#include <StdExpansion1D.h>

Inheritance diagram for Nektar::StdRegions::StdExpansion1D:

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

	StdExpansion1D ()=default

	StdExpansion1D (const StdExpansion1D &T)=default

	~StdExpansion1D () override=default

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

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

void	IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, const NekDouble > &jac, const bool Deformed)

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

	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.

	StdExpansion (const StdExpansion &T)
	Copy Constructor.

virtual	~StdExpansion ()
	Destructor.

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

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

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

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

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

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

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

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

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

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

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.

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

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

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.

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

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

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.

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

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

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion () const

bool	IsNodalNonTensorialExp ()

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

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

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

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.

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

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

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.

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

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

Array< OneD, Array< OneD, NekDouble > >	GetCoords ()

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

DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)

DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)

Array< OneD, const NekDouble >	GetStdFac (const StdFacKey &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 \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\)

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	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)

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.

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.

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.

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.

void	ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1, bool Forwards=true)

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

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

void	PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData, bool Transpose=false)
	interpolate from one set of quadrature points available from FromExp to the set of quadrature points in the current expansion. If the points are the same this routine will just copy the data

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.

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.

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.

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.

void	PhysInterpToGLL (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)

void	PhysInterpToPoints (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset, MatrixType distrib)

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.

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.

void	EquiSpacedToPhys (const int nequi, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

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

void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)

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

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

NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override

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

virtual void	v_IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, const NekDouble > &jac, const bool Deformed)=0

void	v_PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData, bool Transpose) override

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

int	v_GetShapeDimension () const final

bool	v_IsCollocatedBasis () const final

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.

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.

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

std::shared_ptr< Array< OneD, const NekDouble > >	CreateStdFac (const StdFacKey &mkey)

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

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_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)

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.

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.

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

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, bool UseGLL=false) 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 bool	v_IsBoundaryInteriorExpansion () const

virtual bool	v_IsNodalNonTensorialExp ()

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

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

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 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.

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

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

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

virtual NekDouble	v_PhysEvalFirstSecondDeriv (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_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)

virtual void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1, bool Forwards)

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

int	m_elmt_id

int	m_ncoeffs

std::vector< Array< OneD, const NekDouble > >	m_weights

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

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

LibUtilities::NekManager< StdFacKey, Array< OneD, const NekDouble > >	m_stdFacManager

Detailed Description

Definition at line 44 of file StdExpansion1D.h.

Constructor & Destructor Documentation

◆ StdExpansion1D() [1/3]

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

Definition at line 50 of file StdExpansion1D.cpp.

53{

54}

◆ StdExpansion1D() [2/3]

Nektar::StdRegions::StdExpansion1D::StdExpansion1D ( )

default

◆ StdExpansion1D() [3/3]

Nektar::StdRegions::StdExpansion1D::StdExpansion1D ( const StdExpansion1D & T )

default

◆ ~StdExpansion1D()

Nektar::StdRegions::StdExpansion1D::~StdExpansion1D ( )

overridedefault

Member Function Documentation

◆ BaryTensorDeriv() [1/2]

NekDouble Nektar::StdRegions::StdExpansion1D::BaryTensorDeriv	(	const Array< OneD, NekDouble > &	coord,
		const Array< OneD, const NekDouble > &	inarray,
		std::array< NekDouble, 3 > &	firstOrderDerivs
	)

inline

Definition at line 54 of file StdExpansion1D.h.

    {
        return StdExpansion::BaryEvaluate<0, true>(coord[0], &inarray[0],
                                                   firstOrderDerivs[0]);
    }

Referenced by Nektar::StdRegions::StdSegExp::v_PhysEvalFirstDeriv(), and Nektar::StdRegions::StdSegExp::v_PhysEvalFirstSecondDeriv().

◆ BaryTensorDeriv() [2/2]

NekDouble Nektar::StdRegions::StdExpansion1D::BaryTensorDeriv	(	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 64 of file StdExpansion1D.h.

    {
        return StdExpansion::BaryEvaluate<0, true, true>(
            coord[0], &inarray[0], firstOrderDerivs[0], secondOrderDerivs[0]);
    }

◆ IProductWRTBaseKernel()

void Nektar::StdRegions::StdExpansion1D::IProductWRTBaseKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const Array< OneD, const NekDouble > &	jac,
		const bool	Deformed
	)

Definition at line 147 of file StdExpansion1D.cpp.

{
    v_IProductWRTBaseKernel(base0, inarray, outarray, jac, Deformed);
}

References v_IProductWRTBaseKernel().

◆ PhysTensorDeriv()

void Nektar::StdRegions::StdExpansion1D::PhysTensorDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protected

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

Parameters

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

Definition at line 59 of file StdExpansion1D.cpp.

{
    int nquad    = GetTotPoints();
    NekDouble *D = m_base[0]->GetD()->GetRawPtr();
    Array<OneD, const NekDouble> intmp;
 
    // copy inarray data if inarray and outarray are the same.
    if (inarray.data() == outarray.data())
    {
        Array<OneD, NekDouble> wsp(nquad);
        CopyArray(inarray, wsp);
        intmp = wsp;
    }
    else
    {
        intmp = inarray;
    }
 
    // Switch statment using boost_pp and macros. This unfolls into a
    // nested switch statement which runs from SMIN to SMAX for quadratrure
    // order. If you want to see it unwrapped compile in verbose mode and add
    // --preprocess to the c++ command. Default case
#undef PHYSDERIV_Q
#define PHYSDERIV_Q(r, i)                                                      \
    case NQ1(i):                                                               \
        PhysDerivTensor1DKernel(NQ1(i), (const vec_t *)intmp.data(),           \
                                (const vec_t *)D, (vec_t *)outarray.data());   \
        break;
 
    // templated cases on  standard quadrature
    // usage where quad order goes from SMIN to SMAX
    switch (nquad)
    {
        BOOST_PP_FOR((SMIN, SMAX), STDLEV1TEST, STDLEV1UPDATE, PHYSDERIV_Q);
        default:
            PhysDerivTensor1DKernel(nquad, (const vec_t *)intmp.data(),
                                    (const vec_t *)D, (vec_t *)outarray.data());
            break;
    }
}

References Nektar::CopyArray(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::m_base, PHYSDERIV_Q, PhysDerivTensor1DKernel(), STDLEV1TEST, and STDLEV1UPDATE.

Referenced by Nektar::LocalRegions::Expansion1D::v_PhysDeriv(), and Nektar::StdRegions::StdSegExp::v_StdPhysDeriv().

◆ v_GetShapeDimension()

int Nektar::StdRegions::StdExpansion1D::v_GetShapeDimension ( ) const

inlinefinalprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 122 of file StdExpansion1D.h.

    {
        return 1;
    }

◆ v_IProductWRTBase()

void Nektar::StdRegions::StdExpansion1D::v_IProductWRTBase	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

overrideprotectedvirtual

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

Wrapper call to IProductWRTBaseKernel()

Parameters

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

Implements Nektar::StdRegions::StdExpansion.

Definition at line 131 of file StdExpansion1D.cpp.

{
    if (m_base[0]->Collocation())
    {
        v_MultiplyByStdQuadratureMetric(inarray, outarray);
    }
    else
    {
        const Array<OneD, const NekDouble> one(1, 1.0);
        v_IProductWRTBaseKernel(m_base[0]->GetBdata(), inarray, outarray, one,
                                false);
    }
}

References Nektar::StdRegions::StdExpansion::m_base, v_IProductWRTBaseKernel(), and v_MultiplyByStdQuadratureMetric().

Referenced by Nektar::StdRegions::StdSegExp::v_FwdTransBndConstrained(), Nektar::StdRegions::StdSegExp::v_HelmholtzMatrixOp(), and Nektar::StdRegions::StdSegExp::v_LaplacianMatrixOp().

◆ v_IProductWRTBaseKernel()

virtual void Nektar::StdRegions::StdExpansion1D::v_IProductWRTBaseKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const Array< OneD, const NekDouble > &	jac,
		const bool	Deformed
	)

protectedpure virtual

Implemented in Nektar::StdRegions::StdSegExp.

Referenced by IProductWRTBaseKernel(), Nektar::LocalRegions::Expansion1D::v_IProductWRTBase(), and v_IProductWRTBase().

◆ v_IsCollocatedBasis()

bool Nektar::StdRegions::StdExpansion1D::v_IsCollocatedBasis ( ) const

inlinefinalprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 126 of file StdExpansion1D.h.

    {
        return ((m_base[0]->Collocation()));
    }

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

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

◆ v_MultiplyByStdQuadratureMetric()

void Nektar::StdRegions::StdExpansion1D::v_MultiplyByStdQuadratureMetric	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 165 of file StdExpansion1D.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
 
    for (int j = 0; j < nquad0; ++j)
    {
        outarray[j] = inarray[j] * m_weights[0][j];
    }
}

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

Referenced by Nektar::LocalRegions::Expansion1D::v_IProductWRTBase(), and v_IProductWRTBase().

◆ v_PhysDeriv() [1/3]

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
	)

protectedvirtual

Calculate the derivative of the physical points.

See also: StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1636 of file StdExpansion.cpp.

{
    v_StdPhysDeriv(inarray, out_d1, out_d2, out_d3);
}

◆ v_PhysDeriv() [2/3]

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

protectedvirtual

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

See also: StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1641 of file StdExpansion.cpp.

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

◆ v_PhysDeriv() [3/3]

void Nektar::StdRegions::StdExpansion1D::v_PhysDeriv	(	const int	dir,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	out_d0
	)

overrideprotectedvirtual

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

See also: StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 102 of file StdExpansion1D.cpp.

{
    ASSERTL1(dir == 0, "input dir is out of range");
    v_PhysDeriv(inarray, outarray, NullNekDouble1DArray, NullNekDouble1DArray);
}

References ASSERTL1, Nektar::NullNekDouble1DArray, and v_PhysDeriv().

Referenced by Nektar::StdRegions::StdSegExp::v_HelmholtzMatrixOp(), Nektar::StdRegions::StdSegExp::v_LaplacianMatrixOp(), and v_PhysDeriv().

◆ v_PhysInterp()

void Nektar::StdRegions::StdExpansion1D::v_PhysInterp	(	std::shared_ptr< StdExpansion >	fromExp,
		const Array< OneD, const NekDouble > &	fromData,
		Array< OneD, NekDouble > &	toData,
		bool	Transpose
	)

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 156 of file StdExpansion1D.cpp.

{
    LibUtilities::Interp1D(fromExp->GetBasis(0)->GetPointsKey(), fromData,
                           m_base[0]->GetPointsKey(), toData);
}

References Nektar::LibUtilities::Interp1D(), and Nektar::StdRegions::StdExpansion::m_base.

◆ v_StdPhysEvaluate()

NekDouble Nektar::StdRegions::StdExpansion1D::v_StdPhysEvaluate	(	const Array< OneD, const NekDouble > &	coords,
		const Array< OneD, const NekDouble > &	physvals
	)

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 110 of file StdExpansion1D.cpp.

{
    ASSERTL2(Lcoord[0] >= -1 - NekConstants::kNekZeroTol, "Lcoord[0] < -1");
    ASSERTL2(Lcoord[0] <= 1 + NekConstants::kNekZeroTol, "Lcoord[0] >  1");
 
    return StdExpansion::BaryEvaluate<0>(Lcoord[0], &physvals[0]);
}

References ASSERTL2, and Nektar::NekConstants::kNekZeroTol.

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ StdExpansion1D() [1/3]

◆ StdExpansion1D() [2/3]

◆ StdExpansion1D() [3/3]

◆ ~StdExpansion1D()

Member Function Documentation

◆ BaryTensorDeriv() [1/2]

◆ BaryTensorDeriv() [2/2]

◆ IProductWRTBaseKernel()

◆ PhysTensorDeriv()

◆ v_GetShapeDimension()

◆ v_IProductWRTBase()

◆ v_IProductWRTBaseKernel()

◆ v_IsCollocatedBasis()

◆ v_MultiplyByStdQuadratureMetric()

◆ v_PhysDeriv() [1/3]

◆ v_PhysDeriv() [2/3]

◆ v_PhysDeriv() [3/3]

◆ v_PhysInterp()

◆ v_StdPhysEvaluate()