Discrete H2 space: local operators, L2 product and global interpolator. More...

#include <xhess.hpp>

Inheritance diagram for HArDCore2D::XHess:

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Collaboration diagram for HArDCore2D::XHess:

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Classes
struct	LocalOperators
	A structure to store local operators (gradient and potential) More...

struct	TransferOperators

Public Types
typedef std::function< double(const Eigen::Vector2d &)>	FunctionType

typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	GradFunctionType

typedef std::function< double(const Eigen::Vector2d &)>	FunctionType

typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	GradFunctionType

Public Member Functions
	XHess (const DDRCore &ddr_core, const SerendipityProblem &ser_pro, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.

const Mesh &	mesh () const
	Return the mesh.

const size_t &	degree () const
	Return the polynomial degree.

Eigen::VectorXd	interpolate (const FunctionType &q, const GradFunctionType &Dq, const int deg_quad=-1) const
	Interpolator of a continuous function.

const Eigen::MatrixXd &	SgradCell (size_t iT) const
	Return the serendipity reconstruction for the cell of index iT.

const Eigen::MatrixXd &	SgradCell (const Cell &T) const
	Return the serendipity reconstruction for cell T.

const TransferOperators &	TcellOperators (size_t iT) const
	Return cell operators for the cell of index iT.

const TransferOperators &	TcellOperators (const Cell &T) const
	Return cell operators for cell T.

const LocalOperators &	edgeOperators (size_t iE) const
	Return edge operators for the edge of index iE.

const LocalOperators &	edgeOperators (const Edge &E) const
	Return edge operators for edge E.

const LocalOperators &	cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.

const LocalOperators &	cellOperators (const Cell &T) const
	Return cell operators for cell T.

const DDRCore::CellBases &	cellBases (size_t iT) const
	Return cell bases for the cell of index iT.

const DDRCore::CellBases &	cellBases (const Cell &T) const
	Return cell bases for cell T.

const DDRCore::EdgeBases &	edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.

const DDRCore::EdgeBases &	edgeBases (const Edge &E) const
	Return edge bases for edge E.

Eigen::MatrixXd	computeStabilisation (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pkpo_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product for the cell of index iT.

Eigen::MatrixXd	computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pkpo_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const

Eigen::MatrixXd	computeGradientFull (const size_t iT, const VSXGrad &vsx_grad) const

double	evaluatePotential (const size_t iT, const Eigen::VectorXd &vT, const VectorRd &x) const
	Evaluate the value of the potential at a point x.

double	computeL2Norm (const Eigen::VectorXd &v) const
	Compute the L2-norm of a vector of the space.

Eigen::MatrixXd	SerExtension (size_t iT) const

	XHess (const DDRCore &ddr_core, const SerendipityProblem &ser_pro, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.

const Mesh &	mesh () const
	Return the mesh.

const size_t &	degree () const
	Return the polynomial degree.

Eigen::VectorXd	interpolate (const FunctionType &q, const GradFunctionType &Dq, const int deg_quad=-1) const
	Interpolator of a continuous function.

const Eigen::MatrixXd &	SgradCell (size_t iT) const
	Return the serendipity reconstruction for the cell of index iT.

const Eigen::MatrixXd &	SgradCell (const Cell &T) const
	Return the serendipity reconstruction for cell T.

const Eigen::MatrixXd &	EgradCell (size_t iT) const

const Eigen::MatrixXd &	EgradCell (const Cell &T) const
	Return the serendipity reconstruction for cell T.

const TransferOperators &	TcellOperators (size_t iT) const
	Return cell operators for the cell of index iT.

const TransferOperators &	TcellOperators (const Cell &T) const
	Return cell operators for cell T.

const LocalOperators &	edgeOperators (size_t iE) const
	Return edge operators for the edge of index iE.

const LocalOperators &	edgeOperators (const Edge &E) const
	Return edge operators for edge E.

const LocalOperators &	cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.

const LocalOperators &	cellOperators (const Cell &T) const
	Return cell operators for cell T.

const DDRCore::CellBases &	cellBases (size_t iT) const
	Return cell bases for the cell of index iT.

const DDRCore::CellBases &	cellBases (const Cell &T) const
	Return cell bases for cell T.

const DDRCore::EdgeBases &	edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.

const DDRCore::EdgeBases &	edgeBases (const Edge &E) const
	Return edge bases for edge E.

Eigen::MatrixXd	computeStabilisation (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pkpo_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product for the cell of index iT.

Eigen::MatrixXd	computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pkpo_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const

Eigen::MatrixXd	computeGradientFull (const size_t iT, const VSXGrad &vsx_grad) const

Eigen::MatrixXd	potential2 (const size_t iT, const VSXGrad &vsx_grad) const

double	evaluatePotential (const size_t iT, const Eigen::VectorXd &vT, const VectorRd &x) const
	Evaluate the value of the potential at a point x.

double	computeL2Norm (const Eigen::VectorXd &v) const
	Compute the L2-norm of a vector of the space.

Public Member Functions inherited from HArDCore2D::GlobalDOFSpace
	GlobalDOFSpace (const Mesh &mesh, size_t n_local_vertex_dofs, size_t n_local_edge_dofs, size_t n_local_cell_dofs)
	Constructor.

size_t	globalOffset (const Vertex &V) const
	Return the global offset for the unknowns on the vertex V.

size_t	globalOffset (const Edge &E) const
	Return the global offset for the unknowns on the edge E.

size_t	globalOffset (const Cell &T) const
	Return the global offset for the unknowns on the cell T.

Eigen::VectorXd	restrictEdge (size_t iE, const Eigen::VectorXd &vh) const
	Restrict to the edge (including its vertices) of index iE.

Eigen::VectorXd	restrictCell (size_t iT, const Eigen::VectorXd &vh) const
	Restrict to the cell (including vertices and edges) of index iT.

Eigen::VectorXd	restrict (const Edge &E, const Eigen::VectorXd vh) const
	Restrict to an edge.

Eigen::VectorXd	restrict (const Cell &T, const Eigen::VectorXd vh) const
	Restrict to a cell.

Eigen::MatrixXd	extendOperator (const Cell &T, const Edge &E, const Eigen::MatrixXd &opE) const
	Extend an edge operator to a cell.

std::vector< size_t >	globalDOFIndices (const Cell &T) const

void	setLabelDOF (const size_t i, const int label)
	Set a label to the DOF number i (default label is -1)

int	getLabelDOF (const size_t i)
	Get label of DOF number i.

Public Member Functions inherited from HArDCore2D::LocalDOFSpace
	LocalDOFSpace (const Mesh &mesh, size_t n_local_vertex_dofs, size_t n_local_edge_dofs, size_t n_local_cell_dofs)
	Constructor.

const Mesh &	mesh () const
	Returns the mesh.

size_t	numLocalDofsVertex () const
	Returns the number of local vertex DOFs.

size_t	numLocalDofsEdge () const
	Returns the number of local edge DOFs.

size_t	numLocalDofsCell () const
	Returns the number of local cell DOFs.

size_t	dimension () const
	Returns the dimension of the global space (all DOFs for all geometric entities)

size_t	numTotalDofsVertices () const
	Returns the total number of vertex DOFs.

size_t	numTotalDofsEdges () const
	Returns the total number of vertex DOFs.

size_t	numTotalDofsCells () const
	Returns the total number of vertex DOFs.

size_t	dimensionVertex (const Vertex &V) const
	Returns the dimension of the local space on the vertex V.

size_t	dimensionVertex (size_t iV) const
	Returns the dimension of the local space on the vertex of index iV.

size_t	dimensionEdge (const Edge &E) const
	Returns the dimension of the local space on the edge E (including vertices)

size_t	dimensionEdge (size_t iE) const
	Returns the dimension of the local space on the edge of index iE (including vertices)

size_t	dimensionCell (const Cell &T) const
	Returns the dimension of the local space on the cell T (including faces, edges and vertices)

size_t	dimensionCellBoundary (const Cell &T) const
	Returns the dimension of the local space on the boundary of T.

size_t	dimensionCell (size_t iT) const
	Returns the dimension of the local space on the cell of index iT (including faces, edges and vertices)

size_t	dimensionCellBoundary (size_t iT) const
	Returns the dimension of the local space on the boundary of T.

size_t	localOffset (const Edge &E, const Vertex &V) const
	Returns the local offset of the vertex V with respect to the edge E.

size_t	localOffset (const Edge &E) const
	Returns the local offset of the unknowns attached to the edge E.

size_t	localOffset (const Cell &T, const Vertex &V) const
	Returns the local offset of the vertex V with respect to the cell T.

size_t	localOffset (const Cell &T, const Edge &E) const
	Returns the local offset of the edge E with respect to the cell T.

size_t	localOffset (const Cell &T) const
	Returns the local offset of the unknowns attached to the element T.

Additional Inherited Members
Protected Attributes inherited from HArDCore2D::LocalDOFSpace
const Mesh &	m_mesh

size_t	m_n_local_vertex_dofs

size_t	m_n_local_edge_dofs

size_t	m_n_local_cell_dofs

Detailed Description

Discrete H2 space: local operators, L2 product and global interpolator.

Constructor & Destructor Documentation

◆ XHess()

HArDCore2D::XHess::XHess	(	const DDRCore &	ddr_core,
		const SerendipityProblem &	ser_pro,
		bool	use_threads = `true`,
		std::ostream &	output = `std::cout`
	)

Constructor.

Member Function Documentation

◆ cellBases() [1/2]

const DDRCore::CellBases & HArDCore2D::XHess::cellBases ( const Cell & T ) const

inline

Return cell bases for cell T.

◆ cellBases() [2/2]

const DDRCore::CellBases & HArDCore2D::XHess::cellBases ( size_t iT ) const

inline

Return cell bases for the cell of index iT.

◆ cellOperators() [1/2]

const LocalOperators & HArDCore2D::XHess::cellOperators ( const Cell & T ) const

inline

Return cell operators for cell T.

◆ cellOperators() [2/2]

const LocalOperators & HArDCore2D::XHess::cellOperators ( size_t iT ) const

inline

Return cell operators for the cell of index iT.

◆ computeGradientFull()

Eigen::MatrixXd HArDCore2D::XHess::computeGradientFull	(	const size_t	iT,
		const VSXGrad &	vsx_grad
	)		const

Parameters

iT	index of the cell

◆ computeL2Norm()

double HArDCore2D::XHess::computeL2Norm ( const Eigen::VectorXd & v ) const

Compute the L2-norm of a vector of the space.

◆ computeL2Product()

Eigen::MatrixXd HArDCore2D::XHess::computeL2Product	(	const size_t	iT,
		const double &	penalty_factor = `1.`,
		const Eigen::MatrixXd &	mass_Pkpo_T = `Eigen::MatrixXd::Zero(1, 1)`,
		const IntegralWeight &	weight = `IntegralWeight(1.)`
	)		const

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pkpo_T	if pre-computed, the mass matrix of P^{k+1}(T); if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to 1

◆ computeStabilisation()

Eigen::MatrixXd HArDCore2D::XHess::computeStabilisation	(	const size_t	iT,
		const double &	penalty_factor = `1.`,
		const Eigen::MatrixXd &	mass_Pkpo_T = `Eigen::MatrixXd::Zero(1, 1)`,
		const IntegralWeight &	weight = `IntegralWeight(1.)`
	)		const

Compute the matrix of the (weighted) L2-product for the cell of index iT.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pkpo_T	if pre-computed, the mass matrix of P^{k+1}(T); if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to 1

◆ degree()

const size_t & HArDCore2D::XHess::degree ( ) const

inline

Return the polynomial degree.

◆ edgeBases() [1/2]

const DDRCore::EdgeBases & HArDCore2D::XHess::edgeBases ( const Edge & E ) const

inline

Return edge bases for edge E.

◆ edgeBases() [2/2]

const DDRCore::EdgeBases & HArDCore2D::XHess::edgeBases ( size_t iE ) const

inline

Return edge bases for the edge of index iE.

◆ edgeOperators() [1/2]

const LocalOperators & HArDCore2D::XHess::edgeOperators ( const Edge & E ) const

inline

Return edge operators for edge E.

◆ edgeOperators() [2/2]

const LocalOperators & HArDCore2D::XHess::edgeOperators ( size_t iE ) const

inline

Return edge operators for the edge of index iE.

◆ evaluatePotential()

double HArDCore2D::XHess::evaluatePotential	(	const size_t	iT,
		const Eigen::VectorXd &	vT,
		const VectorRd &	x
	)		const

Evaluate the value of the potential at a point x.

Parameters

iT	index of the cell in which to take the potential
vT	vector of local DOFs
x	point at which to evaluate the potential

◆ interpolate()

Eigen::VectorXd HArDCore2D::XHess::interpolate	(	const FunctionType &	q,
		const GradFunctionType &	Dq,
		const int	deg_quad = `-1`
	)		const

Interpolator of a continuous function.

Parameters

q	The function to interpolate
Dq	The gradient of the function
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

◆ mesh()

const Mesh & HArDCore2D::XHess::mesh ( ) const

inline

Return the mesh.

◆ SgradCell() [1/2]

const Eigen::MatrixXd & HArDCore2D::XHess::SgradCell ( const Cell & T ) const

inline

Return the serendipity reconstruction for cell T.

◆ SgradCell() [2/2]

const Eigen::MatrixXd & HArDCore2D::XHess::SgradCell ( size_t iT ) const

inline

Return the serendipity reconstruction for the cell of index iT.

◆ TcellOperators() [1/2]

const TransferOperators & HArDCore2D::XHess::TcellOperators ( const Cell & T ) const

inline

Return cell operators for cell T.

◆ TcellOperators() [2/2]

const TransferOperators & HArDCore2D::XHess::TcellOperators ( size_t iT ) const

inline

Return cell operators for the cell of index iT.

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

src/DDRCore/xhess.hpp
src/DDRCore/xhess_full.hpp
src/DDRCore/xhess.cpp
src/DDRCore/xhess_full.cpp

Classes

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ XHess()

Member Function Documentation

◆ cellBases() [1/2]

◆ cellBases() [2/2]

◆ cellOperators() [1/2]

◆ cellOperators() [2/2]

◆ computeGradientFull()

◆ computeL2Norm()

◆ computeL2Product()

◆ computeStabilisation()

◆ degree()

◆ edgeBases() [1/2]

◆ edgeBases() [2/2]

◆ edgeOperators() [1/2]

◆ edgeOperators() [2/2]

◆ evaluatePotential()

◆ interpolate()

◆ mesh()

◆ SgradCell() [1/2]

◆ SgradCell() [2/2]

◆ TcellOperators() [1/2]

◆ TcellOperators() [2/2]