Classes defining the HHO method (scalar and vector-valued) More...

Classes
class	HArDCore3D::HHOSpace
	Class definition: polynomial bases and operators. More...

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

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

struct	HArDCore3D::HHOSpace::LocalOperators
	A structure to store local operators (gradient, potential, stabilisation) More...

class	HArDCore3D::VHHOSpace
	Class definition: polynomial bases and operators. More...

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

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

struct	HArDCore3D::VHHOSpace::LocalOperators
	A structure to store local operators (gradient, potential, stabilisation) More...

Typedefs
typedef Family< MonomialScalarBasisCell >	HArDCore3D::HHOSpace::PolyBasisCellType

typedef TensorizedVectorFamily< PolyBasisCellType, dimspace >	HArDCore3D::HHOSpace::PolydBasisCellType

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

typedef std::function< double(const VectorRd &)>	HArDCore3D::HHOSpace::FunctionType

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

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

typedef std::function< bool(const Cell &)>	HArDCore3D::CellSelection

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

typedef TensorizedVectorFamily< PolyBasisCellType, dimspace >	HArDCore3D::VHHOSpace::PolydBasisCellType

typedef MatrixFamily< PolyBasisCellType, dimspace >	HArDCore3D::VHHOSpace::PolydxdBasisCellType

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

typedef Family< TensorizedVectorFamily< PolyBasisFaceType, dimspace > >	HArDCore3D::VHHOSpace::PolydBasisFaceType

typedef std::function< VectorRd(const VectorRd &)>	HArDCore3D::VHHOSpace::FunctionType

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

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

Functions
	HArDCore3D::HHOSpace::LocalOperators::LocalOperators (const Eigen::MatrixXd &_gradient, const Eigen::MatrixXd &_potential, const Eigen::MatrixXd &_stabilisation)

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

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

const size_t &	HArDCore3D::HHOSpace::degree () const
	Return the polynomial degree (common face and elements) More...

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

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

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

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

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

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

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

std::vector< std::pair< double, double > >	HArDCore3D::HHOSpace::computeNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Computes the discrete L2 (cell unknowns only) and H1 norms of a list of vectors. More...

std::vector< double >	HArDCore3D::HHOSpace::computeVertexValues (const Eigen::VectorXd &u) const
	Computes the values of the potential reconstruction at the mesh vertices. More...

	HArDCore3D::VHHOSpace::LocalOperators::LocalOperators (const Eigen::MatrixXd &_gradient, const Eigen::MatrixXd &_potential, const Eigen::MatrixXd &_stabilisation, const Eigen::MatrixXd &_potential_div, const Eigen::MatrixXd &_stabilisation_div)

	HArDCore3D::VHHOSpace::VHHOSpace (const Mesh &mesh, size_t K, const CellSelection &BoundaryStab, bool use_threads=true, std::ostream &output=std::cout)
	Constructor (with function to select cells in which boundary faces are used in the stabilisation) More...

	HArDCore3D::VHHOSpace::VHHOSpace (const Mesh &mesh, size_t K, bool use_threads=true, std::ostream &output=std::cout)
	Overloaded constructor when the selection of boundary stabilisation is not entered (all boundary faces are then used) More...

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

const size_t &	HArDCore3D::VHHOSpace::degree () const
	Return the polynomial degree (common face and elements) More...

const CellSelection &	HArDCore3D::VHHOSpace::boundaryStab () const
	Return the function to select the cells with boundary stabilisation. More...

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

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

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

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

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

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

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

std::vector< std::pair< double, double > >	HArDCore3D::VHHOSpace::computeNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Computes the discrete L2 (cell unknowns only) and H1 norms of a list of vectors. More...

std::vector< VectorRd >	HArDCore3D::VHHOSpace::computeVertexValues (const Eigen::VectorXd &u) const
	Computes the values of the potential reconstruction at the mesh vertices. More...

Variables
std::unique_ptr< PolyBasisCellType >	HArDCore3D::HHOSpace::CellBases::Polykpo

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

std::unique_ptr< PolydBasisCellType >	HArDCore3D::HHOSpace::CellBases::Polykd

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

Eigen::MatrixXd	HArDCore3D::HHOSpace::LocalOperators::gradient

Eigen::MatrixXd	HArDCore3D::HHOSpace::LocalOperators::potential

Eigen::MatrixXd	HArDCore3D::HHOSpace::LocalOperators::stabilisation

static const CellSelection	HArDCore3D::allcells = [](const Cell &)->bool {return true;}

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

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

std::unique_ptr< PolydBasisCellType >	HArDCore3D::VHHOSpace::CellBases::Polykpod

std::unique_ptr< PolydBasisCellType >	HArDCore3D::VHHOSpace::CellBases::Polykd

std::unique_ptr< PolydxdBasisCellType >	HArDCore3D::VHHOSpace::CellBases::Polykdxd

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

std::unique_ptr< PolydBasisFaceType >	HArDCore3D::VHHOSpace::FaceBases::Polykd

Eigen::MatrixXd	HArDCore3D::VHHOSpace::LocalOperators::gradient

Eigen::MatrixXd	HArDCore3D::VHHOSpace::LocalOperators::potential

Eigen::MatrixXd	HArDCore3D::VHHOSpace::LocalOperators::stabilisation

Eigen::MatrixXd	HArDCore3D::VHHOSpace::LocalOperators::potential_div

Eigen::MatrixXd	HArDCore3D::VHHOSpace::LocalOperators::stabilisation_div

Detailed Description

Classes defining the HHO method (scalar and vector-valued)

Typedef Documentation

◆ CellSelection

typedef std::function<bool(const Cell &)> HArDCore3D::CellSelection

◆ FunctionType [1/2]

typedef std::function<double(const VectorRd &)> HArDCore3D::HHOSpace::FunctionType

◆ FunctionType [2/2]

typedef std::function<VectorRd(const VectorRd &)> HArDCore3D::VHHOSpace::FunctionType

◆ GeometricSupport [1/4]

typedef Cell HArDCore3D::HHOSpace::CellBases::GeometricSupport

Geometric support.

◆ GeometricSupport [2/4]

typedef Face HArDCore3D::HHOSpace::FaceBases::GeometricSupport

Geometric support.

◆ GeometricSupport [3/4]

typedef Cell HArDCore3D::VHHOSpace::CellBases::GeometricSupport

Geometric support.

◆ GeometricSupport [4/4]

typedef Face HArDCore3D::VHHOSpace::FaceBases::GeometricSupport

Geometric support.

◆ PolyBasisCellType [1/2]

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

◆ PolyBasisCellType [2/2]

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

◆ PolyBasisFaceType [1/2]

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

◆ PolyBasisFaceType [2/2]

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

◆ PolydBasisCellType [1/2]

typedef TensorizedVectorFamily<PolyBasisCellType, dimspace> HArDCore3D::HHOSpace::PolydBasisCellType

◆ PolydBasisCellType [2/2]

typedef TensorizedVectorFamily<PolyBasisCellType, dimspace> HArDCore3D::VHHOSpace::PolydBasisCellType

◆ PolydBasisFaceType

typedef Family<TensorizedVectorFamily<PolyBasisFaceType, dimspace> > HArDCore3D::VHHOSpace::PolydBasisFaceType

◆ PolydxdBasisCellType

typedef MatrixFamily<PolyBasisCellType, dimspace> HArDCore3D::VHHOSpace::PolydxdBasisCellType

Function Documentation

◆ boundaryStab()

const CellSelection& HArDCore3D::VHHOSpace::boundaryStab ( ) const

inline

Return the function to select the cells with boundary stabilisation.

◆ cellBases() [1/4]

const CellBases& HArDCore3D::HHOSpace::cellBases ( const Cell & T ) const

inline

Return cell bases for cell T.

◆ cellBases() [2/4]

const CellBases& HArDCore3D::VHHOSpace::cellBases ( const Cell & T ) const

inline

Return cell bases for cell T.

◆ cellBases() [3/4]

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

inline

Return cell bases for element iT.

◆ cellBases() [4/4]

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

inline

Return cell bases for element iT.

◆ computeNorms() [1/2]

std::vector< std::pair< double, double > > HHOSpace::computeNorms ( const std::vector< Eigen::VectorXd > & list_dofs ) const

Computes the discrete L2 (cell unknowns only) and H1 norms of a list of vectors.

Parameters

list_dofs The list of vectors representing the dofs

◆ computeNorms() [2/2]

std::vector< std::pair< double, double > > VHHOSpace::computeNorms ( const std::vector< Eigen::VectorXd > & list_dofs ) const

Computes the discrete L2 (cell unknowns only) and H1 norms of a list of vectors.

Parameters

list_dofs The list of vectors representing the dofs

◆ computeVertexValues() [1/2]

std::vector< double > HHOSpace::computeVertexValues ( const Eigen::VectorXd & u ) const

Computes the values of the potential reconstruction at the mesh vertices.

Parameters

u	DOFs in the discrete space

◆ computeVertexValues() [2/2]

std::vector< VectorRd > VHHOSpace::computeVertexValues ( const Eigen::VectorXd & u ) const

Computes the values of the potential reconstruction at the mesh vertices.

Parameters

u	DOFs in the discrete space

◆ degree() [1/2]

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

inline

Return the polynomial degree (common face and elements)

◆ degree() [2/2]

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

inline

Return the polynomial degree (common face and elements)

◆ faceBases() [1/4]

const FaceBases& HArDCore3D::HHOSpace::faceBases ( const Face & F ) const

inline

Return cell bases for face F.

◆ faceBases() [2/4]

const FaceBases& HArDCore3D::VHHOSpace::faceBases ( const Face & F ) const

inline

Return cell bases for face F.

◆ faceBases() [3/4]

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

inline

Return face bases for face iF.

◆ faceBases() [4/4]

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

inline

Return face bases for face iF.

◆ HHOSpace()

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

Constructor.

◆ interpolate() [1/2]

Eigen::VectorXd HHOSpace::interpolate	(	const FunctionType &	q,
		const int	doe_cell = `-1`,
		const int	doe_face = `-1`
	)		const

Interpolator of a continuous function.

Parameters

q	The function to interpolate
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() [2/2]

Eigen::VectorXd VHHOSpace::interpolate	(	const FunctionType &	q,
		const int	doe_cell = `-1`,
		const int	doe_face = `-1`
	)		const

Interpolator of a continuous function.

Parameters

q	The function to interpolate
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.

◆ LocalOperators() [1/2]

HArDCore3D::HHOSpace::LocalOperators::LocalOperators	(	const Eigen::MatrixXd &	_gradient,
		const Eigen::MatrixXd &	_potential,
		const Eigen::MatrixXd &	_stabilisation
	)

inline

Parameters

_gradient	Gradient operator
_potential	Potential operator
_stabilisation	Stabilisation bilinear form

◆ LocalOperators() [2/2]

HArDCore3D::VHHOSpace::LocalOperators::LocalOperators	(	const Eigen::MatrixXd &	_gradient,
		const Eigen::MatrixXd &	_potential,
		const Eigen::MatrixXd &	_stabilisation,
		const Eigen::MatrixXd &	_potential_div,
		const Eigen::MatrixXd &	_stabilisation_div
	)

inline

Parameters

_gradient	Gradient operator
_potential	HHO Potential operator
_stabilisation	H1 Stabilisation bilinear form associated to the HHO potential
_potential_div	Potential reconstructed from divergence
_stabilisation_div	L2 Stabilisation associated to _potential_div

◆ mesh() [1/2]

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

inline

Return a const reference to the mesh.

◆ mesh() [2/2]

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

inline

Return a const reference to the mesh.

◆ operators() [1/4]

const LocalOperators& HArDCore3D::HHOSpace::operators ( const Cell & T ) const

inline

Return cell operators for cell T.

◆ operators() [2/4]

const LocalOperators& HArDCore3D::VHHOSpace::operators ( const Cell & T ) const

inline

Return cell operators for cell T.

◆ operators() [3/4]

const LocalOperators& HArDCore3D::HHOSpace::operators ( size_t iT ) const

inline

Return operators for the cell of index iT.

◆ operators() [4/4]

const LocalOperators& HArDCore3D::VHHOSpace::operators ( size_t iT ) const

inline

Return operators for the cell of index iT.

◆ VHHOSpace() [1/2]

HArDCore3D::VHHOSpace::VHHOSpace	(	const Mesh &	mesh,
		size_t	K,
		bool	use_threads = `true`,
		std::ostream &	output = `std::cout`
	)

inline

Overloaded constructor when the selection of boundary stabilisation is not entered (all boundary faces are then used)

◆ VHHOSpace() [2/2]

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

Constructor (with function to select cells in which boundary faces are used in the stabilisation)

Variable Documentation

◆ allcells

const CellSelection HArDCore3D::allcells = [](const Cell &)->bool {return true;}

static

◆ gradient [1/2]

Eigen::MatrixXd HArDCore3D::HHOSpace::LocalOperators::gradient

◆ gradient [2/2]

Eigen::MatrixXd HArDCore3D::VHHOSpace::LocalOperators::gradient

◆ Polyk [1/4]

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

◆ Polyk [2/4]

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

◆ Polyk [3/4]

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

◆ Polyk [4/4]

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

◆ Polykd [1/3]

std::unique_ptr<PolydBasisCellType> HArDCore3D::HHOSpace::CellBases::Polykd

◆ Polykd [2/3]

std::unique_ptr<PolydBasisCellType> HArDCore3D::VHHOSpace::CellBases::Polykd

◆ Polykd [3/3]

std::unique_ptr<PolydBasisFaceType> HArDCore3D::VHHOSpace::FaceBases::Polykd

◆ Polykdxd

std::unique_ptr<PolydxdBasisCellType> HArDCore3D::VHHOSpace::CellBases::Polykdxd

◆ Polykpo [1/2]

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

◆ Polykpo [2/2]

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

◆ Polykpod

std::unique_ptr<PolydBasisCellType> HArDCore3D::VHHOSpace::CellBases::Polykpod

◆ potential [1/2]

Eigen::MatrixXd HArDCore3D::HHOSpace::LocalOperators::potential

◆ potential [2/2]

Eigen::MatrixXd HArDCore3D::VHHOSpace::LocalOperators::potential

◆ potential_div

Eigen::MatrixXd HArDCore3D::VHHOSpace::LocalOperators::potential_div

◆ stabilisation [1/2]

Eigen::MatrixXd HArDCore3D::HHOSpace::LocalOperators::stabilisation

◆ stabilisation [2/2]

Eigen::MatrixXd HArDCore3D::VHHOSpace::LocalOperators::stabilisation

◆ stabilisation_div

Eigen::MatrixXd HArDCore3D::VHHOSpace::LocalOperators::stabilisation_div

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ CellSelection

◆ FunctionType [1/2]

◆ FunctionType [2/2]

◆ GeometricSupport [1/4]

◆ GeometricSupport [2/4]

◆ GeometricSupport [3/4]

◆ GeometricSupport [4/4]

◆ PolyBasisCellType [1/2]

◆ PolyBasisCellType [2/2]

◆ PolyBasisFaceType [1/2]

◆ PolyBasisFaceType [2/2]

◆ PolydBasisCellType [1/2]

◆ PolydBasisCellType [2/2]

◆ PolydBasisFaceType

◆ PolydxdBasisCellType

Function Documentation

◆ boundaryStab()

◆ cellBases() [1/4]

◆ cellBases() [2/4]

◆ cellBases() [3/4]

◆ cellBases() [4/4]

◆ computeNorms() [1/2]

◆ computeNorms() [2/2]

◆ computeVertexValues() [1/2]

◆ computeVertexValues() [2/2]

◆ degree() [1/2]

◆ degree() [2/2]

◆ faceBases() [1/4]

◆ faceBases() [2/4]

◆ faceBases() [3/4]

◆ faceBases() [4/4]

◆ HHOSpace()

◆ interpolate() [1/2]

◆ interpolate() [2/2]

◆ LocalOperators() [1/2]

◆ LocalOperators() [2/2]

◆ mesh() [1/2]

◆ mesh() [2/2]

◆ operators() [1/4]

◆ operators() [2/4]

◆ operators() [3/4]

◆ operators() [4/4]

◆ VHHOSpace() [1/2]

◆ VHHOSpace() [2/2]

Variable Documentation

◆ allcells

◆ gradient [1/2]

◆ gradient [2/2]

◆ Polyk [1/4]

◆ Polyk [2/4]

◆ Polyk [3/4]

◆ Polyk [4/4]

◆ Polykd [1/3]

◆ Polykd [2/3]

◆ Polykd [3/3]

◆ Polykdxd

◆ Polykpo [1/2]

◆ Polykpo [2/2]

◆ Polykpod

◆ potential [1/2]

◆ potential [2/2]

◆ potential_div

◆ stabilisation [1/2]

◆ stabilisation [2/2]

◆ stabilisation_div