Nektar::LocalRegions::TriExp Class Reference

#include <TriExp.h>

Inheritance diagram for Nektar::LocalRegions::TriExp:

Public Member Functions
	TriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const SpatialDomains::Geometry2DSharedPtr &geom)
	Constructor using BasisKey class for quadrature points and order definition. More...
	TriExp (const TriExp &T)
	~TriExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdTriExp
	StdTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)
	StdTriExp ()=default
	StdTriExp (const StdTriExp &T)=default
	~StdTriExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdExpansion2D
	StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)
	StdExpansion2D ()=default
	StdExpansion2D (const StdExpansion2D &T)=default
	~StdExpansion2D () override=default
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)
NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
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	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th trace. More...
int	GetTraceIntNcoeffs (const int i) const
int	GetTraceNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th trace. More...
const LibUtilities::BasisKey	GetTraceBasisKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...
LibUtilities::PointsKey	GetTracePointsKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...
int	NumBndryCoeffs (void) const
int	NumDGBndryCoeffs (void) const
const LibUtilities::PointsKey	GetNodalPointsKey () const
	This function returns the type of expansion Nodal point type if defined. More...
int	GetNtraces () const
	Returns the number of trace elements connected to this element. More...
LibUtilities::ShapeType	DetShapeType () const
	This function returns the shape of the expansion domain. More...
std::shared_ptr< StdExpansion >	GetStdExp () const
std::shared_ptr< StdExpansion >	GetLinStdExp (void) const
int	GetShapeDimension () const
bool	IsBoundaryInteriorExpansion () const
bool	IsNodalNonTensorialExp ()
void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Backward transformation from coefficient space to physical space. More...
void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Forward transformation from physical space to coefficient space. More...
void	FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)
	This function integrates the specified function over the domain. More...
void	FillMode (const int mode, Array< OneD, NekDouble > &outarray)
	This function fills the array outarray with the mode-th mode of the expansion. More...
void	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	this function calculates the inner product of a given function f with the different modes of the expansion More...
void	IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)
void	IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
int	GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id. More...
void	SetElmtId (const int id)
	Set the element id of this expansion when used in a list by returning value of m_elmt_id. More...
void	GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
	this function returns the physical coordinates of the quadrature points of the expansion More...
void	GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
	given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point More...
DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray)
DNekScalBlkMatSharedPtr	GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
void	DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
int	CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
NekDouble	StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
int	GetCoordim ()
void	GetBoundaryMap (Array< OneD, unsigned int > &outarray)
void	GetInteriorMap (Array< OneD, unsigned int > &outarray)
int	GetVertexMap (const int localVertexId, bool useCoeffPacking=false)
void	GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
void	GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray)
void	GetElmtTraceToTraceMap (const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
void	GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eForwards)
void	GetTraceNumModes (const int tid, int &numModes0, int &numModes1, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)
void	MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
DNekMatSharedPtr	CreateGeneralMatrix (const StdMatrixKey &mkey)
	this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) More...
void	GeneralMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)
void	ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)
void	LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)
void	PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void	PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	PhysDeriv_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds)
void	PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn)
void	PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)
void	StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void	StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
NekDouble	PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
	This function evaluates the first derivative of the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)
NekDouble	PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
	This function evaluates the basis function mode mode at a point coords of the domain. More...
void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta. More...
void	LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
	Convert local collapsed coordinates eta into local cartesian coordinate xi. More...
virtual int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray)
virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
virtual void	v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
NekDouble	Linf (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_\infty\) error \( |\epsilon|_\infty = \max |u - u_{exact}|\) where \( u_{exact}\) is given by the array sol. More...
NekDouble	L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_2\) error, \( | \epsilon |_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...
NekDouble	H1 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( H^1\) error, \( | \epsilon |^1_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u - u_{exact})\cdot dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...
const LibUtilities::PointsKeyVector	GetPointsKeys () const
DNekMatSharedPtr	BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
void	PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
	This function performs an interpolation from the physical space points provided at input into an array of equispaced points which are not the collapsed coordinate. So for a tetrahedron you will only get a tetrahedral number of values. More...
void	GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
	This function provides the connectivity of local simplices (triangles or tets) to connect the equispaced data points provided by PhysInterpToSimplexEquiSpaced. More...
void	EquiSpacedToCoeffs (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs a projection/interpolation from the equispaced points sometimes used in post-processing onto the coefficient space. More...
template<class T >
std::shared_ptr< T >	as ()
void	IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)
void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
Public Member Functions inherited from Nektar::LocalRegions::Expansion2D
	Expansion2D (SpatialDomains::Geometry2DSharedPtr pGeom)
	~Expansion2D () override=default
DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)
void	SetTraceToGeomOrientation (Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &inout)
Array< OneD, unsigned int >	GetTraceInverseBoundaryMap (int eid)
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)
SpatialDomains::Geometry2DSharedPtr	GetGeom2D () const
void	ReOrientEdgePhysMap (const int nvert, const StdRegions::Orientation orient, const int nq0, Array< OneD, int > &idmap)
DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override
void	v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp) override
Public Member Functions inherited from Nektar::LocalRegions::Expansion
	Expansion (SpatialDomains::GeometrySharedPtr pGeom)
	Expansion (const Expansion &pSrc)
	~Expansion () override
void	SetTraceExp (const int traceid, ExpansionSharedPtr &f)
ExpansionSharedPtr	GetTraceExp (const int traceid)
DNekScalMatSharedPtr	GetLocMatrix (const LocalRegions::MatrixKey &mkey)
void	DropLocMatrix (const LocalRegions::MatrixKey &mkey)
DNekScalMatSharedPtr	GetLocMatrix (const StdRegions::MatrixType mtype, const StdRegions::ConstFactorMap &factors=StdRegions::NullConstFactorMap, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)
SpatialDomains::GeometrySharedPtr	GetGeom () const
void	Reset ()
IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)
DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)
const SpatialDomains::GeomFactorsSharedPtr &	GetMetricInfo () const
DNekMatSharedPtr	BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
DNekMatSharedPtr	BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
void	ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
NekDouble	VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)
void	NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors)
IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)
void	AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray)
ExpansionSharedPtr	GetLeftAdjacentElementExp () const
ExpansionSharedPtr	GetRightAdjacentElementExp () const
int	GetLeftAdjacentElementTrace () const
int	GetRightAdjacentElementTrace () const
void	SetAdjacentElementExp (int traceid, ExpansionSharedPtr &e)
StdRegions::Orientation	GetTraceOrient (int trace)
void	SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Divided by the metric jacobi and quadrature weights. More...
void	GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray)
	Extract the metric factors to compute the contravariant fluxes along edge edge and stores them into outarray following the local edge orientation (i.e. anticlockwise convention). More...
void	GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=StdRegions::eNoOrientation)
void	GetTracePhysMap (const int edge, Array< OneD, int > &outarray)
void	ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1)
const NormalVector &	GetTraceNormal (const int id)
void	ComputeTraceNormal (const int id)
const Array< OneD, const NekDouble > &	GetPhysNormals (void)
void	SetPhysNormals (Array< OneD, const NekDouble > &normal)
void	SetUpPhysNormals (const int trace)
void	AddRobinMassMatrix (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
void	TraceNormLen (const int traceid, NekDouble &h, NekDouble &p)
void	AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)
const Array< OneD, const NekDouble > &	GetElmtBndNormDirElmtLen (const int nbnd) const
void	StdDerivBaseOnTraceMat (Array< OneD, DNekMatSharedPtr > &DerivMat)

Protected Member Functions
NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrates the specified function over the domain. More...
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) override
	Calculate the derivative of the physical points. More...
void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the derivative of the physical points in a given direction. More...
void	v_PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &out) override
	Physical derivative along a direction vector. More...
void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Transform a given function from physical quadrature space to coefficient space. More...
void	v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray. More...
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true) override
void	v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray) override
void	v_IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Directinoal Derivative in the modal space in the dir direction of varcoeffs. More...
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) override
void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray) override
StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const override
StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const override
void	v_GetCoord (const Array< OneD, const NekDouble > &Lcoords, Array< OneD, NekDouble > &coords) override
void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override
NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals) override
NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coord, const Array< OneD, const NekDouble > &physvals) override
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
void	v_GetTracePhysVals (const int edge, const StdRegions::StdExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) override
void	v_GetTraceQFactors (const int edge, Array< OneD, NekDouble > &outarray) override
void	v_ComputeTraceNormal (const int edge) override
void	v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int mode_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType) override
StdRegions::Orientation	v_GetTraceOrient (int edge) override
void	v_GetTracePhysMap (const int edge, Array< OneD, int > &outarray) override
DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override
DNekMatSharedPtr	v_CreateStdMatrix (const StdRegions::StdMatrixKey &mkey) override
DNekScalMatSharedPtr	v_GetLocMatrix (const MatrixKey &mkey) override
void	v_DropLocMatrix (const MatrixKey &mkey) override
DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const MatrixKey &mkey) override
void	v_DropLocStaticCondMatrix (const MatrixKey &mkey) override
void	v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp) override
void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_ComputeLaplacianMetric () override
void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdRegions::StdMatrixKey &mkey) override
void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors) override
	: This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace. More...
Protected Member Functions inherited from Nektar::StdRegions::StdTriExp
NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrates the specified function over the domain. More...
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) override
	Calculate the derivative of the physical points. More...
void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the derivative of the physical points in a given direction. More...
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) override
void	v_StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Backward tranform for triangular elements. More...
void	v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1) override
void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Transform a given function from physical quadrature space to coefficient space. More...
void	v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray. More...
void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true) override
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) override
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta) override
void	v_LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi) override
void	v_FillMode (const int mode, Array< OneD, NekDouble > &outarray) override
NekDouble	v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) final
NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
int	v_GetNverts () const final
int	v_GetNtraces () const final
LibUtilities::ShapeType	v_DetShapeType () const final
int	v_NumBndryCoeffs () const override
int	v_NumDGBndryCoeffs () const override
int	v_GetTraceNcoeffs (const int i) const override
int	v_GetTraceIntNcoeffs (const int i) const override
int	v_GetTraceNumPoints (const int i) const override
int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset) override
void	v_GetCoords (Array< OneD, NekDouble > &coords_x, Array< OneD, NekDouble > &coords_y, Array< OneD, NekDouble > &coords_z) override
bool	v_IsBoundaryInteriorExpansion () const override
const LibUtilities::BasisKey	v_GetTraceBasisKey (const int i, const int j) const override
int	v_GetVertexMap (int localVertexId, bool useCoeffPacking=false) override
void	v_GetInteriorMap (Array< OneD, unsigned int > &outarray) override
void	v_GetBoundaryMap (Array< OneD, unsigned int > &outarray) override
void	v_GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray) override
void	v_GetTraceInteriorToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation edgeOrient=eForwards) override
DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey) override
DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey) override
void	v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey) override
void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion2D
NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) override
NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
virtual void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0
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)=0
void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray) override
void	v_GetElmtTraceToTraceMap (const unsigned int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q) override
	Determine the mapping to re-orientate the coefficients along the element trace (assumed to align with the standard element) into the orientation of the local trace given by edgeOrient. More...
void	v_GetTraceToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient=eForwards, int P=-1, int Q=-1) override
void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr	CreateStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
	Create the static condensation of a matrix when using a boundary interior decomposition. More...
void	BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
void	LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)
virtual NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
virtual void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv, NekDouble &deriv2)
	This function performs the barycentric interpolation of the polynomial stored in coord at a point physvals using barycentric interpolation weights in direction. More...
template<int DIR>
NekDouble	BaryEvaluateBasis (const NekDouble &coord, const int &mode)
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
	Helper function to pass an unused value by reference into BaryEvaluate. More...
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)
Protected Member Functions inherited from Nektar::LocalRegions::Expansion2D
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) override
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) override
void	v_AddEdgeNormBoundaryInt (const int edge, const ExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) override
void	v_AddRobinMassMatrix (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) override
void	v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs) override
DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) override
void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1) override
void	v_SetUpPhysNormals (const int edge) override
NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec) override
void	v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) override
Protected Member Functions inherited from Nektar::LocalRegions::Expansion
void	ComputeLaplacianMetric ()
void	ComputeQuadratureMetric ()
void	ComputeGmatcdotMF (const Array< TwoD, const NekDouble > &df, const Array< OneD, const NekDouble > &direction, Array< OneD, Array< OneD, NekDouble > > &dfdir)
Array< OneD, NekDouble >	GetMF (const int dir, const int shapedim, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	GetMFDiv (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	GetMFMag (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
void	v_MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_ComputeLaplacianMetric ()
int	v_GetCoordim () const override
void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override
virtual DNekScalMatSharedPtr	v_GetLocMatrix (const LocalRegions::MatrixKey &mkey)
virtual void	v_DropLocMatrix (const LocalRegions::MatrixKey &mkey)
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
virtual void	v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
virtual NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)
virtual void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors)
virtual void	v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray)
virtual StdRegions::Orientation	v_GetTraceOrient (int trace)
void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray)
virtual void	v_GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient)
virtual void	v_GetTracePhysMap (const int edge, Array< OneD, int > &outarray)
virtual void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1=-1)
virtual void	v_ComputeTraceNormal (const int id)
virtual const Array< OneD, const NekDouble > &	v_GetPhysNormals ()
virtual void	v_SetPhysNormals (Array< OneD, const NekDouble > &normal)
virtual void	v_SetUpPhysNormals (const int id)
virtual void	v_AddRobinMassMatrix (const int face, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
virtual void	v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)
virtual void	v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p)
virtual void	v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp)

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

Additional Inherited Members
Protected Attributes inherited from Nektar::StdRegions::StdExpansion
Array< OneD, LibUtilities::BasisSharedPtr >	m_base
int	m_elmt_id
int	m_ncoeffs
LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess >	m_stdMatrixManager
LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess >	m_stdStaticCondMatrixManager
Protected Attributes inherited from Nektar::LocalRegions::Expansion2D
std::vector< bool >	m_requireNeg
Protected Attributes inherited from Nektar::LocalRegions::Expansion
LibUtilities::NekManager< IndexMapKey, IndexMapValues, IndexMapKey::opLess >	m_indexMapManager
std::map< int, ExpansionWeakPtr >	m_traceExp
SpatialDomains::GeometrySharedPtr	m_geom
SpatialDomains::GeomFactorsSharedPtr	m_metricinfo
MetricMap	m_metrics
std::map< int, NormalVector >	m_traceNormals
ExpansionWeakPtr	m_elementLeft
ExpansionWeakPtr	m_elementRight
int	m_elementTraceLeft = -1
int	m_elementTraceRight = -1
std::map< int, Array< OneD, NekDouble > >	m_elmtBndNormDirElmtLen
	the element length in each element boundary(Vertex, edge or face) normal direction calculated based on the local m_metricinfo times the standard element length (which is 2.0) More...

Detailed Description

Definition at line 48 of file TriExp.h.

Constructor & Destructor Documentation

TriExp() [1/2]

Nektar::LocalRegions::TriExp::TriExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		const SpatialDomains::Geometry2DSharedPtr &	geom
	)

Constructor using BasisKey class for quadrature points and order definition.

Definition at line 45 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(
          std::bind(&Expansion2D::CreateMatrix, this, std::placeholders::_1),
          std::string("TriExpMatrix")),
      m_staticCondMatrixManager(std::bind(&Expansion::CreateStaticCondMatrix,
                                          this, std::placeholders::_1),
                                std::string("TriExpStaticCondMatrix"))
{
}

TriExp() [2/2]

Nektar::LocalRegions::TriExp::TriExp

(

const TriExp &

T

)

Definition at line 64 of file TriExp.cpp.

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

~TriExp()

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

overridedefault

Member Function Documentation

v_AlignVectorToCollapsedDir()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 463 of file TriExp.cpp.

{
    ASSERTL1((dir == 0) || (dir == 1) || (dir == 2), "Invalid direction.");
    ASSERTL1((dir == 2) ? (m_geom->GetCoordim() == 3) : true,
             "Invalid direction.");
 
    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(wspsize);
    Array<OneD, NekDouble> tmp3(wspsize);
    Array<OneD, NekDouble> gfac0(wspsize);
    Array<OneD, NekDouble> gfac1(wspsize);
 
    Array<OneD, NekDouble> tmp1 = outarray[0];
    Array<OneD, NekDouble> tmp2 = outarray[1];
 
    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 (int i = 0; i < nquad1; ++i)
    {
        gfac0[i] = 2.0 / (1 - z1[i]);
    }
    for (int i = 0; i < nquad0; ++i)
    {
        gfac1[i] = 0.5 * (1 + z0[i]);
    }
 
    for (int i = 0; i < nquad1; ++i)
    {
        Vmath::Smul(nquad0, gfac0[i], &inarray[0] + i * nquad0, 1,
                    &tmp0[0] + i * nquad0, 1);
    }
 
    for (int 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);
}

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

Referenced by v_IProductWRTDerivBase_SumFac().

v_ComputeLaplacianMetric()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1210 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]]);
        }
    }
}

References Nektar::LocalRegions::Expansion::ComputeQuadratureMetric(), Blas::Dscal(), Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Nektar::LocalRegions::eMetricQuadrature, Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Svtvp(), Vmath::Vmul(), and Vmath::Vvtvp().

v_ComputeTraceNormal()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 818 of file TriExp.cpp.

{
    int i;
    const SpatialDomains::GeomFactorsSharedPtr &geomFactors =
        GetGeom()->GetMetricInfo();
 
    LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
    for (i = 0; i < ptsKeys.size(); ++i)
    {
        // Need at least 2 points for computing normals
        if (ptsKeys[i].GetNumPoints() == 1)
        {
            LibUtilities::PointsKey pKey(2, ptsKeys[i].GetPointsType());
            ptsKeys[i] = pKey;
        }
    }
 
    const SpatialDomains::GeomType type = geomFactors->GetGtype();
    const Array<TwoD, const NekDouble> &df =
        geomFactors->GetDerivFactors(ptsKeys);
    const Array<OneD, const NekDouble> &jac = geomFactors->GetJac(ptsKeys);
 
    // The points of normals should follow trace basis, not local basis.
    LibUtilities::BasisKey tobasis = GetTraceBasisKey(edge);
 
    int nqe = tobasis.GetNumPoints();
    int dim = GetCoordim();
 
    m_traceNormals[edge] = Array<OneD, Array<OneD, NekDouble>>(dim);
    Array<OneD, Array<OneD, NekDouble>> &normal = m_traceNormals[edge];
    for (i = 0; i < dim; ++i)
    {
        normal[i] = Array<OneD, NekDouble>(nqe);
    }
 
    size_t nqb                     = nqe;
    size_t nbnd                    = edge;
    m_elmtBndNormDirElmtLen[nbnd]  = Array<OneD, NekDouble>{nqb, 0.0};
    Array<OneD, NekDouble> &length = m_elmtBndNormDirElmtLen[nbnd];
 
    // Regular geometry case
    if ((type == SpatialDomains::eRegular) ||
        (type == SpatialDomains::eMovingRegular))
    {
        NekDouble fac;
        // Set up normals
        switch (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);
 
        Vmath::Fill(nqb, fac, length, 1);
 
        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, tobasis.GetPointsKey(), work);
        Vmath::Sdiv(nqe, 1.0, &work[0], 1, &work[0], 1);
 
        // interpolate
        for (i = 0; i < GetCoordim(); ++i)
        {
            LibUtilities::Interp1D(from_key, &normals[i * nq],
                                   tobasis.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);
 
        Vmath::Vcopy(nqb, work, 1, length, 1);
 
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vmul(nqe, normal[i], 1, work, 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);
            }
        }
    }
}

References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::LocalRegions::Expansion::GetGeom(), Nektar::LibUtilities::BasisKey::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::LibUtilities::BasisKey::GetPointsKey(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::GetTraceBasisKey(), Nektar::LibUtilities::Interp1D(), Nektar::LocalRegions::Expansion::m_elmtBndNormDirElmtLen, Nektar::LocalRegions::Expansion::m_traceNormals, Vmath::Reverse(), Vmath::Sdiv(), Vmath::Smul(), tinysimd::sqrt(), Vmath::Vcopy(), Vmath::Vmul(), Vmath::Vsqrt(), Vmath::Vvtvp(), and Vmath::Zero().

v_CreateStdMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1073 of file TriExp.cpp.

{
    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);
}

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

v_DropLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1088 of file TriExp.cpp.

{
    m_matrixManager.DeleteObject(mkey);
}

References m_matrixManager.

v_DropLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1098 of file TriExp.cpp.

{
    m_staticCondMatrixManager.DeleteObject(mkey);
}

References m_staticCondMatrixManager.

v_ExtractDataToCoeffs()

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  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1008 of file TriExp.cpp.

{
    int data_order0 = nummodes[mode_offset];
    int fillorder0  = min(m_base[0]->GetNumModes(), data_order0);
    int data_order1 = nummodes[mode_offset + 1];
    int order1      = m_base[1]->GetNumModes();
    int fillorder1  = min(order1, data_order1);
 
    switch (m_base[0]->GetBasisType())
    {
        case LibUtilities::eModified_A:
        case LibUtilities::eOrtho_A:
        {
            int i;
            int cnt  = 0;
            int cnt1 = 0;
 
            ASSERTL1(m_base[1]->GetBasisType() == LibUtilities::eModified_B ||
                         m_base[1]->GetBasisType() == LibUtilities::eOrtho_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");
    }
}

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

v_FwdTrans()

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

overrideprotectedvirtual

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

See also

StdExpansion::FwdTrans

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 249 of file TriExp.cpp.

{
    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;
}

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

v_FwdTransBndConstrained()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 265 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);
 
    if (nmodes[0] == 1 && nmodes[1] == 1)
    {
        outarray[0] = inarray[0];
        return;
    }
 
    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::eForwards};
 
    for (i = 0; i < 3; i++)
    {
        segexp[i]->FwdTransBndConstrained(physEdge[i], coeffEdge[i]);
 
        // this orient goes with the one above and so could
        // probably set both to eForwards
        GetTraceToElementMap(i, mapArray, signArray, orient[i]);
        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];
        }
    }
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdExpansion::DetShapeType(), Blas::Dgemv(), Nektar::StdRegions::eForwards, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::StdRegions::eMass, Nektar::LocalRegions::Expansion2D::GetGeom2D(), Nektar::StdRegions::StdExpansion::GetInteriorMap(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::GetTraceToElementMap(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::IProductWRTBase(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, m_staticCondMatrixManager, Nektar::StdRegions::StdExpansion::MassMatrixOp(), Nektar::StdRegions::StdExpansion::NumBndryCoeffs(), sign, and Vmath::Vsub().

v_GenMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1051 of file TriExp.cpp.

{
    DNekMatSharedPtr returnval;
    switch (mkey.GetMatrixType())
    {
        case StdRegions::eHybridDGHelmholtz:
        case StdRegions::eHybridDGLamToU:
        case StdRegions::eHybridDGLamToQ0:
        case StdRegions::eHybridDGLamToQ1:
        case StdRegions::eHybridDGLamToQ2:
        case StdRegions::eHybridDGHelmBndLam:
        case StdRegions::eInvLaplacianWithUnityMean:
            returnval = Expansion2D::v_GenMatrix(mkey);
            break;
        default:
            returnval = StdTriExp::v_GenMatrix(mkey);
            break;
    }
 
    return returnval;
}

References Nektar::StdRegions::eHybridDGHelmBndLam, Nektar::StdRegions::eHybridDGHelmholtz, Nektar::StdRegions::eHybridDGLamToQ0, Nektar::StdRegions::eHybridDGLamToQ1, Nektar::StdRegions::eHybridDGLamToQ2, Nektar::StdRegions::eHybridDGLamToU, Nektar::StdRegions::eInvLaplacianWithUnityMean, Nektar::StdRegions::StdMatrixKey::GetMatrixType(), and Nektar::LocalRegions::Expansion2D::v_GenMatrix().

v_GetCoord()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 659 of file TriExp.cpp.

{
    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);
    }
}

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

v_GetCoords()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 676 of file TriExp.cpp.

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

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

v_GetLinStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 648 of file TriExp.cpp.

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

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

v_GetLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1083 of file TriExp.cpp.

{
    return m_matrixManager[mkey];
}

References m_matrixManager.

v_GetLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1093 of file TriExp.cpp.

{
    return m_staticCondMatrixManager[mkey];
}

References m_staticCondMatrixManager.

v_GetStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 641 of file TriExp.cpp.

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

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

v_GetTraceOrient()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1046 of file TriExp.cpp.

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

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

v_GetTracePhysMap()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 783 of file TriExp.cpp.

{
    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;
    }
}

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

v_GetTracePhysVals()

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  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 717 of file TriExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nt     = 0;
    // Extract in Cartesian direction because we have to deal with
    // e.g. Gauss-Radau points.
    switch (edge)
    {
        case 0:
            Vmath::Vcopy(nquad0, &(inarray[0]), 1, &(outarray[0]), 1);
            nt = nquad0;
            break;
        case 1:
            Vmath::Vcopy(nquad1, &(inarray[0]) + (nquad0 - 1), nquad0,
                         &(outarray[0]), 1);
            nt = nquad1;
            break;
        case 2:
            Vmath::Vcopy(nquad1, &(inarray[0]), nquad0, &(outarray[0]), 1);
            nt = nquad1;
            break;
        default:
            ASSERTL0(false, "edge value (< 3) is out of range");
            break;
    }
 
    ASSERTL1(EdgeExp->GetBasis(0)->GetPointsType() ==
                 LibUtilities::eGaussLobattoLegendre,
             "Edge expansion should be GLL");
 
    // Interpolate if required
    if (m_base[edge ? 1 : 0]->GetPointsKey() !=
        EdgeExp->GetBasis(0)->GetPointsKey())
    {
        Array<OneD, NekDouble> outtmp(max(nquad0, nquad1));
 
        Vmath::Vcopy(nt, outarray, 1, outtmp, 1);
 
        LibUtilities::Interp1D(m_base[edge ? 1 : 0]->GetPointsKey(), outtmp,
                               EdgeExp->GetBasis(0)->GetPointsKey(), outarray);
    }
 
    if (orient == StdRegions::eNoOrientation)
    {
        orient = GetTraceOrient(edge);
    }
 
    // Reverse data if necessary
    if (orient == StdRegions::eBackwards)
    {
        Vmath::Reverse(EdgeExp->GetNumPoints(0), &outarray[0], 1, &outarray[0],
                       1);
    }
}

References ASSERTL0, ASSERTL1, Nektar::StdRegions::eBackwards, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::StdRegions::eNoOrientation, Nektar::LocalRegions::Expansion::GetTraceOrient(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Reverse(), and Vmath::Vcopy().

v_GetTraceQFactors()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 776 of file TriExp.cpp.

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

References ASSERTL0.

v_HelmholtzMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1147 of file TriExp.cpp.

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

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

v_Integral()

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

overrideprotectedvirtual

Integrates the specified function over the domain.

See also

StdRegions::StdExpansion::Integral.

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 71 of file TriExp.cpp.

{
    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;
}

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

v_IProductWRTBase()

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

overrideprotectedvirtual

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 392 of file TriExp.cpp.

{
    IProductWRTBase_SumFac(inarray, outarray);
}

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

v_IProductWRTBase_SumFac()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 405 of file TriExp.cpp.

{
    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);
    }
}

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

v_IProductWRTDerivBase()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 398 of file TriExp.cpp.

{
    IProductWRTDerivBase_SumFac(dir, inarray, outarray);
}

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

v_IProductWRTDerivBase_SumFac()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 432 of file TriExp.cpp.

{
    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);
 
    Array<OneD, NekDouble> tmp0(4 * wspsize);
    Array<OneD, NekDouble> tmp1(tmp0 + wspsize);
    Array<OneD, NekDouble> tmp2(tmp0 + 2 * wspsize);
    Array<OneD, NekDouble> tmp3(tmp0 + 3 * wspsize);
 
    Array<OneD, Array<OneD, NekDouble>> tmp2D{2};
    tmp2D[0] = tmp1;
    tmp2D[1] = tmp2;
 
    TriExp::v_AlignVectorToCollapsedDir(dir, inarray, tmp2D);
 
    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);
}

References Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), v_AlignVectorToCollapsedDir(), and Vmath::Vadd().

v_IProductWRTDirectionalDerivBase()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 528 of file TriExp.cpp.

{
    IProductWRTDirectionalDerivBase_SumFac(direction, inarray, outarray);
}

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

v_IProductWRTDirectionalDerivBase_SumFac()

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

overrideprotectedvirtual

Directinoal Derivative in the modal space in the dir direction of varcoeffs.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 540 of file TriExp.cpp.

{
    int i;
    int shapedim = 2;
    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);
    }
 
    // Compute gmat \cdot e^j
    Array<OneD, Array<OneD, NekDouble>> dfdir(shapedim);
    Expansion::ComputeGmatcdotMF(df, direction, dfdir);
 
    Vmath::Vmul(nqtot, &dfdir[0][0], 1, &tmp0[0], 1, &tmp0[0], 1);
    Vmath::Vmul(nqtot, &dfdir[1][0], 1, &tmp1[0], 1, &tmp1[0], 1);
    Vmath::Vmul(nqtot, &dfdir[1][0], 1, &inarray[0], 1, &tmp2[0], 1);
 
    Vmath::Vadd(nqtot, &tmp0[0], 1, &tmp1[0], 1, &tmp1[0], 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);
}

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

v_LaplacianMatrixOp() [1/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1110 of file TriExp.cpp.

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

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

v_LaplacianMatrixOp() [2/2]

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  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1117 of file TriExp.cpp.

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

v_LaplacianMatrixOp_MatFree_Kernel()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1154 of file TriExp.cpp.

{
    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.size() >= 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);
}

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().

v_MassLevelCurvatureMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1140 of file TriExp.cpp.

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

v_MassMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1103 of file TriExp.cpp.

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

v_NormalTraceDerivFactors()

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

overrideprotectedvirtual

: This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace.

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1454 of file TriExp.cpp.

{
    int nquad0 = GetNumPoints(0);
    int nquad1 = GetNumPoints(1);
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    if (d0factors.size() != 3)
    {
        d0factors = Array<OneD, Array<OneD, NekDouble>>(3);
        d1factors = Array<OneD, Array<OneD, NekDouble>>(3);
    }
 
    if (d0factors[0].size() != nquad0)
    {
        d0factors[0] = Array<OneD, NekDouble>(nquad0);
        d1factors[0] = Array<OneD, NekDouble>(nquad0);
    }
 
    if (d0factors[1].size() != nquad1)
    {
        d0factors[1] = Array<OneD, NekDouble>(nquad1);
        d0factors[2] = Array<OneD, NekDouble>(nquad1);
        d1factors[1] = Array<OneD, NekDouble>(nquad1);
        d1factors[2] = Array<OneD, NekDouble>(nquad1);
    }
 
    // Outwards normals
    const Array<OneD, const Array<OneD, NekDouble>> &normal_0 =
        GetTraceNormal(0);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_1 =
        GetTraceNormal(1);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_2 =
        GetTraceNormal(2);
 
    int ncoords = normal_0.size();
 
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
 
        // d xi_2/dx n_x
        for (int i = 0; i < nquad0; ++i)
        {
            d1factors[0][i] = df[1][i] * normal_0[0][i];
        }
 
        // d xi_1/dx n_x
        for (int i = 0; i < nquad1; ++i)
        {
            d0factors[1][i] = df[0][(i + 1) * nquad0 - 1] * normal_1[0][i];
            d0factors[2][i] = df[0][i * nquad0] * normal_2[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            // d xi_2/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad0; ++i)
            {
                d1factors[0][i] += df[2 * n + 1][i] * normal_0[n][i];
            }
 
            // d xi_1/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad1; ++i)
            {
                d0factors[1][i] +=
                    df[2 * n][(i + 1) * nquad0 - 1] * normal_1[n][i];
                d0factors[2][i] += df[2 * n][i * nquad0] * normal_2[n][i];
            }
        }
 
        // d0 factors
        // d xi_1/dx n_x
        for (int i = 0; i < nquad0; ++i)
        {
            d0factors[0][i] = df[0][i] * normal_0[0][i];
        }
 
        // d xi_2/dx n_x
        for (int i = 0; i < nquad1; ++i)
        {
            d1factors[1][i] = df[1][(i + 1) * nquad0 - 1] * normal_1[0][i];
            d1factors[2][i] = df[1][i * nquad0] * normal_2[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            // d xi_1/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad0; ++i)
            {
                d0factors[0][i] += df[2 * n][i] * normal_0[n][i];
            }
 
            // d xi_2/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad1; ++i)
            {
                d1factors[1][i] +=
                    df[2 * n + 1][(i + 1) * nquad0 - 1] * normal_1[n][i];
                d1factors[2][i] += df[2 * n + 1][i * nquad0] * normal_2[n][i];
            }
        }
    }
    else
    {
        // d xi_2/dx n_x
        for (int i = 0; i < nquad0; ++i)
        {
            d1factors[0][i] = df[1][0] * normal_0[0][i];
        }
 
        // d xi_1/dx n_x
        for (int i = 0; i < nquad1; ++i)
        {
            d0factors[1][i] = df[0][0] * normal_1[0][i];
            d0factors[2][i] = df[0][0] * normal_2[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            // d xi_2/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad0; ++i)
            {
                d1factors[0][i] += df[2 * n + 1][0] * normal_0[n][i];
            }
 
            // d xi_1/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad1; ++i)
            {
                d0factors[1][i] += df[2 * n][0] * normal_1[n][i];
                d0factors[2][i] += df[2 * n][0] * normal_2[n][i];
            }
        }
 
        // d1factors
        // d xi_1/dx n_x
        for (int i = 0; i < nquad0; ++i)
        {
            d0factors[0][i] = df[0][0] * normal_0[0][i];
        }
 
        // d xi_2/dx n_x
        for (int i = 0; i < nquad1; ++i)
        {
            d1factors[1][i] = df[1][0] * normal_1[0][i];
            d1factors[2][i] = df[1][0] * normal_2[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            // d xi_1/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad0; ++i)
            {
                d0factors[0][i] += df[2 * n][0] * normal_0[n][i];
            }
 
            // d xi_2/dy n_y
            // needs checking for 3D coords
            for (int i = 0; i < nquad1; ++i)
            {
                d1factors[1][i] += df[2 * n + 1][0] * normal_1[n][i];
                d1factors[2][i] += df[2 * n + 1][0] * normal_2[n][i];
            }
        }
    }
}

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

v_NormVectorIProductWRTBase() [1/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 634 of file TriExp.cpp.

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

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

v_NormVectorIProductWRTBase() [2/2]

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  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 606 of file TriExp.cpp.

{
    int nq = m_base[0]->GetNumPoints() * m_base[1]->GetNumPoints();
    Array<OneD, NekDouble> Fn(nq);
 
    const Array<OneD, const Array<OneD, NekDouble>> &normals =
        GetLeftAdjacentElementExp()->GetTraceNormal(
            GetLeftAdjacentElementTrace());
 
    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);
}

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

v_PhysDeriv() [1/2]

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  )

overrideprotectedvirtual

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 94 of file TriExp.cpp.

{
    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.size())
        {
            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.size())
        {
            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.size())
        {
            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.size())
        {
            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.size())
        {
            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.size())
        {
            Vmath::Smul(nqtot, df[4][0], diff0, 1, out_d2, 1);
            Blas::Daxpy(nqtot, df[5][0], diff1, 1, out_d2, 1);
        }
    }
}

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

v_PhysDeriv() [2/2]

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

overrideprotectedvirtual

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

See also

StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 152 of file TriExp.cpp.

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

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

v_PhysDirectionalDeriv()

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

overrideprotectedvirtual

Physical derivative along a direction vector.

See also

StdRegions::StdExpansion::PhysDirectionalDeriv

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

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 184 of file TriExp.cpp.

{
    if (!out.size())
    {
        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
    {
        Array<OneD, Array<OneD, NekDouble>> tangmat(2);
 
        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::Svtvp(nqtot, df[2 * k + i][0], &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);
    }
}

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

v_PhysEvaluate() [1/2]

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

overrideprotectedvirtual

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

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 696 of file TriExp.cpp.

{
    Array<OneD, NekDouble> Lcoord = Array<OneD, NekDouble>(2);
 
    ASSERTL0(m_geom, "m_geom not defined");
    m_geom->GetLocCoords(coord, Lcoord);
 
    return StdExpansion2D::v_PhysEvaluate(Lcoord, physvals);
}

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

v_PhysEvaluate() [2/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 707 of file TriExp.cpp.

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

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

v_ReduceOrderCoeffs()

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

overrideprotectedvirtual

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 1366 of file TriExp.cpp.

{
    int n_coeffs = inarray.size();
    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);
}

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

v_StdPhysEvaluate()

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

overrideprotectedvirtual

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 688 of file TriExp.cpp.

{
    // Evaluate point in local (eta) coordinates.
    return StdExpansion2D::v_PhysEvaluate(Lcoord, physvals);
}

v_SVVLaplacianFilter()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1422 of file TriExp.cpp.

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

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

v_WeakDerivMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdTriExp.

Definition at line 1125 of file TriExp.cpp.

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

v_WeakDirectionalDerivMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1133 of file TriExp.cpp.

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

Member Data Documentation

m_matrixManager

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

private

Definition at line 245 of file TriExp.h.

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

m_staticCondMatrixManager

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

private

Definition at line 247 of file TriExp.h.

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