Quadratures

Classes providing quadratures rules on cells, faces and edges, as well as cost-effective ways to compute Gram matrices of polynomial bases. More...

Namespaces
namespace	HArDCore3D

Classes
struct	HArDCore3D::VecHash
	Hash function for VectorZd type. More...
struct	HArDCore3D::VecFaceHash
	Hash function for VectorZd type. More...
class	HArDCore3D::QuadRuleEdge
class	HArDCore3D::LegendreGauss
class	HArDCore3D::QuadRuleTetra
class	HArDCore3D::QuadRuleTriangle
struct	HArDCore3D::QuadratureNode
	Description of one node and one weight from a quadrature rule. More...

Typedefs
typedef std::unordered_map< VectorZd, double, VecHash >	HArDCore3D::MonomialCellIntegralsType
	Type for list of integrals of monomials.
typedef std::vector< double >	HArDCore3D::MonomialEdgeIntegralsType
	Type for list of edge integrals of monomials.
typedef std::unordered_map< Eigen::Vector2i, double, VecFaceHash >	HArDCore3D::MonomialFaceIntegralsType
	Type for list of face integrals of monomials.
typedef boost::multi_array< double, 3 >	HArDCore3D::Scalar3Tensor
typedef Eigen::Map< Eigen::MatrixXd, Eigen::Unaligned, Eigen::Stride< Eigen::Dynamic, Eigen::Dynamic > >	HArDCore3D::MatrixSlice
typedef Eigen::Map< Eigen::VectorXd, Eigen::Unaligned, Eigen::InnerStride< Eigen::Dynamic > >	HArDCore3D::VectorSlice
typedef std::vector< QuadratureNode >	HArDCore3D::QuadratureRule

Functions
size_t	HArDCore3D::VecHash::operator() (const VectorZd &p) const
std::vector< MonomialCellIntegralsType >	HArDCore3D::IntegrateCellMonomials_onEdges (const Cell &T, const size_t maxdeg)
	Compute all the integrals, on the edges of a cell, of this cell's monomials up to a max degree.
std::vector< MonomialCellIntegralsType >	HArDCore3D::IntegrateCellMonomials_onFaces (const Cell &T, const size_t maxdeg, std::vector< MonomialCellIntegralsType > &integrals_edges)
	Compute all the integrals, on the faces of a cell, of this cell's monomials up to a max degree.
MonomialCellIntegralsType	HArDCore3D::IntegrateCellMonomials (const Cell &T, const int maxdeg)
	Compute all the integrals of a cell's monomials on the cell.
MonomialCellIntegralsType	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::GramMatrix (const Cell &T, const GolyComplBasisCell &basis1, const GolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of GolyCompl bases.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const GolyComplBasisCell &golycompl_basis, const TensorizedVectorFamily< BasisType1, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a GolyCompl basis and a tensorized scalar basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &tens_family, const GolyComplBasisCell &golycompl_basis, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a tensorized scalar basis and a GolyCompl basis.
Eigen::MatrixXd	HArDCore3D::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	HArDCore3D::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.
Eigen::MatrixXd	HArDCore3D::GMGolyComplScalar (const Cell &T, const GolyComplBasisCell &golycompl_basis, const MonomialScalarBasisCell &mono_basis, const size_t s, MonomialCellIntegralsType mono_int_map, const size_t m=3, const size_t k1=3, const size_t k2=3)
	Computes the Gram Matrix of the sth section of a GolyCompl Basis and a monomial basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GMGolyComplScalar (const Cell &T, const GolyComplBasisCell &basis1, const BasisType &basis2, const size_t s, MonomialCellIntegralsType mono_int_map, const size_t m=3, const size_t k1=3, const size_t k2=3)
	Generic template to compute the Gram Matrix of the sth section of a GolyCompl Basis and any basis with an extra power of the mth variable.
Eigen::MatrixXd	HArDCore3D::GMGolyCompl (const Cell &T, const GolyComplBasisCell &basis1, const GolyComplBasisCell &basis2, const size_t s1, const size_t s2, MonomialCellIntegralsType mono_int_map, const size_t m1=3, const size_t m2=3, const size_t k1=3, const size_t k2=3)
	Computes the Gram Matrix of the (optionally k1th derivative of the) s1th section of GolyCompl (optionally multiplied by the m1th variable) and the (optionally k2th derivative of the) s2th section of GolyCompl (optionally multiplied by the m2th variable)
template<typename BasisType >
constexpr bool	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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. homogeneous coordinates, without scaling)
Eigen::MatrixXd	HArDCore3D::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. homogeneous coordinates, without scaling)
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::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. homogeneous coordinates, without scaling)
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::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. homogeneous coordinates, without scaling)
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::GramMatrix (const Cell &T, const CurlBasis< BasisType1 > &basis1, const CurlBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of Curl of any pair of bases.
template<typename BasisType1 , typename BasisType2 >
boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type	HArDCore3D::GramMatrix (const Cell &T, const CurlBasis< BasisType1 > &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a Curl basis and any other basis.
template<typename BasisType1 , typename Basis2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const BasisType1 &basis1, const CurlBasis< Basis2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any basis and a Curl basis.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of a tensorized basis and the curl of another tensorized basis.
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const GolyComplBasisCell &basis1, const GolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Compute the Gram Matrix of the curl of a GolyCompl basis and the curl of another GolyCompl basis.
template<typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const GolyComplBasisCell &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of a GolyCompl basis and the curl of a tensorized basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const GolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of a tensorized basis and the curl of a GolyCompl basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of any basis and the curl of any other basis.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a Curl<Tensorized> basis and a tensorized scalar basis.
template<typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const GolyComplBasisCell &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a Curl<GolyCompl> basis and a tensorized scalar basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of any basis and any other basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const BasisType1 &basis1, const CurlBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of any two bases when one CurlBasis is at a lower level than the other.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const DivergenceBasis< BasisType1 > &basis1, const DivergenceBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of Divergence of any pair of bases.
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalarDiv (const Cell &T, const MonomialScalarBasisCell &mono_basis, const RolyComplBasisCell &rolycompl_basis, const size_t k, MonomialCellIntegralsType mono_int_map)
	Gram Matrix of the divergence of a RolyCompl Basis and the kth derivative of a monomial basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalarDiv (const Cell &T, const BasisType &basis1, const RolyComplBasisCell &basis2, const size_t k, MonomialCellIntegralsType mono_int_map)
	Gram Matrix of the divergence of a RolyCompl basis and the k-th derivative of any scalar basis.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of a tensorized basis and the divergence of another tensorized basis.
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const RolyComplBasisCell &basis1, const RolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Compute the Gram Matrix of the divergence of a RolyCompl basis and the divergence of another RolyCompl basis.
template<typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const RolyComplBasisCell &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of a RolyCompl basis and the divergence of a tensorized basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const RolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of a tensorized basis and the divergence of a RolyCompl basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (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 the divergence of any other basis.
template<typename BasisType1 , typename BasisType2 >
boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type	HArDCore3D::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	HArDCore3D::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 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &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	HArDCore3D::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	HArDCore3D::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 >
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Cell &T, const BasisType1 &basis1, const DivergenceBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of any two bases when one DivergenceBasis is at a lower level than the other.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::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	HArDCore3D::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 family (only valid if, in MatrixFamily and TensorizedVectorFamily, we have N=dimspace).
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, dimspace > &basis1, const DivergenceBasis< MatrixFamily< BasisType2, dimspace > > &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a vector valued basis and the divergence of a MatrixFamily.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::IntegrateEdgeMonomials (const Edge &E, const int maxdeg)
	Compute all integrals of edge monomials up to a total degree.
MonomialEdgeIntegralsType	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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 BasisType >
Eigen::MatrixXd	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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	HArDCore3D::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)
size_t	HArDCore3D::VecFaceHash::operator() (const Eigen::Vector2i &p) const
std::vector< MonomialFaceIntegralsType >	HArDCore3D::IntegrateFaceMonomials_onEdges (const Face &F, const size_t maxdeg)
	Compute all integrals, on the edges of a face, of the face monomials up to a total degree.
MonomialFaceIntegralsType	HArDCore3D::IntegrateFaceMonomials (const Face &F, const int maxdeg)
	Compute all integrals on a face of face monomials up to a total degree.
MonomialFaceIntegralsType	HArDCore3D::CheckIntegralsDegree (const Face &F, const size_t degree, const MonomialFaceIntegralsType &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 BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const BasisType1 &basis1, const BasisType2 &basis2, MonomialFaceIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of bases.
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const MonomialScalarBasisFace &basis1, const MonomialScalarBasisFace &basis2, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const BasisType &basis, MonomialFaceIntegralsType 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	HArDCore3D::GramMatrix (const Face &F, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialFaceIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any pair of tensorized scalar bases.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const TangentFamily< BasisType1 > &basis1, const TangentFamily< BasisType2 > &basis2, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of tangent bases.
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const RolyComplBasisFace &basis1, const RolyComplBasisFace &basis2, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of RolyCompl bases.
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const GolyComplBasisFace &basis1, const GolyComplBasisFace &basis2, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of GolyCompl bases.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const RolyComplBasisFace &basis1, const TangentFamily< BasisType > &basis2, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a RolyCompl basis and a tangent basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const TangentFamily< BasisType > &basis1, const RolyComplBasisFace &basis2, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a RolyCompl basis and a tangent basis.
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalar (const Face &F, const RolyComplBasisFace &rolycompl_basis, const MonomialScalarBasisFace &mono_basis, const size_t m, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of the scalar part of a RolyCompl Basis and a monomial basis with an extra power on the mth variable.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalar (const Face &F, const RolyComplBasisFace &basis1, const BasisType &basis2, const size_t m, MonomialFaceIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of the scalar part of a RolyCompl Basis and any basis with an extra power on the mth variable.
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Face &F, const MonomialScalarBasisFace &basis1, const MonomialScalarBasisFace &basis2, const size_t m, MonomialFaceIntegralsType 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. homogeneous coordinates on the face, no change of variable)
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Face &F, const MonomialScalarBasisFace &basis1, const MonomialScalarBasisFace &basis2, const size_t m, const size_t l, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases, taking a partial derivative of each (w.r.t. homogeneous coordinates on the face, no change of variable)
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Face &F, const BasisType1 &basis1, const BasisType2 &basis2, const size_t m, MonomialFaceIntegralsType 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. homogeneous coordinates on the face, no change of variable)
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Face &F, const BasisType1 &basis1, const BasisType2 &basis2, const size_t m, const size_t l, MonomialFaceIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of scalar bases, taking a partial derivative of each (w.r.t. homogeneous coordinates on the face, no change of variable)
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const CurlBasis< BasisType1 > &basis1, const CurlBasis< BasisType2 > &basis2, MonomialFaceIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a pair of Curl bases.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const CurlBasis< BasisType1 > &basis1, const TangentFamily< BasisType2 > &basis2, MonomialFaceIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a Curl basis and a Tangent basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Face &F, const TangentFamily< BasisType1 > &basis1, const CurlBasis< BasisType2 > &basis2, MonomialFaceIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a Tangent basis and a Curl basis.
template<typename BasisType1 , typename BasisType2 >
boost::disable_if< boost::is_same< BasisType2, MonomialFaceIntegralsType >, Eigen::MatrixXd >::type	HArDCore3D::GramMatrix (const Face &F, const DivergenceBasis< BasisType1 > &basis1, const BasisType2 &basis2, MonomialFaceIntegralsType 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	HArDCore3D::GramMatrix (const Face &F, const BasisType1 &basis1, const DivergenceBasis< Basis2 > &basis2, MonomialFaceIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any basis and a Divergence basis.
template<typename BasisType1 >
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Face &F, const TangentFamily< BasisType1 > &basis1, const MonomialScalarBasisFace &basis2, MonomialFaceIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a Divergence<TangentFamily> basis and a monomial scalar basis.
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Face &F, const RolyComplBasisFace &basis1, const MonomialScalarBasisFace &basis2, MonomialFaceIntegralsType mono_int_map={})
	Computes the Gram Matrix of a Divergence<RolyCompl> basis and a monomial scalar basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Face &F, const BasisType1 &basis1, const BasisType2 &basis2, MonomialFaceIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of any basis and any other basis.
MatrixSlice	HArDCore3D::slice (Scalar3Tensor &tensor, size_t fixed_dim, size_t index)
	Function to slice a 3-tensor with respect to one index (returns a 2-tensor)
VectorSlice	HArDCore3D::slice (Scalar3Tensor &tensor, size_t fixed_dim1, size_t index1, size_t fixed_dim2, size_t index2)
	Function to slice a 3-tensor with respect to two indices (returns a 1-tensor)
template<size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const MonomialScalarBasisCell &basis1, const TensorizedVectorFamily< MonomialScalarBasisCell, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the triple integral product of a scalar times the dot product of two vectors - basis1(basis2 . basis2).
template<size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const TensorizedVectorFamily< MonomialScalarBasisCell, N > &tens_family1, const TensorizedVectorFamily< MonomialScalarBasisCell, N > &tens_family2, MonomialCellIntegralsType mono_int_map={})
	Computes the triple integral product of a vector basis dot the cross product of the second vector basis - tens_family1 . (tens_family2 x tens_family2).
template<size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const GradientBasis< MonomialScalarBasisCell > &grad_basis, const TensorizedVectorFamily< MonomialScalarBasisCell, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Computes the triple integral product of a vector basis dot the cross product of the second vector basis - grad_basis . (tens_family x tens_family).
template<size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const GolyComplBasisCell &golycompl_basis, const TensorizedVectorFamily< MonomialScalarBasisCell, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Computes the triple integral product of a vector basis dot the cross product of the second vector basis - golycompl_basis . (tens_family x tens_family).
template<typename ScalarBasisType1 , typename ScalarBasisType2 , size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const GradientBasis< ShiftedBasis< ScalarBasisType1 > > &grad_shift_basis, const TensorizedVectorFamily< Family< ScalarBasisType2 >, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Handles a derived basis (see other functions for detailed output)
template<typename ScalarBasisType , typename BasisType >
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const GradientBasis< ShiftedBasis< ScalarBasisType > > &grad_shift_basis, const BasisType &basis2, MonomialCellIntegralsType mono_int_map={})
	Handles a derived basis (see other functions for detailed output)
template<typename BasisType , typename ScalarBasisType , size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const BasisType &basis1, const TensorizedVectorFamily< Family< ScalarBasisType >, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Handles a derived basis (see other functions for detailed output)
template<typename BasisType , typename ScalarBasisType , size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const Family< BasisType > &basis1, const Family< TensorizedVectorFamily< ScalarBasisType, N > > &basis2, MonomialCellIntegralsType mono_int_map={})
	Handles a derived basis (see other functions for detailed output)
template<typename BasisType , size_t N>
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const Family< BasisType > &basis1, const TensorizedVectorFamily< MonomialScalarBasisCell, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Handles a derived basis (see other functions for detailed output)
template<typename BasisType1 , typename BasisType2 >
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const BasisType1 &basis1, const Family< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Handles a derived basis (see other functions for detailed output)
template<size_t N, typename ScalarBasisType >
Scalar3Tensor	HArDCore3D::tripleInt (const Cell &T, const TensorizedVectorFamily< Family< ScalarBasisType >, N > &tens_family1, const TensorizedVectorFamily< MonomialScalarBasisCell, N > &tens_family2, MonomialCellIntegralsType mono_int_map={})
	Handles a derived basis (see other functions for detailed output)
	HArDCore3D::QuadRuleEdge::QuadRuleEdge (size_t doe, bool warn)
	HArDCore3D::QuadRuleEdge::~QuadRuleEdge ()
size_t	HArDCore3D::QuadRuleEdge::nq ()
double	HArDCore3D::QuadRuleEdge::xq (size_t i)
double	HArDCore3D::QuadRuleEdge::yq (size_t i)
double	HArDCore3D::QuadRuleEdge::zq (size_t i)
double	HArDCore3D::QuadRuleEdge::wq (size_t i)
void	HArDCore3D::QuadRuleEdge::setup (double xV[], double yV[], double zV[])
	HArDCore3D::LegendreGauss::LegendreGauss (size_t doe)
	HArDCore3D::LegendreGauss::~LegendreGauss ()
void	HArDCore3D::LegendreGauss::sub_rule_01 ()
void	HArDCore3D::LegendreGauss::sub_rule_02 ()
void	HArDCore3D::LegendreGauss::sub_rule_03 ()
void	HArDCore3D::LegendreGauss::sub_rule_04 ()
void	HArDCore3D::LegendreGauss::sub_rule_05 ()
void	HArDCore3D::LegendreGauss::sub_rule_06 ()
void	HArDCore3D::LegendreGauss::sub_rule_07 ()
void	HArDCore3D::LegendreGauss::sub_rule_08 ()
void	HArDCore3D::LegendreGauss::sub_rule_09 ()
void	HArDCore3D::LegendreGauss::sub_rule_10 ()
void	HArDCore3D::LegendreGauss::sub_rule_11 ()
size_t	HArDCore3D::LegendreGauss::npts ()
double	HArDCore3D::LegendreGauss::wq (size_t i)
double	HArDCore3D::LegendreGauss::tq (size_t i)
void	HArDCore3D::QuadRuleTetra::init ()
size_t	HArDCore3D::QuadRuleTetra::required_rule (size_t doe) const
	Compute the minimum rule required to achieve the desired degree of exactness.
	HArDCore3D::QuadRuleTetra::QuadRuleTetra (size_t doe, bool warn)
	Create a quadrature rule with at least the given degree of exactness (if available).
	HArDCore3D::QuadRuleTetra::QuadRuleTetra (size_t _rule=0)
size_t	HArDCore3D::QuadRuleTetra::nq () const
double	HArDCore3D::QuadRuleTetra::xq (int iq) const
double	HArDCore3D::QuadRuleTetra::yq (int iq) const
double	HArDCore3D::QuadRuleTetra::zq (int iq) const
double	HArDCore3D::QuadRuleTetra::wq (int iq) const
void	HArDCore3D::QuadRuleTetra::setup (double(&_xV)[4], double(&_yV)[4], double(&_zV)[4])
void	HArDCore3D::QuadRuleTetra::get_quadrule (int iq, double &_xq, double &_yq, double &_zq, double &_wq) const
	HArDCore3D::QuadRuleTriangle::QuadRuleTriangle (size_t _doe, bool warn)
	Default constructor.
	HArDCore3D::QuadRuleTriangle::~QuadRuleTriangle ()
double	HArDCore3D::QuadRuleTriangle::xq (size_t i)
double	HArDCore3D::QuadRuleTriangle::yq (size_t i)
double	HArDCore3D::QuadRuleTriangle::zq (size_t i)
double	HArDCore3D::QuadRuleTriangle::wq (size_t i)
size_t	HArDCore3D::QuadRuleTriangle::nq ()
void	HArDCore3D::QuadRuleTriangle::setup (double xV[], double yV[], double zV[])
double	HArDCore3D::QuadRuleTriangle::area (double xV[], double yV[], double zV[]) const
	HArDCore3D::QuadratureNode::QuadratureNode (double x, double y, double z, double w)
Eigen::Vector3d	HArDCore3D::QuadratureNode::vector () const
	Returns the quadrature point as an Eigen vector.
QuadratureRule	HArDCore3D::generate_quadrature_rule (const Cell &T, const int doe, const bool force_split=false)
	Generate quadrature rule on mesh element.
QuadratureRule	HArDCore3D::generate_quadrature_rule (const Face &F, const int doe)
	Generate quadrature rule on mesh face.
QuadratureRule	HArDCore3D::generate_quadrature_rule (const Edge &E, const int doe)
	Generate quadrature rule on mesh edge.
double	HArDCore3D::tetra_volume (double x[4], double y[4], double z[4])
double	HArDCore3D::tetra_sum (double func(double x, double y, double z), double x[4], double y[4], double z[4], int nq, double cq0[], double cq1[], double cq2[], double wq[])
size_t	HArDCore3D::tetra_unit_size (size_t rule)
void	HArDCore3D::tetra_unit_set (size_t rule, size_t nq, double cq0[], double cq1[], double cq2[], double wq[])
double	HArDCore3D::parallelipiped_volume_3d (double x[4], double y[4], double z[4])
double	HArDCore3D::tetra_unit_volume ()
double	HArDCore3D::tetra_unit_sum (double func(double x, double y, double z), size_t nq, double xq[], double yq[], double zq[], double wq[])

Variables
static constexpr size_t	HArDCore3D::MAX_DOE_CELL = 14
	Maximum degree of the cell quadrature rules.
static constexpr size_t	HArDCore3D::MAX_DOE_FACE = 20
	Maximum degree of the face quadrature rules.
static constexpr size_t	HArDCore3D::MAX_DOE_EDGE = 20
	Maximum degree of the edge quadrature rules.
static constexpr size_t	HArDCore3D::QuadRuleTetra::num_rules = 15
const size_t	HArDCore3D::QuadRuleTetra::rule
const size_t	HArDCore3D::QuadRuleTetra::nqn
double	HArDCore3D::QuadRuleTetra::vol_T
std::vector< double >	HArDCore3D::QuadRuleTetra::xV
std::vector< double >	HArDCore3D::QuadRuleTetra::yV
std::vector< double >	HArDCore3D::QuadRuleTetra::zV
std::vector< double >	HArDCore3D::QuadRuleTetra::cq0
std::vector< double >	HArDCore3D::QuadRuleTetra::cq1
std::vector< double >	HArDCore3D::QuadRuleTetra::cq2
std::vector< double >	HArDCore3D::QuadRuleTetra::cq3
std::vector< double >	HArDCore3D::QuadRuleTetra::cwq
size_t	HArDCore3D::QuadRuleTriangle::_npts
double *	HArDCore3D::QuadRuleTriangle::qsx
double *	HArDCore3D::QuadRuleTriangle::qsy
double *	HArDCore3D::QuadRuleTriangle::qsz
double *	HArDCore3D::QuadRuleTriangle::qswg
double *	HArDCore3D::QuadRuleTriangle::_xy
double *	HArDCore3D::QuadRuleTriangle::_w
double	HArDCore3D::QuadratureNode::x
double	HArDCore3D::QuadratureNode::y
double	HArDCore3D::QuadratureNode::z
double	HArDCore3D::QuadratureNode::w

Detailed Description

Classes providing quadratures rules on cells, faces and edges, as well as cost-effective ways to compute Gram matrices of polynomial bases.

Typedef Documentation

MatrixSlice

typedef Eigen::Map<Eigen::MatrixXd, Eigen::Unaligned, Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic> > HArDCore3D::MatrixSlice

MonomialCellIntegralsType

typedef std::unordered_map<VectorZd, double, VecHash> HArDCore3D::MonomialCellIntegralsType

Type for list of integrals of monomials.

MonomialEdgeIntegralsType

typedef std::vector<double> HArDCore3D::MonomialEdgeIntegralsType

Type for list of edge integrals of monomials.

MonomialFaceIntegralsType

typedef std::unordered_map<Eigen::Vector2i, double, VecFaceHash> HArDCore3D::MonomialFaceIntegralsType

Type for list of face integrals of monomials.

QuadratureRule

typedef std::vector<QuadratureNode> HArDCore3D::QuadratureRule

Scalar3Tensor

typedef boost::multi_array<double, 3> HArDCore3D::Scalar3Tensor

VectorSlice

typedef Eigen::Map<Eigen::VectorXd, Eigen::Unaligned, Eigen::InnerStride<Eigen::Dynamic> > HArDCore3D::VectorSlice

Function Documentation

area()

double QuadRuleTriangle::area ( double  xV[], double  yV[], double  zV[]  ) const

protected

CheckIntegralsDegree() [1/3]

MonomialCellIntegralsType HArDCore3D::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() [2/3]

MonomialEdgeIntegralsType HArDCore3D::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

CheckIntegralsDegree() [3/3]

MonomialFaceIntegralsType HArDCore3D::CheckIntegralsDegree	(	const Face &	F,
		const size_t	degree,
		const MonomialFaceIntegralsType &	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

F	Face
degree	Expected degree
mono_int_map	Existing list, optional

generate_quadrature_rule() [1/3]

QuadratureRule HArDCore3D::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 pyramids based on the center of mass and the faces, and then cutting these pyramids into tetrahedrons (otherwise, tetrahedrons are not split)

generate_quadrature_rule() [2/3]

QuadratureRule HArDCore3D::generate_quadrature_rule	(	const Edge &	E,
		const int	doe
	)

Generate quadrature rule on mesh edge.

Returns

list of quadrature nodes and weights

Parameters

E	Reference to the mesh edge
doe	Degree of exactness

generate_quadrature_rule() [3/3]

QuadratureRule HArDCore3D::generate_quadrature_rule	(	const Face &	F,
		const int	doe
	)

Generate quadrature rule on mesh face.

Returns

list of quadrature nodes and weights

Parameters

F	Reference to the mesh face
doe	Degree of exactness

get_quadrule()

void QuadRuleTetra::get_quadrule	(	int	iq,
		double &	_xq,
		double &	_yq,
		double &	_zq,
		double &	_wq
	)		const

GMDer() [1/2]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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 HArDCore3D::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

GMGolyCompl()

Eigen::MatrixXd HArDCore3D::GMGolyCompl	(	const Cell &	T,
		const GolyComplBasisCell &	basis1,
		const GolyComplBasisCell &	basis2,
		const size_t	s1,
		const size_t	s2,
		MonomialCellIntegralsType	mono_int_map,
		const size_t	m1 = 3,
		const size_t	m2 = 3,
		const size_t	k1 = 3,
		const size_t	k2 = 3
	)

Computes the Gram Matrix of the (optionally k1th derivative of the) s1th section of GolyCompl (optionally multiplied by the m1th variable) and the (optionally k2th derivative of the) s2th section of GolyCompl (optionally multiplied by the m2th variable)

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis
s1	the first GolyCompl basis has three sections; use the s1th.
s2	the second GolyCompl basis has three sections; use the s2th.
mono_int_map	list of integrals of monomials up to the sum of max degree of basis1 and basis2
m1	Optionally (m1 < 3), add one to the power of the m1th variable
m2	Optionally (m2 < 3), add one to the power of the m2th variable
k1	Optionally (k1 < 3), take the k1th derivative of the first GolyCompl scalar
k2	Optionally (k2 < 3), take the k2th derivative of the second GolyCompl scalar

GMGolyComplScalar() [1/2]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::GMGolyComplScalar	(	const Cell &	T,
		const GolyComplBasisCell &	basis1,
		const BasisType &	basis2,
		const size_t	s,
		MonomialCellIntegralsType	mono_int_map,
		const size_t	m = 3,
		const size_t	k1 = 3,
		const size_t	k2 = 3
	)

Generic template to compute the Gram Matrix of the sth section of a GolyCompl Basis and any basis with an extra power of the mth variable.

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis (columns of the Gram matrix)
s	the GolyCompl basis has three sections; use the sth.
mono_int_map	list of integrals of monomials up to the sum of max degree of basis1 and basis2
m	Optionally (m < 3), add one to the power of the mth variable
k1	Optionally (k1 < 3), take the kth derivative of the GolyCompl scalar
k2	Optionally (k2 < 3), take the kth derivative of the MonomialScalar scalar

GMGolyComplScalar() [2/2]

Eigen::MatrixXd HArDCore3D::GMGolyComplScalar	(	const Cell &	T,
		const GolyComplBasisCell &	golycompl_basis,
		const MonomialScalarBasisCell &	mono_basis,
		const size_t	s,
		MonomialCellIntegralsType	mono_int_map,
		const size_t	m = 3,
		const size_t	k1 = 3,
		const size_t	k2 = 3
	)

Computes the Gram Matrix of the sth section of a GolyCompl Basis and a monomial basis.

Parameters

T	Cell to which the basis corresponds
golycompl_basis	First basis
mono_basis	Second basis
s	the GolyCompl basis has three sections; use the sth.
mono_int_map	list of integrals of monomials up to the sum of max degree of basis1 and basis2
m	Optionally (m < 3), add one to the power of the mth variable
k1	Optionally (k1 < 3), take the kth derivative of the GolyCompl scalar
k2	Optionally (k2 < 3), take the kth derivative of the MonomialScalar scalar

GMRolyComplScalar() [1/4]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::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() [2/4]

Eigen::MatrixXd HArDCore3D::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

GMRolyComplScalar() [3/4]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::GMRolyComplScalar	(	const Face &	F,
		const RolyComplBasisFace &	basis1,
		const BasisType &	basis2,
		const size_t	m,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of the scalar part of a RolyCompl Basis and any basis with an extra power on the mth variable.

Parameters

F	Face 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() [4/4]

Eigen::MatrixXd HArDCore3D::GMRolyComplScalar	(	const Face &	F,
		const RolyComplBasisFace &	rolycompl_basis,
		const MonomialScalarBasisFace &	mono_basis,
		const size_t	m,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Computes the Gram Matrix of the scalar part of a RolyCompl Basis and a monomial basis with an extra power on the mth variable.

Parameters

F	Face 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

GMRolyComplScalarDiv() [1/2]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::GMRolyComplScalarDiv	(	const Cell &	T,
		const BasisType &	basis1,
		const RolyComplBasisCell &	basis2,
		const size_t	k,
		MonomialCellIntegralsType	mono_int_map
	)

Gram Matrix of the divergence of a RolyCompl basis and the k-th derivative of any scalar basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis
basis2	Second basis (columns of the Gram matrix)
k	Take the kth derivative of the scalar basis
mono_int_map	list of integrals of monomials up to the sum of max degree of basis1 and basis2

GMRolyComplScalarDiv() [2/2]

Eigen::MatrixXd HArDCore3D::GMRolyComplScalarDiv	(	const Cell &	T,
		const MonomialScalarBasisCell &	mono_basis,
		const RolyComplBasisCell &	rolycompl_basis,
		const size_t	k,
		MonomialCellIntegralsType	mono_int_map
	)

Gram Matrix of the divergence of a RolyCompl Basis and the kth derivative of a monomial basis.

Computes the Gram Matrix of the divergence of a RolyCompl Basis and the kth derivative of a monomial basis.

Parameters

T	Cell to which the basis corresponds
mono_basis	First basis
rolycompl_basis	Second basis
k	Take the kth derivative of the monomial scalar
mono_int_map	list of integrals of monomials up to the sum of max degree of basis1 and basis2

GMScalarDerivative() [1/8]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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. 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() [2/8]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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. 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() [3/8]

Eigen::MatrixXd HArDCore3D::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. 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() [4/8]

Eigen::MatrixXd HArDCore3D::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. 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

GMScalarDerivative() [5/8]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GMScalarDerivative	(	const Face &	F,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		const size_t	m,
		const size_t	l,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of any pair of scalar bases, taking a partial derivative of each (w.r.t. homogeneous coordinates on the face, no change of variable)

Parameters

F	Face 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() [6/8]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GMScalarDerivative	(	const Face &	F,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		const size_t	m,
		MonomialFaceIntegralsType	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. homogeneous coordinates on the face, no change of variable)

Parameters

F	Face 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() [7/8]

Eigen::MatrixXd HArDCore3D::GMScalarDerivative	(	const Face &	F,
		const MonomialScalarBasisFace &	basis1,
		const MonomialScalarBasisFace &	basis2,
		const size_t	m,
		const size_t	l,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Computes the Gram Matrix of a pair of local scalar monomial bases, taking a partial derivative of each (w.r.t. homogeneous coordinates on the face, no change of variable)

Parameters

F	Face 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() [8/8]

Eigen::MatrixXd HArDCore3D::GMScalarDerivative	(	const Face &	F,
		const MonomialScalarBasisFace &	basis1,
		const MonomialScalarBasisFace &	basis2,
		const size_t	m,
		MonomialFaceIntegralsType	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. homogeneous coordinates on the face, no change of variable)

Parameters

F	Face 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() [1/44]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::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() [2/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [3/44]

template<typename BasisType1 , typename Basis2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Cell &	T,
		const BasisType1 &	basis1,
		const CurlBasis< Basis2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

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

Parameters

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

GramMatrix() [4/44]

template<typename BasisType1 , typename Basis2 >

Eigen::MatrixXd HArDCore3D::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 (scalar 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() [5/44]

template<typename BasisType1 , typename BasisType2 >

boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type HArDCore3D::GramMatrix	(	const Cell &	T,
		const CurlBasis< BasisType1 > &	basis1,
		const BasisType2 &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of a Curl 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() [6/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Cell &	T,
		const CurlBasis< BasisType1 > &	basis1,
		const CurlBasis< BasisType2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of Curl 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() [7/44]

template<typename BasisType1 , typename BasisType2 >

boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type HArDCore3D::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() [8/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Cell &	T,
		const DivergenceBasis< BasisType1 > &	basis1,
		const DivergenceBasis< BasisType2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of Divergence 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() [9/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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 family (only valid if, in MatrixFamily and TensorizedVectorFamily, we have N=dimspace).

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() [10/44]

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Cell &	T,
		const GolyComplBasisCell &	basis1,
		const GolyComplBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Computes the 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() [11/44]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Cell &	T,
		const GolyComplBasisCell &	golycompl_basis,
		const TensorizedVectorFamily< BasisType1, N > &	tens_family,
		MonomialCellIntegralsType	mono_int_map = {}
	)

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

Parameters

T	Cell to which the basis corresponds
golycompl_basis	First basis (GolyCompl 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() [12/44]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::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() [13/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [14/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [15/44]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::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() [16/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [17/44]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::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() [18/44]

Eigen::MatrixXd HArDCore3D::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() [19/44]

Eigen::MatrixXd HArDCore3D::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() [20/44]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore3D::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() [21/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, dimspace > &	basis1,
		const DivergenceBasis< MatrixFamily< BasisType2, dimspace > > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of a vector valued basis and the divergence of a MatrixFamily.

Parameters

T	Cell to which the basis corresponds
basis1	Tensorized family (rows of the Gram matrix)
basis2	Divergence of MatrixFamily (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() [22/44]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::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() [23/44]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	tens_family,
		const GolyComplBasisCell &	golycompl_basis,
		MonomialCellIntegralsType	mono_int_map = {}
	)

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

Parameters

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

GramMatrix() [24/44]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::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() [25/44]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore3D::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() [26/44]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::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() [27/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [28/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [29/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [30/44]

Eigen::MatrixXd HArDCore3D::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() [31/44]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const BasisType &	basis,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

GramMatrix() [32/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face 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() [33/44]

template<typename BasisType1 , typename Basis2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const BasisType1 &	basis1,
		const DivergenceBasis< Basis2 > &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face to which the basis corresponds
basis1	First basis (scalar 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() [34/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const CurlBasis< BasisType1 > &	basis1,
		const CurlBasis< BasisType2 > &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face 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() [35/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const CurlBasis< BasisType1 > &	basis1,
		const TangentFamily< BasisType2 > &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of a Curl basis and a Tangent basis.

Parameters

F	Face 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() [36/44]

template<typename BasisType1 , typename BasisType2 >

boost::disable_if< boost::is_same< BasisType2, MonomialFaceIntegralsType >, Eigen::MatrixXd >::type HArDCore3D::GramMatrix	(	const Face &	F,
		const DivergenceBasis< BasisType1 > &	basis1,
		const BasisType2 &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face to which the basis corresponds
basis1	First basis (rows of the Gram matrix)
basis2	Second basis (scalar 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() [37/44]

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const GolyComplBasisFace &	basis1,
		const GolyComplBasisFace &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Computes the Gram Matrix of a pair of GolyCompl bases.

Parameters

F	Face 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() [38/44]

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const MonomialScalarBasisFace &	basis1,
		const MonomialScalarBasisFace &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face 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() [39/44]

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const RolyComplBasisFace &	basis1,
		const RolyComplBasisFace &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Computes the Gram Matrix of a pair of RolyCompl bases.

Parameters

F	Face 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() [40/44]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const RolyComplBasisFace &	basis1,
		const TangentFamily< BasisType > &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Computes the Gram Matrix of a RolyCompl basis and a tangent basis.

Parameters

F	Face 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() [41/44]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const TangentFamily< BasisType > &	basis1,
		const RolyComplBasisFace &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Computes the Gram Matrix of a RolyCompl basis and a tangent basis.

Parameters

F	Face 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() [42/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const TangentFamily< BasisType1 > &	basis1,
		const CurlBasis< BasisType2 > &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Generic template to compute the Gram Matrix of a Tangent basis and a Curl basis.

Parameters

F	Face 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() [43/44]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const TangentFamily< BasisType1 > &	basis1,
		const TangentFamily< BasisType2 > &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

Computes the Gram Matrix of a pair of tangent bases.

Parameters

F	Face 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() [44/44]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrix	(	const Face &	F,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face 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

GramMatrixCurl() [1/4]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrixCurl	(	const Cell &	T,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of the curl of any 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 the bases

GramMatrixCurl() [2/4]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrixCurl	(	const Cell &	T,
		const BasisType1 &	basis1,
		const CurlBasis< BasisType2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of the curl of any two bases when one CurlBasis is at a lower level than the other.

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 the bases

GramMatrixCurl() [3/4]

template<typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixCurl	(	const Cell &	T,
		const GolyComplBasisCell &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of a Curl<GolyCompl> basis and a tensorized scalar basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (GolyCompl 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

GramMatrixCurl() [4/4]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixCurl	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of a Curl<Tensorized> basis and a tensorized scalar basis.

Parameters

T	Cell to which the basis corresponds
basis1	First basis (tensorized 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

GramMatrixCurlCurl() [1/5]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrixCurlCurl	(	const Cell &	T,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

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

Parameters

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

GramMatrixCurlCurl() [2/5]

Eigen::MatrixXd HArDCore3D::GramMatrixCurlCurl	(	const Cell &	T,
		const GolyComplBasisCell &	basis1,
		const GolyComplBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Compute the Gram Matrix of the curl of a GolyCompl basis and the curl of another GolyCompl basis.

Parameters

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

GramMatrixCurlCurl() [3/5]

template<typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixCurlCurl	(	const Cell &	T,
		const GolyComplBasisCell &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

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

Parameters

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

GramMatrixCurlCurl() [4/5]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixCurlCurl	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const GolyComplBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

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

Parameters

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

GramMatrixCurlCurl() [5/5]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixCurlCurl	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

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

Parameters

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

GramMatrixDiv() [1/7]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::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() [2/7]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrixDiv	(	const Cell &	T,
		const BasisType1 &	basis1,
		const DivergenceBasis< BasisType2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of the divergence of any two bases when one DivergenceBasis is at a lower level than the other.

Parameters

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

GramMatrixDiv() [3/7]

Eigen::MatrixXd HArDCore3D::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 (scalar basis)
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of basis1 and basis2

GramMatrixDiv() [4/7]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixDiv	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	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

GramMatrixDiv() [5/7]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrixDiv	(	const Face &	F,
		const BasisType1 &	basis1,
		const BasisType2 &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face 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() [6/7]

Eigen::MatrixXd HArDCore3D::GramMatrixDiv	(	const Face &	F,
		const RolyComplBasisFace &	basis1,
		const MonomialScalarBasisFace &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

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

GramMatrixDiv() [7/7]

template<typename BasisType1 >

Eigen::MatrixXd HArDCore3D::GramMatrixDiv	(	const Face &	F,
		const TangentFamily< BasisType1 > &	basis1,
		const MonomialScalarBasisFace &	basis2,
		MonomialFaceIntegralsType	mono_int_map = {}
	)

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

Parameters

F	Face 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

GramMatrixDivDiv() [1/5]

template<typename BasisType1 , typename BasisType2 >

Eigen::MatrixXd HArDCore3D::GramMatrixDivDiv	(	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 the divergence of 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 the bases

GramMatrixDivDiv() [2/5]

Eigen::MatrixXd HArDCore3D::GramMatrixDivDiv	(	const Cell &	T,
		const RolyComplBasisCell &	basis1,
		const RolyComplBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Compute the Gram Matrix of the divergence of a RolyCompl basis and the divergence of another RolyCompl 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 the bases

GramMatrixDivDiv() [3/5]

template<typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixDivDiv	(	const Cell &	T,
		const RolyComplBasisCell &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of the divergence of a RolyCompl basis and the divergence of a tensorized 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 the bases

GramMatrixDivDiv() [4/5]

template<typename BasisType1 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixDivDiv	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const RolyComplBasisCell &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of the divergence of a tensorized basis and the divergence of a RolyCompl 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 the bases

GramMatrixDivDiv() [5/5]

template<typename BasisType1 , typename BasisType2 , size_t N>

Eigen::MatrixXd HArDCore3D::GramMatrixDivDiv	(	const Cell &	T,
		const TensorizedVectorFamily< BasisType1, N > &	basis1,
		const TensorizedVectorFamily< BasisType2, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Template to compute the Gram Matrix of the divergence of a tensorized basis and the divergence of another tensorized 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 the bases

init()

void QuadRuleTetra::init ( )

protected

IntegrateCellMonomials()

MonomialCellIntegralsType HArDCore3D::IntegrateCellMonomials	(	const Cell &	T,
		const int	maxdeg
	)

Compute all the integrals of a cell's monomials on the cell.

Parameters

T	Cell
maxdeg	Maximal total degree

IntegrateCellMonomials_onEdges()

std::vector< MonomialCellIntegralsType > HArDCore3D::IntegrateCellMonomials_onEdges	(	const Cell &	T,
		const size_t	maxdeg
	)

Compute all the integrals, on the edges of a cell, of this cell's monomials up to a max degree.

Parameters

T	Cell
maxdeg	Maximal total degree

IntegrateCellMonomials_onFaces()

std::vector< MonomialCellIntegralsType > HArDCore3D::IntegrateCellMonomials_onFaces	(	const Cell &	T,
		const size_t	maxdeg,
		std::vector< MonomialCellIntegralsType > &	integrals_edges
	)

Compute all the integrals, on the faces of a cell, of this cell's monomials up to a max degree.

Parameters

T	Cell
maxdeg	Maximal total degree
integrals_edges	List of integrals of the monomials over the edges

IntegrateEdgeMonomials()

MonomialEdgeIntegralsType HArDCore3D::IntegrateEdgeMonomials	(	const Edge &	E,
		const int	maxdeg
	)

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

Parameters

E	Edge
maxdeg	Maximal total degree

IntegrateFaceMonomials()

MonomialFaceIntegralsType HArDCore3D::IntegrateFaceMonomials	(	const Face &	F,
		const int	maxdeg
	)

Compute all integrals on a face of face monomials up to a total degree.

Parameters

F	Face
maxdeg	Maximal total degree

IntegrateFaceMonomials_onEdges()

std::vector< MonomialFaceIntegralsType > HArDCore3D::IntegrateFaceMonomials_onEdges	(	const Face &	F,
		const size_t	maxdeg
	)

Compute all integrals, on the edges of a face, of the face monomials up to a total degree.

Parameters

F	Face
maxdeg	Maximal total degree

LegendreGauss()

LegendreGauss::LegendreGauss

(

size_t

doe

)

npts()

size_t LegendreGauss::npts

(

)

nq() [1/3]

size_t QuadRuleEdge::nq

(

)

nq() [2/3]

size_t QuadRuleTriangle::nq

(

)

nq() [3/3]

size_t HArDCore3D::QuadRuleTetra::nq ( ) const

inline

operator()() [1/2]

size_t HArDCore3D::VecFaceHash::operator() ( const Eigen::Vector2i &  p ) const

inline

operator()() [2/2]

size_t HArDCore3D::VecHash::operator() ( const VectorZd &  p ) const

inline

parallelipiped_volume_3d()

double HArDCore3D::parallelipiped_volume_3d	(	double	x[4],
		double	y[4],
		double	z[4]
	)

QuadratureNode()

HArDCore3D::QuadratureNode::QuadratureNode ( double  x, double  y, double  z, double  w  )

inline

QuadRuleEdge()

QuadRuleEdge::QuadRuleEdge	(	size_t	doe,
		bool	warn
	)

QuadRuleTetra() [1/2]

QuadRuleTetra::QuadRuleTetra

(

size_t

_rule = 0

)

QuadRuleTetra() [2/2]

QuadRuleTetra::QuadRuleTetra	(	size_t	doe,
		bool	warn
	)

Create a quadrature rule with at least the given degree of exactness (if available).

The smallest such quadrature rule will be chosen. If none are available, the highest degree available will be used.

QuadRuleTriangle()

QuadRuleTriangle::QuadRuleTriangle	(	size_t	_doe,
		bool	warn
	)

Default constructor.

Parameters

doe	degrees of exactness (e.g. how many points for approximating integral
warn

required_rule()

size_t QuadRuleTetra::required_rule ( size_t  doe ) const

protected

Compute the minimum rule required to achieve the desired degree of exactness.

If no such rule exists, returns the highest rule.

setup() [1/3]

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

setup() [2/3]

void QuadRuleTriangle::setup	(	double	xV[],
		double	yV[],
		double	zV[]
	)

setup() [3/3]

void QuadRuleTetra::setup	(	double(&)	_xV[4],
		double(&)	_yV[4],
		double(&)	_zV[4]
	)

slice() [1/2]

MatrixSlice HArDCore3D::slice	(	Scalar3Tensor &	tensor,
		size_t	fixed_dim,
		size_t	index
	)

Function to slice a 3-tensor with respect to one index (returns a 2-tensor)

Slicing is always in order e.g. fixing the index 1 at 5, returns matrix[i][k] = tensor[i][5][k]. The output is an Eigen::Map of the tensor (so accessing the values of the 2-tensor actually access the values of the original 3-tensor)

Parameters

tensor	Tensor to slice
fixed_dim	Position of the index (0, 1, 2) with respect to which we slice (fix the value)
index	Value of the index where the slicing is done

slice() [2/2]

VectorSlice HArDCore3D::slice	(	Scalar3Tensor &	tensor,
		size_t	fixed_dim1,
		size_t	index1,
		size_t	fixed_dim2,
		size_t	index2
	)

Function to slice a 3-tensor with respect to two indices (returns a 1-tensor)

See comment in the other slice function

Parameters

tensor	Tensor to slice
fixed_dim1	Position of the first index (0, 1, 2) with respect to which we slice (fix the value)
index1	Value of the first index to fix
fixed_dim2	Position of the second index (0, 1, 2) with respect to which we slice (fix the value)
index2	Value of the second index to fix

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

(

)

tetra_sum()

double HArDCore3D::tetra_sum	(	double	funcdouble x, double y, double z,
		double	x[4],
		double	y[4],
		double	z[4],
		int	nq,
		double	cq0[],
		double	cq1[],
		double	cq2[],
		double	wq[]
	)

tetra_unit_set()

void HArDCore3D::tetra_unit_set	(	size_t	rule,
		size_t	nq,
		double	cq0[],
		double	cq1[],
		double	cq2[],
		double	wq[]
	)

tetra_unit_size()

size_t HArDCore3D::tetra_unit_size

(

size_t

rule

)

tetra_unit_sum()

double HArDCore3D::tetra_unit_sum	(	double	funcdouble x, double y, double z,
		size_t	nq,
		double	xq[],
		double	yq[],
		double	zq[],
		double	wq[]
	)

tetra_unit_volume()

double HArDCore3D::tetra_unit_volume

(

)

tetra_volume()

double HArDCore3D::tetra_volume	(	double	x[4],
		double	y[4],
		double	z[4]
	)

tq()

double LegendreGauss::tq

(

size_t

i

)

transformGM() [1/3]

template<typename BasisType >

Eigen::MatrixXd HArDCore3D::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 HArDCore3D::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 HArDCore3D::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

tripleInt() [1/11]

template<typename BasisType , typename ScalarBasisType , size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const BasisType &	basis1,
		const TensorizedVectorFamily< Family< ScalarBasisType >, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Handles a derived basis (see other functions for detailed output)

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 the bases

tripleInt() [2/11]

template<typename BasisType1 , typename BasisType2 >

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const BasisType1 &	basis1,
		const Family< BasisType2 > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Handles a derived basis (see other functions for detailed output)

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 the bases

tripleInt() [3/11]

template<typename BasisType , typename ScalarBasisType , size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const Family< BasisType > &	basis1,
		const Family< TensorizedVectorFamily< ScalarBasisType, N > > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Handles a derived basis (see other functions for detailed output)

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 the bases

tripleInt() [4/11]

template<typename BasisType , size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const Family< BasisType > &	basis1,
		const TensorizedVectorFamily< MonomialScalarBasisCell, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Handles a derived basis (see other functions for detailed output)

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 the bases

tripleInt() [5/11]

template<size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const GolyComplBasisCell &	golycompl_basis,
		const TensorizedVectorFamily< MonomialScalarBasisCell, N > &	tens_family,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Computes the triple integral product of a vector basis dot the cross product of the second vector basis - golycompl_basis . (tens_family x tens_family).

If golycompl_basis = \((\phi_i)_i\) and tens_family= \((\psi_j)_j\), then this function returns the tensor \(T_{ijk}=\int_T \phi_i\cdot(\psi_j\times\psi_k)\).

Parameters

T	Cell to which the basis corresponds
golycompl_basis	First basis
tens_family	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

tripleInt() [6/11]

template<size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const GradientBasis< MonomialScalarBasisCell > &	grad_basis,
		const TensorizedVectorFamily< MonomialScalarBasisCell, N > &	tens_family,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Computes the triple integral product of a vector basis dot the cross product of the second vector basis - grad_basis . (tens_family x tens_family).

If grad_basis = \((\phi_i)_i\) and tens_family= \((\psi_j)_j\), then this function returns the tensor \(T_{ijk}=\int_T \phi_i\cdot(\psi_j\times\psi_k)\).

Parameters

T	Cell to which the basis corresponds
grad_basis	First basis
tens_family	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

tripleInt() [7/11]

template<typename ScalarBasisType , typename BasisType >

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const GradientBasis< ShiftedBasis< ScalarBasisType > > &	grad_shift_basis,
		const BasisType &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Handles a derived basis (see other functions for detailed output)

Parameters

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

tripleInt() [8/11]

template<typename ScalarBasisType1 , typename ScalarBasisType2 , size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const GradientBasis< ShiftedBasis< ScalarBasisType1 > > &	grad_shift_basis,
		const TensorizedVectorFamily< Family< ScalarBasisType2 >, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Handles a derived basis (see other functions for detailed output)

Parameters

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

tripleInt() [9/11]

template<size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const MonomialScalarBasisCell &	basis1,
		const TensorizedVectorFamily< MonomialScalarBasisCell, N > &	basis2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Computes the triple integral product of a scalar times the dot product of two vectors - basis1(basis2 . basis2).

If basis1 = \((\phi_i)_i\) and basis2= \((\psi_j)_j\), then this function returns the tensor \(T_{ijk}=\int_T \phi_i(\psi_j\cdot\psi_k)\).

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 the bases

tripleInt() [10/11]

template<size_t N, typename ScalarBasisType >

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const TensorizedVectorFamily< Family< ScalarBasisType >, N > &	tens_family1,
		const TensorizedVectorFamily< MonomialScalarBasisCell, N > &	tens_family2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Handles a derived basis (see other functions for detailed output)

Parameters

T	Cell to which the basis corresponds
tens_family1	First basis
tens_family2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

tripleInt() [11/11]

template<size_t N>

Scalar3Tensor HArDCore3D::tripleInt	(	const Cell &	T,
		const TensorizedVectorFamily< MonomialScalarBasisCell, N > &	tens_family1,
		const TensorizedVectorFamily< MonomialScalarBasisCell, N > &	tens_family2,
		MonomialCellIntegralsType	mono_int_map = {}
	)

Computes the triple integral product of a vector basis dot the cross product of the second vector basis - tens_family1 . (tens_family2 x tens_family2).

If tens_family1 = \((\phi_i)_i\) and tens_family2= \((\psi_j)_j\), then this function returns the tensor \(T_{ijk}=\int_T \phi_i\cdot(\psi_j\times\psi_k)\).

Parameters

T	Cell to which the basis corresponds
tens_family1	First basis
tens_family2	Second basis
mono_int_map	Optional list of integrals of monomials up to the sum of max degree of the bases

useAncestor()

template<typename BasisType >

constexpr bool HArDCore3D::useAncestor ( )

constexpr

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

vector()

Eigen::Vector3d HArDCore3D::QuadratureNode::vector ( ) const

inline

Returns the quadrature point as an Eigen vector.

wq() [1/4]

double HArDCore3D::QuadRuleTetra::wq ( int  iq ) const

inline

wq() [2/4]

double QuadRuleEdge::wq

(

size_t

i

)

wq() [3/4]

double LegendreGauss::wq

(

size_t

i

)

wq() [4/4]

double QuadRuleTriangle::wq

(

size_t

i

)

xq() [1/3]

double HArDCore3D::QuadRuleTetra::xq ( int  iq ) const

inline

xq() [2/3]

double QuadRuleEdge::xq

(

size_t

i

)

xq() [3/3]

double QuadRuleTriangle::xq

(

size_t

i

)

yq() [1/3]

double HArDCore3D::QuadRuleTetra::yq ( int  iq ) const

inline

yq() [2/3]

double QuadRuleEdge::yq

(

size_t

i

)

yq() [3/3]

double QuadRuleTriangle::yq

(

size_t

i

)

zq() [1/3]

double HArDCore3D::QuadRuleTetra::zq ( int  iq ) const

inline

zq() [2/3]

double QuadRuleEdge::zq

(

size_t

i

)

zq() [3/3]

double QuadRuleTriangle::zq

(

size_t

i

)

~LegendreGauss()

LegendreGauss::~LegendreGauss

(

)

~QuadRuleEdge()

QuadRuleEdge::~QuadRuleEdge

(

)

~QuadRuleTriangle()

QuadRuleTriangle::~QuadRuleTriangle

(

)

Variable Documentation

_npts

size_t HArDCore3D::QuadRuleTriangle::_npts

protected

_w

double* HArDCore3D::QuadRuleTriangle::_w

protected

_xy

double* HArDCore3D::QuadRuleTriangle::_xy

protected

cq0

std::vector<double> HArDCore3D::QuadRuleTetra::cq0

protected

cq1

std::vector<double> HArDCore3D::QuadRuleTetra::cq1

protected

cq2

std::vector<double> HArDCore3D::QuadRuleTetra::cq2

protected

cq3

std::vector<double> HArDCore3D::QuadRuleTetra::cq3

protected

cwq

std::vector<double> HArDCore3D::QuadRuleTetra::cwq

protected

MAX_DOE_CELL

constexpr size_t HArDCore3D::MAX_DOE_CELL = 14

staticconstexpr

Maximum degree of the cell quadrature rules.

MAX_DOE_EDGE

constexpr size_t HArDCore3D::MAX_DOE_EDGE = 20

staticconstexpr

Maximum degree of the edge quadrature rules.

MAX_DOE_FACE

constexpr size_t HArDCore3D::MAX_DOE_FACE = 20

staticconstexpr

Maximum degree of the face quadrature rules.

nqn

const size_t HArDCore3D::QuadRuleTetra::nqn

protected

num_rules

constexpr size_t HArDCore3D::QuadRuleTetra::num_rules = 15

staticconstexprprotected

qswg

double* HArDCore3D::QuadRuleTriangle::qswg

protected

qsx

double* HArDCore3D::QuadRuleTriangle::qsx

protected

qsy

double* HArDCore3D::QuadRuleTriangle::qsy

protected

qsz

double* HArDCore3D::QuadRuleTriangle::qsz

protected

rule

const size_t HArDCore3D::QuadRuleTetra::rule

protected

vol_T

double HArDCore3D::QuadRuleTetra::vol_T

protected

w

double HArDCore3D::QuadratureNode::w

x

double HArDCore3D::QuadratureNode::x

xV

std::vector<double> HArDCore3D::QuadRuleTetra::xV

protected

y

double HArDCore3D::QuadratureNode::y

yV

std::vector<double> HArDCore3D::QuadRuleTetra::yV

protected

z

double HArDCore3D::QuadratureNode::z

zV

std::vector<double> HArDCore3D::QuadRuleTetra::zV

protected