The base class for all shapes. More...

#include <StdExpansion.h>

Inheritance diagram for Nektar::StdRegions::StdExpansion:

Public Member Functions
	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 () const

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

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion () const

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	LinearAdvectionMatrixOp (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, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
	This function evaluates the first derivative of the expansion at a single (arbitrary) point of the domain. More...

NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)

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

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
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_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	LinearAdvectionMatrixOp_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)

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

template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv, NekDouble &deriv2)
	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)

template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
	Helper function to pass an unused value by reference into BaryEvaluate. More...

template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)

Protected Attributes
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

Private Member Functions
virtual int	v_GetNverts () const =0

virtual int	v_GetNtraces () const =0

virtual int	v_NumBndryCoeffs () const =0

virtual int	v_NumDGBndryCoeffs () const =0

virtual int	v_GetTraceNcoeffs (const int i) const =0

virtual int	v_GetTraceIntNcoeffs (const int i) const =0

virtual int	v_GetTraceNumPoints (const int i) const =0

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

virtual LibUtilities::PointsKey	v_GetTracePointsKey (const int i, const int j) const

virtual const LibUtilities::PointsKey	v_GetNodalPointsKey () const

virtual LibUtilities::ShapeType	v_DetShapeType () const =0

virtual std::shared_ptr< StdExpansion >	v_GetStdExp () const

virtual std::shared_ptr< StdExpansion >	v_GetLinStdExp (void) const

virtual int	v_GetShapeDimension () const =0

virtual bool	v_IsBoundaryInteriorExpansion () const

virtual bool	v_IsNodalNonTensorialExp ()

virtual void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)=0

virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)=0
	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)=0
	Calculates the inner product of a given function f with the different modes of the expansion. More...

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

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

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

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

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_d1, Array< OneD, NekDouble > &out_d2, Array< OneD, NekDouble > &out_d3)
	Calculate the derivative of the physical points. More...

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

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

virtual void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0)
	Calculate the derivative of the physical points in a given direction. More...

virtual void	v_PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)
	Physical derivative along a direction vector. More...

virtual void	v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2, Array< OneD, NekDouble > &out_d3)

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

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

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

virtual NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)

virtual NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)

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

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)

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

virtual DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey)

virtual DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey)

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

virtual void	v_GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)

virtual int	v_GetCoordim () const

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

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

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

virtual void	v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)

virtual void	v_GetVertexPhysVals (const int vertex, const Array< OneD, const NekDouble > &inarray, NekDouble &outarray)

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

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

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

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

virtual void	v_IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &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_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_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

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

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

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

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

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

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

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

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

virtual DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)

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

Detailed Description

The base class for all shapes.

This is the lowest level basic class for all shapes and so contains the definition of common data and common routine to all elements

Definition at line 64 of file StdExpansion.h.

Constructor & Destructor Documentation

◆ StdExpansion() [1/3]

Nektar::StdRegions::StdExpansion::StdExpansion ( )

Default Constructor.

Default constructor.

Definition at line 42 of file StdExpansion.cpp.

43{

44}

◆ StdExpansion() [2/3]

Nektar::StdRegions::StdExpansion::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.

Definition at line 46 of file StdExpansion.cpp.

    : m_base(numbases), m_elmt_id(0), m_ncoeffs(numcoeffs),
      m_stdMatrixManager(std::bind(&StdExpansion::CreateStdMatrix, this,
                                   std::placeholders::_1),
                         std::string("StdExpansionStdMatrix")),
      m_stdStaticCondMatrixManager(
          std::bind(&StdExpansion::CreateStdStaticCondMatrix, this,
                    std::placeholders::_1),
          std::string("StdExpansionStdStaticCondMatrix"))
{
    switch (m_base.size())
    {
        case 3:
            ASSERTL2(Bc != LibUtilities::NullBasisKey,
                     "NULL Basis attempting to be used.");
            m_base[2] = LibUtilities::BasisManager()[Bc];
            /* Falls through. */
        case 2:
            ASSERTL2(Bb != LibUtilities::NullBasisKey,
                     "NULL Basis attempting to be used.");
            m_base[1] = LibUtilities::BasisManager()[Bb];
            /* Falls through. */
        case 1:
            ASSERTL2(Ba != LibUtilities::NullBasisKey,
                     "NULL Basis attempting to be used.");
            m_base[0] = LibUtilities::BasisManager()[Ba];
            break;
        default:
            break;
            // ASSERTL0(false, "numbases incorrectly specified");
    };
 
} // end constructor

References ASSERTL2, Nektar::LibUtilities::BasisManager(), m_base, and Nektar::LibUtilities::NullBasisKey().

◆ StdExpansion() [3/3]

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

Copy Constructor.

Definition at line 83 of file StdExpansion.cpp.

    : std::enable_shared_from_this<StdExpansion>(T), m_base(T.m_base),
      m_elmt_id(T.m_elmt_id), m_ncoeffs(T.m_ncoeffs),
      m_stdMatrixManager(T.m_stdMatrixManager),
      m_stdStaticCondMatrixManager(T.m_stdStaticCondMatrixManager)
{
}

◆ ~StdExpansion()

Nektar::StdRegions::StdExpansion::~StdExpansion ( )

virtual

Destructor.

Definition at line 92 of file StdExpansion.cpp.

93{

94}

Member Function Documentation

◆ as()

template<class T >

std::shared_ptr< T > Nektar::StdRegions::StdExpansion::as ( )

inline

Definition at line 1153 of file StdExpansion.h.

    {
        return std::dynamic_pointer_cast<T>(shared_from_this());
    }

◆ BaryEvaluate() [1/3]

template<int DIR, bool DERIV = false, bool DERIV2 = false>

NekDouble Nektar::StdRegions::StdExpansion::BaryEvaluate	(	const NekDouble &	coord,
		const NekDouble *	physvals
	)

inlineprotected

Helper function to pass an unused value by reference into BaryEvaluate.

Parameters

coord	The coordinate of the single point.
physvals	The polynomial stored at each quadrature point.

Template Parameters

DIR	The direction of evaluation.
DERIV	Bool to find derivative.

Returns: The value of physvals at coord in direction dir.

Definition at line 1468 of file StdExpansion.h.

    {
        NekDouble unusedValue = 0.0;
        return BaryEvaluate<DIR, DERIV, DERIV2>(coord, physvals, unusedValue,
                                                unusedValue);
    }

◆ BaryEvaluate() [2/3]

template<int DIR, bool DERIV = false, bool DERIV2 = false>

NekDouble Nektar::StdRegions::StdExpansion::BaryEvaluate	(	const NekDouble &	coord,
		const NekDouble *	physvals,
		NekDouble &	deriv
	)

inlineprotected

Definition at line 1477 of file StdExpansion.h.

    {
        NekDouble unusedValue = 0.0;
        return BaryEvaluate<DIR, DERIV, DERIV2>(coord, physvals, deriv,
                                                unusedValue);
    }

◆ BaryEvaluate() [3/3]

template<int DIR, bool DERIV = false, bool DERIV2 = false>

NekDouble Nektar::StdRegions::StdExpansion::BaryEvaluate	(	const NekDouble &	coord,
		const NekDouble *	physvals,
		NekDouble &	deriv,
		NekDouble &	deriv2
	)

inlineprotected

This function performs the barycentric interpolation of the polynomial stored in coord at a point physvals using barycentric interpolation weights in direction.

Template Parameters

DIR.	It can also perform the barycentric interpolation of the derivative of the polynomial if
DERIV	is set to true, which outputs in to

Parameters

deriv.

This method is intended to be used a helper function for StdExpansion::PhysEvaluate and its elemental instances, so that the calling method should provide coord for x, y and z sequentially and the appropriate physvals and weights for that particular direction.

Parameters

coord	The coordinate of the single point.
physvals	The polynomial stored at each quadrature point.
deriv	The value of the derivative.
deriv	The value of the 2nd derivative.

Template Parameters

DIR	The direction of evaluation.
DERIV	Bool to find derivative.

Returns: The value of physvals at coord in direction dir.

Definition at line 1340 of file StdExpansion.h.

    {
        NekDouble numer1 = 0.0, numer2 = 0.0, numer3 = 0.0, numer4 = 0.0,
                  numer5 = 0.0, denom = 0.0;
 
        ASSERTL2(DIR < m_base.size(),
                 "Direction should be less than shape dimension.");
 
        const Array<OneD, const NekDouble> &z  = m_base[DIR]->GetZ();
        const Array<OneD, const NekDouble> &bw = m_base[DIR]->GetBaryWeights();
 
        const size_t nquad = z.size();
 
        for (size_t i = 0; i < nquad; ++i)
        {
            NekDouble xdiff = z[i] - coord;
            NekDouble pval  = physvals[i];
 
            /*
             * (in this specific case) you actually
             * want to do the comparison exactly
             * (believe it or not!) See chapter 7 of
             * the paper here:
             *https://people.maths.ox.ac.uk/trefethen/barycentric.pdf
             */
            if ((!DERIV && xdiff == 0.0) ||
                ((DERIV || DERIV2) && std::abs(xdiff) < 1e-15))
            {
 
                if (DERIV2)
                {
                    DNekMatSharedPtr D0 = m_base[DIR]->GetD();
 
                    // take ith row of z and multiply with physvals
                    Array<OneD, NekDouble> tmp(nquad);
                    for (int kk = 0; kk < nquad; kk++)
                    {
                        tmp[kk] = Vmath::Dot(nquad, &(D0->GetPtr())[kk], nquad,
                                             &physvals[0], 1);
                    }
 
                    deriv2 = Vmath::Dot(nquad, &(D0->GetPtr())[i], nquad,
                                        &tmp[0], 1);
                    deriv  = tmp[i];
                }
                else if (DERIV)
                {
                    DNekMatSharedPtr D0 = m_base[DIR]->GetD();
 
                    // take ith row of z and multiply with physvals
                    deriv = Vmath::Dot(z.size(), &(D0->GetPtr())[i], z.size(),
                                       &physvals[0], 1);
                }
 
                return pval;
            }
 
            NekDouble tmp = bw[i] / xdiff;
            numer1 += tmp * pval;
            denom += tmp;
 
            if (DERIV || DERIV2)
            {
                NekDouble tmp2 = tmp / xdiff;
                numer2 += tmp2 * pval;
                numer3 += tmp2;
 
                if (DERIV2)
                {
                    NekDouble tmp3 = tmp2 / xdiff;
                    numer4 += tmp3 * pval;
                    numer5 += tmp3;
                }
            }
        }
 
        if (DERIV || DERIV2)
        {
            NekDouble denomdenom   = denom * denom;
            NekDouble numer1numer3 = numer1 * numer3;
 
            deriv = (numer2 * denom - numer1numer3) / (denomdenom);
 
            if (DERIV2)
            {
                deriv2 = (2.0 * numer4 / denom) -
                         (2.0 * numer5 * numer1) / (denomdenom) -
                         (2.0 * numer2 * numer3) / (denomdenom) +
                         (2.0 * numer3 * numer1numer3) / (denomdenom * denom);
            }
        }
 
        return numer1 / denom;
    }

References tinysimd::abs(), ASSERTL2, Vmath::Dot(), m_base, and Nektar::UnitTests::z().

◆ BaryEvaluateBasis()

template<int DIR>

NekDouble Nektar::StdRegions::StdExpansion::BaryEvaluateBasis	(	const NekDouble &	coord,
		const int &	mode
	)

inlineprotected

Definition at line 1449 of file StdExpansion.h.

    {
        const int nquad = m_base[DIR]->GetNumPoints();
        return BaryEvaluate<DIR>(coord,
                                 &(m_base[DIR]->GetBdata())[0] + nquad * mode);
    }

References m_base.

◆ BuildInverseTransformationMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdExpansion::BuildInverseTransformationMatrix ( const DNekScalMatSharedPtr & m_transformationmatrix )

inline

Definition at line 1106 of file StdExpansion.h.

    {
        return v_BuildInverseTransformationMatrix(m_transformationmatrix);
    }

References v_BuildInverseTransformationMatrix().

◆ BwdTrans()

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

inline

This function performs the Backward transformation from coefficient space to physical space.

This function is a wrapper around the virtual function v_BwdTrans()

Based on the expansion coefficients, this function evaluates the expansion at the quadrature points. This is equivalent to the operation

\[ u(\xi_{1i}) = \sum_{p=0}^{P-1} \hat{u}_p \phi_p(\xi_{1i}) \]

which can be evaluated as \( {\bf u} = {\bf B}^T {\bf \hat{u}} \) with \({\bf B}[i][j] = \phi_i(\xi_{j})\)

This function requires that the coefficient array \(\mathbf{\hat{u}}\) provided as inarray.

The resulting array \(\mathbf{u}[m]=u(\mathbf{\xi}_m)\) containing the expansion evaluated at the quadrature points, is stored in the outarray.

Parameters

inarray	contains the values of the expansion coefficients (input of the function)
outarray	contains the values of the expansion evaluated at the quadrature points (output of the function)

Definition at line 424 of file StdExpansion.h.

    {
        v_BwdTrans(inarray, outarray);
    }

References v_BwdTrans().

◆ BwdTrans_SumFac()

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

inlineprotected

Definition at line 1203 of file StdExpansion.h.

    {
        v_BwdTrans_SumFac(inarray, outarray);
    }

References v_BwdTrans_SumFac().

Referenced by CreateGeneralMatrix(), and Nektar::StdRegions::StdHexExp::v_BwdTrans().

◆ CalcNumberOfCoefficients()

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

inline

Definition at line 653 of file StdExpansion.h.

    {
        return v_CalcNumberOfCoefficients(nummodes, modes_offset);
    }

References v_CalcNumberOfCoefficients().

◆ CreateGeneralMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdExpansion::CreateGeneralMatrix ( const StdMatrixKey & mkey )

this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\)

Returns: returns the mass matrix

Definition at line 243 of file StdExpansion.cpp.

{
    int i;
    DNekMatSharedPtr returnval;
 
    switch (mkey.GetMatrixType())
    {
        case eInvMass:
        {
            StdMatrixKey masskey(eMass, mkey.GetShapeType(), *this,
                                 NullConstFactorMap, NullVarCoeffMap,
                                 mkey.GetNodalPointsType());
            DNekMatSharedPtr mmat = GetStdMatrix(masskey);
 
            returnval = MemoryManager<DNekMat>::AllocateSharedPtr(
                *mmat); // Populate standard mass matrix.
            returnval->Invert();
        }
        break;
        case eInvNBasisTrans:
        {
            StdMatrixKey tmpkey(eNBasisTrans, mkey.GetShapeType(), *this,
                                NullConstFactorMap, NullVarCoeffMap,
                                mkey.GetNodalPointsType());
            DNekMatSharedPtr tmpmat = GetStdMatrix(tmpkey);
            returnval               = MemoryManager<DNekMat>::AllocateSharedPtr(
                *tmpmat); // Populate  matrix.
            returnval->Invert();
        }
        break;
        case eBwdMat:
        {
            int nq = GetTotPoints();
            Array<OneD, NekDouble> tmpin(m_ncoeffs);
            Array<OneD, NekDouble> tmpout(nq);
 
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, nq);
            Array<OneD, NekDouble> Bwd_data = returnval->GetPtr();
 
            StdRegions::StdMatrixKey matkey(StdRegions::eBwdTrans,
                                            this->DetShapeType(), *this);
            DNekMatSharedPtr MatBwdTrans         = GetStdMatrix(matkey);
            Array<OneD, NekDouble> BwdTrans_data = MatBwdTrans->GetPtr();
 
            for (int i = 0; i < m_ncoeffs; ++i)
            {
                Array<OneD, NekDouble> tmpinn = BwdTrans_data + nq * i;
                Array<OneD, NekDouble> tmpout = Bwd_data + i;
 
                Vmath::Vcopy(nq, tmpinn, 1, tmpout, m_ncoeffs);
            }
        }
        break;
        case eBwdTrans:
        {
            int nq = GetTotPoints();
            Array<OneD, NekDouble> tmpin(m_ncoeffs);
            Array<OneD, NekDouble> tmpout(nq);
 
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(nq, m_ncoeffs);
 
            for (int i = 0; i < m_ncoeffs; ++i)
            {
                Vmath::Zero(m_ncoeffs, tmpin, 1);
                tmpin[i] = 1.0;
 
                BwdTrans_SumFac(tmpin, tmpout);
 
                Vmath::Vcopy(nq, tmpout.get(), 1,
                             returnval->GetRawPtr() + i * nq, 1);
            }
        }
        break;
        case eIProductWRTBase:
        {
            int nq = GetTotPoints();
            Array<OneD, NekDouble> tmpin(nq);
            Array<OneD, NekDouble> tmpout(m_ncoeffs);
 
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, nq);
 
            for (i = 0; i < nq; ++i)
            {
                Vmath::Zero(nq, tmpin, 1);
                tmpin[i] = 1.0;
 
                IProductWRTBase_SumFac(tmpin, tmpout);
 
                Vmath::Vcopy(m_ncoeffs, tmpout.get(), 1,
                             returnval->GetRawPtr() + i * m_ncoeffs, 1);
            }
        }
        break;
        case eIProductWRTDerivBase0:
        {
            int nq = GetTotPoints();
            Array<OneD, NekDouble> tmpin(nq);
            Array<OneD, NekDouble> tmpout(m_ncoeffs);
 
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(nq, m_ncoeffs);
 
            for (i = 0; i < nq; ++i)
            {
                Vmath::Zero(nq, tmpin, 1);
                tmpin[i] = 1.0;
 
                IProductWRTDerivBase_SumFac(0, tmpin, tmpout);
 
                Vmath::Vcopy(m_ncoeffs, tmpout.get(), 1,
                             returnval->GetRawPtr() + i * m_ncoeffs, 1);
            }
        }
        break;
        case eIProductWRTDerivBase1:
        {
            int nq = GetTotPoints();
            Array<OneD, NekDouble> tmpin(nq);
            Array<OneD, NekDouble> tmpout(m_ncoeffs);
 
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(nq, m_ncoeffs);
 
            for (i = 0; i < nq; ++i)
            {
                Vmath::Zero(nq, tmpin, 1);
                tmpin[i] = 1.0;
 
                IProductWRTDerivBase_SumFac(1, tmpin, tmpout);
 
                Vmath::Vcopy(m_ncoeffs, tmpout.get(), 1,
                             returnval->GetRawPtr() + i * m_ncoeffs, 1);
            }
        }
        break;
        case eIProductWRTDerivBase2:
        {
            int nq = GetTotPoints();
            Array<OneD, NekDouble> tmpin(nq);
            Array<OneD, NekDouble> tmpout(m_ncoeffs);
 
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(nq, m_ncoeffs);
 
            for (i = 0; i < nq; ++i)
            {
                Vmath::Zero(nq, tmpin, 1);
                tmpin[i] = 1.0;
 
                IProductWRTDerivBase_SumFac(2, tmpin, tmpout);
 
                Vmath::Vcopy(m_ncoeffs, tmpout.get(), 1,
                             returnval->GetRawPtr() + i * m_ncoeffs, 1);
            }
        }
        break;
        case eDerivBase0:
        {
            int nq = GetTotPoints();
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, nq);
            GenStdMatBwdDeriv(0, returnval);
        }
        break;
        case eDerivBase1:
        {
            int nq = GetTotPoints();
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, nq);
            GenStdMatBwdDeriv(1, returnval);
        }
        break;
        case eDerivBase2:
        {
            int nq = GetTotPoints();
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, nq);
            GenStdMatBwdDeriv(2, returnval);
        }
        break;
        case eEquiSpacedToCoeffs:
        {
            // check to see if equispaced basis
            int nummodes    = m_base[0]->GetNumModes();
            bool equispaced = true;
            for (int i = 1; i < m_base.size(); ++i)
            {
                if (m_base[i]->GetNumModes() != nummodes)
                {
                    equispaced = false;
                }
            }
 
            ASSERTL0(equispaced,
                     "Currently need to have same num modes in all "
                     "directionmodes to use EquiSpacedToCoeff method");
 
            int ntot = GetTotPoints();
            Array<OneD, NekDouble> qmode(ntot);
            Array<OneD, NekDouble> emode(m_ncoeffs);
 
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, m_ncoeffs);
            for (int i = 0; i < m_ncoeffs; ++i)
            {
                // Get mode at quadrature points
                FillMode(i, qmode);
 
                // interpolate to equi spaced
                PhysInterpToSimplexEquiSpaced(qmode, emode, nummodes);
 
                // fill matrix
                Vmath::Vcopy(m_ncoeffs, &emode[0], 1,
                             returnval->GetRawPtr() + i * m_ncoeffs, 1);
            }
            // invert matrix
            returnval->Invert();
        }
        break;
        case eMass:
        case eHelmholtz:
        case eLaplacian:
        case eLaplacian00:
        case eLaplacian01:
        case eLaplacian02:
        case eLaplacian10:
        case eLaplacian11:
        case eLaplacian12:
        case eLaplacian20:
        case eLaplacian21:
        case eLaplacian22:
        case eWeakDeriv0:
        case eWeakDeriv1:
        case eWeakDeriv2:
        case eWeakDirectionalDeriv:
        case eMassLevelCurvature:
        case eLinearAdvection:
        case eLinearAdvectionReaction:
        case eLinearAdvectionDiffusionReaction:
        {
            Array<OneD, NekDouble> tmp(m_ncoeffs);
            returnval =
                MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, m_ncoeffs);
            DNekMat &Mat = *returnval;
 
            for (i = 0; i < m_ncoeffs; ++i)
            {
                Vmath::Zero(m_ncoeffs, tmp, 1);
                tmp[i] = 1.0;
 
                GeneralMatrixOp_MatFree(tmp, tmp, mkey);
 
                Vmath::Vcopy(m_ncoeffs, &tmp[0], 1,
                             &(Mat.GetPtr())[0] + i * m_ncoeffs, 1);
            }
        }
        break;
        default:
        {
            NEKERROR(ErrorUtil::efatal,
                     "This type of matrix, " +
                         static_cast<std::string>(
                             MatrixTypeMap[mkey.GetMatrixType()]) +
                         ", can not be created using a general approach");
        }
        break;
    }
 
    return returnval;
}

◆ CreateStdMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdExpansion::CreateStdMatrix ( const StdMatrixKey & mkey )

inlineprotected

Definition at line 1182 of file StdExpansion.h.

    {
        return v_CreateStdMatrix(mkey);
    }

References v_CreateStdMatrix().

◆ CreateStdStaticCondMatrix()

DNekBlkMatSharedPtr Nektar::StdRegions::StdExpansion::CreateStdStaticCondMatrix ( const StdMatrixKey & mkey )

protected

Create the static condensation of a matrix when using a boundary interior decomposition.

If a matrix system can be represented by \( Mat = \left [ \begin{array}{cc} A & B \\ C & D \end{array} \right ] \) This routine creates a matrix containing the statically condense system of the form \( Mat = \left [ \begin{array}{cc} A - B D^{-1} C & B D^{-1} \\ D^{-1} C & D^{-1} \end{array} \right ] \)

Definition at line 172 of file StdExpansion.cpp.

{
    DNekBlkMatSharedPtr returnval;
 
    DNekMatSharedPtr mat = GetStdMatrix(mkey);
    int nbdry = NumBndryCoeffs(); // also checks to see if this is a boundary
                                  // interior decomposed expansion
    int nint = m_ncoeffs - nbdry;
    DNekMatSharedPtr A =
        MemoryManager<DNekMat>::AllocateSharedPtr(nbdry, nbdry);
    DNekMatSharedPtr B = MemoryManager<DNekMat>::AllocateSharedPtr(nbdry, nint);
    DNekMatSharedPtr C = MemoryManager<DNekMat>::AllocateSharedPtr(nint, nbdry);
    DNekMatSharedPtr D = MemoryManager<DNekMat>::AllocateSharedPtr(nint, nint);
 
    int i, j;
 
    Array<OneD, unsigned int> bmap(nbdry);
    Array<OneD, unsigned int> imap(nint);
    GetBoundaryMap(bmap);
    GetInteriorMap(imap);
 
    for (i = 0; i < nbdry; ++i)
    {
        for (j = 0; j < nbdry; ++j)
        {
            (*A)(i, j) = (*mat)(bmap[i], bmap[j]);
        }
 
        for (j = 0; j < nint; ++j)
        {
            (*B)(i, j) = (*mat)(bmap[i], imap[j]);
        }
    }
 
    for (i = 0; i < nint; ++i)
    {
        for (j = 0; j < nbdry; ++j)
        {
            (*C)(i, j) = (*mat)(imap[i], bmap[j]);
        }
 
        for (j = 0; j < nint; ++j)
        {
            (*D)(i, j) = (*mat)(imap[i], imap[j]);
        }
    }
 
    // Calculate static condensed system
    if (nint)
    {
        D->Invert();
        (*B) = (*B) * (*D);
        (*A) = (*A) - (*B) * (*C);
    }
 
    // set up block matrix system
    Array<OneD, unsigned int> exp_size(2);
    exp_size[0] = nbdry;
    exp_size[1] = nint;
    returnval =
        MemoryManager<DNekBlkMat>::AllocateSharedPtr(exp_size, exp_size);
 
    returnval->SetBlock(0, 0, A);
    returnval->SetBlock(0, 1, B);
    returnval->SetBlock(1, 0, C);
    returnval->SetBlock(1, 1, D);
 
    return returnval;
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), GetBoundaryMap(), GetInteriorMap(), GetStdMatrix(), m_ncoeffs, and NumBndryCoeffs().

◆ DetShapeType()

LibUtilities::ShapeType Nektar::StdRegions::StdExpansion::DetShapeType ( ) const

inline

This function returns the shape of the expansion domain.

This function is a wrapper around the virtual function v_DetShapeType()

The different shape types implemented in the code are defined in the ::ShapeType enumeration list. As a result, the function will return one of the types of this enumeration list.

Returns: returns the shape of the expansion domain

Definition at line 367 of file StdExpansion.h.

    {
        return v_DetShapeType();
    }

References v_DetShapeType().

◆ DropLocStaticCondMatrix()

void Nektar::StdRegions::StdExpansion::DropLocStaticCondMatrix ( const LocalRegions::MatrixKey & mkey )

inline

Definition at line 647 of file StdExpansion.h.

    {
        return v_DropLocStaticCondMatrix(mkey);
    }

References v_DropLocStaticCondMatrix().

◆ EquiSpacedToCoeffs()

void Nektar::StdRegions::StdExpansion::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.

This is primarily used for output purposes to use a more even distribution of points more suitable for alot of postprocessing

Definition at line 1667 of file StdExpansion.cpp.

{
    LibUtilities::ShapeType shape = DetShapeType();
 
    // inarray has to be consistent with NumModes definition
    // There is also a check in GetStdMatrix to see if all
    // modes are of the same size
    ConstFactorMap cmap;
 
    cmap[eFactorConst] = m_base[0]->GetNumModes();
    StdMatrixKey Ikey(eEquiSpacedToCoeffs, shape, *this, cmap);
    DNekMatSharedPtr intmat = GetStdMatrix(Ikey);
 
    NekVector<NekDouble> in(m_ncoeffs, inarray, eWrapper);
    NekVector<NekDouble> out(m_ncoeffs, outarray, eWrapper);
    out = (*intmat) * in;
}

References DetShapeType(), Nektar::StdRegions::eEquiSpacedToCoeffs, Nektar::StdRegions::eFactorConst, Nektar::eWrapper, GetStdMatrix(), m_base, and m_ncoeffs.

◆ EvalBasisNumModesMax()

int Nektar::StdRegions::StdExpansion::EvalBasisNumModesMax ( void ) const

inline

This function returns the maximum number of expansion modes over all local directions.

Returns: returns the maximum number of expansion modes over all local directions

Definition at line 181 of file StdExpansion.h.

    {
        int returnval = 0;
 
        for (size_t i = 0; i < m_base.size(); ++i)
        {
            returnval = std::max(returnval, m_base[i]->GetNumModes());
        }
 
        return returnval;
    }

References m_base.

◆ ExponentialFilter()

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

inline

Definition at line 779 of file StdExpansion.h.

    {
        v_ExponentialFilter(array, alpha, exponent, cutoff);
    }

References v_ExponentialFilter().

◆ FillMode()

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

inline

This function fills the array outarray with the mode-th mode of the expansion.

This function is a wrapper around the virtual function v_FillMode()

The requested mode is evaluated at the quadrature points

Parameters

mode	the mode that should be filled
outarray	contains the values of the mode-th mode of the expansion evaluated at the quadrature points (output of the function)

Definition at line 491 of file StdExpansion.h.

    {
        v_FillMode(mode, outarray);
    }

References v_FillMode().

Referenced by CreateGeneralMatrix(), Nektar::LocalRegions::Expansion2D::v_GenMatrix(), and Nektar::LocalRegions::Expansion3D::v_GenMatrix().

◆ FwdTrans()

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

inline

This function performs the Forward transformation from physical space to coefficient space.

This function is a wrapper around the virtual function v_FwdTrans()

Given a function evaluated at the quadrature points, this function calculates the expansion coefficients such that the resulting expansion approximates the original function.

The calculation of the expansion coefficients is done using a Galerkin projection. This is equivalent to the operation:

\[ \mathbf{\hat{u}} = \mathbf{M}^{-1} \mathbf{I}\]

where

\(\mathbf{M}[p][q]= \int\phi_p(\mathbf{\xi})\phi_q( \mathbf{\xi}) d\mathbf{\xi}\) is the Mass matrix
\(\mathbf{I}[p] = \int\phi_p(\mathbf{\xi}) u(\mathbf{\xi}) d\mathbf{\xi}\)

This function takes the array inarray as the values of the function evaluated at the quadrature points (i.e. \(\mathbf{u}\)), and stores the resulting coefficients \(\mathbf{\hat{u}}\) in the outarray

Parameters

inarray	array of the function discretely evaluated at the quadrature points
outarray	array of the function coefficieints

Definition at line 1799 of file StdExpansion.h.

{
    v_FwdTrans(inarray, outarray);
}

References v_FwdTrans().

◆ FwdTransBndConstrained()

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

inline

Definition at line 437 of file StdExpansion.h.

    {
        v_FwdTransBndConstrained(inarray, outarray);
    }

References v_FwdTransBndConstrained().

◆ GeneralMatrixOp()

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

Definition at line 517 of file StdExpansion.cpp.

{
    switch (mkey.GetMatrixType())
    {
        case eMass:
            MassMatrixOp(inarray, outarray, mkey);
            break;
        case eWeakDeriv0:
            WeakDerivMatrixOp(0, inarray, outarray, mkey);
            break;
        case eWeakDeriv1:
            WeakDerivMatrixOp(1, inarray, outarray, mkey);
            break;
        case eWeakDeriv2:
            WeakDerivMatrixOp(2, inarray, outarray, mkey);
            break;
        case eWeakDirectionalDeriv:
            WeakDirectionalDerivMatrixOp(inarray, outarray, mkey);
            break;
        case eMassLevelCurvature:
            MassLevelCurvatureMatrixOp(inarray, outarray, mkey);
            break;
        case eLinearAdvection:
            LinearAdvectionMatrixOp(inarray, outarray, mkey);
            break;
        case eLinearAdvectionReaction:
            LinearAdvectionDiffusionReactionMatrixOp(inarray, outarray, mkey,
                                                     false);
            break;
        case eLinearAdvectionDiffusionReaction:
            LinearAdvectionDiffusionReactionMatrixOp(inarray, outarray, mkey);
            break;
        case eLaplacian:
            LaplacianMatrixOp(inarray, outarray, mkey);
            break;
        case eLaplacian00:
            LaplacianMatrixOp(0, 0, inarray, outarray, mkey);
            break;
        case eLaplacian01:
            LaplacianMatrixOp(0, 1, inarray, outarray, mkey);
            break;
        case eLaplacian02:
            LaplacianMatrixOp(0, 2, inarray, outarray, mkey);
            break;
        case eLaplacian10:
            LaplacianMatrixOp(1, 0, inarray, outarray, mkey);
            break;
        case eLaplacian11:
            LaplacianMatrixOp(1, 1, inarray, outarray, mkey);
            break;
        case eLaplacian12:
            LaplacianMatrixOp(1, 2, inarray, outarray, mkey);
            break;
        case eLaplacian20:
            LaplacianMatrixOp(2, 0, inarray, outarray, mkey);
            break;
        case eLaplacian21:
            LaplacianMatrixOp(2, 1, inarray, outarray, mkey);
            break;
        case eLaplacian22:
            LaplacianMatrixOp(2, 2, inarray, outarray, mkey);
            break;
        case eHelmholtz:
            HelmholtzMatrixOp(inarray, outarray, mkey);
            break;
        default:
            NEKERROR(ErrorUtil::efatal,
                     "This matrix does not have an operator");
            break;
    }
}

◆ GeneralMatrixOp_MatFree()

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

protected

Definition at line 591 of file StdExpansion.cpp.

{
    switch (mkey.GetMatrixType())
    {
        case eMass:
            MassMatrixOp_MatFree(inarray, outarray, mkey);
            break;
        case eWeakDeriv0:
            WeakDerivMatrixOp_MatFree(0, inarray, outarray, mkey);
            break;
        case eWeakDeriv1:
            WeakDerivMatrixOp_MatFree(1, inarray, outarray, mkey);
            break;
        case eWeakDeriv2:
            WeakDerivMatrixOp_MatFree(2, inarray, outarray, mkey);
            break;
        case eWeakDirectionalDeriv:
            WeakDirectionalDerivMatrixOp_MatFree(inarray, outarray, mkey);
            break;
        case eMassLevelCurvature:
            MassLevelCurvatureMatrixOp_MatFree(inarray, outarray, mkey);
            break;
        case eLinearAdvection:
            LinearAdvectionMatrixOp_MatFree(inarray, outarray, mkey);
            break;
        case eLinearAdvectionReaction:
            LinearAdvectionDiffusionReactionMatrixOp_MatFree(inarray, outarray,
                                                             mkey, false);
            break;
        case eLinearAdvectionDiffusionReaction:
            LinearAdvectionDiffusionReactionMatrixOp_MatFree(inarray, outarray,
                                                             mkey);
            break;
        case eLaplacian:
            LaplacianMatrixOp_MatFree(inarray, outarray, mkey);
            break;
        case eLaplacian00:
            LaplacianMatrixOp_MatFree(0, 0, inarray, outarray, mkey);
            break;
        case eLaplacian01:
            LaplacianMatrixOp_MatFree(0, 1, inarray, outarray, mkey);
            break;
        case eLaplacian02:
            LaplacianMatrixOp_MatFree(0, 2, inarray, outarray, mkey);
            break;
        case eLaplacian10:
            LaplacianMatrixOp_MatFree(1, 0, inarray, outarray, mkey);
            break;
        case eLaplacian11:
            LaplacianMatrixOp_MatFree(1, 1, inarray, outarray, mkey);
            break;
        case eLaplacian12:
            LaplacianMatrixOp_MatFree(1, 2, inarray, outarray, mkey);
            break;
        case eLaplacian20:
            LaplacianMatrixOp_MatFree(2, 0, inarray, outarray, mkey);
            break;
        case eLaplacian21:
            LaplacianMatrixOp_MatFree(2, 1, inarray, outarray, mkey);
            break;
        case eLaplacian22:
            LaplacianMatrixOp_MatFree(2, 2, inarray, outarray, mkey);
            break;
        case eHelmholtz:
            HelmholtzMatrixOp_MatFree(inarray, outarray, mkey);
            break;
        default:
            NEKERROR(ErrorUtil::efatal,
                     "This matrix does not have an operator");
            break;
    }
}

Referenced by CreateGeneralMatrix().

◆ GenMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdExpansion::GenMatrix ( const StdMatrixKey & mkey )

inline

Definition at line 844 of file StdExpansion.h.

    {
        return v_GenMatrix(mkey);
    }

References v_GenMatrix().

Referenced by Nektar::LocalRegions::Expansion2D::CreateMatrix(), Nektar::LocalRegions::Expansion3D::CreateMatrix(), Nektar::LocalRegions::SegExp::CreateMatrix(), and Nektar::StdRegions::StdQuadExp::v_CreateStdMatrix().

◆ GenStdMatBwdDeriv()

void Nektar::StdRegions::StdExpansion::GenStdMatBwdDeriv	(	const int	dir,
		DNekMatSharedPtr &	mat
	)

inline

Definition at line 1165 of file StdExpansion.h.

    {
        v_GenStdMatBwdDeriv(dir, mat);
    }

References v_GenStdMatBwdDeriv().

Referenced by CreateGeneralMatrix().

◆ GetBase()

const Array< OneD, const LibUtilities::BasisSharedPtr > & Nektar::StdRegions::StdExpansion::GetBase ( ) const

inline

This function gets the shared point to basis.

Returns: returns the shared pointer to the bases

Definition at line 100 of file StdExpansion.h.

    {
        return (m_base);
    }

References m_base.

Referenced by Nektar::StdRegions::StdPrismExp::v_PhysEvaluate(), Nektar::StdRegions::StdPyrExp::v_PhysEvaluate(), Nektar::StdRegions::StdTetExp::v_PhysEvaluate(), and Nektar::StdRegions::StdTriExp::v_PhysEvaluate().

◆ GetBasis()

const LibUtilities::BasisSharedPtr & Nektar::StdRegions::StdExpansion::GetBasis ( int dir ) const

inline

This function gets the shared point to basis in the dir direction.

Returns: returns the shared pointer to the basis in directin dir

Definition at line 112 of file StdExpansion.h.

    {
        ASSERTL1(dir < m_base.size(), "dir is larger than number of bases");
        return (m_base[dir]);
    }

References ASSERTL1, and m_base.

Referenced by Nektar::LocalRegions::Expansion1D::AddHDGHelmholtzTraceTerms(), Nektar::LocalRegions::Expansion1D::AddNormTraceInt(), and Nektar::StdRegions::StdQuadExp::v_GetTraceBasisKey().

◆ GetBasisNumModes()

int Nektar::StdRegions::StdExpansion::GetBasisNumModes ( const int dir ) const

inline

This function returns the number of expansion modes in the dir direction.

Parameters

dir	the direction

Returns: returns the number of expansion modes in the dir direction

Definition at line 169 of file StdExpansion.h.

    {
        ASSERTL1(dir < m_base.size(), "dir is larger than m_numbases");
        return (m_base[dir]->GetNumModes());
    }

References ASSERTL1, and m_base.

◆ GetBasisType()

LibUtilities::BasisType Nektar::StdRegions::StdExpansion::GetBasisType ( const int dir ) const

inline

This function returns the type of basis used in the dir direction.

The different types of bases implemented in the code are defined in the LibUtilities::BasisType enumeration list. As a result, the function will return one of the types of this enumeration list.

Parameters

dir	the direction

Returns: returns the type of basis used in the dir direction

Definition at line 156 of file StdExpansion.h.

    {
        ASSERTL1(dir < m_base.size(), "dir is larger than m_numbases");
        return (m_base[dir]->GetBasisType());
    }

References ASSERTL1, GetBasisType(), and m_base.

◆ GetBoundaryMap()

void Nektar::StdRegions::StdExpansion::GetBoundaryMap ( Array< OneD, unsigned int > & outarray )

inline

Definition at line 669 of file StdExpansion.h.

    {
        v_GetBoundaryMap(outarray);
    }

References v_GetBoundaryMap().

◆ GetCoord()

void Nektar::StdRegions::StdExpansion::GetCoord	(	const Array< OneD, const NekDouble > &	Lcoord,
		Array< OneD, NekDouble > &	coord
	)

inline

given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point

This function is a wrapper around the virtual function v_GetCoord()

Parameters

Lcoords	the coordinates in the local collapsed coordinate system
coords	the physical coordinates (output of the function)

Definition at line 597 of file StdExpansion.h.

    {
        v_GetCoord(Lcoord, coord);
    }

References v_GetCoord().

◆ GetCoordim()

int Nektar::StdRegions::StdExpansion::GetCoordim ( )

inline

Definition at line 664 of file StdExpansion.h.

    {
        return v_GetCoordim();
    }

References v_GetCoordim().

◆ GetCoords()

void Nektar::StdRegions::StdExpansion::GetCoords	(	Array< OneD, NekDouble > &	coords_1,
		Array< OneD, NekDouble > &	coords_2 = `NullNekDouble1DArray`,
		Array< OneD, NekDouble > &	coords_3 = `NullNekDouble1DArray`
	)

inline

this function returns the physical coordinates of the quadrature points of the expansion

This function is a wrapper around the virtual function v_GetCoords()

Parameters

coords an array containing the coordinates of the quadrature points (output of the function)

Definition at line 579 of file StdExpansion.h.

    {
        v_GetCoords(coords_1, coords_2, coords_3);
    }

References v_GetCoords().

Referenced by main().

◆ GetElmtId()

int Nektar::StdRegions::StdExpansion::GetElmtId ( )

inline

Get the element id of this expansion when used in a list by returning value of m_elmt_id.

Definition at line 558 of file StdExpansion.h.

    {
        return m_elmt_id;
    }

References m_elmt_id.

◆ GetElmtTraceToTraceMap()

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

inline

Definition at line 699 of file StdExpansion.h.

    {
        v_GetElmtTraceToTraceMap(tid, maparray, signarray, traceOrient, P, Q);
    }

References Nektar::LibUtilities::P, and v_GetElmtTraceToTraceMap().

Referenced by Nektar::StdRegions::StdExpansion3D::v_GetTraceToElementMap().

◆ GetInteriorMap()

void Nektar::StdRegions::StdExpansion::GetInteriorMap ( Array< OneD, unsigned int > & outarray )

inline

Definition at line 674 of file StdExpansion.h.

    {
        v_GetInteriorMap(outarray);
    }

References v_GetInteriorMap().

Referenced by Nektar::LocalRegions::Expansion::CreateStaticCondMatrix(), CreateStdStaticCondMatrix(), Nektar::LocalRegions::QuadExp::v_FwdTransBndConstrained(), Nektar::LocalRegions::TriExp::v_FwdTransBndConstrained(), and Nektar::StdRegions::StdQuadExp::v_FwdTransBndConstrained().

◆ GetLinStdExp()

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

inline

Definition at line 377 of file StdExpansion.h.

    {
        return v_GetLinStdExp();
    }

References v_GetLinStdExp().

Referenced by Nektar::LocalRegions::Expansion3D::v_AddRobinMassMatrix().

◆ GetLocStaticCondMatrix()

DNekScalBlkMatSharedPtr Nektar::StdRegions::StdExpansion::GetLocStaticCondMatrix ( const LocalRegions::MatrixKey & mkey )

inline

Definition at line 641 of file StdExpansion.h.

    {
        return v_GetLocStaticCondMatrix(mkey);
    }

References v_GetLocStaticCondMatrix().

Referenced by Nektar::LocalRegions::Expansion2D::CreateMatrix(), and Nektar::LocalRegions::Expansion3D::CreateMatrix().

◆ GetNcoeffs()

int Nektar::StdRegions::StdExpansion::GetNcoeffs ( void ) const

inline

This function returns the total number of coefficients used in the expansion.

Returns: returns the total number of coefficients (which is equivalent to the total number of modes) used in the expansion

Definition at line 124 of file StdExpansion.h.

    {
        return (m_ncoeffs);
    }

References m_ncoeffs.

◆ GetNodalPointsKey()

const LibUtilities::PointsKey Nektar::StdRegions::StdExpansion::GetNodalPointsKey ( ) const

inline

This function returns the type of expansion Nodal point type if defined.

This function is a wrapper around the virtual function v_GetNodalPointsKey()

Definition at line 339 of file StdExpansion.h.

    {
        return v_GetNodalPointsKey();
    };

References v_GetNodalPointsKey().

◆ GetNtraces()

int Nektar::StdRegions::StdExpansion::GetNtraces ( ) const

inline

Returns the number of trace elements connected to this element.

For example, a quadrilateral has four edges, so this function would return 4.

Definition at line 351 of file StdExpansion.h.

    {
        return v_GetNtraces();
    }

References v_GetNtraces().

◆ GetNumBases()

int Nektar::StdRegions::StdExpansion::GetNumBases ( ) const

inline

This function returns the number of 1D bases used in the expansion.

Returns: returns the number of 1D bases used in the expansion, which is equal to number dimension of the expansion

Definition at line 91 of file StdExpansion.h.

    {
        return m_base.size();
    }

References m_base.

◆ GetNumPoints()

int Nektar::StdRegions::StdExpansion::GetNumPoints ( const int dir ) const

inline

This function returns the number of quadrature points in the dir direction.

Parameters

dir	the direction

Returns: returns the number of quadrature points in the dir direction

Definition at line 218 of file StdExpansion.h.

    {
        ASSERTL1(dir < m_base.size() || dir == 0,
                 "dir is larger than m_numbases");
        return (m_base.size() > 0 ? m_base[dir]->GetNumPoints() : 1);
    }

References ASSERTL1, and m_base.

◆ GetNverts()

int Nektar::StdRegions::StdExpansion::GetNverts ( ) const

inline

This function returns the number of vertices of the expansion domain.

This function is a wrapper around the virtual function v_GetNverts()

Returns: returns the number of vertices of the expansion domain

Definition at line 246 of file StdExpansion.h.

    {
        return v_GetNverts();
    }

References v_GetNverts().

Referenced by Nektar::CoupledLocalToGlobalC0ContMap::CoupledLocalToGlobalC0ContMap(), Nektar::LocalRegions::Expansion3D::GetInverseBoundaryMaps(), Nektar::LocalRegions::Expansion3D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion3D::v_BuildInverseTransformationMatrix(), Nektar::LocalRegions::Expansion3D::v_BuildTransformationMatrix(), Nektar::LocalRegions::Expansion2D::v_BuildVertexMatrix(), Nektar::LocalRegions::Expansion3D::v_BuildVertexMatrix(), and Nektar::LocalRegions::Expansion3D::v_ReOrientTracePhysMap().

◆ GetPoints()

const Array< OneD, const NekDouble > & Nektar::StdRegions::StdExpansion::GetPoints ( const int dir ) const

inline

This function returns a pointer to the array containing the quadrature points in dir direction.

Parameters

dir	the direction

Returns: returns a pointer to the array containing the quadrature points in dir direction

Definition at line 232 of file StdExpansion.h.

    {
        return m_base[dir]->GetZ();
    }

References m_base.

◆ GetPointsKeys()

const LibUtilities::PointsKeyVector Nektar::StdRegions::StdExpansion::GetPointsKeys ( ) const

inline

Definition at line 1095 of file StdExpansion.h.

    {
        LibUtilities::PointsKeyVector p;
        p.reserve(m_base.size());
        for (size_t i = 0; i < m_base.size(); ++i)
        {
            p.push_back(m_base[i]->GetPointsKey());
        }
        return p;
    }

References m_base, and CellMLToNektar.cellml_metadata::p.

◆ GetPointsType()

LibUtilities::PointsType Nektar::StdRegions::StdExpansion::GetPointsType ( const int dir ) const

inline

This function returns the type of quadrature points used in the dir direction.

The different types of quadrature points implemented in the code are defined in the LibUtilities::PointsType enumeration list. As a result, the function will return one of the types of this enumeration list.

Parameters

dir	the direction

Returns: returns the type of quadrature points used in the dir direction

Definition at line 205 of file StdExpansion.h.

    {
        ASSERTL1(dir < m_base.size(), "dir is larger than m_numbases");
        return (m_base[dir]->GetPointsType());
    }

References ASSERTL1, GetPointsType(), and m_base.

◆ GetShapeDimension()

int Nektar::StdRegions::StdExpansion::GetShapeDimension ( ) const

inline

Definition at line 382 of file StdExpansion.h.

    {
        return v_GetShapeDimension();
    }

References v_GetShapeDimension().

Referenced by v_GetCoordim().

◆ GetSimplexEquiSpacedConnectivity()

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

inline

This function provides the connectivity of local simplices (triangles or tets) to connect the equispaced data points provided by PhysInterpToSimplexEquiSpaced.

This is a virtual call to the function v_GetSimplexEquiSpaceConnectivity

Definition at line 1134 of file StdExpansion.h.

    {
        v_GetSimplexEquiSpacedConnectivity(conn, standard);
    }

References v_GetSimplexEquiSpacedConnectivity().

◆ GetStdExp()

std::shared_ptr< StdExpansion > Nektar::StdRegions::StdExpansion::GetStdExp ( ) const

inline

Definition at line 372 of file StdExpansion.h.

    {
        return v_GetStdExp();
    }

References v_GetStdExp().

◆ GetStdMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdExpansion::GetStdMatrix ( const StdMatrixKey & mkey )

inline

Definition at line 603 of file StdExpansion.h.

    {
        return m_stdMatrixManager[mkey];
    }

References m_stdMatrixManager.

◆ GetStdStaticCondMatrix()

DNekBlkMatSharedPtr Nektar::StdRegions::StdExpansion::GetStdStaticCondMatrix ( const StdMatrixKey & mkey )

inline

Definition at line 608 of file StdExpansion.h.

    {
        return m_stdStaticCondMatrixManager[mkey];
    }

References m_stdStaticCondMatrixManager.

Referenced by Nektar::LocalRegions::Expansion::CreateStaticCondMatrix().

◆ GetTotPoints()

int Nektar::StdRegions::StdExpansion::GetTotPoints ( ) const

inline

This function returns the total number of quadrature points used in the element.

Returns: returns the total number of quadrature points

Definition at line 134 of file StdExpansion.h.

    {
        int nqtot = 1;
 
        for (size_t i = 0; i < m_base.size(); ++i)
        {
            nqtot *= m_base[i]->GetNumPoints();
        }
 
        return nqtot;
    }

References m_base.

◆ GetTraceBasisKey()

const LibUtilities::BasisKey Nektar::StdRegions::StdExpansion::GetTraceBasisKey	(	const int	i,
		int	k = `-1`
	)		const

inline

This function returns the basis key belonging to the i-th trace.

This function is a wrapper around the virtual function v_GetTraceBasisKey()

Parameters

i	specifies which trace id
k	is the direction of the basis key for 2D traces

Returns: returns the number of Basis key of the ith trace in the k th direction (when trace is a 2D object)

Definition at line 299 of file StdExpansion.h.

    {
        return v_GetTraceBasisKey(i, k);
    }

References v_GetTraceBasisKey().

◆ GetTraceCoeffMap()

void Nektar::StdRegions::StdExpansion::GetTraceCoeffMap	(	const unsigned int	traceid,
		Array< OneD, unsigned int > &	maparray
	)

inline

Definition at line 693 of file StdExpansion.h.

    {
        v_GetTraceCoeffMap(traceid, maparray);
    }

References v_GetTraceCoeffMap().

Referenced by Nektar::StdRegions::StdExpansion3D::v_GetTraceToElementMap().

◆ GetTraceInteriorToElementMap()

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

inline

Definition at line 708 of file StdExpansion.h.

    {
        v_GetTraceInteriorToElementMap(tid, maparray, signarray, traceOrient);
    }

References v_GetTraceInteriorToElementMap().

Referenced by Nektar::LocalRegions::Expansion3D::GetInverseBoundaryMaps(), Nektar::LocalRegions::Expansion2D::GetTraceInverseBoundaryMap(), Nektar::LocalRegions::Expansion3D::GetTraceInverseBoundaryMap(), and Nektar::MultiRegions::AssemblyMapCG::SetUpUniversalC0ContMap().

◆ GetTraceIntNcoeffs()

int Nektar::StdRegions::StdExpansion::GetTraceIntNcoeffs ( const int i ) const

inline

Definition at line 266 of file StdExpansion.h.

    {
        return v_GetTraceIntNcoeffs(i);
    }

References v_GetTraceIntNcoeffs().

Referenced by Nektar::LocalRegions::Expansion3D::GetInverseBoundaryMaps(), Nektar::LocalRegions::Expansion3D::GetTraceInverseBoundaryMap(), Nektar::LocalRegions::Expansion3D::v_BuildInverseTransformationMatrix(), and Nektar::LocalRegions::Expansion3D::v_BuildTransformationMatrix().

◆ GetTraceNcoeffs()

int Nektar::StdRegions::StdExpansion::GetTraceNcoeffs ( const int i ) const

inline

This function returns the number of expansion coefficients belonging to the i-th trace.

This function is a wrapper around the virtual function v_GetTraceNcoeffs()

Parameters

i	specifies which trace

Returns: returns the number of expansion coefficients belonging to the i-th trace

Definition at line 261 of file StdExpansion.h.

    {
        return v_GetTraceNcoeffs(i);
    }

References v_GetTraceNcoeffs().

Referenced by Nektar::MultiRegions::AssemblyMapCG::AssemblyMapCG(), Nektar::CoupledLocalToGlobalC0ContMap::CoupledLocalToGlobalC0ContMap(), Nektar::MultiRegions::AssemblyMapCG::CreateGraph(), Nektar::LocalRegions::Expansion2D::GetTraceInverseBoundaryMap(), Nektar::LocalRegions::Expansion3D::SetFaceToGeomOrientation(), Nektar::LocalRegions::Expansion2D::SetTraceToGeomOrientation(), Nektar::LocalRegions::Expansion3D::SetTraceToGeomOrientation(), Nektar::MultiRegions::AssemblyMapCG::SetUpUniversalC0ContMap(), Nektar::LocalRegions::Expansion2D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion3D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion3D::v_GenMatrix(), Nektar::StdRegions::StdPrismExp::v_GetElmtTraceToTraceMap(), Nektar::StdRegions::StdPyrExp::v_GetElmtTraceToTraceMap(), Nektar::StdRegions::StdNodalTriExp::v_GetTraceInteriorToElementMap(), Nektar::StdRegions::StdQuadExp::v_GetTraceInteriorToElementMap(), Nektar::StdRegions::StdTriExp::v_GetTraceInteriorToElementMap(), and Nektar::StdRegions::StdNodalTriExp::v_GetTraceToElementMap().

◆ GetTraceNumModes()

void Nektar::StdRegions::StdExpansion::GetTraceNumModes	(	const int	tid,
		int &	numModes0,
		int &	numModes1,
		const Orientation	traceOrient = `eDir1FwdDir1_Dir2FwdDir2`
	)

inline

Definition at line 716 of file StdExpansion.h.

    {
        v_GetTraceNumModes(tid, numModes0, numModes1, traceOrient);
    }

References v_GetTraceNumModes().

Referenced by Nektar::LocalRegions::Expansion3D::GetTraceInverseBoundaryMap().

◆ GetTraceNumPoints()

int Nektar::StdRegions::StdExpansion::GetTraceNumPoints ( const int i ) const

inline

This function returns the number of quadrature points belonging to the i-th trace.

This function is a wrapper around the virtual function v_GetTraceNumPoints()

Parameters

i	specifies which trace id

Returns: returns the number of quadrature points belonging to the i-th trace

Definition at line 281 of file StdExpansion.h.

    {
        return v_GetTraceNumPoints(i);
    }

References v_GetTraceNumPoints().

Referenced by Nektar::LocalRegions::Expansion::StdDerivBaseOnTraceMat(), and Nektar::LocalRegions::Expansion3D::v_GetTracePhysVals().

◆ GetTracePointsKey()

LibUtilities::PointsKey Nektar::StdRegions::StdExpansion::GetTracePointsKey	(	const int	i,
		int	k = `-1`
	)		const

inline

This function returns the basis key belonging to the i-th trace.

This function is a wrapper around the virtual function v_GetTracePointsKey()

Parameters

i	specifies which trace id
k	is the direction of the basis key for 2D traces

Returns: returns the number of Points key of the ith trace in the k th direction (when trace is a 2D object)

Definition at line 317 of file StdExpansion.h.

    {
        return v_GetTracePointsKey(i, k);
    }

References v_GetTracePointsKey().

◆ GetTraceToElementMap()

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

inline

Definition at line 684 of file StdExpansion.h.

    {
        v_GetTraceToElementMap(tid, maparray, signarray, traceOrient, P, Q);
    }

References Nektar::LibUtilities::P, and v_GetTraceToElementMap().

◆ GetVertexMap()

int Nektar::StdRegions::StdExpansion::GetVertexMap	(	const int	localVertexId,
		bool	useCoeffPacking = `false`
	)

inline

Definition at line 679 of file StdExpansion.h.

    {
        return v_GetVertexMap(localVertexId, useCoeffPacking);
    }

References v_GetVertexMap().

◆ H1()

NekDouble Nektar::StdRegions::StdExpansion::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.

This function takes the physical value space array m_phys as approximate solution

Parameters

sol	array of solution function at physical quadrature points

Returns: returns the \( H_1 \) error as a double.

Definition at line 139 of file StdExpansion.cpp.

{
    int i;
    NekDouble val;
    int ntot    = GetTotPoints();
    int coordim = v_GetCoordim();
    Array<OneD, NekDouble> wsp(3 * ntot);
    Array<OneD, NekDouble> wsp_deriv = wsp + ntot;
    Array<OneD, NekDouble> sum       = wsp_deriv + ntot;
 
    if (sol == NullNekDouble1DArray)
    {
        Vmath::Vcopy(ntot, phys, 1, wsp, 1);
        Vmath::Vmul(ntot, phys, 1, phys, 1, sum, 1);
    }
    else
    {
        Vmath::Vsub(ntot, sol, 1, phys, 1, wsp, 1);
        Vmath::Vmul(ntot, wsp, 1, wsp, 1, sum, 1);
    }
 
    for (i = 0; i < coordim; ++i)
    {
        v_PhysDeriv(i, wsp, wsp_deriv);
        Vmath::Vvtvp(ntot, wsp_deriv, 1, wsp_deriv, 1, sum, 1, sum, 1);
    }
 
    val = sqrt(v_Integral(sum));
 
    return val;
}

References GetTotPoints(), Nektar::NullNekDouble1DArray, tinysimd::sqrt(), v_GetCoordim(), v_Integral(), v_PhysDeriv(), Vmath::Vcopy(), Vmath::Vmul(), Vmath::Vsub(), and Vmath::Vvtvp().

◆ HelmholtzMatrixOp()

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

inline

Parameters

inarray	Input array \( \mathbf{u} \).
outarray	Output array \( \boldsymbol{\nabla^2u} + \lambda \boldsymbol{u} \).
mkey

Definition at line 837 of file StdExpansion.h.

    {
        v_HelmholtzMatrixOp(inarray, outarray, mkey);
    }

References v_HelmholtzMatrixOp().

Referenced by GeneralMatrixOp().

◆ HelmholtzMatrixOp_MatFree()

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

inlineprotected

Definition at line 1284 of file StdExpansion.h.

    {
        v_HelmholtzMatrixOp_MatFree(inarray, outarray, mkey);
    }

References v_HelmholtzMatrixOp_MatFree().

Referenced by GeneralMatrixOp_MatFree(), v_HelmholtzMatrixOp(), Nektar::LocalRegions::QuadExp::v_HelmholtzMatrixOp(), and Nektar::LocalRegions::TriExp::v_HelmholtzMatrixOp().

◆ HelmholtzMatrixOp_MatFree_GenericImpl()

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

protected

Definition at line 986 of file StdExpansion.cpp.

{
    NekDouble lambda = mkey.GetConstFactor(eFactorLambda);
    Array<OneD, NekDouble> tmp(m_ncoeffs);
    StdMatrixKey mkeymass(eMass, DetShapeType(), *this);
    StdMatrixKey mkeylap(eLaplacian, DetShapeType(), *this,
                         mkey.GetConstFactors(), mkey.GetVarCoeffs(),
                         mkey.GetNodalPointsType());
 
    MassMatrixOp(inarray, tmp, mkeymass);
    LaplacianMatrixOp(inarray, outarray, mkeylap);
 
    Blas::Daxpy(m_ncoeffs, lambda, tmp, 1, outarray, 1);
}

References Blas::Daxpy(), DetShapeType(), Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eMass, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetConstFactors(), Nektar::StdRegions::StdMatrixKey::GetNodalPointsType(), Nektar::StdRegions::StdMatrixKey::GetVarCoeffs(), LaplacianMatrixOp(), m_ncoeffs, and MassMatrixOp().

Referenced by Nektar::StdRegions::StdNodalTriExp::v_HelmholtzMatrixOp(), v_HelmholtzMatrixOp_MatFree(), Nektar::StdRegions::StdExpansion2D::v_HelmholtzMatrixOp_MatFree(), and Nektar::StdRegions::StdExpansion3D::v_HelmholtzMatrixOp_MatFree().

◆ Integral()

NekDouble Nektar::StdRegions::StdExpansion::Integral ( const Array< OneD, const NekDouble > & inarray )

inline

This function integrates the specified function over the domain.

This function is a wrapper around the virtual function v_Integral()

Based on the values of the function evaluated at the quadrature points (which are stored in inarray), this function calculates the integral of this function over the domain. This is equivalent to the numerical evaluation of the operation

\[ I=\int u(\mathbf{\xi})d \mathbf{\xi}\]

Parameters

inarray values of the function to be integrated evaluated at the quadrature points (i.e. inarray[m]= \(u(\mathbf{\xi}_m)\))

Returns

returns the value of the calculated integral

        Inputs:\n

inarray: definition of function to be returned at quadrature point of expansion.

Outputs:

returns \(\int^1_{-1}\int^1_{-1} u(\xi_1, \xi_2) J[i,j] d \xi_1 d \xi_2 \) where \(inarray[i,j] = u(\xi_{1i},\xi_{2j}) \) and \( J[i,j] \) is the Jacobian evaluated at the quadrature point.

Definition at line 473 of file StdExpansion.h.

    {
        return v_Integral(inarray);
    }

References v_Integral().

Referenced by Nektar::LocalRegions::Expansion1D::v_VectorFlux().

◆ IProductWRTBase() [1/2]

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

inline

Definition at line 534 of file StdExpansion.h.

    {
        v_IProductWRTBase(base, inarray, outarray, coll_check);
    }

References v_IProductWRTBase().

◆ IProductWRTBase() [2/2]

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

inline

this function calculates the inner product of a given function f with the different modes of the expansion

This function is a wrapper around the virtual function v_IProductWRTBase()

This is equivalent to the numerical evaluation of

\[ I[p] = \int \phi_p(\mathbf{x}) f(\mathbf{x}) d\mathbf{x}\]

\( \begin{array}{rcl} I_{pq} = (\phi_q \phi_q, u) & = & \sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \phi_p(\xi_{0,i}) \phi_q(\xi_{1,j}) w^0_i w^1_j u(\xi_{0,i} \xi_{1,j}) J_{i,j}\\ & = & \sum_{i=0}^{nq_0} \phi_p(\xi_{0,i}) \sum_{j=0}^{nq_1} \phi_q(\xi_{1,j}) \tilde{u}_{i,j} J_{i,j} \end{array} \)

where

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

which can be implemented as

\( f_{qi} = \sum_{j=0}^{nq_1} \phi_q(\xi_{1,j}) \tilde{u}_{i,j} = {\bf B_1 U} \) \( I_{pq} = \sum_{i=0}^{nq_0} \phi_p(\xi_{0,i}) f_{qi} = {\bf B_0 F} \)

\param inarray contains the values of the function \a f
evaluated at the quadrature points
\param outarray contains the values of the inner product of \a f
with the different modes, i.e. \f$ outarray[p] = I[p]\f$
(output of the function)

Definition at line 528 of file StdExpansion.h.

    {
        v_IProductWRTBase(inarray, outarray);
    }

References v_IProductWRTBase().

◆ IProductWRTBase_SumFac()

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

inline

Definition at line 1158 of file StdExpansion.h.

    {
        v_IProductWRTBase_SumFac(inarray, outarray, multiplybyweights);
    }

References v_IProductWRTBase_SumFac().

Referenced by CreateGeneralMatrix(), Nektar::LocalRegions::QuadExp::v_IProductWRTBase(), and Nektar::LocalRegions::TriExp::v_IProductWRTBase().

◆ IProductWRTDerivBase()

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

inline

Definition at line 541 of file StdExpansion.h.

    {
        v_IProductWRTDerivBase(dir, inarray, outarray);
    }

References v_IProductWRTDerivBase().

◆ IProductWRTDerivBase_SumFac()

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

inlineprotected

Definition at line 1209 of file StdExpansion.h.

    {
        v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
    }

References v_IProductWRTDerivBase_SumFac().

Referenced by CreateGeneralMatrix(), Nektar::LocalRegions::QuadExp::v_IProductWRTDerivBase(), Nektar::LocalRegions::TriExp::v_IProductWRTDerivBase(), Nektar::StdRegions::StdHexExp::v_IProductWRTDerivBase(), and Nektar::StdRegions::StdSegExp::v_IProductWRTDerivBase().

◆ IProductWRTDirectionalDerivBase()

void Nektar::StdRegions::StdExpansion::IProductWRTDirectionalDerivBase	(	const Array< OneD, const NekDouble > &	direction,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 548 of file StdExpansion.h.

    {
        v_IProductWRTDirectionalDerivBase(direction, inarray, outarray);
    }

References v_IProductWRTDirectionalDerivBase().

◆ IProductWRTDirectionalDerivBase_SumFac()

void Nektar::StdRegions::StdExpansion::IProductWRTDirectionalDerivBase_SumFac	(	const Array< OneD, const NekDouble > &	direction,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

inlineprotected

Definition at line 1216 of file StdExpansion.h.

    {
        v_IProductWRTDirectionalDerivBase_SumFac(direction, inarray, outarray);
    }

References v_IProductWRTDirectionalDerivBase_SumFac().

Referenced by Nektar::LocalRegions::HexExp::v_IProductWRTDirectionalDerivBase(), and Nektar::LocalRegions::TriExp::v_IProductWRTDirectionalDerivBase().

◆ IsBoundaryInteriorExpansion()

bool Nektar::StdRegions::StdExpansion::IsBoundaryInteriorExpansion ( ) const

inline

Definition at line 387 of file StdExpansion.h.

    {
        return v_IsBoundaryInteriorExpansion();
    }

References v_IsBoundaryInteriorExpansion().

Referenced by Nektar::LocalRegions::Expansion2D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion3D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion1D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion2D::v_AddRobinTraceContribution(), Nektar::LocalRegions::Expansion1D::v_AddRobinTraceContribution(), Nektar::LocalRegions::Expansion1D::v_GenMatrix(), Nektar::LocalRegions::Expansion2D::v_GenMatrix(), and Nektar::LocalRegions::Expansion3D::v_GenMatrix().

◆ IsNodalNonTensorialExp()

bool Nektar::StdRegions::StdExpansion::IsNodalNonTensorialExp ( )

inline

Definition at line 392 of file StdExpansion.h.

    {
        return v_IsNodalNonTensorialExp();
    }

References v_IsNodalNonTensorialExp().

◆ L2()

NekDouble Nektar::StdRegions::StdExpansion::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.

This function takes the physical value space array m_phys as approximate solution

Parameters

sol	array of solution function at physical quadrature points

Returns: returns the \( L_2 \) error as a double.

Definition at line 117 of file StdExpansion.cpp.

{
    NekDouble val;
    int ntot = GetTotPoints();
    Array<OneD, NekDouble> wsp(ntot);
 
    if (sol.size() == 0)
    {
        Vmath::Vmul(ntot, phys, 1, phys, 1, wsp, 1);
    }
    else
    {
        Vmath::Vsub(ntot, sol, 1, phys, 1, wsp, 1);
        Vmath::Vmul(ntot, wsp, 1, wsp, 1, wsp, 1);
    }
 
    val = v_Integral(wsp);
 
    return (val < 0.0) ? 0.0 : sqrt(val);
}

References GetTotPoints(), tinysimd::sqrt(), v_Integral(), Vmath::Vmul(), and Vmath::Vsub().

◆ LaplacianMatrixOp() [1/2]

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

inline

Definition at line 759 of file StdExpansion.h.

    {
        v_LaplacianMatrixOp(inarray, outarray, mkey);
    }

References v_LaplacianMatrixOp().

Referenced by GeneralMatrixOp(), HelmholtzMatrixOp_MatFree_GenericImpl(), LaplacianMatrixOp_MatFree_GenericImpl(), and LinearAdvectionDiffusionReactionMatrixOp_MatFree().

◆ LaplacianMatrixOp() [2/2]

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

inline

Definition at line 785 of file StdExpansion.h.

    {
        v_LaplacianMatrixOp(k1, k2, inarray, outarray, mkey);
    }

References v_LaplacianMatrixOp().

◆ LaplacianMatrixOp_MatFree() [1/2]

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

inlineprotected

Definition at line 1241 of file StdExpansion.h.

    {
        v_LaplacianMatrixOp_MatFree(inarray, outarray, mkey);
    }

References v_LaplacianMatrixOp_MatFree().

Referenced by GeneralMatrixOp_MatFree(), v_LaplacianMatrixOp(), Nektar::LocalRegions::PrismExp::v_LaplacianMatrixOp(), Nektar::LocalRegions::QuadExp::v_LaplacianMatrixOp(), Nektar::LocalRegions::TriExp::v_LaplacianMatrixOp(), Nektar::StdRegions::StdHexExp::v_LaplacianMatrixOp(), Nektar::StdRegions::StdNodalTriExp::v_LaplacianMatrixOp(), Nektar::StdRegions::StdQuadExp::v_LaplacianMatrixOp(), and Nektar::StdRegions::StdTriExp::v_LaplacianMatrixOp().

◆ LaplacianMatrixOp_MatFree() [2/2]

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

protected

Definition at line 683 of file StdExpansion.cpp.

{
    ASSERTL1(k1 >= 0 && k1 < GetCoordim(), "invalid first  argument");
    ASSERTL1(k2 >= 0 && k2 < GetCoordim(), "invalid second argument");
 
    int nq = GetTotPoints();
    Array<OneD, NekDouble> tmp(nq);
    Array<OneD, NekDouble> dtmp(nq);
    VarCoeffType varcoefftypes[3][3] = {
        {eVarCoeffD00, eVarCoeffD01, eVarCoeffD02},
        {eVarCoeffD10, eVarCoeffD11, eVarCoeffD12},
        {eVarCoeffD20, eVarCoeffD21, eVarCoeffD22}};
 
    ConstFactorType constcoefftypes[3][3] = {
        {eFactorCoeffD00, eFactorCoeffD01, eFactorCoeffD02},
        {eFactorCoeffD01, eFactorCoeffD11, eFactorCoeffD12},
        {eFactorCoeffD02, eFactorCoeffD12, eFactorCoeffD22}};
 
    v_BwdTrans(inarray, tmp);
    v_PhysDeriv(k2, tmp, dtmp);
    if (mkey.GetNVarCoeff() && (!mkey.ConstFactorExists(eFactorSVVDiffCoeff)))
    {
        if (k1 == k2)
        {
            // By default, k1 == k2 has \sigma = 1 (diagonal entries)
            if (mkey.HasVarCoeff(varcoefftypes[k1][k1]))
            {
                Vmath::Vmul(nq, mkey.GetVarCoeff(varcoefftypes[k1][k1]), 1,
                            dtmp, 1, dtmp, 1);
            }
            v_IProductWRTDerivBase_SumFac(k1, dtmp, outarray);
        }
        else
        {
            // By default, k1 != k2 has \sigma = 0 (off-diagonal entries)
            if (mkey.HasVarCoeff(varcoefftypes[k1][k2]))
            {
                Vmath::Vmul(nq, mkey.GetVarCoeff(varcoefftypes[k1][k2]), 1,
                            dtmp, 1, dtmp, 1);
                v_IProductWRTDerivBase_SumFac(k1, dtmp, outarray);
            }
            else if (mkey.HasVarCoeff(
                         varcoefftypes[k2][k1])) // Check symmetric varcoeff
            {
                Vmath::Vmul(nq, mkey.GetVarCoeff(varcoefftypes[k2][k1]), 1,
                            dtmp, 1, dtmp, 1);
                v_IProductWRTDerivBase_SumFac(k1, dtmp, outarray);
            }
            else
            {
                Vmath::Zero(GetNcoeffs(), outarray, 1);
            }
        }
    }
    else if (mkey.ConstFactorExists(eFactorCoeffD00) &&
             (!mkey.ConstFactorExists(eFactorSVVDiffCoeff)))
    {
        if (k1 == k2)
        {
            // By default, k1 == k2 has \sigma = 1 (diagonal entries)
            if (mkey.ConstFactorExists(constcoefftypes[k1][k1]))
            {
                Vmath::Smul(nq, mkey.GetConstFactor(constcoefftypes[k1][k1]),
                            dtmp, 1, dtmp, 1);
            }
            v_IProductWRTDerivBase(k1, dtmp, outarray);
        }
        else
        {
            // By default, k1 != k2 has \sigma = 0 (off-diagonal entries)
            if (mkey.ConstFactorExists(constcoefftypes[k1][k2]))
            {
                Vmath::Smul(nq, mkey.GetConstFactor(constcoefftypes[k1][k2]),
                            dtmp, 1, dtmp, 1);
                v_IProductWRTDerivBase(k1, dtmp, outarray);
            }
            else
            {
                Vmath::Zero(GetNcoeffs(), outarray, 1);
            }
        }
    }
    else
    {
        // Multiply by svv tensor
        if (mkey.ConstFactorExists(eFactorSVVDiffCoeff))
        {
            Vmath::Vcopy(nq, dtmp, 1, tmp, 1);
            SVVLaplacianFilter(dtmp, mkey);
            Vmath::Vadd(nq, tmp, 1, dtmp, 1, dtmp, 1);
        }
        v_IProductWRTDerivBase(k1, dtmp, outarray);
    }
}

◆ LaplacianMatrixOp_MatFree_GenericImpl()

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

protected

Definition at line 780 of file StdExpansion.cpp.

{
    const int dim = GetCoordim();
 
    int i, j;
 
    Array<OneD, NekDouble> store(m_ncoeffs);
    Array<OneD, NekDouble> store2(m_ncoeffs, 0.0);
 
    if ((mkey.GetNVarCoeff() == 0 &&
         !mkey.ConstFactorExists(eFactorCoeffD00)) ||
        mkey.ConstFactorExists(eFactorSVVDiffCoeff))
    {
        // just call diagonal matrix form of laplcian operator
        for (i = 0; i < dim; ++i)
        {
            LaplacianMatrixOp(i, i, inarray, store, mkey);
            Vmath::Vadd(m_ncoeffs, store, 1, store2, 1, store2, 1);
        }
    }
    else
    {
        const MatrixType mtype[3][3] = {
            {eLaplacian00, eLaplacian01, eLaplacian02},
            {eLaplacian10, eLaplacian11, eLaplacian12},
            {eLaplacian20, eLaplacian21, eLaplacian22}};
        StdMatrixKeySharedPtr mkeyij;
 
        for (i = 0; i < dim; i++)
        {
            for (j = 0; j < dim; j++)
            {
                mkeyij = MemoryManager<StdMatrixKey>::AllocateSharedPtr(
                    mkey, mtype[i][j]);
                LaplacianMatrixOp(i, j, inarray, store, *mkeyij);
                Vmath::Vadd(m_ncoeffs, store, 1, store2, 1, store2, 1);
            }
        }
    }
 
    Vmath::Vcopy(m_ncoeffs, store2.get(), 1, outarray.get(), 1);
}

Referenced by Nektar::StdRegions::StdNodalTriExp::v_LaplacianMatrixOp(), v_LaplacianMatrixOp_MatFree(), Nektar::StdRegions::StdExpansion2D::v_LaplacianMatrixOp_MatFree(), and Nektar::StdRegions::StdExpansion3D::v_LaplacianMatrixOp_MatFree().

◆ LaplacianMatrixOp_MatFree_Kernel()

void Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp
	)

inlineprotected

Definition at line 1248 of file StdExpansion.h.

    {
        v_LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp);
    }

References v_LaplacianMatrixOp_MatFree_Kernel().

Referenced by Nektar::StdRegions::StdExpansion2D::v_HelmholtzMatrixOp_MatFree(), Nektar::StdRegions::StdExpansion3D::v_HelmholtzMatrixOp_MatFree(), Nektar::StdRegions::StdExpansion2D::v_LaplacianMatrixOp_MatFree(), and Nektar::StdRegions::StdExpansion3D::v_LaplacianMatrixOp_MatFree().

◆ LinearAdvectionDiffusionReactionMatrixOp()

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

inline

Definition at line 822 of file StdExpansion.h.

    {
        v_LinearAdvectionDiffusionReactionMatrixOp(inarray, outarray, mkey,
                                                   addDiffusionTerm);
    }

References v_LinearAdvectionDiffusionReactionMatrixOp().

Referenced by GeneralMatrixOp().

◆ LinearAdvectionDiffusionReactionMatrixOp_MatFree()

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

protected

Definition at line 916 of file StdExpansion.cpp.

{
    int i, ndir = 0;
 
    VarCoeffType varcoefftypes[] = {eVarCoeffVelX, eVarCoeffVelY,
                                    eVarCoeffVelZ};
    // Count advection velocities
    for (auto &x : varcoefftypes)
    {
        if (mkey.HasVarCoeff(x))
        {
            ndir++;
        }
    }
 
    ASSERTL0(ndir, "Must define at least one advection velocity");
    ASSERTL1(ndir <= GetCoordim(),
             "Number of constants is larger than coordinate dimensions");
 
    NekDouble lambda = mkey.GetConstFactor(eFactorLambda);
    int totpts       = GetTotPoints();
    Array<OneD, NekDouble> tmp(3 * totpts);
    Array<OneD, NekDouble> tmp_deriv = tmp + totpts;
    Array<OneD, NekDouble> tmp_adv   = tmp_deriv + totpts;
 
    v_BwdTrans(inarray, tmp); // transform this mode \phi_i into PhysSpace
 
    // calculate advection u dx + v dy + ..
    Vmath::Zero(totpts, tmp_adv, 1);
    for (i = 0; i < ndir; ++i)
    {
        v_PhysDeriv(i, tmp, tmp_deriv);
        Vmath::Vvtvp(totpts, mkey.GetVarCoeff(varcoefftypes[i]), 1, tmp_deriv,
                     1, tmp_adv, 1, tmp_adv, 1);
    }
 
    // Add reaction term if lambda != 0.0
    if (lambda)
    {
        // Add mass varcoeff
        if (mkey.HasVarCoeff(eVarCoeffMass))
        {
            Vmath::Vmul(totpts, mkey.GetVarCoeff(eVarCoeffMass), 1, tmp, 1, tmp,
                        1);
        }
 
        Vmath::Svtvp(totpts, -lambda, tmp, 1, tmp_adv, 1, tmp_adv, 1);
    }
 
    // Create mass matrix = Advection - Reaction
    v_IProductWRTBase(tmp_adv,
                      outarray); // Create mass matrix of Advection - Reaction
 
    // Add Laplacian matrix
    if (addDiffusionTerm)
    {
        Array<OneD, NekDouble> lap(m_ncoeffs);
        StdMatrixKey mkeylap(eLaplacian, DetShapeType(), *this,
                             mkey.GetConstFactors(), mkey.GetVarCoeffs(),
                             mkey.GetNodalPointsType());
        LaplacianMatrixOp(inarray, lap, mkeylap);
 
        Vmath::Vadd(m_ncoeffs, lap, 1, outarray, 1, outarray,
                    1); // += Laplacian
    }
}

References ASSERTL0, ASSERTL1, DetShapeType(), Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eVarCoeffMass, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, Nektar::StdRegions::eVarCoeffVelZ, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetConstFactors(), GetCoordim(), Nektar::StdRegions::StdMatrixKey::GetNodalPointsType(), GetTotPoints(), Nektar::StdRegions::StdMatrixKey::GetVarCoeff(), Nektar::StdRegions::StdMatrixKey::GetVarCoeffs(), Nektar::StdRegions::StdMatrixKey::HasVarCoeff(), LaplacianMatrixOp(), m_ncoeffs, Vmath::Svtvp(), v_BwdTrans(), v_IProductWRTBase(), v_PhysDeriv(), Vmath::Vadd(), Vmath::Vmul(), Vmath::Vvtvp(), and Vmath::Zero().

Referenced by GeneralMatrixOp_MatFree(), and v_LinearAdvectionDiffusionReactionMatrixOp().

◆ LinearAdvectionMatrixOp()

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

inline

Definition at line 815 of file StdExpansion.h.

    {
        v_LinearAdvectionMatrixOp(inarray, outarray, mkey);
    }

References v_LinearAdvectionMatrixOp().

Referenced by GeneralMatrixOp().

◆ LinearAdvectionMatrixOp_MatFree()

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

protected

Definition at line 876 of file StdExpansion.cpp.

{
    int i, ndir = 0;
 
    VarCoeffType varcoefftypes[] = {eVarCoeffVelX, eVarCoeffVelY,
                                    eVarCoeffVelZ};
    // Count advection velocities
    for (auto &x : varcoefftypes)
    {
        if (mkey.HasVarCoeff(x))
        {
            ndir++;
        }
    }
 
    ASSERTL0(ndir, "Must define at least one advection velocity");
    ASSERTL1(ndir <= GetCoordim(),
             "Number of constants is larger than coordinate dimensions");
 
    int totpts = GetTotPoints();
    Array<OneD, NekDouble> tmp(3 * totpts);
    Array<OneD, NekDouble> tmp_deriv = tmp + totpts;
    Array<OneD, NekDouble> tmp_adv   = tmp_deriv + totpts;
 
    v_BwdTrans(inarray, tmp); // transform to PhysSpace
 
    // Evaluate advection (u dx + v dy + w dz)
    Vmath::Zero(totpts, tmp_adv, 1);
    for (i = 0; i < ndir; ++i)
    {
        v_PhysDeriv(i, tmp, tmp_deriv);
        Vmath::Vvtvp(totpts, mkey.GetVarCoeff(varcoefftypes[i]), 1, tmp_deriv,
                     1, tmp_adv, 1, tmp_adv, 1);
    }
 
    v_IProductWRTBase(tmp_adv, outarray);
}

References ASSERTL0, ASSERTL1, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, Nektar::StdRegions::eVarCoeffVelZ, GetCoordim(), GetTotPoints(), Nektar::StdRegions::StdMatrixKey::GetVarCoeff(), Nektar::StdRegions::StdMatrixKey::HasVarCoeff(), v_BwdTrans(), v_IProductWRTBase(), v_PhysDeriv(), Vmath::Vvtvp(), and Vmath::Zero().

Referenced by GeneralMatrixOp_MatFree(), and v_LinearAdvectionMatrixOp().

◆ Linf()

NekDouble Nektar::StdRegions::StdExpansion::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.

This function takes the physical value space array m_phys as approximate solution

Parameters

sol	array of solution function at physical quadrature points

Returns: returns the \( L_\infty \) error as a NekDouble.

Definition at line 96 of file StdExpansion.cpp.

{
    NekDouble val;
    int ntot = GetTotPoints();
    Array<OneD, NekDouble> wsp(ntot);
 
    if (sol == NullNekDouble1DArray)
    {
        Vmath::Vabs(ntot, phys, 1, wsp, 1);
    }
    else
    {
        Vmath::Vsub(ntot, sol, 1, phys, 1, wsp, 1);
        Vmath::Vabs(ntot, wsp, 1, wsp, 1);
    }
 
    val = Vmath::Vamax(ntot, wsp, 1);
    return val;
}

References GetTotPoints(), Nektar::NullNekDouble1DArray, Vmath::Vabs(), Vmath::Vamax(), and Vmath::Vsub().

◆ LocCollapsedToLocCoord()

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

inline

Convert local collapsed coordinates eta into local cartesian coordinate xi.

Definition at line 1012 of file StdExpansion.h.

    {
        v_LocCollapsedToLocCoord(eta, xi);
    }

References v_LocCollapsedToLocCoord().

◆ LocCoordToLocCollapsed()

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

inline

Convert local cartesian coordinate xi into local collapsed coordinates eta.

Definition at line 1002 of file StdExpansion.h.

    {
        v_LocCoordToLocCollapsed(xi, eta);
    }

References v_LocCoordToLocCollapsed().

◆ MassLevelCurvatureMatrixOp()

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

inline

Definition at line 808 of file StdExpansion.h.

    {
        v_MassLevelCurvatureMatrixOp(inarray, outarray, mkey);
    }

References v_MassLevelCurvatureMatrixOp().

Referenced by GeneralMatrixOp().

◆ MassLevelCurvatureMatrixOp_MatFree()

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

protected

Definition at line 869 of file StdExpansion.cpp.

873{

874}

Referenced by GeneralMatrixOp_MatFree(), and v_MassLevelCurvatureMatrixOp().

◆ MassMatrixOp()

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

inline

Definition at line 752 of file StdExpansion.h.

    {
        v_MassMatrixOp(inarray, outarray, mkey);
    }

References v_MassMatrixOp().

Referenced by GeneralMatrixOp(), HelmholtzMatrixOp_MatFree_GenericImpl(), Nektar::LocalRegions::QuadExp::v_FwdTransBndConstrained(), Nektar::LocalRegions::SegExp::v_FwdTransBndConstrained(), Nektar::LocalRegions::TriExp::v_FwdTransBndConstrained(), Nektar::StdRegions::StdQuadExp::v_FwdTransBndConstrained(), Nektar::StdRegions::StdSegExp::v_FwdTransBndConstrained(), and Nektar::StdRegions::StdTriExp::v_FwdTransBndConstrained().

◆ MassMatrixOp_MatFree()

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

protected

Definition at line 666 of file StdExpansion.cpp.

{
    int nq = GetTotPoints();
    Array<OneD, NekDouble> tmp(nq);
 
    v_BwdTrans(inarray, tmp);
 
    if (mkey.HasVarCoeff(eVarCoeffMass))
    {
        Vmath::Vmul(nq, mkey.GetVarCoeff(eVarCoeffMass), 1, tmp, 1, tmp, 1);
    }
 
    v_IProductWRTBase(tmp, outarray);
}

References Nektar::StdRegions::eVarCoeffMass, GetTotPoints(), Nektar::StdRegions::StdMatrixKey::GetVarCoeff(), Nektar::StdRegions::StdMatrixKey::HasVarCoeff(), v_BwdTrans(), v_IProductWRTBase(), and Vmath::Vmul().

Referenced by GeneralMatrixOp_MatFree(), v_MassMatrixOp(), Nektar::StdRegions::StdHexExp::v_MassMatrixOp(), Nektar::StdRegions::StdNodalTriExp::v_MassMatrixOp(), Nektar::StdRegions::StdQuadExp::v_MassMatrixOp(), and Nektar::StdRegions::StdTriExp::v_MassMatrixOp().

◆ MultiplyByQuadratureMetric()

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

inline

Definition at line 723 of file StdExpansion.h.

    {
        v_MultiplyByQuadratureMetric(inarray, outarray);
    }

References v_MultiplyByQuadratureMetric().

◆ MultiplyByStdQuadratureMetric()

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

inline

Definition at line 729 of file StdExpansion.h.

    {
        v_MultiplyByStdQuadratureMetric(inarray, outarray);
    }

References v_MultiplyByStdQuadratureMetric().

◆ NormVectorIProductWRTBase() [1/4]

void Nektar::StdRegions::StdExpansion::NormVectorIProductWRTBase	(	const Array< OneD, const Array< OneD, NekDouble > > &	Fvec,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 634 of file StdExpansion.h.

    {
        v_NormVectorIProductWRTBase(Fvec, outarray);
    }

References v_NormVectorIProductWRTBase().

◆ NormVectorIProductWRTBase() [2/4]

void Nektar::StdRegions::StdExpansion::NormVectorIProductWRTBase	(	const Array< OneD, const NekDouble > &	Fx,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 613 of file StdExpansion.h.

    {
        v_NormVectorIProductWRTBase(Fx, outarray);
    }

References v_NormVectorIProductWRTBase().

Referenced by Nektar::LocalRegions::Expansion3D::v_NormVectorIProductWRTBase(), Nektar::LocalRegions::QuadExp::v_NormVectorIProductWRTBase(), Nektar::LocalRegions::SegExp::v_NormVectorIProductWRTBase(), and Nektar::LocalRegions::TriExp::v_NormVectorIProductWRTBase().

◆ NormVectorIProductWRTBase() [3/4]

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

inline

Definition at line 626 of file StdExpansion.h.

    {
        v_NormVectorIProductWRTBase(Fx, Fy, Fz, outarray);
    }

References v_NormVectorIProductWRTBase().

◆ NormVectorIProductWRTBase() [4/4]

void Nektar::StdRegions::StdExpansion::NormVectorIProductWRTBase	(	const Array< OneD, const NekDouble > &	Fx,
		const Array< OneD, NekDouble > &	Fy,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 619 of file StdExpansion.h.

    {
        v_NormVectorIProductWRTBase(Fx, Fy, outarray);
    }

References v_NormVectorIProductWRTBase().

◆ NumBndryCoeffs()

int Nektar::StdRegions::StdExpansion::NumBndryCoeffs ( void ) const

inline

Definition at line 322 of file StdExpansion.h.

    {
        return v_NumBndryCoeffs();
    }

References v_NumBndryCoeffs().

◆ NumDGBndryCoeffs()

int Nektar::StdRegions::StdExpansion::NumDGBndryCoeffs ( void ) const

inline

Definition at line 327 of file StdExpansion.h.

    {
        return v_NumDGBndryCoeffs();
    }

References v_NumDGBndryCoeffs().

Referenced by Nektar::LocalRegions::Expansion2D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion3D::v_AddRobinMassMatrix(), Nektar::LocalRegions::Expansion1D::v_GenMatrix(), Nektar::LocalRegions::Expansion2D::v_GenMatrix(), and Nektar::LocalRegions::Expansion3D::v_GenMatrix().

◆ PhysDeriv() [1/2]

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

inline

Definition at line 849 of file StdExpansion.h.

    {
        v_PhysDeriv(inarray, out_d0, out_d1, out_d2);
    }

References v_PhysDeriv().

Referenced by Nektar::LocalRegions::Expansion2D::v_GenMatrix(), Nektar::LocalRegions::Expansion3D::v_GenMatrix(), Nektar::LocalRegions::SegExp::v_HelmholtzMatrixOp(), Nektar::LocalRegions::SegExp::v_LaplacianMatrixOp(), Nektar::MultiRegions::ExpListHomogeneous1D::v_PhysDeriv(), Nektar::MultiRegions::ExpListHomogeneous2D::v_PhysDeriv(), Nektar::LocalRegions::HexExp::v_PhysDeriv(), Nektar::LocalRegions::SegExp::v_PhysDeriv(), Nektar::LocalRegions::TriExp::v_PhysDeriv(), Nektar::StdRegions::StdHexExp::v_PhysDeriv(), Nektar::StdRegions::StdPrismExp::v_PhysEvaluate(), Nektar::StdRegions::StdPyrExp::v_PhysEvaluate(), Nektar::StdRegions::StdTetExp::v_PhysEvaluate(), and Nektar::StdRegions::StdTriExp::v_PhysEvaluate().

◆ PhysDeriv() [2/2]

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

inline

Definition at line 857 of file StdExpansion.h.

    {
        v_PhysDeriv(dir, inarray, outarray);
    }

References v_PhysDeriv().

◆ PhysDeriv_n()

void Nektar::StdRegions::StdExpansion::PhysDeriv_n	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_dn
	)

inline

Definition at line 869 of file StdExpansion.h.

    {
        v_PhysDeriv_n(inarray, out_dn);
    }

References v_PhysDeriv_n().

◆ PhysDeriv_s()

void Nektar::StdRegions::StdExpansion::PhysDeriv_s	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_ds
	)

inline

Definition at line 863 of file StdExpansion.h.

    {
        v_PhysDeriv_s(inarray, out_ds);
    }

References v_PhysDeriv_s().

◆ PhysDirectionalDeriv()

void Nektar::StdRegions::StdExpansion::PhysDirectionalDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		const Array< OneD, const NekDouble > &	direction,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 875 of file StdExpansion.h.

    {
        v_PhysDirectionalDeriv(inarray, direction, outarray);
    }

References v_PhysDirectionalDeriv().

◆ PhysEvaluate() [1/4]

NekDouble Nektar::StdRegions::StdExpansion::PhysEvaluate	(	const Array< OneD, const NekDouble > &	coords,
		const Array< OneD, const NekDouble > &	physvals
	)

inline

This function evaluates the expansion at a single (arbitrary) point of the domain.

This function is a wrapper around the virtual function v_PhysEvaluate()

Based on the value of the expansion at the quadrature points provided in physvals, this function calculates the value of the expansion at an arbitrary single points (with coordinates \( \mathbf{x_c}\) given by the pointer coords). This operation, equivalent to

\[ u(\mathbf{x_c}) = \sum_p \phi_p(\mathbf{x_c}) \hat{u}_p \]

is evaluated using Lagrangian interpolants through the quadrature points:

\[ u(\mathbf{x_c}) = \sum_p h_p(\mathbf{x_c}) u_p\]

Parameters

coords	the coordinates of the single point
physvals	the interpolated field at the quadrature points

Returns: returns the value of the expansion at the single point

Definition at line 919 of file StdExpansion.h.

    {
        return v_PhysEvaluate(coords, physvals);
    }

References v_PhysEvaluate().

Referenced by Nektar::StdRegions::StdPrismExp::v_PhysEvaluate(), Nektar::StdRegions::StdPyrExp::v_PhysEvaluate(), Nektar::StdRegions::StdTetExp::v_PhysEvaluate(), and Nektar::StdRegions::StdTriExp::v_PhysEvaluate().

◆ PhysEvaluate() [2/4]

NekDouble Nektar::StdRegions::StdExpansion::PhysEvaluate	(	const Array< OneD, DNekMatSharedPtr > &	I,
		const Array< OneD, const NekDouble > &	physvals
	)

inline

This function evaluates the expansion at a single (arbitrary) point of the domain.

This function is a wrapper around the virtual function v_PhysEvaluate()

Based on the value of the expansion at the quadrature points provided in physvals, this function calculates the value of the expansion at an arbitrary single points associated with the interpolation matrices provided in \( I \).

Parameters

I	an Array of lagrange interpolantes evaluated at the coordinate and going through the local physical quadrature
physvals	the interpolated field at the quadrature points

Returns: returns the value of the expansion at the single point

Definition at line 974 of file StdExpansion.h.

    {
        return v_PhysEvaluate(I, physvals);
    }

References v_PhysEvaluate().

◆ PhysEvaluate() [3/4]

NekDouble Nektar::StdRegions::StdExpansion::PhysEvaluate	(	const Array< OneD, NekDouble > &	coord,
		const Array< OneD, const NekDouble > &	inarray,
		std::array< NekDouble, 3 > &	firstOrderDerivs
	)

inline

This function evaluates the first derivative of the expansion at a single (arbitrary) point of the domain.

This function is a wrapper around the virtual function v_PhysEvaluate()

Based on the value of the expansion at the quadrature points provided in physvals, this function calculates the value of the expansion at a set of points given in coords

Definition at line 936 of file StdExpansion.h.

    {
        return v_PhysEvaluate(coord, inarray, firstOrderDerivs);
    }

References v_PhysEvaluate().

◆ PhysEvaluate() [4/4]

NekDouble Nektar::StdRegions::StdExpansion::PhysEvaluate	(	const Array< OneD, NekDouble > &	coord,
		const Array< OneD, const NekDouble > &	inarray,
		std::array< NekDouble, 3 > &	firstOrderDerivs,
		std::array< NekDouble, 6 > &	secondOrderDerivs
	)

inline

Definition at line 944 of file StdExpansion.h.

    {
        return v_PhysEvaluate(coord, inarray, firstOrderDerivs,
                              secondOrderDerivs);
    }

References v_PhysEvaluate().

◆ PhysEvaluateBasis()

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

inline

This function evaluates the basis function mode mode at a point coords of the domain.

This function uses barycentric interpolation with the tensor product separation of the basis function to improve performance.

Parameters

coord	The coordinate inside the standard region.
mode	The mode number to be evaluated.

Returns: The value of the basis function mode at coords.

Definition at line 992 of file StdExpansion.h.

    {
        return v_PhysEvaluateBasis(coords, mode);
    }

References v_PhysEvaluateBasis().

◆ PhysInterpToSimplexEquiSpaced()

void Nektar::StdRegions::StdExpansion::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.

This is primarily used for output purposes to get a better distribution of points more suitable for most postprocessing

Definition at line 1619 of file StdExpansion.cpp.

{
    LibUtilities::ShapeType shape = DetShapeType();
    DNekMatSharedPtr intmat;
 
    int nqtot = GetTotPoints();
    int np    = 0;
    if (npset == -1) // use values from basis num points()
    {
        int nqbase;
        for (int i = 0; i < m_base.size(); ++i)
        {
            nqbase = m_base[i]->GetNumPoints();
            np     = std::max(np, nqbase);
        }
 
        StdMatrixKey Ikey(ePhysInterpToEquiSpaced, shape, *this);
        intmat = GetStdMatrix(Ikey);
    }
    else
    {
        np = npset;
 
        ConstFactorMap cmap;
        cmap[eFactorConst] = np;
        StdMatrixKey Ikey(ePhysInterpToEquiSpaced, shape, *this, cmap);
        intmat = GetStdMatrix(Ikey);
    }
 
    NekVector<NekDouble> in(nqtot, inarray, eWrapper);
    NekVector<NekDouble> out(
        LibUtilities::GetNumberOfCoefficients(shape, np, np, np), outarray,
        eWrapper);
    out = (*intmat) * in;
}

References DetShapeType(), Nektar::StdRegions::eFactorConst, Nektar::StdRegions::ePhysInterpToEquiSpaced, Nektar::eWrapper, Nektar::LibUtilities::GetNumberOfCoefficients(), GetStdMatrix(), GetTotPoints(), and m_base.

Referenced by CreateGeneralMatrix().

◆ ReduceOrderCoeffs()

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

inline

Definition at line 766 of file StdExpansion.h.

    {
        v_ReduceOrderCoeffs(numMin, inarray, outarray);
    }

References v_ReduceOrderCoeffs().

◆ SetElmtId()

void Nektar::StdRegions::StdExpansion::SetElmtId ( const int id )

inline

Set the element id of this expansion when used in a list by returning value of m_elmt_id.

Definition at line 565 of file StdExpansion.h.

    {
        m_elmt_id = id;
    }

References m_elmt_id.

◆ StdPhysDeriv() [1/2]

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

inline

Definition at line 882 of file StdExpansion.h.

    {
        v_StdPhysDeriv(inarray, out_d0, out_d1, out_d2);
    }

References v_StdPhysDeriv().

Referenced by Nektar::LocalRegions::Expansion::StdDerivBaseOnTraceMat().

◆ StdPhysDeriv() [2/2]

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

inline

Definition at line 890 of file StdExpansion.h.

    {
        v_StdPhysDeriv(dir, inarray, outarray);
    }

References v_StdPhysDeriv().

◆ StdPhysEvaluate()

NekDouble Nektar::StdRegions::StdExpansion::StdPhysEvaluate	(	const Array< OneD, const NekDouble > &	Lcoord,
		const Array< OneD, const NekDouble > &	physvals
	)

Definition at line 1004 of file StdExpansion.cpp.

{
    return v_StdPhysEvaluate(Lcoord, physvals);
}

References v_StdPhysEvaluate().

◆ SVVLaplacianFilter()

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

inline

Definition at line 773 of file StdExpansion.h.

    {
        v_SVVLaplacianFilter(array, mkey);
    }

References v_SVVLaplacianFilter().

Referenced by LaplacianMatrixOp_MatFree().

◆ v_BuildInverseTransformationMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdExpansion::v_BuildInverseTransformationMatrix ( const DNekScalMatSharedPtr & m_transformationmatrix )

privatevirtual

Reimplemented in Nektar::LocalRegions::Expansion3D.

Definition at line 1612 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for LocalRegions");
    return NullDNekMatSharedPtr;
}

References Nektar::ErrorUtil::efatal, NEKERROR, and Nektar::NullDNekMatSharedPtr.

Referenced by BuildInverseTransformationMatrix().

◆ v_BwdTrans()

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

privatepure virtual

Implemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Referenced by BwdTrans(), LaplacianMatrixOp_MatFree(), LinearAdvectionDiffusionReactionMatrixOp_MatFree(), LinearAdvectionMatrixOp_MatFree(), MassMatrixOp_MatFree(), WeakDerivMatrixOp_MatFree(), and WeakDirectionalDerivMatrixOp_MatFree().

◆ v_BwdTrans_SumFac()

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

privatevirtual

Reimplemented in Nektar::LocalRegions::NodalTriExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1445 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by BwdTrans_SumFac().

◆ v_CalcNumberOfCoefficients()

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

virtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1011 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not defined for this class");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by CalcNumberOfCoefficients().

◆ v_CreateStdMatrix()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1329 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function has not "
                                "been defined for this element");
    DNekMatSharedPtr returnval;
    return returnval;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by CreateStdMatrix().

◆ v_DetShapeType()

virtual LibUtilities::ShapeType Nektar::StdRegions::StdExpansion::v_DetShapeType ( ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::TetExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdSegExp, and Nektar::StdRegions::StdTetExp.

Referenced by DetShapeType().

◆ v_DropLocStaticCondMatrix()

void Nektar::StdRegions::StdExpansion::v_DropLocStaticCondMatrix ( const LocalRegions::MatrixKey & mkey )

virtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1057 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for LocalRegions");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by DropLocStaticCondMatrix().

◆ v_ExponentialFilter()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdQuadExp, and Nektar::StdRegions::StdSegExp.

Definition at line 1504 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This function is not defined in StdExpansion.");
}

References ASSERTL0.

Referenced by ExponentialFilter().

◆ v_FillMode()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1313 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function has not "
                                "been defined for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by FillMode().

◆ v_FwdTrans()

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

privatepure virtual

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

See also: StdExpansion::FwdTrans

Referenced by FwdTrans().

◆ v_FwdTransBndConstrained()

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

privatevirtual

Reimplemented in Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1169 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This method has not been defined");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by FwdTransBndConstrained().

◆ v_GenMatrix()

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

privatevirtual

Definition at line 1320 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function has not "
                                "been defined for this element");
    DNekMatSharedPtr returnval;
    return returnval;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GenMatrix().

◆ v_GenStdMatBwdDeriv()

virtual void Nektar::StdRegions::StdExpansion::v_GenStdMatBwdDeriv	(	const int	dir,
		DNekMatSharedPtr &	mat
	)

inlineprotectedvirtual

Reimplemented in Nektar::StdRegions::StdExpansion2D, and Nektar::StdRegions::StdExpansion3D.

Definition at line 1306 of file StdExpansion.h.

    {
        NEKERROR(ErrorUtil::efatal, "not defined");
    }

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GenStdMatBwdDeriv().

◆ v_GetBoundaryMap()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1358 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetBoundaryMap().

◆ v_GetCoord()

void Nektar::StdRegions::StdExpansion::v_GetCoord	(	const Array< OneD, const NekDouble > &	Lcoord,
		Array< OneD, NekDouble > &	coord
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1346 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Write coordinate definition method");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetCoord().

◆ v_GetCoordim()

int Nektar::StdRegions::StdExpansion::v_GetCoordim ( ) const

privatevirtual

Reimplemented in Nektar::LocalRegions::Expansion.

Definition at line 1353 of file StdExpansion.cpp.

{
    return GetShapeDimension();
}

References GetShapeDimension().

Referenced by GetCoordim(), and H1().

◆ v_GetCoords()

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

privatevirtual

Definition at line 1338 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Write coordinate definition method");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetCoords().

◆ v_GetElmtTraceToTraceMap()

void Nektar::StdRegions::StdExpansion::v_GetElmtTraceToTraceMap	(	const unsigned int	tid,
		Array< OneD, unsigned int > &	maparray,
		Array< OneD, int > &	signarray,
		Orientation	traceOrient = `eForwards`,
		int	P = `-1`,
		int	Q = `-1`
	)

privatevirtual

Reimplemented in Nektar::StdRegions::StdExpansion2D, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, and Nektar::StdRegions::StdTetExp.

Definition at line 1394 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetElmtTraceToTraceMap().

◆ v_GetInteriorMap()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1364 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetInteriorMap().

◆ v_GetLinStdExp()

std::shared_ptr< StdExpansion > Nektar::StdRegions::StdExpansion::v_GetLinStdExp ( void ) const

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1129 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This method is not defined for this expansion");
    StdExpansionSharedPtr returnval;
    return returnval;
}

References ASSERTL0.

Referenced by GetLinStdExp().

◆ v_GetLocStaticCondMatrix()

DNekScalBlkMatSharedPtr Nektar::StdRegions::StdExpansion::v_GetLocStaticCondMatrix ( const LocalRegions::MatrixKey & mkey )

virtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1050 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for LocalRegions");
    return NullDNekScalBlkMatSharedPtr;
}

References Nektar::ErrorUtil::efatal, NEKERROR, and Nektar::NullDNekScalBlkMatSharedPtr.

Referenced by GetLocStaticCondMatrix().

◆ v_GetNodalPointsKey()

const LibUtilities::PointsKey Nektar::StdRegions::StdExpansion::v_GetNodalPointsKey ( ) const

privatevirtual

Reimplemented in Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1115 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This function is not valid or not defined");
 
    return LibUtilities::NullPointsKey;
}

References ASSERTL0, and Nektar::LibUtilities::NullPointsKey().

Referenced by GetNodalPointsKey().

◆ v_GetNtraces()

virtual int Nektar::StdRegions::StdExpansion::v_GetNtraces ( ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdExpansion0D, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTriExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, and Nektar::StdRegions::StdTetExp.

Referenced by GetNtraces().

◆ v_GetNverts()

virtual int Nektar::StdRegions::StdExpansion::v_GetNverts ( ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTriExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, and Nektar::StdRegions::StdTetExp.

Referenced by GetNverts().

◆ v_GetShapeDimension()

virtual int Nektar::StdRegions::StdExpansion::v_GetShapeDimension ( ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdExpansion0D, Nektar::StdRegions::StdExpansion1D, Nektar::StdRegions::StdExpansion2D, and Nektar::StdRegions::StdExpansion3D.

Referenced by GetShapeDimension().

◆ v_GetSimplexEquiSpacedConnectivity()

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

privatevirtual

Reimplemented in Nektar::LocalRegions::PrismExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1657 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "GetSimplexEquiSpacedConnectivity not"
             " implemented for " +
                 static_cast<std::string>(
                     LibUtilities::ShapeTypeMap[DetShapeType()]));
}

References DetShapeType(), Nektar::ErrorUtil::efatal, NEKERROR, and Nektar::LibUtilities::ShapeTypeMap.

Referenced by GetSimplexEquiSpacedConnectivity().

◆ v_GetStdExp()

std::shared_ptr< StdExpansion > Nektar::StdRegions::StdExpansion::v_GetStdExp ( void ) const

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1122 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This method is not defined for this expansion");
    StdExpansionSharedPtr returnval;
    return returnval;
}

References ASSERTL0.

Referenced by GetStdExp().

◆ v_GetTraceBasisKey()

const LibUtilities::BasisKey Nektar::StdRegions::StdExpansion::v_GetTraceBasisKey	(	const int	i,
		const int	k
	)		const

privatevirtual

Reimplemented in Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, and Nektar::StdRegions::StdTetExp.

Definition at line 1101 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This function is not valid or not defined");
    return LibUtilities::NullBasisKey;
}

References ASSERTL0, and Nektar::LibUtilities::NullBasisKey().

Referenced by GetTraceBasisKey().

◆ v_GetTraceCoeffMap()

void Nektar::StdRegions::StdExpansion::v_GetTraceCoeffMap	(	const unsigned int	traceid,
		Array< OneD, unsigned int > &	maparray
	)

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdExpansion2D, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1387 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetTraceCoeffMap().

◆ v_GetTraceInteriorToElementMap()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, and Nektar::StdRegions::StdTetExp.

Definition at line 1404 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetTraceInteriorToElementMap().

◆ v_GetTraceIntNcoeffs()

virtual int Nektar::StdRegions::StdExpansion::v_GetTraceIntNcoeffs ( const int i ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Referenced by GetTraceIntNcoeffs().

◆ v_GetTraceNcoeffs()

virtual int Nektar::StdRegions::StdExpansion::v_GetTraceNcoeffs ( const int i ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Referenced by GetTraceNcoeffs().

◆ v_GetTraceNumModes()

void Nektar::StdRegions::StdExpansion::v_GetTraceNumModes	(	const int	fid,
		int &	numModes0,
		int &	numModes1,
		Orientation	traceOrient = `eDir1FwdDir1_Dir2FwdDir2`
	)

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, and Nektar::StdRegions::StdTetExp.

Definition at line 1413 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetTraceNumModes().

◆ v_GetTraceNumPoints()

virtual int Nektar::StdRegions::StdExpansion::v_GetTraceNumPoints ( const int i ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Referenced by GetTraceNumPoints().

◆ v_GetTracePointsKey()

LibUtilities::PointsKey Nektar::StdRegions::StdExpansion::v_GetTracePointsKey	(	const int	i,
		const int	j
	)		const

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, and Nektar::StdRegions::StdTetExp.

Definition at line 1108 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This function is not valid or not defined");
    return LibUtilities::NullPointsKey;
}

References ASSERTL0, and Nektar::LibUtilities::NullPointsKey().

Referenced by GetTracePointsKey().

◆ v_GetTraceToElementMap()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdExpansion2D, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdSegExp, and Nektar::StdRegions::StdExpansion3D.

Definition at line 1377 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetTraceToElementMap().

◆ v_GetVertexMap()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1370 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetVertexMap().

◆ v_GetVertexPhysVals()

void Nektar::StdRegions::StdExpansion::v_GetVertexPhysVals	(	const int	vertex,
		const Array< OneD, const NekDouble > &	inarray,
		NekDouble &	outarray
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 1421 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for "
                                "this shape or library");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_HelmholtzMatrixOp()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1577 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    HelmholtzMatrixOp_MatFree(inarray, outarray, mkey);
}

References HelmholtzMatrixOp_MatFree().

Referenced by HelmholtzMatrixOp().

◆ v_HelmholtzMatrixOp_MatFree()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdExpansion2D, and Nektar::StdRegions::StdExpansion3D.

Definition at line 1603 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    HelmholtzMatrixOp_MatFree_GenericImpl(inarray, outarray, mkey);
}

References HelmholtzMatrixOp_MatFree_GenericImpl().

Referenced by HelmholtzMatrixOp_MatFree().

◆ v_Integral()

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

privatevirtual

Integrates the specified function over the domain.

See also: StdRegions::StdExpansion::Integral.

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, Nektar::LocalRegions::TriExp, Nektar::StdRegions::StdExpansion3D, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1180 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for "
                                "local expansions");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by H1(), Integral(), and L2().

◆ v_IProductWRTBase() [1/2]

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

inlineprivatevirtual

Reimplemented in Nektar::LocalRegions::SegExp, Nektar::StdRegions::StdPointExp, and Nektar::StdRegions::StdSegExp.

Definition at line 1542 of file StdExpansion.h.

    {
        NEKERROR(ErrorUtil::efatal, "StdExpansion::v_IProductWRTBase has no "
                                    "(and should have no) implementation");
    }

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_IProductWRTBase() [2/2]

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

privatepure virtual

Calculates the inner product of a given function f with the different modes of the expansion.

Referenced by IProductWRTBase(), LinearAdvectionDiffusionReactionMatrixOp_MatFree(), LinearAdvectionMatrixOp_MatFree(), MassMatrixOp_MatFree(), WeakDerivMatrixOp_MatFree(), and WeakDirectionalDerivMatrixOp_MatFree().

◆ v_IProductWRTBase_SumFac()

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

privatevirtual

Definition at line 1452 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by IProductWRTBase_SumFac().

◆ v_IProductWRTDerivBase()

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

privatevirtual

Definition at line 1147 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This method has not been defined");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by IProductWRTDerivBase(), and LaplacianMatrixOp_MatFree().

◆ v_IProductWRTDerivBase_SumFac()

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

privatevirtual

Definition at line 1471 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by IProductWRTDerivBase_SumFac(), and LaplacianMatrixOp_MatFree().

◆ v_IProductWRTDirectionalDerivBase()

void Nektar::StdRegions::StdExpansion::v_IProductWRTDirectionalDerivBase	(	const Array< OneD, const NekDouble > &	direction,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, and Nektar::LocalRegions::TriExp.

Definition at line 1158 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This method has not been defined");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by IProductWRTDirectionalDerivBase().

◆ v_IProductWRTDirectionalDerivBase_SumFac()

void Nektar::StdRegions::StdExpansion::v_IProductWRTDirectionalDerivBase_SumFac	(	const Array< OneD, const NekDouble > &	direction,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, and Nektar::LocalRegions::TriExp.

Definition at line 1463 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by IProductWRTDirectionalDerivBase_SumFac().

◆ v_IsBoundaryInteriorExpansion()

bool Nektar::StdRegions::StdExpansion::v_IsBoundaryInteriorExpansion ( ) const

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1136 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This function has not been defined for this expansion");
    return false;
}

References ASSERTL0.

Referenced by IsBoundaryInteriorExpansion().

◆ v_IsNodalNonTensorialExp()

bool Nektar::StdRegions::StdExpansion::v_IsNodalNonTensorialExp ( )

privatevirtual

Reimplemented in Nektar::StdRegions::StdNodalPrismExp, Nektar::StdRegions::StdNodalTetExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1142 of file StdExpansion.cpp.

{
    return false;
}

Referenced by IsNodalNonTensorialExp().

◆ v_LaplacianMatrixOp() [1/2]

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1488 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    LaplacianMatrixOp_MatFree(inarray, outarray, mkey);
}

References LaplacianMatrixOp_MatFree().

Referenced by LaplacianMatrixOp().

◆ v_LaplacianMatrixOp() [2/2]

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1521 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    LaplacianMatrixOp_MatFree(k1, k2, inarray, outarray, mkey);
}

References LaplacianMatrixOp_MatFree().

◆ v_LaplacianMatrixOp_MatFree()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdExpansion2D, and Nektar::StdRegions::StdExpansion3D.

Definition at line 1586 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    LaplacianMatrixOp_MatFree_GenericImpl(inarray, outarray, mkey);
}

References LaplacianMatrixOp_MatFree_GenericImpl().

Referenced by LaplacianMatrixOp_MatFree().

◆ v_LaplacianMatrixOp_MatFree_Kernel()

void Nektar::StdRegions::StdExpansion::v_LaplacianMatrixOp_MatFree_Kernel	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1595 of file StdExpansion.cpp.

{
    ASSERTL0(false, "Not implemented.");
}

References ASSERTL0.

Referenced by LaplacianMatrixOp_MatFree_Kernel().

◆ v_LinearAdvectionDiffusionReactionMatrixOp()

void Nektar::StdRegions::StdExpansion::v_LinearAdvectionDiffusionReactionMatrixOp	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdMatrixKey &	mkey,
		bool	addDiffusionTerm = `true`
	)

privatevirtual

Definition at line 1566 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    LinearAdvectionDiffusionReactionMatrixOp_MatFree(inarray, outarray, mkey,
                                                     addDiffusionTerm);
}

References LinearAdvectionDiffusionReactionMatrixOp_MatFree().

Referenced by LinearAdvectionDiffusionReactionMatrixOp().

◆ v_LinearAdvectionMatrixOp()

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

privatevirtual

Definition at line 1557 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    LinearAdvectionMatrixOp_MatFree(inarray, outarray, mkey);
}

References LinearAdvectionMatrixOp_MatFree().

Referenced by LinearAdvectionMatrixOp().

◆ v_LocCollapsedToLocCoord()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1094 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not defined for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by LocCollapsedToLocCoord().

◆ v_LocCoordToLocCollapsed()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1087 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not defined for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by LocCoordToLocCollapsed().

◆ v_MassLevelCurvatureMatrixOp()

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

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 1548 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    MassLevelCurvatureMatrixOp_MatFree(inarray, outarray, mkey);
}

References MassLevelCurvatureMatrixOp_MatFree().

Referenced by MassLevelCurvatureMatrixOp().

◆ v_MassMatrixOp()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 1479 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    MassMatrixOp_MatFree(inarray, outarray, mkey);
}

References MassMatrixOp_MatFree().

Referenced by MassMatrixOp().

◆ v_MultiplyByQuadratureMetric()

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

privatevirtual

Reimplemented in Nektar::LocalRegions::Expansion.

Definition at line 1430 of file StdExpansion.cpp.

{
    v_MultiplyByStdQuadratureMetric(inarray, outarray);
}

References v_MultiplyByStdQuadratureMetric().

Referenced by MultiplyByQuadratureMetric().

◆ v_MultiplyByStdQuadratureMetric()

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

protectedvirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1437 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "Method does not exist for this shape or library");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by Nektar::LocalRegions::Expansion::ComputeQuadratureMetric(), MultiplyByStdQuadratureMetric(), Nektar::StdRegions::StdExpansion3D::v_Integral(), and v_MultiplyByQuadratureMetric().

◆ v_NormVectorIProductWRTBase() [1/4]

void Nektar::StdRegions::StdExpansion::v_NormVectorIProductWRTBase	(	const Array< OneD, const Array< OneD, NekDouble > > &	Fvec,
		Array< OneD, NekDouble > &	outarray
	)

virtual

Reimplemented in Nektar::LocalRegions::Expansion3D, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, and Nektar::LocalRegions::TriExp.

Definition at line 1043 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not valid for this class");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_NormVectorIProductWRTBase() [2/4]

void Nektar::StdRegions::StdExpansion::v_NormVectorIProductWRTBase	(	const Array< OneD, const NekDouble > &	Fx,
		Array< OneD, NekDouble > &	outarray
	)

virtual

Reimplemented in Nektar::LocalRegions::PointExp.

Definition at line 1019 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not valid for this class");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by NormVectorIProductWRTBase().

◆ v_NormVectorIProductWRTBase() [3/4]

void Nektar::StdRegions::StdExpansion::v_NormVectorIProductWRTBase	(	const Array< OneD, const NekDouble > &	Fx,
		const Array< OneD, const NekDouble > &	Fy,
		Array< OneD, NekDouble > &	outarray
	)

virtual

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 1026 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not valid for this class");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_NormVectorIProductWRTBase() [4/4]

void Nektar::StdRegions::StdExpansion::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

Reimplemented in Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 1034 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not valid for this class");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_NumBndryCoeffs()

virtual int Nektar::StdRegions::StdExpansion::v_NumBndryCoeffs ( ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdQuadExp, Nektar::LocalRegions::SegExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Referenced by NumBndryCoeffs().

◆ v_NumDGBndryCoeffs()

virtual int Nektar::StdRegions::StdExpansion::v_NumDGBndryCoeffs ( ) const

privatepure virtual

Implemented in Nektar::StdRegions::StdPointExp, Nektar::StdRegions::StdQuadExp, Nektar::LocalRegions::SegExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Referenced by NumDGBndryCoeffs().

◆ v_PhysDeriv() [1/2]

void Nektar::StdRegions::StdExpansion::v_PhysDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_d1,
		Array< OneD, NekDouble > &	out_d2,
		Array< OneD, NekDouble > &	out_d3
	)

privatevirtual

Calculate the derivative of the physical points.

See also: StdRegions::StdExpansion::PhysDeriv

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::TetExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::TriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::SegExp, Nektar::StdRegions::StdSegExp, and Nektar::StdRegions::StdTetExp.

Definition at line 1192 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for "
                                "local expansions");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by H1(), LaplacianMatrixOp_MatFree(), LinearAdvectionDiffusionReactionMatrixOp_MatFree(), LinearAdvectionMatrixOp_MatFree(), PhysDeriv(), and WeakDerivMatrixOp_MatFree().

◆ v_PhysDeriv() [2/2]

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

privatevirtual

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

See also: StdRegions::StdExpansion::PhysDeriv

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TriExp, Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1222 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for "
                                "specific element types");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_PhysDeriv_n()

void Nektar::StdRegions::StdExpansion::v_PhysDeriv_n	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_dn
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 1209 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for "
                                "local expansions");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by PhysDeriv_n().

◆ v_PhysDeriv_s()

void Nektar::StdRegions::StdExpansion::v_PhysDeriv_s	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_ds
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 1202 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for "
                                "local expansions");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by PhysDeriv_s().

◆ v_PhysDirectionalDeriv()

void Nektar::StdRegions::StdExpansion::v_PhysDirectionalDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		const Array< OneD, const NekDouble > &	direction,
		Array< OneD, NekDouble > &	outarray
	)

privatevirtual

Physical derivative along a direction vector.

See also: StdRegions::StdExpansion::PhysDirectionalDeriv

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 1236 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is only valid for "
                                "specific element types");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by PhysDirectionalDeriv(), and WeakDirectionalDerivMatrixOp_MatFree().

◆ v_PhysEvaluate() [1/4]

NekDouble Nektar::StdRegions::StdExpansion::v_PhysEvaluate	(	const Array< OneD, const NekDouble > &	coords,
		const Array< OneD, const NekDouble > &	physvals
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::TetExp, Nektar::StdRegions::StdExpansion0D, Nektar::StdRegions::StdExpansion1D, Nektar::StdRegions::StdExpansion2D, and Nektar::StdRegions::StdExpansion3D.

Definition at line 1262 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by PhysEvaluate().

◆ v_PhysEvaluate() [2/4]

NekDouble Nektar::StdRegions::StdExpansion::v_PhysEvaluate	(	const Array< OneD, DNekMatSharedPtr > &	I,
		const Array< OneD, const NekDouble > &	physvals
	)

privatevirtual

Reimplemented in Nektar::StdRegions::StdExpansion2D, and Nektar::StdRegions::StdExpansion3D.

Definition at line 1270 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_PhysEvaluate() [3/4]

NekDouble Nektar::StdRegions::StdExpansion::v_PhysEvaluate	(	const Array< OneD, NekDouble > &	coord,
		const Array< OneD, const NekDouble > &	inarray,
		std::array< NekDouble, 3 > &	firstOrderDerivs
	)

privatevirtual

Definition at line 1286 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "PhysEvaluate first order derivative method does not exist"
             " for this shape type: " +
                 static_cast<std::string>(
                     LibUtilities::ShapeTypeMap[DetShapeType()]));
    return 0;
}

References DetShapeType(), Nektar::ErrorUtil::efatal, NEKERROR, and Nektar::LibUtilities::ShapeTypeMap.

◆ v_PhysEvaluate() [4/4]

NekDouble Nektar::StdRegions::StdExpansion::v_PhysEvaluate	(	const Array< OneD, NekDouble > &	coord,
		const Array< OneD, const NekDouble > &	inarray,
		std::array< NekDouble, 3 > &	firstOrderDerivs,
		std::array< NekDouble, 6 > &	secondOrderDerivs
	)

privatevirtual

Reimplemented in Nektar::LocalRegions::SegExp, Nektar::StdRegions::StdExpansion1D, and Nektar::StdRegions::StdSegExp.

Definition at line 1299 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "PhysEvaluate second order derivative method does not exist"
             " for this shape type: " +
                 static_cast<std::string>(
                     LibUtilities::ShapeTypeMap[DetShapeType()]));
    return 0;
}

References DetShapeType(), Nektar::ErrorUtil::efatal, NEKERROR, and Nektar::LibUtilities::ShapeTypeMap.

◆ v_PhysEvaluateBasis()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdTriExp, and Nektar::StdRegions::StdQuadExp.

Definition at line 1278 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by PhysEvaluateBasis().

◆ v_ReduceOrderCoeffs()

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

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::TriExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1513 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This function is not defined in StdExpansion.");
}

References ASSERTL0.

Referenced by ReduceOrderCoeffs().

◆ v_SetCoeffsToOrientation() [1/2]

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

protectedvirtual

Definition at line 1071 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not defined for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_SetCoeffsToOrientation() [2/2]

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

protectedvirtual

Reimplemented in Nektar::LocalRegions::Expansion, and Nektar::LocalRegions::SegExp.

Definition at line 1063 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not defined for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_StdPhysDeriv() [1/2]

void Nektar::StdRegions::StdExpansion::v_StdPhysDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_d1,
		Array< OneD, NekDouble > &	out_d2,
		Array< OneD, NekDouble > &	out_d3
	)

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdTetExp, Nektar::LocalRegions::NodalTriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, and Nektar::StdRegions::StdSegExp.

Definition at line 1245 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by StdPhysDeriv().

◆ v_StdPhysDeriv() [2/2]

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, and Nektar::StdRegions::StdTriExp.

Definition at line 1254 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_StdPhysEvaluate()

NekDouble Nektar::StdRegions::StdExpansion::v_StdPhysEvaluate	(	const Array< OneD, const NekDouble > &	Lcoord,
		const Array< OneD, const NekDouble > &	physvals
	)

protectedvirtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::SegExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1078 of file StdExpansion.cpp.

{
    NEKERROR(ErrorUtil::efatal, "This function is not defined for this shape");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by StdPhysEvaluate().

◆ v_SVVLaplacianFilter()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdPrismExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdSegExp, Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::PrismExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::TetExp, and Nektar::LocalRegions::TriExp.

Definition at line 1497 of file StdExpansion.cpp.

{
    ASSERTL0(false, "This function is not defined in StdExpansion.");
}

References ASSERTL0.

Referenced by SVVLaplacianFilter().

◆ v_WeakDerivMatrixOp()

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

privatevirtual

Reimplemented in Nektar::StdRegions::StdHexExp, Nektar::StdRegions::StdNodalTriExp, Nektar::StdRegions::StdQuadExp, Nektar::StdRegions::StdTriExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 1530 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    WeakDerivMatrixOp_MatFree(i, inarray, outarray, mkey);
}

References WeakDerivMatrixOp_MatFree().

Referenced by WeakDerivMatrixOp().

◆ v_WeakDirectionalDerivMatrixOp()

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

privatevirtual

Reimplemented in Nektar::LocalRegions::HexExp, Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 1539 of file StdExpansion.cpp.

{
    // If this function is not reimplemented on shape level, the function
    // below will be called
    WeakDirectionalDerivMatrixOp_MatFree(inarray, outarray, mkey);
}

References WeakDirectionalDerivMatrixOp_MatFree().

Referenced by WeakDirectionalDerivMatrixOp().

◆ WeakDerivMatrixOp()

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

inline

Definition at line 793 of file StdExpansion.h.

    {
        v_WeakDerivMatrixOp(i, inarray, outarray, mkey);
    }

References v_WeakDerivMatrixOp().

Referenced by GeneralMatrixOp().

◆ WeakDerivMatrixOp_MatFree()

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

protected

Definition at line 825 of file StdExpansion.cpp.

{
    Array<OneD, NekDouble> tmp(GetTotPoints());
    int nq = GetTotPoints();
 
    v_BwdTrans(inarray, tmp);
    v_PhysDeriv(k1, tmp, tmp);
 
    VarCoeffType keys[] = {eVarCoeffD00, eVarCoeffD11, eVarCoeffD22};
    if (mkey.HasVarCoeff(keys[k1]))
    {
        Vmath::Vmul(nq, &(mkey.GetVarCoeff(keys[k1]))[0], 1, &tmp[0], 1,
                    &tmp[0], 1);
    }
 
    v_IProductWRTBase(tmp, outarray);
}

References Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, GetTotPoints(), Nektar::StdRegions::StdMatrixKey::GetVarCoeff(), Nektar::StdRegions::StdMatrixKey::HasVarCoeff(), v_BwdTrans(), v_IProductWRTBase(), v_PhysDeriv(), and Vmath::Vmul().

Referenced by GeneralMatrixOp_MatFree(), v_WeakDerivMatrixOp(), Nektar::StdRegions::StdHexExp::v_WeakDerivMatrixOp(), Nektar::StdRegions::StdNodalTriExp::v_WeakDerivMatrixOp(), Nektar::StdRegions::StdQuadExp::v_WeakDerivMatrixOp(), and Nektar::StdRegions::StdTriExp::v_WeakDerivMatrixOp().

◆ WeakDirectionalDerivMatrixOp()

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

inline

Definition at line 801 of file StdExpansion.h.

    {
        v_WeakDirectionalDerivMatrixOp(inarray, outarray, mkey);
    }

References v_WeakDirectionalDerivMatrixOp().

Referenced by GeneralMatrixOp().

◆ WeakDirectionalDerivMatrixOp_MatFree()

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

protected

Definition at line 845 of file StdExpansion.cpp.

{
    int nq = GetTotPoints();
 
    Array<OneD, NekDouble> tmp(nq), Dtmp(nq);
    Array<OneD, NekDouble> Mtmp(nq), Mout(m_ncoeffs);
 
    v_BwdTrans(inarray, tmp);
    v_PhysDirectionalDeriv(tmp, mkey.GetVarCoeff(eVarCoeffMF), Dtmp);
 
    v_IProductWRTBase(Dtmp, outarray);
 
    // Compte M_{div tv}
    Vmath::Vmul(nq, &(mkey.GetVarCoeff(eVarCoeffMFDiv))[0], 1, &tmp[0], 1,
                &Mtmp[0], 1);
 
    v_IProductWRTBase(Mtmp, Mout);
 
    // Add D_tv + M_{div tv}
    Vmath::Vadd(m_ncoeffs, &Mout[0], 1, &outarray[0], 1, &outarray[0], 1);
}

References Nektar::StdRegions::eVarCoeffMF, Nektar::StdRegions::eVarCoeffMFDiv, GetTotPoints(), Nektar::StdRegions::StdMatrixKey::GetVarCoeff(), m_ncoeffs, v_BwdTrans(), v_IProductWRTBase(), v_PhysDirectionalDeriv(), Vmath::Vadd(), and Vmath::Vmul().

Referenced by GeneralMatrixOp_MatFree(), and v_WeakDirectionalDerivMatrixOp().

Member Data Documentation

◆ m_base

Array<OneD, LibUtilities::BasisSharedPtr> Nektar::StdRegions::StdExpansion::m_base

protected

Bases needed for the expansion

Definition at line 1173 of file StdExpansion.h.

◆ m_elmt_id

int Nektar::StdRegions::StdExpansion::m_elmt_id

protected

Definition at line 1174 of file StdExpansion.h.

Referenced by GetElmtId(), and SetElmtId().

◆ m_ncoeffs

int Nektar::StdRegions::StdExpansion::m_ncoeffs

protected

Total number of coefficients used in the expansion

Definition at line 1175 of file StdExpansion.h.

◆ m_stdMatrixManager

LibUtilities::NekManager<StdMatrixKey, DNekMat, StdMatrixKey::opLess> Nektar::StdRegions::StdExpansion::m_stdMatrixManager

protected

Definition at line 1178 of file StdExpansion.h.

Referenced by GetStdMatrix(), and Nektar::LocalRegions::Expansion2D::v_AddEdgeNormBoundaryInt().

◆ m_stdStaticCondMatrixManager

LibUtilities::NekManager<StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess> Nektar::StdRegions::StdExpansion::m_stdStaticCondMatrixManager

protected

Definition at line 1180 of file StdExpansion.h.

Referenced by GetStdStaticCondMatrix(), Nektar::StdRegions::StdQuadExp::v_FwdTransBndConstrained(), Nektar::StdRegions::StdSegExp::v_FwdTransBndConstrained(), and Nektar::StdRegions::StdTriExp::v_FwdTransBndConstrained().

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ StdExpansion() [1/3]

◆ StdExpansion() [2/3]

◆ StdExpansion() [3/3]

◆ ~StdExpansion()

Member Function Documentation

◆ as()

◆ BaryEvaluate() [1/3]

◆ BaryEvaluate() [2/3]

◆ BaryEvaluate() [3/3]

◆ BaryEvaluateBasis()

◆ BuildInverseTransformationMatrix()

◆ BwdTrans()

◆ BwdTrans_SumFac()

◆ CalcNumberOfCoefficients()

◆ CreateGeneralMatrix()

◆ CreateStdMatrix()

◆ CreateStdStaticCondMatrix()

◆ DetShapeType()

◆ DropLocStaticCondMatrix()

◆ EquiSpacedToCoeffs()

◆ EvalBasisNumModesMax()

◆ ExponentialFilter()

◆ FillMode()

◆ FwdTrans()

◆ FwdTransBndConstrained()

◆ GeneralMatrixOp()

◆ GeneralMatrixOp_MatFree()

◆ GenMatrix()

◆ GenStdMatBwdDeriv()

◆ GetBase()

◆ GetBasis()

◆ GetBasisNumModes()

◆ GetBasisType()

◆ GetBoundaryMap()

◆ GetCoord()

◆ GetCoordim()

◆ GetCoords()

◆ GetElmtId()

◆ GetElmtTraceToTraceMap()

◆ GetInteriorMap()

◆ GetLinStdExp()

◆ GetLocStaticCondMatrix()

◆ GetNcoeffs()

◆ GetNodalPointsKey()

◆ GetNtraces()

◆ GetNumBases()

◆ GetNumPoints()

◆ GetNverts()

◆ GetPoints()

◆ GetPointsKeys()

◆ GetPointsType()

◆ GetShapeDimension()

◆ GetSimplexEquiSpacedConnectivity()

◆ GetStdExp()

◆ GetStdMatrix()

◆ GetStdStaticCondMatrix()

◆ GetTotPoints()

◆ GetTraceBasisKey()

◆ GetTraceCoeffMap()

◆ GetTraceInteriorToElementMap()

◆ GetTraceIntNcoeffs()

◆ GetTraceNcoeffs()

◆ GetTraceNumModes()

◆ GetTraceNumPoints()

◆ GetTracePointsKey()

◆ GetTraceToElementMap()

◆ GetVertexMap()

◆ H1()

◆ HelmholtzMatrixOp()

◆ HelmholtzMatrixOp_MatFree()

◆ HelmholtzMatrixOp_MatFree_GenericImpl()

◆ Integral()

◆ IProductWRTBase() [1/2]

◆ IProductWRTBase() [2/2]