Nektar::LocalRegions::HexExp Class Reference

#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, const SpatialDomains::HexGeomSharedPtr &geom)
	Constructor using BasisKey class for quadrature points and order definition. More...
	HexExp (const HexExp &T)
	Copy Constructor. More...
virtual	~HexExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdHexExp
	StdHexExp ()
	StdHexExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)
	StdHexExp (const StdHexExp &T)
virtual	~StdHexExp () override
Public Member Functions inherited from Nektar::StdRegions::StdExpansion3D
	StdExpansion3D ()
	StdExpansion3D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)
	StdExpansion3D (const StdExpansion3D &T)
virtual	~StdExpansion3D () override
void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d1, Array< OneD, NekDouble > &outarray_d2, Array< OneD, NekDouble > &outarray_d3)
	Calculate the 3D derivative in the local tensor/collapsed coordinate at the physical points. More...
void	BwdTrans_SumFacKernel (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, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
void	IProductWRTBase_SumFacKernel (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, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
int	GetNedges () const
	return the number of edges in 3D expansion More...
int	GetEdgeNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th edge. More...
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. More...
	StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey)
	Constructor. More...
	StdExpansion (const StdExpansion &T)
	Copy Constructor. More...
virtual	~StdExpansion ()
	Destructor. More...
int	GetNumBases () const
	This function returns the number of 1D bases used in the expansion. More...
const Array< OneD, const LibUtilities::BasisSharedPtr > &	GetBase () const
	This function gets the shared point to basis. More...
const LibUtilities::BasisSharedPtr &	GetBasis (int dir) const
	This function gets the shared point to basis in the dir direction. More...
int	GetNcoeffs (void) const
	This function returns the total number of coefficients used in the expansion. More...
int	GetTotPoints () const
	This function returns the total number of quadrature points used in the element. More...
LibUtilities::BasisType	GetBasisType (const int dir) const
	This function returns the type of basis used in the dir direction. More...
int	GetBasisNumModes (const int dir) const
	This function returns the number of expansion modes in the dir direction. More...
int	EvalBasisNumModesMax (void) const
	This function returns the maximum number of expansion modes over all local directions. More...
LibUtilities::PointsType	GetPointsType (const int dir) const
	This function returns the type of quadrature points used in the dir direction. More...
int	GetNumPoints (const int dir) const
	This function returns the number of quadrature points in the dir direction. More...
const Array< OneD, const NekDouble > &	GetPoints (const int dir) const
	This function returns a pointer to the array containing the quadrature points in dir direction. More...
int	GetNverts () const
	This function returns the number of vertices of the expansion domain. More...
int	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th trace. More...
int	GetTraceIntNcoeffs (const int i) const
int	GetTraceNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th trace. More...
const LibUtilities::BasisKey	GetTraceBasisKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...
LibUtilities::PointsKey	GetTracePointsKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...
int	NumBndryCoeffs (void) const
int	NumDGBndryCoeffs (void) const
const LibUtilities::PointsKey	GetNodalPointsKey () const
	This function returns the type of expansion Nodal point type if defined. More...
int	GetNtraces () const
	Returns the number of trace elements connected to this element. More...
LibUtilities::ShapeType	DetShapeType () const
	This function returns the shape of the expansion domain. More...
std::shared_ptr< StdExpansion >	GetStdExp () const
std::shared_ptr< StdExpansion >	GetLinStdExp (void) const
int	GetShapeDimension () const
bool	IsBoundaryInteriorExpansion () const
bool	IsNodalNonTensorialExp ()
void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Backward transformation from coefficient space to physical space. More...
void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Forward transformation from physical space to coefficient space. More...
void	FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)
	This function integrates the specified function over the domain. More...
void	FillMode (const int mode, Array< OneD, NekDouble > &outarray)
	This function fills the array outarray with the mode-th mode of the expansion. More...
void	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	this function calculates the inner product of a given function f with the different modes of the expansion More...
void	IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)
void	IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
int	GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id. More...
void	SetElmtId (const int id)
	Set the element id of this expansion when used in a list by returning value of m_elmt_id. More...
void	GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
	this function returns the physical coordinates of the quadrature points of the expansion More...
void	GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
	given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point More...
DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray)
DNekScalBlkMatSharedPtr	GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
void	DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
int	CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
NekDouble	StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
int	GetCoordim ()
void	GetBoundaryMap (Array< OneD, unsigned int > &outarray)
void	GetInteriorMap (Array< OneD, unsigned int > &outarray)
int	GetVertexMap (const int localVertexId, bool useCoeffPacking=false)
void	GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
void	GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray)
void	GetElmtTraceToTraceMap (const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
void	GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eForwards)
void	GetTraceNumModes (const int tid, int &numModes0, int &numModes1, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)
void	MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
DNekMatSharedPtr	CreateGeneralMatrix (const StdMatrixKey &mkey)
	this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) More...
void	GeneralMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)
void	ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)
void	LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)
void	PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void	PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	PhysDeriv_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds)
void	PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn)
void	PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)
void	StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void	StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
NekDouble	PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
	This function evaluates the first derivative of the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)
NekDouble	PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
	This function evaluates the basis function mode mode at a point coords of the domain. More...
void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta. More...
void	LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
	Convert local collapsed coordinates eta into local cartesian coordinate xi. More...
virtual int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray)
virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
virtual void	v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
NekDouble	Linf (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_\infty\) error \( |\epsilon|_\infty = \max |u - u_{exact}|\) where \( u_{exact}\) is given by the array sol. More...
NekDouble	L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_2\) error, \( | \epsilon |_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...
NekDouble	H1 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( H^1\) error, \( | \epsilon |^1_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u - u_{exact})\cdot dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...
const LibUtilities::PointsKeyVector	GetPointsKeys () const
DNekMatSharedPtr	BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
void	PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
	This function performs an interpolation from the physical space points provided at input into an array of equispaced points which are not the collapsed coordinate. So for a tetrahedron you will only get a tetrahedral number of values. More...
void	GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
	This function provides the connectivity of local simplices (triangles or tets) to connect the equispaced data points provided by PhysInterpToSimplexEquiSpaced. More...
void	EquiSpacedToCoeffs (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs a projection/interpolation from the equispaced points sometimes used in post-processing onto the coefficient space. More...
template<class T >
std::shared_ptr< T >	as ()
void	IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)
void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
Public Member Functions inherited from Nektar::LocalRegions::Expansion3D
	Expansion3D (SpatialDomains::Geometry3DSharedPtr pGeom)
virtual	~Expansion3D () override=default
void	SetTraceToGeomOrientation (Array< OneD, NekDouble > &inout)
	Align trace orientation with the geometry orientation. More...
void	SetFaceToGeomOrientation (const int face, Array< OneD, NekDouble > &inout)
	Align face orientation with the geometry orientation. More...
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::Geometry3DSharedPtr	GetGeom3D () const
void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1) 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)
Public Member Functions inherited from Nektar::LocalRegions::Expansion
	Expansion (SpatialDomains::GeometrySharedPtr pGeom)
	Expansion (const Expansion &pSrc)
virtual	~Expansion ()
void	SetTraceExp (const int traceid, ExpansionSharedPtr &f)
ExpansionSharedPtr	GetTraceExp (const int traceid)
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::GeometrySharedPtr	GetGeom () const
void	Reset ()
IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)
DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)
const SpatialDomains::GeomFactorsSharedPtr &	GetMetricInfo () const
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. More...
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). More...
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	GetTracePhysMap (const int edge, Array< OneD, int > &outarray)
void	ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1)
const NormalVector &	GetTraceNormal (const int id)
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)

Protected Member Functions
virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrate the physical point list inarray over region. More...
virtual void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2) override
	Calculate the derivative of the physical points. More...
virtual void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the derivative of the physical points in a single direction. More...
virtual 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. More...
virtual 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)->_coeffs. More...
virtual 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. More...
virtual void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true) override
	Calculate the inner product of inarray with respect to the given basis B = base0 * base1 * base2. More...
virtual void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculates the inner product \( I_{pqr} = (u, \partial_{x_i} \phi_{pqr}) \). More...
virtual void	v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray) override
virtual void	v_IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals) override
virtual NekDouble	v_PhysEvaluate (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. More...
virtual NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
virtual 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. More...
virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override
virtual LibUtilities::ShapeType	v_DetShapeType () const override
	Return the region shape using the enum-list of ShapeType. More...
virtual StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const override
virtual StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const override
virtual void	v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int mode_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType) override
virtual void	v_GetTracePhysMap (const int face, Array< OneD, int > &outarray) override
void	v_ComputeTraceNormal (const int face) override
virtual void	v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdRegions::StdMatrixKey &mkey) override
virtual DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override
virtual DNekMatSharedPtr	v_CreateStdMatrix (const StdRegions::StdMatrixKey &mkey) override
virtual DNekScalMatSharedPtr	v_GetLocMatrix (const MatrixKey &mkey) override
void	v_DropLocMatrix (const MatrixKey &mkey) override
virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const MatrixKey &mkey) override
void	v_DropLocStaticCondMatrix (const MatrixKey &mkey) override
virtual void	v_ComputeLaplacianMetric () override
Protected Member Functions inherited from Nektar::StdRegions::StdHexExp
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
	Differentiation Methods. More...
virtual void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2) override
virtual void	v_StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_BwdTrans_SumFacKernel (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, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2) override
void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multbyweights=true) override
void	v_IProductWRTBase_SumFacKernel (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, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2) override
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta) override
virtual void	v_LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi) override
virtual void	v_FillMode (const int mode, Array< OneD, NekDouble > &outarray) override
NekDouble	v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) final override
virtual NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
virtual int	v_GetNverts () const override
virtual int	v_GetNedges () const override
virtual int	v_GetNtraces () const override
virtual LibUtilities::ShapeType	v_DetShapeType () const override
virtual int	v_NumBndryCoeffs () const override
virtual int	v_NumDGBndryCoeffs () const override
virtual int	v_GetTraceNcoeffs (const int i) const override
virtual int	v_GetTraceIntNcoeffs (const int i) const override
virtual int	v_GetTraceNumPoints (const int i) const override
virtual LibUtilities::PointsKey	v_GetTracePointsKey (const int i, const int j) const override
virtual int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset) override
virtual const LibUtilities::BasisKey	v_GetTraceBasisKey (const int i, const int k) const override
virtual bool	v_IsBoundaryInteriorExpansion () const override
virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_x, Array< OneD, NekDouble > &coords_y, Array< OneD, NekDouble > &coords_z) override
virtual void	v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation faceOrient=eDir1FwdDir1_Dir2FwdDir2) override
virtual int	v_GetEdgeNcoeffs (const int i) const override
virtual int	v_GetVertexMap (int localVertexId, bool useCoeffPacking=false) override
virtual void	v_GetInteriorMap (Array< OneD, unsigned int > &outarray) override
virtual void	v_GetBoundaryMap (Array< OneD, unsigned int > &outarray) override
virtual void	v_GetTraceCoeffMap (const unsigned int fid, Array< OneD, unsigned int > &maparray) override
virtual void	v_GetElmtTraceToTraceMap (const unsigned int fid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation faceOrient, int P, int Q) override
virtual 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
virtual DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey) override
virtual DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey) override
virtual 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_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual 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
virtual NekDouble	v_PhysEvaluate (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. More...
virtual NekDouble	v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) override
virtual NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
virtual void	v_BwdTrans_SumFacKernel (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, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0
virtual void	v_IProductWRTBase_SumFacKernel (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, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0
virtual void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrates the specified function over the domain. More...
virtual int	v_GetNedges (void) const
virtual int	v_GetEdgeNcoeffs (const int i) const
NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
virtual void	v_GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards)
virtual void	v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient, int P, int Q) override
virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr	CreateStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
	Create the static condensation of a matrix when using a boundary interior decomposition. More...
void	BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
void	LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)
virtual NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
virtual void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv, NekDouble &deriv2)
	This function performs the barycentric interpolation of the polynomial stored in coord at a point physvals using barycentric interpolation weights in direction. More...
template<int DIR>
NekDouble	BaryEvaluateBasis (const NekDouble &coord, const int &mode)
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
	Helper function to pass an unused value by reference into BaryEvaluate. More...
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)
Protected Member Functions inherited from Nektar::LocalRegions::Expansion3D
virtual 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). More...
virtual DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override
virtual void	v_AddFaceNormBoundaryInt (const int face, const ExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) override
virtual void	v_AddRobinMassMatrix (const int face, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) override
virtual StdRegions::Orientation	v_GetTraceOrient (int face) override
virtual 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 local face orientation and point distribution defined by defined in FaceExp. More...
virtual 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)
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType) override
virtual DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &transformationmatrix) override
	Build inverse and inverse transposed transformation matrix: \(\mathbf{R^{-1}}\) and \(\mathbf{R^{-T}}\). More...
virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) override
virtual void	v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) override
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)
virtual 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)
virtual void	v_ComputeLaplacianMetric ()
virtual int	v_GetCoordim () const override
virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override
virtual DNekScalMatSharedPtr	v_GetLocMatrix (const LocalRegions::MatrixKey &mkey)
virtual void	v_DropLocMatrix (const LocalRegions::MatrixKey &mkey)
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
virtual void	v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType)
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 void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
virtual NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)
virtual void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors)
virtual void	v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray)
virtual StdRegions::Orientation	v_GetTraceOrient (int trace)
virtual 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 void	v_GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient)
virtual void	v_GetTracePhysMap (const int edge, Array< OneD, int > &outarray)
virtual void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1=-1)
virtual void	v_ComputeTraceNormal (const int id)
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_AddRobinMassMatrix (const int face, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
virtual void	v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)
virtual void	v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p)
virtual void	v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp)

Private Member Functions
virtual void	v_LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp) override
virtual void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors) 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. More...

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
LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess >	m_stdMatrixManager
LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess >	m_stdStaticCondMatrixManager
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::GeometrySharedPtr	m_geom
SpatialDomains::GeomFactorsSharedPtr	m_metricinfo
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_metricinfo times the standard element length (which is 2.0) More...

Detailed Description

Defines a hexahedral local expansion.

Definition at line 50 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,
		const SpatialDomains::HexGeomSharedPtr &	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 59 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),
          std::string("HexExpMatrix")),
      m_staticCondMatrixManager(std::bind(&Expansion::CreateStaticCondMatrix,
                                          this, std::placeholders::_1),
                                std::string("HexExpStaticCondMatrix"))
{
}

HexExp() [2/2]

Nektar::LocalRegions::HexExp::HexExp

(

const HexExp &

T

)

Copy Constructor.

Parameters

T	HexExp to copy.

Definition at line 82 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()

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

overridevirtualdefault

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 474 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_metricinfo->GetDerivFactors(GetPointsKeys());
 
    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_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nq, &df[3 * dir][0], 1, tmp1.get(), 1, tmp2.get(), 1);
        Vmath::Vmul(nq, &df[3 * dir + 1][0], 1, tmp1.get(), 1, tmp3.get(), 1);
        Vmath::Vmul(nq, &df[3 * dir + 2][0], 1, tmp1.get(), 1, tmp4.get(), 1);
    }
    else
    {
        Vmath::Smul(nq, df[3 * dir][0], tmp1.get(), 1, tmp2.get(), 1);
        Vmath::Smul(nq, df[3 * dir + 1][0], tmp1.get(), 1, tmp3.get(), 1);
        Vmath::Smul(nq, df[3 * dir + 2][0], tmp1.get(), 1, tmp4.get(), 1);
    }
}

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

Referenced by v_IProductWRTDerivBase_SumFac().

v_ComputeLaplacianMetric()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1428 of file HexExp.cpp.

{
    if (m_metrics.count(eMetricQuadrature) == 0)
    {
        ComputeQuadratureMetric();
    }
 
    const SpatialDomains::GeomType type = m_metricinfo->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_metricinfo->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);
            }
            MultiplyByQuadratureMetric(m_metrics[m[i][j]], m_metrics[m[i][j]]);
        }
    }
}

References Nektar::LocalRegions::Expansion::ComputeQuadratureMetric(), Nektar::SpatialDomains::eDeformed, Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Nektar::LocalRegions::eMetricQuadrature, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), and Vmath::Vcopy().

v_ComputeTraceNormal()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 882 of file HexExp.cpp.

{
    int i;
    const SpatialDomains::GeomFactorsSharedPtr &geomFactors =
        GetGeom()->GetMetricInfo();
    SpatialDomains::GeomType type = 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 =
        geomFactors->GetDerivFactors(ptsKeys);
    const Array<OneD, const NekDouble> &jac = geomFactors->GetJac(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::LocalRegions::Expansion::GetGeom(), 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_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::StdHexExp.

Definition at line 1323 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_DetShapeType()

LibUtilities::ShapeType Nektar::LocalRegions::HexExp::v_DetShapeType ( ) const

overrideprotectedvirtual

Return the region shape using the enum-list of ShapeType.

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 659 of file HexExp.cpp.

{
    return LibUtilities::eHexahedron;
}

References Nektar::LibUtilities::eHexahedron.

v_DropLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1340 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 1350 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 664 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, Vmath::Vcopy(), and Vmath::Zero().

v_FwdTrans()

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

overrideprotectedvirtual

Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in (this)->_coeffs.

Parameters

inarray	Input array
outarray	Output array

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 299 of file HexExp.cpp.

{
    if (m_base[0]->Collocation() && m_base[1]->Collocation() &&
        m_base[2]->Collocation())
    {
        Vmath::Vcopy(GetNcoeffs(), &inarray[0], 1, &outarray[0], 1);
    }
    else
    {
        IProductWRTBase(inarray, outarray);
 
        // get Mass matrix inverse
        MatrixKey masskey(StdRegions::eInvMass, DetShapeType(), *this);
        DNekScalMatSharedPtr matsys = m_matrixManager[masskey];
 
        // copy inarray in case inarray == outarray
        DNekVec in(m_ncoeffs, outarray);
        DNekVec out(m_ncoeffs, outarray, eWrapper);
 
        out = (*matsys) * in;
    }
}

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::IProductWRTBase(), Nektar::StdRegions::StdExpansion::m_base, m_matrixManager, Nektar::StdRegions::StdExpansion::m_ncoeffs, and Vmath::Vcopy().

v_GenMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 1301 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 630 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, 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::StdHexExp.

Definition at line 647 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::StdRegions::StdExpansion.

Definition at line 610 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 1335 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 1345 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::StdRegions::StdExpansion.

Definition at line 603 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 767 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::StdHexExp.

Definition at line 1195 of file HexExp.cpp.

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

References Nektar::StdRegions::StdExpansion3D::v_HelmholtzMatrixOp_MatFree().

v_Integral()

NekDouble Nektar::LocalRegions::HexExp::v_Integral ( const Array< OneD, const NekDouble > &  inarray )

overrideprotectedvirtual

Integrate the physical point list inarray over region.

Parameters

inarray

definition of function to be returned at quadrature points of expansion.

Returns

\(\int^1_{-1}\int^1_{-1} \int^1_{-1} u(\eta_1, \eta_2, \eta_3) J[i,j,k] d \eta_1 d \eta_2 d \eta_3 \) where \(inarray[i,j,k] = u(\eta_{1i},\eta_{2j},\eta_{3k}) \) and \( J[i,j,k] \) is the Jacobian evaluated at the quadrature point.

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 103 of file HexExp.cpp.

{
    int nquad0                       = m_base[0]->GetNumPoints();
    int nquad1                       = m_base[1]->GetNumPoints();
    int nquad2                       = m_base[2]->GetNumPoints();
    Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
    NekDouble returnVal;
    Array<OneD, NekDouble> tmp(nquad0 * nquad1 * nquad2);
 
    // multiply inarray with Jacobian
 
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nquad0 * nquad1 * nquad2, &jac[0], 1,
                    (NekDouble *)&inarray[0], 1, &tmp[0], 1);
    }
    else
    {
        Vmath::Smul(nquad0 * nquad1 * nquad2, (NekDouble)jac[0],
                    (NekDouble *)&inarray[0], 1, &tmp[0], 1);
    }
 
    // call StdHexExp version;
    returnVal = StdHexExp::v_Integral(tmp);
 
    return returnVal;
}

References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Smul(), and Vmath::Vmul().

v_IProductWRTBase()

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

overrideprotectedvirtual

Calculate the inner product of inarray with respect to the elements basis.

Parameters

inarray	Input array of physical space data.
outarray	Output array of data.

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 334 of file HexExp.cpp.

{
    HexExp::v_IProductWRTBase_SumFac(inarray, outarray);
}

References v_IProductWRTBase_SumFac().

v_IProductWRTBase_SumFac()

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

overrideprotectedvirtual

Calculate the inner product of inarray with respect to the given basis B = base0 * base1 * base2.

\( \begin{array}{rcl} I_{pqr} = (\phi_{pqr}, u)_{\delta} & = & \sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \sum_{k=0}^{nq_2} \psi_{p}^{a} (\xi_{1i}) \psi_{q}^{a} (\xi_{2j}) \psi_{r}^{a} (\xi_{3k}) w_i w_j w_k u(\xi_{1,i} \xi_{2,j} \xi_{3,k}) J_{i,j,k}\\ & = & \sum_{i=0}^{nq_0} \psi_p^a(\xi_{1,i}) \sum_{j=0}^{nq_1} \psi_{q}^a(\xi_{2,j}) \sum_{k=0}^{nq_2} \psi_{r}^a u(\xi_{1i},\xi_{2j},\xi_{3k}) J_{i,j,k} \end{array} \)
where \( \phi_{pqr} (\xi_1 , \xi_2 , \xi_3) = \psi_p^a ( \xi_1) \psi_{q}^a (\xi_2) \psi_{r}^a (\xi_3) \)
which can be implemented as
\(f_{r} (\xi_{3k}) = \sum_{k=0}^{nq_3} \psi_{r}^a u(\xi_{1i},\xi_{2j},\xi_{3k}) J_{i,j,k} = {\bf B_3 U} \)
\( g_{q} (\xi_{3k}) = \sum_{j=0}^{nq_1} \psi_{q}^a (\xi_{2j}) f_{r} (\xi_{3k}) = {\bf B_2 F} \)
\( (\phi_{pqr}, u)_{\delta} = \sum_{k=0}^{nq_0} \psi_{p}^a (\xi_{3k}) g_{q} (\xi_{3k}) = {\bf B_1 G} \)

Parameters

base0	Basis to integrate wrt in first dimension.
base1	Basis to integrate wrt in second dimension.
base2	Basis to integrate wrt in third dimension.
inarray	Input array.
outarray	Output array.
coll_check	(not used)

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 372 of file HexExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
    int order0 = m_base[0]->GetNumModes();
    int order1 = m_base[1]->GetNumModes();
 
    Array<OneD, NekDouble> wsp(nquad0 * nquad1 * (nquad2 + order0) +
                               order0 * order1 * nquad2);
 
    if (multiplybyweights)
    {
        Array<OneD, NekDouble> tmp(inarray.size());
 
        MultiplyByQuadratureMetric(inarray, tmp);
        IProductWRTBase_SumFacKernel(
            m_base[0]->GetBdata(), m_base[1]->GetBdata(), m_base[2]->GetBdata(),
            tmp, outarray, wsp, true, true, true);
    }
    else
    {
        IProductWRTBase_SumFacKernel(
            m_base[0]->GetBdata(), m_base[1]->GetBdata(), m_base[2]->GetBdata(),
            inarray, outarray, wsp, true, true, true);
    }
}

References Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric().

Referenced by v_IProductWRTBase().

v_IProductWRTDerivBase()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 402 of file HexExp.cpp.

{
    HexExp::v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
}

References v_IProductWRTDerivBase_SumFac().

v_IProductWRTDerivBase_SumFac()

void Nektar::LocalRegions::HexExp::v_IProductWRTDerivBase_SumFac ( 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::StdHexExp.

Definition at line 429 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 int nm0 = m_base[0]->GetNumModes();
    const int nm1 = m_base[1]->GetNumModes();
 
    Array<OneD, NekDouble> alloc(4 * nq + m_ncoeffs + nm0 * nq2 * (nq1 + nm1));
    Array<OneD, NekDouble> tmp1(alloc);           // Quad metric
    Array<OneD, NekDouble> tmp2(alloc + nq);      // Dir1 metric
    Array<OneD, NekDouble> tmp3(alloc + 2 * nq);  // Dir2 metric
    Array<OneD, NekDouble> tmp4(alloc + 3 * nq);  // Dir3 metric
    Array<OneD, NekDouble> tmp5(alloc + 4 * nq);  // iprod tmp
    Array<OneD, NekDouble> wsp(tmp5 + m_ncoeffs); // Wsp
 
    MultiplyByQuadratureMetric(inarray, tmp1);
 
    Array<OneD, Array<OneD, NekDouble>> tmp2D{3};
    tmp2D[0] = tmp2;
    tmp2D[1] = tmp3;
    tmp2D[2] = tmp4;
 
    HexExp::v_AlignVectorToCollapsedDir(dir, tmp1, tmp2D);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                                 m_base[2]->GetBdata(), tmp2, outarray, wsp,
                                 false, true, true);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                                 m_base[2]->GetBdata(), tmp3, tmp5, wsp, true,
                                 false, true);
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                                 m_base[2]->GetDbdata(), tmp4, tmp5, wsp, true,
                                 true, false);
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
}

References ASSERTL1, Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), v_AlignVectorToCollapsedDir(), and Vmath::Vadd().

Referenced by v_IProductWRTDerivBase().

v_IProductWRTDirectionalDerivBase()

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

inlineoverrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 117 of file HexExp.h.

    {
        IProductWRTDirectionalDerivBase_SumFac(direction, inarray, outarray);
    }

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

v_IProductWRTDirectionalDerivBase_SumFac()

void Nektar::LocalRegions::HexExp::v_IProductWRTDirectionalDerivBase_SumFac ( 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 516 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;
    const int nm0 = m_base[0]->GetNumModes();
    const int nm1 = m_base[1]->GetNumModes();
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    Array<OneD, NekDouble> alloc(4 * nq + m_ncoeffs + nm0 * nq2 * (nq1 + nm1));
    Array<OneD, NekDouble> tmp1(alloc);           // Quad metric
    Array<OneD, NekDouble> tmp2(alloc + nq);      // Dir1 metric
    Array<OneD, NekDouble> tmp3(alloc + 2 * nq);  // Dir2 metric
    Array<OneD, NekDouble> tmp4(alloc + 3 * nq);  // Dir3 metric
    Array<OneD, NekDouble> tmp5(alloc + 4 * nq);  // iprod tmp
    Array<OneD, NekDouble> wsp(tmp5 + m_ncoeffs); // Wsp
 
    MultiplyByQuadratureMetric(inarray, tmp1);
 
    Array<OneD, Array<OneD, NekDouble>> dfdir(shapedim);
    Expansion::ComputeGmatcdotMF(df, direction, dfdir);
 
    Vmath::Vmul(nq, &dfdir[0][0], 1, tmp1.get(), 1, tmp2.get(), 1);
    Vmath::Vmul(nq, &dfdir[1][0], 1, tmp1.get(), 1, tmp3.get(), 1);
    Vmath::Vmul(nq, &dfdir[2][0], 1, tmp1.get(), 1, tmp4.get(), 1);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                                 m_base[2]->GetBdata(), tmp2, outarray, wsp,
                                 false, true, true);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                                 m_base[2]->GetBdata(), tmp3, tmp5, wsp, true,
                                 false, true);
 
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                                 m_base[2]->GetDbdata(), tmp4, tmp5, wsp, true,
                                 true, false);
 
    Vmath::Vadd(m_ncoeffs, tmp5, 1, outarray, 1, outarray, 1);
}

References Nektar::LocalRegions::Expansion::ComputeGmatcdotMF(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), 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::StdHexExp.

Definition at line 1158 of file HexExp.cpp.

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

References Nektar::StdRegions::StdExpansion3D::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::StdHexExp.

Definition at line 1165 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 1355 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);
 
    StdExpansion3D::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);
 
    // outarray = m = (D_xi1 * B)^T * k
    // wsp1     = n = (D_xi2 * B)^T * l
    IProductWRTBase_SumFacKernel(dbase0, base1, base2, wsp3, outarray, wsp0,
                                 false, true, true);
    IProductWRTBase_SumFacKernel(base0, dbase1, base2, wsp4, wsp2, wsp0, true,
                                 false, true);
    Vmath::Vadd(m_ncoeffs, wsp2.get(), 1, outarray.get(), 1, outarray.get(), 1);
    IProductWRTBase_SumFacKernel(base0, base1, dbase2, wsp5, wsp2, wsp0, true,
                                 true, false);
    Vmath::Vadd(m_ncoeffs, wsp2.get(), 1, outarray.get(), 1, outarray.get(), 1);
}

References ASSERTL1, Nektar::LocalRegions::Expansion::ComputeLaplacianMetric(), Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::m_ncoeffs, 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 1188 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::StdHexExp.

Definition at line 1151 of file HexExp.cpp.

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

v_NormalTraceDerivFactors()

void Nektar::LocalRegions::HexExp::v_NormalTraceDerivFactors ( Array< OneD, Array< OneD, NekDouble > > &  factors, Array< OneD, Array< OneD, NekDouble > > &  d0factors, Array< OneD, Array< OneD, NekDouble > > &  d1factors  )

overrideprivatevirtual

: 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.

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1470 of file HexExp.cpp.

{
    int nquad0 = GetNumPoints(0);
    int nquad1 = GetNumPoints(1);
    int nquad2 = GetNumPoints(2);
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    if (d0factors.size() != 6)
    {
        d0factors = Array<OneD, Array<OneD, NekDouble>>(6);
        d1factors = Array<OneD, Array<OneD, NekDouble>>(6);
        d2factors = Array<OneD, Array<OneD, NekDouble>>(6);
    }
 
    if (d0factors[0].size() != nquad0 * nquad1)
    {
        d0factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d0factors[5] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d1factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d1factors[5] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d2factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d2factors[5] = Array<OneD, NekDouble>(nquad0 * nquad1);
    }
 
    if (d0factors[1].size() != nquad0 * nquad2)
    {
        d0factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d0factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d1factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d1factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d2factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d2factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
    }
 
    if (d0factors[2].size() != nquad1 * nquad2)
    {
        d0factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d0factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d1factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d1factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d2factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d2factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
    }
 
    // Outwards normals
    const Array<OneD, const Array<OneD, NekDouble>> &normal_0 =
        GetTraceNormal(0);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_1 =
        GetTraceNormal(1);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_2 =
        GetTraceNormal(2);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_3 =
        GetTraceNormal(3);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_4 =
        GetTraceNormal(4);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_5 =
        GetTraceNormal(5);
 
    int ncoords = normal_0.size();
 
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        // faces 0 and 5
        for (int i = 0; i < nquad0 * nquad1; ++i)
        {
            d0factors[0][i] = df[0][i] * normal_0[0][i];
            d1factors[0][i] = df[1][i] * normal_0[0][i];
            d2factors[0][i] = df[2][i] * normal_0[0][i];
 
            d0factors[5][i] =
                df[0][nquad0 * nquad1 * (nquad2 - 1) + i] * normal_5[0][i];
            d1factors[5][i] =
                df[1][nquad0 * nquad1 * (nquad2 - 1) + i] * normal_5[0][i];
            d2factors[5][i] =
                df[2][nquad0 * nquad1 * (nquad2 - 1) + i] * normal_5[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                d0factors[0][i] += df[3 * n][i] * normal_0[n][i];
                d1factors[0][i] += df[3 * n + 1][i] * normal_0[n][i];
                d2factors[0][i] += df[3 * n + 2][i] * normal_0[n][i];
 
                d0factors[5][i] +=
                    df[3 * n][nquad0 * nquad1 * (nquad2 - 1) + i] *
                    normal_5[n][i];
                d1factors[5][i] +=
                    df[3 * n + 1][nquad0 * nquad1 * (nquad2 - 1) + i] *
                    normal_5[n][i];
                d2factors[5][i] +=
                    df[3 * n + 2][nquad0 * nquad1 * (nquad2 - 1) + i] *
                    normal_5[n][i];
            }
        }
 
        // faces 1 and 3
        for (int j = 0; j < nquad2; ++j)
        {
            for (int i = 0; i < nquad0; ++i)
            {
                d0factors[1][j * nquad0 + i] = df[0][j * nquad0 * nquad1 + i] *
                                               normal_1[0][j * nquad0 + i];
                d1factors[1][j * nquad0 + i] = df[1][j * nquad0 * nquad1 + i] *
                                               normal_1[0][j * nquad0 + i];
                d2factors[1][j * nquad0 + i] = df[2][j * nquad0 * nquad1 + i] *
                                               normal_1[0][j * nquad0 + i];
 
                d0factors[3][j * nquad0 + i] =
                    df[0][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
                d1factors[3][j * nquad0 + i] =
                    df[1][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
                d2factors[3][j * nquad0 + i] =
                    df[2][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
            }
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int j = 0; j < nquad2; ++j)
            {
                for (int i = 0; i < nquad0; ++i)
                {
                    d0factors[1][j * nquad0 + i] +=
                        df[3 * n][j * nquad0 * nquad1 + i] *
                        normal_1[0][j * nquad0 + i];
                    d1factors[1][j * nquad0 + i] +=
                        df[3 * n + 1][j * nquad0 * nquad1 + i] *
                        normal_1[0][j * nquad0 + i];
                    d2factors[1][j * nquad0 + i] +=
                        df[3 * n + 2][j * nquad0 * nquad1 + i] *
                        normal_1[0][j * nquad0 + i];
 
                    d0factors[3][j * nquad0 + i] +=
                        df[3 * n][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                    d1factors[3][j * nquad0 + i] +=
                        df[3 * n + 1][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                    d2factors[3][j * nquad0 + i] +=
                        df[3 * n + 2][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                }
            }
        }
 
        // faces 2 and 4
        for (int j = 0; j < nquad2; ++j)
        {
            for (int i = 0; i < nquad1; ++i)
            {
                d0factors[2][j * nquad1 + i] =
                    df[0][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d1factors[2][j * nquad1 + i] =
                    df[1][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d2factors[2][j * nquad1 + i] =
                    df[2][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
 
                d0factors[4][j * nquad1 + i] =
                    df[0][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
                d1factors[4][j * nquad1 + i] =
                    df[1][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
                d2factors[4][j * nquad1 + i] =
                    df[2][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
            }
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int j = 0; j < nquad2; ++j)
            {
                for (int i = 0; i < nquad1; ++i)
                {
                    d0factors[2][j * nquad1 + i] +=
                        df[3 * n][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad1 + i];
                    d1factors[2][j * nquad1 + i] +=
                        df[3 * n + 1]
                          [j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad1 + i];
                    d2factors[2][j * nquad1 + i] +=
                        df[3 * n + 2]
                          [j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad1 + i];
 
                    d0factors[4][j * nquad1 + i] +=
                        df[3 * n][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad1 + i];
                    d1factors[4][j * nquad1 + i] +=
                        df[3 * n + 1][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad1 + i];
                    d2factors[4][j * nquad1 + i] +=
                        df[3 * n + 2][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad1 + i];
                }
            }
        }
    }
    else
    {
        // Faces 0 and 5
        for (int i = 0; i < nquad0 * nquad1; ++i)
        {
            d0factors[0][i] = df[0][0] * normal_0[0][i];
            d0factors[5][i] = df[0][0] * normal_5[0][i];
 
            d1factors[0][i] = df[1][0] * normal_0[0][i];
            d1factors[5][i] = df[1][0] * normal_5[0][i];
 
            d2factors[0][i] = df[2][0] * normal_0[0][i];
            d2factors[5][i] = df[2][0] * normal_5[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                d0factors[0][i] += df[3 * n][0] * normal_0[n][i];
                d0factors[5][i] += df[3 * n][0] * normal_5[n][i];
 
                d1factors[0][i] += df[3 * n + 1][0] * normal_0[n][i];
                d1factors[5][i] += df[3 * n + 1][0] * normal_5[n][i];
 
                d2factors[0][i] += df[3 * n + 2][0] * normal_0[n][i];
                d2factors[5][i] += df[3 * n + 2][0] * normal_5[n][i];
            }
        }
 
        // faces 1 and 3
        for (int i = 0; i < nquad0 * nquad2; ++i)
        {
            d0factors[1][i] = df[0][0] * normal_1[0][i];
            d0factors[3][i] = df[0][0] * normal_3[0][i];
 
            d1factors[1][i] = df[1][0] * normal_1[0][i];
            d1factors[3][i] = df[1][0] * normal_3[0][i];
 
            d2factors[1][i] = df[2][0] * normal_1[0][i];
            d2factors[3][i] = df[2][0] * normal_3[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad2; ++i)
            {
                d0factors[1][i] += df[3 * n][0] * normal_1[n][i];
                d0factors[3][i] += df[3 * n][0] * normal_3[n][i];
 
                d1factors[1][i] += df[3 * n + 1][0] * normal_1[n][i];
                d1factors[3][i] += df[3 * n + 1][0] * normal_3[n][i];
 
                d2factors[1][i] += df[3 * n + 2][0] * normal_1[n][i];
                d2factors[3][i] += df[3 * n + 2][0] * normal_3[n][i];
            }
        }
 
        // faces 2 and 4
        for (int i = 0; i < nquad1 * nquad2; ++i)
        {
            d0factors[2][i] = df[0][0] * normal_2[0][i];
            d0factors[4][i] = df[0][0] * normal_4[0][i];
 
            d1factors[2][i] = df[1][0] * normal_2[0][i];
            d1factors[4][i] = df[1][0] * normal_4[0][i];
 
            d2factors[2][i] = df[2][0] * normal_2[0][i];
            d2factors[4][i] = df[2][0] * normal_4[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad1 * nquad2; ++i)
            {
                d0factors[2][i] += df[3 * n][0] * normal_2[n][i];
                d0factors[4][i] += df[3 * n][0] * normal_4[n][i];
 
                d1factors[2][i] += df[3 * n + 1][0] * normal_2[n][i];
                d1factors[4][i] += df[3 * n + 1][0] * normal_4[n][i];
 
                d2factors[2][i] += df[3 * n + 2][0] * normal_2[n][i];
                d2factors[4][i] += df[3 * n + 2][0] * normal_4[n][i];
            }
        }
    }
}

References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::LocalRegions::Expansion::GetTraceNormal(), and Nektar::LocalRegions::Expansion::m_metricinfo.

v_PhysDeriv() [1/2]

void Nektar::LocalRegions::HexExp::v_PhysDeriv ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  out_d0, Array< OneD, NekDouble > &  out_d1, Array< OneD, NekDouble > &  out_d2  )

overrideprotectedvirtual

Calculate the derivative of the physical points.

For Hexahedral region can use the Tensor_Deriv function defined under StdExpansion.

Parameters

inarray	Input array
out_d0	Derivative of inarray in first direction.
out_d1	Derivative of inarray in second direction.
out_d2	Derivative of inarray in third direction.

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 144 of file HexExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
    int ntot   = nquad0 * nquad1 * nquad2;
 
    Array<TwoD, const NekDouble> df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
    Array<OneD, NekDouble> Diff0 = Array<OneD, NekDouble>(ntot);
    Array<OneD, NekDouble> Diff1 = Array<OneD, NekDouble>(ntot);
    Array<OneD, NekDouble> Diff2 = Array<OneD, NekDouble>(ntot);
 
    StdHexExp::v_PhysDeriv(inarray, Diff0, Diff1, Diff2);
 
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        if (out_d0.size())
        {
            Vmath::Vmul(ntot, &df[0][0], 1, &Diff0[0], 1, &out_d0[0], 1);
            Vmath::Vvtvp(ntot, &df[1][0], 1, &Diff1[0], 1, &out_d0[0], 1,
                         &out_d0[0], 1);
            Vmath::Vvtvp(ntot, &df[2][0], 1, &Diff2[0], 1, &out_d0[0], 1,
                         &out_d0[0], 1);
        }
 
        if (out_d1.size())
        {
            Vmath::Vmul(ntot, &df[3][0], 1, &Diff0[0], 1, &out_d1[0], 1);
            Vmath::Vvtvp(ntot, &df[4][0], 1, &Diff1[0], 1, &out_d1[0], 1,
                         &out_d1[0], 1);
            Vmath::Vvtvp(ntot, &df[5][0], 1, &Diff2[0], 1, &out_d1[0], 1,
                         &out_d1[0], 1);
        }
 
        if (out_d2.size())
        {
            Vmath::Vmul(ntot, &df[6][0], 1, &Diff0[0], 1, &out_d2[0], 1);
            Vmath::Vvtvp(ntot, &df[7][0], 1, &Diff1[0], 1, &out_d2[0], 1,
                         &out_d2[0], 1);
            Vmath::Vvtvp(ntot, &df[8][0], 1, &Diff2[0], 1, &out_d2[0], 1,
                         &out_d2[0], 1);
        }
    }
    else // regular geometry
    {
        if (out_d0.size())
        {
            Vmath::Smul(ntot, df[0][0], &Diff0[0], 1, &out_d0[0], 1);
            Blas::Daxpy(ntot, df[1][0], &Diff1[0], 1, &out_d0[0], 1);
            Blas::Daxpy(ntot, df[2][0], &Diff2[0], 1, &out_d0[0], 1);
        }
 
        if (out_d1.size())
        {
            Vmath::Smul(ntot, df[3][0], &Diff0[0], 1, &out_d1[0], 1);
            Blas::Daxpy(ntot, df[4][0], &Diff1[0], 1, &out_d1[0], 1);
            Blas::Daxpy(ntot, df[5][0], &Diff2[0], 1, &out_d1[0], 1);
        }
 
        if (out_d2.size())
        {
            Vmath::Smul(ntot, df[6][0], &Diff0[0], 1, &out_d2[0], 1);
            Blas::Daxpy(ntot, df[7][0], &Diff1[0], 1, &out_d2[0], 1);
            Blas::Daxpy(ntot, df[8][0], &Diff2[0], 1, &out_d2[0], 1);
        }
    }
}

References Blas::Daxpy(), Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Smul(), Vmath::Vmul(), and Vmath::Vvtvp().

v_PhysDeriv() [2/2]

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

overrideprotectedvirtual

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

Parameters

dir	Direction in which to compute derivative. Valid values are 0, 1, 2.
inarray	Input array.
outarray	Output array.

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 225 of file HexExp.cpp.

{
    switch (dir)
    {
        case 0:
        {
            PhysDeriv(inarray, outarray, NullNekDouble1DArray,
                      NullNekDouble1DArray);
        }
        break;
        case 1:
        {
            PhysDeriv(inarray, NullNekDouble1DArray, outarray,
                      NullNekDouble1DArray);
        }
        break;
        case 2:
        {
            PhysDeriv(inarray, NullNekDouble1DArray, NullNekDouble1DArray,
                      outarray);
        }
        break;
        default:
        {
            ASSERTL1(false, "input dir is out of range");
        }
        break;
    }
}

References ASSERTL1, Nektar::NullNekDouble1DArray, and Nektar::StdRegions::StdExpansion::PhysDeriv().

v_PhysDirectionalDeriv()

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

overrideprotectedvirtual

Physical derivative along a direction vector.

See also

StdRegions::StdExpansion::PhysDirectionalDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 257 of file HexExp.cpp.

{
 
    int shapedim = 3;
    int nquad0   = m_base[0]->GetNumPoints();
    int nquad1   = m_base[1]->GetNumPoints();
    int nquad2   = m_base[2]->GetNumPoints();
    int ntot     = nquad0 * nquad1 * nquad2;
 
    Array<TwoD, const NekDouble> df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
    Array<OneD, NekDouble> Diff0 = Array<OneD, NekDouble>(ntot);
    Array<OneD, NekDouble> Diff1 = Array<OneD, NekDouble>(ntot);
    Array<OneD, NekDouble> Diff2 = Array<OneD, NekDouble>(ntot);
 
    StdHexExp::v_PhysDeriv(inarray, Diff0, Diff1, Diff2);
 
    Array<OneD, Array<OneD, NekDouble>> dfdir(shapedim);
    Expansion::ComputeGmatcdotMF(df, direction, dfdir);
 
    Vmath::Vmul(ntot, &dfdir[0][0], 1, &Diff0[0], 1, &outarray[0], 1);
    Vmath::Vvtvp(ntot, &dfdir[1][0], 1, &Diff1[0], 1, &outarray[0], 1,
                 &outarray[0], 1);
    Vmath::Vvtvp(ntot, &dfdir[2][0], 1, &Diff2[0], 1, &outarray[0], 1,
                 &outarray[0], 1);
}

References Nektar::LocalRegions::Expansion::ComputeGmatcdotMF(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Vmul(), and Vmath::Vvtvp().

v_PhysEvaluate() [1/2]

NekDouble Nektar::LocalRegions::HexExp::v_PhysEvaluate ( const Array< OneD, const NekDouble > &  coords, const Array< OneD, const NekDouble > &  physvals  )

overrideprotectedvirtual

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

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

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

is evaluated using Lagrangian interpolants through the quadrature points:

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

This function requires that the physical value array \(\mathbf{u}\) (implemented as the attribute #phys) is set.

Parameters

coords

the coordinates of the single point

Returns

returns the value of the expansion at the single point

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 583 of file HexExp.cpp.

{
    Array<OneD, NekDouble> Lcoord = Array<OneD, NekDouble>(3);
 
    ASSERTL0(m_geom, "m_geom not defined");
    m_geom->GetLocCoords(coord, Lcoord);
    return StdExpansion3D::v_PhysEvaluate(Lcoord, physvals);
}

References ASSERTL0, and Nektar::LocalRegions::Expansion::m_geom.

v_PhysEvaluate() [2/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 593 of file HexExp.cpp.

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

References ASSERTL0, 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 1213 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_StdPhysEvaluate()

NekDouble Nektar::LocalRegions::HexExp::v_StdPhysEvaluate ( const Array< OneD, const NekDouble > &  Lcoord, const Array< OneD, const NekDouble > &  physvals  )

overrideprotectedvirtual

Given the local cartesian coordinate Lcoord evaluate the value of physvals at this point by calling through to the StdExpansion method

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 575 of file HexExp.cpp.

{
    // Evaluate point in local coordinates.
    return StdExpansion3D::v_PhysEvaluate(Lcoord, physvals);
}

v_SVVLaplacianFilter()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdHexExp.

Definition at line 1271 of file HexExp.cpp.

{
    int nq = GetTotPoints();
 
    // Calculate sqrt of the Jacobian
    Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
    Array<OneD, NekDouble> sqrt_jac(nq);
    if (m_metricinfo->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::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::LocalRegions::Expansion::m_metricinfo, 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::StdHexExp.

Definition at line 1173 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 1181 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 246 of file HexExp.h.

Referenced by v_DropLocMatrix(), v_FwdTrans(), and v_GetLocMatrix().

m_staticCondMatrixManager

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

private

Definition at line 248 of file HexExp.h.

Referenced by v_DropLocStaticCondMatrix(), and v_GetLocStaticCondMatrix().