#include <StdNodalTriExp.h>

Inheritance diagram for Nektar::StdRegions::StdNodalTriExp:

Public Member Functions
	StdNodalTriExp ()

	StdNodalTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::PointsType Ntype)

	StdNodalTriExp (const StdNodalTriExp &T)

	~StdNodalTriExp ()

void	NodalToModal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	NodalToModalTranspose (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	ModalToNodal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GetNodalPoints (Array< OneD, const NekDouble > &x, Array< OneD, const NekDouble > &y)

DNekMatSharedPtr	GenNBasisTransMatrix ()

Public Member Functions inherited from Nektar::StdRegions::StdTriExp
	StdTriExp ()

	StdTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)

	StdTriExp (const StdTriExp &T)

	~StdTriExp ()

Public Member Functions inherited from Nektar::StdRegions::StdExpansion2D
	StdExpansion2D ()

	StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)

	StdExpansion2D (const StdExpansion2D &T)

virtual	~StdExpansion2D ()

void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d0, Array< OneD, NekDouble > &outarray_d1)
	Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points. More...

NekDouble	Integral (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &w0, const Array< OneD, const NekDouble > &w1)

void	BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)

void	IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)

Public Member Functions inherited from Nektar::StdRegions::StdExpansion
	StdExpansion ()
	Default Constructor. More...

	StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey)
	Constructor. More...

	StdExpansion (const StdExpansion &T)
	Copy Constructor. More...

virtual	~StdExpansion ()
	Destructor. More...

int	GetNumBases () const
	This function returns the number of 1D bases used in the expansion. More...

const Array< OneD, const LibUtilities::BasisSharedPtr > &	GetBase () const
	This function gets the shared point to basis. More...

const LibUtilities::BasisSharedPtr &	GetBasis (int dir) const
	This function gets the shared point to basis in the dir direction. More...

int	GetNcoeffs (void) const
	This function returns the total number of coefficients used in the expansion. More...

int	GetTotPoints () const
	This function returns the total number of quadrature points used in the element. More...

LibUtilities::BasisType	GetBasisType (const int dir) const
	This function returns the type of basis used in the dir direction. More...

int	GetBasisNumModes (const int dir) const
	This function returns the number of expansion modes in the dir direction. More...

int	EvalBasisNumModesMax (void) const
	This function returns the maximum number of expansion modes over all local directions. More...

LibUtilities::PointsType	GetPointsType (const int dir) const
	This function returns the type of quadrature points used in the dir direction. More...

int	GetNumPoints (const int dir) const
	This function returns the number of quadrature points in the dir direction. More...

const Array< OneD, const NekDouble > &	GetPoints (const int dir) const
	This function returns a pointer to the array containing the quadrature points in dir direction. More...

int	GetNverts () const
	This function returns the number of vertices of the expansion domain. More...

int	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th trace. More...

int	GetTraceIntNcoeffs (const int i) const

int	GetTraceNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th trace. More...

const LibUtilities::BasisKey	GetTraceBasisKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...

LibUtilities::PointsKey	GetTracePointsKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...

int	NumBndryCoeffs (void) const

int	NumDGBndryCoeffs (void) const

const LibUtilities::PointsKey	GetNodalPointsKey () const
	This function returns the type of expansion Nodal point type if defined. More...

int	GetNtraces () const
	Returns the number of trace elements connected to this element. More...

LibUtilities::ShapeType	DetShapeType () const
	This function returns the shape of the expansion domain. More...

std::shared_ptr< StdExpansion >	GetStdExp (void) const

std::shared_ptr< StdExpansion >	GetLinStdExp (void) const

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion ()

bool	IsNodalNonTensorialExp ()

void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Backward transformation from coefficient space to physical space. More...

void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Forward transformation from physical space to coefficient space. More...

void	FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)
	This function integrates the specified function over the domain. More...

void	FillMode (const int mode, Array< OneD, NekDouble > &outarray)
	This function fills the array outarray with the mode-th mode of the expansion. More...

void	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	this function calculates the inner product of a given function f with the different modes of the expansion More...

void	IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)

void	IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

int	GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id. More...

void	SetElmtId (const int id)
	Set the element id of this expansion when used in a list by returning value of m_elmt_id. More...

void	GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
	this function returns the physical coordinates of the quadrature points of the expansion More...

void	GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
	given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point More...

DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)

DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)

void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)

void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, NekDouble > &Fy, Array< OneD, NekDouble > &outarray)

void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)

void	NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble >> &Fvec, Array< OneD, NekDouble > &outarray)

DNekScalBlkMatSharedPtr	GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

void	DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

int	CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)

NekDouble	StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)

int	GetCoordim ()

void	GetBoundaryMap (Array< OneD, unsigned int > &outarray)

void	GetInteriorMap (Array< OneD, unsigned int > &outarray)

int	GetVertexMap (const int localVertexId, bool useCoeffPacking=false)

void	GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)

void	GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray)

void	GetElmtTraceToTraceMap (const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)

void	GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eForwards)

void	GetTraceNumModes (const int tid, int &numModes0, int &numModes1, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)

void	MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

DNekMatSharedPtr	CreateGeneralMatrix (const StdMatrixKey &mkey)
	this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) More...

void	GeneralMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)

void	ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)

void	LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)

void	HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)

void	PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)

void	PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	PhysDeriv_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds)

void	PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn)

void	PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)

void	StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)

void	StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

NekDouble	PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

NekDouble	PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

NekDouble	PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
	This function evaluates the basis function mode `mode` at a point `coords` of the domain. More...

void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta. More...

void	LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
	Convert local collapsed coordinates eta into local cartesian coordinate xi. More...

virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)

virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)

virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)

virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble >> &Fvec, Array< OneD, NekDouble > &outarray)

virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

virtual void	v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

NekDouble	Linf (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_\infty\) error \( \|\epsilon\|_\infty = \max \|u - u_{exact}\|\) where \( u_{exact}\) is given by the array sol. More...

NekDouble	L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_2\) error, \( \| \epsilon \|_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...

NekDouble	H1 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( H^1\) error, \( \| \epsilon \|^1_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u - u_{exact})\cdot dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...

const LibUtilities::PointsKeyVector	GetPointsKeys () const

DNekMatSharedPtr	BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)

void	PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
	This function performs an interpolation from the physical space points provided at input into an array of equispaced points which are not the collapsed coordinate. So for a tetrahedron you will only get a tetrahedral number of values. More...

void	GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
	This function provides the connectivity of local simplices (triangles or tets) to connect the equispaced data points provided by PhysInterpToSimplexEquiSpaced. More...

void	EquiSpacedToCoeffs (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs a projection/interpolation from the equispaced points sometimes used in post-processing onto the coefficient space. More...

template<class T >
std::shared_ptr< T >	as ()

void	IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)

void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)

Protected Member Functions
virtual const LibUtilities::PointsKey	v_GetNodalPointsKey () const

virtual bool	v_IsNodalNonTensorialExp ()

virtual void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Backward tranform for triangular elements. More...

virtual void	v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Transform a given function from physical quadrature space to coefficient space. More...

virtual void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray. More...

virtual void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)

virtual void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_FillMode (const int mode, Array< OneD, NekDouble > &outarray)

virtual int	v_NumBndryCoeffs () const

virtual int	v_GetVertexMap (int localVertexId, bool useCoeffPacking=false)

virtual void	v_GetTraceToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient=eForwards, int P=-1, int Q=-1)

virtual void	v_GetTraceInteriorToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation edgeOrient=eForwards)

virtual void	v_GetInteriorMap (Array< OneD, unsigned int > &outarray)

virtual void	v_GetBoundaryMap (Array< OneD, unsigned int > &outarray)

virtual void	v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual void	v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual void	v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual void	v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual void	v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey)

virtual DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey)

Protected Member Functions inherited from Nektar::StdRegions::StdTriExp
virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray)
	Integrates the specified function over the domain. More...

virtual void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
	Calculate the derivative of the physical points. More...

virtual void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Calculate the derivative of the physical points in a given direction. More...

virtual void	v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)

virtual void	v_StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)

virtual void	v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_IProductWRTBase_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)

virtual void	v_IProductWRTDerivBase_MatOp (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)

virtual void	v_LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)

NekDouble	v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) final

virtual int	v_GetNverts () const

virtual int	v_GetNtraces () const

virtual LibUtilities::ShapeType	v_DetShapeType () const

virtual int	v_NumDGBndryCoeffs () const

virtual int	v_GetTraceNcoeffs (const int i) const

virtual int	v_GetTraceNumPoints (const int i) const

virtual int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)

virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_x, Array< OneD, NekDouble > &coords_y, Array< OneD, NekDouble > &coords_z)

virtual bool	v_IsBoundaryInteriorExpansion ()

virtual const LibUtilities::BasisKey	v_GetTraceBasisKey (const int i, const int j) const

virtual void	v_GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray)

virtual void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)

virtual void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_GeneralMatrixOp_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)

Protected Member Functions inherited from Nektar::StdRegions::StdExpansion2D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

virtual NekDouble	v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)

virtual void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)

virtual void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)

virtual void	v_GetElmtTraceToTraceMap (const unsigned int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q)
	Determine the mapping to re-orientate the coefficients along the element trace (assumed to align with the standard element) into the orientation of the local trace given by edgeOrient. More...

virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)

Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr	CreateStdMatrix (const StdMatrixKey &mkey)

DNekBlkMatSharedPtr	CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
	Create the static condensation of a matrix when using a boundary interior decomposition. More...

void	BwdTrans_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)

void	LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)

void	HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)

virtual NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)

template<int DIR>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
	This function performs the barycentric interpolation of the polynomial stored in `coord` at a point `physvals` using barycentric interpolation weights in direction. More...

template<int DIR>
NekDouble	BaryEvaluateBasis (const NekDouble &coord, const int &mode)

Protected Attributes
LibUtilities::PointsKey	m_nodalPointsKey

Protected Attributes inherited from Nektar::StdRegions::StdExpansion
Array< OneD, LibUtilities::BasisSharedPtr >	m_base

int	m_elmt_id

int	m_ncoeffs

LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess >	m_stdMatrixManager

LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess >	m_stdStaticCondMatrixManager

Detailed Description

Definition at line 47 of file StdNodalTriExp.h.

Constructor & Destructor Documentation

◆ StdNodalTriExp() [1/3]

Nektar::StdRegions::StdNodalTriExp::StdNodalTriExp ( )

Definition at line 46 of file StdNodalTriExp.cpp.

                                : StdTriExp(), m_nodalPointsKey()
 {
 }

◆ StdNodalTriExp() [2/3]

Nektar::StdRegions::StdNodalTriExp::StdNodalTriExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		const LibUtilities::PointsType	Ntype
	)

Definition at line 50 of file StdNodalTriExp.cpp.

     : StdExpansion(LibUtilities::StdTriData::getNumberOfCoefficients(
                        Ba.GetNumModes(), Bb.GetNumModes()),
                    2, Ba, Bb),
       StdExpansion2D(LibUtilities::StdTriData::getNumberOfCoefficients(
                          Ba.GetNumModes(), Bb.GetNumModes()),
                      Ba, Bb),
       StdTriExp(Ba, Bb), m_nodalPointsKey(Ba.GetNumModes(), Ntype)
 {
     ASSERTL0(m_base[0]->GetNumModes() == m_base[1]->GetNumModes(),
              "Nodal basis initiated with different orders in the a "
              "and b directions");
 }

References ASSERTL0, and Nektar::StdRegions::StdExpansion::m_base.

◆ StdNodalTriExp() [3/3]

Nektar::StdRegions::StdNodalTriExp::StdNodalTriExp ( const StdNodalTriExp & T )

Definition at line 66 of file StdNodalTriExp.cpp.

     : StdExpansion(T), StdExpansion2D(T), StdTriExp(T),
       m_nodalPointsKey(T.m_nodalPointsKey)
 {
 }

◆ ~StdNodalTriExp()

Nektar::StdRegions::StdNodalTriExp::~StdNodalTriExp ( )

Definition at line 72 of file StdNodalTriExp.cpp.

73 {

74 }

Member Function Documentation

◆ GenNBasisTransMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdNodalTriExp::GenNBasisTransMatrix ( )

Definition at line 132 of file StdNodalTriExp.cpp.

 {
     int i, j;
     Array<OneD, const NekDouble> r, s;
     Array<OneD, NekDouble> c(2);
     DNekMatSharedPtr Mat;
  
     Mat = MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, m_ncoeffs);
     GetNodalPoints(r, s);
  
     // Store the values of m_phys in a temporary array
     int nqtot = GetTotPoints();
     Array<OneD, NekDouble> phys(nqtot);
  
     for (i = 0; i < m_ncoeffs; ++i)
     {
         // fill physical space with mode i
         StdTriExp::v_FillMode(i, phys);
  
         // interpolate mode i to the Nodal points 'j' and
         // store in outarray
         for (j = 0; j < m_ncoeffs; ++j)
         {
             c[0]         = r[j];
             c[1]         = s[j];
             (*Mat)(j, i) = StdTriExp::v_PhysEvaluate(c, phys);
         }
     }
     return Mat;
 }

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), GetNodalPoints(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdTriExp::v_FillMode(), and Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate().

Referenced by v_GenMatrix().

◆ GetNodalPoints()

void Nektar::StdRegions::StdNodalTriExp::GetNodalPoints	(	Array< OneD, const NekDouble > &	x,
		Array< OneD, const NekDouble > &	y
	)

Definition at line 126 of file StdNodalTriExp.cpp.

 {
     LibUtilities::PointsManager()[m_nodalPointsKey]->GetPoints(x, y);
 }

References m_nodalPointsKey, and Nektar::LibUtilities::PointsManager().

Referenced by GenNBasisTransMatrix().

◆ ModalToNodal()

void Nektar::StdRegions::StdNodalTriExp::ModalToNodal	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Definition at line 113 of file StdNodalTriExp.cpp.

 {
     StdMatrixKey Nkey(eNBasisTrans, DetShapeType(), *this, NullConstFactorMap,
                       NullVarCoeffMap, m_nodalPointsKey.GetPointsType());
     DNekMatSharedPtr vdm = GetStdMatrix(Nkey);
  
     // Multiply out matrix
     NekVector<NekDouble> modal(m_ncoeffs, inarray, eWrapper);
     NekVector<NekDouble> nodal(m_ncoeffs, outarray, eWrapper);
     nodal = (*vdm) * modal;
 }

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eNBasisTrans, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, and Nektar::StdRegions::NullVarCoeffMap.

Referenced by Nektar::GlobalMapping::UpdateGeometry().

◆ NodalToModal()

void Nektar::StdRegions::StdNodalTriExp::NodalToModal	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Definition at line 85 of file StdNodalTriExp.cpp.

 {
     StdMatrixKey Nkey(eInvNBasisTrans, DetShapeType(), *this,
                       NullConstFactorMap, NullVarCoeffMap,
                       m_nodalPointsKey.GetPointsType());
     DNekMatSharedPtr inv_vdm = GetStdMatrix(Nkey);
  
     NekVector<NekDouble> nodal(m_ncoeffs, inarray, eWrapper);
     NekVector<NekDouble> modal(m_ncoeffs, outarray, eWrapper);
     modal = (*inv_vdm) * nodal;
 }

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eInvNBasisTrans, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, and Nektar::StdRegions::NullVarCoeffMap.

Referenced by v_BwdTrans_SumFac().

◆ NodalToModalTranspose()

void Nektar::StdRegions::StdNodalTriExp::NodalToModalTranspose	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Definition at line 99 of file StdNodalTriExp.cpp.

 {
     StdMatrixKey Nkey(eInvNBasisTrans, DetShapeType(), *this,
                       NullConstFactorMap, NullVarCoeffMap,
                       m_nodalPointsKey.GetPointsType());
     DNekMatSharedPtr inv_vdm = GetStdMatrix(Nkey);
  
     NekVector<NekDouble> nodal(m_ncoeffs, inarray, eCopy);
     NekVector<NekDouble> modal(m_ncoeffs, outarray, eWrapper);
     modal = Transpose(*inv_vdm) * nodal;
 }

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvNBasisTrans, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, Nektar::StdRegions::NullVarCoeffMap, and Nektar::Transpose().

Referenced by Nektar::LocalRegions::NodalTriExp::IProductWRTBase_SumFac(), Nektar::LocalRegions::NodalTriExp::IProductWRTDerivBase_SumFac(), v_IProductWRTBase_SumFac(), and v_IProductWRTDerivBase_SumFac().

◆ v_BwdTrans()

void Nektar::StdRegions::StdNodalTriExp::v_BwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Backward tranform for triangular elements.

Note: 'q' (base[1]) runs fastest in this element.

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 167 of file StdNodalTriExp.cpp.

 {
     v_BwdTrans_SumFac(inarray, outarray);
 }

References v_BwdTrans_SumFac().

Referenced by v_FillMode().

◆ v_BwdTrans_SumFac()

void Nektar::StdRegions::StdNodalTriExp::v_BwdTrans_SumFac	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 173 of file StdNodalTriExp.cpp.

 {
     Array<OneD, NekDouble> tmp(m_ncoeffs);
     NodalToModal(inarray, tmp);
     StdTriExp::v_BwdTrans_SumFac(tmp, outarray);
 }

References Nektar::StdRegions::StdExpansion::m_ncoeffs, NodalToModal(), and Nektar::StdRegions::StdTriExp::v_BwdTrans_SumFac().

Referenced by v_BwdTrans().

◆ v_CreateStdMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdNodalTriExp::v_CreateStdMatrix ( const StdMatrixKey & mkey )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 407 of file StdNodalTriExp.cpp.

 {
     return StdNodalTriExp::v_GenMatrix(mkey);
 }

References v_GenMatrix().

◆ v_FillMode()

void Nektar::StdRegions::StdNodalTriExp::v_FillMode	(	const int	mode,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 237 of file StdNodalTriExp.cpp.

 {
     ASSERTL2(mode >= m_ncoeffs,
              "calling argument mode is larger than total expansion order");
  
     Vmath::Zero(m_ncoeffs, outarray, 1);
     outarray[mode] = 1.0;
     v_BwdTrans(outarray, outarray);
 }

References ASSERTL2, Nektar::StdRegions::StdExpansion::m_ncoeffs, v_BwdTrans(), and Vmath::Zero().

◆ v_FwdTrans()

void Nektar::StdRegions::StdNodalTriExp::v_FwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Transform a given function from physical quadrature space to coefficient space.

See also: StdExpansion::FwdTrans

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 182 of file StdNodalTriExp.cpp.

 {
     v_IProductWRTBase(inarray, outarray);
  
     // get Mass matrix inverse
     StdMatrixKey masskey(eInvMass, DetShapeType(), *this, NullConstFactorMap,
                          NullVarCoeffMap, m_nodalPointsKey.GetPointsType());
     DNekMatSharedPtr matsys = GetStdMatrix(masskey);
  
     // copy inarray in case inarray == outarray
     NekVector<NekDouble> in(m_ncoeffs, outarray, eCopy);
     NekVector<NekDouble> out(m_ncoeffs, outarray, eWrapper);
  
     out = (*matsys) * in;
 }

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, Nektar::StdRegions::NullVarCoeffMap, and v_IProductWRTBase().

◆ v_GenMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdNodalTriExp::v_GenMatrix ( const StdMatrixKey & mkey )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 390 of file StdNodalTriExp.cpp.

 {
     DNekMatSharedPtr Mat;
  
     switch (mkey.GetMatrixType())
     {
         case eNBasisTrans:
             Mat = GenNBasisTransMatrix();
             break;
         default:
             Mat = StdExpansion::CreateGeneralMatrix(mkey);
             break;
     }
  
     return Mat;
 }

References Nektar::StdRegions::StdExpansion::CreateGeneralMatrix(), Nektar::StdRegions::eNBasisTrans, GenNBasisTransMatrix(), and Nektar::StdRegions::StdMatrixKey::GetMatrixType().

Referenced by v_CreateStdMatrix().

◆ v_GetBoundaryMap()

void Nektar::StdRegions::StdNodalTriExp::v_GetBoundaryMap ( Array< OneD, unsigned int > & outarray )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 372 of file StdNodalTriExp.cpp.

 {
     unsigned int i;
     if (outarray.size() != NumBndryCoeffs())
     {
         outarray = Array<OneD, unsigned int>(NumBndryCoeffs());
     }
  
     for (i = 0; i < NumBndryCoeffs(); i++)
     {
         outarray[i] = i;
     }
 }

References Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

◆ v_GetInteriorMap()

void Nektar::StdRegions::StdNodalTriExp::v_GetInteriorMap ( Array< OneD, unsigned int > & outarray )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 358 of file StdNodalTriExp.cpp.

 {
     unsigned int i;
     if (outarray.size() != GetNcoeffs() - NumBndryCoeffs())
     {
         outarray = Array<OneD, unsigned int>(GetNcoeffs() - NumBndryCoeffs());
     }
  
     for (i = NumBndryCoeffs(); i < GetNcoeffs(); i++)
     {
         outarray[i - NumBndryCoeffs()] = i;
     }
 }

References Nektar::StdRegions::StdExpansion::GetNcoeffs(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

◆ v_GetNodalPointsKey()

virtual const LibUtilities::PointsKey Nektar::StdRegions::StdNodalTriExp::v_GetNodalPointsKey ( ) const

inlineprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 76 of file StdNodalTriExp.h.

     {
         return m_nodalPointsKey;
     };

References m_nodalPointsKey.

◆ v_GetTraceInteriorToElementMap()

void Nektar::StdRegions::StdNodalTriExp::v_GetTraceInteriorToElementMap	(	const int	eid,
		Array< OneD, unsigned int > &	maparray,
		Array< OneD, int > &	signarray,
		const Orientation	edgeOrient = `eForwards`
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 319 of file StdNodalTriExp.cpp.

 {
     ASSERTL0(eid >= 0 && eid <= 2, "Local Edge ID must be between 0 and 2");
  
     const int nEdgeIntCoeffs = GetTraceNcoeffs(eid) - 2;
  
     if (maparray.size() != nEdgeIntCoeffs)
     {
         maparray = Array<OneD, unsigned int>(nEdgeIntCoeffs);
     }
  
     if (signarray.size() != nEdgeIntCoeffs)
     {
         signarray = Array<OneD, int>(nEdgeIntCoeffs, 1);
     }
     else
     {
         fill(signarray.get(), signarray.get() + nEdgeIntCoeffs, 1);
     }
  
     Orientation orient = edgeOrient;
     if (eid == 2)
     {
         orient = orient == eForwards ? eBackwards : eForwards;
     }
  
     for (int i = 0; i < nEdgeIntCoeffs; i++)
     {
         maparray[i] = eid * nEdgeIntCoeffs + 3 + i;
     }
  
     if (orient == eBackwards)
     {
         reverse(maparray.get(), maparray.get() + nEdgeIntCoeffs);
     }
 }

References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::StdRegions::eForwards, and Nektar::StdRegions::StdExpansion::GetTraceNcoeffs().

◆ v_GetTraceToElementMap()

void Nektar::StdRegions::StdNodalTriExp::v_GetTraceToElementMap	(	const int	eid,
		Array< OneD, unsigned int > &	maparray,
		Array< OneD, int > &	signarray,
		Orientation	edgeOrient = `eForwards`,
		int	P = `-1`,
		int	Q = `-1`
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion2D.

Definition at line 270 of file StdNodalTriExp.cpp.

 {
     boost::ignore_unused(Q);
  
     ASSERTL0(eid >= 0 && eid <= 2, "Local Edge ID must be between 0 and 2");
  
     const int nEdgeCoeffs = GetTraceNcoeffs(eid);
  
     ASSERTL0(P == -1 || P == nEdgeCoeffs,
              "Nodal triangle not set up to deal with variable "
              "polynomial order.");
  
     if (maparray.size() != nEdgeCoeffs)
     {
         maparray = Array<OneD, unsigned int>(nEdgeCoeffs);
     }
  
     if (signarray.size() != nEdgeCoeffs)
     {
         signarray = Array<OneD, int>(nEdgeCoeffs, 1);
     }
     else
     {
         fill(signarray.get(), signarray.get() + nEdgeCoeffs, 1);
     }
  
     Orientation orient = edgeOrient;
     if (eid == 2)
     {
         orient = orient == eForwards ? eBackwards : eForwards;
     }
  
     maparray[0]               = eid;
     maparray[nEdgeCoeffs - 1] = eid == 2 ? 0 : eid + 1;
     for (int i = 2; i < nEdgeCoeffs; i++)
     {
         maparray[i - 1] = eid * (nEdgeCoeffs - 2) + 1 + i;
     }
  
     if (orient == eBackwards)
     {
         reverse(maparray.get(), maparray.get() + nEdgeCoeffs);
     }
 }

References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::StdRegions::eForwards, Nektar::StdRegions::StdExpansion::GetTraceNcoeffs(), and Nektar::LibUtilities::P.

◆ v_GetVertexMap()

int Nektar::StdRegions::StdNodalTriExp::v_GetVertexMap	(	int	localVertexId,
		bool	useCoeffPacking = `false`
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 261 of file StdNodalTriExp.cpp.

 {
     boost::ignore_unused(useCoeffPacking);
     ASSERTL0(localVertexId >= 0 && localVertexId <= 2,
              "Local Vertex ID must be between 0 and 2");
     return localVertexId;
 }

References ASSERTL0.

◆ v_HelmholtzMatrixOp()

void Nektar::StdRegions::StdNodalTriExp::v_HelmholtzMatrixOp	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 446 of file StdNodalTriExp.cpp.

 {
     StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(inarray, outarray,
                                                         mkey);
 }

References Nektar::StdRegions::StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl().

◆ v_IProductWRTBase()

void Nektar::StdRegions::StdNodalTriExp::v_IProductWRTBase	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray.

\( \begin{array}{rcl} I_{pq} = (\phi^A_q \phi^B_{pq}, u) &=& \sum_{i=0}^{nq_0}\sum_{j=0}^{nq_1} \phi^A_p(\eta_{0,i})\phi^B_{pq}(\eta_{1,j}) w^0_i w^1_j u(\xi_{0,i} \xi_{1,j}) \\ & = & \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) \tilde{u}_{i,j} \end{array} \)

where

\( \tilde{u}_{i,j} = w^0_i w^1_j u(\xi_{0,i},\xi_{1,j}) \)

which can be implemented as

\( f_{pj} = \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \tilde{u}_{i,j} \rightarrow {\bf B_1 U} \) \( I_{pq} = \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) f_{pj} \rightarrow {\bf B_2[p*skip] f[skip]} \)

Recall: \( \eta_{1} = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \, \eta_2 = \xi_2\)

Note: For the orthgonality of this expansion to be realised the 'q' ordering must run fastest in contrast to the Quad and Hex ordering where 'p' index runs fastest to be consistent with the quadrature ordering.

In the triangular space the i (i.e. \(\eta_1\) direction) ordering still runs fastest by convention.

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 203 of file StdNodalTriExp.cpp.

 {
     v_IProductWRTBase_SumFac(inarray, outarray);
 }

References v_IProductWRTBase_SumFac().

Referenced by v_FwdTrans().

◆ v_IProductWRTBase_SumFac()

void Nektar::StdRegions::StdNodalTriExp::v_IProductWRTBase_SumFac	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		bool	multiplybyweights = `true`
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 210 of file StdNodalTriExp.cpp.

 {
     StdTriExp::v_IProductWRTBase_SumFac(inarray, outarray, multiplybyweights);
     NodalToModalTranspose(outarray, outarray);
 }

References NodalToModalTranspose(), and Nektar::StdRegions::StdTriExp::v_IProductWRTBase_SumFac().

Referenced by v_IProductWRTBase().

◆ v_IProductWRTDerivBase()

void Nektar::StdRegions::StdNodalTriExp::v_IProductWRTDerivBase	(	const int	dir,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 218 of file StdNodalTriExp.cpp.

 {
     v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
 }

References v_IProductWRTDerivBase_SumFac().

◆ v_IProductWRTDerivBase_SumFac()

void Nektar::StdRegions::StdNodalTriExp::v_IProductWRTDerivBase_SumFac	(	const int	dir,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 225 of file StdNodalTriExp.cpp.

 {
     StdTriExp::v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
     NodalToModalTranspose(outarray, outarray);
 }

References NodalToModalTranspose(), and Nektar::StdRegions::StdTriExp::v_IProductWRTDerivBase_SumFac().

Referenced by v_IProductWRTDerivBase().

◆ v_IsNodalNonTensorialExp()

bool Nektar::StdRegions::StdNodalTriExp::v_IsNodalNonTensorialExp ( )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 76 of file StdNodalTriExp.cpp.

 {
     return true;
 }

◆ v_LaplacianMatrixOp() [1/2]

void Nektar::StdRegions::StdNodalTriExp::v_LaplacianMatrixOp	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 423 of file StdNodalTriExp.cpp.

 {
     StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(inarray, outarray,
                                                         mkey);
 }

References Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl().

◆ v_LaplacianMatrixOp() [2/2]

void Nektar::StdRegions::StdNodalTriExp::v_LaplacianMatrixOp	(	const int	k1,
		const int	k2,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 431 of file StdNodalTriExp.cpp.

 {
     StdExpansion::LaplacianMatrixOp_MatFree(k1, k2, inarray, outarray, mkey);
 }

References Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree().

◆ v_MassMatrixOp()

void Nektar::StdRegions::StdNodalTriExp::v_MassMatrixOp	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 416 of file StdNodalTriExp.cpp.

 {
     StdExpansion::MassMatrixOp_MatFree(inarray, outarray, mkey);
 }

References Nektar::StdRegions::StdExpansion::MassMatrixOp_MatFree().

◆ v_NumBndryCoeffs()

int Nektar::StdRegions::StdNodalTriExp::v_NumBndryCoeffs ( ) const

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 252 of file StdNodalTriExp.cpp.

 {
     return 3 + (GetBasisNumModes(0) - 2) + 2 * (GetBasisNumModes(1) - 2);
 }

References Nektar::StdRegions::StdExpansion::GetBasisNumModes().

◆ v_WeakDerivMatrixOp()

void Nektar::StdRegions::StdNodalTriExp::v_WeakDerivMatrixOp	(	const int	i,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Reimplemented in Nektar::LocalRegions::NodalTriExp.

Definition at line 439 of file StdNodalTriExp.cpp.

 {
     StdExpansion::WeakDerivMatrixOp_MatFree(i, inarray, outarray, mkey);
 }

References Nektar::StdRegions::StdExpansion::WeakDerivMatrixOp_MatFree().

Member Data Documentation

◆ m_nodalPointsKey

LibUtilities::PointsKey Nektar::StdRegions::StdNodalTriExp::m_nodalPointsKey

protected

Definition at line 74 of file StdNodalTriExp.h.

Referenced by Nektar::LocalRegions::NodalTriExp::CreateStdMatrix(), Nektar::LocalRegions::NodalTriExp::FwdTrans(), GetNodalPoints(), ModalToNodal(), NodalToModal(), NodalToModalTranspose(), v_FwdTrans(), Nektar::LocalRegions::NodalTriExp::v_GetLinStdExp(), v_GetNodalPointsKey(), and Nektar::LocalRegions::NodalTriExp::v_GetStdExp().

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ StdNodalTriExp() [1/3]

◆ StdNodalTriExp() [2/3]

◆ StdNodalTriExp() [3/3]

◆ ~StdNodalTriExp()

Member Function Documentation

◆ GenNBasisTransMatrix()

◆ GetNodalPoints()

◆ ModalToNodal()

◆ NodalToModal()

◆ NodalToModalTranspose()

◆ v_BwdTrans()

◆ v_BwdTrans_SumFac()

◆ v_CreateStdMatrix()

◆ v_FillMode()

◆ v_FwdTrans()

◆ v_GenMatrix()

◆ v_GetBoundaryMap()

◆ v_GetInteriorMap()

◆ v_GetNodalPointsKey()

◆ v_GetTraceInteriorToElementMap()

◆ v_GetTraceToElementMap()

◆ v_GetVertexMap()

◆ v_HelmholtzMatrixOp()

◆ v_IProductWRTBase()

◆ v_IProductWRTBase_SumFac()

◆ v_IProductWRTDerivBase()

◆ v_IProductWRTDerivBase_SumFac()

◆ v_IsNodalNonTensorialExp()

◆ v_LaplacianMatrixOp() [1/2]

◆ v_LaplacianMatrixOp() [2/2]

◆ v_MassMatrixOp()

◆ v_NumBndryCoeffs()

◆ v_WeakDerivMatrixOp()

Member Data Documentation

◆ m_nodalPointsKey