Classes providing quadratures on edges and in cells. More...

Namespaces
namespace	HArDCore2D

Classes
struct	HArDCore2D::VecHash
	Hash function for VectorZd type. More...

class	HArDCore2D::QuadRuleEdge

class	HArDCore2D::LegendreGauss

struct	HArDCore2D::QuadratureNode
	Description of one node and one weight from a quadrature rule. More...

Typedefs
typedef std::unordered_map< VectorZd, double, VecHash >	HArDCore2D::MonomialCellIntegralsType
	Type for list of integrals of monomials.

typedef std::vector< double >	HArDCore2D::MonomialEdgeIntegralsType
	Type for list of edge integrals of monomials.

typedef std::vector< QuadratureNode >	HArDCore2D::QuadratureRule

Functions
size_t	HArDCore2D::VecHash::operator() (const VectorZd &p) const

MonomialCellIntegralsType	HArDCore2D::IntegrateCellMonomials (const Cell &T, const size_t maxdeg)
	Compute all integrals on a cell of monomials up to a total degree, using vertex values.

MonomialCellIntegralsType	HArDCore2D::CheckIntegralsDegree (const Cell &T, const size_t degree, const MonomialCellIntegralsType &mono_int_map={})
	Checks if the degree of an existing list of monomial integrals is sufficient, other re-compute and return a proper list.

template<typename BasisType >
Eigen::MatrixXd	HArDCore2D::transformGM (const Family< BasisType > &family_basis, const char RC, const Eigen::MatrixXd &anc_GM)
	Transforms a Gram Matrix from an ancestor to a family basis.

template<typename BasisType >
Eigen::MatrixXd	HArDCore2D::transformGM (const RestrictedBasis< BasisType > &restr_basis, const char RC, const Eigen::MatrixXd &anc_GM)
	Transforms a Gram Matrix from an ancestor to a restricted basis.

template<typename BasisType >
Eigen::MatrixXd	HArDCore2D::transformGM (const ShiftedBasis< BasisType > &shifted_basis, const char RC, const Eigen::MatrixXd &anc_GM)
	Transforms a Gram Matrix from an ancestor to a shifted basis.

Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const MonomialScalarBasisCell &basis1, const MonomialScalarBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases.

template<typename BasisType >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const BasisType &basis, MonomialCellIntegralsType mono_int_map={})
	This overload to simplify the call to GramMatrix in case the two bases are the same.

template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any pair of tensorized scalar bases.

Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const RolyComplBasisCell &basis1, const RolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of RolyCompl bases.

template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const RolyComplBasisCell &rolycompl_basis, const TensorizedVectorFamily< BasisType1, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a RolyCompl basis and a tensorized scalar basis.

template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &tens_family, const RolyComplBasisCell &rolycompl_basis, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a tensorized scalar basis and a RolyCompl basis.

Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const GolyComplBasisCell &basis1, const GolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of a pair of GolyCompl bases.

Eigen::MatrixXd	HArDCore2D::GMRolyComplScalar (const Cell &T, const RolyComplBasisCell &rolycompl_basis, const MonomialScalarBasisCell &mono_basis, const size_t m, MonomialCellIntegralsType mono_int_map)
	Computes the Gram Matrix of the mth component of a RolyCompl Basis and a monomial basis.

template<typename BasisType >
Eigen::MatrixXd	HArDCore2D::GMRolyComplScalar (const Cell &T, const RolyComplBasisCell &basis1, const BasisType &basis2, const size_t m, MonomialCellIntegralsType mono_int_map)
	Generic template to compute the Gram Matrix of the mth component of a RolyCompl Basis and any basis.

template<typename BasisType >
constexpr bool	HArDCore2D::useAncestor ()
	Determines if the ancestor of a basis will be used to compute a Gram matrix for this basis.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of bases.

Eigen::MatrixXd	HArDCore2D::GMScalarDerivative (const Cell &T, const MonomialScalarBasisCell &basis1, const MonomialScalarBasisCell &basis2, const size_t m, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases, taking a partial derivative of the first (w.r.t. the homogeneous coordinates, without scaling)

Eigen::MatrixXd	HArDCore2D::GMScalarDerivative (const Cell &T, const MonomialScalarBasisCell &basis1, const MonomialScalarBasisCell &basis2, const size_t m, const size_t l, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases, taking partial derivatives of each of them (w.r.t. the homogeneous coordinates, without scaling)

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GMScalarDerivative (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, const size_t m, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of scalar bases, taking a partial derivative of the first (w.r.t. the homogeneous coordinates, without scaling)

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GMScalarDerivative (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, const size_t m, const size_t l, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of scalar bases, taking partial derivatives of each of them (w.r.t. the homogeneous coordinates, without scaling)

template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const GradientBasis< BasisType1 > &grad_basis, const TensorizedVectorFamily< BasisType2, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a gradient basis and a tensorized scalar basis.

template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &tens_family, const GradientBasis< BasisType2 > &grad_basis, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a tensorized scalar basis and a gradient basis.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const GradientBasis< BasisType1 > &grad_basis1, const GradientBasis< BasisType2 > &grad_basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a gradient basis and another gradient basis.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const CurlBasis< BasisType1 > &basis1, const CurlBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a pair of Curl bases.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const CurlBasis< BasisType1 > &curl_basis, const TensorizedVectorFamily< BasisType2, 2 > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a curl basis and a tensorized scalar basis.

template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &tens_family, const CurlBasis< BasisType2 > &curl_basis, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a tensorized scalar basis and a gradient basis.

template<typename BasisType1 , typename BasisType2 >
boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type	HArDCore2D::GramMatrix (const Cell &T, const DivergenceBasis< BasisType1 > &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a Divergence basis and any other basis.

template<typename BasisType1 , typename Basis2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const BasisType1 &basis1, const DivergenceBasis< Basis2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any basis and a Divergence basis.

template<typename BasisType1 >
Eigen::MatrixXd	HArDCore2D::GramMatrixDiv (const Cell &T, const TensorizedVectorFamily< BasisType1, 2 > &basis1, const MonomialScalarBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a Divergence<Tensorized> basis and a monomial scalar basis.

Eigen::MatrixXd	HArDCore2D::GramMatrixDiv (const Cell &T, const RolyComplBasisCell &basis1, const MonomialScalarBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a Divergence<RolyCompl> basis and a monomial scalar basis.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrixDiv (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of any basis and any other basis.

template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const MatrixFamily< BasisType1, N > &basis1, const MatrixFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of any pair of MatrixFamily bases.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const DivergenceBasis< MatrixFamily< BasisType1, dimspace > > &basis1, const TensorizedVectorFamily< BasisType2, dimspace > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of the divergence of a MatrixFamily and a tensorized basis.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const GradientBasis< TensorizedVectorFamily< BasisType1, dimspace > > &basis1, const MatrixFamily< BasisType2, dimspace > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of the gradient basis of a tensorized family and a matrix family (only valid if N=dimspace in Tensorized and MatrixFamily).

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const MatrixFamily< BasisType1, dimspace > &basis1, const GradientBasis< TensorizedVectorFamily< BasisType2, dimspace > > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of a Matrix family and the gradient of a tensorized family.

template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Cell &T, const GradientBasis< TensorizedVectorFamily< BasisType1, N > > &basis1, const GradientBasis< TensorizedVectorFamily< BasisType2, N > > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of two gradient bases of tensorized families.

MonomialEdgeIntegralsType	HArDCore2D::IntegrateEdgeMonomials (const Edge &E, const size_t maxdeg)
	Compute all integrals of edge monomials up to a total degree.

MonomialEdgeIntegralsType	HArDCore2D::CheckIntegralsDegree (const Edge &E, const size_t degree, const MonomialEdgeIntegralsType &mono_int_map={})
	Checks if the degree of an existing list of monomial integrals is sufficient, other re-compute and return a proper list.

Eigen::MatrixXd	HArDCore2D::GramMatrix (const Edge &E, const MonomialScalarBasisEdge &basis1, const MonomialScalarBasisEdge &basis2, MonomialEdgeIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Edge &E, const BasisType1 &basis1, const BasisType2 &basis2, MonomialEdgeIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of bases.

template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Edge &E, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialEdgeIntegralsType mono_int_map={})
	GramMatrix of two tensorized families on the edge.

template<typename BasisType >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Edge &E, const BasisType &basis, MonomialEdgeIntegralsType mono_int_map={})
	This overload to simplify the call to GramMatrix in case the two bases are the same.

Eigen::MatrixXd	HArDCore2D::GMDer (const Edge &E, const MonomialScalarBasisEdge &basis1, const MonomialScalarBasisEdge &basis2, MonomialEdgeIntegralsType mono_int_map={})
	Computes the Gram Matrix of the derivative of a monomial basis with another monomial basis.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GMDer (const Edge &E, const BasisType1 &basis1, const BasisType2 &basis2, MonomialEdgeIntegralsType mono_int_map={})
	Generic template for GMDer with derived bases.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Edge &E, const GradientBasis< BasisType1 > &basis1, const BasisType2 &basis2, MonomialEdgeIntegralsType mono_int_map={})
	Computes the Gram Matrix of a gradient basis (considering the tangential gradient as a scalar) and a scalar basis.

template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore2D::GramMatrix (const Edge &E, const BasisType1 &basis1, const GradientBasis< BasisType2 > &basis2, MonomialEdgeIntegralsType mono_int_map={})
	Computes the Gram Matrix of a scalar basis and a gradient basis (considering the tangential gradient as a scalar)

	HArDCore2D::QuadRuleEdge::QuadRuleEdge (size_t doe, bool warn)

	HArDCore2D::QuadRuleEdge::~QuadRuleEdge ()

size_t	HArDCore2D::QuadRuleEdge::nq ()

double	HArDCore2D::QuadRuleEdge::xq (size_t i)

double	HArDCore2D::QuadRuleEdge::yq (size_t i)

double	HArDCore2D::QuadRuleEdge::wq (size_t i)

void	HArDCore2D::QuadRuleEdge::setup (double xV[], double yV[])

	HArDCore2D::LegendreGauss::LegendreGauss (size_t doe)

	HArDCore2D::LegendreGauss::~LegendreGauss ()

void	HArDCore2D::LegendreGauss::sub_rule_01 ()

void	HArDCore2D::LegendreGauss::sub_rule_02 ()

void	HArDCore2D::LegendreGauss::sub_rule_03 ()

void	HArDCore2D::LegendreGauss::sub_rule_04 ()

void	HArDCore2D::LegendreGauss::sub_rule_05 ()

void	HArDCore2D::LegendreGauss::sub_rule_06 ()

void	HArDCore2D::LegendreGauss::sub_rule_07 ()

void	HArDCore2D::LegendreGauss::sub_rule_08 ()

void	HArDCore2D::LegendreGauss::sub_rule_09 ()

void	HArDCore2D::LegendreGauss::sub_rule_10 ()

void	HArDCore2D::LegendreGauss::sub_rule_11 ()

size_t	HArDCore2D::LegendreGauss::npts ()

double	HArDCore2D::LegendreGauss::wq (size_t i)

double	HArDCore2D::LegendreGauss::tq (size_t i)

	HArDCore2D::QuadratureNode::QuadratureNode (double x, double y, double w)

Eigen::Vector2d	HArDCore2D::QuadratureNode::vector () const
	Returns the quadrature point as an Eigen vector.

QuadratureRule	HArDCore2D::generate_quadrature_rule (const Cell &T, const int doe, const bool force_split=false)
	Generate quadrature rule on mesh element.

QuadratureRule	HArDCore2D::generate_quadrature_rule (const Edge &E, const int doe)
	Generate quadrature rule on mesh face.

Variables
double	HArDCore2D::QuadratureNode::x

double	HArDCore2D::QuadratureNode::y

double	HArDCore2D::QuadratureNode::w

Detailed Description

Classes providing quadratures on edges and in cells.

Typedef Documentation

◆ MonomialCellIntegralsType

typedef std::unordered_map<VectorZd, double, VecHash> HArDCore2D::MonomialCellIntegralsType

Type for list of integrals of monomials.

◆ MonomialEdgeIntegralsType

typedef std::vector<double> HArDCore2D::MonomialEdgeIntegralsType

Type for list of edge integrals of monomials.

◆ QuadratureRule

typedef std::vector<QuadratureNode> HArDCore2D::QuadratureRule

Function Documentation

◆ CheckIntegralsDegree() [1/2]

MonomialCellIntegralsType HArDCore2D::CheckIntegralsDegree	(	const Cell &	T,
		const size_t	degree,
		const MonomialCellIntegralsType &	mono_int_map = `{}`
	)

Checks if the degree of an existing list of monomial integrals is sufficient, other re-compute and return a proper list.

Parameters

T	Cell
degree	Expected degree
mono_int_map	Existing list, optional

◆ CheckIntegralsDegree() [2/2]

MonomialEdgeIntegralsType HArDCore2D::CheckIntegralsDegree	(	const Edge &	E,
		const size_t	degree,
		const MonomialEdgeIntegralsType &	mono_int_map = `{}`
	)

Checks if the degree of an existing list of monomial integrals is sufficient, other re-compute and return a proper list.

Parameters

E	Edge
degree	Expected degree
mono_int_map	Existing list, optional

◆ generate_quadrature_rule() [1/2]

QuadratureRule HArDCore2D::generate_quadrature_rule	(	const Cell &	T,
		const int	doe,
		const bool	force_split = `false`
	)

Generate quadrature rule on mesh element.

Returns: list of quadrature nodes and weights

Parameters

T	Reference to the mesh cell
doe	Degree of exactness
force_split	TRUE if we want the quadrature nodes to be computed by forcing the splitting of the cell into triangles based on its center of mass and edges (otherwise, for simple cells, quadrature nodes are computed by splitting in fewer triangles)

◆ generate_quadrature_rule() [2/2]

QuadratureRule HArDCore2D::generate_quadrature_rule	(	const Edge &	E,
		const int	doe
	)

Generate quadrature rule on mesh face.

Returns: list of quadrature nodes and weights

Parameters

E	Reference to the mesh face
doe	Degree of exactness

◆ GMDer() [1/2]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GMDer	(	const Edge &	E,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

Generic template for GMDer with derived bases.

Parameters

E	Edge to which the basis corresponds
basis1	First basis (rows of the Gram matrix), to be differentiated
basis2	Second basis (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GMDer() [2/2]

Eigen::MatrixXd HArDCore2D::GMDer	(	const Edge &	E,
		const MonomialScalarBasisEdge &	basis1,
		const MonomialScalarBasisEdge &	basis2,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of the derivative of a monomial basis with another monomial basis.

Parameters

E	Edge to which the basis corresponds
basis1	First basis, to be differentiated
basis2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GMRolyComplScalar() [1/2]

template<typename BasisType >

Eigen::MatrixXd HArDCore2D::GMRolyComplScalar	(	const Cell &	T,
		const RolyComplBasisCell &	basis1,
		const BasisType &	basis2,
		const size_t	m,
		MonomialCellIntegralsType	mono_int_map
	)

Generic template to compute the Gram Matrix of the mth component of a RolyCompl Basis and any basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis (columns of the Gram matrix)
m	Differentiate basis1 with respect to the mth variable
mono_int_map	list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GMRolyComplScalar() [2/2]

Eigen::MatrixXd HArDCore2D::GMRolyComplScalar	(	const Cell &	T,
		const RolyComplBasisCell &	rolycompl_basis,
		const MonomialScalarBasisCell &	mono_basis,
		const size_t	m,
		MonomialCellIntegralsType	mono_int_map
	)

Computes the Gram Matrix of the mth component of a RolyCompl Basis and a monomial basis.

Parameters

T	Cell to which the basis corresponds
rolycompl_basis	First basis
mono_basis	Second basis
m	Add one to the power of the mth variable
mono_int_map	list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GMScalarDerivative() [1/4]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GMScalarDerivative	(	const Cell &	T,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		const size_t	m,
		const size_t	l,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Generic template to compute the Gram Matrix of any pair of scalar bases, taking partial derivatives of each of them (w.r.t. the homogeneous coordinates, without scaling)

Parameters

T	Cell to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
m	Differentiate basis1 with respect to the mth variable
l	Differentiate basis2 with respect to the lth variable
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GMScalarDerivative() [2/4]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GMScalarDerivative	(	const Cell &	T,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		const size_t	m,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Generic template to compute the Gram Matrix of any pair of scalar bases, taking a partial derivative of the first (w.r.t. the homogeneous coordinates, without scaling)

Parameters

T	Cell to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
m	Differentiate basis1 with respect to the mth variable
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GMScalarDerivative() [3/4]

Eigen::MatrixXd HArDCore2D::GMScalarDerivative	(	const Cell &	T,
		const MonomialScalarBasisCell &	basis1,
		const MonomialScalarBasisCell &	basis2,
		const size_t	m,
		const size_t	l,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a pair of local scalar monomial bases, taking partial derivatives of each of them (w.r.t. the homogeneous coordinates, without scaling)

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis
m	Differentiate basis1 with respect to the mth variable
l	Differentiate basis2 with respect to the lth variable
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GMScalarDerivative() [4/4]

Eigen::MatrixXd HArDCore2D::GMScalarDerivative	(	const Cell &	T,
		const MonomialScalarBasisCell &	basis1,
		const MonomialScalarBasisCell &	basis2,
		const size_t	m,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a pair of local scalar monomial bases, taking a partial derivative of the first (w.r.t. the homogeneous coordinates, without scaling)

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis
m	Differentiate basis1 with respect to the mth variable
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [1/27]

template<typename BasisType >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const BasisType &	basis,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

This overload to simplify the call to GramMatrix in case the two bases are the same.

◆ GramMatrix() [2/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Generic template to compute the Gram Matrix of any pair of bases.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [3/27]

template<typename BasisType1 , typename Basis2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const BasisType1 &	basis1,
		const DivergenceBasis< Basis2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of any basis and a Divergence basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (tensorized basis)
basis2	Second basis (divergence basis)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [4/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const CurlBasis< BasisType1 > &	basis1,
		const CurlBasis< BasisType2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Generic template to compute the Gram Matrix of a pair of Curl bases.

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [5/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const CurlBasis< BasisType1 > &	curl_basis,
		const TensorizedVectorFamily< BasisType2, 2 > &	tens_family,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a curl basis and a tensorized scalar basis.

Parameters

T	Cell to which the basis corresponds
curl_basis	First basis (rows of the Gram matrix) - curl basis
tens_family	Second basis (columns of the Gram matrix) - tensorized basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

◆ GramMatrix() [6/27]

template<typename BasisType1 , typename BasisType2 >

boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type HArDCore2D::GramMatrix	(	const Cell &	T,
		const DivergenceBasis< BasisType1 > &	basis1,
		const BasisType2 &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Generic template to compute the Gram Matrix of a Divergence basis and any other basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [7/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const DivergenceBasis< MatrixFamily< BasisType1, dimspace > > &	basis1,
		const TensorizedVectorFamily< BasisType2, dimspace > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Gram Matrix of the divergence of a MatrixFamily and a tensorized basis.

Parameters

T	Cell to which the basis corresponds
basis1	Divergence of MatrixFamily (rows of the Gram matrix)
basis2	Tensorized family (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [8/27]

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const GolyComplBasisCell &	basis1,
		const GolyComplBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Gram Matrix of a pair of GolyCompl bases.

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [9/27]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const GradientBasis< BasisType1 > &	grad_basis,
		const TensorizedVectorFamily< BasisType2, N > &	tens_family,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a gradient basis and a tensorized scalar basis.

Parameters

T	Cell to which the basis corresponds
grad_basis	First basis (rows of the Gram matrix) - gradient basis
tens_family	Second basis (columns of the Gram matrix) - tensorized basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

◆ GramMatrix() [10/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const GradientBasis< BasisType1 > &	grad_basis1,
		const GradientBasis< BasisType2 > &	grad_basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a gradient basis and another gradient basis.

Parameters

T	Cell to which the basis corresponds
grad_basis1	First basis (rows of the Gram matrix) - gradient basis
grad_basis2	Second basis (columns of the Gram matrix) - gradient basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

◆ GramMatrix() [11/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const GradientBasis< TensorizedVectorFamily< BasisType1, dimspace > > &	basis1,
		const MatrixFamily< BasisType2, dimspace > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Gram Matrix of the gradient basis of a tensorized family and a matrix family (only valid if N=dimspace in Tensorized and MatrixFamily).

Parameters

T	Cell to which the basis corresponds
basis1	Gradient of tensorized (rows of the Gram matrix)
basis2	Matrix family (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [12/27]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const GradientBasis< TensorizedVectorFamily< BasisType1, N > > &	basis1,
		const GradientBasis< TensorizedVectorFamily< BasisType2, N > > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Gram Matrix of two gradient bases of tensorized families.

Parameters

T	Cell to which the basis corresponds
basis1	First family
basis2	Second family (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [13/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const MatrixFamily< BasisType1, dimspace > &	basis1,
		const GradientBasis< TensorizedVectorFamily< BasisType2, dimspace > > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Gram Matrix of a Matrix family and the gradient of a tensorized family.

Parameters

T	Cell to which the basis corresponds
basis1	Matrix family (rows of the Gram matrix)
basis2	Gradient of tensorized (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [14/27]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const MatrixFamily< BasisType1, N > &	basis1,
		const MatrixFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Gram Matrix of any pair of MatrixFamily bases.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [15/27]

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const MonomialScalarBasisCell &	basis1,
		const MonomialScalarBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a pair of local scalar monomial bases.

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [16/27]

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const RolyComplBasisCell &	basis1,
		const RolyComplBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a pair of RolyCompl bases.

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [17/27]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const RolyComplBasisCell &	rolycompl_basis,
		const TensorizedVectorFamily< BasisType1, N > &	tens_family,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a RolyCompl basis and a tensorized scalar basis.

Parameters

T	Cell to which the basis corresponds
rolycompl_basis	First basis (RolyCompl basis)
tens_family	Second basis (tensorized basis)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [18/27]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of any pair of tensorized scalar bases.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [19/27]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	tens_family,
		const CurlBasis< BasisType2 > &	curl_basis,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a tensorized scalar basis and a gradient basis.

Parameters

T	Cell to which the basis corresponds
tens_family	First basis (rows of the Gram matrix) - gradient basis
curl_basis	Second basis (columns of the Gram matrix) - tensorized basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

◆ GramMatrix() [20/27]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	tens_family,
		const GradientBasis< BasisType2 > &	grad_basis,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a tensorized scalar basis and a gradient basis.

Parameters

T	Cell to which the basis corresponds
tens_family	First basis (rows of the Gram matrix) - gradient basis
grad_basis	Second basis (columns of the Gram matrix) - tensorized basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

◆ GramMatrix() [21/27]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	tens_family,
		const RolyComplBasisCell &	rolycompl_basis,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a tensorized scalar basis and a RolyCompl basis.

Parameters

T	Cell to which the basis corresponds
tens_family	First basis (tensorized basis)
rolycompl_basis	Second basis (RolyCompl basis)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [22/27]

template<typename BasisType >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Edge &	E,
		const BasisType &	basis,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

This overload to simplify the call to GramMatrix in case the two bases are the same.

◆ GramMatrix() [23/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Edge &	E,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

Generic template to compute the Gram Matrix of any pair of bases.

Parameters

E	Edge to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [24/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Edge &	E,
		const BasisType1 &	basis1,
		const GradientBasis< BasisType2 > &	basis2,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a scalar basis and a gradient basis (considering the tangential gradient as a scalar)

Parameters

E	Edge to which the basis corresponds
basis1	Scalar basis
basis2	Gradient basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [25/27]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Edge &	E,
		const GradientBasis< BasisType1 > &	basis1,
		const BasisType2 &	basis2,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a gradient basis (considering the tangential gradient as a scalar) and a scalar basis.

Parameters

E	Edge to which the basis corresponds
basis1	Gradient basis
basis2	Scalar basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [26/27]

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Edge &	E,
		const MonomialScalarBasisEdge &	basis1,
		const MonomialScalarBasisEdge &	basis2,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a pair of local scalar monomial bases.

Parameters

E	Edge to which the basis corresponds
basis1	First basis
basis2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrix() [27/27]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore2D::GramMatrix	(	const Edge &	E,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialEdgeIntegralsType	mono_int_map = `{}`
	)

GramMatrix of two tensorized families on the edge.

Parameters

E	Edge to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (columns of the Gram matrix)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrixDiv() [1/3]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore2D::GramMatrixDiv	(	const Cell &	T,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of the divergence of any basis and any other basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (vector basis)
basis2	Second basis (scalar basis)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

◆ GramMatrixDiv() [2/3]

Eigen::MatrixXd HArDCore2D::GramMatrixDiv	(	const Cell &	T,
		const RolyComplBasisCell &	basis1,
		const MonomialScalarBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Computes the Gram Matrix of a Divergence<RolyCompl> basis and a monomial scalar basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (RolyCompl basis)
basis2	Second basis (tensorized basis)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ GramMatrixDiv() [3/3]

template<typename BasisType1 >

Eigen::MatrixXd HArDCore2D::GramMatrixDiv	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, 2 > &	basis1,
		const MonomialScalarBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = `{}`
	)

Template to compute the Gram Matrix of a Divergence<Tensorized> basis and a monomial scalar basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (divergence basis)
basis2	Second basis (monomial scalar basis)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

◆ IntegrateCellMonomials()

MonomialCellIntegralsType HArDCore2D::IntegrateCellMonomials	(	const Cell &	T,
		const size_t	maxdeg
	)

Compute all integrals on a cell of monomials up to a total degree, using vertex values.

Parameters

T	Cell
maxdeg	Maximal total degree

◆ IntegrateEdgeMonomials()

MonomialEdgeIntegralsType HArDCore2D::IntegrateEdgeMonomials	(	const Edge &	E,
		const size_t	maxdeg
	)

Compute all integrals of edge monomials up to a total degree.

Parameters

E	Edge
maxdeg	Maximal total degree

◆ LegendreGauss()

LegendreGauss::LegendreGauss ( size_t doe )

◆ npts()

size_t LegendreGauss::npts ( )

◆ nq()

size_t QuadRuleEdge::nq ( )

◆ operator()()

size_t HArDCore2D::VecHash::operator() ( const VectorZd & p ) const

inline

◆ QuadratureNode()

HArDCore2D::QuadratureNode::QuadratureNode	(	double	x,
		double	y,
		double	w
	)

inline

◆ QuadRuleEdge()

QuadRuleEdge::QuadRuleEdge	(	size_t	doe,
		bool	warn
	)

◆ setup()

void QuadRuleEdge::setup	(	double	xV[],
		double	yV[]
	)

◆ sub_rule_01()

void LegendreGauss::sub_rule_01 ( )

◆ sub_rule_02()

void LegendreGauss::sub_rule_02 ( )

◆ sub_rule_03()

void LegendreGauss::sub_rule_03 ( )

◆ sub_rule_04()

void LegendreGauss::sub_rule_04 ( )

◆ sub_rule_05()

void LegendreGauss::sub_rule_05 ( )

◆ sub_rule_06()

void LegendreGauss::sub_rule_06 ( )

◆ sub_rule_07()

void LegendreGauss::sub_rule_07 ( )

◆ sub_rule_08()

void LegendreGauss::sub_rule_08 ( )

◆ sub_rule_09()

void LegendreGauss::sub_rule_09 ( )

◆ sub_rule_10()

void LegendreGauss::sub_rule_10 ( )

◆ sub_rule_11()

void LegendreGauss::sub_rule_11 ( )

◆ tq()

double LegendreGauss::tq ( size_t i )

◆ transformGM() [1/3]

template<typename BasisType >

Eigen::MatrixXd HArDCore2D::transformGM	(	const Family< BasisType > &	family_basis,
		const char	RC,
		const Eigen::MatrixXd &	anc_GM
	)

inline

Transforms a Gram Matrix from an ancestor to a family basis.

Parameters

family_basis	Family
RC	R if transformation applied on rows (left), C if applied on columns (right)
anc_GM	Gram matrix of the ancestor basis

◆ transformGM() [2/3]

template<typename BasisType >

Eigen::MatrixXd HArDCore2D::transformGM	(	const RestrictedBasis< BasisType > &	restr_basis,
		const char	RC,
		const Eigen::MatrixXd &	anc_GM
	)

inline

Transforms a Gram Matrix from an ancestor to a restricted basis.

Parameters

restr_basis	Restricted basis
RC	R if transformation applied on rows (left), C if applied on columns (right)
anc_GM	Gram matrix of the ancestor basis

◆ transformGM() [3/3]

template<typename BasisType >

Eigen::MatrixXd HArDCore2D::transformGM	(	const ShiftedBasis< BasisType > &	shifted_basis,
		const char	RC,
		const Eigen::MatrixXd &	anc_GM
	)

inline

Transforms a Gram Matrix from an ancestor to a shifted basis.

Parameters

shifted_basis	Shifted basis
RC	R if transformation applied on rows (left), C if applied on columns (right)
anc_GM	Gram matrix of the ancestor basis

◆ useAncestor()

template<typename BasisType >

constexpr bool HArDCore2D::useAncestor ( )

constexpr

Determines if the ancestor of a basis will be used to compute a Gram matrix for this basis.

◆ vector()

Eigen::Vector2d HArDCore2D::QuadratureNode::vector ( ) const

inline

Returns the quadrature point as an Eigen vector.

◆ wq() [1/2]

double QuadRuleEdge::wq ( size_t i )

◆ wq() [2/2]

double LegendreGauss::wq ( size_t i )

◆ xq()

double QuadRuleEdge::xq ( size_t i )

◆ yq()

double QuadRuleEdge::yq ( size_t i )

◆ ~LegendreGauss()

LegendreGauss::~LegendreGauss ( )

◆ ~QuadRuleEdge()

QuadRuleEdge::~QuadRuleEdge ( )

Variable Documentation

◆ w

double HArDCore2D::QuadratureNode::w

◆ x

double HArDCore2D::QuadratureNode::x

◆ y

double HArDCore2D::QuadratureNode::y

Namespaces

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ MonomialCellIntegralsType

◆ MonomialEdgeIntegralsType

◆ QuadratureRule

Function Documentation

◆ CheckIntegralsDegree() [1/2]

◆ CheckIntegralsDegree() [2/2]

◆ generate_quadrature_rule() [1/2]

◆ generate_quadrature_rule() [2/2]

◆ GMDer() [1/2]

◆ GMDer() [2/2]

◆ GMRolyComplScalar() [1/2]

◆ GMRolyComplScalar() [2/2]

◆ GMScalarDerivative() [1/4]

◆ GMScalarDerivative() [2/4]

◆ GMScalarDerivative() [3/4]

◆ GMScalarDerivative() [4/4]

◆ GramMatrix() [1/27]

◆ GramMatrix() [2/27]

◆ GramMatrix() [3/27]

◆ GramMatrix() [4/27]

◆ GramMatrix() [5/27]

◆ GramMatrix() [6/27]

◆ GramMatrix() [7/27]

◆ GramMatrix() [8/27]

◆ GramMatrix() [9/27]

◆ GramMatrix() [10/27]

◆ GramMatrix() [11/27]

◆ GramMatrix() [12/27]

◆ GramMatrix() [13/27]

◆ GramMatrix() [14/27]

◆ GramMatrix() [15/27]

◆ GramMatrix() [16/27]

◆ GramMatrix() [17/27]

◆ GramMatrix() [18/27]

◆ GramMatrix() [19/27]

◆ GramMatrix() [20/27]

◆ GramMatrix() [21/27]

◆ GramMatrix() [22/27]

◆ GramMatrix() [23/27]

◆ GramMatrix() [24/27]

◆ GramMatrix() [25/27]

◆ GramMatrix() [26/27]

◆ GramMatrix() [27/27]

◆ GramMatrixDiv() [1/3]

◆ GramMatrixDiv() [2/3]

◆ GramMatrixDiv() [3/3]

◆ IntegrateCellMonomials()

◆ IntegrateEdgeMonomials()

◆ LegendreGauss()

◆ npts()

◆ nq()

◆ operator()()

◆ QuadratureNode()

◆ QuadRuleEdge()

◆ setup()

◆ sub_rule_01()

◆ sub_rule_02()

◆ sub_rule_03()

◆ sub_rule_04()

◆ sub_rule_05()

◆ sub_rule_06()

◆ sub_rule_07()

◆ sub_rule_08()

◆ sub_rule_09()

◆ sub_rule_10()

◆ sub_rule_11()

◆ tq()

◆ transformGM() [1/3]

◆ transformGM() [2/3]

◆ transformGM() [3/3]

◆ useAncestor()

◆ vector()

◆ wq() [1/2]