Class representing a segment element in reference space. More...

#include <StdSegExp.h>

Inheritance diagram for Nektar::StdRegions::StdSegExp:

Public Member Functions
	StdSegExp ()
	Default constructor. More...

	StdSegExp (const LibUtilities::BasisKey &Ba)
	Constructor using BasisKey class for quadrature points and order definition. More...

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

	~StdSegExp ()

Public Member Functions inherited from Nektar::StdRegions::StdExpansion1D
	StdExpansion1D ()

	StdExpansion1D (int numcoeffs, const LibUtilities::BasisKey &Ba)

	StdExpansion1D (const StdExpansion1D &T)

virtual	~StdExpansion1D ()

void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray. More...

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	FwdTrans_BndConstrained (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	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 NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray)
	Integrate the physical point list inarray over region and return the value. More...

virtual void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
	Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray. 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=NullNekDouble1DArray, 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 (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Backward transform from coefficient space given in inarray and evaluate at the physical quadrature points outarray. More...

virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in outarray. More...

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

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

virtual void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Inner product of inarray over region with respect to the expansion basis (this)->m_base[0] and return in outarray. More...

virtual void	v_IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)
	Inner product of inarray over region with respect to expansion basis base and return in 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_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 void	v_LaplacianMatrixOp (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 void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)

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

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

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

virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_0, Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2)

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

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

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

virtual int	v_GetNverts () const

virtual int	v_GetNtraces () const

virtual int	v_GetTraceNcoeffs (const int i) const

virtual int	v_GetTraceNumPoints (const int i) const

virtual int	v_NumBndryCoeffs () const

virtual int	v_NumDGBndryCoeffs () const

virtual bool	v_IsBoundaryInteriorExpansion ()

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

virtual LibUtilities::ShapeType	v_DetShapeType () const
	Return Shape of region, using ShapeType enum list. i.e. Segment. More...

virtual DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey)

virtual DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey)

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

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

virtual void	v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q)

Protected Member Functions inherited from Nektar::StdRegions::StdExpansion1D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override

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)

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

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)

Additional Inherited Members
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

Class representing a segment element in reference space.

All interface of this class sits in StdExpansion class

Definition at line 53 of file StdSegExp.h.

Constructor & Destructor Documentation

◆ StdSegExp() [1/3]

Nektar::StdRegions::StdSegExp::StdSegExp ( )

Default constructor.

Definition at line 50 of file StdSegExp.cpp.

51 {

52 }

◆ StdSegExp() [2/3]

Nektar::StdRegions::StdSegExp::StdSegExp ( const LibUtilities::BasisKey & Ba )

Constructor using BasisKey class for quadrature points and order definition.

Parameters

Ba	BasisKey class definition containing order and quadrature points.

Definition at line 62 of file StdSegExp.cpp.

                                                           :
         StdExpansion(Ba.GetNumModes(), 1, Ba),
         StdExpansion1D(Ba.GetNumModes(),Ba)
         {
         }

◆ StdSegExp() [3/3]

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

Copy Constructor.

Definition at line 71 of file StdSegExp.cpp.

                                               :
                 StdExpansion(T),
                 StdExpansion1D(T)
         {
         }

◆ ~StdSegExp()

Nektar::StdRegions::StdSegExp::~StdSegExp ( )

Definition at line 78 of file StdSegExp.cpp.

79 {

80 }

Member Function Documentation

◆ v_BwdTrans()

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

protectedvirtual

Backward transform from coefficient space given in inarray and evaluate at the physical quadrature points outarray.

Operation can be evaluated as \( u(\xi_{1i}) = \sum_{p=0}^{order-1} \hat{u}_p \phi_p(\xi_{1i}) \) or equivalently \( {\bf u} = {\bf B}^T {\bf \hat{u}} \) where \({\bf B}[i][j] = \phi_i(\xi_{1j}), \mbox{\_coeffs}[p] = {\bf \hat{u}}[p] \)

The function takes the coefficient array inarray as input for the transformation

Parameters

inarray	the coeffficients of the expansion
outarray	the resulting array of the values of the function at the physical quadrature points will be stored in the array outarray

Implements Nektar::StdRegions::StdExpansion.

Definition at line 223 of file StdSegExp.cpp.

         {
             int  nquad = m_base[0]->GetNumPoints();
  
             if(m_base[0]->Collocation())
             {
                 Vmath::Vcopy(nquad, inarray, 1, outarray, 1);
             }
             else
             {
  
             Blas::Dgemv('N',nquad,m_base[0]->GetNumModes(),1.0,
                         (m_base[0]->GetBdata()).get(),
                         nquad,&inarray[0],1,0.0,&outarray[0],1);
  
             }
         }

References Blas::Dgemv(), Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vcopy().

Referenced by v_BwdTrans_SumFac(), v_HelmholtzMatrixOp(), and v_LaplacianMatrixOp().

◆ v_BwdTrans_SumFac()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 393 of file StdSegExp.cpp.

         {
             v_BwdTrans(inarray, outarray);
         }

References v_BwdTrans().

◆ v_CalcNumberOfCoefficients()

int Nektar::StdRegions::StdSegExp::v_CalcNumberOfCoefficients	(	const std::vector< unsigned int > &	nummodes,
		int &	modes_offset
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 732 of file StdSegExp.cpp.

         {
             int nmodes = nummodes[modes_offset];
             modes_offset += 1;
  
             return nmodes;
         }

◆ v_CreateStdMatrix()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 812 of file StdSegExp.cpp.

         {
             return v_GenMatrix(mkey);
         }

References v_GenMatrix().

◆ v_DetShapeType()

LibUtilities::ShapeType Nektar::StdRegions::StdSegExp::v_DetShapeType ( ) const

protectedvirtual

Return Shape of region, using ShapeType enum list. i.e. Segment.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 85 of file StdSegExp.cpp.

         {
             return LibUtilities::eSegment;
         }

References Nektar::LibUtilities::eSegment.

Referenced by v_FwdTrans(), v_FwdTrans_BndConstrained(), and v_GenMatrix().

◆ v_ExponentialFilter()

void Nektar::StdRegions::StdSegExp::v_ExponentialFilter	(	Array< OneD, NekDouble > &	array,
		const NekDouble	alpha,
		const NekDouble	exponent,
		const NekDouble	cutoff
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 629 of file StdSegExp.cpp.

         {
             // Generate an orthogonal expansion
             int nq     = m_base[0]->GetNumPoints();
             int nmodes = m_base[0]->GetNumModes();
             int P  = nmodes - 1;
             // Declare orthogonal basis.
             LibUtilities::PointsKey pKey(nq,m_base[0]->GetPointsType());
  
             LibUtilities::BasisKey B(LibUtilities::eOrtho_A, nmodes, pKey);
             StdSegExp OrthoExp(B);
  
             // Cutoff
             int Pcut = cutoff*P;
  
             // Project onto orthogonal space.
             Array<OneD, NekDouble> orthocoeffs(OrthoExp.GetNcoeffs());
             OrthoExp.FwdTrans(array,orthocoeffs);
  
             //
             NekDouble fac;
             for(int j = 0; j < nmodes; ++j)
             {
                 //to filter out only the "high-modes"
                 if(j > Pcut)
                 {
                     fac = (NekDouble) (j - Pcut) / ( (NekDouble) (P - Pcut) );
                     fac = pow(fac, exponent);
                     orthocoeffs[j] *= exp(-alpha*fac);
                 }
             }
  
             // backward transform to physical space
             OrthoExp.BwdTrans(orthocoeffs,array);
         }

References Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::LibUtilities::eOrtho_A, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::m_base, and main::P.

◆ v_FillMode()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 528 of file StdSegExp.cpp.

         {
             int   nquad = m_base[0]->GetNumPoints();
             const NekDouble * base  = m_base[0]->GetBdata().get();
  
             ASSERTL2(mode <= m_ncoeffs,
              "calling argument mode is larger than total expansion order");
  
             Vmath::Vcopy(nquad,(NekDouble *)base+mode*nquad,1, &outarray[0],1);
         }

References ASSERTL2, Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, and Vmath::Vcopy().

◆ v_FwdTrans()

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

protectedvirtual

Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in outarray.

Perform a forward transform using a Galerkin projection by taking the inner product of the physical points and multiplying by the inverse of the mass matrix using the Solve method of the standard matrix container holding the local mass matrix, i.e. \( {\bf \hat{u}} = {\bf M}^{-1} {\bf I} \) where \( {\bf I}[p] = \int^1_{-1} \phi_p(\xi_1) u(\xi_1) d\xi_1 \)

This function stores the expansion coefficients calculated by the transformation in the coefficient space array outarray

Parameters

inarray	array of physical quadrature points to be transformed
outarray	the coeffficients of the expansion

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 297 of file StdSegExp.cpp.

         {
             if(m_base[0]->Collocation())
             {
                 Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
             }
             else
             {
                 v_IProductWRTBase(inarray,outarray);
  
                 // get Mass matrix inverse
                 StdMatrixKey      masskey(eInvMass,v_DetShapeType(),*this);
                 DNekMatSharedPtr  matsys = GetStdMatrix(masskey);
  
                 NekVector<NekDouble> in(m_ncoeffs,outarray,eCopy);
                 NekVector<NekDouble> out(m_ncoeffs,outarray,eWrapper);
  
                 out = (*matsys)*in;
             }
         }

References Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, v_DetShapeType(), v_IProductWRTBase(), and Vmath::Vcopy().

Referenced by v_FwdTrans_BndConstrained().

◆ v_FwdTrans_BndConstrained()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 319 of file StdSegExp.cpp.

         {
             if(m_base[0]->Collocation())
             {
                 Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
             }
             else
             {
                 int nInteriorDofs = m_ncoeffs-2;
                 int offset        = 0;
  
                 switch(m_base[0]->GetBasisType())
                 {
                 case LibUtilities::eGLL_Lagrange:
                     {
                         offset = 1;
                     }
                     break;
                 case LibUtilities::eGauss_Lagrange:
                 {
                     nInteriorDofs = m_ncoeffs;
                     offset = 0;
                 }
                 break;
                 case LibUtilities::eModified_A:
                 case LibUtilities::eModified_B:
                     {
                         offset = 2;
                     }
                     break;
                 default:
                     ASSERTL0(false,"This type of FwdTrans is not defined for this expansion type");
                 }
  
                 fill(outarray.get(), outarray.get()+m_ncoeffs, 0.0 );
  
                 if(m_base[0]->GetBasisType() != LibUtilities::eGauss_Lagrange)
                 {
                     outarray[GetVertexMap(0)] = inarray[0];
                     outarray[GetVertexMap(1)] = inarray[m_base[0]->GetNumPoints()-1];
  
                     if(m_ncoeffs>2)
                     {
                         // ideally, we would like to have tmp0 to be replaced by
                         // outarray (currently MassMatrixOp does not allow aliasing)
                         Array<OneD, NekDouble> tmp0(m_ncoeffs);
                         Array<OneD, NekDouble> tmp1(m_ncoeffs);
  
                         StdMatrixKey      masskey(eMass,v_DetShapeType(),*this);
                         MassMatrixOp(outarray,tmp0,masskey);
                         v_IProductWRTBase(inarray,tmp1);
  
                         Vmath::Vsub(m_ncoeffs, tmp1, 1, tmp0, 1, tmp1, 1);
  
                         // get Mass matrix inverse (only of interior DOF)
                         DNekMatSharedPtr  matsys =
                         (m_stdStaticCondMatrixManager[masskey])-> GetBlock(1,1);
  
                         Blas::Dgemv('N',nInteriorDofs,nInteriorDofs,1.0,
                                 &(matsys->GetPtr())[0],nInteriorDofs,tmp1.get()
                                 +offset,1,0.0,outarray.get()+offset,1);
                     }
                 }
                 else
                 {
                     StdSegExp::v_FwdTrans(inarray, outarray);
                 }
             }
  
         }

References ASSERTL0, Blas::Dgemv(), Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGLL_Lagrange, Nektar::StdRegions::eMass, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetVertexMap(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::m_stdStaticCondMatrixManager, Nektar::StdRegions::StdExpansion::MassMatrixOp(), v_DetShapeType(), v_FwdTrans(), v_IProductWRTBase(), Vmath::Vcopy(), and Vmath::Vsub().

◆ v_GenMatrix()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 746 of file StdSegExp.cpp.

         {
             DNekMatSharedPtr Mat;
             MatrixType mattype;
  
             switch(mattype = mkey.GetMatrixType())
             {
             case ePhysInterpToEquiSpaced:
                 {
                     int nq = m_base[0]->GetNumPoints();
  
                     // take definition from key
                     if(mkey.ConstFactorExists(eFactorConst))
                     {
                         nq = (int) mkey.GetConstFactor(eFactorConst);
                     }
  
                     int neq = LibUtilities::StdSegData::
                                               getNumberOfCoefficients(nq);
                     Array<OneD, NekDouble >   coords (1);
                     DNekMatSharedPtr          I     ;
                     Mat                     = MemoryManager<DNekMat>::
                                                 AllocateSharedPtr(neq, nq);
  
                     for(int i = 0; i < neq; ++i)
                     {
                         coords[0] = -1.0 + 2*i/(NekDouble)(neq-1);
                         I         = m_base[0]->GetI(coords);
                         Vmath::Vcopy(nq, I->GetRawPtr(), 1,
                                          Mat->GetRawPtr()+i,neq);
                     }
                 }
                 break;
             case eFwdTrans:
                 {
                     Mat = MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs,m_ncoeffs);
                     StdMatrixKey iprodkey(eIProductWRTBase,v_DetShapeType(),*this);
                     DNekMat &Iprod = *GetStdMatrix(iprodkey);
                     StdMatrixKey imasskey(eInvMass,v_DetShapeType(),*this);
                     DNekMat &Imass = *GetStdMatrix(imasskey);
  
                     (*Mat) = Imass*Iprod;
                 }
                 break;
             default:
                 {
                     Mat = StdExpansion::CreateGeneralMatrix(mkey);
  
                     if(mattype ==  eMass)
                     {
                         // For Fourier basis set the imaginary component
                         // of mean mode to have a unit diagonal component
                         // in mass matrix
                         if(m_base[0]->GetBasisType() == LibUtilities::eFourier)
                         {
                             (*Mat)(1,1) = 1.0;
                         }
                     }
                 }
                 break;
             }
  
             return Mat;
         }

Referenced by v_CreateStdMatrix().

◆ v_GetBoundaryMap()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 822 of file StdSegExp.cpp.

         {
             if(outarray.size() != NumBndryCoeffs())
             {
                 outarray = Array<OneD, unsigned int>(NumBndryCoeffs());
             }
             const LibUtilities::BasisType Btype = GetBasisType(0);
             int nummodes = m_base[0]->GetNumModes();
  
             outarray[0] = 0;
  
             switch(Btype)
             {
             case LibUtilities::eGLL_Lagrange:
             case LibUtilities::eGauss_Lagrange:
             case LibUtilities::eChebyshev:
             case LibUtilities::eFourier:
                 outarray[1]= nummodes-1;
                 break;
             case LibUtilities::eModified_A:
             case LibUtilities::eModified_B:
                 outarray[1] = 1;
                 break;
             default:
                 ASSERTL0(0,"Mapping array is not defined for this expansion");
                 break;
             }
         }

References ASSERTL0, Nektar::LibUtilities::eChebyshev, Nektar::LibUtilities::eFourier, Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

◆ v_GetCoords()

void Nektar::StdRegions::StdSegExp::v_GetCoords	(	Array< OneD, NekDouble > &	coords_0,
		Array< OneD, NekDouble > &	coords_1,
		Array< OneD, NekDouble > &	coords_2
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 682 of file StdSegExp.cpp.

         {
             boost::ignore_unused(coords_1, coords_2);
             Blas::Dcopy(GetNumPoints(0),(m_base[0]->GetZ()).get(),
                         1,&coords_0[0],1);
         }

References Blas::Dcopy(), Nektar::StdRegions::StdExpansion::GetNumPoints(), and Nektar::StdRegions::StdExpansion::m_base.

◆ v_GetInteriorMap()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 851 of file StdSegExp.cpp.

         {
             int i;
             if(outarray.size()!=GetNcoeffs()-NumBndryCoeffs())
             {
                 outarray = Array<OneD, unsigned int>(GetNcoeffs()-NumBndryCoeffs());
             }
             const LibUtilities::BasisType Btype = GetBasisType(0);
  
             switch(Btype)
             {
             case LibUtilities::eGLL_Lagrange:
             case LibUtilities::eGauss_Lagrange:
             case LibUtilities::eChebyshev:
             case LibUtilities::eFourier:
                 for(i = 0 ; i < GetNcoeffs()-2;i++)
                 {
                     outarray[i] = i+1;
                 }
                 break;
             case LibUtilities::eModified_A:
             case LibUtilities::eModified_B:
                 for(i = 0 ; i < GetNcoeffs()-2;i++)
                 {
                     outarray[i] = i+2;
                 }
                 break;
             default:
                 ASSERTL0(0,"Mapping array is not defined for this expansion");
                 break;
             }
         }

References ASSERTL0, Nektar::LibUtilities::eChebyshev, Nektar::LibUtilities::eFourier, Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

◆ v_GetNtraces()

int Nektar::StdRegions::StdSegExp::v_GetNtraces ( ) const

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 705 of file StdSegExp.cpp.

         {
             return 2;
         }

◆ v_GetNverts()

int Nektar::StdRegions::StdSegExp::v_GetNverts ( ) const

protectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 700 of file StdSegExp.cpp.

         {
             return 2;
         }

◆ v_GetSimplexEquiSpacedConnectivity()

void Nektar::StdRegions::StdSegExp::v_GetSimplexEquiSpacedConnectivity	(	Array< OneD, int > &	conn,
		bool	standard = `true`
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 900 of file StdSegExp.cpp.

         {
             boost::ignore_unused(standard);
             int np = m_base[0]->GetNumPoints();
  
             conn     = Array<OneD, int>(2*(np-1));
             int cnt  = 0;
             for(int i = 0; i < np-1; ++i)
             {
                 conn[cnt++] = i;
                 conn[cnt++] = i+1;
             }
         }

References Nektar::StdRegions::StdExpansion::m_base.

◆ v_GetTraceNcoeffs()

int Nektar::StdRegions::StdSegExp::v_GetTraceNcoeffs ( const int i ) const

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 710 of file StdSegExp.cpp.

         {
             boost::ignore_unused(i);
             return 1;
         }

◆ v_GetTraceNumPoints()

int Nektar::StdRegions::StdSegExp::v_GetTraceNumPoints ( const int i ) const

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 716 of file StdSegExp.cpp.

         {
             boost::ignore_unused(i);
             return 1;
         }

◆ v_GetTraceToElementMap()

void Nektar::StdRegions::StdSegExp::v_GetTraceToElementMap	(	const int	tid,
		Array< OneD, unsigned int > &	maparray,
		Array< OneD, int > &	signarray,
		Orientation	edgeOrient,
		int	P,
		int	Q
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 916 of file StdSegExp.cpp.

         {
             boost::ignore_unused(P,Q,orient);
             int order0 = m_base[0]->GetNumModes();
     
             ASSERTL0(tid < 2,"eid must be between 0 and 1");
  
             if (maparray.size() != 2)
             {
                 maparray = Array<OneD, unsigned int>(2);
             }
  
             if(signarray.size() != 2)
             {
                 signarray = Array<OneD, int>(2, 1);
             }
             else
             {
                 fill(signarray.get(), signarray.get()+2, 1);
             }
  
             const LibUtilities::BasisType bType = GetBasisType(0);
  
             if (bType == LibUtilities::eModified_A)
             {
                 maparray[0] = 0;
                 maparray[1] = 1;
             }
             else if(bType == LibUtilities::eGLL_Lagrange ||
                     bType == LibUtilities::eGauss_Lagrange)
             {
                 maparray[0] = 0;
                 maparray[1] = order0-1;
             }
             else
             {
                 ASSERTL0(false,"Unknown Basis");
             }
         }

References ASSERTL0, Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, and main::P.

◆ v_GetVertexMap()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 884 of file StdSegExp.cpp.

         {
             boost::ignore_unused(useCoeffPacking);
             ASSERTL0((localVertexId==0)||(localVertexId==1),"local vertex id"
                      "must be between 0 or 1");
  
             int localDOF = localVertexId;
  
             if( (m_base[0]->GetBasisType()==LibUtilities::eGLL_Lagrange) &&
                 (localVertexId==1) )
             {
                 localDOF = m_base[0]->GetNumModes()-1;
             }
             return localDOF;
         }

References ASSERTL0, Nektar::LibUtilities::eGLL_Lagrange, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

◆ v_HelmholtzMatrixOp()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 566 of file StdSegExp.cpp.

         {
             int    nquad = m_base[0]->GetNumPoints();
  
             Array<OneD,NekDouble> physValues(nquad);
             Array<OneD,NekDouble> dPhysValuesdx(nquad);
             Array<OneD,NekDouble> wsp(m_ncoeffs);
  
             v_BwdTrans(inarray,physValues);
  
             // mass matrix operation
             v_IProductWRTBase((m_base[0]->GetBdata()),physValues,wsp,1);
  
             // Laplacian matrix operation
             v_PhysDeriv(physValues,dPhysValuesdx);
             v_IProductWRTBase(m_base[0]->GetDbdata(),dPhysValuesdx,outarray,1);
             Blas::Daxpy(m_ncoeffs, mkey.GetConstFactor(eFactorLambda), wsp.get(), 1, outarray.get(), 1);
         }

References Blas::Daxpy(), Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, v_BwdTrans(), v_IProductWRTBase(), and v_PhysDeriv().

◆ v_Integral()

NekDouble Nektar::StdRegions::StdSegExp::v_Integral ( const Array< OneD, const NekDouble > & inarray )

protectedvirtual

Integrate the physical point list inarray over region and return the value.

Parameters

inarray definition of function to be integrated evauluated at quadrature point of expansion.

Returns: returns \(\int^1_{-1} u(\xi_1)d \xi_1 \) where \(inarray[i] = u(\xi_{1i}) \)

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 123 of file StdSegExp.cpp.

         {
             NekDouble Int = 0.0;
             int    nquad0 = m_base[0]->GetNumPoints();
             Array<OneD, NekDouble> tmp(nquad0);
             Array<OneD, const NekDouble> z  = m_base[0]->GetZ();
             Array<OneD, const NekDouble> w0 = m_base[0]->GetW();
  
             // multiply by integration constants
             Vmath::Vmul(nquad0, inarray, 1, w0, 1, tmp, 1);
  
             Int = Vmath::Vsum(nquad0, tmp, 1);
  
             return Int;
         }

References Nektar::StdRegions::StdExpansion::m_base, Vmath::Vmul(), and Vmath::Vsum().

◆ v_IProductWRTBase() [1/2]

void Nektar::StdRegions::StdSegExp::v_IProductWRTBase	(	const Array< OneD, const NekDouble > &	base,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		int	coll_check
	)

protectedvirtual

Inner product of inarray over region with respect to expansion basis base and return in outarray.

Calculate \( I[p] = \int^{1}_{-1} \phi_p(\xi_1) u(\xi_1) d\xi_1 = \sum_{i=0}^{nq-1} \phi_p(\xi_{1i}) u(\xi_{1i}) w_i \) where \( outarray[p] = I[p], inarray[i] = u(\xi_{1i}), base[p*nq+i] = \phi_p(\xi_{1i}) \).

Parameters

base	an array defining the local basis for the inner product usually passed from Basis->GetBdata() or Basis->GetDbdata()
inarray	physical point array of function to be integrated \( u(\xi_1) \)
coll_check	flag to identify when a Basis->Collocation() call should be performed to see if this is a GLL_Lagrange basis with a collocation property. (should be set to 0 if taking the inner product with respect to the derivative of basis)
outarray	the values of the inner product with respect to each basis over region will be stored in the array outarray as output of the function

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 428 of file StdSegExp.cpp.

         {
             boost::ignore_unused(coll_check);
  
             int    nquad = m_base[0]->GetNumPoints();
             Array<OneD, NekDouble> tmp(nquad);
             Array<OneD, const NekDouble> w =  m_base[0]->GetW();
  
             Vmath::Vmul(nquad, inarray, 1, w, 1, tmp, 1);
  
             /* Comment below was a bug for collocated basis
             if(coll_check&&m_base[0]->Collocation())
             {
                 Vmath::Vcopy(nquad, tmp, 1, outarray, 1);
             }
             else
             {
                 Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                             &tmp[0],1,0.0,outarray.get(),1);
             }*/
  
             // Correct implementation
             Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                         &tmp[0],1,0.0,outarray.get(),1);
         }

References Blas::Dgemv(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, and Vmath::Vmul().

◆ v_IProductWRTBase() [2/2]

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

protectedvirtual

Inner product of inarray over region with respect to the expansion basis (this)->m_base[0] and return in outarray.

Wrapper call to StdSegExp::IProductWRTBase

Parameters

inarray	array of function values evaluated at the physical collocation points
outarray	the values of the inner product with respect to each basis over region will be stored in the array outarray as output of the function

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 468 of file StdSegExp.cpp.

         {
             v_IProductWRTBase(m_base[0]->GetBdata(),inarray,outarray,1);
         }

References Nektar::StdRegions::StdExpansion::m_base.

Referenced by v_FwdTrans(), v_FwdTrans_BndConstrained(), v_HelmholtzMatrixOp(), v_IProductWRTDerivBase(), and v_LaplacianMatrixOp().

◆ v_IProductWRTBase_SumFac()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 484 of file StdSegExp.cpp.

         {
             int    nquad = m_base[0]->GetNumPoints();
             Array<OneD, NekDouble> tmp(nquad);
             Array<OneD, const NekDouble> w =  m_base[0]->GetW();
             Array<OneD, const NekDouble> base =  m_base[0]->GetBdata();
  
             if(multiplybyweights)
             {
                 Vmath::Vmul(nquad, inarray, 1, w, 1, tmp, 1);
  
                 Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                                 &tmp[0],1,0.0,outarray.get(),1);
             }
             else
             {
                 Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                             &inarray[0],1,0.0,outarray.get(),1);
             }
         }

References Blas::Dgemv(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, and Vmath::Vmul().

◆ v_IProductWRTDerivBase()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 474 of file StdSegExp.cpp.

         {
             boost::ignore_unused(dir);
             ASSERTL1(dir >= 0 && dir < 1,"input dir is out of range");
             v_IProductWRTBase(m_base[0]->GetDbdata(),inarray,outarray,1);
         }

References ASSERTL1, Nektar::StdRegions::StdExpansion::m_base, and v_IProductWRTBase().

◆ v_IsBoundaryInteriorExpansion()

bool Nektar::StdRegions::StdSegExp::v_IsBoundaryInteriorExpansion ( )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 90 of file StdSegExp.cpp.

         {
  
             bool returnval = false;
  
             if(m_base[0]->GetBasisType() == LibUtilities::eModified_A)
             {
                 returnval = true;
             }
  
             if(m_base[0]->GetBasisType() == LibUtilities::eGLL_Lagrange)
             {
                 returnval = true;
             }
  
             return returnval;
         }

References Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

◆ v_LaplacianMatrixOp()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 546 of file StdSegExp.cpp.

         {
             boost::ignore_unused(mkey);
  
             int    nquad = m_base[0]->GetNumPoints();
  
             Array<OneD,NekDouble> physValues(nquad);
             Array<OneD,NekDouble> dPhysValuesdx(nquad);
  
             v_BwdTrans(inarray,physValues);
  
             // Laplacian matrix operation
             v_PhysDeriv(physValues,dPhysValuesdx);
             v_IProductWRTBase(m_base[0]->GetDbdata(),dPhysValuesdx,outarray,1);
         }

References Nektar::StdRegions::StdExpansion::m_base, v_BwdTrans(), v_IProductWRTBase(), and v_PhysDeriv().

◆ v_LocCollapsedToLocCoord()

void Nektar::StdRegions::StdSegExp::v_LocCollapsedToLocCoord	(	const Array< OneD, const NekDouble > &	eta,
		Array< OneD, NekDouble > &	xi
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 521 of file StdSegExp.cpp.

         {
             xi[0] = eta[0];
         }

◆ v_LocCoordToLocCollapsed()

void Nektar::StdRegions::StdSegExp::v_LocCoordToLocCollapsed	(	const Array< OneD, const NekDouble > &	xi,
		Array< OneD, NekDouble > &	eta
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 515 of file StdSegExp.cpp.

         {
             eta[0] = xi[0];
         }

◆ v_MultiplyByStdQuadratureMetric()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 670 of file StdSegExp.cpp.

         {
             int nquad0 = m_base[0]->GetNumPoints();
  
             const Array<OneD, const NekDouble>& w0 = m_base[0]->GetW();
  
             Vmath::Vmul(nquad0, inarray.get(),1,
                         w0.get(),1,outarray.get(),1);
         }

References Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vmul().

◆ v_NumBndryCoeffs()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 722 of file StdSegExp.cpp.

         {
             return 2;
         }

◆ v_NumDGBndryCoeffs()

int Nektar::StdRegions::StdSegExp::v_NumDGBndryCoeffs ( ) const

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 727 of file StdSegExp.cpp.

         {
             return 2;
         }

◆ v_PhysDeriv() [1/2]

void Nektar::StdRegions::StdSegExp::v_PhysDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_d0,
		Array< OneD, NekDouble > &	out_d1 = `NullNekDouble1DArray`,
		Array< OneD, NekDouble > &	out_d2 = `NullNekDouble1DArray`
	)

protectedvirtual

Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray.

This is a wrapper around StdExpansion1D::Tensor_Deriv

Parameters

inarray	array of a function evaluated at the quadrature points
outarray	the resulting array of the derivative \( du/d_{\xi_1}\|_{\xi_{1i}} \) will be stored in the array outarra

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 156 of file StdSegExp.cpp.

         {
             boost::ignore_unused(out_d1, out_d2);
             PhysTensorDeriv(inarray,out_d0);
         }

References Nektar::StdRegions::StdExpansion1D::PhysTensorDeriv().

Referenced by v_HelmholtzMatrixOp(), and v_LaplacianMatrixOp().

◆ v_PhysDeriv() [2/2]

void Nektar::StdRegions::StdSegExp::v_PhysDeriv	(	const int	dir,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_d0
	)

protectedvirtual

Calculate the derivative of the physical points in a given direction.

See also: StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 166 of file StdSegExp.cpp.

         {
             boost::ignore_unused(dir);
             ASSERTL1(dir==0,"input dir is out of range");
             PhysTensorDeriv(inarray,outarray);
             // PhysDeriv(inarray, outarray);
         }

References ASSERTL1, and Nektar::StdRegions::StdExpansion1D::PhysTensorDeriv().

◆ v_PhysEvaluateBasis()

NekDouble Nektar::StdRegions::StdSegExp::v_PhysEvaluateBasis	(	const Array< OneD, const NekDouble > &	coords,
		int	mode
	)

finalprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 539 of file StdSegExp.cpp.

         {
             return StdExpansion::BaryEvaluateBasis<0>(coords[0], mode);
         }

◆ v_ReduceOrderCoeffs()

void Nektar::StdRegions::StdSegExp::v_ReduceOrderCoeffs	(	int	numMin,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 243 of file StdSegExp.cpp.

         {
             int n_coeffs = inarray.size();
  
             Array<OneD, NekDouble> coeff(n_coeffs);
             Array<OneD, NekDouble> coeff_tmp(n_coeffs,0.0);
             Array<OneD, NekDouble> tmp;
             Array<OneD, NekDouble> tmp2;
  
             int       nmodes0 = m_base[0]->GetNumModes();
  
             Vmath::Vcopy(n_coeffs,inarray,1,coeff_tmp,1);
  
             const LibUtilities::PointsKey Pkey0(
                 nmodes0, LibUtilities::eGaussLobattoLegendre);
  
             LibUtilities::BasisKey b0(m_base[0]->GetBasisType(),nmodes0,Pkey0);
  
             LibUtilities::BasisKey bortho0(LibUtilities::eOrtho_A,nmodes0,Pkey0);
  
             LibUtilities::InterpCoeff1D(
                 b0, coeff_tmp, bortho0, coeff);
  
             Vmath::Zero(n_coeffs,coeff_tmp,1);
  
             Vmath::Vcopy(numMin,
                          tmp  = coeff,1,
                          tmp2 = coeff_tmp,1);
  
             LibUtilities::InterpCoeff1D(
                 bortho0, coeff_tmp, b0, outarray);
         }

References Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eOrtho_A, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::LibUtilities::InterpCoeff1D(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Vcopy(), and Vmath::Zero().

◆ v_StdPhysDeriv() [1/2]

void Nektar::StdRegions::StdSegExp::v_StdPhysDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_d0,
		Array< OneD, NekDouble > &	out_d1 = `NullNekDouble1DArray`,
		Array< OneD, NekDouble > &	out_d2 = `NullNekDouble1DArray`
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 176 of file StdSegExp.cpp.

         {
             boost::ignore_unused(out_d1, out_d2);
             PhysTensorDeriv(inarray,out_d0);
             // PhysDeriv(inarray, out_d0);
         }

References Nektar::StdRegions::StdExpansion1D::PhysTensorDeriv().

◆ v_StdPhysDeriv() [2/2]

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 187 of file StdSegExp.cpp.

         {
             boost::ignore_unused(dir);
             ASSERTL1(dir==0,"input dir is out of range");
             PhysTensorDeriv(inarray,outarray);
             // PhysDeriv(inarray, outarray);
         }

References ASSERTL1, and Nektar::StdRegions::StdExpansion1D::PhysTensorDeriv().

◆ v_SVVLaplacianFilter()

void Nektar::StdRegions::StdSegExp::v_SVVLaplacianFilter	(	Array< OneD, NekDouble > &	array,
		const StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 588 of file StdSegExp.cpp.

         {
             // Generate an orthogonal expansion
             int nq = m_base[0]->GetNumPoints();
             int nmodes = m_base[0]->GetNumModes();
             // Declare orthogonal basis.
             LibUtilities::PointsKey pKey(nq,m_base[0]->GetPointsType());
  
             LibUtilities::BasisKey B(LibUtilities::eOrtho_A, nmodes, pKey);
             StdSegExp OrthoExp(B);
  
             //SVV parameters loaded from the .xml case file
             NekDouble  SvvDiffCoeff  = mkey.GetConstFactor(eFactorSVVDiffCoeff);
             int cutoff = (int) (mkey.GetConstFactor(eFactorSVVCutoffRatio))*nmodes;
  
             Array<OneD, NekDouble> orthocoeffs(OrthoExp.GetNcoeffs());
  
             // project onto modal  space.
             OrthoExp.FwdTrans(array,orthocoeffs);
  
             //
             for(int j = 0; j < nmodes; ++j)
             {
                 if(j >= cutoff)//to filter out only the "high-modes"
                 {
                      orthocoeffs[j] *=
                          (SvvDiffCoeff*exp(-(j-nmodes)*(j-nmodes)/
                                             ((NekDouble)((j-cutoff+1)*
                                                  (j-cutoff+1)))));
                  }
                 else
                 {
                      orthocoeffs[j] *= 0.0;
                 }
             }
  
             // backward transform to physical space
             OrthoExp.BwdTrans(orthocoeffs,array);
         }

References Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::eFactorSVVDiffCoeff, Nektar::LibUtilities::eOrtho_A, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetPointsType(), and Nektar::StdRegions::StdExpansion::m_base.

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ StdSegExp() [1/3]

◆ StdSegExp() [2/3]

◆ StdSegExp() [3/3]

◆ ~StdSegExp()

Member Function Documentation

◆ v_BwdTrans()

◆ v_BwdTrans_SumFac()

◆ v_CalcNumberOfCoefficients()

◆ v_CreateStdMatrix()

◆ v_DetShapeType()

◆ v_ExponentialFilter()

◆ v_FillMode()

◆ v_FwdTrans()

◆ v_FwdTrans_BndConstrained()

◆ v_GenMatrix()

◆ v_GetBoundaryMap()

◆ v_GetCoords()

◆ v_GetInteriorMap()

◆ v_GetNtraces()

◆ v_GetNverts()

◆ v_GetSimplexEquiSpacedConnectivity()

◆ v_GetTraceNcoeffs()

◆ v_GetTraceNumPoints()

◆ v_GetTraceToElementMap()

◆ v_GetVertexMap()

◆ v_HelmholtzMatrixOp()

◆ v_Integral()

◆ v_IProductWRTBase() [1/2]

◆ v_IProductWRTBase() [2/2]

◆ v_IProductWRTBase_SumFac()

◆ v_IProductWRTDerivBase()

◆ v_IsBoundaryInteriorExpansion()

◆ v_LaplacianMatrixOp()

◆ v_LocCollapsedToLocCoord()

◆ v_LocCoordToLocCollapsed()

◆ v_MultiplyByStdQuadratureMetric()

◆ v_NumBndryCoeffs()

◆ v_NumDGBndryCoeffs()

◆ v_PhysDeriv() [1/2]

◆ v_PhysDeriv() [2/2]

◆ v_PhysEvaluateBasis()

◆ v_ReduceOrderCoeffs()

◆ v_StdPhysDeriv() [1/2]

◆ v_StdPhysDeriv() [2/2]

◆ v_SVVLaplacianFilter()