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

#include <sxcurl.hpp>

Inheritance diagram for HArDCore2D::SXCurl:

Collaboration diagram for HArDCore2D::SXCurl:

Classes
struct	TransferOperators
	A structure to store the serendipity, extension and reduction operators. More...

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

Public Member Functions
	SXCurl (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 &v, const int deg_quad=-1) const
	Interpolator of a continuous function.

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

const Eigen::MatrixXd &	EcurlCell (size_t iT) const
	Return the extension for the cell of index iT.

const Eigen::MatrixXd &	RcurlCell (size_t iT) const
	Return the reduction for the cell of index iT.

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

const Eigen::MatrixXd &	EcurlCell (const Cell &T) const
	Return the extension for cell T.

const Eigen::MatrixXd &	RcurlCell (const Cell &T) const
	Return the reduction for cell T.

const Eigen::MatrixXd	cellCurl (size_t iT) const
	Return the full curl operator on the cell of index iT.

const Eigen::MatrixXd	cellCurl (const Cell &T) const
	Return the full curl operator on cell T.

const Eigen::MatrixXd	cellPotential (size_t iT) const
	Return the potential operator on the cell of index iT.

const Eigen::MatrixXd	cellPotential (const Cell &T) const
	Return the potential operator on cell T.

Eigen::MatrixXd	computeStabilisation (const size_t iT, const double &penalty_factor=1., const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the local stabilisation matrix.

Eigen::MatrixXd	computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk2_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product.

Eigen::MatrixXd	computeL2ProductGradient (const size_t iT, const SXGrad &sx_grad, const std::string &side, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk2_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product as 'computeL2Product', with application of the discrete gradient on the left/right/both sides (depending on argument "side").

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

Public Member Functions inherited from HArDCore2D::VariableDOFSpace
	VariableDOFSpace (const Mesh &mesh, const Eigen::VectorXd n_local_vertex_dofs, const Eigen::VectorXd n_local_edge_dofs, const Eigen::VectorXd n_local_cell_dofs)
	Constructor.

	VariableDOFSpace (const Mesh &mesh, size_t n_local_vertex_dofs, const Eigen::VectorXd n_local_edge_dofs, const Eigen::VectorXd n_local_cell_dofs)
	Simpler constructor if all vertices have the same number of DOFs.

	VariableDOFSpace (const Mesh &mesh, size_t n_local_vertex_dofs, size_t n_local_edge_dofs, const Eigen::VectorXd n_local_cell_dofs)
	Simpler constructor if all vertices/edges have the same number of DOFs.

	VariableDOFSpace (const Mesh &mesh, size_t n_local_vertex_dofs, size_t n_local_edge_dofs, size_t n_local_cell_dofs)
	Simpler constructor if all vertices/edges/cells have the same number of DOFs.

const Mesh &	mesh () const
	Returns the mesh.

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

size_t	numLocalDofsVertex (const Vertex &V) const
	Returns the number of local DOFs on vertex V.

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

size_t	numLocalDofsEdge (const Edge &E) const
	Returns the number of local DOFs on edge E.

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

size_t	numLocalDofsCell (const Cell &T) const
	Returns the number of local DOFs on cell T.

size_t	nDOFs_vertices () const
	Total number of vertices DOFs.

size_t	nDOFs_edges () const
	Total number of edges DOFs.

size_t	nDOFs_cells () const
	Total number of cells DOFs.

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

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	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	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.

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, edges and faces) 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
	Returns a vector listing the global DOFs attached to the element T: vertex DOFs, edge DOFs, face DOFs and element DOFs.

std::vector< size_t >	globalDOFIndices (const Edge &E) const
	Returns a vector listing the global DOFs attached to the edge E: vertex DOFs, edge DOFs,.

Detailed Description

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

On each edge, the DOFs correspond to the polynomial bases on the edge provided by m_ddr_core. On each face/element, the DOFs are first those of the \(\mathcal{R}^{k-1}\) component and then of the \(\mathcal{R}^{c,\ell+1}\) component, each one of them following the bases of these spaces provided by m_ddr_core or restriction thereof.

Member Typedef Documentation

◆ FunctionType

typedef std::function<Eigen::Vector2d(const Eigen::Vector2d &)> HArDCore2D::SXCurl::FunctionType

Constructor & Destructor Documentation

◆ SXCurl()

SXCurl::SXCurl	(	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::SXCurl::cellBases ( const Cell & T ) const

inline

Return cell bases for cell T.

◆ cellBases() [2/2]

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

inline

Return cell bases for the face of index iT.

◆ cellCurl() [1/2]

const Eigen::MatrixXd HArDCore2D::SXCurl::cellCurl ( const Cell & T ) const

inline

Return the full curl operator on cell T.

◆ cellCurl() [2/2]

const Eigen::MatrixXd HArDCore2D::SXCurl::cellCurl ( size_t iT ) const

inline

Return the full curl operator on the cell of index iT.

◆ cellPotential() [1/2]

const Eigen::MatrixXd HArDCore2D::SXCurl::cellPotential ( const Cell & T ) const

inline

Return the potential operator on cell T.

◆ cellPotential() [2/2]

const Eigen::MatrixXd HArDCore2D::SXCurl::cellPotential ( size_t iT ) const

inline

Return the potential operator on the cell of index iT.

◆ computeL2Product()

Eigen::MatrixXd HArDCore2D::SXCurl::computeL2Product	(	const size_t	iT,
		const double &	penalty_factor = `1.`,
		const Eigen::MatrixXd &	mass_Pk2_T = `Eigen::MatrixXd::Zero(1,1)`,
		const IntegralWeight &	weight = `IntegralWeight(1.)`
	)		const

inline

Compute the matrix of the (weighted) L2-product.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pk2_T	if pre-computed, the mass matrix of (P^k(T))^2; 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

◆ computeL2ProductGradient()

Eigen::MatrixXd SXCurl::computeL2ProductGradient	(	const size_t	iT,
		const SXGrad &	sx_grad,
		const std::string &	side,
		const double &	penalty_factor = `1.`,
		const Eigen::MatrixXd &	mass_Pk2_T = `Eigen::MatrixXd::Zero(1,1)`,
		const IntegralWeight &	weight = `IntegralWeight(1.)`
	)		const

Compute the matrix of the (weighted) L2-product as 'computeL2Product', with application of the discrete gradient on the left/right/both sides (depending on argument "side").

Parameters

iT	index of the cell
sx_grad	instance of SXGrad to access the full gradients
side	which side (left, right, both) we apply the gradient to
penalty_factor	pre-factor for stabilisation term
mass_Pk2_T	if pre-computed, the mass matrix of (P^k(T))^2; if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to constant 1.

◆ computeStabilisation()

Eigen::MatrixXd SXCurl::computeStabilisation	(	const size_t	iT,
		const double &	penalty_factor = `1.`,
		const IntegralWeight &	weight = `IntegralWeight(1.)`
	)		const

Compute the local stabilisation matrix.

◆ degree()

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

inline

Return the polynomial degree.

◆ EcurlCell() [1/2]

const Eigen::MatrixXd & HArDCore2D::SXCurl::EcurlCell ( const Cell & T ) const

inline

Return the extension for cell T.

◆ EcurlCell() [2/2]

const Eigen::MatrixXd & HArDCore2D::SXCurl::EcurlCell ( size_t iT ) const

inline

Return the extension for the cell of index iT.

◆ edgeBases() [1/2]

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

inline

Return edge bases for edge E.

◆ edgeBases() [2/2]

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

inline

Return edge bases for the edge of index iE.

◆ interpolate()

Eigen::VectorXd SXCurl::interpolate	(	const FunctionType &	v,
		const int	deg_quad = `-1`
	)		const

Interpolator of a continuous function.

Parameters

v	The function to interpolate
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::SXCurl::mesh ( ) const

inline

Return the mesh.

◆ RcurlCell() [1/2]

const Eigen::MatrixXd & HArDCore2D::SXCurl::RcurlCell ( const Cell & T ) const

inline

Return the reduction for cell T.

◆ RcurlCell() [2/2]

const Eigen::MatrixXd & HArDCore2D::SXCurl::RcurlCell ( size_t iT ) const

inline

Return the reduction for the cell of index iT.

◆ ScurlCell() [1/2]

const Eigen::MatrixXd & HArDCore2D::SXCurl::ScurlCell ( const Cell & T ) const

inline

Return the serendipity reconstruction for cell T.

◆ ScurlCell() [2/2]

const Eigen::MatrixXd & HArDCore2D::SXCurl::ScurlCell ( size_t iT ) const

inline

Return the serendipity reconstruction for the cell of index iT.

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

src/DDRCore/sxcurl.hpp
src/DDRCore/sxcurl.cpp

Classes

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ FunctionType

Constructor & Destructor Documentation

◆ SXCurl()

Member Function Documentation

◆ cellBases() [1/2]

◆ cellBases() [2/2]

◆ cellCurl() [1/2]

◆ cellCurl() [2/2]

◆ cellPotential() [1/2]

◆ cellPotential() [2/2]

◆ computeL2Product()

◆ computeL2ProductGradient()

◆ computeStabilisation()

◆ degree()

◆ EcurlCell() [1/2]

◆ EcurlCell() [2/2]

◆ edgeBases() [1/2]

◆ edgeBases() [2/2]

◆ interpolate()

◆ mesh()

◆ RcurlCell() [1/2]

◆ RcurlCell() [2/2]

◆ ScurlCell() [1/2]

◆ ScurlCell() [2/2]