#include <TriExp.h>

Inheritance diagram for Nektar::LocalRegions::TriExp:

Collaboration diagram for Nektar::LocalRegions::TriExp:

Public Member Functions
	TriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const SpatialDomains::TriGeomSharedPtr &geom)
	Constructor using BasisKey class for quadrature points and order definition. More...

	TriExp (const TriExp &T)

	~TriExp ()

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

	StdTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)

	StdTriExp (const StdTriExp &T)

	~StdTriExp ()

Public Member Functions inherited from Nektar::StdRegions::StdExpansion2D
	StdExpansion2D ()

	StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)

	StdExpansion2D (const StdExpansion2D &T)

virtual	~StdExpansion2D ()

void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d0, Array< OneD, NekDouble > &outarray_d1)
	Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points. More...

NekDouble	Integral (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &w0, const Array< OneD, const NekDouble > &w1)

void	BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)

void	IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)

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	GetNedges () const
	This function returns the number of edges of the expansion domain. More...

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

int	GetTotalEdgeIntNcoeffs () const

int	GetEdgeNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th edge. More...

int	DetCartesianDirOfEdge (const int edge)

const LibUtilities::BasisKey	DetEdgeBasisKey (const int i) const

const LibUtilities::BasisKey	DetFaceBasisKey (const int i, const int k) const

int	GetFaceNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th face. More...

int	GetFaceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th face. More...

int	GetFaceIntNcoeffs (const int i) const

int	GetTotalFaceIntNcoeffs () const

int	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th edge/face. More...

LibUtilities::PointsKey	GetFacePointsKey (const int i, const int j) const

int	NumBndryCoeffs (void) const

int	NumDGBndryCoeffs (void) const

LibUtilities::BasisType	GetEdgeBasisType (const int i) const
	This function returns the type of expansion basis on the i-th edge. More...

const LibUtilities::PointsKey	GetNodalPointsKey () const
	This function returns the type of expansion Nodal point type if defined. More...

int	GetNfaces () const
	This function returns the number of faces of the expansion domain. More...

int	GetNtrace () 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...

boost::shared_ptr< StdExpansion >	GetStdExp (void) const

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

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion ()

bool	IsNodalNonTensorialExp ()

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

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

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

NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)
	This function integrates the specified function over the domain. More...

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

void	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	this function calculates the inner product of a given function f with the different modes of the expansion More...

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

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

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)

IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)

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

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

virtual void	SetUpPhysNormals (const int edge)

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)

StdRegions::Orientation	GetForient (int face)

StdRegions::Orientation	GetEorient (int edge)

StdRegions::Orientation	GetPorient (int point)

StdRegions::Orientation	GetCartesianEorient (int edge)

void	SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)

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

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	GetEdgeInteriorMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)

void	GetFaceNumModes (const int fid, const Orientation faceOrient, int &numModes0, int &numModes1)

void	GetFaceInteriorMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)

void	GetEdgeToElementMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int P=-1)

void	GetFaceToElementMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int nummodesA=-1, int nummodesB=-1)

void	GetEdgePhysVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Extract the physical values along edge edge from inarray into outarray following the local edge orientation and point distribution defined by defined in EdgeExp. More...

void	GetEdgePhysVals (const int edge, const boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GetTracePhysVals (const int edge, const boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

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

void	GetEdgeInterpVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GetEdgeQFactors (const int edge, 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	GetFacePhysVals (const int face, const boost::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=eNoOrientation)

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

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

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

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

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

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

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

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

DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)

void	PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)

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

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

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

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

void	StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)

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

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

void	AddRobinEdgeContribution (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, Array< OneD, NekDouble > &coeffs)

NekDouble	PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

NekDouble	PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

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

const boost::shared_ptr < SpatialDomains::GeomFactors > &	GetMetricInfo (void) const

virtual int	v_GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id. More...

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

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

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 StdRegions::Orientation	v_GetForient (int face)

virtual StdRegions::Orientation	v_GetPorient (int point)

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 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 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 NormalVector &	GetEdgeNormal (const int edge) const

void	ComputeEdgeNormal (const int edge)

void	NegateEdgeNormal (const int edge)

bool	EdgeNormalNegated (const int edge)

void	ComputeFaceNormal (const int face)

void	NegateFaceNormal (const int face)

bool	FaceNormalNegated (const int face)

void	ComputeVertexNormal (const int vertex)

const NormalVector &	GetFaceNormal (const int face) const

const NormalVector &	GetVertexNormal (const int vertex) const

const NormalVector &	GetSurfaceNormal (const int id) const

const LibUtilities::PointsKeyVector	GetPointsKeys () const

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

Array< OneD, unsigned int >	GetFaceInverseBoundaryMap (int fid, StdRegions::Orientation faceOrient=eNoOrientation)

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 >
boost::shared_ptr< T >	as ()

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

Public Member Functions inherited from Nektar::LocalRegions::Expansion2D
	Expansion2D (SpatialDomains::Geometry2DSharedPtr pGeom)

virtual	~Expansion2D ()

void	SetTraceToGeomOrientation (Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &inout)

Expansion1DSharedPtr	GetEdgeExp (int edge, bool SetUpNormal=true)

void	SetEdgeExp (const int edge, Expansion1DSharedPtr &e)

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

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

void	AddEdgeBoundaryInt (const int edge, ExpansionSharedPtr &EdgeExp, Array< OneD, NekDouble > &edgePhys, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)

void	AddHDGHelmholtzEdgeTerms (const NekDouble tau, const int edge, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &edgePhys, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray)

void	AddHDGHelmholtzTraceTerms (const NekDouble tau, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray)

Expansion3DSharedPtr	GetLeftAdjacentElementExp () const

Expansion3DSharedPtr	GetRightAdjacentElementExp () const

int	GetLeftAdjacentElementFace () const

int	GetRightAdjacentElementFace () const

void	SetAdjacentElementExp (int face, Expansion3DSharedPtr &f)

SpatialDomains::Geometry2DSharedPtr	GetGeom2D () const

void	ReOrientEdgePhysMap (const int nvert, const StdRegions::Orientation orient, const int nq0, Array< OneD, int > &idmap)

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

	Expansion (const Expansion &pSrc)

virtual	~Expansion ()

DNekScalMatSharedPtr	GetLocMatrix (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 ()

virtual const SpatialDomains::GeomFactorsSharedPtr &	v_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 boost::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 boost::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

void	AddFaceNormBoundaryInt (const int face, const boost::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)

Protected Member Functions
virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray)
	Integrates the specified function over the domain. More...

virtual void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
	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)
	Calculate the derivative of the physical points in a given direction. More...

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

virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Transform a given function from physical quadrature space to coefficient space. More...

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

virtual void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray. More...

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

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

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

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

virtual void	v_IProductWRTDerivBase_MatOp (const int dir, const Array< OneD, const NekDouble > &inarray, 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 StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const

virtual StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const

virtual void	v_GetCoord (const Array< OneD, const NekDouble > &Lcoords, Array< OneD, NekDouble > &coords)

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

virtual NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)

virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coord, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

virtual void	v_GetEdgePhysVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Extract the physical values along edge edge from inarray into outarray following the local edge orientation and point distribution defined by defined in EdgeExp. More...

virtual void	v_GetEdgePhysVals (const int edge, const StdRegions::StdExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_GetTracePhysVals (const int edge, const StdRegions::StdExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient)

virtual void	v_GetEdgeInterpVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_GetEdgeQFactors (const int edge, Array< OneD, NekDouble > &outarray)

virtual void	v_ComputeEdgeNormal (const int edge)

virtual int	v_GetCoordim ()

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

virtual StdRegions::Orientation	v_GetEorient (int edge)

virtual StdRegions::Orientation	v_GetCartesianEorient (int edge)

virtual const LibUtilities::BasisSharedPtr &	v_GetBasis (int dir) const

virtual int	v_GetNumPoints (const int dir) const

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

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

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

virtual DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)

virtual DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)

virtual DNekScalMatSharedPtr	v_GetLocMatrix (const MatrixKey &mkey)

virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const MatrixKey &mkey)

void	v_DropLocStaticCondMatrix (const MatrixKey &mkey)

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

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

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

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

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

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

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

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

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

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

virtual void	v_ComputeLaplacianMetric ()

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

Protected Member Functions inherited from Nektar::StdRegions::StdTriExp
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=NullNekDouble1DArray)

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

virtual void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Backward tranform for triangular elements. More...

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

virtual void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)

virtual void	v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)

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

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

virtual int	v_GetNverts () const

virtual int	v_GetNedges () const

virtual LibUtilities::ShapeType	v_DetShapeType () const

virtual int	v_NumBndryCoeffs () const

virtual int	v_NumDGBndryCoeffs () const

virtual int	v_GetEdgeNcoeffs (const int i) const

virtual int	v_GetEdgeNumPoints (const int i) const

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

virtual LibUtilities::BasisType	v_GetEdgeBasisType (const int i) const

virtual bool	v_IsBoundaryInteriorExpansion ()

virtual int	v_DetCartesianDirOfEdge (const int edge)

virtual const LibUtilities::BasisKey	v_DetEdgeBasisKey (const int edge) const

virtual void	v_GetEdgeToElementMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int P=-1)

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

virtual void	v_GetEdgeInteriorMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)

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

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

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

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

Protected Member Functions inherited from Nektar::StdRegions::StdExpansion2D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)

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

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

virtual int	v_GetTraceNcoeffs (const int i) const

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...

IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)
	Create an IndexMap which contains mapping information linking any specific element shape with either its boundaries, edges, faces, verteces, etc. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Protected Member Functions inherited from Nektar::LocalRegions::Expansion2D
virtual void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &edgeCoeffs, Array< OneD, NekDouble > &out_d)

virtual void	v_AddEdgeNormBoundaryInt (const int edge, const ExpansionSharedPtr &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 ExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

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

virtual void	v_AddRobinEdgeContribution (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, Array< OneD, NekDouble > &coeffs)

virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)

void	GetPhysEdgeVarCoeffsFromElement (const int edge, ExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &varcoeff, Array< OneD, NekDouble > &outarray)

void	ReOrientQuadEdgePhysMap (const StdRegions::Orientation orient, const int nq0, Array< OneD, int > &idmap)

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

virtual void	v_NegateEdgeNormal (const int edge)

virtual bool	v_EdgeNormalNegated (const int edge)

virtual void	v_SetUpPhysNormals (const int edge)

const StdRegions::NormalVector &	v_GetEdgeNormal (const int edge) const

const StdRegions::NormalVector &	v_GetSurfaceNormal (const int id) const

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

void	ComputeQuadratureMetric ()

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

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

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

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

Private Member Functions
	TriExp ()

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

LibUtilities::NekManager < IndexMapKey, IndexMapValues, IndexMapKey::opLess >	m_IndexMapManager

Protected Attributes inherited from Nektar::LocalRegions::Expansion2D
std::vector< Expansion1DWeakPtr >	m_edgeExp

std::vector< bool >	m_requireNeg

std::map< int, StdRegions::NormalVector >	m_edgeNormals

std::map< int, bool >	m_negatedNormals

Expansion3DWeakPtr	m_elementLeft

Expansion3DWeakPtr	m_elementRight

int	m_elementFaceLeft

int	m_elementFaceRight

Protected Attributes inherited from Nektar::LocalRegions::Expansion
SpatialDomains::GeometrySharedPtr	m_geom

SpatialDomains::GeomFactorsSharedPtr	m_metricinfo

MetricMap	m_metrics

Detailed Description

Definition at line 51 of file TriExp.h.

Constructor & Destructor Documentation

Nektar::LocalRegions::TriExp::TriExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		const SpatialDomains::TriGeomSharedPtr &	geom
	)

Constructor using BasisKey class for quadrature points and order definition.

Definition at line 47 of file TriExp.cpp.

                                                                   :
             StdExpansion  (LibUtilities::StdTriData::getNumberOfCoefficients(Ba.GetNumModes(),(Bb.GetNumModes())),2,Ba,Bb),
             StdExpansion2D(LibUtilities::StdTriData::getNumberOfCoefficients(Ba.GetNumModes(),(Bb.GetNumModes())),Ba,Bb),
             StdTriExp(Ba,Bb),
             Expansion     (geom),
             Expansion2D   (geom),
             m_matrixManager(
                     boost::bind(&TriExp::CreateMatrix, this, _1),
                     std::string("TriExpMatrix")),
             m_staticCondMatrixManager(
                     boost::bind(&TriExp::CreateStaticCondMatrix, this, _1),
                     std::string("TriExpStaticCondMatrix"))
         {
         }

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

Definition at line 65 of file TriExp.cpp.

                                      :
             StdExpansion(T),
             StdExpansion2D(T),
             StdTriExp(T),
             Expansion(T),
             Expansion2D(T),
             m_matrixManager(T.m_matrixManager),
             m_staticCondMatrixManager(T.m_staticCondMatrixManager)
         {
         }

Nektar::LocalRegions::TriExp::~TriExp ( )

Definition at line 77 of file TriExp.cpp.

78 {

79 }

Nektar::LocalRegions::TriExp::TriExp ( )

private

Member Function Documentation

DNekScalMatSharedPtr Nektar::LocalRegions::TriExp::CreateMatrix ( const MatrixKey & mkey )

protectedvirtual

Definition at line 1083 of file TriExp.cpp.

         {
             DNekScalMatSharedPtr returnval;
             LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
 
             ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,"Geometric information is not set up");
 
             switch(mkey.GetMatrixType())
             {
             case StdRegions::eMass:
                 {
                     if((m_metricinfo->GetGtype() == SpatialDomains::eDeformed)||
                        (mkey.GetNVarCoeff()))
                     {
                         NekDouble one = 1.0;
                         DNekMatSharedPtr mat = GenMatrix(mkey);
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                     }
                     else
                     {
                         NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                         DNekMatSharedPtr mat = GetStdMatrix(mkey);
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,mat);
                     }
                 }
                 break;
             case StdRegions::eInvMass:
                 {
                     if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
                     {
                         NekDouble one = 1.0;
                         StdRegions::StdMatrixKey masskey(StdRegions::eMass,DetShapeType(),
                                                          *this);
                         DNekMatSharedPtr mat = GenMatrix(masskey);
                         mat->Invert();
 
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                     }
                     else
                     {
                         NekDouble fac = 1.0/(m_metricinfo->GetJac(ptsKeys))[0];
                         DNekMatSharedPtr mat = GetStdMatrix(mkey);
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(fac,mat);
 
                     }
                 }
                 break;
             case StdRegions::eWeakDeriv0:
             case StdRegions::eWeakDeriv1:
             case StdRegions::eWeakDeriv2:
                 {
                     if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed || mkey.GetNVarCoeff())
                     {
                         NekDouble one = 1.0;
                         DNekMatSharedPtr mat = GenMatrix(mkey);
 
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                     }
                     else
                     {
                         NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                         Array<TwoD, const NekDouble> df = m_metricinfo->GetDerivFactors(ptsKeys);
                         int dir = 0;
                         switch(mkey.GetMatrixType())
                         {
                             case StdRegions::eWeakDeriv0:
                                 dir = 0;
                                 break;
                             case StdRegions::eWeakDeriv1:
                                 dir = 1;
                                 break;
                             case StdRegions::eWeakDeriv2:
                                 dir = 2;
                                 break;
                             default:
                                 break;
                         }
 
                         MatrixKey deriv0key(StdRegions::eWeakDeriv0,
                                             mkey.GetShapeType(), *this);
                         MatrixKey deriv1key(StdRegions::eWeakDeriv1,
                                             mkey.GetShapeType(), *this);
 
                         DNekMat &deriv0 = *GetStdMatrix(deriv0key);
                         DNekMat &deriv1 = *GetStdMatrix(deriv1key);
 
                         int rows = deriv0.GetRows();
                         int cols = deriv1.GetColumns();
 
                         DNekMatSharedPtr WeakDeriv = MemoryManager<DNekMat>::AllocateSharedPtr(rows,cols);
                         (*WeakDeriv) = df[2*dir][0]*deriv0 + df[2*dir+1][0]*deriv1;
 
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,WeakDeriv);
                     }
                 }
                 break;
             case StdRegions::eLaplacian:
                 {
                     if( (m_metricinfo->GetGtype() == SpatialDomains::eDeformed) ||
                         (mkey.GetNVarCoeff() > 0)||(mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio)))
                     {
                         NekDouble one = 1.0;
                         DNekMatSharedPtr mat = GenMatrix(mkey);
 
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                     }
                     else
                     {
                         MatrixKey lap00key(StdRegions::eLaplacian00,
                                            mkey.GetShapeType(), *this);
                         MatrixKey lap01key(StdRegions::eLaplacian01,
                                            mkey.GetShapeType(), *this);
                         MatrixKey lap11key(StdRegions::eLaplacian11,
                                            mkey.GetShapeType(), *this);
 
                         DNekMat &lap00 = *GetStdMatrix(lap00key);
                         DNekMat &lap01 = *GetStdMatrix(lap01key);
                         DNekMat &lap11 = *GetStdMatrix(lap11key);
 
                         NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                         Array<TwoD, const NekDouble> gmat =
                                                 m_metricinfo->GetGmat(ptsKeys);
 
                         int rows = lap00.GetRows();
                         int cols = lap00.GetColumns();
 
                         DNekMatSharedPtr lap = MemoryManager<DNekMat>::AllocateSharedPtr(rows,cols);
 
                         (*lap) = gmat[0][0] * lap00 +
                                  gmat[1][0] * (lap01 + Transpose(lap01)) +
                                  gmat[3][0] * lap11;
 
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,lap);
                     }
                 }
                 break;
             case StdRegions::eInvLaplacianWithUnityMean:
                 {
                     DNekMatSharedPtr mat = GenMatrix(mkey);
                     returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0,mat);
                 }
                 break;
             case StdRegions::eHelmholtz:
                 {
                     NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorLambda);
 
                     MatrixKey masskey(mkey, StdRegions::eMass);
                     DNekScalMat &MassMat = *(this->m_matrixManager[masskey]);
 
                     MatrixKey lapkey(mkey, StdRegions::eLaplacian);
                     DNekScalMat &LapMat = *(this->m_matrixManager[lapkey]);
 
                     int rows = LapMat.GetRows();
                     int cols = LapMat.GetColumns();
 
                     DNekMatSharedPtr helm = MemoryManager<DNekMat>::AllocateSharedPtr(rows,cols);
 
                     NekDouble one = 1.0;
                     (*helm) = LapMat + factor*MassMat;
 
                     returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,helm);
                 }
                 break;
             case StdRegions::eIProductWRTBase:
                 {
                     if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
                     {
                         NekDouble one = 1.0;
                         DNekMatSharedPtr mat = GenMatrix(mkey);
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                     }
                     else
                     {
                         NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                         DNekMatSharedPtr mat = GetStdMatrix(mkey);
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,mat);
                     }
                 }
                 break;
             case StdRegions::eIProductWRTDerivBase0:
             case StdRegions::eIProductWRTDerivBase1:
             case StdRegions::eIProductWRTDerivBase2:
                 {
                     if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
                     {
                         NekDouble one = 1.0;
                         DNekMatSharedPtr mat = GenMatrix(mkey);
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                     }
                     else
                     {
                         NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
 
                         const Array<TwoD, const NekDouble>& df = m_metricinfo->GetDerivFactors(ptsKeys);
                         int dir = 0;
 
                         switch(mkey.GetMatrixType())
                         {
                             case StdRegions::eIProductWRTDerivBase0:
                                 dir = 0;
                                 break;
                             case StdRegions::eIProductWRTDerivBase1:
                                 dir = 1;
                                 break;
                             case StdRegions::eIProductWRTDerivBase2:
                                 dir = 2;
                                 break;
                             default:
                                 break;
                         }
 
                         MatrixKey iProdDeriv0Key(StdRegions::eIProductWRTDerivBase0,
                                                  mkey.GetShapeType(), *this);
                         MatrixKey iProdDeriv1Key(StdRegions::eIProductWRTDerivBase1,
                                                  mkey.GetShapeType(), *this);
 
                         DNekMat &stdiprod0 = *GetStdMatrix(iProdDeriv0Key);
                         DNekMat &stdiprod1 = *GetStdMatrix(iProdDeriv0Key);
 
                         int rows = stdiprod0.GetRows();
                         int cols = stdiprod1.GetColumns();
 
                         DNekMatSharedPtr mat = MemoryManager<DNekMat>::AllocateSharedPtr(rows,cols);
                         (*mat) = df[2*dir][0]*stdiprod0 + df[2*dir+1][0]*stdiprod1;
 
                         returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,mat);
                     }
                 }
                 break;
 
             case StdRegions::eInvHybridDGHelmholtz:
                 {
                     NekDouble one = 1.0;
 
                     MatrixKey hkey(StdRegions::eHybridDGHelmholtz, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
 
                     DNekMatSharedPtr mat = GenMatrix(hkey);
 
                     mat->Invert();
                     returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                 }
                 break;
             case StdRegions::ePreconLinearSpace:
                 {
                     NekDouble one = 1.0;
                     MatrixKey helmkey(StdRegions::eHelmholtz, mkey.GetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                     DNekScalBlkMatSharedPtr helmStatCond = GetLocStaticCondMatrix(helmkey);
                     DNekScalMatSharedPtr A =helmStatCond->GetBlock(0,0);
                     DNekMatSharedPtr R=BuildVertexMatrix(A);
 
                     returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,R);
                 }
                 break;
             default:
                 {
                     NekDouble        one = 1.0;
                     DNekMatSharedPtr mat = GenMatrix(mkey);
 
                     returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                 }
                 break;
             }
 
             return returnval;
         }

DNekScalBlkMatSharedPtr Nektar::LocalRegions::TriExp::CreateStaticCondMatrix ( const MatrixKey & mkey )

protectedvirtual

Definition at line 1350 of file TriExp.cpp.

         {
             DNekScalBlkMatSharedPtr returnval;
             LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
 
             ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,"Geometric information is not set up");
 
             // set up block matrix system
             unsigned int nbdry = NumBndryCoeffs();
             unsigned int nint = (unsigned int)(m_ncoeffs - nbdry);
             unsigned int exp_size[] = {nbdry,nint};
             unsigned int nblks = 2;
             returnval = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(nblks,nblks,exp_size,exp_size); //Really need a constructor which takes Arrays
             NekDouble factor = 1.0;
 
             switch(mkey.GetMatrixType())
             {
                 // this can only use stdregions statically condensed system for mass matrix
             case StdRegions::eMass:
                 if((m_metricinfo->GetGtype() == SpatialDomains::eDeformed)||(mkey.GetNVarCoeff()))
                 {
                     factor = 1.0;
                     goto UseLocRegionsMatrix;
                 }
                 else
                 {
                     factor = (m_metricinfo->GetJac(ptsKeys))[0];
                     goto UseStdRegionsMatrix;
                 }
                 break;
             default:     // use Deformed case for both regular and deformed geometries
                 factor = 1.0;
                 goto UseLocRegionsMatrix;
                 break;
             UseStdRegionsMatrix:
                 {
                     NekDouble            invfactor = 1.0/factor;
                     NekDouble            one = 1.0;
                     DNekBlkMatSharedPtr  mat = GetStdStaticCondMatrix(mkey);
                     DNekScalMatSharedPtr Atmp;
                     DNekMatSharedPtr     Asubmat;
 
                     returnval->SetBlock(0,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,Asubmat = mat->GetBlock(0,0)));
                     returnval->SetBlock(0,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,Asubmat = mat->GetBlock(0,1)));
                     returnval->SetBlock(1,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,Asubmat = mat->GetBlock(1,0)));
                     returnval->SetBlock(1,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(invfactor,Asubmat = mat->GetBlock(1,1)));
                 }
                 break;
 
                 UseLocRegionsMatrix:
                 {
                     int i,j;
                     NekDouble            invfactor = 1.0/factor;
                     NekDouble            one = 1.0;
 
                     DNekScalMat &mat = *GetLocMatrix(mkey);
 
                     DNekMatSharedPtr A = MemoryManager<DNekMat>::AllocateSharedPtr(nbdry,nbdry);
                     DNekMatSharedPtr B = MemoryManager<DNekMat>::AllocateSharedPtr(nbdry,nint);
                     DNekMatSharedPtr C = MemoryManager<DNekMat>::AllocateSharedPtr(nint,nbdry);
                     DNekMatSharedPtr D = MemoryManager<DNekMat>::AllocateSharedPtr(nint,nint);
 
                     Array<OneD,unsigned int> bmap(nbdry);
                     Array<OneD,unsigned int> imap(nint);
                     GetBoundaryMap(bmap);
                     GetInteriorMap(imap);
 
                     for(i = 0; i < nbdry; ++i)
                     {
                         for(j = 0; j < nbdry; ++j)
                         {
                             (*A)(i,j) = mat(bmap[i],bmap[j]);
                         }
 
                         for(j = 0; j < nint; ++j)
                         {
                             (*B)(i,j) = mat(bmap[i],imap[j]);
                         }
                     }
 
                     for(i = 0; i < nint; ++i)
                     {
                         for(j = 0; j < nbdry; ++j)
                         {
                             (*C)(i,j) = mat(imap[i],bmap[j]);
                         }
 
                         for(j = 0; j < nint; ++j)
                         {
                             (*D)(i,j) = mat(imap[i],imap[j]);
                         }
                     }
 
                     // Calculate static condensed system
                     if(nint)
                     {
                         D->Invert();
                         (*B) = (*B)*(*D);
                         (*A) = (*A) - (*B)*(*C);
                     }
 
                     DNekScalMatSharedPtr     Atmp;
 
                     returnval->SetBlock(0,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,A));
                     returnval->SetBlock(0,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,B));
                     returnval->SetBlock(1,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,C));
                     returnval->SetBlock(1,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(invfactor,D));
 
                 }
             }
 
             return returnval;
         }

void Nektar::LocalRegions::TriExp::v_ComputeEdgeNormal ( const int edge )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 814 of file TriExp.cpp.

References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::StdRegions::StdExpansion::GetEorient(), Nektar::LocalRegions::Expansion::GetGeom(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion2D::m_edgeNormals, Vmath::Reverse(), Vmath::Sdiv(), Vmath::Smul(), Vmath::Vmul(), Vmath::Vsqrt(), Vmath::Vvtvp(), and Vmath::Zero().

         {
             int i;
             const SpatialDomains::GeomFactorsSharedPtr & geomFactors = GetGeom()->GetMetricInfo();
             LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
             const SpatialDomains::GeomType type = geomFactors->GetGtype();
             const Array<TwoD, const NekDouble> & df = geomFactors->GetDerivFactors(ptsKeys);
             const Array<OneD, const NekDouble> & jac  = geomFactors->GetJac(ptsKeys);
             int nqe = m_base[0]->GetNumPoints();
             int dim = GetCoordim();
 
             m_edgeNormals[edge] = Array<OneD, Array<OneD, NekDouble> >(dim);
             Array<OneD, Array<OneD, NekDouble> > &normal = m_edgeNormals[edge];
             for (i = 0; i < dim; ++i)
             {
                 normal[i] = Array<OneD, NekDouble>(nqe);
             }
 
             // Regular geometry case
             if((type == SpatialDomains::eRegular)||(type == SpatialDomains::eMovingRegular))
             {
                 NekDouble fac;
                 // Set up normals
                 switch(edge)
                 {
                 case 0:
                     for(i = 0; i < GetCoordim(); ++i)
                     {
                         Vmath::Fill(nqe,-df[2*i+1][0],normal[i],1);
                     }
                     break;
                 case 1:
                     for(i = 0; i < GetCoordim(); ++i)
                     {
                         Vmath::Fill(nqe,df[2*i+1][0] + df[2*i][0],normal[i],1);
                     }
                         break;
                 case 2:
                     for(i = 0; i < GetCoordim(); ++i)
                     {
                         Vmath::Fill(nqe,-df[2*i][0],normal[i],1);
                     }
                     break;
                 default:
                     ASSERTL0(false,"Edge is out of range (edge < 3)");
                 }
 
                 // normalise
                 fac = 0.0;
                 for(i =0 ; i < GetCoordim(); ++i)
                 {
                     fac += normal[i][0]*normal[i][0];
                 }
                 fac = 1.0/sqrt(fac);
                 for (i = 0; i < GetCoordim(); ++i)
                 {
                     Vmath::Smul(nqe,fac,normal[i],1,normal[i],1);
                 }
             }
             else   // Set up deformed normals
             {
                 int j;
 
                 int nquad0 = ptsKeys[0].GetNumPoints();
                 int nquad1 = ptsKeys[1].GetNumPoints();
 
                 LibUtilities::PointsKey from_key;
 
                 Array<OneD,NekDouble> normals(GetCoordim()*max(nquad0,nquad1),0.0);
                 Array<OneD,NekDouble> edgejac(GetCoordim()*max(nquad0,nquad1),0.0);
 
                 // Extract Jacobian along edges and recover local
                 // derivates (dx/dr) for polynomial interpolation by
                 // multiplying m_gmat by jacobian
                 switch(edge)
                 {
                 case 0:
                     for(j = 0; j < nquad0; ++j)
                     {
                         edgejac[j] = jac[j];
                         for(i = 0; i < GetCoordim(); ++i)
                         {
                             normals[i*nquad0+j] = -df[2*i+1][j]*edgejac[j];
                         }
                     }
                     from_key = ptsKeys[0];
                     break;
                 case 1:
                     for(j = 0; j < nquad1; ++j)
                     {
                         edgejac[j] = jac[nquad0*j+nquad0-1];
                         for(i = 0; i < GetCoordim(); ++i)
                         {
                             normals[i*nquad1+j] = (df[2*i][nquad0*j + nquad0-1] +  df[2*i+1][nquad0*j + nquad0-1])*edgejac[j];
                         }
                     }
                     from_key = ptsKeys[1];
                     break;
                 case 2:
                     for(j = 0; j < nquad1; ++j)
                     {
                         edgejac[j] = jac[nquad0*j];
                         for(i = 0; i < GetCoordim(); ++i)
                         {
                             normals[i*nquad1+j] = -df[2*i][nquad0*j]*edgejac[j];
                         }
                     }
                     from_key = ptsKeys[1];
                     break;
                 default:
                     ASSERTL0(false,"edge is out of range (edge < 3)");
 
                 }
 
                 int nq  = from_key.GetNumPoints();
                 Array<OneD,NekDouble> work(nqe,0.0);
 
                 // interpolate Jacobian and invert
                 LibUtilities::Interp1D(from_key,jac,m_base[0]->GetPointsKey(),work);
                 Vmath::Sdiv(nq,1.0,&work[0],1,&work[0],1);
 
                 // interpolate
                 for(i = 0; i < GetCoordim(); ++i)
                 {
                     LibUtilities::Interp1D(from_key,&normals[i*nq],m_base[0]->GetPointsKey(),&normal[i][0]);
                     Vmath::Vmul(nqe,work,1,normal[i],1,normal[i],1);
                 }
 
                 //normalise normal vectors
                 Vmath::Zero(nqe,work,1);
                 for(i = 0; i < GetCoordim(); ++i)
                 {
                     Vmath::Vvtvp(nqe,normal[i],1, normal[i],1,work,1,work,1);
                 }
 
                 Vmath::Vsqrt(nqe,work,1,work,1);
                 Vmath::Sdiv(nqe,1.0,work,1,work,1);
 
                 for(i = 0; i < GetCoordim(); ++i)
                 {
                     Vmath::Vmul(nqe,normal[i],1,work,1,normal[i],1);
                 }
 
                 // Reverse direction so that points are in
                 // anticlockwise direction if edge >=2
                 if(edge >= 2)
                 {
                     for(i = 0; i < GetCoordim(); ++i)
                     {
                         Vmath::Reverse(nqe,normal[i],1, normal[i],1);
                     }
                 }
             }
             if(GetGeom()->GetEorient(edge) == StdRegions::eBackwards)
             {
                 for(i = 0; i < GetCoordim(); ++i)
                 {
                     if(geomFactors->GetGtype() == SpatialDomains::eDeformed)
                     {
                         Vmath::Reverse(nqe, normal[i], 1, normal[i],1);
                     }
                 }
             }
         }

void Nektar::LocalRegions::TriExp::v_ComputeLaplacianMetric ( )

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1616 of file TriExp.cpp.

         {
             if (m_metrics.count(eMetricQuadrature) == 0)
             {
                 ComputeQuadratureMetric();
             }
 
             unsigned int i, j;
             const SpatialDomains::GeomType type = m_metricinfo->GetGtype();
             const unsigned int nqtot = GetTotPoints();
             const unsigned int dim = 2;
             const MetricType m[3][3] = { {eMetricLaplacian00, eMetricLaplacian01, eMetricLaplacian02},
                                        {eMetricLaplacian01, eMetricLaplacian11, eMetricLaplacian12},
                                        {eMetricLaplacian02, eMetricLaplacian12, eMetricLaplacian22}
             };
 
             Array<OneD, NekDouble> dEta_dXi[2] = {Array<OneD, NekDouble>(nqtot,1.0),
                                                   Array<OneD, NekDouble>(nqtot,1.0)};
 
             for (i = 0; i < dim; ++i)
             {
                 for (j = i; j < dim; ++j)
                 {
                     m_metrics[m[i][j]] = Array<OneD, NekDouble>(nqtot);
                 }
             }
 
             const Array<OneD, const NekDouble>& z0 = m_base[0]->GetZ();
             const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
             const unsigned int nquad0 = m_base[0]->GetNumPoints();
             const unsigned int nquad1 = m_base[1]->GetNumPoints();
             const Array<TwoD, const NekDouble>& df   =
                                 m_metricinfo->GetDerivFactors(GetPointsKeys());
 
             for(i = 0; i < nquad1; i++)
             {
                 Blas::Dscal(nquad0,2.0/(1-z1[i]),&dEta_dXi[0][0]+i*nquad0,1);
                 Blas::Dscal(nquad0,2.0/(1-z1[i]),&dEta_dXi[1][0]+i*nquad0,1);
             }
             for(i = 0; i < nquad0; i++)
             {
                 Blas::Dscal(nquad1,0.5*(1+z0[i]),&dEta_dXi[1][0]+i,nquad0);
             }
 
             Array<OneD, NekDouble> tmp(nqtot);
             if((type == SpatialDomains::eRegular ||
                 type == SpatialDomains::eMovingRegular))
             {
                 Vmath::Smul (nqtot,df[0][0],&dEta_dXi[0][0],1,&tmp[0],1);
                 Vmath::Svtvp(nqtot,df[1][0],&dEta_dXi[1][0],1,&tmp[0],1,&tmp[0],1);
 
                 Vmath::Vmul (nqtot,&tmp[0],1,   &tmp[0],1,&m_metrics[eMetricLaplacian00][0],1);
                 Vmath::Smul (nqtot,df[1][0],&tmp[0],1,&m_metrics[eMetricLaplacian01][0],1);
 
 
                 Vmath::Smul (nqtot,df[2][0],&dEta_dXi[0][0],1,&tmp[0],1);
                 Vmath::Svtvp(nqtot,df[3][0],&dEta_dXi[1][0],1,&tmp[0],1,&tmp[0],1);
 
                 Vmath::Vvtvp(nqtot,&tmp[0],1,   &tmp[0],1,&m_metrics[eMetricLaplacian00][0],1,&m_metrics[eMetricLaplacian00][0],1);
                 Vmath::Svtvp(nqtot,df[3][0],&tmp[0],1,&m_metrics[eMetricLaplacian01][0],1,&m_metrics[eMetricLaplacian01][0],1);
 
                 if(GetCoordim() == 3)
                 {
                     Vmath::Smul (nqtot,df[4][0],&dEta_dXi[0][0],1,&tmp[0],1);
                     Vmath::Svtvp(nqtot,df[5][0],&dEta_dXi[1][0],1,&tmp[0],1,&tmp[0],1);
 
                     Vmath::Vvtvp(nqtot,&tmp[0],1,   &tmp[0],1,&m_metrics[eMetricLaplacian00][0],1,&m_metrics[eMetricLaplacian00][0],1);
                     Vmath::Svtvp(nqtot,df[5][0],&tmp[0],1,&m_metrics[eMetricLaplacian01][0],1,&m_metrics[eMetricLaplacian01][0],1);
                 }
 
                 NekDouble g2 = df[1][0]*df[1][0] + df[3][0]*df[3][0];
                 if(GetCoordim() == 3)
                 {
                     g2 += df[5][0]*df[5][0];
                 }
                 Vmath::Fill(nqtot,g2,&m_metrics[eMetricLaplacian11][0],1);
             }
             else
             {
 
                 Vmath::Vmul (nqtot,&df[0][0],1,&dEta_dXi[0][0],1,&tmp[0],1);
                 Vmath::Vvtvp(nqtot,&df[1][0],1,&dEta_dXi[1][0],1,&tmp[0],1,&tmp[0],1);
 
                 Vmath::Vmul (nqtot,&tmp[0],  1,&tmp[0],  1,&m_metrics[eMetricLaplacian00][0],1);
                 Vmath::Vmul (nqtot,&df[1][0],1,&tmp[0],  1,&m_metrics[eMetricLaplacian01][0],1);
                 Vmath::Vmul (nqtot,&df[1][0],1,&df[1][0],1,&m_metrics[eMetricLaplacian11][0],1);
 
 
                 Vmath::Vmul (nqtot,&df[2][0],1,&dEta_dXi[0][0],1,&tmp[0],1);
                 Vmath::Vvtvp(nqtot,&df[3][0],1,&dEta_dXi[1][0],1,&tmp[0],1,&tmp[0],1);
 
                 Vmath::Vvtvp(nqtot,&tmp[0],  1,&tmp[0],  1,&m_metrics[eMetricLaplacian00][0],1,&m_metrics[eMetricLaplacian00][0],1);
                 Vmath::Vvtvp(nqtot,&df[3][0],1,&tmp[0],  1,&m_metrics[eMetricLaplacian01][0],1,&m_metrics[eMetricLaplacian01][0],1);
                 Vmath::Vvtvp(nqtot,&df[3][0],1,&df[3][0],1,&m_metrics[eMetricLaplacian11][0],1,&m_metrics[eMetricLaplacian11][0],1);
 
                 if(GetCoordim() == 3)
                 {
                     Vmath::Vmul (nqtot,&df[4][0],1,&dEta_dXi[0][0],1,&tmp[0],1);
                     Vmath::Vvtvp(nqtot,&df[5][0],1,&dEta_dXi[1][0],1,&tmp[0],1,&tmp[0],1);
 
                     Vmath::Vvtvp(nqtot,&tmp[0],  1,&tmp[0],  1,&m_metrics[eMetricLaplacian00][0],1,&m_metrics[eMetricLaplacian00][0],1);
                     Vmath::Vvtvp(nqtot,&df[5][0],1,&tmp[0],  1,&m_metrics[eMetricLaplacian01][0],1,&m_metrics[eMetricLaplacian01][0],1);
                     Vmath::Vvtvp(nqtot,&df[5][0],1,&df[5][0],1,&m_metrics[eMetricLaplacian11][0],1,&m_metrics[eMetricLaplacian11][0],1);
                 }
             }
 
             for (unsigned int i = 0; i < dim; ++i)
             {
                 for (unsigned int j = i; j < dim; ++j)
                 {
                     MultiplyByQuadratureMetric(m_metrics[m[i][j]],
                                                m_metrics[m[i][j]]);
 
                 }
             }
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1072 of file TriExp.cpp.

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

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

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1476 of file TriExp.cpp.

References m_staticCondMatrixManager.

         {
             m_staticCondMatrixManager.DeleteObject(mkey);
         }

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

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 985 of file TriExp.cpp.

References ASSERTL0, ASSERTL1, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vcopy(), and Vmath::Zero().

         {
             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);
 
             switch(m_base[0]->GetBasisType())
             {
             case LibUtilities::eModified_A:
                 {
                     int i;
                     int cnt  = 0;
                     int cnt1 = 0;
 
                     ASSERTL1(m_base[1]->GetBasisType() == LibUtilities::eModified_B,
                              "Extraction routine not set up for this basis");
 
                     Vmath::Zero(m_ncoeffs,coeffs,1);
                     for(i = 0; i < fillorder0; ++i)
                     {
                         Vmath::Vcopy(fillorder1-i,&data[cnt],1,&coeffs[cnt1],1);
                         cnt  += data_order1-i;
                         cnt1 += order1-i;
                     }
                 }
                 break;
             default:
                 ASSERTL0(false,"basis is either not set up or not hierarchicial");
             }
         }

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

protectedvirtual

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

See also: StdExpansion::FwdTrans

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 245 of file TriExp.cpp.

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::IProductWRTBase(), m_matrixManager, and Nektar::StdRegions::StdExpansion::m_ncoeffs.

         {
             IProductWRTBase(inarray,outarray);
 
             // get Mass matrix inverse
             MatrixKey             masskey(StdRegions::eInvMass,
                                           DetShapeType(),*this);
             DNekScalMatSharedPtr  matsys = m_matrixManager[masskey];
 
             // copy inarray in case inarray == outarray
             NekVector<NekDouble> in (m_ncoeffs,outarray,eCopy);
             NekVector<NekDouble> out(m_ncoeffs,outarray,eWrapper);
 
             out = (*matsys)*in;
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 263 of file TriExp.cpp.

         {
             int i,j;
             int npoints[2] = {m_base[0]->GetNumPoints(),
                               m_base[1]->GetNumPoints()};
             int nmodes[2]  = {m_base[0]->GetNumModes(),
                               m_base[1]->GetNumModes()};
 
             fill(outarray.get(), outarray.get()+m_ncoeffs, 0.0 );
 
             Array<OneD, NekDouble> physEdge[3];
             Array<OneD, NekDouble> coeffEdge[3];
             for(i = 0; i < 3; i++)
             {
                 // define physEdge and add 1 so can interpolate grl10 points if necessary
                 physEdge[i]  = Array<OneD, NekDouble>(max(npoints[i!=0],npoints[0])); 
                 coeffEdge[i] = Array<OneD, NekDouble>(nmodes[i!=0]);
             }
 
             for(i = 0; i < npoints[0]; i++)
             {
                 physEdge[0][i] = inarray[i];
             }
 
             // extract data in cartesian directions
             for(i = 0; i < npoints[1]; i++)
             {
                 physEdge[1][i] = inarray[npoints[0]-1+i*npoints[0]];
                 physEdge[2][i] = inarray[i*npoints[0]];
             }
 
             SegExpSharedPtr segexp[3];
             segexp[0] = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(m_base[0]->GetBasisKey(),GetGeom2D()->GetEdge(0));
             
             if(m_base[1]->GetPointsType() == LibUtilities::eGaussLobattoLegendre)
             {
                 for(i = 1; i < 3; i++)
                 {
                     segexp[i] = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(m_base[i!=0]->GetBasisKey(),GetGeom2D()->GetEdge(i));
                 }
             }
             else // interploate using edge 0 GLL distribution
             {
                 for(i = 1; i < 3; i++)
                 {
                     segexp[i] = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(m_base[0]->GetBasisKey(),GetGeom2D()->GetEdge(i));
 
                     LibUtilities::Interp1D(m_base[1]->GetPointsKey(),physEdge[i],
                                            m_base[0]->GetPointsKey(),physEdge[i]);
                 }
                 npoints[1] = npoints[0];
             }
             
 
             Array<OneD, unsigned int> mapArray;
             Array<OneD, int>          signArray;
             NekDouble sign;
             // define an orientation to get EdgeToElmtMapping from Cartesian data 
             StdRegions::Orientation orient[3] = {StdRegions::eForwards,StdRegions::eForwards,
                                                  StdRegions::eBackwards};
 
             for(i = 0; i < 3; i++)
             {
                 segexp[i]->FwdTrans_BndConstrained(physEdge[i],coeffEdge[i]);
 
                 // this orient goes with the one above and so could
                 // probably set both to eForwards
                 GetEdgeToElementMap(i,orient[i],mapArray,signArray);
                 for(j=0; j < nmodes[i!=0]; j++)
                 {
                     sign = (NekDouble) signArray[j];
                     outarray[ mapArray[j] ] = sign * coeffEdge[i][j];
                 }
             }
 
             int nBoundaryDofs = NumBndryCoeffs();
             int nInteriorDofs = m_ncoeffs - nBoundaryDofs;
 
             if (nInteriorDofs > 0) {
                 Array<OneD, NekDouble> tmp0(m_ncoeffs);
                 Array<OneD, NekDouble> tmp1(m_ncoeffs);
 
                 StdRegions::StdMatrixKey  stdmasskey(StdRegions::eMass,DetShapeType(),*this);
                 MassMatrixOp(outarray,tmp0,stdmasskey);
                 IProductWRTBase(inarray,tmp1);
 
                 Vmath::Vsub(m_ncoeffs, tmp1, 1, tmp0, 1, tmp1, 1);
 
                 // get Mass matrix inverse (only of interior DOF)
                 // use block (1,1) of the static condensed system
                 // note: this block alreay contains the inverse matrix
                 MatrixKey             masskey(StdRegions::eMass,DetShapeType(),*this);
                 DNekScalMatSharedPtr  matsys = (m_staticCondMatrixManager[masskey])->GetBlock(1,1);
 
                 Array<OneD, NekDouble> rhs(nInteriorDofs);
                 Array<OneD, NekDouble> result(nInteriorDofs);
 
                 GetInteriorMap(mapArray);
 
                 for(i = 0; i < nInteriorDofs; i++)
                 {
                     rhs[i] = tmp1[ mapArray[i] ];
                 }
 
                 Blas::Dgemv('N', nInteriorDofs, nInteriorDofs, matsys->Scale(), &((matsys->GetOwnedMatrix())->GetPtr())[0],
                             nInteriorDofs,rhs.get(),1,0.0,result.get(),1);
 
                 for(i = 0; i < nInteriorDofs; i++)
                 {
                     outarray[ mapArray[i] ] = result[i];
                 }
             }
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1541 of file TriExp.cpp.

References Nektar::LocalRegions::Expansion::GetLocMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, and Vmath::Vcopy().

         {
             DNekScalMatSharedPtr   mat = GetLocMatrix(mkey);
 
             if(inarray.get() == outarray.get())
             {
                 Array<OneD,NekDouble> tmp(m_ncoeffs);
                 Vmath::Vcopy(m_ncoeffs,inarray.get(),1,tmp.get(),1);
 
                 Blas::Dgemv('N',m_ncoeffs,m_ncoeffs,mat->Scale(),(mat->GetOwnedMatrix())->GetPtr().get(),
                             m_ncoeffs, tmp.get(), 1, 0.0, outarray.get(), 1);
             }
             else
             {
                 Blas::Dgemv('N',m_ncoeffs,m_ncoeffs,mat->Scale(),(mat->GetOwnedMatrix())->GetPtr().get(),
                             m_ncoeffs, inarray.get(), 1, 0.0, outarray.get(), 1);
             }
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1049 of file TriExp.cpp.

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::Expansion2D::v_GenMatrix().

         {
             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 = Expansion2D::v_GenMatrix(mkey);
                 break;
             default:
                 returnval = StdTriExp::v_GenMatrix(mkey);
                 break;
             }
 
             return returnval;
         }

const LibUtilities::BasisSharedPtr & Nektar::LocalRegions::TriExp::v_GetBasis ( int dir ) const

protectedvirtual

Definition at line 1036 of file TriExp.cpp.

References ASSERTL1, and Nektar::StdRegions::StdExpansion::m_base.

             {
           ASSERTL1(dir >= 0 &&dir <= 1,"input dir is out of range");
           return m_base[dir];
         }

StdRegions::Orientation Nektar::LocalRegions::TriExp::v_GetCartesianEorient ( int edge )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1030 of file TriExp.cpp.

References Nektar::LocalRegions::Expansion2D::GetGeom2D().

         {
             return GetGeom2D()->GetCartesianEorient(edge);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 597 of file TriExp.cpp.

References ASSERTL1, and Nektar::LocalRegions::Expansion::m_geom.

         {
             int  i;
 
             ASSERTL1(Lcoords[0] >= -1.0 && Lcoords[1] <= 1.0 &&
                      Lcoords[1] >= -1.0 && Lcoords[1]  <=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);
             }
         }

int Nektar::LocalRegions::TriExp::v_GetCoordim ( void )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion2D.

Definition at line 979 of file TriExp.cpp.

References Nektar::LocalRegions::Expansion::m_geom.

         {
             return m_geom->GetCoordim();
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 614 of file TriExp.cpp.

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

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

void Nektar::LocalRegions::TriExp::v_GetEdgeInterpVals	(	const int	edge,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 757 of file TriExp.cpp.

References ASSERTL0.

         {
             ASSERTL0(false,
                      "Routine not implemented for triangular elements");
         }

void Nektar::LocalRegions::TriExp::v_GetEdgePhysMap	(	const int	edge,
		Array< OneD, int > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 775 of file TriExp.cpp.

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

         {
             int nquad0 = m_base[0]->GetNumPoints();
             int nquad1 = m_base[1]->GetNumPoints();
             
             // Get points in Cartesian orientation
             switch (edge)
             {
                 case 0:
                     outarray = Array<OneD, int>(nquad0);
                     for (int i = 0; i < nquad0; ++i)
                     {
                         outarray[i] = i;
                     }
                     break;
                 case 1:
                     outarray = Array<OneD, int>(nquad1);
                     for (int i = 0; i < nquad1; ++i)
                     {
                         outarray[i] = (nquad0-1) + i * nquad0;
                     }
                     break;
                 case 2:
                     outarray = Array<OneD, int>(nquad1);
                     for (int i = 0; i < nquad1; ++i)
                     {
                         outarray[i] =  i*nquad0;
                     }
                     break;
                 default:
                     ASSERTL0(false, "edge value (< 3) is out of range");
                     break;
             }
             
         }

void Nektar::LocalRegions::TriExp::v_GetEdgePhysVals	(	const int	edge,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Extract the physical values along edge edge from inarray into outarray following the local edge orientation and point distribution defined by defined in EdgeExp.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 657 of file TriExp.cpp.

References ASSERTL0, Nektar::StdRegions::eForwards, Nektar::StdRegions::StdExpansion::GetEorient(), Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vcopy().

Referenced by v_GetTracePhysVals().

         {
             int nquad0 = m_base[0]->GetNumPoints();
             int nquad1 = m_base[1]->GetNumPoints();
 
             StdRegions::Orientation edgedir = GetEorient(edge);
             switch(edge)
             {
                 case 0:
                     if (edgedir == StdRegions::eForwards)
                     {
                         Vmath::Vcopy(nquad0,&(inarray[0]),1,&(outarray[0]),1);
                     }
                     else
                     {
                         Vmath::Vcopy(nquad0,&(inarray[0])+(nquad0-1),-1,
                                      &(outarray[0]),1);
                     }
                     break;
                 case 1:
                     if (edgedir == StdRegions::eForwards)
                     {
                         Vmath::Vcopy(nquad1,&(inarray[0])+(nquad0-1),nquad0,
                                      &(outarray[0]),1);
                     }
                     else
                     {
                         Vmath::Vcopy(nquad1,&(inarray[0])+(nquad0*nquad1-1),
                                      -nquad0, &(outarray[0]),1);
                     }
                     break;
                 case 2:
                     if (edgedir == StdRegions::eForwards)
                     {
                         Vmath::Vcopy(nquad1,&(inarray[0]) + nquad0*(nquad1-1),
                                      -nquad0,&(outarray[0]),1);
                     }
                     else
                     {
                         Vmath::Vcopy(nquad1,&(inarray[0]),nquad0,
                                      &(outarray[0]),1);
                     }
                 break;
             default:
                 ASSERTL0(false,"edge value (< 3) is out of range");
                 break;
             }
         }

void Nektar::LocalRegions::TriExp::v_GetEdgePhysVals	(	const int	edge,
		const StdRegions::StdExpansionSharedPtr &	EdgeExp,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Definition at line 709 of file TriExp.cpp.

References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::StdRegions::StdExpansion::GetCartesianEorient(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Reverse(), and Vmath::Vcopy().

         {
             int nquad0 = m_base[0]->GetNumPoints();
             int nquad1 = m_base[1]->GetNumPoints();
 
             // get points in Cartesian orientation
             switch(edge)
             {
             case 0:
                 Vmath::Vcopy(nquad0, &(inarray[0]), 1, &(outarray[0]), 1);
                 break;
             case 1:
                 Vmath::Vcopy(nquad1, &(inarray[0])+(nquad0-1),
                              nquad0, &(outarray[0]), 1);
                 break;
             case 2:
                 Vmath::Vcopy(nquad1, &(inarray[0]), nquad0, &(outarray[0]), 1);
                 break;
             default:
                 ASSERTL0(false,"edge value (< 3) is out of range");
                 break;
             }
 
             // Interpolate if required
             if(m_base[edge?1:0]->GetPointsKey() != EdgeExp->GetBasis(0)->GetPointsKey())
             {
                 Array<OneD,NekDouble> outtmp(max(nquad0,nquad1));
         
                 outtmp = outarray;
                 
                 LibUtilities::Interp1D(m_base[edge?1:0]->GetPointsKey(),
                                        outtmp,
                                        EdgeExp->GetBasis(0)->GetPointsKey(),
                                        outarray);
             }
             
             //Reverse data if necessary
             if(GetCartesianEorient(edge) == StdRegions::eBackwards)
             {
                 Vmath::Reverse(EdgeExp->GetNumPoints(0),&outarray[0],1,
                                &outarray[0],1);
             }
 
         }

void Nektar::LocalRegions::TriExp::v_GetEdgeQFactors	(	const int	edge,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 765 of file TriExp.cpp.

References ASSERTL0.

         {
             ASSERTL0(false, 
                      "Routine not implemented for triangular elements");
         }

StdRegions::Orientation Nektar::LocalRegions::TriExp::v_GetEorient ( int edge )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1024 of file TriExp.cpp.

References Nektar::LocalRegions::Expansion2D::GetGeom2D().

         {
             return GetGeom2D()->GetEorient(edge);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 586 of file TriExp.cpp.

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

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

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

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1465 of file TriExp.cpp.

References m_matrixManager.

         {
             return m_matrixManager[mkey];
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1471 of file TriExp.cpp.

References m_staticCondMatrixManager.

         {
             return m_staticCondMatrixManager[mkey];
         }

int Nektar::LocalRegions::TriExp::v_GetNumPoints ( const int dir ) const

protectedvirtual

Definition at line 1043 of file TriExp.cpp.

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

         {
             return GetNumPoints(dir);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 578 of file TriExp.cpp.

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

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

void Nektar::LocalRegions::TriExp::v_GetTracePhysVals	(	const int	edge,
		const StdRegions::StdExpansionSharedPtr &	EdgeExp,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		StdRegions::Orientation	orient
	)

protectedvirtual

Definition at line 647 of file TriExp.cpp.

References v_GetEdgePhysVals().

         {
             v_GetEdgePhysVals(edge,EdgeExp,inarray,outarray);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1533 of file TriExp.cpp.

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

         {
             TriExp::HelmholtzMatrixOp_MatFree(inarray,outarray,mkey);
         }

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

protectedvirtual

Integrates the specified function over the domain.

See also: StdRegions::StdExpansion::Integral.

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 83 of file TriExp.cpp.

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

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

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

protectedvirtual

Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray.

$\begin{array}{rcl} I_{pq} = (\phi^A_q \phi^B_{pq}, u) &=& \sum_{i=0}^{nq_0}\sum_{j=0}^{nq_1} \phi^A_p(\eta_{0,i})\phi^B_{pq}(\eta_{1,j}) w^0_i w^1_j u(\xi_{0,i} \xi_{1,j}) \\ & = & \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) \tilde{u}_{i,j} \end{array}$

where

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

which can be implemented as

$f_{pj} = \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \tilde{u}_{i,j} \rightarrow {\bf B_1 U}$ $I_{pq} = \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) f_{pj} \rightarrow {\bf B_2[p*skip] f[skip]}$

Recall: $\eta_{1} = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \, \eta_2 = \xi_2$

Note: For the orthgonality of this expansion to be realised the 'q' ordering must run fastest in contrast to the Quad and Hex ordering where 'p' index runs fastest to be consistent with the quadrature ordering.

In the triangular space the i (i.e. $\eta_1$ direction) ordering still runs fastest by convention.

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 379 of file TriExp.cpp.

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

         {
             IProductWRTBase_SumFac(inarray,outarray);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 420 of file TriExp.cpp.

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eIProductWRTBase, Nektar::StdRegions::StdExpansion::GetTotPoints(), m_matrixManager, and Nektar::StdRegions::StdExpansion::m_ncoeffs.

         {
             int nq = GetTotPoints();
             MatrixKey      iprodmatkey(StdRegions::eIProductWRTBase,DetShapeType(),*this);
             DNekScalMatSharedPtr iprodmat = m_matrixManager[iprodmatkey];
 
             Blas::Dgemv('N',m_ncoeffs,nq,iprodmat->Scale(),(iprodmat->GetOwnedMatrix())->GetPtr().get(),
                         m_ncoeffs, inarray.get(), 1, 0.0, outarray.get(), 1);
 
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 394 of file TriExp.cpp.

References Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric().

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

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 386 of file TriExp.cpp.

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

         {
             IProductWRTDerivBase_SumFac(dir,inarray,outarray);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 503 of file TriExp.cpp.

References ASSERTL1, Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eIProductWRTDerivBase0, Nektar::StdRegions::eIProductWRTDerivBase1, Nektar::StdRegions::eIProductWRTDerivBase2, Nektar::StdRegions::StdExpansion::GetTotPoints(), m_matrixManager, and Nektar::StdRegions::StdExpansion::m_ncoeffs.

         {
             int nq = GetTotPoints();
             StdRegions::MatrixType mtype = StdRegions::eIProductWRTDerivBase0;
 
             switch(dir)
             {
             case 0:
                 {
                     mtype = StdRegions::eIProductWRTDerivBase0;
                 }
                 break;
             case 1:
                 {
                     mtype = StdRegions::eIProductWRTDerivBase1;
                 }
                 break;
             case 2:
                 {
                     mtype = StdRegions::eIProductWRTDerivBase2;
                 }
                 break;
             default:
                 {
                     ASSERTL1(false,"input dir is out of range");
                 }
                 break;
             }
 
             MatrixKey      iprodmatkey(mtype,DetShapeType(),*this);
             DNekScalMatSharedPtr iprodmat = m_matrixManager[iprodmatkey];
 
             Blas::Dgemv('N',m_ncoeffs,nq,iprodmat->Scale(),(iprodmat->GetOwnedMatrix())->GetPtr().get(),
                         m_ncoeffs, inarray.get(), 1, 0.0, outarray.get(), 1);
 
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 433 of file TriExp.cpp.

References ASSERTL1, Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().

         {
             ASSERTL1((dir==0)||(dir==1)||(dir==2),"Invalid direction.");
             ASSERTL1((dir==2)?(m_geom->GetCoordim()==3):true,"Invalid direction.");
 
             int    i;
             int    nquad0 = m_base[0]->GetNumPoints();
             int    nquad1 = m_base[1]->GetNumPoints();
             int    nqtot  = nquad0*nquad1;
             int    nmodes0 = m_base[0]->GetNumModes();
             int    wspsize = max(max(nqtot,m_ncoeffs),nquad1*nmodes0);
 
             const Array<TwoD, const NekDouble>& df =
                                 m_metricinfo->GetDerivFactors(GetPointsKeys());
 
             Array<OneD, NekDouble> tmp0 (6*wspsize);
             Array<OneD, NekDouble> tmp1 (tmp0 +   wspsize);
             Array<OneD, NekDouble> tmp2 (tmp0 + 2*wspsize);
             Array<OneD, NekDouble> tmp3 (tmp0 + 3*wspsize);
             Array<OneD, NekDouble> gfac0(tmp0 + 4*wspsize);
             Array<OneD, NekDouble> gfac1(tmp0 + 5*wspsize);
 
             const Array<OneD, const NekDouble>& z0 = m_base[0]->GetZ();
             const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
 
             // set up geometric factor: 2/(1-z1)
             for(i = 0; i < nquad1; ++i)
             {
                 gfac0[i] = 2.0/(1-z1[i]);
             }
             for(i = 0; i < nquad0; ++i)
             {
                 gfac1[i] = 0.5*(1+z0[i]);
             }
 
             for(i = 0; i < nquad1; ++i)
             {
                 Vmath::Smul(nquad0,gfac0[i],&inarray[0]+i*nquad0,1,&tmp0[0]+i*nquad0,1);
             }
 
             for(i = 0; i < nquad1; ++i)
             {
                 Vmath::Vmul(nquad0,&gfac1[0],1,&tmp0[0]+i*nquad0,1,&tmp1[0]+i*nquad0,1);
             }
 
             if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 Vmath::Vmul(nqtot,&df[2*dir][0],  1,&tmp0[0],   1,&tmp0[0],1);
                 Vmath::Vmul(nqtot,&df[2*dir+1][0],1,&tmp1[0],   1,&tmp1[0],1);
                 Vmath::Vmul(nqtot,&df[2*dir+1][0],1,&inarray[0],1,&tmp2[0],1);
             }
             else
             {
                 Vmath::Smul(nqtot, df[2*dir][0],   tmp0,    1, tmp0, 1);
                 Vmath::Smul(nqtot, df[2*dir+1][0], tmp1,    1, tmp1, 1);
                 Vmath::Smul(nqtot, df[2*dir+1][0], inarray, 1, tmp2, 1);
             }
             Vmath::Vadd(nqtot, tmp0, 1, tmp1, 1, tmp1, 1);
 
             MultiplyByQuadratureMetric(tmp1,tmp1);
             MultiplyByQuadratureMetric(tmp2,tmp2);
 
             IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),m_base[1]->GetBdata() ,tmp1,tmp3    ,tmp0);
             IProductWRTBase_SumFacKernel(m_base[0]->GetBdata() ,m_base[1]->GetDbdata(),tmp2,outarray,tmp0);
             Vmath::Vadd(m_ncoeffs, tmp3, 1, outarray, 1, outarray, 1);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1491 of file TriExp.cpp.

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

         {
                 TriExp::LaplacianMatrixOp_MatFree(inarray,outarray,mkey);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1499 of file TriExp.cpp.

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

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1563 of file TriExp.cpp.

References ASSERTL1, Nektar::LocalRegions::Expansion::ComputeLaplacianMetric(), Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian11, Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vadd(), and Vmath::Vvtvvtp().

         {
             if (m_metrics.count(eMetricLaplacian00) == 0)
             {
                 ComputeLaplacianMetric();
             }
 
             int       nquad0  = m_base[0]->GetNumPoints();
             int       nquad1  = m_base[1]->GetNumPoints();
             int       nqtot   = nquad0*nquad1;
             int       nmodes0 = m_base[0]->GetNumModes();
             int       nmodes1 = m_base[1]->GetNumModes();
             int       wspsize = max(max(max(nqtot,m_ncoeffs),nquad1*nmodes0),nquad0*nmodes1);
 
             ASSERTL1(wsp.num_elements() >= 3*wspsize,
                      "Workspace is of insufficient 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>& dbase0 = m_base[0]->GetDbdata();
             const Array<OneD, const NekDouble>& dbase1 = m_base[1]->GetDbdata();
             const Array<OneD, const NekDouble>& metric00 = m_metrics[eMetricLaplacian00];
             const Array<OneD, const NekDouble>& metric01 = m_metrics[eMetricLaplacian01];
             const Array<OneD, const NekDouble>& metric11 = m_metrics[eMetricLaplacian11];
 
             // Allocate temporary storage
             Array<OneD,NekDouble> wsp0(wsp);
             Array<OneD,NekDouble> wsp1(wsp+wspsize);
             Array<OneD,NekDouble> wsp2(wsp+2*wspsize);
 
             StdExpansion2D::PhysTensorDeriv(inarray,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,&wsp1[0],1,&metric01[0],1,&wsp2[0],1,&wsp0[0],1);
             Vmath::Vvtvvtp(nqtot,&metric01[0],1,&wsp1[0],1,&metric11[0],1,&wsp2[0],1,&wsp2[0],1);
 
             // outarray = m = (D_xi1 * B)^T * k
             // wsp1     = n = (D_xi2 * B)^T * l
             IProductWRTBase_SumFacKernel(dbase0,base1,wsp0,outarray,wsp1);
             IProductWRTBase_SumFacKernel(base0,dbase1,wsp2,wsp1,    wsp0);
 
             // outarray = outarray + wsp1
             //          = L * u_hat
             Vmath::Vadd(m_ncoeffs,wsp1.get(),1,outarray.get(),1,outarray.get(),1);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1525 of file TriExp.cpp.

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

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1483 of file TriExp.cpp.

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

void Nektar::LocalRegions::TriExp::v_NormVectorIProductWRTBase	(	const Array< OneD, const NekDouble > &	Fx,
		const Array< OneD, const NekDouble > &	Fy,
		const Array< OneD, const NekDouble > &	Fz,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 542 of file TriExp.cpp.

References Nektar::SpatialDomains::eDeformed, Nektar::LocalRegions::Expansion2D::GetLeftAdjacentElementExp(), Nektar::LocalRegions::Expansion2D::GetLeftAdjacentElementFace(), Nektar::StdRegions::StdExpansion::IProductWRTBase(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Svtsvtp(), Vmath::Svtvp(), Vmath::Vvtvp(), and Vmath::Vvtvvtp().

         {
             int nq = m_base[0]->GetNumPoints()*m_base[1]->GetNumPoints();
             Array<OneD, NekDouble > Fn(nq);
 
             const Array<OneD, const Array<OneD, NekDouble> > &normals = 
                 GetLeftAdjacentElementExp()->GetFaceNormal(
                     GetLeftAdjacentElementFace());
             
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 Vmath::Vvtvvtp(nq,&normals[0][0],1,&Fx[0],1,
                                   &normals[1][0],1,&Fy[0],1,&Fn[0],1);
                 Vmath::Vvtvp  (nq,&normals[2][0],1,&Fz[0],1,&Fn[0],1,&Fn[0],1);
             }
             else
             {
                 Vmath::Svtsvtp(nq,normals[0][0],&Fx[0],1,
                                   normals[1][0],&Fy[0],1,&Fn[0],1);
                 Vmath::Svtvp  (nq,normals[2][0],&Fz[0],1,&Fn[0],1,&Fn[0],1);
             }
 
             IProductWRTBase(Fn,outarray);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 571 of file TriExp.cpp.

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

         {
             NormVectorIProductWRTBase(Fvec[0], Fvec[1], Fvec[2], outarray);
         }

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

protectedvirtual

Calculate the derivative of the physical points.

$\frac{\partial u}{\partial x_1} = \left . \frac{2.0}{1-\eta_2} \frac{\partial u}{\partial d\eta_1} \right |_{\eta_2}$

$\frac{\partial u}{\partial x_2} = \left . \frac{1+\eta_1}{1-\eta_2} \frac{\partial u}{\partial d\eta_1} \right |_{\eta_2} + \left . \frac{\partial u}{\partial d\eta_2} \right |_{\eta_1}$

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 107 of file TriExp.cpp.

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

         {
             int    nquad0 = m_base[0]->GetNumPoints();
             int    nquad1 = m_base[1]->GetNumPoints();
             int     nqtot = nquad0*nquad1;
             const Array<TwoD, const NekDouble>& df
                             = m_metricinfo->GetDerivFactors(GetPointsKeys());
 
             Array<OneD,NekDouble> diff0(2*nqtot);
             Array<OneD,NekDouble> diff1(diff0+nqtot);
 
             StdTriExp::v_PhysDeriv(inarray, diff0, diff1);
 
             if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 if(out_d0.num_elements())
                 {
                     Vmath::Vmul  (nqtot,df[0],1,diff0,1, out_d0, 1);
                     Vmath::Vvtvp (nqtot,df[1],1,diff1,1, out_d0, 1, out_d0,1);
                 }
 
                 if(out_d1.num_elements())
                 {
                     Vmath::Vmul  (nqtot,df[2],1,diff0,1, out_d1, 1);
                     Vmath::Vvtvp (nqtot,df[3],1,diff1,1, out_d1, 1, out_d1,1);
                 }
 
                 if(out_d2.num_elements())
                 {
                     Vmath::Vmul  (nqtot,df[4],1,diff0,1, out_d2, 1);
                     Vmath::Vvtvp (nqtot,df[5],1,diff1,1, out_d2, 1, out_d2,1);
                 }
             }
             else // regular geometry
             {
                 if(out_d0.num_elements())
                 {
                     Vmath::Smul (nqtot, df[0][0], diff0, 1, out_d0, 1);
                     Blas::Daxpy (nqtot, df[1][0], diff1, 1, out_d0, 1);
                 }
 
                 if(out_d1.num_elements())
                 {
                     Vmath::Smul (nqtot, df[2][0], diff0, 1, out_d1, 1);
                     Blas::Daxpy (nqtot, df[3][0], diff1, 1, out_d1, 1);
                 }
 
                 if(out_d2.num_elements())
                 {
                     Vmath::Smul (nqtot, df[4][0], diff0, 1, out_d2, 1);
                     Blas::Daxpy (nqtot, df[5][0], diff1, 1, out_d2, 1);
                 }
             }
         }

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

protectedvirtual

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

See also: StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 166 of file TriExp.cpp.

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

         {
             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;
             }
         }

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

protectedvirtual

Physical derivative along a direction vector.

See also: StdRegions::StdExpansion::PhysDirectionalDeriv

D_v = D^v_xi * du/d_xi + D^v_eta * du/d_eta

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 195 of file TriExp.cpp.

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

         {
             if(! out.num_elements())
             {
                 return;
             }
 
             int    nquad0 = m_base[0]->GetNumPoints();
             int    nquad1 = m_base[1]->GetNumPoints();
             int    nqtot = nquad0*nquad1;
 
             const Array<TwoD, const NekDouble>& df =
                                 m_metricinfo->GetDerivFactors(GetPointsKeys());
 
             Array<OneD,NekDouble> diff0(2*nqtot);
             Array<OneD,NekDouble> diff1(diff0+nqtot);
 
             // diff0 = du/d_xi, diff1 = du/d_eta
             StdTriExp::v_PhysDeriv(inarray, diff0, diff1);
 
             if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 Array<OneD, Array<OneD, NekDouble> > tangmat(2);
 
 
                 // D^v_xi = v_x*d_xi/dx + v_y*d_xi/dy + v_z*d_xi/dz
                 // D^v_eta = v_x*d_eta/dx + v_y*d_eta/dy + v_z*d_eta/dz
                 for (int i=0; i< 2; ++i)
                 {
                     tangmat[i] = Array<OneD, NekDouble>(nqtot,0.0);
                     for (int k=0; k<(m_geom->GetCoordim()); ++k)
                     {
                         Vmath::Vvtvp(nqtot,&df[2*k+i][0],1,&direction[k*nqtot],1,&tangmat[i][0],1,&tangmat[i][0],1);
                     }
                 }
 
                 /// D_v = D^v_xi * du/d_xi + D^v_eta * du/d_eta
                 Vmath::Vmul  (nqtot,&tangmat[0][0],1,&diff0[0],1, &out[0], 1);
                 Vmath::Vvtvp (nqtot,&tangmat[1][0],1,&diff1[0],1, &out[0], 1, &out[0],1);
             }
             else
             {
                 ASSERTL1(m_metricinfo->GetGtype() == SpatialDomains::eDeformed,"Wrong route");
             }
         }

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

protectedvirtual

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

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

Based on the value of the expansion at the quadrature points, 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 #m_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::StdExpansion2D.

Definition at line 636 of file TriExp.cpp.

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

         {
             Array<OneD,NekDouble> Lcoord = Array<OneD,NekDouble>(2);
 
             ASSERTL0(m_geom,"m_geom not defined");
             m_geom->GetLocCoords(coord,Lcoord);
 
             return StdTriExp::v_PhysEvaluate(Lcoord, physvals);
         }

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

protectedvirtual

Function is used to compute exactly the advective numerical flux on theinterface 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. Furthermore, this function is used to compute the sensor value in each element.

Parameters

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

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1745 of file TriExp.cpp.

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

         {
             int n_coeffs = inarray.num_elements();
             int nquad0   = m_base[0]->GetNumPoints();
             int nquad1   = m_base[1]->GetNumPoints();
             int nqtot    = nquad0*nquad1;
             int nmodes0  = m_base[0]->GetNumModes();
             int nmodes1  = m_base[1]->GetNumModes();
             int numMin2  = nmodes0, i;
 
             Array<OneD, NekDouble> coeff(n_coeffs,0.0);
             Array<OneD, NekDouble> phys_tmp(nqtot,0.0);
             Array<OneD, NekDouble> tmp, tmp2;
 
             const LibUtilities::PointsKey Pkey0 = m_base[0]->GetPointsKey();
             const LibUtilities::PointsKey Pkey1 = m_base[1]->GetPointsKey();
 
             LibUtilities::BasisKey b0(
                 m_base[0]->GetBasisType(), nmodes0, Pkey0);
             LibUtilities::BasisKey b1(
                 m_base[1]->GetBasisType(), nmodes1, Pkey1);
             LibUtilities::BasisKey bortho0(
                 LibUtilities::eOrtho_A,    nmodes0, Pkey0);
             LibUtilities::BasisKey bortho1(
                 LibUtilities::eOrtho_B,    nmodes1, Pkey1);
 
             // Check if it is also possible to use the same InterCoeff routine
             // which is also used for Quadrilateral and Hexagonal shaped
             // elements
 
             // For now, set up the used basis on the standard element to
             // calculate the phys values, set up the orthogonal basis to do a
             // forward transform, to obtain the coefficients in orthogonal
             // coefficient space
             StdRegions::StdTriExpSharedPtr m_OrthoTriExp;
             StdRegions::StdTriExpSharedPtr m_TriExp;
 
             m_TriExp      = MemoryManager<StdRegions::StdTriExp>
                 ::AllocateSharedPtr(b0,      b1);
             m_OrthoTriExp = MemoryManager<StdRegions::StdTriExp>
                 ::AllocateSharedPtr(bortho0, bortho1);
 
             m_TriExp     ->BwdTrans(inarray,phys_tmp);
             m_OrthoTriExp->FwdTrans(phys_tmp, coeff);
 
             for (i = 0; i < n_coeffs; i++)
             {
                 if (i == numMin)
                 {
                     coeff[i]  = 0.0;
                     numMin   += numMin2 - 1;
                     numMin2  -= 1.0;
                 }
             }
 
             m_OrthoTriExp->BwdTrans(coeff,phys_tmp);
             m_TriExp     ->FwdTrans(phys_tmp, outarray);
         }

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

protectedvirtual

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 628 of file TriExp.cpp.

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

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1807 of file TriExp.cpp.

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

         {
             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
             StdTriExp::v_SVVLaplacianFilter( array, mkey);
             
             // Divide by sqrt(Jac)
             Vmath::Vdiv(nq,array,1,sqrt_jac,1,array,1);
         }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1508 of file TriExp.cpp.

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

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1517 of file TriExp.cpp.

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

Member Data Documentation

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

private

Definition at line 288 of file TriExp.h.

Referenced by CreateMatrix(), v_FwdTrans(), v_GetLocMatrix(), v_IProductWRTBase_MatOp(), and v_IProductWRTDerivBase_MatOp().

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

private

Definition at line 289 of file TriExp.h.

Referenced by v_DropLocStaticCondMatrix(), v_FwdTrans_BndConstrained(), and v_GetLocStaticCondMatrix().

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation