussianQuadratureRule< ELEMENT_DIM > *	mpQuadRule

Protected Attributes inherited from AbstractFeAssemblerCommon< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >
ReplicatableVector	mCurrentSolutionOrGuessReplicated

Protected Attributes inherited from AbstractFeAssemblerInterface< CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >
Vec	mVectorToAssemble

Mat	mMatrixToAssemble

bool	mAssembleMatrix

bool	mAssembleVector

bool	mZeroMatrixBeforeAssembly

bool	mZeroVectorBeforeAssembly

PetscInt	mOwnershipRangeLo

PetscInt	mOwnershipRangeHi

Detailed Description

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
class AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >

An abstract class for creating finite element vectors or matrices that are defined by integrals over the computational domain of functions of basis functions (for example, stiffness or mass matrices), that require assembly by looping over each element in the mesh and computing the element-wise integrals and adding it to the full matrix or vector.

This class is used for VOLUME integrals. For surface integrals there is a similar class, AbstractFeSurfaceIntegralAssembler.

This class can be used to assemble a matrix OR a vector OR one of each. The template booleans CAN_ASSEMBLE_VECTOR and CAN_ASSEMBLE_MATRIX should be chosen accordingly.

The class provides the functionality to loop over elements, perform element-wise integration (using Gaussian quadrature and linear basis functions), and add the results to the final matrix or vector. The concrete class which inherits from this must implement either COMPUTE_MATRIX_TERM or COMPUTE_VECTOR_TERM or both, which should return the INTEGRAND, as a function of the basis functions.

The final template parameter defines how much interpolation (onto quadrature points) is required by the concrete class.

CARDIAC: only interpolates the first component of the unknown (ie the voltage) NORMAL: interpolates the position X and all components of the unknown u NONLINEAR: interpolates X, u and grad(u). Also computes the gradient of the basis functions when assembling vectors.

This class inherits from AbstractFeAssemblerCommon which is where some member variables (the matrix/vector to be created, for example) are defined.

Definition at line 78 of file AbstractFeVolumeIntegralAssembler.hpp.

Member Typedef Documentation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

typedef LinearBasisFunction<ELEMENT_DIM> AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::BasisFunction

protected

Basis function for use with normal elements.

Definition at line 89 of file AbstractFeVolumeIntegralAssembler.hpp.

Constructor & Destructor Documentation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AbstractFeVolumeIntegralAssembler ( AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > * pMesh )

Constructor.

Parameters

pMesh The mesh

Definition at line 244 of file AbstractFeVolumeIntegralAssembler.hpp.

References AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::mpQuadRule.

Referenced by AbstractFeVolumeIntegralAssembler< DIM, DIM, 2, false, true, CARDIAC >::ElementAssemblyCriterion().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

virtual AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::~AbstractFeVolumeIntegralAssembler ( )

inlinevirtual

Destructor.

Definition at line 237 of file AbstractFeVolumeIntegralAssembler.hpp.

Member Function Documentation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

void AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AssembleOnElement	(	Element< ELEMENT_DIM, SPACE_DIM > &	rElement,
		c_matrix< double, PROBLEM_DIM (ELEMENT_DIM+1), PROBLEM_DIM (ELEMENT_DIM+1) > &	rAElem,
		c_vector< double, PROBLEM_DIM *(ELEMENT_DIM+1)> &	rBElem
	)

protectedvirtual

Calculate the contribution of a single element to the linear system.

Parameters

rElement	The element to assemble on.
rAElem	The element's contribution to the LHS matrix is returned in this n by n matrix, where n is the no. of nodes in this element. There is no need to zero this matrix before calling.
rBElem	The element's contribution to the RHS vector is returned in this vector of length n, the no. of nodes in this element. There is no need to zero this vector before calling.

Called by AssembleSystem(). Calls ComputeMatrixTerm() etc.

Todo:: #1320 This assumes that the Jacobian is constant on an element. This is true for linear basis functions, but not for any other type of basis function.

Definition at line 345 of file AbstractFeVolumeIntegralAssembler.hpp.

Referenced by AbstractFeVolumeIntegralAssembler< DIM, DIM, 2, false, true, CARDIAC >::ComputeVectorTerm(), and AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::DoAssemble().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

virtual c_matrix<double,PROBLEM_DIM(ELEMENT_DIM+1),PROBLEM_DIM(ELEMENT_DIM+1)> AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::ComputeMatrixTerm	(	c_vector< double, ELEMENT_DIM+1 > &	rPhi,
		c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &	rGradPhi,
		ChastePoint< SPACE_DIM > &	rX,
		c_vector< double, PROBLEM_DIM > &	rU,
		c_matrix< double, PROBLEM_DIM, SPACE_DIM > &	rGradU,
		Element< ELEMENT_DIM, SPACE_DIM > *	pElement
	)

inlineprotectedvirtual

Returns: the matrix to be added to element stiffness matrix for a given Gauss point, ie, essentially the INTEGRAND in the integral definition of the matrix. The arguments are the bases, bases gradients, x and current solution computed at the Gauss point. The returned matrix will be multiplied by the Gauss weight and Jacobian determinant and added to the element stiffness matrix (see AssembleOnElement()).

** This method has to be implemented in the concrete class if CAN_ASSEMBLE_MATRIX is true. **

NOTE: When INTERPOLATION_LEVEL==NORMAL, rGradU does not get set up and should not be used.

Parameters

rPhi	The basis functions, rPhi(i) = phi_i, i=1..numBases.
rGradPhi	Basis gradients, rGradPhi(i,j) = d(phi_j)/d(X_i).
rX	The point in space.
rU	The unknown as a vector, u(i) = u_i.
rGradU	The gradient of the unknown as a matrix, rGradU(i,j) = d(u_i)/d(X_j).
pElement	Pointer to the element.

Reimplemented in LinearParabolicPdeSystemWithCoupledOdeSystemSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >.

Definition at line 143 of file AbstractFeVolumeIntegralAssembler.hpp.

Referenced by AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AssembleOnElement().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

void AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::ComputeTransformedBasisFunctionDerivatives	(	const ChastePoint< ELEMENT_DIM > &	rPoint,
		const c_matrix< double, ELEMENT_DIM, SPACE_DIM > &	rInverseJacobian,
		c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &	rReturnValue
	)

protected

Compute the derivatives of all basis functions at a point within an element. This method will transform the results, for use within Gaussian quadrature for example.

This is almost identical to LinearBasisFunction::ComputeTransformedBasisFunctionDerivatives, except that it is also templated over SPACE_DIM and can handle cases such as 1d in 3d space.

Todo:: #1319 Template LinearBasisFunction over SPACE_DIM and remove this method?

Parameters

rPoint	The point at which to compute the basis functions. The results are undefined if this is not within the canonical element.
rInverseJacobian	The inverse of the Jacobian matrix mapping the real element into the canonical element.
rReturnValue	A reference to a vector, to be filled in

Returns: The derivatives of the basis functions, in local index order. Each entry is a vector (c_vector<double, SPACE_DIM> instance) giving the derivative along each axis.

Definition at line 332 of file AbstractFeVolumeIntegralAssembler.hpp.

References LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunctionDerivatives().

Referenced by AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AssembleOnElement().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

virtual c_vector<double,PROBLEM_DIM*(ELEMENT_DIM+1)> AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::ComputeVectorTerm	(	c_vector< double, ELEMENT_DIM+1 > &	rPhi,
		c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &	rGradPhi,
		ChastePoint< SPACE_DIM > &	rX,
		c_vector< double, PROBLEM_DIM > &	rU,
		c_matrix< double, PROBLEM_DIM, SPACE_DIM > &	rGradU,
		Element< ELEMENT_DIM, SPACE_DIM > *	pElement
	)

inlineprotectedvirtual

Returns: the vector to be added to element stiffness vector for a given Gauss point, ie, essentially the INTEGRAND in the integral definition of the vector. The arguments are the bases, x and current solution computed at the Gauss point. The returned vector will be multiplied by the Gauss weight and Jacobian determinant and added to the element stiffness matrix (see AssembleOnElement()).

** This method has to be implemented in the concrete class if CAN_ASSEMBLE_VECTOR is true. **

NOTE: When INTERPOLATION_LEVEL==NORMAL, rGradPhi and rGradU do not get set up and should not be used.

Parameters

rPhi	The basis functions, rPhi(i) = phi_i, i=1..numBases
rGradPhi	Basis gradients, rGradPhi(i,j) = d(phi_j)/d(X_i)
rX	The point in space
rU	The unknown as a vector, u(i) = u_i
rGradU	The gradient of the unknown as a matrix, rGradU(i,j) = d(u_i)/d(X_j)
pElement	Pointer to the element

Reimplemented in LinearParabolicPdeSystemWithCoupledOdeSystemSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >.

Definition at line 178 of file AbstractFeVolumeIntegralAssembler.hpp.

Referenced by AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AssembleOnElement().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

void AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::DoAssemble ( )

protectedvirtual

The main assembly method. Should only be called through Assemble(), AssembleMatrix() or AssembleVector() which set mAssembleMatrix, mAssembleVector accordingly.

Implements AbstractFeAssemblerInterface< CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >.

Definition at line 257 of file AbstractFeVolumeIntegralAssembler.hpp.

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

virtual bool AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::ElementAssemblyCriterion ( Element< ELEMENT_DIM, SPACE_DIM > & rElement )

inlineprotectedvirtual

Returns: true if we should include this (volume) element when assembling. Returns true here but can be overridden by the concrete assembler if not all elements should be included.

Parameters

rElement the element

Reimplemented in AbstractCorrectionTermAssembler< ELEM_DIM, SPACE_DIM, PROBLEM_DIM >.

Definition at line 219 of file AbstractFeVolumeIntegralAssembler.hpp.

Referenced by AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::DoAssemble().

Member Data Documentation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::mpMesh

protected

Mesh to be solved on.

Definition at line 83 of file AbstractFeVolumeIntegralAssembler.hpp.

Referenced by AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AssembleOnElement(), and AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::DoAssemble().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>

GaussianQuadratureRule<ELEMENT_DIM>* AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::mpQuadRule

protected

Quadrature rule for use on normal elements.

Definition at line 86 of file AbstractFeVolumeIntegralAssembler.hpp.

Referenced by AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AbstractFeVolumeIntegralAssembler(), AbstractFeVolumeIntegralAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL >::AssembleOnElement(), and AbstractFeVolumeIntegralAssembler< DIM, DIM, 2, false, true, CARDIAC >::~AbstractFeVolumeIntegralAssembler().

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

pde/src/solver/AbstractFeVolumeIntegralAssembler.hpp

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation