#include <HexExp.h>

Inheritance diagram for Nektar::LocalRegions::HexExp:

Public Member Functions
	HexExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc, SpatialDomains::Geometry3D *geom)
	Constructor using BasisKey class for quadrature points and order definition.

	HexExp (const HexExp &T)
	Copy Constructor.

	~HexExp () override=default

Public Member Functions inherited from Nektar::StdRegions::StdHexExp
	StdHexExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)

	StdHexExp (const StdHexExp &T)=default

	~StdHexExp () override=default

Public Member Functions inherited from Nektar::StdRegions::StdExpansion3D
	StdExpansion3D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)

	StdExpansion3D ()=default

	StdExpansion3D (const StdExpansion3D &T)=default

	~StdExpansion3D () override=default

void	IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, NekDouble > &jac, const bool Deformed, bool CollDir0=false, bool CollDir1=false, bool CollDir2=false)

int	GetNedges () const
	return the number of edges in 3D expansion

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

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

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 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)

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)

Public Member Functions inherited from Nektar::LocalRegions::Expansion3D
	Expansion3D (SpatialDomains::Geometry3D *pGeom)

	~Expansion3D () override=default

void	SetTraceToGeomOrientation (Array< OneD, NekDouble > &inout)
	Align trace orientation with the geometry orientation.

void	SetFaceToGeomOrientation (const int face, Array< OneD, NekDouble > &inout)
	Align face orientation with the geometry orientation.

void	AddHDGHelmholtzFaceTerms (const NekDouble tau, const int edge, Array< OneD, NekDouble > &facePhys, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray)

void	AddNormTraceInt (const int dir, Array< OneD, ExpansionSharedPtr > &FaceExp, Array< OneD, Array< OneD, NekDouble > > &faceCoeffs, Array< OneD, NekDouble > &outarray)

void	AddNormTraceInt (const int dir, Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &FaceExp, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs)

void	AddFaceBoundaryInt (const int face, ExpansionSharedPtr &FaceExp, Array< OneD, NekDouble > &facePhys, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)

SpatialDomains::Geometry3D *	GetGeom3D () const

void	v_ReOrientTracePhysVals (const StdRegions::Orientation orient, const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const int nq0, const int nq1, bool Forwards) override

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

Array< OneD, unsigned int >	GetEdgeInverseBoundaryMap (int eid)

Array< OneD, unsigned int >	GetTraceInverseBoundaryMap (int fid, StdRegions::Orientation faceOrient=StdRegions::eNoOrientation, int P1=-1, int P2=-1)

void	GetInverseBoundaryMaps (Array< OneD, unsigned int > &vmap, Array< OneD, Array< OneD, unsigned int > > &emap, Array< OneD, Array< OneD, unsigned int > > &fmap)

DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)

void	GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=StdRegions::eNoOrientation)

void	GetLocTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

Public Member Functions inherited from Nektar::LocalRegions::Expansion
	Expansion (SpatialDomains::Geometry *pGeom)

	Expansion (const Expansion &pSrc)

	~Expansion () override

void	SetTraceExp (const int traceid, ExpansionSharedPtr &f)

ExpansionSharedPtr	GetTraceExp (const int traceid)

ExpansionSharedPtr	GetLocTraceExp (const int traceid)

StdRegions::StdExpansionSharedPtr	GetStdExp () const

StdRegions::StdExpansionSharedPtr	GetLinStdExp (void) const

DNekScalMatSharedPtr	GetLocMatrix (const LocalRegions::MatrixKey &mkey)

void	DropLocMatrix (const LocalRegions::MatrixKey &mkey)

DNekScalMatSharedPtr	GetLocMatrix (const StdRegions::MatrixType mtype, const StdRegions::ConstFactorMap &factors=StdRegions::NullConstFactorMap, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)

SpatialDomains::Geometry *	GetGeom () const

void	Reset ()

IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)

DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)

SpatialDomains::GeomFactors *	GetGeomFactors () const
	Get the geometric factors for this object, generating them if required.

DNekMatSharedPtr	BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)

DNekMatSharedPtr	BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)

void	ExtractDataToCoeffs (const NekDouble data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble coeffs, std::vector< LibUtilities::BasisType > &fromType)

void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)

void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

void	AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

void	DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)

NekDouble	VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)

void	NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors)

IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)

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

ExpansionSharedPtr	GetLeftAdjacentElementExp () const

ExpansionSharedPtr	GetRightAdjacentElementExp () const

int	GetLeftAdjacentElementTrace () const

int	GetRightAdjacentElementTrace () const

void	SetAdjacentElementExp (int traceid, ExpansionSharedPtr &e)

StdRegions::Orientation	GetTraceOrient (int trace)

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

void	DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Divided by the metric jacobi and quadrature weights.

void	GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray)
	Extract the metric factors to compute the contravariant fluxes along edge edge and stores them into outarray following the local edge orientation (i.e. anticlockwise convention).

void	GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=StdRegions::eNoOrientation)

void	GetLocTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GetTracePhysMap (const int edge, Array< OneD, int > &outarray)

void	ReOrientTracePhysVals (const StdRegions::Orientation orient, const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const int nq0, const int nq1, bool Forwards=true)

const NormalVector &	GetTraceNormal (const int id)

const std::map< int, NormalVector > &	GetTraceNormals (void)

void	ComputeTraceNormal (const int id)

const Array< OneD, const NekDouble > &	GetPhysNormals (void)

void	SetPhysNormals (Array< OneD, const NekDouble > &normal)

void	SetUpPhysNormals (const int trace)

void	AddRobinMassMatrix (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)

void	TraceNormLen (const int traceid, NekDouble &h, NekDouble &p)

void	AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)

const Array< OneD, const NekDouble > &	GetElmtBndNormDirElmtLen (const int nbnd) const

void	StdDerivBaseOnTraceMat (Array< OneD, DNekMatSharedPtr > &DerivMat)

void	PhysDerivBaseOnTraceMat (const int traceid, Array< OneD, DNekMatSharedPtr > &DerivMat)

void	PhysBaseOnTraceMat (const int traceid, DNekMatSharedPtr &BdataMat)

void	GenGeomFactors ()
	Handles generation of geometry factors.

Protected Member Functions
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculates the inner product \( I_{pqr} = (u, \partial_{x_i} \phi_{pqr}) \).

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

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

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

void	v_GetCoord (const Array< OneD, const NekDouble > &Lcoords, Array< OneD, NekDouble > &coords) override
	Retrieves the physical coordinates of a given set of reference coordinates.

void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override

StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const override

StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const override

void	v_ExtractDataToCoeffs (const NekDouble data, const std::vector< unsigned int > &nummodes, const int mode_offset, NekDouble coeffs, std::vector< LibUtilities::BasisType > &fromType) override

void	v_GetTracePhysMap (const int face, Array< OneD, int > &outarray) override

void	v_ComputeTraceNormal (const int face) override

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

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

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

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

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

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

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

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

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

DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override

DNekMatSharedPtr	v_CreateStdMatrix (const StdRegions::StdMatrixKey &mkey) override

DNekScalMatSharedPtr	v_GetLocMatrix (const MatrixKey &mkey) override

void	v_DropLocMatrix (const MatrixKey &mkey) override

DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const MatrixKey &mkey) override

void	v_DropLocStaticCondMatrix (const MatrixKey &mkey) override

void	v_ComputeLaplacianMetric () override

Protected Member Functions inherited from Nektar::StdRegions::StdHexExp
void	v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2) override
	Differentiation Methods.

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

void	v_IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, NekDouble > &jac, const bool Deformed, bool CollDir0=false, bool CollDir1=false, bool CollDir2=false) override
	Inner product of inarray over region with respect to the expansion basis (this)->m_base[0] and return in outarray.

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

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

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

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

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

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

int	v_GetNverts () const override

int	v_GetNedges () const override

int	v_GetNtraces () const override

LibUtilities::ShapeType	v_DetShapeType () const override

int	v_NumBndryCoeffs () const override

int	v_NumDGBndryCoeffs () const override

int	v_GetTraceNcoeffs (const int i) const override

int	v_GetTraceIntNcoeffs (const int i) const override

int	v_GetTraceNumPoints (const int i) const override

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

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

const LibUtilities::BasisKey	v_GetTraceBasisKey (const int i, const int k, bool useGLL=false) const override

bool	v_IsBoundaryInteriorExpansion () const override

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

void	v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation faceOrient=eDir1FwdDir1_Dir2FwdDir2) override

int	v_GetEdgeNcoeffs (const int i) const override

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

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

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

void	v_GetTraceCoeffMap (const unsigned int fid, Array< OneD, unsigned int > &maparray) override

void	v_GetElmtTraceToTraceMap (const unsigned int fid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation faceOrient, int P, int Q) override

void	v_GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override

void	v_GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override

DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey) override

DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey) override

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

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

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

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

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

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

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

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

Protected Member Functions inherited from Nektar::StdRegions::StdExpansion3D
void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2)
	Calculate the 3D derivative in the local tensor/collapsed coordinate at the physical points.

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

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

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

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

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

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

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

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

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

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

void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1, bool Forwards) override
	This method produces a mapping.

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)

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 const LibUtilities::PointsKey	v_GetNodalPointsKey () const

virtual bool	v_IsNodalNonTensorialExp ()

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

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

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)

Protected Member Functions inherited from Nektar::LocalRegions::Expansion3D
void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, ExpansionSharedPtr > &FaceExp, Array< OneD, Array< OneD, NekDouble > > &faceCoeffs, Array< OneD, NekDouble > &out_d) override
	Evaluate coefficients of weak deriviative in the direction dir given the input coefficicents incoeffs and the imposed boundary values in EdgeExp (which will have its phys space updated).

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

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

void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the inner product of inarray with respect to the elements basis.

void	v_AddFaceNormBoundaryInt (const int face, const ExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) override

void	v_AddRobinMassMatrix (const int face, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) override

StdRegions::Orientation	v_GetTraceOrient (int face) override

void	v_GetTracePhysVals (const int face, const StdRegions::StdExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) override
	Extract the physical values along face face from inarray into outarray following the face orientation and point distribution defined by defined in FaceExp.

void	v_GetLocTracePhysVals (const int face, const StdRegions::StdExpansionSharedPtr &FaceExp, const NekDouble *inarray, Array< OneD, NekDouble > &outarray) override
	Extract the physical values along face face from inarray into outarray following the local elemental face orientation and point distribution defined by defined in FaceExp.

void	v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp) override

void	GetPhysFaceVarCoeffsFromElement (const int face, ExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &varcoeff, Array< OneD, NekDouble > &outarray)

DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType) override

DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &transformationmatrix) override
	Build inverse and inverse transposed transformation matrix: \(\mathbf{R^{-1}}\) and \(\mathbf{R^{-T}}\).

DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) override

void	v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) override

void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors, Array< OneD, Array< OneD, NekDouble > > &d2factors) override
	: This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace.

Protected Member Functions inherited from Nektar::LocalRegions::Expansion
void	ComputeLaplacianMetric ()

void	ComputeQuadratureMetric ()

void	ComputeGmatcdotMF (const Array< TwoD, const NekDouble > &df, const Array< OneD, const NekDouble > &direction, Array< OneD, Array< OneD, NekDouble > > &dfdir)

Array< OneD, NekDouble >	GetMF (const int dir, const int shapedim, const StdRegions::VarCoeffMap &varcoeffs)

Array< OneD, NekDouble >	GetMFDiv (const int dir, const StdRegions::VarCoeffMap &varcoeffs)

Array< OneD, NekDouble >	GetMFMag (const int dir, const StdRegions::VarCoeffMap &varcoeffs)

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

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

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

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

int	v_GetCoordim () const override

virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)

virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

virtual void	v_AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

virtual NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)

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

virtual void	v_GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray)

virtual const Array< OneD, const NekDouble > &	v_GetPhysNormals ()

virtual void	v_SetPhysNormals (Array< OneD, const NekDouble > &normal)

virtual void	v_SetUpPhysNormals (const int id)

virtual void	v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)

Private Member Functions
void	v_LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp) override

Private Attributes
LibUtilities::NekManager< MatrixKey, DNekScalMat, MatrixKey::opLess >	m_matrixManager

LibUtilities::NekManager< MatrixKey, DNekScalBlkMat, MatrixKey::opLess >	m_staticCondMatrixManager

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

Protected Attributes inherited from Nektar::LocalRegions::Expansion3D
std::map< int, NormalVector >	m_faceNormals

Protected Attributes inherited from Nektar::LocalRegions::Expansion
LibUtilities::NekManager< IndexMapKey, IndexMapValues, IndexMapKey::opLess >	m_indexMapManager

std::map< int, ExpansionWeakPtr >	m_traceExp

SpatialDomains::Geometry *	m_geom

SpatialDomains::GeomFactorsUniquePtr	m_geomFactors

MetricMap	m_metrics

std::map< int, NormalVector >	m_traceNormals

ExpansionWeakPtr	m_elementLeft

ExpansionWeakPtr	m_elementRight

int	m_elementTraceLeft = -1

int	m_elementTraceRight = -1

std::map< int, Array< OneD, NekDouble > >	m_elmtBndNormDirElmtLen
	the element length in each element boundary(Vertex, edge or face) normal direction calculated based on the local m_geomFactors times the standard element length (which is 2.0)

Detailed Description

Defines a hexahedral local expansion.

Definition at line 48 of file HexExp.h.

Constructor & Destructor Documentation

◆ HexExp() [1/2]

Nektar::LocalRegions::HexExp::HexExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		const LibUtilities::BasisKey &	Bc,
		SpatialDomains::Geometry3D *	geom
	)

Constructor using BasisKey class for quadrature points and order definition.

Parameters

Ba	Basis key for first coordinate.
Bb	Basis key for second coordinate.
Bc	Basis key for third coordinate.

Definition at line 57 of file HexExp.cpp.

    : StdExpansion(Ba.GetNumModes() * Bb.GetNumModes() * Bc.GetNumModes(), 3,
                   Ba, Bb, Bc),
      StdExpansion3D(Ba.GetNumModes() * Bb.GetNumModes() * Bc.GetNumModes(), Ba,
                     Bb, Bc),
      StdHexExp(Ba, Bb, Bc), Expansion(geom), Expansion3D(geom),
      m_matrixManager(
          std::bind(&Expansion3D::CreateMatrix, this, std::placeholders::_1)),
      m_staticCondMatrixManager(std::bind(&Expansion::CreateStaticCondMatrix,
                                          this, std::placeholders::_1))
{
}

◆ HexExp() [2/2]

Nektar::LocalRegions::HexExp::HexExp ( const HexExp & T )

Copy Constructor.

Parameters

T	HexExp to copy.

Definition at line 78 of file HexExp.cpp.

    : StdExpansion(T), StdExpansion3D(T), StdHexExp(T), Expansion(T),
      Expansion3D(T), m_matrixManager(T.m_matrixManager),
      m_staticCondMatrixManager(T.m_staticCondMatrixManager)
{
}

◆ ~HexExp()

Nektar::LocalRegions::HexExp::~HexExp ( )

overridedefault

Member Function Documentation

◆ v_AlignVectorToCollapsedDir()

void Nektar::LocalRegions::HexExp::v_AlignVectorToCollapsedDir	(	const int	dir,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, Array< OneD, NekDouble > > &	outarray
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 153 of file HexExp.cpp.

{
    ASSERTL1((dir == 0) || (dir == 1) || (dir == 2), "Invalid direction.");
 
    const int nq0 = m_base[0]->GetNumPoints();
    const int nq1 = m_base[1]->GetNumPoints();
    const int nq2 = m_base[2]->GetNumPoints();
    const int nq  = nq0 * nq1 * nq2;
 
    const Array<TwoD, const NekDouble> &df = m_geomFactors->GetDerivFactors();
 
    Array<OneD, NekDouble> tmp1(nq); // Quad metric
 
    Array<OneD, NekDouble> tmp2 = outarray[0]; // Dir1 metric
    Array<OneD, NekDouble> tmp3 = outarray[1]; // Dir2 metric
    Array<OneD, NekDouble> tmp4 = outarray[2];
 
    Vmath::Vcopy(nq, inarray, 1, tmp1, 1); // Dir3 metric
 
    if (m_geomFactors->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nq, &df[3 * dir][0], 1, tmp1.data(), 1, tmp2.data(), 1);
        Vmath::Vmul(nq, &df[3 * dir + 1][0], 1, tmp1.data(), 1, tmp3.data(), 1);
        Vmath::Vmul(nq, &df[3 * dir + 2][0], 1, tmp1.data(), 1, tmp4.data(), 1);
    }
    else
    {
        Vmath::Smul(nq, df[3 * dir][0], tmp1.data(), 1, tmp2.data(), 1);
        Vmath::Smul(nq, df[3 * dir + 1][0], tmp1.data(), 1, tmp3.data(), 1);
        Vmath::Smul(nq, df[3 * dir + 2][0], tmp1.data(), 1, tmp4.data(), 1);
    }
}

References ASSERTL1, Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geomFactors, Vmath::Smul(), Vmath::Vcopy(), and Vmath::Vmul().

Referenced by v_IProductWRTDerivBase().

◆ v_ComputeLaplacianMetric()

void Nektar::LocalRegions::HexExp::v_ComputeLaplacianMetric ( )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1086 of file HexExp.cpp.

{
    const SpatialDomains::GeomType type = m_geomFactors->GetGtype();
    const unsigned int nqtot            = GetTotPoints();
    const unsigned int dim              = 3;
    const MetricType m[3][3]            = {
        {eMetricLaplacian00, eMetricLaplacian01, eMetricLaplacian02},
        {eMetricLaplacian01, eMetricLaplacian11, eMetricLaplacian12},
        {eMetricLaplacian02, eMetricLaplacian12, eMetricLaplacian22}};
 
    for (unsigned int i = 0; i < dim; ++i)
    {
        for (unsigned int j = i; j < dim; ++j)
        {
            m_metrics[m[i][j]] = Array<OneD, NekDouble>(nqtot);
            const Array<TwoD, const NekDouble> &gmat =
                m_geomFactors->GetGmat(GetPointsKeys());
            if (type == SpatialDomains::eDeformed)
            {
                Vmath::Vcopy(nqtot, &gmat[i * dim + j][0], 1,
                             &m_metrics[m[i][j]][0], 1);
            }
            else
            {
                Vmath::Fill(nqtot, gmat[i * dim + j][0], &m_metrics[m[i][j]][0],
                            1);
            }
        }
    }
}

◆ v_ComputeTraceNormal()

void Nektar::LocalRegions::HexExp::v_ComputeTraceNormal ( const int face )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 532 of file HexExp.cpp.

{
    int i;
    SpatialDomains::GeomType type = m_geomFactors->GetGtype();
 
    LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
    for (i = 0; i < ptsKeys.size(); ++i)
    {
        // Need at least 2 points for computing normals
        if (ptsKeys[i].GetNumPoints() == 1)
        {
            LibUtilities::PointsKey pKey(2, ptsKeys[i].GetPointsType());
            ptsKeys[i] = pKey;
        }
    }
 
    const Array<TwoD, const NekDouble> &df =
        m_geomFactors->ComputeDerivFactors(ptsKeys);
    const Array<OneD, const NekDouble> &jac =
        m_geomFactors->ComputeJac(ptsKeys);
 
    LibUtilities::BasisKey tobasis0 = GetTraceBasisKey(face, 0);
    LibUtilities::BasisKey tobasis1 = GetTraceBasisKey(face, 1);
 
    // Number of quadrature points in face expansion.
    int nq_face = tobasis0.GetNumPoints() * tobasis1.GetNumPoints();
 
    int vCoordDim = GetCoordim();
 
    m_traceNormals[face] = Array<OneD, Array<OneD, NekDouble>>(vCoordDim);
    Array<OneD, Array<OneD, NekDouble>> &normal = m_traceNormals[face];
    for (i = 0; i < vCoordDim; ++i)
    {
        normal[i] = Array<OneD, NekDouble>(nq_face);
    }
 
    size_t nqb                     = nq_face;
    size_t nbnd                    = face;
    m_elmtBndNormDirElmtLen[nbnd]  = Array<OneD, NekDouble>{nqb, 0.0};
    Array<OneD, NekDouble> &length = m_elmtBndNormDirElmtLen[nbnd];
 
    // Regular geometry case
    if ((type == SpatialDomains::eRegular) ||
        (type == SpatialDomains::eMovingRegular))
    {
        NekDouble fac;
        // Set up normals
        switch (face)
        {
            case 0:
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = -df[3 * i + 2][0];
                }
                break;
            case 1:
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = -df[3 * i + 1][0];
                }
                break;
            case 2:
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = df[3 * i][0];
                }
                break;
            case 3:
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = df[3 * i + 1][0];
                }
                break;
            case 4:
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = -df[3 * i][0];
                }
                break;
            case 5:
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = df[3 * i + 2][0];
                }
                break;
            default:
                ASSERTL0(false, "face is out of range (edge < 5)");
        }
 
        // normalise
        fac = 0.0;
        for (i = 0; i < vCoordDim; ++i)
        {
            fac += normal[i][0] * normal[i][0];
        }
        fac = 1.0 / sqrt(fac);
 
        Vmath::Fill(nqb, fac, length, 1);
        for (i = 0; i < vCoordDim; ++i)
        {
            Vmath::Fill(nq_face, fac * normal[i][0], normal[i], 1);
        }
    }
    else // Set up deformed normals
    {
        int j, k;
 
        int nqe0  = ptsKeys[0].GetNumPoints();
        int nqe1  = ptsKeys[1].GetNumPoints();
        int nqe2  = ptsKeys[2].GetNumPoints();
        int nqe01 = nqe0 * nqe1;
        int nqe02 = nqe0 * nqe2;
        int nqe12 = nqe1 * nqe2;
 
        int nqe;
        if (face == 0 || face == 5)
        {
            nqe = nqe01;
        }
        else if (face == 1 || face == 3)
        {
            nqe = nqe02;
        }
        else
        {
            nqe = nqe12;
        }
 
        LibUtilities::PointsKey points0;
        LibUtilities::PointsKey points1;
 
        Array<OneD, NekDouble> faceJac(nqe);
        Array<OneD, NekDouble> normals(vCoordDim * nqe, 0.0);
 
        // Extract Jacobian along face and recover local
        // derivates (dx/dr) for polynomial interpolation by
        // multiplying m_gmat by jacobian
        switch (face)
        {
            case 0:
                for (j = 0; j < nqe; ++j)
                {
                    normals[j]           = -df[2][j] * jac[j];
                    normals[nqe + j]     = -df[5][j] * jac[j];
                    normals[2 * nqe + j] = -df[8][j] * jac[j];
                    faceJac[j]           = jac[j];
                }
 
                points0 = ptsKeys[0];
                points1 = ptsKeys[1];
                break;
            case 1:
                for (j = 0; j < nqe0; ++j)
                {
                    for (k = 0; k < nqe2; ++k)
                    {
                        int idx                     = j + nqe01 * k;
                        normals[j + k * nqe0]       = -df[1][idx] * jac[idx];
                        normals[nqe + j + k * nqe0] = -df[4][idx] * jac[idx];
                        normals[2 * nqe + j + k * nqe0] =
                            -df[7][idx] * jac[idx];
                        faceJac[j + k * nqe0] = jac[idx];
                    }
                }
                points0 = ptsKeys[0];
                points1 = ptsKeys[2];
                break;
            case 2:
                for (j = 0; j < nqe1; ++j)
                {
                    for (k = 0; k < nqe2; ++k)
                    {
                        int idx               = nqe0 - 1 + nqe0 * j + nqe01 * k;
                        normals[j + k * nqe1] = df[0][idx] * jac[idx];
                        normals[nqe + j + k * nqe1]     = df[3][idx] * jac[idx];
                        normals[2 * nqe + j + k * nqe1] = df[6][idx] * jac[idx];
                        faceJac[j + k * nqe1]           = jac[idx];
                    }
                }
                points0 = ptsKeys[1];
                points1 = ptsKeys[2];
                break;
            case 3:
                for (j = 0; j < nqe0; ++j)
                {
                    for (k = 0; k < nqe2; ++k)
                    {
                        int idx = nqe0 * (nqe1 - 1) + j + nqe01 * k;
                        normals[j + k * nqe0]           = df[1][idx] * jac[idx];
                        normals[nqe + j + k * nqe0]     = df[4][idx] * jac[idx];
                        normals[2 * nqe + j + k * nqe0] = df[7][idx] * jac[idx];
                        faceJac[j + k * nqe0]           = jac[idx];
                    }
                }
                points0 = ptsKeys[0];
                points1 = ptsKeys[2];
                break;
            case 4:
                for (j = 0; j < nqe1; ++j)
                {
                    for (k = 0; k < nqe2; ++k)
                    {
                        int idx                     = j * nqe0 + nqe01 * k;
                        normals[j + k * nqe1]       = -df[0][idx] * jac[idx];
                        normals[nqe + j + k * nqe1] = -df[3][idx] * jac[idx];
                        normals[2 * nqe + j + k * nqe1] =
                            -df[6][idx] * jac[idx];
                        faceJac[j + k * nqe1] = jac[idx];
                    }
                }
                points0 = ptsKeys[1];
                points1 = ptsKeys[2];
                break;
            case 5:
                for (j = 0; j < nqe01; ++j)
                {
                    int idx              = j + nqe01 * (nqe2 - 1);
                    normals[j]           = df[2][idx] * jac[idx];
                    normals[nqe + j]     = df[5][idx] * jac[idx];
                    normals[2 * nqe + j] = df[8][idx] * jac[idx];
                    faceJac[j]           = jac[idx];
                }
                points0 = ptsKeys[0];
                points1 = ptsKeys[1];
                break;
            default:
                ASSERTL0(false, "face is out of range (face < 5)");
        }
 
        Array<OneD, NekDouble> work(nq_face, 0.0);
        // Interpolate Jacobian and invert
        LibUtilities::Interp2D(points0, points1, faceJac,
                               tobasis0.GetPointsKey(), tobasis1.GetPointsKey(),
                               work);
 
        Vmath::Sdiv(nq_face, 1.0, &work[0], 1, &work[0], 1);
 
        // interpolate
        for (i = 0; i < GetCoordim(); ++i)
        {
            LibUtilities::Interp2D(points0, points1, &normals[i * nqe],
                                   tobasis0.GetPointsKey(),
                                   tobasis1.GetPointsKey(), &normal[i][0]);
            Vmath::Vmul(nq_face, work, 1, normal[i], 1, normal[i], 1);
        }
 
        // normalise normal vectors
        Vmath::Zero(nq_face, work, 1);
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vvtvp(nq_face, normal[i], 1, normal[i], 1, work, 1, work, 1);
        }
 
        Vmath::Vsqrt(nq_face, work, 1, work, 1);
        Vmath::Sdiv(nq_face, 1.0, work, 1, work, 1);
 
        Vmath::Vcopy(nqb, work, 1, length, 1);
 
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vmul(nq_face, normal[i], 1, work, 1, normal[i], 1);
        }
    }
}

References ASSERTL0, Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::LibUtilities::BasisKey::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::LibUtilities::BasisKey::GetPointsKey(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::GetTraceBasisKey(), Nektar::LibUtilities::Interp2D(), Nektar::LocalRegions::Expansion::m_elmtBndNormDirElmtLen, Nektar::LocalRegions::Expansion::m_geomFactors, Nektar::LocalRegions::Expansion::m_traceNormals, Vmath::Sdiv(), tinysimd::sqrt(), Vmath::Vcopy(), Vmath::Vmul(), Vmath::Vsqrt(), Vmath::Vvtvp(), and Vmath::Zero().

◆ v_CreateStdMatrix()

DNekMatSharedPtr Nektar::LocalRegions::HexExp::v_CreateStdMatrix ( const StdRegions::StdMatrixKey & mkey )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 972 of file HexExp.cpp.

{
    LibUtilities::BasisKey bkey0 = m_base[0]->GetBasisKey();
    LibUtilities::BasisKey bkey1 = m_base[1]->GetBasisKey();
    LibUtilities::BasisKey bkey2 = m_base[2]->GetBasisKey();
 
    StdRegions::StdHexExpSharedPtr tmp =
        MemoryManager<StdHexExp>::AllocateSharedPtr(bkey0, bkey1, bkey2);
 
    return tmp->GetStdMatrix(mkey);
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and Nektar::StdRegions::StdExpansion::m_base.

◆ v_DropLocMatrix()

void Nektar::LocalRegions::HexExp::v_DropLocMatrix ( const MatrixKey & mkey )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 989 of file HexExp.cpp.

{
    m_matrixManager.DeleteObject(mkey);
}

References m_matrixManager.

◆ v_DropLocStaticCondMatrix()

void Nektar::LocalRegions::HexExp::v_DropLocStaticCondMatrix ( const MatrixKey & mkey )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 999 of file HexExp.cpp.

{
    m_staticCondMatrixManager.DeleteObject(mkey);
}

References m_staticCondMatrixManager.

◆ v_ExtractDataToCoeffs()

void Nektar::LocalRegions::HexExp::v_ExtractDataToCoeffs	(	const NekDouble *	data,
		const std::vector< unsigned int > &	nummodes,
		const int	mode_offset,
		NekDouble *	coeffs,
		std::vector< LibUtilities::BasisType > &	fromType
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 314 of file HexExp.cpp.

{
    int data_order0 = nummodes[mode_offset];
    int fillorder0  = min(m_base[0]->GetNumModes(), data_order0);
    int data_order1 = nummodes[mode_offset + 1];
    int order1      = m_base[1]->GetNumModes();
    int fillorder1  = min(order1, data_order1);
    int data_order2 = nummodes[mode_offset + 2];
    int order2      = m_base[2]->GetNumModes();
    int fillorder2  = min(order2, data_order2);
 
    // Check if same basis
    if (fromType[0] != m_base[0]->GetBasisType() ||
        fromType[1] != m_base[1]->GetBasisType() ||
        fromType[2] != m_base[2]->GetBasisType())
    {
        // Construct a hex with the appropriate basis type at our
        // quadrature points, and one more to do a forwards
        // transform. We can then copy the output to coeffs.
        StdRegions::StdHexExp tmpHex(
            LibUtilities::BasisKey(fromType[0], data_order0,
                                   m_base[0]->GetPointsKey()),
            LibUtilities::BasisKey(fromType[1], data_order1,
                                   m_base[1]->GetPointsKey()),
            LibUtilities::BasisKey(fromType[2], data_order2,
                                   m_base[2]->GetPointsKey()));
        StdRegions::StdHexExp tmpHex2(m_base[0]->GetBasisKey(),
                                      m_base[1]->GetBasisKey(),
                                      m_base[2]->GetBasisKey());
 
        Array<OneD, const NekDouble> tmpData(tmpHex.GetNcoeffs(), data);
        Array<OneD, NekDouble> tmpBwd(tmpHex2.GetTotPoints());
        Array<OneD, NekDouble> tmpOut(tmpHex2.GetNcoeffs());
 
        tmpHex.BwdTrans(tmpData, tmpBwd);
        tmpHex2.FwdTrans(tmpBwd, tmpOut);
        Vmath::Vcopy(tmpOut.size(), &tmpOut[0], 1, coeffs, 1);
 
        return;
    }
 
    switch (m_base[0]->GetBasisType())
    {
        case LibUtilities::eModified_A:
        {
            int i, j;
            int cnt  = 0;
            int cnt1 = 0;
 
            ASSERTL1(m_base[1]->GetBasisType() == LibUtilities::eModified_A,
                     "Extraction routine not set up for this basis");
            ASSERTL1(m_base[2]->GetBasisType() == LibUtilities::eModified_A,
                     "Extraction routine not set up for this basis");
 
            Vmath::Zero(m_ncoeffs, coeffs, 1);
            for (j = 0; j < fillorder0; ++j)
            {
                for (i = 0; i < fillorder1; ++i)
                {
                    Vmath::Vcopy(fillorder2, &data[cnt], 1, &coeffs[cnt1], 1);
                    cnt += data_order2;
                    cnt1 += order2;
                }
 
                // count out data for j iteration
                for (i = fillorder1; i < data_order1; ++i)
                {
                    cnt += data_order2;
                }
 
                for (i = fillorder1; i < order1; ++i)
                {
                    cnt1 += order2;
                }
            }
            break;
        }
        case LibUtilities::eGLL_Lagrange:
        {
            LibUtilities::PointsKey p0(nummodes[0],
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey p1(nummodes[1],
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey p2(nummodes[2],
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey t0(m_base[0]->GetNumModes(),
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey t1(m_base[1]->GetNumModes(),
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey t2(m_base[2]->GetNumModes(),
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::Interp3D(p0, p1, p2, data, t0, t1, t2, coeffs);
        }
        break;
        default:
            ASSERTL0(false, "basis is either not set up or not "
                            "hierarchicial");
    }
}

References ASSERTL0, ASSERTL1, Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::LibUtilities::Interp3D(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, tinysimd::min(), Vmath::Vcopy(), and Vmath::Zero().

◆ v_GenMatrix()

DNekMatSharedPtr Nektar::LocalRegions::HexExp::v_GenMatrix ( const StdRegions::StdMatrixKey & mkey )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 950 of file HexExp.cpp.

{
    DNekMatSharedPtr returnval;
 
    switch (mkey.GetMatrixType())
    {
        case StdRegions::eHybridDGHelmholtz:
        case StdRegions::eHybridDGLamToU:
        case StdRegions::eHybridDGLamToQ0:
        case StdRegions::eHybridDGLamToQ1:
        case StdRegions::eHybridDGLamToQ2:
        case StdRegions::eHybridDGHelmBndLam:
        case StdRegions::eInvLaplacianWithUnityMean:
            returnval = Expansion3D::v_GenMatrix(mkey);
            break;
        default:
            returnval = StdHexExp::v_GenMatrix(mkey);
    }
 
    return returnval;
}

References Nektar::StdRegions::eHybridDGHelmBndLam, Nektar::StdRegions::eHybridDGHelmholtz, Nektar::StdRegions::eHybridDGLamToQ0, Nektar::StdRegions::eHybridDGLamToQ1, Nektar::StdRegions::eHybridDGLamToQ2, Nektar::StdRegions::eHybridDGLamToU, Nektar::StdRegions::eInvLaplacianWithUnityMean, Nektar::StdRegions::StdMatrixKey::GetMatrixType(), and Nektar::LocalRegions::Expansion3D::v_GenMatrix().

◆ v_GetCoord()

void Nektar::LocalRegions::HexExp::v_GetCoord	(	const Array< OneD, const NekDouble > &	Lcoords,
		Array< OneD, NekDouble > &	coords
	)

overrideprotectedvirtual

Retrieves the physical coordinates of a given set of reference coordinates.

Parameters

Lcoords	Local coordinates in reference space.
coords	Corresponding coordinates in physical space.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 287 of file HexExp.cpp.

{
    int i;
 
    ASSERTL1(Lcoords[0] >= -1.0 && Lcoords[0] <= 1.0 && Lcoords[1] >= -1.0 &&
                 Lcoords[1] <= 1.0 && Lcoords[2] >= -1.0 && Lcoords[2] <= 1.0,
             "Local coordinates are not in region [-1,1]");
 
    m_geom->FillGeom();
 
    for (i = 0; i < m_geom->GetCoordim(); ++i)
    {
        coords[i] = m_geom->GetCoord(i, Lcoords);
    }
}

References ASSERTL1, Nektar::SpatialDomains::Geometry::FillGeom(), Nektar::SpatialDomains::Geometry::GetCoord(), Nektar::SpatialDomains::Geometry::GetCoordim(), and Nektar::LocalRegions::Expansion::m_geom.

◆ v_GetCoords()

void Nektar::LocalRegions::HexExp::v_GetCoords	(	Array< OneD, NekDouble > &	coords_1,
		Array< OneD, NekDouble > &	coords_2,
		Array< OneD, NekDouble > &	coords_3
	)

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 304 of file HexExp.cpp.

{
    Expansion::v_GetCoords(coords_0, coords_1, coords_2);
}

References Nektar::LocalRegions::Expansion::v_GetCoords().

◆ v_GetLinStdExp()

StdRegions::StdExpansionSharedPtr Nektar::LocalRegions::HexExp::v_GetLinStdExp ( void ) const

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 267 of file HexExp.cpp.

{
    LibUtilities::BasisKey bkey0(m_base[0]->GetBasisType(), 2,
                                 m_base[0]->GetPointsKey());
    LibUtilities::BasisKey bkey1(m_base[1]->GetBasisType(), 2,
                                 m_base[1]->GetPointsKey());
    LibUtilities::BasisKey bkey2(m_base[2]->GetBasisType(), 2,
                                 m_base[2]->GetPointsKey());
 
    return MemoryManager<StdRegions::StdHexExp>::AllocateSharedPtr(bkey0, bkey1,
                                                                   bkey2);
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

◆ v_GetLocMatrix()

DNekScalMatSharedPtr Nektar::LocalRegions::HexExp::v_GetLocMatrix ( const MatrixKey & mkey )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 984 of file HexExp.cpp.

{
    return m_matrixManager[mkey];
}

References m_matrixManager.

◆ v_GetLocStaticCondMatrix()

DNekScalBlkMatSharedPtr Nektar::LocalRegions::HexExp::v_GetLocStaticCondMatrix ( const MatrixKey & mkey )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 994 of file HexExp.cpp.

{
    return m_staticCondMatrixManager[mkey];
}

References m_staticCondMatrixManager.

◆ v_GetStdExp()

StdRegions::StdExpansionSharedPtr Nektar::LocalRegions::HexExp::v_GetStdExp ( void ) const

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 260 of file HexExp.cpp.

{
    return MemoryManager<StdRegions::StdHexExp>::AllocateSharedPtr(
        m_base[0]->GetBasisKey(), m_base[1]->GetBasisKey(),
        m_base[2]->GetBasisKey());
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and Nektar::StdRegions::StdExpansion::m_base.

◆ v_GetTracePhysMap()

void Nektar::LocalRegions::HexExp::v_GetTracePhysMap	(	const int	face,
		Array< OneD, int > &	outarray
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 417 of file HexExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
 
    int nq0 = 0;
    int nq1 = 0;
 
    switch (face)
    {
        case 0:
            nq0 = nquad0;
            nq1 = nquad1;
 
            // Directions A and B positive
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                outarray[i] = i;
            }
 
            break;
        case 1:
            nq0 = nquad0;
            nq1 = nquad2;
            // Direction A and B positive
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            // Direction A and B positive
            for (int k = 0; k < nquad2; k++)
            {
                for (int i = 0; i < nquad0; ++i)
                {
                    outarray[k * nquad0 + i] = nquad0 * nquad1 * k + i;
                }
            }
            break;
        case 2:
            nq0 = nquad1;
            nq1 = nquad2;
 
            // Direction A and B positive
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            for (int i = 0; i < nquad1 * nquad2; i++)
            {
                outarray[i] = nquad0 - 1 + i * nquad0;
            }
            break;
        case 3:
            nq0 = nquad0;
            nq1 = nquad2;
 
            // Direction A and B positive
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            for (int k = 0; k < nquad2; k++)
            {
                for (int i = 0; i < nquad0; i++)
                {
                    outarray[k * nquad0 + i] =
                        (nquad0 * (nquad1 - 1)) + (k * nquad0 * nquad1) + i;
                }
            }
            break;
        case 4:
            nq0 = nquad1;
            nq1 = nquad2;
 
            // Direction A and B positive
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            for (int i = 0; i < nquad1 * nquad2; i++)
            {
                outarray[i] = i * nquad0;
            }
            break;
        case 5:
            nq0 = nquad0;
            nq1 = nquad1;
            // Directions A and B positive
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            for (int i = 0; i < nquad0 * nquad1; i++)
            {
                outarray[i] = nquad0 * nquad1 * (nquad2 - 1) + i;
            }
 
            break;
        default:
            ASSERTL0(false, "face value (> 5) is out of range");
            break;
    }
}

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

◆ v_HelmholtzMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 844 of file HexExp.cpp.

{
    HexExp::v_HelmholtzMatrixOp_MatFree(inarray, outarray, mkey);
}

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

◆ v_IProductWRTDerivBase()

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

overrideprotectedvirtual

Calculates the inner product \( I_{pqr} = (u, \partial_{x_i} \phi_{pqr}) \).

The derivative of the basis functions is performed using the chain rule in order to incorporate the geometric factors. Assuming that the basis functions are a tensor product \(\phi_{pqr}(\xi_1,\xi_2,\xi_3) = \phi_1(\xi_1)\phi_2(\xi_2)\phi_3(\xi_3)\), in the hexahedral element, this is straightforward and yields the result

\[ I_{pqr} = \sum_{k=1}^3 \left(u, \frac{\partial u}{\partial \xi_k} \frac{\partial \xi_k}{\partial x_i}\right) \]

Parameters

dir	Direction in which to take the derivative.
inarray	The function \( u \).
outarray	Value of the inner product.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 108 of file HexExp.cpp.

{
    ASSERTL1((dir == 0) || (dir == 1) || (dir == 2), "Invalid direction.");
 
    const int nq0 = m_base[0]->GetNumPoints();
    const int nq1 = m_base[1]->GetNumPoints();
    const int nq2 = m_base[2]->GetNumPoints();
    const int nq  = nq0 * nq1 * nq2;
 
    Array<OneD, NekDouble> tmp2(nq);        // Dir1 metric
    Array<OneD, NekDouble> tmp3(nq);        // Dir2 metric
    Array<OneD, NekDouble> tmp4(nq);        // Dir3 metric
    Array<OneD, NekDouble> tmp5(m_ncoeffs); // iprod tmp
 
    Array<OneD, Array<OneD, NekDouble>> tmp2D{3};
    tmp2D[0] = tmp2;
    tmp2D[1] = tmp3;
    tmp2D[2] = tmp4;
 
    const Array<OneD, const NekDouble> &jac = m_geomFactors->GetJac();
    bool Deformed = (m_geomFactors->GetGtype() == SpatialDomains::eDeformed);
 
    const bool CollDir0 = m_base[0]->Collocation();
    const bool CollDir1 = m_base[1]->Collocation();
    const bool CollDir2 = m_base[2]->Collocation();
 
    HexExp::v_AlignVectorToCollapsedDir(dir, inarray, tmp2D);
 
    v_IProductWRTBaseKernel(m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                            m_base[2]->GetBdata(), tmp2, outarray, jac,
                            Deformed, false, CollDir1, CollDir2);
 
    v_IProductWRTBaseKernel(m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                            m_base[2]->GetBdata(), tmp3, tmp5, jac, Deformed,
                            CollDir0, false, CollDir2);
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
 
    v_IProductWRTBaseKernel(m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                            m_base[2]->GetDbdata(), tmp4, tmp5, jac, Deformed,
                            CollDir0, CollDir1, false);
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
}

References ASSERTL1, Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geomFactors, Nektar::StdRegions::StdExpansion::m_ncoeffs, v_AlignVectorToCollapsedDir(), Nektar::StdRegions::StdHexExp::v_IProductWRTBaseKernel(), and Vmath::Vadd().

◆ v_IProductWRTDirectionalDerivBase()

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

overrideprotectedvirtual

Parameters

dir	Vector direction in which to take the derivative.
inarray	The function \( u \).
outarray	Value of the inner product.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 194 of file HexExp.cpp.

{
    int shapedim  = 3;
    const int nq0 = m_base[0]->GetNumPoints();
    const int nq1 = m_base[1]->GetNumPoints();
    const int nq2 = m_base[2]->GetNumPoints();
    const int nq  = nq0 * nq1 * nq2;
 
    Array<OneD, NekDouble> tmp2(nq);        // Dir1 metric
    Array<OneD, NekDouble> tmp3(nq);        // Dir2 metric
    Array<OneD, NekDouble> tmp4(nq);        // Dir3 metric
    Array<OneD, NekDouble> tmp5(m_ncoeffs); // iprod tmp
 
    Array<OneD, Array<OneD, NekDouble>> tmp2D{3};
    tmp2D[0] = tmp2;
    tmp2D[1] = tmp3;
    tmp2D[2] = tmp4;
 
    const Array<OneD, const NekDouble> &jac = m_geomFactors->GetJac();
    bool Deformed = (m_geomFactors->GetGtype() == SpatialDomains::eDeformed);
 
    const bool CollDir0 = m_base[0]->Collocation();
    const bool CollDir1 = m_base[1]->Collocation();
    const bool CollDir2 = m_base[2]->Collocation();
 
    const Array<TwoD, const NekDouble> &df = m_geomFactors->GetDerivFactors();
 
    Array<OneD, Array<OneD, NekDouble>> dfdir(shapedim);
    Expansion::ComputeGmatcdotMF(df, direction, dfdir);
 
    Vmath::Vmul(nq, &dfdir[0][0], 1, inarray.data(), 1, tmp2.data(), 1);
    Vmath::Vmul(nq, &dfdir[1][0], 1, inarray.data(), 1, tmp3.data(), 1);
    Vmath::Vmul(nq, &dfdir[2][0], 1, inarray.data(), 1, tmp4.data(), 1);
 
    v_IProductWRTBaseKernel(m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                            m_base[2]->GetBdata(), tmp2, outarray, jac,
                            Deformed, false, CollDir1, CollDir2);
 
    v_IProductWRTBaseKernel(m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                            m_base[2]->GetBdata(), tmp3, tmp5, jac, Deformed,
                            CollDir0, false, CollDir2);
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
 
    v_IProductWRTBaseKernel(m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                            m_base[2]->GetDbdata(), tmp4, tmp5, jac, Deformed,
                            CollDir0, CollDir1, false);
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
}

References Nektar::LocalRegions::Expansion::ComputeGmatcdotMF(), Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geomFactors, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdHexExp::v_IProductWRTBaseKernel(), Vmath::Vadd(), and Vmath::Vmul().

◆ v_LaplacianMatrixOp() [1/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 807 of file HexExp.cpp.

{
    HexExp::v_LaplacianMatrixOp_MatFree(inarray, outarray, mkey);
}

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

◆ v_LaplacianMatrixOp() [2/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 814 of file HexExp.cpp.

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

◆ v_LaplacianMatrixOp_MatFree_Kernel()

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

overrideprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1004 of file HexExp.cpp.

{
    // This implementation is only valid when there are no
    // coefficients associated to the Laplacian operator
    if (m_metrics.count(eMetricLaplacian00) == 0)
    {
        ComputeLaplacianMetric();
    }
 
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
    int nqtot  = nquad0 * nquad1 * nquad2;
 
    ASSERTL1(wsp.size() >= 6 * nqtot, "Insufficient workspace size.");
 
    const Array<OneD, const NekDouble> &base0  = m_base[0]->GetBdata();
    const Array<OneD, const NekDouble> &base1  = m_base[1]->GetBdata();
    const Array<OneD, const NekDouble> &base2  = m_base[2]->GetBdata();
    const Array<OneD, const NekDouble> &dbase0 = m_base[0]->GetDbdata();
    const Array<OneD, const NekDouble> &dbase1 = m_base[1]->GetDbdata();
    const Array<OneD, const NekDouble> &dbase2 = m_base[2]->GetDbdata();
    const Array<OneD, const NekDouble> &metric00 =
        m_metrics[eMetricLaplacian00];
    const Array<OneD, const NekDouble> &metric01 =
        m_metrics[eMetricLaplacian01];
    const Array<OneD, const NekDouble> &metric02 =
        m_metrics[eMetricLaplacian02];
    const Array<OneD, const NekDouble> &metric11 =
        m_metrics[eMetricLaplacian11];
    const Array<OneD, const NekDouble> &metric12 =
        m_metrics[eMetricLaplacian12];
    const Array<OneD, const NekDouble> &metric22 =
        m_metrics[eMetricLaplacian22];
 
    // Allocate temporary storage
    Array<OneD, NekDouble> wsp0(wsp);
    Array<OneD, NekDouble> wsp1(wsp + 1 * nqtot);
    Array<OneD, NekDouble> wsp2(wsp + 2 * nqtot);
    Array<OneD, NekDouble> wsp3(wsp + 3 * nqtot);
    Array<OneD, NekDouble> wsp4(wsp + 4 * nqtot);
    Array<OneD, NekDouble> wsp5(wsp + 5 * nqtot);
 
    PhysTensorDeriv(inarray, wsp0, wsp1, wsp2);
 
    // wsp0 = k = g0 * wsp1 + g1 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
    // wsp2 = l = g1 * wsp1 + g2 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
    // where g0, g1 and g2 are the metric terms set up in the GeomFactors class
    // especially for this purpose
    Vmath::Vvtvvtp(nqtot, &metric00[0], 1, &wsp0[0], 1, &metric01[0], 1,
                   &wsp1[0], 1, &wsp3[0], 1);
    Vmath::Vvtvp(nqtot, &metric02[0], 1, &wsp2[0], 1, &wsp3[0], 1, &wsp3[0], 1);
    Vmath::Vvtvvtp(nqtot, &metric01[0], 1, &wsp0[0], 1, &metric11[0], 1,
                   &wsp1[0], 1, &wsp4[0], 1);
    Vmath::Vvtvp(nqtot, &metric12[0], 1, &wsp2[0], 1, &wsp4[0], 1, &wsp4[0], 1);
    Vmath::Vvtvvtp(nqtot, &metric02[0], 1, &wsp0[0], 1, &metric12[0], 1,
                   &wsp1[0], 1, &wsp5[0], 1);
    Vmath::Vvtvp(nqtot, &metric22[0], 1, &wsp2[0], 1, &wsp5[0], 1, &wsp5[0], 1);
 
    const bool CollDir0 = m_base[0]->Collocation();
    const bool CollDir1 = m_base[1]->Collocation();
    const bool CollDir2 = m_base[2]->Collocation();
 
    const Array<OneD, const NekDouble> &jac = m_geomFactors->GetJac();
    bool Deformed = (m_geomFactors->GetGtype() == SpatialDomains::eDeformed);
 
    // outarray = m = (D_xi1 * B)^T * k
    // wsp1     = n = (D_xi2 * B)^T * l
    v_IProductWRTBaseKernel(dbase0, base1, base2, wsp3, outarray, jac, Deformed,
                            false, CollDir1, CollDir2);
    v_IProductWRTBaseKernel(base0, dbase1, base2, wsp4, wsp2, jac, Deformed,
                            CollDir0, false, CollDir2);
    Vmath::Vadd(m_ncoeffs, wsp2.data(), 1, outarray.data(), 1, outarray.data(),
                1);
    v_IProductWRTBaseKernel(base0, base1, dbase2, wsp5, wsp2, jac, Deformed,
                            CollDir0, CollDir1, false);
    Vmath::Vadd(m_ncoeffs, wsp2.data(), 1, outarray.data(), 1, outarray.data(),
                1);
}

References ASSERTL1, Nektar::LocalRegions::Expansion::ComputeLaplacianMetric(), Nektar::SpatialDomains::eDeformed, Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geomFactors, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion3D::PhysTensorDeriv(), Nektar::StdRegions::StdHexExp::v_IProductWRTBaseKernel(), Vmath::Vadd(), Vmath::Vvtvp(), and Vmath::Vvtvvtp().

◆ v_MassLevelCurvatureMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 837 of file HexExp.cpp.

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

◆ v_MassMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 800 of file HexExp.cpp.

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

◆ v_PhysEvalFirstDeriv()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 249 of file HexExp.cpp.

{
    Array<OneD, NekDouble> Lcoord(3);
    ASSERTL0(m_geom, "m_geom not defined");
    m_geom->GetLocCoords(coord, Lcoord);
    return StdHexExp::v_PhysEvalFirstDeriv(Lcoord, inarray, firstOrderDerivs);
}

References ASSERTL0, Nektar::SpatialDomains::Geometry::GetLocCoords(), and Nektar::LocalRegions::Expansion::m_geom.

◆ v_ReduceOrderCoeffs()

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

overrideprotectedvirtual

This function is used to compute exactly the advective numerical flux on the interface of two elements with different expansions, hence an appropriate number of Gauss points has to be used. The number of Gauss points has to be equal to the number used by the highest polynomial degree of the two adjacent elements

Parameters

numMin	Is the reduced polynomial order
inarray	Input array of coefficients
dumpVar	Output array of reduced coefficients.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 862 of file HexExp.cpp.

{
    int n_coeffs = inarray.size();
    int nmodes0  = m_base[0]->GetNumModes();
    int nmodes1  = m_base[1]->GetNumModes();
    int nmodes2  = m_base[2]->GetNumModes();
    int numMax   = nmodes0;
 
    Array<OneD, NekDouble> coeff(n_coeffs);
    Array<OneD, NekDouble> coeff_tmp1(nmodes0 * nmodes1, 0.0);
    Array<OneD, NekDouble> coeff_tmp2(n_coeffs, 0.0);
    Array<OneD, NekDouble> tmp, tmp2, tmp3, tmp4;
 
    Vmath::Vcopy(n_coeffs, inarray, 1, coeff_tmp2, 1);
 
    const LibUtilities::PointsKey Pkey0(nmodes0,
                                        LibUtilities::eGaussLobattoLegendre);
    const LibUtilities::PointsKey Pkey1(nmodes1,
                                        LibUtilities::eGaussLobattoLegendre);
    const LibUtilities::PointsKey Pkey2(nmodes2,
                                        LibUtilities::eGaussLobattoLegendre);
 
    LibUtilities::BasisKey b0(m_base[0]->GetBasisType(), nmodes0, Pkey0);
    LibUtilities::BasisKey b1(m_base[1]->GetBasisType(), nmodes1, Pkey1);
    LibUtilities::BasisKey b2(m_base[2]->GetBasisType(), nmodes2, Pkey2);
    LibUtilities::BasisKey bortho0(LibUtilities::eOrtho_A, nmodes0, Pkey0);
    LibUtilities::BasisKey bortho1(LibUtilities::eOrtho_A, nmodes1, Pkey1);
    LibUtilities::BasisKey bortho2(LibUtilities::eOrtho_A, nmodes2, Pkey2);
 
    LibUtilities::InterpCoeff3D(b0, b1, b2, coeff_tmp2, bortho0, bortho1,
                                bortho2, coeff);
 
    Vmath::Zero(n_coeffs, coeff_tmp2, 1);
 
    int cnt = 0, cnt2 = 0;
 
    for (int u = 0; u < numMin + 1; ++u)
    {
        for (int i = 0; i < numMin; ++i)
        {
            Vmath::Vcopy(numMin, tmp = coeff + cnt + cnt2, 1,
                         tmp2 = coeff_tmp1 + cnt, 1);
 
            cnt = i * numMax;
        }
 
        Vmath::Vcopy(nmodes0 * nmodes1, tmp3 = coeff_tmp1, 1,
                     tmp4 = coeff_tmp2 + cnt2, 1);
 
        cnt2 = u * nmodes0 * nmodes1;
    }
 
    LibUtilities::InterpCoeff3D(bortho0, bortho1, bortho2, coeff_tmp2, b0, b1,
                                b2, outarray);
}

References Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eOrtho_A, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::LibUtilities::InterpCoeff3D(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Vcopy(), and Vmath::Zero().

◆ v_SVVLaplacianFilter()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 920 of file HexExp.cpp.

{
    int nq = GetTotPoints();
 
    // Calculate sqrt of the Jacobian
    Array<OneD, const NekDouble> jac = m_geomFactors->GetJac();
    Array<OneD, NekDouble> sqrt_jac(nq);
    if (m_geomFactors->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vsqrt(nq, jac, 1, sqrt_jac, 1);
    }
    else
    {
        Vmath::Fill(nq, sqrt(jac[0]), sqrt_jac, 1);
    }
 
    // Multiply array by sqrt(Jac)
    Vmath::Vmul(nq, sqrt_jac, 1, array, 1, array, 1);
 
    // Apply std region filter
    StdHexExp::v_SVVLaplacianFilter(array, mkey);
 
    // Divide by sqrt(Jac)
    Vmath::Vdiv(nq, array, 1, sqrt_jac, 1, array, 1);
}

References Nektar::SpatialDomains::eDeformed, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::LocalRegions::Expansion::m_geomFactors, tinysimd::sqrt(), Vmath::Vdiv(), Vmath::Vmul(), and Vmath::Vsqrt().

◆ v_WeakDerivMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 822 of file HexExp.cpp.

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

◆ v_WeakDirectionalDerivMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 830 of file HexExp.cpp.

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

Member Data Documentation

◆ m_matrixManager

LibUtilities::NekManager<MatrixKey, DNekScalMat, MatrixKey::opLess> Nektar::LocalRegions::HexExp::m_matrixManager

private

Definition at line 180 of file HexExp.h.

Referenced by v_DropLocMatrix(), and v_GetLocMatrix().

◆ m_staticCondMatrixManager

LibUtilities::NekManager<MatrixKey, DNekScalBlkMat, MatrixKey::opLess> Nektar::LocalRegions::HexExp::m_staticCondMatrixManager

private

Definition at line 182 of file HexExp.h.

Referenced by v_DropLocStaticCondMatrix(), and v_GetLocStaticCondMatrix().

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ HexExp() [1/2]

◆ HexExp() [2/2]

◆ ~HexExp()

Member Function Documentation

◆ v_AlignVectorToCollapsedDir()

◆ v_ComputeLaplacianMetric()

◆ v_ComputeTraceNormal()

◆ v_CreateStdMatrix()

◆ v_DropLocMatrix()

◆ v_DropLocStaticCondMatrix()

◆ v_ExtractDataToCoeffs()

◆ v_GenMatrix()

◆ v_GetCoord()

◆ v_GetCoords()

◆ v_GetLinStdExp()

◆ v_GetLocMatrix()

◆ v_GetLocStaticCondMatrix()

◆ v_GetStdExp()

◆ v_GetTracePhysMap()

◆ v_HelmholtzMatrixOp()

◆ v_IProductWRTDerivBase()

◆ v_IProductWRTDirectionalDerivBase()

◆ v_LaplacianMatrixOp() [1/2]

◆ v_LaplacianMatrixOp() [2/2]

◆ v_LaplacianMatrixOp_MatFree_Kernel()

◆ v_MassLevelCurvatureMatrixOp()

◆ v_MassMatrixOp()

◆ v_PhysEvalFirstDeriv()

◆ v_ReduceOrderCoeffs()

◆ v_SVVLaplacianFilter()

◆ v_WeakDerivMatrixOp()

◆ v_WeakDirectionalDerivMatrixOp()

Member Data Documentation

◆ m_matrixManager

◆ m_staticCondMatrixManager