DDRCore

Classes providing tools to the Discrete De Rham sequence. More...

Classes
class	HArDCore2D::DDRCore
	Construct all polynomial spaces for the DDR sequence. More...
struct	HArDCore2D::DDRCore::CellBases
	Structure to store element bases. More...
struct	HArDCore2D::DDRCore::EdgeBases
	Structure to store edge bases. More...
class	HArDCore2D::EXCurl
	Extended XCurl space, with vector-valued polynomials on the edges. More...
struct	HArDCore2D::EXCurl::hhoLocalOperators
	A structure to store the local HHO operators. More...
class	HArDCore2D::SerendipityProblem
	Construct all polynomial spaces for the DDR sequence. More...
class	HArDCore2D::SXGrad
	Discrete Serendipity Hgrad space: local operators, L2 product and global interpolator. More...
struct	HArDCore2D::SXGrad::TransferOperators
	A structure to store the serendipity, extension and reduction operators. More...
class	HArDCore2D::VSXGrad
	Vector version of sXgrad, the arbitrary order space with nodal primal unknowns. More...
struct	HArDCore2D::VSXGrad::LocalOperators
struct	HArDCore2D::VSXGrad::CellBases
struct	HArDCore2D::VSXGrad::EdgeBases
class	HArDCore2D::XCurl
	Discrete Hcurl space: local operators, L2 product and global interpolator. More...
struct	HArDCore2D::XCurl::LocalOperators
	A structure to store the local operators (curl and potential) More...
class	HArDCore2D::XGrad
	Discrete H1 space: local operators, L2 product and global interpolator. More...
struct	HArDCore2D::XGrad::LocalOperators
	A structure to store local operators (gradient and potential) More...
class	HArDCore2D::XHess
	Discrete H2 space: local operators, L2 product and global interpolator. More...
struct	HArDCore2D::XHess::LocalOperators
	A structure to store local operators (gradient and potential) More...
struct	HArDCore2D::XHess::TransferOperators
class	HArDCore2D::XRot
	Discrete H1 space: local operators, L2 product and global interpolator. More...
struct	HArDCore2D::XRot::LocalOperators
	A structure to store local operators (vector rotor and potential) More...
class	HArDCore2D::XRotRot
	Discrete HRotRot space: local operators, L2 product and global interpolator. More...
struct	HArDCore2D::XRotRot::LocalOperators
	A structure to store the local operators (scalar rotor and potential) More...

Typedefs
typedef Family< MonomialScalarBasisCell >	HArDCore2D::DDRCore::PolyBasisCellType
typedef TensorizedVectorFamily< PolyBasisCellType, 2 >	HArDCore2D::DDRCore::Poly2BasisCellType
typedef Family< GradientBasis< ShiftedBasis< MonomialScalarBasisCell > > >	HArDCore2D::DDRCore::GolyBasisCellType
typedef Family< GolyComplBasisCell >	HArDCore2D::DDRCore::GolyComplBasisCellType
typedef Family< CurlBasis< ShiftedBasis< MonomialScalarBasisCell > > >	HArDCore2D::DDRCore::RolyBasisCellType
typedef Family< RolyComplBasisCell >	HArDCore2D::DDRCore::RolyComplBasisCellType
typedef Family< MonomialScalarBasisEdge >	HArDCore2D::DDRCore::PolyBasisEdgeType
typedef Cell	HArDCore2D::DDRCore::CellBases::GeometricSupport
	Geometric support.
typedef Edge	HArDCore2D::DDRCore::EdgeBases::GeometricSupport
	Geometric support.
typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	HArDCore2D::EXCurl::FunctionType
typedef MatrixFamily< DDRCore::PolyBasisCellType, dimspace >	HArDCore2D::EXCurl::Polyk2x2Type
typedef TensorizedVectorFamily< DDRCore::PolyBasisCellType, dimspace >	HArDCore2D::EXCurl::Polykpo2Type
typedef RestrictedBasis< DDRCore::PolyBasisCellType >	HArDCore2D::SerendipityProblem::PolylBasisCellType
typedef RestrictedBasis< DDRCore::RolyComplBasisCellType >	HArDCore2D::SerendipityProblem::RolyCompllpoBasisCellType
typedef Eigen::FullPivLU< Eigen::MatrixXd >	HArDCore2D::SerendipityProblem::InverseProblem
	Type for inverses of matrix for serendipity problem.
typedef std::function< double(const Eigen::Vector2d &)>	HArDCore2D::SXGrad::FunctionType
typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	HArDCore2D::VSXGrad::FunctionType
typedef Family< MonomialScalarBasisCell >	HArDCore2D::VSXGrad::PolyBasisCellType
typedef TensorizedVectorFamily< DDRCore::PolyBasisCellType, dimspace >	HArDCore2D::VSXGrad::Poly2BasisCellType
typedef MatrixFamily< DDRCore::PolyBasisCellType, dimspace >	HArDCore2D::VSXGrad::Poly2x2BasisCellType
typedef Family< MonomialScalarBasisEdge >	HArDCore2D::VSXGrad::PolyBasisEdgeType
typedef TensorizedVectorFamily< DDRCore::PolyBasisEdgeType, dimspace >	HArDCore2D::VSXGrad::Poly2BasisEdgeType
typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	HArDCore2D::XCurl::FunctionType
typedef std::function< double(const Eigen::Vector2d &)>	HArDCore2D::XGrad::FunctionType
typedef std::function< double(const Eigen::Vector2d &)>	HArDCore2D::XHess::FunctionType
typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	HArDCore2D::XHess::GradFunctionType
typedef std::function< double(const Eigen::Vector2d &)>	HArDCore2D::XRot::FunctionType
typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	HArDCore2D::XRotRot::FunctionType
typedef std::function< double(const Eigen::Vector2d &)>	HArDCore2D::XRotRot::RotType

Functions
	HArDCore2D::DDRCore::DDRCore (const Mesh &mesh, size_t K, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::DDRCore::mesh () const
	Return a const reference to the mesh.
const size_t &	HArDCore2D::DDRCore::degree () const
	Return the polynomial degree.
const CellBases &	HArDCore2D::DDRCore::cellBases (size_t iT) const
	Return cell bases for element iT.
const EdgeBases &	HArDCore2D::DDRCore::edgeBases (size_t iE) const
	Return edge bases for edge iE.
	HArDCore2D::EXCurl::hhoLocalOperators::hhoLocalOperators (const Eigen::MatrixXd &_gradient, const Eigen::MatrixXd &_symmetric_gradient, const Eigen::MatrixXd &_potential, const Eigen::MatrixXd &_stabilisation)
	HArDCore2D::EXCurl::EXCurl (const DDRCore &ddr_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::EXCurl::mesh () const
	Return the mesh.
const size_t &	HArDCore2D::EXCurl::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::EXCurl::interpolate (const FunctionType &v, const int deg_quad=-1) const
	Interpolator of a continuous function.
const Eigen::MatrixXd	HArDCore2D::EXCurl::ddrPotential (size_t iT) const
	Return cell potential for the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::EXCurl::ddrCurl (size_t iT) const
	Return cell (scalar) curl for the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::EXCurl::ddrPotential (const Cell &T) const
	Return cell potential for cell T.
const Eigen::MatrixXd	HArDCore2D::EXCurl::ddrCurl (const Cell &T) const
	Return cell (scalar) curl for cell T.
const hhoLocalOperators &	HArDCore2D::EXCurl::hhoOperators (size_t iT) const
	Return hho operators for the cell of index iT.
const hhoLocalOperators &	HArDCore2D::EXCurl::hhoOperators (const Cell &T) const
	Return cell operators for cell T.
const DDRCore::CellBases &	HArDCore2D::EXCurl::cellBases (size_t iT) const
	Return ddrcore cell bases for the cell of index iT.
const DDRCore::CellBases &	HArDCore2D::EXCurl::cellBases (const Cell &T) const
	Return ddrcore cell bases for cell T.
const Polyk2x2Type &	HArDCore2D::EXCurl::Polyk2x2 (size_t iT) const
	Return basis for Matricial P^k space.
const Polykpo2Type &	HArDCore2D::EXCurl::Polykpo2 (size_t iT) const
	Return basis for the (P^{k+1})^2 space.
const DDRCore::EdgeBases &	HArDCore2D::EXCurl::edgeBases (size_t iE) const
	Return ddrcore edge bases for the edge of index iE.
const DDRCore::EdgeBases &	HArDCore2D::EXCurl::edgeBases (const Edge &E) const
	Return ddrcore edge bases for edge E.
Eigen::MatrixXd	HArDCore2D::EXCurl::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk2_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product for the cell of index iT.
Eigen::MatrixXd	HArDCore2D::EXCurl::computeL2ProductGradient (const size_t iT, const XGrad &x_grad, const std::string &side, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk2_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product as 'computeL2Product', with application of the discrete gradient on the left/right/both sides (depending on argument "side").
Eigen::MatrixXd	HArDCore2D::EXCurl::computeL2Product_with_Ops (const size_t iT, const std::vector< Eigen::MatrixXd > &leftOp, const std::vector< Eigen::MatrixXd > &rightOp, const double &penalty_factor, const Eigen::MatrixXd &w_mass_Pk2_T, const IntegralWeight &weight) const
	Compute the matrix of the L2 product, applying leftOp and rightOp to the variables. Probably not directly called, mostly invoked through the wrappers computeL2Product and computeL2ProductGradient.
	HArDCore2D::SerendipityProblem::SerendipityProblem (const DDRCore &ddrcore, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const std::vector< size_t > &	HArDCore2D::SerendipityProblem::serendipityEdges (size_t iT) const
	Return the list of serendipity edges in a cell.
const int	HArDCore2D::SerendipityProblem::n_serendipityEdges (size_t iT) const
	Return the number of serendipity edges in a cell.
const int	HArDCore2D::SerendipityProblem::serDegreeCell (size_t iT) const
	Return the serendipity degree ell_T in a cell.
size_t	HArDCore2D::SerendipityProblem::dimCellPolyl (size_t iT) const
	Return the dimension of P^l on cell of index iT.
size_t	HArDCore2D::SerendipityProblem::dimCellPolyl (const Cell &T) const
	Return the dimension of P^{l+1} on cell T.
const PolylBasisCellType &	HArDCore2D::SerendipityProblem::cellBasisPolyl (size_t iT) const
	Return the basis of P^l on cell of index iT.
const PolylBasisCellType &	HArDCore2D::SerendipityProblem::cellBasisPolyl (const Cell &T) const
	Return the basis of P^l on cell T.
Eigen::VectorXd	HArDCore2D::SerendipityProblem::nDOFs_cells_SXGrad () const
	Number of DOFs on cells for serendipity XGrad space.
size_t	HArDCore2D::SerendipityProblem::dimCellRolyCompllpo (size_t iT) const
	Return the dimension of R^{c,l+1} on cell of index iT.
size_t	HArDCore2D::SerendipityProblem::dimCellRolyCompllpo (const Cell &T) const
	Return the dimension of R^{c,l+1} on cell T.
const RolyCompllpoBasisCellType &	HArDCore2D::SerendipityProblem::cellBasisRolyCompllpo (size_t iT) const
	Return the basis of R^{c,l+1} on cell of index iT.
const RolyCompllpoBasisCellType &	HArDCore2D::SerendipityProblem::cellBasisRolyCompllpo (const Cell &T) const
	Return the basis of R^{c,l+1} on cell T.
Eigen::VectorXd	HArDCore2D::SerendipityProblem::nDOFs_cells_SXCurl () const
	Number of DOFs on cells for serendipity XCurl space.
Eigen::VectorXd	HArDCore2D::SerendipityProblem::nDOFs_cells_SXRotRot () const
	Number of DOFs on cells for serendipity XRotRot space.
const Eigen::MatrixXd	HArDCore2D::SerendipityProblem::SerendipityOperatorCell (const size_t iT, const Eigen::MatrixXd &LT) const
	Compute the serendipity operator on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::SerendipityProblem::SerendipityOperatorCell (const Cell &T, const Eigen::MatrixXd &LT) const
	Compute the serendipity operator on the Cell T.
const Mesh &	HArDCore2D::SerendipityProblem::mesh () const
	Return a const reference to the mesh.
const DDRCore &	HArDCore2D::SerendipityProblem::ddrCore () const
	Return a const reference to the underlying DDR core.
	HArDCore2D::SXGrad::TransferOperators::TransferOperators (const Eigen::MatrixXd &_serendipity, const Eigen::MatrixXd &_extension, const Eigen::MatrixXd &_reduction)
	HArDCore2D::SXGrad::SXGrad (const DDRCore &ddr_core, const SerendipityProblem &ser_pro, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::SXGrad::mesh () const
	Return the mesh.
const size_t &	HArDCore2D::SXGrad::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::SXGrad::interpolate (const FunctionType &q, const int deg_quad=-1) const
const Eigen::MatrixXd &	HArDCore2D::SXGrad::SgradCell (size_t iT) const
	Return the serendipity reconstruction for the cell of index iT.
const Eigen::MatrixXd &	HArDCore2D::SXGrad::EgradCell (size_t iT) const
	Return the extension for the cell of index iT.
const Eigen::MatrixXd &	HArDCore2D::SXGrad::RgradCell (size_t iT) const
	Return the reduction for the cell of index iT.
const Eigen::MatrixXd &	HArDCore2D::SXGrad::SgradCell (const Cell &T) const
	Return the serendipity reconstruction for cell T.
const Eigen::MatrixXd &	HArDCore2D::SXGrad::EgradCell (const Cell &T) const
	Return the extension for cell T.
const Eigen::MatrixXd &	HArDCore2D::SXGrad::RgradCell (const Cell &T) const
	Return the reduction for cell T.
const TransferOperators &	HArDCore2D::SXGrad::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const TransferOperators &	HArDCore2D::SXGrad::cellOperators (const Cell &T) const
	Return cell operators for cell T.
const Eigen::MatrixXd	HArDCore2D::SXGrad::edgeGradient (size_t iE) const
	Return the full gradient operator on the edge of index iE.
const Eigen::MatrixXd	HArDCore2D::SXGrad::edgeGradient (const Edge &E) const
	Return the full gradient operator on edge E.
const Eigen::MatrixXd	HArDCore2D::SXGrad::edgePotential (size_t iE) const
	Return the potential operator on the edge of index iE.
const Eigen::MatrixXd	HArDCore2D::SXGrad::edgePotential (const Edge &E) const
	Return the potential operator on edge E.
const Eigen::MatrixXd	HArDCore2D::SXGrad::cellGradient (size_t iT) const
	Return the full gradient operator on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::SXGrad::cellGradient (const Cell &T) const
	Return the full gradient operator on cell T.
const Eigen::MatrixXd	HArDCore2D::SXGrad::cellPotential (size_t iT) const
	Return the potential operator on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::SXGrad::cellPotential (const Cell &T) const
	Return the potential operator on cell T.
Eigen::MatrixXd	HArDCore2D::SXGrad::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk2_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product.
double	HArDCore2D::SXGrad::computeL2Norm (const Eigen::VectorXd &v) const
	Compute the L2-norm of a vector of the space.
Eigen::MatrixXd	HArDCore2D::SXGrad::computeStabilisation (const size_t iT, const IntegralWeight &weight=IntegralWeight(1.)) const
	Computes only the stabilisation matrix of the (weighted) L2-product for the cell of index iT.
std::vector< double >	HArDCore2D::SXGrad::computeVertexValues (const Eigen::VectorXd &u) const
	Computes the values of the potential reconstruction at the mesh vertices.
const DDRCore::CellBases &	HArDCore2D::SXGrad::cellBases (size_t iT) const
	Return cell bases for the cell of index iT.
const DDRCore::CellBases &	HArDCore2D::SXGrad::cellBases (const Cell &T) const
	Return cell bases for cell T.
const DDRCore::EdgeBases &	HArDCore2D::SXGrad::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.
const DDRCore::EdgeBases &	HArDCore2D::SXGrad::edgeBases (const Edge &E) const
	Return edge bases for edge E.
	HArDCore2D::VSXGrad::LocalOperators::LocalOperators (const Eigen::MatrixXd &_rot, const Eigen::MatrixXd &_potential)
	HArDCore2D::VSXGrad::VSXGrad (const DDRCore &ddr_core, const SerendipityProblem &sp, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::VSXGrad::mesh () const
	Return the mesh.
const SXGrad &	HArDCore2D::VSXGrad::sXgrad () const
	Return the underlying sXgrad space.
const size_t &	HArDCore2D::VSXGrad::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::VSXGrad::interpolate (const FunctionType &q, const int doe_cell=-1) const
	Interpolator of a continuous function.
auto	HArDCore2D::VSXGrad::PolykE (size_t iE) const -> const PolyBasisEdgeType &
auto	HArDCore2D::VSXGrad::PolykpoE (size_t iE) const -> const PolyBasisEdgeType &
auto	HArDCore2D::VSXGrad::PolykptwoE (size_t iE) const -> const PolyBasisEdgeType &
auto	HArDCore2D::VSXGrad::Polykpo (size_t iT) const -> const PolyBasisCellType &
auto	HArDCore2D::VSXGrad::Polykmo (size_t iT) const -> const PolyBasisCellType &
auto	HArDCore2D::VSXGrad::Polyk (size_t iT) const -> const PolyBasisCellType &
auto	HArDCore2D::VSXGrad::Polykptwo (size_t iT) const -> const PolyBasisCellType &
auto	HArDCore2D::VSXGrad::Polyk2 (size_t iT) const -> const Poly2BasisCellType &
const Eigen::MatrixXd	HArDCore2D::VSXGrad::edgeGradient (size_t iE) const
	Return the gradient operator (expressed on Polyk3) on the edge of index iE.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::edgeGradient (const Edge &E) const
	Return the gradient operator (expressed on Polyk3) on edge E.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::edgePotential (size_t iE) const
	Return the potential operator (expressed on Polykpo3) on the edge of index iE.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::edgePotential (const Edge &E) const
	Return the potential operator (expressed on Polykpo3) on edge E.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellGradient (size_t iT) const
	Return the gradient operator (expressed on Polyk3x3) on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellGradient (const Cell &T) const
	Return the gradient operator (expressed on Polyk3x3) on cell T.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellSymGradient (size_t iT) const
	Return the symmetric gradient operator (expressed on Polyk3x3) on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellSymGradient (const Cell &T) const
	Return the symmetric gradient operator (expressed on Polyk3x3) on cell T.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellDivergence (size_t iT) const
	Return the divergence operator (expressed on the ancester of Polyk3x3, which should be m_sxgrad.cellBases(iT).Polyk) on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellDivergence (const Cell &T) const
	Return the divergence operator (expressed on the ancester of Polyk3x3, which should be m_sxgrad.cellBases(iT).Polyk) on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellPotential (size_t iT) const
	Return the potential operator (expressed on Polykpo3) on the cell of index iT.
const Eigen::MatrixXd	HArDCore2D::VSXGrad::cellPotential (const Cell &T) const
	Return the potential operator on cell T.
Eigen::MatrixXd	HArDCore2D::VSXGrad::_permute_bases (size_t iT)
Eigen::MatrixXd	HArDCore2D::VSXGrad::computeStabilisation (const size_t iT, const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the H^1-stabilisation (based on the L^2 stabilisation implemented in SXgrad)
std::vector< double >	HArDCore2D::VSXGrad::computeH1norms (const std::vector< Eigen::VectorXd > &list_dofs, const std::string typegrad="full") const
	Compute the H^1 discrete norm, with full or symmetric gradient.
std::vector< VectorRd >	HArDCore2D::VSXGrad::computeVertexValues (const Eigen::VectorXd &u) const
	Computes the values of the potential reconstruction at the mesh vertices.
const CellBases &	HArDCore2D::VSXGrad::cellBases (size_t iT) const
	Return vector/matrix cell bases for the face of index iT.
const CellBases &	HArDCore2D::VSXGrad::cellBases (const Cell &T) const
	Return vector/matrix cell bases for cell T.
const EdgeBases &	HArDCore2D::VSXGrad::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.
const EdgeBases &	HArDCore2D::VSXGrad::edgeBases (const Edge &E) const
	Return edge bases for edge E.
const LocalOperators &	HArDCore2D::VSXGrad::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const LocalOperators &	HArDCore2D::VSXGrad::cellOperators (const Cell &T) const
	Return cell operators for cell T.
	HArDCore2D::XCurl::LocalOperators::LocalOperators (const Eigen::MatrixXd &_curl, const Eigen::MatrixXd &_potential)
	HArDCore2D::XCurl::XCurl (const DDRCore &ddr_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::XCurl::mesh () const
	Return the mesh.
const size_t &	HArDCore2D::XCurl::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::XCurl::interpolate (const FunctionType &v, const int deg_quad=-1) const
	Interpolator of a continuous function.
const LocalOperators &	HArDCore2D::XCurl::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const LocalOperators &	HArDCore2D::XCurl::cellOperators (const Cell &T) const
	Return cell operators for cell T.
const DDRCore::CellBases &	HArDCore2D::XCurl::cellBases (size_t iT) const
	Return cell bases for the cell of index iT.
const DDRCore::CellBases &	HArDCore2D::XCurl::cellBases (const Cell &T) const
	Return cell bases for cell T.
const DDRCore::EdgeBases &	HArDCore2D::XCurl::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.
const DDRCore::EdgeBases &	HArDCore2D::XCurl::edgeBases (const Edge &E) const
	Return edge bases for edge E.
Eigen::MatrixXd	HArDCore2D::XCurl::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk2_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product for the cell of index iT.
Eigen::MatrixXd	HArDCore2D::XCurl::computeL2ProductGradient (const size_t iT, const XGrad &x_grad, const std::string &side, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pk2_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product as 'computeL2Product', with application of the discrete gradient on the left/right/both sides (depending on argument "side").
Eigen::MatrixXd	HArDCore2D::XCurl::computeL2Product_with_Ops (const size_t iT, const std::vector< Eigen::MatrixXd > &leftOp, const std::vector< Eigen::MatrixXd > &rightOp, const double &penalty_factor, const Eigen::MatrixXd &w_mass_Pk2_T, const IntegralWeight &weight) const
	Compute the matrix of the L2 product, applying leftOp and rightOp to the variables. Probably not directly called, mostly invoked through the wrappers computeL2Product and computeL2ProductGradient.
	HArDCore2D::XGrad::LocalOperators::LocalOperators (const Eigen::MatrixXd &_gradient, const Eigen::MatrixXd &_potential)
	HArDCore2D::XGrad::XGrad (const DDRCore &ddr_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::XGrad::mesh () const
	Return the mesh.
const size_t &	HArDCore2D::XGrad::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::XGrad::interpolate (const FunctionType &q, const int deg_quad=-1) const
	Interpolator of a continuous function.
const LocalOperators &	HArDCore2D::XGrad::edgeOperators (size_t iE) const
	Return edge operators for the edge of index iE.
const LocalOperators &	HArDCore2D::XGrad::edgeOperators (const Edge &E) const
	Return edge operators for edge E.
const LocalOperators &	HArDCore2D::XGrad::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const LocalOperators &	HArDCore2D::XGrad::cellOperators (const Cell &T) const
	Return cell operators for cell T.
const DDRCore::CellBases &	HArDCore2D::XGrad::cellBases (size_t iT) const
	Return cell bases for the cell of index iT.
const DDRCore::CellBases &	HArDCore2D::XGrad::cellBases (const Cell &T) const
	Return cell bases for cell T.
const DDRCore::EdgeBases &	HArDCore2D::XGrad::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.
const DDRCore::EdgeBases &	HArDCore2D::XGrad::edgeBases (const Edge &E) const
	Return edge bases for edge E.
Eigen::MatrixXd	HArDCore2D::XGrad::computeStabilisation (const size_t iT, const IntegralWeight &weight=IntegralWeight(1.)) const
	Computes only the stabilisation matrix of the (weighted) L2-product for the cell of index iT. This stabilisation is based on cell and face potentials.
Eigen::MatrixXd	HArDCore2D::XGrad::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pkpo_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product for the cell of index iT.
double	HArDCore2D::XGrad::evaluatePotential (const size_t iT, const Eigen::VectorXd &vT, const VectorRd &x) const
	Evaluate the value of the potential at a point x.
double	HArDCore2D::XGrad::computeL2Norm (const Eigen::VectorXd &v) const
	Compute the L2-norm of a vector of the space.
	HArDCore2D::XHess::LocalOperators::LocalOperators (const Eigen::MatrixXd &_gradient, const Eigen::MatrixXd &_potential)
	HArDCore2D::XHess::TransferOperators::TransferOperators (const Eigen::MatrixXd &_serendipity)
	HArDCore2D::XHess::XHess (const DDRCore &ddr_core, const SerendipityProblem &ser_pro, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::XHess::mesh () const
	Return the mesh.
const size_t &	HArDCore2D::XHess::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::XHess::interpolate (const FunctionType &q, const GradFunctionType &Dq, const int deg_quad=-1) const
	Interpolator of a continuous function.
const Eigen::MatrixXd &	HArDCore2D::XHess::SgradCell (size_t iT) const
	Return the serendipity reconstruction for the cell of index iT.
const Eigen::MatrixXd &	HArDCore2D::XHess::SgradCell (const Cell &T) const
	Return the serendipity reconstruction for cell T.
const TransferOperators &	HArDCore2D::XHess::TcellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const TransferOperators &	HArDCore2D::XHess::TcellOperators (const Cell &T) const
	Return cell operators for cell T.
const LocalOperators &	HArDCore2D::XHess::edgeOperators (size_t iE) const
	Return edge operators for the edge of index iE.
const LocalOperators &	HArDCore2D::XHess::edgeOperators (const Edge &E) const
	Return edge operators for edge E.
const LocalOperators &	HArDCore2D::XHess::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const LocalOperators &	HArDCore2D::XHess::cellOperators (const Cell &T) const
	Return cell operators for cell T.
const DDRCore::CellBases &	HArDCore2D::XHess::cellBases (size_t iT) const
	Return cell bases for the cell of index iT.
const DDRCore::CellBases &	HArDCore2D::XHess::cellBases (const Cell &T) const
	Return cell bases for cell T.
const DDRCore::EdgeBases &	HArDCore2D::XHess::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.
const DDRCore::EdgeBases &	HArDCore2D::XHess::edgeBases (const Edge &E) const
	Return edge bases for edge E.
Eigen::MatrixXd	HArDCore2D::XHess::computeL2Product (const size_t iT, const double &penalty_factor=1., const Eigen::MatrixXd &mass_Pkpo_T=Eigen::MatrixXd::Zero(1, 1), const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product for the cell of index iT.
double	HArDCore2D::XHess::evaluatePotential (const size_t iT, const Eigen::VectorXd &vT, const VectorRd &x) const
	Evaluate the value of the potential at a point x.
double	HArDCore2D::XHess::computeL2Norm (const Eigen::VectorXd &v) const
	Compute the L2-norm of a vector of the space.
	HArDCore2D::XRot::LocalOperators::LocalOperators (const Eigen::MatrixXd &_rotor, const Eigen::MatrixXd &_rotor_rhs, const Eigen::MatrixXd &_potential)
	HArDCore2D::XRot::XRot (const DDRCore &ddr_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::XRot::mesh () const
	Return the mesh.
const bool	HArDCore2D::XRot::useThreads () const
	Return true if we use thread-based parallelism.
const size_t &	HArDCore2D::XRot::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::XRot::interpolate (const FunctionType &q, const int deg_quad=-1) const
	Interpolator of a continuous function.
const Eigen::MatrixXd &	HArDCore2D::XRot::edgePotential (size_t iE) const
	Return edge potential for the edge of index iE.
const Eigen::MatrixXd &	HArDCore2D::XRot::edgePotential (const Edge &E) const
	Return edge potential for the edge E.
const LocalOperators &	HArDCore2D::XRot::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const LocalOperators &	HArDCore2D::XRot::cellOperators (const Cell &T) const
	Return cell operators for cell T.
const DDRCore::CellBases &	HArDCore2D::XRot::cellBases (size_t iT) const
	Return cell bases for the cell of index iT.
const DDRCore::CellBases &	HArDCore2D::XRot::cellBases (const Cell &T) const
	Return cell bases for cell T.
const DDRCore::EdgeBases &	HArDCore2D::XRot::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.
const DDRCore::EdgeBases &	HArDCore2D::XRot::edgeBases (const Edge &E) const
	Return edge bases for edge E.
Eigen::MatrixXd	HArDCore2D::XRot::computeRotorL2Product (const size_t iT, const double &penalty_factor_cell=1., const double &penalty_factor_edge=1.) const
	Compute rotor L2-product.
double	HArDCore2D::XRot::computeRotorL2Norm (const Eigen::VectorXd &v) const
	Compute rotor L2-norm.
	HArDCore2D::XRotRot::LocalOperators::LocalOperators (const Eigen::MatrixXd &_rotor, const Eigen::MatrixXd &_potential)
	HArDCore2D::XRotRot::XRotRot (const DDRCore &ddr_core, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore2D::XRotRot::mesh () const
	Return the mesh.
const size_t &	HArDCore2D::XRotRot::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore2D::XRotRot::interpolate (const FunctionType &v, const RotType &rot_v, const int deg_quad=-1) const
	Interpolator of a continuous function.
const LocalOperators &	HArDCore2D::XRotRot::cellOperators (size_t iT) const
	Return cell operators for the cell of index iT.
const LocalOperators &	HArDCore2D::XRotRot::cellOperators (const Cell &T) const
	Return cell operators for cell T.
Eigen::MatrixXd	HArDCore2D::XRotRot::cellRotor (size_t iT) const
	Return cell rotor for cell of index iT.
Eigen::MatrixXd	HArDCore2D::XRotRot::cellRotor (const Cell &T) const
	Return cell rotor for cell T.
const DDRCore::CellBases &	HArDCore2D::XRotRot::cellBases (size_t iT) const
	Return cell bases for the cell of index iT.
const DDRCore::CellBases &	HArDCore2D::XRotRot::cellBases (const Cell &T) const
	Return cell bases for cell T.
const DDRCore::EdgeBases &	HArDCore2D::XRotRot::edgeBases (size_t iE) const
	Return edge bases for the edge of index iE.
const DDRCore::EdgeBases &	HArDCore2D::XRotRot::edgeBases (const Edge &E) const
	Return edge bases for edge E.
Eigen::MatrixXd	HArDCore2D::XRotRot::computeL2Product (size_t iT, const double &penalty_factor=1., const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product for the cell of index iT.
Eigen::MatrixXd	HArDCore2D::XRotRot::computeGradientPotentialL2Product (size_t iT, const XGrad *x_grad, const double &penalty_factor=1., const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) L2-product as 'computeL2Product', with application of the discrete gradient on the left side.
Eigen::MatrixXd	HArDCore2D::XRotRot::computeGradientL2Product (size_t iT, const XGrad *x_grad, const double &penalty_factor=1., const IntegralWeight &weight=IntegralWeight(1.)) const
	Compute the matrix of the (weighted) gradient-gradient L2-product.
template<typename LeftOperatorFillerType , typename RightOperatorFillerType >
Eigen::MatrixXd	HArDCore2D::XRotRot::computeL2ProductWithOperatorFillers (size_t iT, const double &penalty_factor, const IntegralWeight &weight, LeftOperatorFillerType fillLeftOp, RightOperatorFillerType fillRightOp) const
	Compute the matrix of the L2 product given operators filling functions.
double	HArDCore2D::XRotRot::computeL2Norm (const Eigen::VectorXd &v) const
	Compute the L2-norm of a vector of the space.
double	HArDCore2D::XRotRot::computeGradientL2Norm (const Eigen::VectorXd &v, const XGrad *x_grad) const
	Compute the L2-norm of the discrete gradient of a vector in XGrad.

Variables
std::unique_ptr< PolyBasisCellType >	HArDCore2D::DDRCore::CellBases::Polykpo
std::unique_ptr< PolyBasisCellType >	HArDCore2D::DDRCore::CellBases::Polyk
std::unique_ptr< PolyBasisCellType >	HArDCore2D::DDRCore::CellBases::Polykmo
std::unique_ptr< PolyBasisCellType >	HArDCore2D::DDRCore::CellBases::Polykmtwo
std::unique_ptr< Poly2BasisCellType >	HArDCore2D::DDRCore::CellBases::Polyk2
std::unique_ptr< Poly2BasisCellType >	HArDCore2D::DDRCore::CellBases::Polykmo2
std::unique_ptr< RolyBasisCellType >	HArDCore2D::DDRCore::CellBases::Rolykmo
std::unique_ptr< RolyComplBasisCellType >	HArDCore2D::DDRCore::CellBases::RolyComplk
std::unique_ptr< RolyComplBasisCellType >	HArDCore2D::DDRCore::CellBases::RolyComplkmo
std::unique_ptr< RolyComplBasisCellType >	HArDCore2D::DDRCore::CellBases::RolyComplkp2
std::unique_ptr< GolyComplBasisCellType >	HArDCore2D::DDRCore::CellBases::GolyComplkp2
std::unique_ptr< PolyBasisEdgeType >	HArDCore2D::DDRCore::EdgeBases::Polykpo
std::unique_ptr< PolyBasisEdgeType >	HArDCore2D::DDRCore::EdgeBases::Polyk
std::unique_ptr< PolyBasisEdgeType >	HArDCore2D::DDRCore::EdgeBases::Polykmo
Eigen::MatrixXd	HArDCore2D::EXCurl::hhoLocalOperators::gradient
Eigen::MatrixXd	HArDCore2D::EXCurl::hhoLocalOperators::symmetric_gradient
Eigen::MatrixXd	HArDCore2D::EXCurl::hhoLocalOperators::potential
Eigen::MatrixXd	HArDCore2D::EXCurl::hhoLocalOperators::stabilisation
Eigen::MatrixXd	HArDCore2D::SXGrad::TransferOperators::serendipity
Eigen::MatrixXd	HArDCore2D::SXGrad::TransferOperators::extension
Eigen::MatrixXd	HArDCore2D::SXGrad::TransferOperators::reduction
Eigen::MatrixXd	HArDCore2D::VSXGrad::LocalOperators::rot
Eigen::MatrixXd	HArDCore2D::VSXGrad::LocalOperators::potential
std::unique_ptr< Poly2BasisCellType >	HArDCore2D::VSXGrad::CellBases::Polykmo2
std::unique_ptr< Poly2BasisCellType >	HArDCore2D::VSXGrad::CellBases::Polykptwo2
std::unique_ptr< Poly2x2BasisCellType >	HArDCore2D::VSXGrad::CellBases::Polykpo2x2
std::unique_ptr< Poly2BasisEdgeType >	HArDCore2D::VSXGrad::EdgeBases::Polykmo2
std::unique_ptr< Poly2BasisEdgeType >	HArDCore2D::VSXGrad::EdgeBases::Polyk2
std::unique_ptr< Poly2BasisEdgeType >	HArDCore2D::VSXGrad::EdgeBases::Polykpo2
std::unique_ptr< Poly2BasisEdgeType >	HArDCore2D::VSXGrad::EdgeBases::Polykptwo2
Eigen::MatrixXd	HArDCore2D::XCurl::LocalOperators::curl
Eigen::MatrixXd	HArDCore2D::XCurl::LocalOperators::potential
Eigen::MatrixXd	HArDCore2D::XGrad::LocalOperators::gradient
Eigen::MatrixXd	HArDCore2D::XGrad::LocalOperators::potential
Eigen::MatrixXd	HArDCore2D::XHess::LocalOperators::gradient
Eigen::MatrixXd	HArDCore2D::XHess::LocalOperators::potential
Eigen::MatrixXd	HArDCore2D::XHess::TransferOperators::serendipity
Eigen::MatrixXd	HArDCore2D::XRot::LocalOperators::rotor
Eigen::MatrixXd	HArDCore2D::XRot::LocalOperators::rotor_rhs
Eigen::MatrixXd	HArDCore2D::XRot::LocalOperators::potential
Eigen::MatrixXd	HArDCore2D::XRotRot::LocalOperators::rotor
Eigen::MatrixXd	HArDCore2D::XRotRot::LocalOperators::potential

Detailed Description

Classes providing tools to the Discrete De Rham sequence.

Typedef Documentation

FunctionType [1/8]

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

FunctionType [2/8]

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

FunctionType [3/8]

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

FunctionType [4/8]

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

FunctionType [5/8]

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

FunctionType [6/8]

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

FunctionType [7/8]

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

FunctionType [8/8]

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

GeometricSupport [1/2]

typedef Cell HArDCore2D::DDRCore::CellBases::GeometricSupport

Geometric support.

GeometricSupport [2/2]

typedef Edge HArDCore2D::DDRCore::EdgeBases::GeometricSupport

Geometric support.

GolyBasisCellType

typedef Family<GradientBasis<ShiftedBasis<MonomialScalarBasisCell> > > HArDCore2D::DDRCore::GolyBasisCellType

GolyComplBasisCellType

typedef Family<GolyComplBasisCell> HArDCore2D::DDRCore::GolyComplBasisCellType

GradFunctionType

typedef std::function<Eigen::Vector2d(const Eigen::Vector2d &)> HArDCore2D::XHess::GradFunctionType

InverseProblem

typedef Eigen::FullPivLU<Eigen::MatrixXd> HArDCore2D::SerendipityProblem::InverseProblem

Type for inverses of matrix for serendipity problem.

Poly2BasisCellType [1/2]

typedef TensorizedVectorFamily<PolyBasisCellType, 2> HArDCore2D::DDRCore::Poly2BasisCellType

Poly2BasisCellType [2/2]

typedef TensorizedVectorFamily<DDRCore::PolyBasisCellType, dimspace> HArDCore2D::VSXGrad::Poly2BasisCellType

Poly2BasisEdgeType

typedef TensorizedVectorFamily<DDRCore::PolyBasisEdgeType, dimspace> HArDCore2D::VSXGrad::Poly2BasisEdgeType

Poly2x2BasisCellType

typedef MatrixFamily<DDRCore::PolyBasisCellType, dimspace> HArDCore2D::VSXGrad::Poly2x2BasisCellType

PolyBasisCellType [1/2]

typedef Family<MonomialScalarBasisCell> HArDCore2D::DDRCore::PolyBasisCellType

PolyBasisCellType [2/2]

typedef Family<MonomialScalarBasisCell> HArDCore2D::VSXGrad::PolyBasisCellType

PolyBasisEdgeType [1/2]

typedef Family<MonomialScalarBasisEdge> HArDCore2D::DDRCore::PolyBasisEdgeType

PolyBasisEdgeType [2/2]

typedef Family<MonomialScalarBasisEdge> HArDCore2D::VSXGrad::PolyBasisEdgeType

Polyk2x2Type

typedef MatrixFamily<DDRCore::PolyBasisCellType, dimspace> HArDCore2D::EXCurl::Polyk2x2Type

Polykpo2Type

typedef TensorizedVectorFamily<DDRCore::PolyBasisCellType, dimspace> HArDCore2D::EXCurl::Polykpo2Type

PolylBasisCellType

typedef RestrictedBasis<DDRCore::PolyBasisCellType > HArDCore2D::SerendipityProblem::PolylBasisCellType

RolyBasisCellType

typedef Family<CurlBasis<ShiftedBasis<MonomialScalarBasisCell> > > HArDCore2D::DDRCore::RolyBasisCellType

RolyComplBasisCellType

typedef Family<RolyComplBasisCell> HArDCore2D::DDRCore::RolyComplBasisCellType

RolyCompllpoBasisCellType

typedef RestrictedBasis<DDRCore::RolyComplBasisCellType > HArDCore2D::SerendipityProblem::RolyCompllpoBasisCellType

RotType

typedef std::function<double(const Eigen::Vector2d &)> HArDCore2D::XRotRot::RotType

Function Documentation

_permute_bases()

Eigen::MatrixXd VSXGrad::_permute_bases

(

size_t

iT

)

cellBases() [1/17]

const DDRCore::CellBases & HArDCore2D::EXCurl::cellBases ( const Cell &  T ) const

inline

Return ddrcore cell bases for cell T.

cellBases() [2/17]

const DDRCore::CellBases & HArDCore2D::SXGrad::cellBases ( const Cell &  T ) const

inline

Return cell bases for cell T.

cellBases() [3/17]

const CellBases & HArDCore2D::VSXGrad::cellBases ( const Cell &  T ) const

inline

Return vector/matrix cell bases for cell T.

cellBases() [4/17]

const DDRCore::CellBases & HArDCore2D::XCurl::cellBases ( const Cell &  T ) const

inline

Return cell bases for cell T.

cellBases() [5/17]

const DDRCore::CellBases & HArDCore2D::XGrad::cellBases ( const Cell &  T ) const

inline

Return cell bases for cell T.

cellBases() [6/17]

const DDRCore::CellBases & HArDCore2D::XHess::cellBases ( const Cell &  T ) const

inline

Return cell bases for cell T.

cellBases() [7/17]

const DDRCore::CellBases & HArDCore2D::XRot::cellBases ( const Cell &  T ) const

inline

Return cell bases for cell T.

cellBases() [8/17]

const DDRCore::CellBases & HArDCore2D::XRotRot::cellBases ( const Cell &  T ) const

inline

Return cell bases for cell T.

cellBases() [9/17]

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

inline

Return cell bases for element iT.

cellBases() [10/17]

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

inline

Return ddrcore cell bases for the cell of index iT.

cellBases() [11/17]

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

inline

Return cell bases for the cell of index iT.

cellBases() [12/17]

const CellBases & HArDCore2D::VSXGrad::cellBases ( size_t  iT ) const

inline

Return vector/matrix cell bases for the face of index iT.

cellBases() [13/17]

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

inline

Return cell bases for the cell of index iT.

cellBases() [14/17]

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

inline

Return cell bases for the cell of index iT.

cellBases() [15/17]

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

inline

Return cell bases for the cell of index iT.

cellBases() [16/17]

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

inline

Return cell bases for the cell of index iT.

cellBases() [17/17]

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

inline

Return cell bases for the cell of index iT.

cellBasisPolyl() [1/2]

const PolylBasisCellType & HArDCore2D::SerendipityProblem::cellBasisPolyl ( const Cell &  T ) const

inline

Return the basis of P^l on cell T.

cellBasisPolyl() [2/2]

const PolylBasisCellType & HArDCore2D::SerendipityProblem::cellBasisPolyl ( size_t  iT ) const

inline

Return the basis of P^l on cell of index iT.

cellBasisRolyCompllpo() [1/2]

const RolyCompllpoBasisCellType & HArDCore2D::SerendipityProblem::cellBasisRolyCompllpo ( const Cell &  T ) const

inline

Return the basis of R^{c,l+1} on cell T.

cellBasisRolyCompllpo() [2/2]

const RolyCompllpoBasisCellType & HArDCore2D::SerendipityProblem::cellBasisRolyCompllpo ( size_t  iT ) const

inline

Return the basis of R^{c,l+1} on cell of index iT.

cellDivergence() [1/2]

const Eigen::MatrixXd HArDCore2D::VSXGrad::cellDivergence ( const Cell &  T ) const

inline

Return the divergence operator (expressed on the ancester of Polyk3x3, which should be m_sxgrad.cellBases(iT).Polyk) on the cell of index iT.

cellDivergence() [2/2]

const Eigen::MatrixXd HArDCore2D::VSXGrad::cellDivergence ( size_t  iT ) const

inline

Return the divergence operator (expressed on the ancester of Polyk3x3, which should be m_sxgrad.cellBases(iT).Polyk) on the cell of index iT.

cellGradient() [1/4]

const Eigen::MatrixXd HArDCore2D::SXGrad::cellGradient ( const Cell &  T ) const

inline

Return the full gradient operator on cell T.

cellGradient() [2/4]

const Eigen::MatrixXd HArDCore2D::VSXGrad::cellGradient ( const Cell &  T ) const

inline

Return the gradient operator (expressed on Polyk3x3) on cell T.

cellGradient() [3/4]

const Eigen::MatrixXd HArDCore2D::SXGrad::cellGradient ( size_t  iT ) const

inline

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

cellGradient() [4/4]

const Eigen::MatrixXd HArDCore2D::VSXGrad::cellGradient ( size_t  iT ) const

inline

Return the gradient operator (expressed on Polyk3x3) on the cell of index iT.

cellOperators() [1/14]

const TransferOperators & HArDCore2D::SXGrad::cellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

cellOperators() [2/14]

const LocalOperators & HArDCore2D::VSXGrad::cellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

cellOperators() [3/14]

const LocalOperators & HArDCore2D::XCurl::cellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

cellOperators() [4/14]

const LocalOperators & HArDCore2D::XGrad::cellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

cellOperators() [5/14]

const LocalOperators & HArDCore2D::XHess::cellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

cellOperators() [6/14]

const LocalOperators & HArDCore2D::XRot::cellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

cellOperators() [7/14]

const LocalOperators & HArDCore2D::XRotRot::cellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

cellOperators() [8/14]

const TransferOperators & HArDCore2D::SXGrad::cellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

cellOperators() [9/14]

const LocalOperators & HArDCore2D::VSXGrad::cellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

cellOperators() [10/14]

const LocalOperators & HArDCore2D::XCurl::cellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

cellOperators() [11/14]

const LocalOperators & HArDCore2D::XGrad::cellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

cellOperators() [12/14]

const LocalOperators & HArDCore2D::XHess::cellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

cellOperators() [13/14]

const LocalOperators & HArDCore2D::XRot::cellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

cellOperators() [14/14]

const LocalOperators & HArDCore2D::XRotRot::cellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

cellPotential() [1/4]

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

inline

Return the potential operator on cell T.

cellPotential() [2/4]

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

inline

Return the potential operator on cell T.

cellPotential() [3/4]

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

inline

Return the potential operator on the cell of index iT.

cellPotential() [4/4]

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

inline

Return the potential operator (expressed on Polykpo3) on the cell of index iT.

cellRotor() [1/2]

Eigen::MatrixXd HArDCore2D::XRotRot::cellRotor ( const Cell &  T ) const

inline

Return cell rotor for cell T.

cellRotor() [2/2]

Eigen::MatrixXd HArDCore2D::XRotRot::cellRotor ( size_t  iT ) const

inline

Return cell rotor for cell of index iT.

cellSymGradient() [1/2]

const Eigen::MatrixXd HArDCore2D::VSXGrad::cellSymGradient ( const Cell &  T ) const

inline

Return the symmetric gradient operator (expressed on Polyk3x3) on cell T.

cellSymGradient() [2/2]

const Eigen::MatrixXd HArDCore2D::VSXGrad::cellSymGradient ( size_t  iT ) const

inline

Return the symmetric gradient operator (expressed on Polyk3x3) on the cell of index iT.

computeGradientL2Norm()

double XRotRot::computeGradientL2Norm	(	const Eigen::VectorXd &	v,
		const XGrad *	x_grad
	)		const

Compute the L2-norm of the discrete gradient of a vector in XGrad.

computeGradientL2Product()

Eigen::MatrixXd XRotRot::computeGradientL2Product	(	size_t	iT,
		const XGrad *	x_grad,
		const double &	penalty_factor = 1.,
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

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

Parameters

iT	Index of the cell
x_grad	Instance of XGrad to access the full gradients
penalty_factor	Pre-factor for stabilisation term
weight	Weight function in the L2 product, defaults to constant 1.

computeGradientPotentialL2Product()

Eigen::MatrixXd XRotRot::computeGradientPotentialL2Product	(	size_t	iT,
		const XGrad *	x_grad,
		const double &	penalty_factor = 1.,
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

Compute the matrix of the (weighted) L2-product as 'computeL2Product', with application of the discrete gradient on the left side.

Parameters

iT	Index of the cell
x_grad	Instance of XGrad to access the full gradients
penalty_factor	Pre-factor for stabilisation term
weight	Weight function in the L2 product, defaults to constant 1.

computeH1norms()

std::vector< double > VSXGrad::computeH1norms	(	const std::vector< Eigen::VectorXd > &	list_dofs,
		const std::string	typegrad = "full"
	)		const

Compute the H^1 discrete norm, with full or symmetric gradient.

Parameters

list_dofs	The list of vectors representing the dofs
typegrad	computes the norm using the "full" or "symmetric" gradient

computeL2Norm() [1/4]

double SXGrad::computeL2Norm

(

const Eigen::VectorXd &

v

)

const

Compute the L2-norm of a vector of the space.

computeL2Norm() [2/4]

double XGrad::computeL2Norm

(

const Eigen::VectorXd &

v

)

const

Compute the L2-norm of a vector of the space.

computeL2Norm() [3/4]

double XHess::computeL2Norm

(

const Eigen::VectorXd &

v

)

const

Compute the L2-norm of a vector of the space.

computeL2Norm() [4/4]

double XRotRot::computeL2Norm

(

const Eigen::VectorXd &

v

)

const

Compute the L2-norm of a vector of the space.

computeL2Product() [1/6]

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

Compute the matrix of the (weighted) L2-product for the cell of index iT.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pk2_T	if pre-computed, the mass matrix of (P^k(T))^3; if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to 1

computeL2Product() [2/6]

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

inline

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

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pk2_T	if pre-computed, the mass matrix of (P^k(T))^3; if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to 1

computeL2Product() [3/6]

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

Compute the matrix of the (weighted) L2-product for the cell of index iT.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pk2_T	if pre-computed, the mass matrix of (P^k(T))^3; if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to 1

computeL2Product() [4/6]

Eigen::MatrixXd XGrad::computeL2Product	(	const size_t	iT,
		const double &	penalty_factor = 1.,
		const Eigen::MatrixXd &	mass_Pkpo_T = Eigen::MatrixXd::Zero(1,1),
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

Compute the matrix of the (weighted) L2-product for the cell of index iT.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pkpo_T	if pre-computed, the mass matrix of P^{k+1}(T); if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to 1

computeL2Product() [5/6]

Eigen::MatrixXd XHess::computeL2Product	(	const size_t	iT,
		const double &	penalty_factor = 1.,
		const Eigen::MatrixXd &	mass_Pkpo_T = Eigen::MatrixXd::Zero(1,1),
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

Compute the matrix of the (weighted) L2-product for the cell of index iT.

Parameters

iT	index of the cell
penalty_factor	pre-factor for stabilisation term
mass_Pkpo_T	if pre-computed, the mass matrix of P^{k+1}(T); if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to 1

computeL2Product() [6/6]

Eigen::MatrixXd XRotRot::computeL2Product	(	size_t	iT,
		const double &	penalty_factor = 1.,
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

Compute the matrix of the (weighted) L2-product for the cell of index iT.

Parameters

iT	Index of the cell
penalty_factor	Pre-factor for stabilisation term
weight	Weight function in the L2 product, defaults to 1

computeL2Product_with_Ops() [1/2]

Eigen::MatrixXd HArDCore2D::EXCurl::computeL2Product_with_Ops	(	const size_t	iT,
		const std::vector< Eigen::MatrixXd > &	leftOp,
		const std::vector< Eigen::MatrixXd > &	rightOp,
		const double &	penalty_factor,
		const Eigen::MatrixXd &	w_mass_Pk2_T,
		const IntegralWeight &	weight
	)		const

Compute the matrix of the L2 product, applying leftOp and rightOp to the variables. Probably not directly called, mostly invoked through the wrappers computeL2Product and computeL2ProductGradient.

Parameters

iT	index of the cell
leftOp	edge and element operators to apply on the left
rightOp	edge and element operators to apply on the right
penalty_factor	pre-factor for stabilisation term
w_mass_Pk2_T	mass matrix of (P^k(T))^3 weighted by weight
weight	weight function in the L2 product

computeL2Product_with_Ops() [2/2]

Eigen::MatrixXd XCurl::computeL2Product_with_Ops	(	const size_t	iT,
		const std::vector< Eigen::MatrixXd > &	leftOp,
		const std::vector< Eigen::MatrixXd > &	rightOp,
		const double &	penalty_factor,
		const Eigen::MatrixXd &	w_mass_Pk2_T,
		const IntegralWeight &	weight
	)		const

Compute the matrix of the L2 product, applying leftOp and rightOp to the variables. Probably not directly called, mostly invoked through the wrappers computeL2Product and computeL2ProductGradient.

Parameters

iT	index of the cell
leftOp	edge and element operators to apply on the left
rightOp	edge and element operators to apply on the right
penalty_factor	pre-factor for stabilisation term
w_mass_Pk2_T	mass matrix of (P^k(T))^3 weighted by weight
weight	weight function in the L2 product

computeL2ProductGradient() [1/2]

Eigen::MatrixXd EXCurl::computeL2ProductGradient	(	const size_t	iT,
		const XGrad &	x_grad,
		const std::string &	side,
		const double &	penalty_factor = 1.,
		const Eigen::MatrixXd &	mass_Pk2_T = Eigen::MatrixXd::Zero(1,1),
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

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

Parameters

iT	index of the cell
x_grad	instance of XGrad to access the full gradients
side	which side (left, right, both) we apply the gradient to
penalty_factor	pre-factor for stabilisation term
mass_Pk2_T	if pre-computed, the mass matrix of (P^k(T))^3; if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to constant 1.

computeL2ProductGradient() [2/2]

Eigen::MatrixXd XCurl::computeL2ProductGradient	(	const size_t	iT,
		const XGrad &	x_grad,
		const std::string &	side,
		const double &	penalty_factor = 1.,
		const Eigen::MatrixXd &	mass_Pk2_T = Eigen::MatrixXd::Zero(1,1),
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

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

Parameters

iT	index of the cell
x_grad	instance of XGrad to access the full gradients
side	which side (left, right, both) we apply the gradient to
penalty_factor	pre-factor for stabilisation term
mass_Pk2_T	if pre-computed, the mass matrix of (P^k(T))^3; if none is pre-computed, passing Eigen::MatrixXd::Zero(1,1) will force the calculation
weight	weight function in the L2 product, defaults to constant 1.

computeL2ProductWithOperatorFillers()

template<typename LeftOperatorFillerType , typename RightOperatorFillerType >

Eigen::MatrixXd HArDCore2D::XRotRot::computeL2ProductWithOperatorFillers	(	size_t	iT,
		const double &	penalty_factor,
		const IntegralWeight &	weight,
		LeftOperatorFillerType	fillLeftOp,
		RightOperatorFillerType	fillRightOp
	)		const

Compute the matrix of the L2 product given operators filling functions.

Parameters

iT	Index of the cell
penalty_factor	Penalty factor for stabilisation term
weight	Weight function in the L2 product
fillLeftOp	Function to fill the left-hand side operator
fillRightOp	Function to fill the right-hand side operator

computeRotorL2Norm()

double XRot::computeRotorL2Norm

(

const Eigen::VectorXd &

v

)

const

Compute rotor L2-norm.

computeRotorL2Product()

Eigen::MatrixXd XRot::computeRotorL2Product	(	const size_t	iT,
		const double &	penalty_factor_cell = 1.,
		const double &	penalty_factor_edge = 1.
	)		const

Compute rotor L2-product.

Parameters

iT	Index of the cell
penalty_factor_cell	Coefficient for the cell-based term
penalty_factor_edge	Coefficient for the edge-based term

computeStabilisation() [1/3]

Eigen::MatrixXd HArDCore2D::SXGrad::computeStabilisation ( const size_t  iT, const IntegralWeight &  weight = IntegralWeight(1.)  ) const

inline

Computes only the stabilisation matrix of the (weighted) L2-product for the cell of index iT.

Parameters

iT	index of the cell
weight	weight function in the stabilisation, defaults to 1

computeStabilisation() [2/3]

Eigen::MatrixXd HArDCore2D::VSXGrad::computeStabilisation ( const size_t  iT, const IntegralWeight &  weight = IntegralWeight(1.)  ) const

inline

Compute the H^1-stabilisation (based on the L^2 stabilisation implemented in SXgrad)

Parameters

iT	index of the cell
weight	weight function in the L2 product, defaults to 1

computeStabilisation() [3/3]

Eigen::MatrixXd XGrad::computeStabilisation	(	const size_t	iT,
		const IntegralWeight &	weight = IntegralWeight(1.)
	)		const

Computes only the stabilisation matrix of the (weighted) L2-product for the cell of index iT. This stabilisation is based on cell and face potentials.

Parameters

iT	index of the cell
weight	weight function in the stabilisation, defaults to 1

computeVertexValues() [1/2]

std::vector< double > HArDCore2D::SXGrad::computeVertexValues

(

const Eigen::VectorXd &

u

)

const

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

Parameters

u	DOFs in the discrete space

computeVertexValues() [2/2]

std::vector< VectorRd > VSXGrad::computeVertexValues

(

const Eigen::VectorXd &

u

)

const

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

Parameters

u	DOFs in the discrete space

ddrCore()

const DDRCore & HArDCore2D::SerendipityProblem::ddrCore ( ) const

inline

Return a const reference to the underlying DDR core.

DDRCore()

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

Constructor.

ddrCurl() [1/2]

const Eigen::MatrixXd HArDCore2D::EXCurl::ddrCurl ( const Cell &  T ) const

inline

Return cell (scalar) curl for cell T.

ddrCurl() [2/2]

const Eigen::MatrixXd HArDCore2D::EXCurl::ddrCurl ( size_t  iT ) const

inline

Return cell (scalar) curl for the cell of index iT.

ddrPotential() [1/2]

const Eigen::MatrixXd HArDCore2D::EXCurl::ddrPotential ( const Cell &  T ) const

inline

Return cell potential for cell T.

ddrPotential() [2/2]

const Eigen::MatrixXd HArDCore2D::EXCurl::ddrPotential ( size_t  iT ) const

inline

Return cell potential for the cell of index iT.

degree() [1/9]

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

inline

Return the polynomial degree.

degree() [2/9]

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

inline

Return the polynomial degree.

degree() [3/9]

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

inline

Return the polynomial degree.

degree() [4/9]

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

inline

Return the polynomial degree.

degree() [5/9]

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

inline

Return the polynomial degree.

degree() [6/9]

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

inline

Return the polynomial degree.

degree() [7/9]

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

inline

Return the polynomial degree.

degree() [8/9]

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

inline

Return the polynomial degree.

degree() [9/9]

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

inline

Return the polynomial degree.

dimCellPolyl() [1/2]

size_t HArDCore2D::SerendipityProblem::dimCellPolyl ( const Cell &  T ) const

inline

Return the dimension of P^{l+1} on cell T.

dimCellPolyl() [2/2]

size_t HArDCore2D::SerendipityProblem::dimCellPolyl ( size_t  iT ) const

inline

Return the dimension of P^l on cell of index iT.

dimCellRolyCompllpo() [1/2]

size_t HArDCore2D::SerendipityProblem::dimCellRolyCompllpo ( const Cell &  T ) const

inline

Return the dimension of R^{c,l+1} on cell T.

dimCellRolyCompllpo() [2/2]

size_t HArDCore2D::SerendipityProblem::dimCellRolyCompllpo ( size_t  iT ) const

inline

Return the dimension of R^{c,l+1} on cell of index iT.

edgeBases() [1/17]

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

inline

Return ddrcore edge bases for edge E.

edgeBases() [2/17]

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

inline

Return edge bases for edge E.

edgeBases() [3/17]

const EdgeBases & HArDCore2D::VSXGrad::edgeBases ( const Edge &  E ) const

inline

Return edge bases for edge E.

edgeBases() [4/17]

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

inline

Return edge bases for edge E.

edgeBases() [5/17]

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

inline

Return edge bases for edge E.

edgeBases() [6/17]

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

inline

Return edge bases for edge E.

edgeBases() [7/17]

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

inline

Return edge bases for edge E.

edgeBases() [8/17]

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

inline

Return edge bases for edge E.

edgeBases() [9/17]

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

inline

Return edge bases for edge iE.

edgeBases() [10/17]

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

inline

Return ddrcore edge bases for the edge of index iE.

edgeBases() [11/17]

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

inline

Return edge bases for the edge of index iE.

edgeBases() [12/17]

const EdgeBases & HArDCore2D::VSXGrad::edgeBases ( size_t  iE ) const

inline

Return edge bases for the edge of index iE.

edgeBases() [13/17]

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

inline

Return edge bases for the edge of index iE.

edgeBases() [14/17]

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

inline

Return edge bases for the edge of index iE.

edgeBases() [15/17]

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

inline

Return edge bases for the edge of index iE.

edgeBases() [16/17]

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

inline

Return edge bases for the edge of index iE.

edgeBases() [17/17]

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

inline

Return edge bases for the edge of index iE.

edgeGradient() [1/4]

const Eigen::MatrixXd HArDCore2D::SXGrad::edgeGradient ( const Edge &  E ) const

inline

Return the full gradient operator on edge E.

edgeGradient() [2/4]

const Eigen::MatrixXd HArDCore2D::VSXGrad::edgeGradient ( const Edge &  E ) const

inline

Return the gradient operator (expressed on Polyk3) on edge E.

edgeGradient() [3/4]

const Eigen::MatrixXd HArDCore2D::SXGrad::edgeGradient ( size_t  iE ) const

inline

Return the full gradient operator on the edge of index iE.

edgeGradient() [4/4]

const Eigen::MatrixXd HArDCore2D::VSXGrad::edgeGradient ( size_t  iE ) const

inline

Return the gradient operator (expressed on Polyk3) on the edge of index iE.

edgeOperators() [1/4]

const LocalOperators & HArDCore2D::XGrad::edgeOperators ( const Edge &  E ) const

inline

Return edge operators for edge E.

edgeOperators() [2/4]

const LocalOperators & HArDCore2D::XHess::edgeOperators ( const Edge &  E ) const

inline

Return edge operators for edge E.

edgeOperators() [3/4]

const LocalOperators & HArDCore2D::XGrad::edgeOperators ( size_t  iE ) const

inline

Return edge operators for the edge of index iE.

edgeOperators() [4/4]

const LocalOperators & HArDCore2D::XHess::edgeOperators ( size_t  iE ) const

inline

Return edge operators for the edge of index iE.

edgePotential() [1/6]

const Eigen::MatrixXd HArDCore2D::SXGrad::edgePotential ( const Edge &  E ) const

inline

Return the potential operator on edge E.

edgePotential() [2/6]

const Eigen::MatrixXd HArDCore2D::VSXGrad::edgePotential ( const Edge &  E ) const

inline

Return the potential operator (expressed on Polykpo3) on edge E.

edgePotential() [3/6]

const Eigen::MatrixXd & HArDCore2D::XRot::edgePotential ( const Edge &  E ) const

inline

Return edge potential for the edge E.

edgePotential() [4/6]

const Eigen::MatrixXd HArDCore2D::SXGrad::edgePotential ( size_t  iE ) const

inline

Return the potential operator on the edge of index iE.

edgePotential() [5/6]

const Eigen::MatrixXd HArDCore2D::VSXGrad::edgePotential ( size_t  iE ) const

inline

Return the potential operator (expressed on Polykpo3) on the edge of index iE.

edgePotential() [6/6]

const Eigen::MatrixXd & HArDCore2D::XRot::edgePotential ( size_t  iE ) const

inline

Return edge potential for the edge of index iE.

EgradCell() [1/2]

const Eigen::MatrixXd & HArDCore2D::SXGrad::EgradCell ( const Cell &  T ) const

inline

Return the extension for cell T.

EgradCell() [2/2]

const Eigen::MatrixXd & HArDCore2D::SXGrad::EgradCell ( size_t  iT ) const

inline

Return the extension for the cell of index iT.

evaluatePotential() [1/2]

double XGrad::evaluatePotential	(	const size_t	iT,
		const Eigen::VectorXd &	vT,
		const VectorRd &	x
	)		const

Evaluate the value of the potential at a point x.

Parameters

iT	index of the cell in which to take the potential
vT	vector of local DOFs
x	point at which to evaluate the potential

evaluatePotential() [2/2]

double XHess::evaluatePotential	(	const size_t	iT,
		const Eigen::VectorXd &	vT,
		const VectorRd &	x
	)		const

Evaluate the value of the potential at a point x.

Parameters

iT	index of the cell in which to take the potential
vT	vector of local DOFs
x	point at which to evaluate the potential

EXCurl()

EXCurl::EXCurl	(	const DDRCore &	ddr_core,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

hhoLocalOperators()

HArDCore2D::EXCurl::hhoLocalOperators::hhoLocalOperators ( const Eigen::MatrixXd &  _gradient, const Eigen::MatrixXd &  _symmetric_gradient, const Eigen::MatrixXd &  _potential, const Eigen::MatrixXd &  _stabilisation  )

inline

Parameters

_gradient	gradient operator
_symmetric_gradient	symmetric gradient operator
_potential	Potential operator
_stabilisation	Stabilisation

hhoOperators() [1/2]

const hhoLocalOperators & HArDCore2D::EXCurl::hhoOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

hhoOperators() [2/2]

const hhoLocalOperators & HArDCore2D::EXCurl::hhoOperators ( size_t  iT ) const

inline

Return hho operators for the cell of index iT.

interpolate() [1/8]

Eigen::VectorXd XHess::interpolate	(	const FunctionType &	q,
		const GradFunctionType &	Dq,
		const int	deg_quad = -1
	)		const

Interpolator of a continuous function.

Parameters

q	The function to interpolate
Dq	The gradient of the function
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

interpolate() [2/8]

Eigen::VectorXd SXGrad::interpolate	(	const FunctionType &	q,
		const int	deg_quad = -1
	)		const

Parameters

q	The function to interpolate
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

interpolate() [3/8]

Eigen::VectorXd XGrad::interpolate	(	const FunctionType &	q,
		const int	deg_quad = -1
	)		const

Interpolator of a continuous function.

Parameters

q	The function to interpolate
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

interpolate() [4/8]

Eigen::VectorXd XRot::interpolate	(	const FunctionType &	q,
		const int	deg_quad = -1
	)		const

Interpolator of a continuous function.

Parameters

q	The function to interpolate
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

interpolate() [5/8]

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

Interpolator of a continuous function.

Parameters

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

interpolate() [6/8]

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

Interpolator of a continuous function.

Parameters

v	The function to interpolate
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

interpolate() [7/8]

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

Interpolator of a continuous function.

Parameters

v	The function to interpolate
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

interpolate() [8/8]

Eigen::VectorXd XRotRot::interpolate	(	const FunctionType &	v,
		const RotType &	rot_v,
		const int	deg_quad = -1
	)		const

Interpolator of a continuous function.

Parameters

v	The function to interpolate
rot_v	Rotor of the function to interpolate
deg_quad	The optional degre of quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

LocalOperators() [1/6]

HArDCore2D::XCurl::LocalOperators::LocalOperators ( const Eigen::MatrixXd &  _curl, const Eigen::MatrixXd &  _potential  )

inline

Parameters

_curl	Curl operator
_potential	Potential operator

LocalOperators() [2/6]

HArDCore2D::XGrad::LocalOperators::LocalOperators ( const Eigen::MatrixXd &  _gradient, const Eigen::MatrixXd &  _potential  )

inline

Parameters

_gradient	Gradient operator
_potential	Potential operator

LocalOperators() [3/6]

HArDCore2D::XHess::LocalOperators::LocalOperators ( const Eigen::MatrixXd &  _gradient, const Eigen::MatrixXd &  _potential  )

inline

Parameters

_gradient	Gradient operator
_potential	Potential operator

LocalOperators() [4/6]

HArDCore2D::VSXGrad::LocalOperators::LocalOperators ( const Eigen::MatrixXd &  _rot, const Eigen::MatrixXd &  _potential  )

inline

Parameters

_rot	Curl operator
_potential	Potential operator

LocalOperators() [5/6]

HArDCore2D::XRotRot::LocalOperators::LocalOperators ( const Eigen::MatrixXd &  _rotor, const Eigen::MatrixXd &  _potential  )

inline

Parameters

_rotor	Rot operator
_potential	Potential operator

LocalOperators() [6/6]

HArDCore2D::XRot::LocalOperators::LocalOperators ( const Eigen::MatrixXd &  _rotor, const Eigen::MatrixXd &  _rotor_rhs, const Eigen::MatrixXd &  _potential  )

inline

Parameters

_rotor	Vector rotor operator
_rotor_rhs	Vector rotor right-hand side
_potential	Potential operator

mesh() [1/10]

const Mesh & HArDCore2D::DDRCore::mesh ( ) const

inline

Return a const reference to the mesh.

mesh() [2/10]

const Mesh & HArDCore2D::EXCurl::mesh ( ) const

inline

Return the mesh.

mesh() [3/10]

const Mesh & HArDCore2D::SerendipityProblem::mesh ( ) const

inline

Return a const reference to the mesh.

mesh() [4/10]

const Mesh & HArDCore2D::SXGrad::mesh ( ) const

inline

Return the mesh.

mesh() [5/10]

const Mesh & HArDCore2D::VSXGrad::mesh ( ) const

inline

Return the mesh.

mesh() [6/10]

const Mesh & HArDCore2D::XCurl::mesh ( ) const

inline

Return the mesh.

mesh() [7/10]

const Mesh & HArDCore2D::XGrad::mesh ( ) const

inline

Return the mesh.

mesh() [8/10]

const Mesh & HArDCore2D::XHess::mesh ( ) const

inline

Return the mesh.

mesh() [9/10]

const Mesh & HArDCore2D::XRot::mesh ( ) const

inline

Return the mesh.

mesh() [10/10]

const Mesh & HArDCore2D::XRotRot::mesh ( ) const

inline

Return the mesh.

n_serendipityEdges()

const int HArDCore2D::SerendipityProblem::n_serendipityEdges ( size_t  iT ) const

inline

Return the number of serendipity edges in a cell.

nDOFs_cells_SXCurl()

Eigen::VectorXd SerendipityProblem::nDOFs_cells_SXCurl

(

)

const

Number of DOFs on cells for serendipity XCurl space.

nDOFs_cells_SXGrad()

Eigen::VectorXd SerendipityProblem::nDOFs_cells_SXGrad

(

)

const

Number of DOFs on cells for serendipity XGrad space.

nDOFs_cells_SXRotRot()

Eigen::VectorXd SerendipityProblem::nDOFs_cells_SXRotRot

(

)

const

Number of DOFs on cells for serendipity XRotRot space.

Polyk()

auto HArDCore2D::VSXGrad::Polyk ( size_t  iT ) const -> const PolyBasisCellType&

inline

Polyk2()

auto HArDCore2D::VSXGrad::Polyk2 ( size_t  iT ) const -> const Poly2BasisCellType&

inline

Polyk2x2()

const Polyk2x2Type & HArDCore2D::EXCurl::Polyk2x2 ( size_t  iT ) const

inline

Return basis for Matricial P^k space.

PolykE()

auto HArDCore2D::VSXGrad::PolykE ( size_t  iE ) const -> const PolyBasisEdgeType&

inline

Polykmo()

auto HArDCore2D::VSXGrad::Polykmo ( size_t  iT ) const -> const PolyBasisCellType&

inline

Polykpo()

auto HArDCore2D::VSXGrad::Polykpo ( size_t  iT ) const -> const PolyBasisCellType&

inline

Polykpo2()

const Polykpo2Type & HArDCore2D::EXCurl::Polykpo2 ( size_t  iT ) const

inline

Return basis for the (P^{k+1})^2 space.

PolykpoE()

auto HArDCore2D::VSXGrad::PolykpoE ( size_t  iE ) const -> const PolyBasisEdgeType&

inline

Polykptwo()

auto HArDCore2D::VSXGrad::Polykptwo ( size_t  iT ) const -> const PolyBasisCellType&

inline

PolykptwoE()

auto HArDCore2D::VSXGrad::PolykptwoE ( size_t  iE ) const -> const PolyBasisEdgeType&

inline

RgradCell() [1/2]

const Eigen::MatrixXd & HArDCore2D::SXGrad::RgradCell ( const Cell &  T ) const

inline

Return the reduction for cell T.

RgradCell() [2/2]

const Eigen::MatrixXd & HArDCore2D::SXGrad::RgradCell ( size_t  iT ) const

inline

Return the reduction for the cell of index iT.

serDegreeCell()

const int HArDCore2D::SerendipityProblem::serDegreeCell ( size_t  iT ) const

inline

Return the serendipity degree ell_T in a cell.

serendipityEdges()

const std::vector< size_t > & HArDCore2D::SerendipityProblem::serendipityEdges ( size_t  iT ) const

inline

Return the list of serendipity edges in a cell.

SerendipityOperatorCell() [1/2]

const Eigen::MatrixXd HArDCore2D::SerendipityProblem::SerendipityOperatorCell ( const Cell &  T, const Eigen::MatrixXd &  LT  ) const

inline

Compute the serendipity operator on the Cell T.

SerendipityOperatorCell() [2/2]

const Eigen::MatrixXd SerendipityProblem::SerendipityOperatorCell	(	const size_t	iT,
		const Eigen::MatrixXd &	LT
	)		const

Compute the serendipity operator on the cell of index iT.

SerendipityProblem()

SerendipityProblem::SerendipityProblem	(	const DDRCore &	ddrcore,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

SgradCell() [1/4]

const Eigen::MatrixXd & HArDCore2D::SXGrad::SgradCell ( const Cell &  T ) const

inline

Return the serendipity reconstruction for cell T.

SgradCell() [2/4]

const Eigen::MatrixXd & HArDCore2D::XHess::SgradCell ( const Cell &  T ) const

inline

Return the serendipity reconstruction for cell T.

SgradCell() [3/4]

const Eigen::MatrixXd & HArDCore2D::SXGrad::SgradCell ( size_t  iT ) const

inline

Return the serendipity reconstruction for the cell of index iT.

SgradCell() [4/4]

const Eigen::MatrixXd & HArDCore2D::XHess::SgradCell ( size_t  iT ) const

inline

Return the serendipity reconstruction for the cell of index iT.

sXgrad()

const SXGrad & HArDCore2D::VSXGrad::sXgrad ( ) const

inline

Return the underlying sXgrad space.

SXGrad()

SXGrad::SXGrad	(	const DDRCore &	ddr_core,
		const SerendipityProblem &	ser_pro,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

TcellOperators() [1/2]

const TransferOperators & HArDCore2D::XHess::TcellOperators ( const Cell &  T ) const

inline

Return cell operators for cell T.

TcellOperators() [2/2]

const TransferOperators & HArDCore2D::XHess::TcellOperators ( size_t  iT ) const

inline

Return cell operators for the cell of index iT.

TransferOperators() [1/2]

HArDCore2D::XHess::TransferOperators::TransferOperators ( const Eigen::MatrixXd &  _serendipity )

inline

Parameters

_serendipity

Serendipity reconstruction

TransferOperators() [2/2]

HArDCore2D::SXGrad::TransferOperators::TransferOperators ( const Eigen::MatrixXd &  _serendipity, const Eigen::MatrixXd &  _extension, const Eigen::MatrixXd &  _reduction  )

inline

Parameters

_serendipity	Serendipity reconstruction
_extension	Extension SXGrad->XGrad
_reduction	Reduction XGrad->SXGrad

useThreads()

const bool HArDCore2D::XRot::useThreads ( ) const

inline

Return true if we use thread-based parallelism.

VSXGrad()

VSXGrad::VSXGrad	(	const DDRCore &	ddr_core,
		const SerendipityProblem &	sp,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

XCurl()

XCurl::XCurl	(	const DDRCore &	ddr_core,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

XGrad()

XGrad::XGrad	(	const DDRCore &	ddr_core,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

XHess()

XHess::XHess	(	const DDRCore &	ddr_core,
		const SerendipityProblem &	ser_pro,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

XRot()

XRot::XRot	(	const DDRCore &	ddr_core,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

XRotRot()

XRotRot::XRotRot	(	const DDRCore &	ddr_core,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

Variable Documentation

curl

Eigen::MatrixXd HArDCore2D::XCurl::LocalOperators::curl

extension

Eigen::MatrixXd HArDCore2D::SXGrad::TransferOperators::extension

GolyComplkp2

std::unique_ptr<GolyComplBasisCellType> HArDCore2D::DDRCore::CellBases::GolyComplkp2

gradient [1/3]

Eigen::MatrixXd HArDCore2D::EXCurl::hhoLocalOperators::gradient

gradient [2/3]

Eigen::MatrixXd HArDCore2D::XGrad::LocalOperators::gradient

gradient [3/3]

Eigen::MatrixXd HArDCore2D::XHess::LocalOperators::gradient

Polyk [1/2]

std::unique_ptr<PolyBasisCellType> HArDCore2D::DDRCore::CellBases::Polyk

Polyk [2/2]

std::unique_ptr<PolyBasisEdgeType> HArDCore2D::DDRCore::EdgeBases::Polyk

Polyk2 [1/2]

std::unique_ptr<Poly2BasisCellType> HArDCore2D::DDRCore::CellBases::Polyk2

Polyk2 [2/2]

std::unique_ptr<Poly2BasisEdgeType> HArDCore2D::VSXGrad::EdgeBases::Polyk2

Polykmo [1/2]

std::unique_ptr<PolyBasisCellType> HArDCore2D::DDRCore::CellBases::Polykmo

Polykmo [2/2]

std::unique_ptr<PolyBasisEdgeType> HArDCore2D::DDRCore::EdgeBases::Polykmo

Polykmo2 [1/3]

std::unique_ptr<Poly2BasisCellType> HArDCore2D::DDRCore::CellBases::Polykmo2

Polykmo2 [2/3]

std::unique_ptr<Poly2BasisCellType> HArDCore2D::VSXGrad::CellBases::Polykmo2

Polykmo2 [3/3]

std::unique_ptr<Poly2BasisEdgeType> HArDCore2D::VSXGrad::EdgeBases::Polykmo2

Polykmtwo

std::unique_ptr<PolyBasisCellType> HArDCore2D::DDRCore::CellBases::Polykmtwo

Polykpo [1/2]

std::unique_ptr<PolyBasisCellType> HArDCore2D::DDRCore::CellBases::Polykpo

Polykpo [2/2]

std::unique_ptr<PolyBasisEdgeType> HArDCore2D::DDRCore::EdgeBases::Polykpo

Polykpo2

std::unique_ptr<Poly2BasisEdgeType> HArDCore2D::VSXGrad::EdgeBases::Polykpo2

Polykpo2x2

std::unique_ptr<Poly2x2BasisCellType> HArDCore2D::VSXGrad::CellBases::Polykpo2x2

Polykptwo2 [1/2]

std::unique_ptr<Poly2BasisCellType> HArDCore2D::VSXGrad::CellBases::Polykptwo2

Polykptwo2 [2/2]

std::unique_ptr<Poly2BasisEdgeType> HArDCore2D::VSXGrad::EdgeBases::Polykptwo2

potential [1/7]

Eigen::MatrixXd HArDCore2D::EXCurl::hhoLocalOperators::potential

potential [2/7]

Eigen::MatrixXd HArDCore2D::VSXGrad::LocalOperators::potential

potential [3/7]

Eigen::MatrixXd HArDCore2D::XCurl::LocalOperators::potential

potential [4/7]

Eigen::MatrixXd HArDCore2D::XGrad::LocalOperators::potential

potential [5/7]

Eigen::MatrixXd HArDCore2D::XHess::LocalOperators::potential

potential [6/7]

Eigen::MatrixXd HArDCore2D::XRot::LocalOperators::potential

potential [7/7]

Eigen::MatrixXd HArDCore2D::XRotRot::LocalOperators::potential

reduction

Eigen::MatrixXd HArDCore2D::SXGrad::TransferOperators::reduction

RolyComplk

std::unique_ptr<RolyComplBasisCellType> HArDCore2D::DDRCore::CellBases::RolyComplk

RolyComplkmo

std::unique_ptr<RolyComplBasisCellType> HArDCore2D::DDRCore::CellBases::RolyComplkmo

RolyComplkp2

std::unique_ptr<RolyComplBasisCellType> HArDCore2D::DDRCore::CellBases::RolyComplkp2

Rolykmo

std::unique_ptr<RolyBasisCellType> HArDCore2D::DDRCore::CellBases::Rolykmo

rot

Eigen::MatrixXd HArDCore2D::VSXGrad::LocalOperators::rot

rotor [1/2]

Eigen::MatrixXd HArDCore2D::XRot::LocalOperators::rotor

rotor [2/2]

Eigen::MatrixXd HArDCore2D::XRotRot::LocalOperators::rotor

rotor_rhs

Eigen::MatrixXd HArDCore2D::XRot::LocalOperators::rotor_rhs

serendipity [1/2]

Eigen::MatrixXd HArDCore2D::SXGrad::TransferOperators::serendipity

serendipity [2/2]

Eigen::MatrixXd HArDCore2D::XHess::TransferOperators::serendipity

stabilisation

Eigen::MatrixXd HArDCore2D::EXCurl::hhoLocalOperators::stabilisation

symmetric_gradient

Eigen::MatrixXd HArDCore2D::EXCurl::hhoLocalOperators::symmetric_gradient