Classes providing tools to the de Rham VEM sequence. More...

Classes
class	HArDCore3D::VCurl
	Virtual Hcurl space: local operators, L2 product and global interpolator. More...

struct	HArDCore3D::VCurl::LocalOperators
	A structure to store the local operators (projections of curl and function, dof of curl in Vdiv) More...

class	HArDCore3D::VDiv
	Virtual Hdiv space: local operators, L2 product and global interpolator. More...

struct	HArDCore3D::VDiv::LocalOperators
	A structure to store the local operators (projections of div and function) More...

class	HArDCore3D::VEMCore
	Construct all polynomial spaces for the VEM sequence. More...

struct	HArDCore3D::VEMCore::CellBases
	Structure to store element bases. More...

struct	HArDCore3D::VEMCore::FaceBases
	Structure to store face bases. More...

struct	HArDCore3D::VEMCore::EdgeBases
	Structure to store edge bases. More...

class	HArDCore3D::VGrad
	Virtual H1 space: local operators, L2 product and global interpolator. More...

struct	HArDCore3D::VGrad::LocalOperators
	A structure to store local operators (projection of gradient and function, dof of gradient in Vcurl) More...

Typedefs
typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::VCurl::FunctionType

typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::VDiv::FunctionType

typedef std::function< double(const Eigen::Vector3d &)>	HArDCore3D::VDiv::DivergenceType

typedef Family< MonomialScalarBasisCell >	HArDCore3D::VEMCore::PolyBasisCellType

typedef TensorizedVectorFamily< PolyBasisCellType, 3 >	HArDCore3D::VEMCore::Poly3BasisCellType

typedef Family< GradientBasis< ShiftedBasis< MonomialScalarBasisCell > > >	HArDCore3D::VEMCore::GolyBasisCellType

typedef Family< GolyComplBasisCell >	HArDCore3D::VEMCore::GolyComplBasisCellType

typedef Family< CurlBasis< GolyComplBasisCell > >	HArDCore3D::VEMCore::RolyBasisCellType

typedef Family< RolyComplBasisCell >	HArDCore3D::VEMCore::RolyComplBasisCellType

typedef Family< MonomialScalarBasisFace >	HArDCore3D::VEMCore::PolyBasisFaceType

typedef TangentFamily< PolyBasisFaceType >	HArDCore3D::VEMCore::Poly2BasisFaceType

typedef Family< CurlBasis< ShiftedBasis< MonomialScalarBasisFace > > >	HArDCore3D::VEMCore::RolyBasisFaceType

typedef Family< RolyComplBasisFace >	HArDCore3D::VEMCore::RolyComplBasisFaceType

typedef Family< MonomialScalarBasisEdge >	HArDCore3D::VEMCore::PolyBasisEdgeType

typedef Cell	HArDCore3D::VEMCore::CellBases::GeometricSupport
	Geometric support. More...

typedef Face	HArDCore3D::VEMCore::FaceBases::GeometricSupport
	Geometric support. More...

typedef Edge	HArDCore3D::VEMCore::EdgeBases::GeometricSupport
	Geometric support. More...

typedef std::function< double(const Eigen::Vector3d &)>	HArDCore3D::VGrad::FunctionType

typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::VGrad::GradientType

Functions
	HArDCore3D::VCurl::LocalOperators::LocalOperators (const Eigen::MatrixXd &_proj_curl, const Eigen::MatrixXd &_dofs_curl, const Eigen::MatrixXd &_proj_function)

	HArDCore3D::VCurl::VCurl (const VEMCore &vem_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor. More...

const Mesh &	HArDCore3D::VCurl::mesh () const
	Return the mesh. More...

const size_t &	HArDCore3D::VCurl::degree () const
	Return the polynomial degree. More...

Eigen::VectorXd	HArDCore3D::VCurl::interpolate (const FunctionType &v, const FunctionType &curl_v, const int doe_cell=-1, const int doe_face=-1, const int doe_edge=-1) const
	Interpolator of a continuous function. More...

const LocalOperators &	HArDCore3D::VCurl::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT. More...

const LocalOperators &	HArDCore3D::VCurl::cellOperators (const Cell &T) const
	Return cell operators for cell T. More...

const LocalOperators &	HArDCore3D::VCurl::faceOperators (size_t iF) const
	Return face operators for the face of index iF. More...

const LocalOperators &	HArDCore3D::VCurl::faceOperators (const Face &F) const
	Return face operators for face F. More...

const VEMCore::CellBases &	HArDCore3D::VCurl::cellBases (size_t iT) const
	Return cell bases for the face of index iT. More...

const VEMCore::CellBases &	HArDCore3D::VCurl::cellBases (const Cell &T) const
	Return cell bases for cell T. More...

const VEMCore::FaceBases &	HArDCore3D::VCurl::faceBases (size_t iF) const
	Return face bases for the face of index iF. More...

const VEMCore::FaceBases &	HArDCore3D::VCurl::faceBases (const Face &F) const
	Return cell bases for face F. More...

const VEMCore::EdgeBases &	HArDCore3D::VCurl::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE. More...

const VEMCore::EdgeBases &	HArDCore3D::VCurl::edgeBases (const Edge &E) const
	Return edge bases for edge E. More...

Eigen::MatrixXd	HArDCore3D::VCurl::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk3_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. More...

	HArDCore3D::VDiv::LocalOperators::LocalOperators (const Eigen::MatrixXd &_proj_divergence, const Eigen::MatrixXd &_proj_function)

	HArDCore3D::VDiv::VDiv (const VEMCore &vem_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor. More...

const Mesh &	HArDCore3D::VDiv::mesh () const
	Return the mesh. More...

const size_t &	HArDCore3D::VDiv::degree () const
	Return the polynomial degree. More...

Eigen::VectorXd	HArDCore3D::VDiv::interpolate (const FunctionType &v, const DivergenceType &div_v, const int doe_cell=-1, const int doe_face=-1) const
	Interpolator of a continuous function. More...

const LocalOperators &	HArDCore3D::VDiv::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT. More...

const LocalOperators &	HArDCore3D::VDiv::cellOperators (const Cell &T) const
	Return cell operators for cell T. More...

const LocalOperators &	HArDCore3D::VDiv::faceOperators (size_t iF) const
	Return face operators for the face of index iF. More...

const LocalOperators &	HArDCore3D::VDiv::faceOperators (const Face &F) const
	Return face operators for face F. More...

const VEMCore::CellBases &	HArDCore3D::VDiv::cellBases (size_t iT) const
	Return cell bases for the face of index iT. More...

const VEMCore::CellBases &	HArDCore3D::VDiv::cellBases (const Cell &T) const
	Return cell bases for cell T. More...

const VEMCore::FaceBases &	HArDCore3D::VDiv::faceBases (size_t iF) const
	Return face bases for the face of index iF. More...

const VEMCore::FaceBases &	HArDCore3D::VDiv::faceBases (const Face &F) const
	Return cell bases for face F. More...

const VEMCore::EdgeBases &	HArDCore3D::VDiv::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE. More...

const VEMCore::EdgeBases &	HArDCore3D::VDiv::edgeBases (const Edge &E) const
	Return edge bases for edge E. More...

Eigen::MatrixXd	HArDCore3D::VDiv::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk3_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. The stabilisation here is based on cell and face potentials. More...

	HArDCore3D::VEMCore::VEMCore (const Mesh &mesh, size_t K, bool use_threads=true, std::ostream &output=std::cout)
	Constructor. More...

const Mesh &	HArDCore3D::VEMCore::mesh () const
	Return a const reference to the mesh. More...

const size_t &	HArDCore3D::VEMCore::degree () const
	Return the polynomial degree. More...

const CellBases &	HArDCore3D::VEMCore::cellBases (size_t iT) const
	Return cell bases for element iT. More...

const FaceBases &	HArDCore3D::VEMCore::faceBases (size_t iF) const
	Return face bases for face iF. More...

const EdgeBases &	HArDCore3D::VEMCore::edgeBases (size_t iE) const
	Return edge bases for edge iE. More...

	HArDCore3D::VGrad::LocalOperators::LocalOperators (const Eigen::MatrixXd &_proj_gradient, const Eigen::MatrixXd &_dofs_gradient, const Eigen::MatrixXd &_proj_function)

	HArDCore3D::VGrad::VGrad (const VEMCore &vem_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor. More...

const Mesh &	HArDCore3D::VGrad::mesh () const
	Return the mesh. More...

const size_t &	HArDCore3D::VGrad::degree () const
	Return the polynomial degree. More...

Eigen::VectorXd	HArDCore3D::VGrad::interpolate (const FunctionType &q, const GradientType &grad_q, const int doe_cell=-1, const int doe_face=-1, const int doe_edge=-1) const
	Interpolator of a continuous function. More...

const LocalOperators &	HArDCore3D::VGrad::edgeOperators (size_t iE) const
	Return edge operators for the edge of index iE. More...

const LocalOperators &	HArDCore3D::VGrad::edgeOperators (const Edge &E) const
	Return edge operators for edge E. More...

const LocalOperators &	HArDCore3D::VGrad::faceOperators (size_t iF) const
	Return face operators for the face of index iF. More...

const LocalOperators &	HArDCore3D::VGrad::faceOperators (const Face &F) const
	Return face operators for face F. More...

const LocalOperators &	HArDCore3D::VGrad::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT. More...

const LocalOperators &	HArDCore3D::VGrad::cellOperators (const Cell &T) const
	Return cell operators for cell T. More...

const VEMCore::CellBases &	HArDCore3D::VGrad::cellBases (size_t iT) const
	Return cell bases for the cell of index iT. More...

const VEMCore::CellBases &	HArDCore3D::VGrad::cellBases (const Cell &T) const
	Return cell bases for cell T. More...

const VEMCore::FaceBases &	HArDCore3D::VGrad::faceBases (size_t iF) const
	Return face bases for the face of index iF. More...

const VEMCore::FaceBases &	HArDCore3D::VGrad::faceBases (const Face &F) const
	Return cell bases for face F. More...

const VEMCore::EdgeBases &	HArDCore3D::VGrad::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE. More...

const VEMCore::EdgeBases &	HArDCore3D::VGrad::edgeBases (const Edge &E) const
	Return edge bases for edge E. More...

Eigen::MatrixXd	HArDCore3D::VGrad::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pkmo_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. The stabilisation here is based on cell and face potentials. NOT COMPLETE: only computes the consistent component of this L2 product. More...

Variables
Eigen::MatrixXd	HArDCore3D::VCurl::LocalOperators::proj_curl

Eigen::MatrixXd	HArDCore3D::VCurl::LocalOperators::dofs_curl

Eigen::MatrixXd	HArDCore3D::VCurl::LocalOperators::proj_function

Eigen::MatrixXd	HArDCore3D::VDiv::LocalOperators::proj_divergence

Eigen::MatrixXd	HArDCore3D::VDiv::LocalOperators::proj_function

std::unique_ptr< PolyBasisCellType >	HArDCore3D::VEMCore::CellBases::Polykpo

std::unique_ptr< PolyBasisCellType >	HArDCore3D::VEMCore::CellBases::Polyk

std::unique_ptr< PolyBasisCellType >	HArDCore3D::VEMCore::CellBases::Polykmo

std::unique_ptr< ShiftedBasis< PolyBasisCellType > >	HArDCore3D::VEMCore::CellBases::Polyk0

std::unique_ptr< ShiftedBasis< PolyBasisCellType > >	HArDCore3D::VEMCore::CellBases::Polykpo0

std::unique_ptr< Poly3BasisCellType >	HArDCore3D::VEMCore::CellBases::Polyk3

std::unique_ptr< GolyBasisCellType >	HArDCore3D::VEMCore::CellBases::Golykmo

std::unique_ptr< GolyComplBasisCellType >	HArDCore3D::VEMCore::CellBases::GolyComplk

std::unique_ptr< GolyComplBasisCellType >	HArDCore3D::VEMCore::CellBases::GolyComplkpo

std::unique_ptr< RolyBasisCellType >	HArDCore3D::VEMCore::CellBases::Rolykmo

std::unique_ptr< RolyComplBasisCellType >	HArDCore3D::VEMCore::CellBases::RolyComplk

std::unique_ptr< RolyComplBasisCellType >	HArDCore3D::VEMCore::CellBases::RolyComplkp2

std::unique_ptr< PolyBasisFaceType >	HArDCore3D::VEMCore::FaceBases::Polykp2

std::unique_ptr< PolyBasisFaceType >	HArDCore3D::VEMCore::FaceBases::Polykpo

std::unique_ptr< PolyBasisFaceType >	HArDCore3D::VEMCore::FaceBases::Polyk

std::unique_ptr< PolyBasisFaceType >	HArDCore3D::VEMCore::FaceBases::Polykmo

std::unique_ptr< ShiftedBasis< PolyBasisFaceType > >	HArDCore3D::VEMCore::FaceBases::Polyk0

std::unique_ptr< TangentFamily< PolyBasisFaceType > >	HArDCore3D::VEMCore::FaceBases::Polykpo2

std::unique_ptr< Poly2BasisFaceType >	HArDCore3D::VEMCore::FaceBases::Polyk2

std::unique_ptr< RolyBasisFaceType >	HArDCore3D::VEMCore::FaceBases::Rolykmo

std::unique_ptr< RolyComplBasisFaceType >	HArDCore3D::VEMCore::FaceBases::RolyComplkmo

std::unique_ptr< RolyComplBasisFaceType >	HArDCore3D::VEMCore::FaceBases::RolyComplk

std::unique_ptr< RolyComplBasisFaceType >	HArDCore3D::VEMCore::FaceBases::RolyComplkpo

std::unique_ptr< PolyBasisEdgeType >	HArDCore3D::VEMCore::EdgeBases::Polykpo

std::unique_ptr< PolyBasisEdgeType >	HArDCore3D::VEMCore::EdgeBases::Polyk

std::unique_ptr< PolyBasisEdgeType >	HArDCore3D::VEMCore::EdgeBases::Polykmo

Eigen::MatrixXd	HArDCore3D::VGrad::LocalOperators::proj_gradient

Eigen::MatrixXd	HArDCore3D::VGrad::LocalOperators::dofs_gradient

Eigen::MatrixXd	HArDCore3D::VGrad::LocalOperators::proj_function

Detailed Description

Classes providing tools to the de Rham VEM sequence.

Typedef Documentation

◆ DivergenceType

typedef std::function<double(const Eigen::Vector3d &)> HArDCore3D::VDiv::DivergenceType

◆ FunctionType [1/3]

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::VCurl::FunctionType

◆ FunctionType [2/3]

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::VDiv::FunctionType

◆ FunctionType [3/3]

typedef std::function<double(const Eigen::Vector3d &)> HArDCore3D::VGrad::FunctionType

◆ GeometricSupport [1/3]

typedef Cell HArDCore3D::VEMCore::CellBases::GeometricSupport

Geometric support.

◆ GeometricSupport [2/3]

typedef Face HArDCore3D::VEMCore::FaceBases::GeometricSupport

Geometric support.

◆ GeometricSupport [3/3]

typedef Edge HArDCore3D::VEMCore::EdgeBases::GeometricSupport

Geometric support.

◆ GolyBasisCellType

typedef Family<GradientBasis<ShiftedBasis<MonomialScalarBasisCell> > > HArDCore3D::VEMCore::GolyBasisCellType

◆ GolyComplBasisCellType

typedef Family<GolyComplBasisCell> HArDCore3D::VEMCore::GolyComplBasisCellType

◆ GradientType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::VGrad::GradientType

◆ Poly2BasisFaceType

typedef TangentFamily<PolyBasisFaceType> HArDCore3D::VEMCore::Poly2BasisFaceType

◆ Poly3BasisCellType

typedef TensorizedVectorFamily<PolyBasisCellType, 3> HArDCore3D::VEMCore::Poly3BasisCellType

◆ PolyBasisCellType

typedef Family<MonomialScalarBasisCell> HArDCore3D::VEMCore::PolyBasisCellType

◆ PolyBasisEdgeType

typedef Family<MonomialScalarBasisEdge> HArDCore3D::VEMCore::PolyBasisEdgeType

◆ PolyBasisFaceType

typedef Family<MonomialScalarBasisFace> HArDCore3D::VEMCore::PolyBasisFaceType

◆ RolyBasisCellType

typedef Family<CurlBasis<GolyComplBasisCell> > HArDCore3D::VEMCore::RolyBasisCellType

◆ RolyBasisFaceType

typedef Family<CurlBasis<ShiftedBasis<MonomialScalarBasisFace> > > HArDCore3D::VEMCore::RolyBasisFaceType

◆ RolyComplBasisCellType

typedef Family<RolyComplBasisCell> HArDCore3D::VEMCore::RolyComplBasisCellType

◆ RolyComplBasisFaceType

typedef Family<RolyComplBasisFace> HArDCore3D::VEMCore::RolyComplBasisFaceType

Function Documentation

◆ cellBases() [1/7]

const VEMCore::CellBases& HArDCore3D::VCurl::cellBases ( const Cell & T ) const

inline

Return cell bases for cell T.

◆ cellBases() [2/7]

const VEMCore::CellBases& HArDCore3D::VDiv::cellBases ( const Cell & T ) const

inline

Return cell bases for cell T.

◆ cellBases() [3/7]

const VEMCore::CellBases& HArDCore3D::VGrad::cellBases ( const Cell & T ) const

inline

Return cell bases for cell T.

◆ cellBases() [4/7]

const VEMCore::CellBases& HArDCore3D::VCurl::cellBases ( size_t iT ) const

inline

Return cell bases for the face of index iT.

◆ cellBases() [5/7]

const VEMCore::CellBases& HArDCore3D::VDiv::cellBases ( size_t iT ) const

inline

Return cell bases for the face of index iT.

◆ cellBases() [6/7]

const CellBases& HArDCore3D::VEMCore::cellBases ( size_t iT ) const

inline

Return cell bases for element iT.

◆ cellBases() [7/7]

const VEMCore::CellBases& HArDCore3D::VGrad::cellBases ( size_t iT ) const

inline

Return cell bases for the cell of index iT.

◆ cellOperators() [1/6]

const LocalOperators& HArDCore3D::VCurl::cellOperators ( const Cell & T ) const

inline

Return cell operators for cell T.

◆ cellOperators() [2/6]

const LocalOperators& HArDCore3D::VDiv::cellOperators ( const Cell & T ) const

inline

Return cell operators for cell T.

◆ cellOperators() [3/6]

const LocalOperators& HArDCore3D::VGrad::cellOperators ( const Cell & T ) const

inline

Return cell operators for cell T.

◆ cellOperators() [4/6]

const LocalOperators& HArDCore3D::VCurl::cellOperators ( size_t iT ) const

inline

Return cell operators for the cell of index iT.

◆ cellOperators() [5/6]

const LocalOperators& HArDCore3D::VDiv::cellOperators ( size_t iT ) const

inline

Return cell operators for the cell of index iT.

◆ cellOperators() [6/6]

const LocalOperators& HArDCore3D::VGrad::cellOperators ( size_t iT ) const

inline

Return cell operators for the cell of index iT.

◆ computeL2Product() [1/3]

Eigen::MatrixXd VCurl::computeL2Product	(	const size_t	iT,
		const double &	penalty_factor = `1.`,
		const Eigen::MatrixXd &	mass_Pk3_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_Pk3_T	if pre-computed, the mass matrix of (P^k(T))^3; 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

◆ computeL2Product() [2/3]

Eigen::MatrixXd VDiv::computeL2Product	(	const size_t	iT,
		const double &	penalty_factor = `1.`,
		const Eigen::MatrixXd &	mass_Pk3_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. The stabilisation here is based on cell and face potentials.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pk3_T	if pre-computed, the mass matrix of (P^k(T))^3; 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

◆ computeL2Product() [3/3]

Eigen::MatrixXd VGrad::computeL2Product	(	const size_t	iT,
		const double &	penalty_factor = `1.`,
		const Eigen::MatrixXd &	mass_Pkmo_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. The stabilisation here is based on cell and face potentials. NOT COMPLETE: only computes the consistent component of this L2 product.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pkmo_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() [1/4]

const size_t& HArDCore3D::VCurl::degree ( ) const

inline

Return the polynomial degree.

◆ degree() [2/4]

const size_t& HArDCore3D::VDiv::degree ( ) const

inline

Return the polynomial degree.

◆ degree() [3/4]

const size_t& HArDCore3D::VEMCore::degree ( ) const

inline

Return the polynomial degree.

◆ degree() [4/4]

const size_t& HArDCore3D::VGrad::degree ( ) const

inline

Return the polynomial degree.

◆ edgeBases() [1/7]

const VEMCore::EdgeBases& HArDCore3D::VCurl::edgeBases ( const Edge & E ) const

inline

Return edge bases for edge E.

◆ edgeBases() [2/7]

const VEMCore::EdgeBases& HArDCore3D::VDiv::edgeBases ( const Edge & E ) const

inline

Return edge bases for edge E.

◆ edgeBases() [3/7]

const VEMCore::EdgeBases& HArDCore3D::VGrad::edgeBases ( const Edge & E ) const

inline

Return edge bases for edge E.

◆ edgeBases() [4/7]

const VEMCore::EdgeBases& HArDCore3D::VCurl::edgeBases ( size_t iE ) const

inline

Return edge bases for the edge of index iE.

◆ edgeBases() [5/7]

const VEMCore::EdgeBases& HArDCore3D::VDiv::edgeBases ( size_t iE ) const

inline

Return edge bases for the edge of index iE.

◆ edgeBases() [6/7]

const EdgeBases& HArDCore3D::VEMCore::edgeBases ( size_t iE ) const

inline

Return edge bases for edge iE.

◆ edgeBases() [7/7]

const VEMCore::EdgeBases& HArDCore3D::VGrad::edgeBases ( size_t iE ) const

inline

Return edge bases for the edge of index iE.

◆ edgeOperators() [1/2]

const LocalOperators& HArDCore3D::VGrad::edgeOperators ( const Edge & E ) const

inline

Return edge operators for edge E.

◆ edgeOperators() [2/2]

const LocalOperators& HArDCore3D::VGrad::edgeOperators ( size_t iE ) const

inline

Return edge operators for the edge of index iE.

◆ faceBases() [1/7]

const VEMCore::FaceBases& HArDCore3D::VCurl::faceBases ( const Face & F ) const

inline

Return cell bases for face F.

◆ faceBases() [2/7]

const VEMCore::FaceBases& HArDCore3D::VDiv::faceBases ( const Face & F ) const

inline

Return cell bases for face F.

◆ faceBases() [3/7]

const VEMCore::FaceBases& HArDCore3D::VGrad::faceBases ( const Face & F ) const

inline

Return cell bases for face F.

◆ faceBases() [4/7]

const VEMCore::FaceBases& HArDCore3D::VCurl::faceBases ( size_t iF ) const

inline

Return face bases for the face of index iF.

◆ faceBases() [5/7]

const VEMCore::FaceBases& HArDCore3D::VDiv::faceBases ( size_t iF ) const

inline

Return face bases for the face of index iF.

◆ faceBases() [6/7]

const FaceBases& HArDCore3D::VEMCore::faceBases ( size_t iF ) const

inline

Return face bases for face iF.

◆ faceBases() [7/7]

const VEMCore::FaceBases& HArDCore3D::VGrad::faceBases ( size_t iF ) const

inline

Return face bases for the face of index iF.

◆ faceOperators() [1/6]

const LocalOperators& HArDCore3D::VCurl::faceOperators ( const Face & F ) const

inline

Return face operators for face F.

◆ faceOperators() [2/6]

const LocalOperators& HArDCore3D::VDiv::faceOperators ( const Face & F ) const

inline

Return face operators for face F.

◆ faceOperators() [3/6]

const LocalOperators& HArDCore3D::VGrad::faceOperators ( const Face & F ) const

inline

Return face operators for face F.

◆ faceOperators() [4/6]

const LocalOperators& HArDCore3D::VCurl::faceOperators ( size_t iF ) const

inline

Return face operators for the face of index iF.

◆ faceOperators() [5/6]

const LocalOperators& HArDCore3D::VDiv::faceOperators ( size_t iF ) const

inline

Return face operators for the face of index iF.

◆ faceOperators() [6/6]

const LocalOperators& HArDCore3D::VGrad::faceOperators ( size_t iF ) const

inline

Return face operators for the face of index iF.

◆ interpolate() [1/3]

Eigen::VectorXd VGrad::interpolate	(	const FunctionType &	q,
		const GradientType &	grad_q,
		const int	doe_cell = `-1`,
		const int	doe_face = `-1`,
		const int	doe_edge = `-1`
	)		const

Interpolator of a continuous function.

Parameters

q	The function to interpolate
grad_q	Its gradient
doe_cell	The optional degre of cell quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_face	The optional degre of face quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_edge	The optional degre of edge quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

◆ interpolate() [2/3]

Eigen::VectorXd VDiv::interpolate	(	const FunctionType &	v,
		const DivergenceType &	div_v,
		const int	doe_cell = `-1`,
		const int	doe_face = `-1`
	)		const

Interpolator of a continuous function.

Parameters

v	The function to interpolate
div_v	Its div
doe_cell	The optional degre of cell quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_face	The optional degre of face quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

◆ interpolate() [3/3]

Eigen::VectorXd VCurl::interpolate	(	const FunctionType &	v,
		const FunctionType &	curl_v,
		const int	doe_cell = `-1`,
		const int	doe_face = `-1`,
		const int	doe_edge = `-1`
	)		const

Interpolator of a continuous function.

Parameters

v	The function to interpolate
curl_v	Its curl
doe_cell	The optional degre of cell quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_face	The optional degre of face quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_edge	The optional degre of edge quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

◆ LocalOperators() [1/3]

HArDCore3D::VCurl::LocalOperators::LocalOperators	(	const Eigen::MatrixXd &	_proj_curl,
		const Eigen::MatrixXd &	_dofs_curl,
		const Eigen::MatrixXd &	_proj_function
	)

inline

Parameters

_proj_curl	Projecton in \(P^k\) of curl (or rot for faces) of the function
_dofs_curl	DOFs of curl/rot on Vdiv
_proj_function	Projection in \(P^{k+1}\) (for faces) or \(P^k\) (for elements) of the function

◆ LocalOperators() [2/3]

HArDCore3D::VDiv::LocalOperators::LocalOperators	(	const Eigen::MatrixXd &	_proj_divergence,
		const Eigen::MatrixXd &	_proj_function
	)

inline

Parameters

_proj_divergence	Projecton in \(P^k\) of div (or rot for faces) of the function
_proj_function	Projection in \(P^{k}\) (for faces) or \(P^k\) (for elements) of the function

◆ LocalOperators() [3/3]

HArDCore3D::VGrad::LocalOperators::LocalOperators	(	const Eigen::MatrixXd &	_proj_gradient,
		const Eigen::MatrixXd &	_dofs_gradient,
		const Eigen::MatrixXd &	_proj_function
	)

inline

Parameters

_proj_gradient	Projection of gradient on \(P^k\)
_dofs_gradient	DOFs of gradient in Vcurl
_proj_function	Projection of function (on \(P^{k+1}\) for edge, \(P^k\) for faces, \(P^{k-1}\) for cells)

◆ mesh() [1/4]

const Mesh& HArDCore3D::VCurl::mesh ( ) const

inline

Return the mesh.

◆ mesh() [2/4]

const Mesh& HArDCore3D::VDiv::mesh ( ) const

inline

Return the mesh.

◆ mesh() [3/4]

const Mesh& HArDCore3D::VEMCore::mesh ( ) const

inline

Return a const reference to the mesh.

◆ mesh() [4/4]

const Mesh& HArDCore3D::VGrad::mesh ( ) const

inline

Return the mesh.

◆ VCurl()

VCurl::VCurl	(	const VEMCore &	vem_core,
		bool	use_threads = `true`,
		std::ostream &	output = `std::cout`
	)

Constructor.

◆ VDiv()

VDiv::VDiv	(	const VEMCore &	vem_core,
		bool	use_threads = `true`,
		std::ostream &	output = `std::cout`
	)

Constructor.

◆ VEMCore()

VEMCore::VEMCore	(	const Mesh &	mesh,
		size_t	K,
		bool	use_threads = `true`,
		std::ostream &	output = `std::cout`
	)

Constructor.

◆ VGrad()

VGrad::VGrad	(	const VEMCore &	vem_core,
		bool	use_threads = `true`,
		std::ostream &	output = `std::cout`
	)

Constructor.

Variable Documentation

◆ dofs_curl

Eigen::MatrixXd HArDCore3D::VCurl::LocalOperators::dofs_curl

◆ dofs_gradient

Eigen::MatrixXd HArDCore3D::VGrad::LocalOperators::dofs_gradient

◆ GolyComplk

std::unique_ptr<GolyComplBasisCellType> HArDCore3D::VEMCore::CellBases::GolyComplk

◆ GolyComplkpo

std::unique_ptr<GolyComplBasisCellType> HArDCore3D::VEMCore::CellBases::GolyComplkpo

◆ Golykmo

std::unique_ptr<GolyBasisCellType> HArDCore3D::VEMCore::CellBases::Golykmo

◆ Polyk [1/3]

std::unique_ptr<PolyBasisCellType> HArDCore3D::VEMCore::CellBases::Polyk

◆ Polyk [2/3]

std::unique_ptr<PolyBasisFaceType> HArDCore3D::VEMCore::FaceBases::Polyk

◆ Polyk [3/3]

std::unique_ptr<PolyBasisEdgeType> HArDCore3D::VEMCore::EdgeBases::Polyk

◆ Polyk0 [1/2]

std::unique_ptr<ShiftedBasis<PolyBasisCellType> > HArDCore3D::VEMCore::CellBases::Polyk0

◆ Polyk0 [2/2]

std::unique_ptr<ShiftedBasis<PolyBasisFaceType> > HArDCore3D::VEMCore::FaceBases::Polyk0

◆ Polyk2

std::unique_ptr<Poly2BasisFaceType> HArDCore3D::VEMCore::FaceBases::Polyk2

◆ Polyk3

std::unique_ptr<Poly3BasisCellType> HArDCore3D::VEMCore::CellBases::Polyk3

◆ Polykmo [1/3]

std::unique_ptr<PolyBasisCellType> HArDCore3D::VEMCore::CellBases::Polykmo

◆ Polykmo [2/3]

std::unique_ptr<PolyBasisFaceType> HArDCore3D::VEMCore::FaceBases::Polykmo

◆ Polykmo [3/3]

std::unique_ptr<PolyBasisEdgeType> HArDCore3D::VEMCore::EdgeBases::Polykmo

◆ Polykp2

std::unique_ptr<PolyBasisFaceType> HArDCore3D::VEMCore::FaceBases::Polykp2

◆ Polykpo [1/3]

std::unique_ptr<PolyBasisCellType> HArDCore3D::VEMCore::CellBases::Polykpo

◆ Polykpo [2/3]

std::unique_ptr<PolyBasisFaceType> HArDCore3D::VEMCore::FaceBases::Polykpo

◆ Polykpo [3/3]

std::unique_ptr<PolyBasisEdgeType> HArDCore3D::VEMCore::EdgeBases::Polykpo

◆ Polykpo0

std::unique_ptr<ShiftedBasis<PolyBasisCellType> > HArDCore3D::VEMCore::CellBases::Polykpo0

◆ Polykpo2

std::unique_ptr<TangentFamily<PolyBasisFaceType> > HArDCore3D::VEMCore::FaceBases::Polykpo2

◆ proj_curl

Eigen::MatrixXd HArDCore3D::VCurl::LocalOperators::proj_curl

◆ proj_divergence

Eigen::MatrixXd HArDCore3D::VDiv::LocalOperators::proj_divergence

◆ proj_function [1/3]

Eigen::MatrixXd HArDCore3D::VCurl::LocalOperators::proj_function

◆ proj_function [2/3]

Eigen::MatrixXd HArDCore3D::VDiv::LocalOperators::proj_function

◆ proj_function [3/3]

Eigen::MatrixXd HArDCore3D::VGrad::LocalOperators::proj_function

◆ proj_gradient

Eigen::MatrixXd HArDCore3D::VGrad::LocalOperators::proj_gradient

◆ RolyComplk [1/2]

std::unique_ptr<RolyComplBasisCellType> HArDCore3D::VEMCore::CellBases::RolyComplk

◆ RolyComplk [2/2]

std::unique_ptr<RolyComplBasisFaceType> HArDCore3D::VEMCore::FaceBases::RolyComplk

◆ RolyComplkmo

std::unique_ptr<RolyComplBasisFaceType> HArDCore3D::VEMCore::FaceBases::RolyComplkmo

◆ RolyComplkp2

std::unique_ptr<RolyComplBasisCellType> HArDCore3D::VEMCore::CellBases::RolyComplkp2

◆ RolyComplkpo

std::unique_ptr<RolyComplBasisFaceType> HArDCore3D::VEMCore::FaceBases::RolyComplkpo

◆ Rolykmo [1/2]

std::unique_ptr<RolyBasisCellType> HArDCore3D::VEMCore::CellBases::Rolykmo

◆ Rolykmo [2/2]

std::unique_ptr<RolyBasisFaceType> HArDCore3D::VEMCore::FaceBases::Rolykmo

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ DivergenceType

◆ FunctionType [1/3]

◆ FunctionType [2/3]

◆ FunctionType [3/3]

◆ GeometricSupport [1/3]

◆ GeometricSupport [2/3]

◆ GeometricSupport [3/3]

◆ GolyBasisCellType

◆ GolyComplBasisCellType

◆ GradientType

◆ Poly2BasisFaceType

◆ Poly3BasisCellType

◆ PolyBasisCellType

◆ PolyBasisEdgeType

◆ PolyBasisFaceType

◆ RolyBasisCellType

◆ RolyBasisFaceType

◆ RolyComplBasisCellType

◆ RolyComplBasisFaceType

Function Documentation

◆ cellBases() [1/7]

◆ cellBases() [2/7]

◆ cellBases() [3/7]

◆ cellBases() [4/7]

◆ cellBases() [5/7]

◆ cellBases() [6/7]

◆ cellBases() [7/7]

◆ cellOperators() [1/6]

◆ cellOperators() [2/6]

◆ cellOperators() [3/6]

◆ cellOperators() [4/6]

◆ cellOperators() [5/6]

◆ cellOperators() [6/6]

◆ computeL2Product() [1/3]

◆ computeL2Product() [2/3]

◆ computeL2Product() [3/3]

◆ degree() [1/4]

◆ degree() [2/4]

◆ degree() [3/4]

◆ degree() [4/4]

◆ edgeBases() [1/7]

◆ edgeBases() [2/7]

◆ edgeBases() [3/7]

◆ edgeBases() [4/7]

◆ edgeBases() [5/7]

◆ edgeBases() [6/7]

◆ edgeBases() [7/7]

◆ edgeOperators() [1/2]

◆ edgeOperators() [2/2]

◆ faceBases() [1/7]

◆ faceBases() [2/7]

◆ faceBases() [3/7]

◆ faceBases() [4/7]

◆ faceBases() [5/7]

◆ faceBases() [6/7]

◆ faceBases() [7/7]

◆ faceOperators() [1/6]

◆ faceOperators() [2/6]

◆ faceOperators() [3/6]

◆ faceOperators() [4/6]

◆ faceOperators() [5/6]

◆ faceOperators() [6/6]

◆ interpolate() [1/3]

◆ interpolate() [2/3]

◆ interpolate() [3/3]

◆ LocalOperators() [1/3]

◆ LocalOperators() [2/3]

◆ LocalOperators() [3/3]

◆ mesh() [1/4]

◆ mesh() [2/4]

◆ mesh() [3/4]

◆ mesh() [4/4]

◆ VCurl()

◆ VDiv()