#include <Expansion2D.h>

Inheritance diagram for Nektar::LocalRegions::Expansion2D:

Public Member Functions
	Expansion2D (SpatialDomains::Geometry2DSharedPtr pGeom)

virtual	~Expansion2D ()

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

Expansion1DSharedPtr	GetEdgeExp (int edge, bool SetUpNormal=true)

void	SetEdgeExp (const int edge, Expansion1DSharedPtr &e)

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

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

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

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

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

Expansion3DSharedPtr	GetLeftAdjacentElementExp () const

Expansion3DSharedPtr	GetRightAdjacentElementExp () const

int	GetLeftAdjacentElementFace () const

int	GetRightAdjacentElementFace () const

void	SetAdjacentElementExp (int face, Expansion3DSharedPtr &f)

SpatialDomains::Geometry2DSharedPtr	GetGeom2D () const

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

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

	Expansion (const Expansion &pSrc)

virtual	~Expansion ()

DNekScalMatSharedPtr	GetLocMatrix (const LocalRegions::MatrixKey &mkey)

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

SpatialDomains::GeometrySharedPtr	GetGeom () const

void	Reset ()

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)

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

	StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey)
	Constructor. More...

	StdExpansion (const StdExpansion &T)
	Copy Constructor. More...

virtual	~StdExpansion ()
	Destructor. More...

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

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

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

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

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

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

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

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

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

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

const Array< OneD, const NekDouble > &	GetPoints (const int dir) const
	This function returns a pointer to the array containing the quadrature points in dir direction. More...

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

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

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

int	GetTotalEdgeIntNcoeffs () const

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

int	DetCartesianDirOfEdge (const int edge)

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

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

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

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

int	GetFaceIntNcoeffs (const int i) const

int	GetTotalFaceIntNcoeffs () const

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

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

int	NumBndryCoeffs (void) const

int	NumDGBndryCoeffs (void) const

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

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

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

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

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

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

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

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion ()

bool	IsNodalNonTensorialExp ()

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

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

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

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

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

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

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

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

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)

IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)

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

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

virtual void	SetUpPhysNormals (const int edge)

void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)

void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, NekDouble > &Fy, Array< OneD, NekDouble > &outarray)

void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)

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

DNekScalBlkMatSharedPtr	GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

void	DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

StdRegions::Orientation	GetForient (int face)

StdRegions::Orientation	GetEorient (int edge)

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

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

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

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

int	GetCoordim ()

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

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

int	GetVertexMap (const int localVertexId, bool useCoeffPacking=false)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

DNekMatSharedPtr	CreateGeneralMatrix (const StdMatrixKey &mkey)
	this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) More...

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

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

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

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

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

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

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

DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual 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)

virtual StdRegions::Orientation	v_GetForient (int face)

virtual StdRegions::Orientation	v_GetEorient (int edge)

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 NormalVector &	GetEdgeNormal (const int edge) const

void	ComputeEdgeNormal (const int edge)

void	NegateEdgeNormal (const int edge)

bool	EdgeNormalNegated (const int edge)

void	ComputeFaceNormal (const int face)

void	NegateFaceNormal (const int face)

bool	FaceNormalNegated (const int face)

void	ComputeVertexNormal (const int vertex)

void	NegateVertexNormal (const int vertex)

bool	VertexNormalNegated (const int vertex)

const NormalVector &	GetFaceNormal (const int face) const

const NormalVector &	GetVertexNormal (const int vertex) const

const NormalVector &	GetSurfaceNormal (const int id) const

const LibUtilities::PointsKeyVector	GetPointsKeys () const

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

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

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

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)

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

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

	StdExpansion2D (const StdExpansion2D &T)

virtual	~StdExpansion2D ()

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

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

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

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

Protected Member Functions
virtual Array< OneD, NekDouble >	v_GetMF (const int dir, const int shapedim, const StdRegions::VarCoeffMap &varcoeffs)

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

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

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

virtual void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &edgeCoeffs, Array< OneD, NekDouble > &out_d)

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

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

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

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

virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)

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

Array< OneD, NekDouble >	v_GetnEdgecdotMF (const int dir, const int edge, ExpansionSharedPtr &EdgeExp_e, const Array< OneD, const Array< OneD, NekDouble > > &normals, const StdRegions::VarCoeffMap &varcoeffs)

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

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

virtual void	v_NegateEdgeNormal (const int edge)

virtual bool	v_EdgeNormalNegated (const int edge)

virtual void	v_SetUpPhysNormals (const int edge)

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

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

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

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)

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

virtual void	v_ComputeLaplacianMetric ()

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

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

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

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

virtual DNekScalMatSharedPtr	v_GetLocMatrix (const LocalRegions::MatrixKey &mkey)

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

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)

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

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

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

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

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

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

void	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	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)

Protected Member Functions inherited from Nektar::StdRegions::StdExpansion2D
virtual NekDouble	v_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...

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

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

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

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

virtual int	v_GetTraceNcoeffs (const int i) const

Protected Attributes
std::vector< Expansion1DWeakPtr >	m_edgeExp

std::vector< bool >	m_requireNeg

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

std::map< int, bool >	m_negatedNormals

Expansion3DWeakPtr	m_elementLeft

Expansion3DWeakPtr	m_elementRight

int	m_elementFaceLeft

int	m_elementFaceRight

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

SpatialDomains::GeomFactorsSharedPtr	m_metricinfo

MetricMap	m_metrics

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

int	m_elmt_id

int	m_ncoeffs

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

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

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

Detailed Description

Definition at line 58 of file Expansion2D.h.

Constructor & Destructor Documentation

◆ Expansion2D()

Nektar::LocalRegions::Expansion2D::Expansion2D ( SpatialDomains::Geometry2DSharedPtr pGeom )

Definition at line 52 of file Expansion2D.cpp.

References m_elementFaceLeft, and m_elementFaceRight.

                                                                         :
             StdExpansion(), Expansion(pGeom), StdExpansion2D()
         {
             m_elementFaceLeft  = -1;
             m_elementFaceRight = -1;
         }

◆ ~Expansion2D()

virtual Nektar::LocalRegions::Expansion2D::~Expansion2D ( )

inlinevirtual

Definition at line 65 of file Expansion2D.h.

References AddEdgeBoundaryInt(), AddHDGHelmholtzEdgeTerms(), AddHDGHelmholtzTraceTerms(), AddNormTraceInt(), GetEdgeExp(), GetGeom2D(), GetLeftAdjacentElementExp(), GetLeftAdjacentElementFace(), GetRightAdjacentElementExp(), GetRightAdjacentElementFace(), LOCAL_REGIONS_EXPORT, Nektar::StdRegions::NullVarCoeffMap, ReOrientEdgePhysMap(), SetAdjacentElementExp(), SetEdgeExp(), and SetTraceToGeomOrientation().

65 {}

Member Function Documentation

◆ AddEdgeBoundaryInt()

void Nektar::LocalRegions::Expansion2D::AddEdgeBoundaryInt	(	const int	edge,
		ExpansionSharedPtr &	EdgeExp,
		Array< OneD, NekDouble > &	edgePhys,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::VarCoeffMap &	varcoeffs = `StdRegions:: NullVarCoeffMap`
	)

inline

For a given edge add the {F}_1j contributions

Variable coeffs

Definition at line 437 of file Expansion2D.cpp.

References Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, Nektar::StdRegions::StdExpansion::GetEdgeToElementMap(), GetPhysEdgeVarCoeffsFromElement(), sign, Nektar::StdRegions::StdExpansion::v_GetEorient(), and Vmath::Vmul().

Referenced by AddNormTraceInt(), and ~Expansion2D().

         {
             int i;
             int order_e = EdgeExp->GetNcoeffs();
             int nquad_e = EdgeExp->GetNumPoints(0);
             Array<OneD,unsigned int> map;
             Array<OneD,int> sign;
             Array<OneD, NekDouble> coeff(order_e);
 
             GetEdgeToElementMap(edge, v_GetEorient(edge), map, sign);
 
             StdRegions::VarCoeffType VarCoeff[3] = {StdRegions::eVarCoeffD00,
                                                     StdRegions::eVarCoeffD11,
                                                     StdRegions::eVarCoeffD22};
             StdRegions::VarCoeffMap::const_iterator x;
 
             /// @TODO Variable coeffs
             if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
             {
                 Array<OneD, NekDouble> work(nquad_e);
                 GetPhysEdgeVarCoeffsFromElement(
                     edge, EdgeExp, x->second, work);
                 Vmath::Vmul(nquad_e, work, 1, edgePhys, 1, edgePhys, 1);
             }
 
             EdgeExp->IProductWRTBase(edgePhys, coeff);
 
             // add data to out array
             for(i = 0; i < order_e; ++i)
             {
                 outarray[map[i]] += sign[i]*coeff[i];
             }
         }

◆ AddHDGHelmholtzEdgeTerms()

void Nektar::LocalRegions::Expansion2D::AddHDGHelmholtzEdgeTerms	(	const NekDouble	tau,
		const int	edge,
		Array< OneD, ExpansionSharedPtr > &	EdgeExp,
		Array< OneD, NekDouble > &	edgePhys,
		const StdRegions::VarCoeffMap &	dirForcing,
		Array< OneD, NekDouble > &	outarray
	)

inline

: What direction to use here??

: Document this (probably not needed)

Definition at line 511 of file Expansion2D.cpp.

Referenced by AddHDGHelmholtzTraceTerms(), and ~Expansion2D().

         {
             bool mmf = (varcoeffs.find(StdRegions::eVarCoeffMF1x) !=
                         varcoeffs.end());
             int i, j, n;
             int nquad_e = EdgeExp[edge]->GetNumPoints(0);
             int order_e = EdgeExp[edge]->GetNcoeffs();
             int coordim = mmf ? 2 : GetCoordim();
             int ncoeffs = GetNcoeffs();
 
             Array<OneD, NekDouble> inval   (nquad_e);
             Array<OneD, NekDouble> outcoeff(order_e);
             Array<OneD, NekDouble> tmpcoeff(ncoeffs);
 
             const Array<OneD, const Array<OneD, NekDouble> > &normals
                                 = GetEdgeNormal(edge);
 
             Array<OneD,unsigned int> emap;
             Array<OneD,int> sign;
 
             StdRegions::Orientation edgedir = GetEorient(edge);
 
             DNekVec                Coeffs  (ncoeffs,outarray,eWrapper);
             DNekVec                Tmpcoeff(ncoeffs,tmpcoeff,eWrapper);
 
             GetEdgeToElementMap(edge,edgedir,emap,sign);
 
             StdRegions::MatrixType DerivType[3] =
             {
                 StdRegions::eWeakDeriv0,
                 StdRegions::eWeakDeriv1,
                 StdRegions::eWeakDeriv2
             };
 
             StdRegions::VarCoeffType VarCoeff[3] =
             {
                 StdRegions::eVarCoeffD00,
                 StdRegions::eVarCoeffD11,
                 StdRegions::eVarCoeffD22
             };
 
             StdRegions::VarCoeffMap::const_iterator x;
             /// @TODO: What direction to use here??
             if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
             {
                 Array<OneD, NekDouble> work(nquad_e);
                 GetPhysEdgeVarCoeffsFromElement(
                     edge, EdgeExp[edge], x->second, work);
                 Vmath::Vmul(nquad_e, work, 1, edgePhys, 1, edgePhys, 1);
             }
 
             //================================================================
             // Add F = \tau <phi_i,in_phys>
             // Fill edge and take inner product
             EdgeExp[edge]->IProductWRTBase(edgePhys, outcoeff);
             // add data to out array
             for(i = 0; i < order_e; ++i)
             {
                 outarray[emap[i]] += sign[i] * tau * outcoeff[i];
             }
             //================================================================
 
             //===============================================================
             // Add -\sum_i D_i^T M^{-1} G_i + E_i M^{-1} G_i = 
             //                         \sum_i D_i M^{-1} G_i term
 
             // Two independent direction
             DNekScalMatSharedPtr invMass;
             for(n = 0; n < coordim; ++n)
             {
                 if (mmf)
                 {
                     StdRegions::VarCoeffMap Weight;
                     Weight[StdRegions::eVarCoeffMass] = v_GetMFMag(n,varcoeffs);
 
                     MatrixKey invMasskey( StdRegions::eInvMass,
                                           DetShapeType(), *this,
                                           StdRegions::NullConstFactorMap,
                                           Weight);
 
                     invMass = GetLocMatrix(invMasskey);
 
                     Array<OneD, NekDouble> ncdotMF_e =
                             v_GetnEdgecdotMF(n, edge, EdgeExp[edge], normals,
                                              varcoeffs);
 
                     Vmath::Vmul(nquad_e, ncdotMF_e, 1, edgePhys, 1, inval, 1);
                 }
                 else
                 {
                     Vmath::Vmul(nquad_e, normals[n], 1, edgePhys, 1, inval, 1);
                     invMass = GetLocMatrix(StdRegions::eInvMass);
                 }
 
                 if (m_negatedNormals[edge])
                 {
                     Vmath::Neg(nquad_e, inval, 1);
                 }
 
                 // Multiply by variable coefficient
                 /// @TODO: Document this (probably not needed)
 //                StdRegions::VarCoeffMap::const_iterator x;
 //                if ((x = varcoeffs.find(VarCoeff[n])) != varcoeffs.end())
 //                {
 //                    GetPhysEdgeVarCoeffsFromElement(edge,EdgeExp[edge],x->second,varcoeff_work);
 //                    Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[edge]->GetPhys(),1,EdgeExp[edge]->UpdatePhys(),1);
 //                }
 
                 EdgeExp[edge]->IProductWRTBase(inval, outcoeff);
 
                 // M^{-1} G
                 for(i = 0; i < ncoeffs; ++i)
                 {
                     tmpcoeff[i] = 0;
                     for(j = 0; j < order_e; ++j)
                     {
                         tmpcoeff[i] += (*invMass)(i,emap[j]) * sign[j]
                                                              * outcoeff[j];
                     }
                 }
 
                 if (mmf)
                 {
                     StdRegions::VarCoeffMap VarCoeffDirDeriv;
                     VarCoeffDirDeriv[StdRegions::eVarCoeffMF] =
                             v_GetMF(n,coordim,varcoeffs);
                     VarCoeffDirDeriv[StdRegions::eVarCoeffMFDiv] =
                             v_GetMFDiv(n,varcoeffs);
 
                     MatrixKey Dmatkey( StdRegions::eWeakDirectionalDeriv,
                                        DetShapeType(), *this,
                                        StdRegions::NullConstFactorMap,
                                        VarCoeffDirDeriv);
 
                     DNekScalMat &Dmat = *GetLocMatrix(Dmatkey);
 
                     Coeffs = Coeffs  + Dmat*Tmpcoeff;
                 }
                 else
                 {
                     if(varcoeffs.find(VarCoeff[n]) != varcoeffs.end())
                     {
                         MatrixKey mkey(DerivType[n], DetShapeType(), *this,
                                 StdRegions::NullConstFactorMap, varcoeffs);
 
                         DNekScalMat &Dmat = *GetLocMatrix(mkey);
                         Coeffs = Coeffs  + Dmat*Tmpcoeff;
                     }
                     else
                     {
                         DNekScalMat &Dmat = *GetLocMatrix(DerivType[n]);
                         Coeffs = Coeffs  + Dmat*Tmpcoeff;
                     }
                 }
             }
         }

◆ AddHDGHelmholtzTraceTerms()

void Nektar::LocalRegions::Expansion2D::AddHDGHelmholtzTraceTerms	(	const NekDouble	tau,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, ExpansionSharedPtr > &	EdgeExp,
		const StdRegions::VarCoeffMap &	dirForcing,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 479 of file Expansion2D.cpp.

References AddHDGHelmholtzEdgeTerms(), ASSERTL0, Nektar::StdRegions::StdExpansion::GetNedges(), Nektar::StdRegions::StdExpansion::GetTotPoints(), and Vmath::Vcopy().

Referenced by v_GenMatrix(), and ~Expansion2D().

         {
             ASSERTL0(&inarray[0] != &outarray[0],
                      "Input and output arrays use the same memory");
 
             int e, cnt, order_e, nedges = GetNedges();
             Array<OneD, const NekDouble> tmp;
             
             cnt = 0;
 
             for(e = 0; e < nedges; ++e)
             {
                 order_e = EdgeExp[e]->GetNcoeffs();  
                 Array<OneD, NekDouble> edgeCoeffs(order_e);
                 Array<OneD, NekDouble> edgePhys  (EdgeExp[e]->GetTotPoints());
 
                 Vmath::Vcopy(order_e, tmp = inarray + cnt, 1, edgeCoeffs, 1);
                 EdgeExp[e]->BwdTrans(edgeCoeffs, edgePhys);
                 AddHDGHelmholtzEdgeTerms(
                     tau, e, EdgeExp, edgePhys, dirForcing, outarray);
 
                 cnt += order_e;
             }
         }

◆ AddNormTraceInt() [1/2]

void Nektar::LocalRegions::Expansion2D::AddNormTraceInt	(	const int	dir,
		Array< OneD, ExpansionSharedPtr > &	EdgeExp,
		Array< OneD, Array< OneD, NekDouble > > &	edgeCoeffs,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 402 of file Expansion2D.cpp.

References AddEdgeBoundaryInt(), Nektar::StdRegions::StdExpansion::GetEdgeNormal(), Nektar::StdRegions::StdExpansion::GetNedges(), m_negatedNormals, Vmath::Neg(), and Vmath::Vmul().

Referenced by v_DGDeriv(), v_GenMatrix(), and ~Expansion2D().

         {
             int e;
             int nquad_e;
             int nedges = GetNedges();
 
             for(e = 0; e < nedges; ++e)
             {
                 nquad_e = EdgeExp[e]->GetNumPoints(0);
 
                 Array<OneD, NekDouble> edgePhys(nquad_e);
                 const Array<OneD, const Array<OneD, NekDouble> > &normals
                     = GetEdgeNormal(e);
                 
                 EdgeExp[e]->BwdTrans(edgeCoeffs[e], edgePhys);
                 
                 Vmath::Vmul(nquad_e, normals[dir], 1, edgePhys, 1, edgePhys, 1);
 
                 if (m_negatedNormals[e])
                 {
                     Vmath::Neg(nquad_e, edgePhys, 1);
                 }
 
                 AddEdgeBoundaryInt(e, EdgeExp[e], edgePhys, outarray);
             }
         }

◆ AddNormTraceInt() [2/2]

void Nektar::LocalRegions::Expansion2D::AddNormTraceInt	(	const int	dir,
		Array< OneD, const NekDouble > &	inarray,
		Array< OneD, ExpansionSharedPtr > &	EdgeExp,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::VarCoeffMap &	varcoeffs
	)

inline

Computes the C matrix entries due to the presence of the identity matrix in Eqn. 32.

: Document this

Definition at line 330 of file Expansion2D.cpp.

References AddEdgeBoundaryInt(), Nektar::StdRegions::eVarCoeffMF1x, Nektar::StdRegions::StdExpansion::GetEdgeNormal(), Nektar::StdRegions::StdExpansion::GetNedges(), m_negatedNormals, Vmath::Neg(), v_GetnEdgecdotMF(), and Vmath::Vmul().

         {
             int i,e,cnt;
             int order_e,nquad_e;
             int nedges = GetNedges();
 
             cnt = 0;
             for(e = 0; e < nedges; ++e)
             {
                 order_e = EdgeExp[e]->GetNcoeffs();
                 nquad_e = EdgeExp[e]->GetNumPoints(0);
 
                 const Array<OneD, const Array<OneD, NekDouble> > &normals
                     = GetEdgeNormal(e);
                 Array<OneD, NekDouble> edgeCoeffs(order_e);
                 Array<OneD, NekDouble> edgePhys  (nquad_e);
                 
                 for(i = 0; i < order_e; ++i)
                 {
                     edgeCoeffs[i] = inarray[i+cnt];
                 }
                 cnt += order_e;
                 
                 EdgeExp[e]->BwdTrans(edgeCoeffs, edgePhys);
                 
                 // Multiply by variable coefficient
                 /// @TODO: Document this
                 // StdRegions::VarCoeffType VarCoeff[3] = {StdRegions::eVarCoeffD00,
                 //                                         StdRegions::eVarCoeffD11,
                 //                                         StdRegions::eVarCoeffD22};
                 // StdRegions::VarCoeffMap::const_iterator x;
                 // Array<OneD, NekDouble> varcoeff_work(nquad_e);
 
                 // if ((x = varcoeffs.find(VarCoeff[dir])) != varcoeffs.end())
                 // {
                 //     GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
                 //     Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
                 // }
 
                 if (varcoeffs.find(StdRegions::eVarCoeffMF1x) !=
                         varcoeffs.end())
                 {
                     // MMF case
                     Array<OneD, NekDouble> ncdotMF_e =
                             v_GetnEdgecdotMF(dir, e, EdgeExp[e], normals,
                                              varcoeffs);
 
                     Vmath::Vmul(nquad_e, ncdotMF_e, 1,
                                          edgePhys,  1,
                                          edgePhys,  1);
                 }
                 else
                 {
                     Vmath::Vmul(nquad_e, normals[dir], 1,
                                          edgePhys,     1,
                                          edgePhys,     1);
                 }
 
                 if (m_negatedNormals[e])
                 {
                     Vmath::Neg(nquad_e, edgePhys, 1);
                 }
 
                 AddEdgeBoundaryInt(e, EdgeExp[e], edgePhys, outarray, varcoeffs);
             }
         }

◆ GetEdgeExp()

Expansion1DSharedPtr Nektar::LocalRegions::Expansion2D::GetEdgeExp	(	int	edge,
		bool	SetUpNormal = `true`
	)

inline

Definition at line 222 of file Expansion2D.h.

References ASSERTL1, Nektar::StdRegions::StdExpansion::GetNedges(), and m_edgeExp.

Referenced by v_GenMatrix(), and ~Expansion2D().

         {
             boost::ignore_unused(SetUpNormal);
             ASSERTL1(edge < GetNedges(), "Edge out of range.");
             return m_edgeExp[edge].lock();
         }

◆ GetGeom2D()

SpatialDomains::Geometry2DSharedPtr Nektar::LocalRegions::Expansion2D::GetGeom2D ( ) const

inline

Definition at line 291 of file Expansion2D.h.

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

Referenced by Nektar::MultiRegions::ExpList1D::ExpList1D(), Nektar::MultiRegions::ExpList2D::ExpList2D(), v_AddEdgeNormBoundaryInt(), Nektar::LocalRegions::TriExp::v_FwdTrans_BndConstrained(), Nektar::LocalRegions::QuadExp::v_FwdTrans_BndConstrained(), v_GetEdgeInverseBoundaryMap(), Nektar::LocalRegions::TriExp::v_GetEorient(), and ~Expansion2D().

         {
             return std::dynamic_pointer_cast<SpatialDomains::
                 Geometry2D>(m_geom);
         }

◆ GetLeftAdjacentElementExp()

Expansion3DSharedPtr Nektar::LocalRegions::Expansion2D::GetLeftAdjacentElementExp ( ) const

inline

Definition at line 245 of file Expansion2D.h.

References ASSERTL1, GetRightAdjacentElementExp(), and m_elementLeft.

Referenced by SetEdgeExp(), Nektar::MultiRegions::ExpList2D::v_GetNormals(), Nektar::LocalRegions::QuadExp::v_NormVectorIProductWRTBase(), Nektar::LocalRegions::TriExp::v_NormVectorIProductWRTBase(), v_VectorFlux(), and ~Expansion2D().

         {
             ASSERTL1(m_elementLeft.lock().get(),
                      "Left adjacent element not set.");
             return m_elementLeft.lock();
         }

◆ GetLeftAdjacentElementFace()

int Nektar::LocalRegions::Expansion2D::GetLeftAdjacentElementFace ( ) const

inline

Definition at line 261 of file Expansion2D.h.

References m_elementFaceLeft.

Referenced by Nektar::LocalRegions::QuadExp::v_NormVectorIProductWRTBase(), Nektar::LocalRegions::TriExp::v_NormVectorIProductWRTBase(), v_VectorFlux(), and ~Expansion2D().

         {
             return m_elementFaceLeft;
         }

◆ GetPhysEdgeVarCoeffsFromElement()

void Nektar::LocalRegions::Expansion2D::GetPhysEdgeVarCoeffsFromElement	(	const int	edge,
		ExpansionSharedPtr &	EdgeExp,
		const Array< OneD, const NekDouble > &	varcoeff,
		Array< OneD, NekDouble > &	outarray
	)

protected

Extracts the variable coefficients along an edge

Definition at line 678 of file Expansion2D.cpp.

References Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::GetEdgeToElementMap(), Nektar::StdRegions::StdExpansion::GetEorient(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), and sign.

Referenced by AddEdgeBoundaryInt(), AddHDGHelmholtzEdgeTerms(), v_GenMatrix(), and v_GetnEdgecdotMF().

         {
             Array<OneD, NekDouble> tmp(GetNcoeffs());
             Array<OneD, NekDouble> edgetmp(EdgeExp->GetNcoeffs());
 
             // FwdTrans varcoeffs
             FwdTrans(varcoeff, tmp);
 
             // Map to edge
             Array<OneD,unsigned int>    emap;
             Array<OneD, int>            sign;
             StdRegions::Orientation edgedir = GetEorient(edge);
             GetEdgeToElementMap(edge,edgedir,emap,sign);
 
             for (unsigned int i = 0; i < EdgeExp->GetNcoeffs(); ++i)
             {
                 edgetmp[i] = tmp[emap[i]];
             }
 
             // BwdTrans
             EdgeExp->BwdTrans(edgetmp, outarray);
         }

◆ GetRightAdjacentElementExp()

Expansion3DSharedPtr Nektar::LocalRegions::Expansion2D::GetRightAdjacentElementExp ( ) const

inline

Definition at line 253 of file Expansion2D.h.

References ASSERTL1, m_elementLeft, and m_elementRight.

Referenced by GetLeftAdjacentElementExp(), and ~Expansion2D().

         {
             ASSERTL1(m_elementLeft.lock().get(),
                      "Right adjacent element not set.");
             
             return m_elementRight.lock();
         }

◆ GetRightAdjacentElementFace()

int Nektar::LocalRegions::Expansion2D::GetRightAdjacentElementFace ( ) const

inline

Definition at line 266 of file Expansion2D.h.

References m_elementFaceRight.

Referenced by ~Expansion2D().

         {
             return m_elementFaceRight;
         }

◆ ReOrientEdgePhysMap()

void Nektar::LocalRegions::Expansion2D::ReOrientEdgePhysMap	(	const int	nvert,
		const StdRegions::Orientation	orient,
		const int	nq0,
		Array< OneD, int > &	idmap
	)

Definition at line 1601 of file Expansion2D.cpp.

References ASSERTL0, Nektar::StdRegions::eBackwards, and Nektar::StdRegions::eForwards.

Referenced by ~Expansion2D().

         {
             boost::ignore_unused(nvert);
 
             if (idmap.num_elements() != nq0)
             {
                 idmap = Array<OneD, int>(nq0);
             }
             switch (orient)
             {
                 case StdRegions::eForwards:
                     // Fwd
                     for (int i = 0; i < nq0; ++i)
                     {
                         idmap[i] = i;
                     }
                     break;
                 case StdRegions::eBackwards:
                 {
                     // Bwd
                     for (int i = 0; i < nq0; ++i)
                     {
                         idmap[i] = nq0-1-i;
                     }
                 }
                     break;
                 default:
                     ASSERTL0(false, "Unknown orientation");
                     break;
             }
         }

◆ ReOrientQuadEdgePhysMap()

void Nektar::LocalRegions::Expansion2D::ReOrientQuadEdgePhysMap	(	const StdRegions::Orientation	orient,
		const int	nq0,
		Array< OneD, int > &	idmap
	)

protected

◆ SetAdjacentElementExp()

void Nektar::LocalRegions::Expansion2D::SetAdjacentElementExp	(	int	face,
		Expansion3DSharedPtr &	f
	)

inline

Definition at line 271 of file Expansion2D.h.

References ASSERTL1, m_elementFaceLeft, m_elementFaceRight, m_elementLeft, and m_elementRight.

Referenced by Nektar::MultiRegions::DisContField3D::SetUpDG(), and ~Expansion2D().

         {
             if (m_elementLeft.lock().get())
             {
                 ASSERTL1(!m_elementRight.lock().get(),
                          "Both adjacent elements already set.");
                 
                 m_elementRight     = f;
                 m_elementFaceRight = face;
             }
             else
             {
                 m_elementLeft      = f;
                 m_elementFaceLeft  = face;
             }
         }

◆ SetEdgeExp()

void Nektar::LocalRegions::Expansion2D::SetEdgeExp	(	const int	edge,
		Expansion1DSharedPtr &	e
	)

inline

Definition at line 231 of file Expansion2D.h.

References ASSERTL1, GetLeftAdjacentElementExp(), Nektar::StdRegions::StdExpansion::GetNedges(), and m_edgeExp.

Referenced by ~Expansion2D().

         {
             unsigned int nEdges = GetNedges();
             ASSERTL1(edge < nEdges, "Edge out of range.");
             if (m_edgeExp.size() < nEdges)
             {
                 m_edgeExp.resize(nEdges);
             }
             m_edgeExp[edge] = e;
         }

◆ SetTraceToGeomOrientation()

void Nektar::LocalRegions::Expansion2D::SetTraceToGeomOrientation	(	Array< OneD, ExpansionSharedPtr > &	EdgeExp,
		Array< OneD, NekDouble > &	inout
	)

Definition at line 309 of file Expansion2D.cpp.

References Nektar::StdRegions::StdExpansion::GetEdgeNcoeffs(), Nektar::StdRegions::StdExpansion::GetEorient(), and Nektar::StdRegions::StdExpansion::GetNedges().

Referenced by v_GenMatrix(), and ~Expansion2D().

         {
             int i, cnt = 0;
             int nedges = GetNedges();
             Array<OneD, NekDouble> e_tmp;
             
             for(i = 0; i < nedges; ++i)
             {
                 EdgeExp[i]->SetCoeffsToOrientation(GetEorient(i),
                                                    e_tmp = inout + cnt, 
                                                    e_tmp = inout + cnt);
                 cnt += GetEdgeNcoeffs(i);
             }
         }

◆ v_AddEdgeNormBoundaryInt() [1/2]

void Nektar::LocalRegions::Expansion2D::v_AddEdgeNormBoundaryInt	(	const int	edge,
		const ExpansionSharedPtr &	EdgeExp,
		const Array< OneD, const NekDouble > &	Fx,
		const Array< OneD, const NekDouble > &	Fy,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Definition at line 59 of file Expansion2D.cpp.

References Nektar::LocalRegions::Expansion::AddEdgeNormBoundaryInt(), ASSERTL1, Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::StdRegions::StdExpansion::GetEdgeNormal(), GetGeom2D(), Nektar::StdRegions::StdExpansion::GetNedges(), m_edgeExp, m_negatedNormals, m_requireNeg, Vmath::Neg(), Vmath::Vmul(), and Vmath::Vvtvp().

         {
             ASSERTL1(GetCoordim() == 2,
                      "Routine only set up for two-dimensions");
 
             const Array<OneD, const Array<OneD, NekDouble> > normals
                                     = GetEdgeNormal(edge);
 
             if (m_requireNeg.size() == 0)
             {
                 m_requireNeg.resize(GetNedges());
                 
                 for (int i = 0; i < GetNedges(); ++i)
                 {
                     m_requireNeg[i] = false;
                     if (m_negatedNormals[i])
                     {
                         m_requireNeg[i] = true;
                         continue;
                     }
                     
                     Expansion1DSharedPtr edgeExp =
                                     m_edgeExp[i].lock()->as<Expansion1D>();
 
                     if (edgeExp->GetRightAdjacentElementExp())
                     {
                         if (edgeExp->GetRightAdjacentElementExp()->GetGeom2D()
                             ->GetGlobalID() == GetGeom2D()->GetGlobalID())
                         {
                             m_requireNeg[i] = true;
                         }
                     }
                 }
             }
 
             // We allow the case of mixed polynomial order by supporting only
             // those modes on the edge common to both adjoining elements. This
             // is enforced here by taking the minimum size and padding with
             // zeros.
             int nquad_e = min(EdgeExp->GetNumPoints(0),
                               int(normals[0].num_elements()));
 
             int nEdgePts = EdgeExp->GetTotPoints();
             Array<OneD, NekDouble> edgePhys(nEdgePts);
             Vmath::Vmul (nquad_e, normals[0], 1, Fx, 1, edgePhys, 1);
             Vmath::Vvtvp(nquad_e, normals[1], 1, Fy, 1, edgePhys, 1,
                                   edgePhys,   1);
 
             Expansion1DSharedPtr locExp = EdgeExp->as<Expansion1D>();
 
             if (m_negatedNormals[edge])
             {
                 Vmath::Neg(nquad_e, edgePhys, 1);
             }
             else if (locExp->GetRightAdjacentElementEdge() != -1)
             {
                 if (locExp->GetRightAdjacentElementExp()->GetGeom2D()->GetGlobalID() 
                     == GetGeom2D()->GetGlobalID())
                 {
                     Vmath::Neg(nquad_e, edgePhys, 1);
                 }
             }
 
             AddEdgeNormBoundaryInt(edge, EdgeExp, edgePhys, outarray);
         }

◆ v_AddEdgeNormBoundaryInt() [2/2]

void Nektar::LocalRegions::Expansion2D::v_AddEdgeNormBoundaryInt	(	const int	edge,
		const ExpansionSharedPtr &	EdgeExp,
		const Array< OneD, const NekDouble > &	Fn,
		Array< OneD, NekDouble > &	outarray
	)

protectedvirtual

Definition at line 130 of file Expansion2D.cpp.

         {
             int i;
 
             if (m_requireNeg.size() == 0)
             {
                 m_requireNeg.resize(GetNedges());
                 
                 for (i = 0; i < GetNedges(); ++i)
                 {
                     m_requireNeg[i] = false;
                     if (m_negatedNormals[i])
                     {
                         m_requireNeg[i] = true;
                         continue;
                     }
 
                     Expansion1DSharedPtr edgeExp = 
                                 m_edgeExp[i].lock()->as<Expansion1D>();
 
                     if (edgeExp->GetRightAdjacentElementExp())
                     {
                         if (edgeExp->GetRightAdjacentElementExp()->GetGeom2D()
                             ->GetGlobalID() == GetGeom2D()->GetGlobalID())
                         {
                             m_requireNeg[i] = true;
                         }
                     }
                 }
             }
 
             StdRegions::IndexMapKey ikey(
                 StdRegions::eEdgeToElement, DetShapeType(),
                 GetBasisNumModes(0), GetBasisNumModes(1), 0,
                 edge, GetEorient(edge));
             StdRegions::IndexMapValuesSharedPtr map =
                 StdExpansion::GetIndexMap(ikey);
 
             // Order of the element
             int order_e = map->num_elements();
             // Order of the trace
             int n_coeffs = EdgeExp->GetNcoeffs();
 
             Array<OneD, NekDouble> edgeCoeffs(n_coeffs);
             if(n_coeffs!=order_e) // Going to orthogonal space
             {
                 EdgeExp->FwdTrans(Fn, edgeCoeffs);
                 Expansion1DSharedPtr locExp = EdgeExp->as<Expansion1D>();
                 
                 if (m_requireNeg[edge])
                 {
                     Vmath::Neg(n_coeffs, edgeCoeffs, 1);
                 }
                 
                 Array<OneD, NekDouble> coeff(n_coeffs,0.0);
                 LibUtilities::BasisType btype = ((LibUtilities::BasisType) 1); //1-->Ortho_A
                 LibUtilities::BasisKey bkey_ortho(btype,EdgeExp->GetBasis(0)->GetNumModes(),EdgeExp->GetBasis(0)->GetPointsKey());
                 LibUtilities::BasisKey bkey(EdgeExp->GetBasis(0)->GetBasisType(),EdgeExp->GetBasis(0)->GetNumModes(),EdgeExp->GetBasis(0)->GetPointsKey());
                 LibUtilities::InterpCoeff1D(bkey,edgeCoeffs,bkey_ortho,coeff);
 
                 // Cutting high frequencies
                 for(i = order_e; i < n_coeffs; i++)
                 {
                     coeff[i] = 0.0;
                 }   
 
                 LibUtilities::InterpCoeff1D(bkey_ortho,coeff,bkey,edgeCoeffs);
                 
                 StdRegions::StdMatrixKey masskey(StdRegions::eMass,LibUtilities::eSegment,*EdgeExp);
                 EdgeExp->MassMatrixOp(edgeCoeffs, edgeCoeffs, masskey);
             }
             else
             {
                 EdgeExp->IProductWRTBase(Fn, edgeCoeffs);
 
                 Expansion1DSharedPtr locExp = EdgeExp->as<Expansion1D>();
                 
                 if (m_requireNeg[edge])
                 {
                     Vmath::Neg(n_coeffs, edgeCoeffs, 1);
                 }
             }
             
             // Implementation for all the basis except Gauss points
             if(EdgeExp->GetBasis(0)->GetBasisType() !=
                    LibUtilities::eGauss_Lagrange)
             {
                 // add data to outarray if forward edge normal is outwards
                 for(i = 0; i < order_e; ++i)
                 {
                     outarray[(*map)[i].index] +=
                         (*map)[i].sign * edgeCoeffs[i];
                 }
             }
             else
             {
                 int nCoeffs0, nCoeffs1;
                 int j;
                 
                 StdRegions::ConstFactorMap factors;
                 factors[StdRegions::eFactorGaussEdge] = edge;
                 StdRegions::StdMatrixKey key(StdRegions::eGaussDG,
                                              DetShapeType(),*this,factors);
                 
                 DNekMatSharedPtr mat_gauss = m_stdMatrixManager[key];
                 
                 switch(edge)
                 {
                     case 0:
                     {
                         nCoeffs1 = m_base[1]->GetNumModes();
                         
                         for(i = 0; i < order_e; ++i)
                         {
                             for(j = 0; j < nCoeffs1; j++)
                             {
                                 outarray[(*map)[i].index + j*order_e] +=
                                     mat_gauss->GetPtr()[j]*
                                     (*map)[i].sign*edgeCoeffs[i];
                             }
                         }
                         break;
                     }
                     case 1:
                     {
                         nCoeffs0 = m_base[0]->GetNumModes();
                         
                         for(i = 0; i < order_e; ++i)
                         {
                             for(j = 0; j < nCoeffs0; j++)
                             {
                                 outarray[(*map)[i].index - j] +=
                                     mat_gauss->GetPtr()[order_e - 1 -j]*
                                     (*map)[i].sign*edgeCoeffs[i];
                             }
                         }
                         break;
                     }
                     case 2:
                     {
                         nCoeffs1 = m_base[1]->GetNumModes();
                         
                         for(i = 0; i < order_e; ++i)
                         {
                             for(j = 0; j < nCoeffs1; j++)
                             {
                                 outarray[(*map)[i].index - j*order_e] +=
                                     mat_gauss->GetPtr()[order_e - 1 - j]*
                                     (*map)[i].sign*edgeCoeffs[i];
                             }
                         }
                         break;
                     }
                     case 3:
                     {
                         nCoeffs0 = m_base[0]->GetNumModes();
                         
                         for(i = 0; i < order_e; ++i)
                         {
                             for(j = 0; j < nCoeffs0; j++)
                             {
                                 outarray[(*map)[i].index + j] +=
                                     mat_gauss->GetPtr()[j]*
                                     (*map)[i].sign*edgeCoeffs[i];
                             }
                         }
                         break;
                     }
                     default:
                         ASSERTL0(false,"edge value (< 3) is out of range");
                         break;
                 }
             }
         }

◆ v_AddRobinEdgeContribution()

void Nektar::LocalRegions::Expansion2D::v_AddRobinEdgeContribution	(	const int	edgeid,
		const Array< OneD, const NekDouble > &	primCoeffs,
		Array< OneD, NekDouble > &	coeffs
	)

protectedvirtual

Given an edge and vector of element coefficients:

maps those elemental coefficients corresponding to the edge into an edge-vector.
resets the element coefficients
multiplies the edge vector by the edge mass matrix
maps the edge coefficients back onto the elemental coefficients

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1461 of file Expansion2D.cpp.

References ASSERTL1, Nektar::StdRegions::eMass, Nektar::LibUtilities::eSegment, Nektar::StdRegions::eVarCoeffMass, Nektar::StdRegions::StdExpansion::GetEdgeToElementMap(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::IsBoundaryInteriorExpansion(), m_edgeExp, Nektar::StdRegions::NullConstFactorMap, sign, Nektar::StdRegions::StdExpansion::v_GetEorient(), and Vmath::Zero().

         {
             ASSERTL1(IsBoundaryInteriorExpansion(),
                      "Not set up for non boundary-interior expansions");
             int i;
             ExpansionSharedPtr edgeExp = m_edgeExp[edgeid].lock();
             int order_e = edgeExp->GetNcoeffs();
 
             Array<OneD,unsigned int> map;
             Array<OneD,int> sign;
 
             StdRegions::VarCoeffMap varcoeffs;
             varcoeffs[StdRegions::eVarCoeffMass] = primCoeffs;
 
             LocalRegions::MatrixKey mkey(StdRegions::eMass,LibUtilities::eSegment, *edgeExp, StdRegions::NullConstFactorMap, varcoeffs);
             DNekScalMat &edgemat = *edgeExp->GetLocMatrix(mkey);
 
             NekVector<NekDouble> vEdgeCoeffs (order_e);
 
             GetEdgeToElementMap(edgeid,v_GetEorient(edgeid),map,sign);
 
             for (i = 0; i < order_e; ++i)
             {
                 vEdgeCoeffs[i] = coeffs[map[i]]*sign[i];
             }
             Vmath::Zero(GetNcoeffs(), coeffs, 1);
 
             vEdgeCoeffs = edgemat * vEdgeCoeffs;
 
             for (i = 0; i < order_e; ++i)
             {
                 coeffs[map[i]] = vEdgeCoeffs[i]*sign[i];
             }
         }

◆ v_AddRobinMassMatrix()

void Nektar::LocalRegions::Expansion2D::v_AddRobinMassMatrix	(	const int	edgeid,
		const Array< OneD, const NekDouble > &	primCoeffs,
		DNekMatSharedPtr &	inoutmat
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1336 of file Expansion2D.cpp.

         {
             ASSERTL1(IsBoundaryInteriorExpansion(),
                      "Not set up for non boundary-interior expansions");
             ASSERTL1(inoutmat->GetRows() == inoutmat->GetColumns(),
                      "Assuming that input matrix was square");
             int i,j;
             int id1,id2;
             ExpansionSharedPtr edgeExp = m_edgeExp[edge].lock();
             int order_e = edgeExp->GetNcoeffs();
          
             Array<OneD,unsigned int> map;
             Array<OneD,int> sign;
             
             StdRegions::VarCoeffMap varcoeffs;
             varcoeffs[StdRegions::eVarCoeffMass] = primCoeffs;
 
             LocalRegions::MatrixKey mkey(StdRegions::eMass,LibUtilities::eSegment, *edgeExp, StdRegions::NullConstFactorMap, varcoeffs);
             DNekScalMat &edgemat = *edgeExp->GetLocMatrix(mkey);
 
             // Now need to identify a map which takes the local edge
             // mass matrix to the matrix stored in inoutmat;
             // This can currently be deduced from the size of the matrix
             
             // - if inoutmat.m_rows() == v_NCoeffs() it is a full
             //   matrix system
             
             // - if inoutmat.m_rows() == v_NumBndCoeffs() it is a
             //  boundary CG system
 
             // - if inoutmat.m_rows() == v_NumDGBndCoeffs() it is a
             //  trace DG system
             int rows = inoutmat->GetRows();
 
             if (rows == GetNcoeffs())
             {
                 GetEdgeToElementMap(edge,v_GetEorient(edge),map,sign);
             }
             else if(rows == NumBndryCoeffs())
             {
                 int nbndry = NumBndryCoeffs();
                 Array<OneD,unsigned int> bmap(nbndry);
 
                 GetEdgeToElementMap(edge,v_GetEorient(edge),map,sign);
 
                 GetBoundaryMap(bmap);
                 
                 for(i = 0; i < order_e; ++i)
                 {
                     for(j = 0; j < nbndry; ++j)
                     {
                         if(map[i] == bmap[j])
                         {
                             map[i] = j;
                             break;
                         }
                     }
                     ASSERTL1(j != nbndry,"Did not find number in map");
                 }
             }
             else if (rows == NumDGBndryCoeffs())
             {
                 // possibly this should be a separate method
                 int cnt = 0; 
                 map  = Array<OneD, unsigned int> (order_e);
                 sign = Array<OneD, int> (order_e,1);
                 
                 for(i = 0; i < edge; ++i)
                 {
                     cnt += GetEdgeNcoeffs(i);
                 }
                 
                 for(i = 0; i < order_e; ++i)
                 {
                     map[i] = cnt++;
                 }
                 // check for mapping reversal 
                 if(GetEorient(edge) == StdRegions::eBackwards)
                 {
                     switch(edgeExp->GetBasis(0)->GetBasisType())
                     {
                     case LibUtilities::eGauss_Lagrange:
                         reverse( map.get() , map.get()+order_e);
                         break;
                     case LibUtilities::eGLL_Lagrange:
                         reverse( map.get() , map.get()+order_e);
                         break;
                     case LibUtilities::eModified_A:
                         {
                             swap(map[0],map[1]);
                             for(i = 3; i < order_e; i+=2)
                             {
                                 sign[i] = -1;
                             }  
                         }
                         break;
                     default:
                         ASSERTL0(false,"Edge boundary type not valid for this method");
                     }
                 }
             }
             else
             {
                 ASSERTL0(false,"Could not identify matrix type from dimension");
             }
 
             for(i = 0; i < order_e; ++i)
             {
                 id1 = map[i];
                 for(j = 0; j < order_e; ++j)
                 {
                     id2 = map[j];
                     (*inoutmat)(id1,id2) +=  edgemat(i,j)*sign[i]*sign[j];
                 }
             }
         }

◆ v_BuildVertexMatrix()

DNekMatSharedPtr Nektar::LocalRegions::Expansion2D::v_BuildVertexMatrix ( const DNekScalMatSharedPtr & r_bnd )

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1496 of file Expansion2D.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::eFULL, Nektar::StdRegions::StdExpansion::GetNverts(), and Nektar::StdRegions::StdExpansion::GetVertexMap().

         {
             MatrixStorage storage = eFULL;
             DNekMatSharedPtr m_vertexmatrix;
 
             int nVerts, vid1, vid2, vMap1, vMap2;
             NekDouble VertexValue;
 
             nVerts = GetNverts();
 
             m_vertexmatrix =
                 MemoryManager<DNekMat>::AllocateSharedPtr(
                     nVerts, nVerts, 0.0, storage);
             DNekMat &VertexMat = (*m_vertexmatrix);
 
             for (vid1 = 0; vid1 < nVerts; ++vid1)
             {
                 vMap1 = GetVertexMap(vid1);
 
                 for (vid2 = 0; vid2 < nVerts; ++vid2)
                 {
                     vMap2 = GetVertexMap(vid2);
                     VertexValue = (*r_bnd)(vMap1, vMap2);
                     VertexMat.SetValue(vid1, vid2, VertexValue);
                 }
             }
 
             return m_vertexmatrix;
         }

◆ v_DGDeriv()

void Nektar::LocalRegions::Expansion2D::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
	)

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1298 of file Expansion2D.cpp.

References AddNormTraceInt(), Nektar::StdRegions::eInvMass, Nektar::StdRegions::eWeakDeriv0, Nektar::StdRegions::eWeakDeriv1, Nektar::StdRegions::eWeakDeriv2, Nektar::eWrapper, Nektar::LocalRegions::Expansion::GetLocMatrix(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Vmath::Neg(), and Nektar::Transpose().

         {
             StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                                    StdRegions::eWeakDeriv1,
                                                    StdRegions::eWeakDeriv2};
 
             int ncoeffs = GetNcoeffs();
 
             DNekScalMat &InvMass = *GetLocMatrix(StdRegions::eInvMass);
             DNekScalMat &Dmat    = *GetLocMatrix(DerivType[dir]);
 
             Array<OneD, NekDouble> coeffs = incoeffs;
             DNekVec     Coeffs  (ncoeffs,coeffs, eWrapper);
 
             Coeffs = Transpose(Dmat)*Coeffs;
             Vmath::Neg(ncoeffs, coeffs,1);
 
             // Add the boundary integral including the relevant part of
             // the normal
             AddNormTraceInt(dir, EdgeExp, edgeCoeffs, coeffs);
 
             DNekVec Out_d (ncoeffs,out_d,eWrapper);
 
             Out_d  = InvMass*Coeffs;
         }

◆ v_EdgeNormalNegated()

bool Nektar::LocalRegions::Expansion2D::v_EdgeNormalNegated ( const int edge )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1596 of file Expansion2D.cpp.

References m_negatedNormals.

         {
             return m_negatedNormals[edge];
         }

◆ v_GenMatrix()

DNekMatSharedPtr Nektar::LocalRegions::Expansion2D::v_GenMatrix ( const StdRegions::StdMatrixKey & mkey )

protectedvirtual

Computes matrices needed for the HDG formulation. References to equations relate to the following paper: R. M. Kirby, S. J. Sherwin, B. Cockburn, To CG or to HDG: A Comparative Study, J. Sci. Comp P1-30 DOI 10.1007/s10915-011-9501-7

TODO: Add variable coeffs

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::NodalTriExp.

Definition at line 713 of file Expansion2D.cpp.

Referenced by Nektar::LocalRegions::NodalTriExp::v_GenMatrix(), Nektar::LocalRegions::QuadExp::v_GenMatrix(), and Nektar::LocalRegions::TriExp::v_GenMatrix().

         {
             DNekMatSharedPtr returnval;
             
             switch(mkey.GetMatrixType())
             {
             // (Z^e)^{-1} (Eqn. 33, P22)
             case StdRegions::eHybridDGHelmholtz:
                 {
                     ASSERTL1(IsBoundaryInteriorExpansion(),
                              "HybridDGHelmholtz matrix not set up "
                              "for non boundary-interior expansions");
                     
                     int       i,j,k;
                     NekDouble lambdaval = mkey.GetConstFactor(StdRegions::eFactorLambda);
                     NekDouble tau       = mkey.GetConstFactor(StdRegions::eFactorTau);
                     int       ncoeffs   = GetNcoeffs();
                     int       nedges    = GetNedges();
                     int       shapedim  = 2;
                     const StdRegions::VarCoeffMap &varcoeffs
                                         = mkey.GetVarCoeffs();
                     bool      mmf       =
                         (varcoeffs.find(StdRegions::eVarCoeffMF1x) !=
                          varcoeffs.end());
 
                     Array<OneD,unsigned int> emap;
                     Array<OneD,int> sign;
                     StdRegions::Orientation edgedir = StdRegions::eForwards;
                     ExpansionSharedPtr EdgeExp;
                     ExpansionSharedPtr EdgeExp2;
 
                     int order_e, coordim = GetCoordim();
                     DNekScalMat  &invMass = *GetLocMatrix(StdRegions::eInvMass);
                     StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                                            StdRegions::eWeakDeriv1,
                                                            StdRegions::eWeakDeriv2};
                     DNekMat LocMat(ncoeffs,ncoeffs); 
 
                     returnval = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,ncoeffs);
                     DNekMat &Mat = *returnval;
                     Vmath::Zero(ncoeffs*ncoeffs,Mat.GetPtr(),1);
 
                     StdRegions::VarCoeffType Coeffs[3] = {StdRegions::eVarCoeffD00,
                                                           StdRegions::eVarCoeffD11,
                                                           StdRegions::eVarCoeffD22};
                     
                     StdRegions::VarCoeffMap::const_iterator x;
 
                     for(i=0;  i < coordim; ++i)
                     {
                         if (mmf)
                         {
                             if(i < shapedim)
                             {
                                 StdRegions::VarCoeffMap VarCoeffDirDeriv;
                                 VarCoeffDirDeriv[StdRegions::eVarCoeffMF] =
                                         v_GetMF(i,shapedim,varcoeffs);
                                 VarCoeffDirDeriv[StdRegions::eVarCoeffMFDiv] =
                                         v_GetMFDiv(i,varcoeffs);
 
                                 MatrixKey Dmatkey(StdRegions::
                                                         eWeakDirectionalDeriv,
                                                   DetShapeType(), *this,
                                                   StdRegions::
                                                         NullConstFactorMap,
                                                   VarCoeffDirDeriv);
 
                                 DNekScalMat &Dmat = *GetLocMatrix(Dmatkey);
 
                                 StdRegions::VarCoeffMap Weight;
                                 Weight[StdRegions::eVarCoeffMass] =
                                         v_GetMFMag(i,mkey.GetVarCoeffs());
 
                                 MatrixKey invMasskey( StdRegions::eInvMass,
                                                       DetShapeType(), *this,
                                                       StdRegions::
                                                             NullConstFactorMap,
                                                       Weight);
 
                                 DNekScalMat &invMass =
                                         *GetLocMatrix(invMasskey);
 
                                 Mat = Mat + Dmat*invMass*Transpose(Dmat);
                             }
                         }
                         else if(mkey.HasVarCoeff(Coeffs[i]))
                         {
                             MatrixKey DmatkeyL( DerivType[i],
                                                 DetShapeType(), *this,
                                                 StdRegions::NullConstFactorMap,
                                                 mkey.GetVarCoeffAsMap(
                                                         Coeffs[i]));
 
                             MatrixKey DmatkeyR( DerivType[i],
                                                 DetShapeType(), *this);
 
                             DNekScalMat &DmatL = *GetLocMatrix(DmatkeyL);
                             DNekScalMat &DmatR = *GetLocMatrix(DmatkeyR);
                             Mat = Mat + DmatL*invMass*Transpose(DmatR);
                         }
                         else
                         {
                             DNekScalMat &Dmat = *GetLocMatrix(DerivType[i]);
                             Mat = Mat + Dmat*invMass*Transpose(Dmat);
                         }
 
                     }
 
                     // Add Mass Matrix Contribution for Helmholtz problem
                     DNekScalMat  &Mass = *GetLocMatrix(StdRegions::eMass);
                     Mat = Mat + lambdaval*Mass;
 
                     // Add tau*E_l using elemental mass matrices on each edge
                     for(i = 0; i < nedges; ++i)
                     {
                         EdgeExp = GetEdgeExp(i);
                         EdgeExp2 = GetEdgeExp(i);
                         order_e = EdgeExp->GetNcoeffs();  
                         int nq = EdgeExp->GetNumPoints(0);
                         GetEdgeToElementMap(i,edgedir,emap,sign);
 
                         // @TODO: Document
                         StdRegions::VarCoeffMap edgeVarCoeffs;
                         if (mkey.HasVarCoeff(StdRegions::eVarCoeffD00))
                         {
                             Array<OneD, NekDouble> mu(nq);
                             GetPhysEdgeVarCoeffsFromElement(i, EdgeExp2, mkey.GetVarCoeff(StdRegions::eVarCoeffD00), mu);
                             edgeVarCoeffs[StdRegions::eVarCoeffMass] = mu;
                         }
                         DNekScalMat &eMass = *EdgeExp->GetLocMatrix(StdRegions::eMass, StdRegions::NullConstFactorMap, edgeVarCoeffs);
                         //DNekScalMat &eMass = *EdgeExp->GetLocMatrix(StdRegions::eMass);
 
                         for(j = 0; j < order_e; ++j)
                         {
                             for(k = 0; k < order_e; ++k)
                             {
                                 Mat(emap[j],emap[k]) = Mat(emap[j],emap[k]) + tau*sign[j]*sign[k]*eMass(j,k);
                             }
                         }
                     }
                 }
                 break;
             // U^e (P22)
             case StdRegions::eHybridDGLamToU:
                 {
                     int       i,j,k;
                     int       nbndry  = NumDGBndryCoeffs();
                     int       ncoeffs = GetNcoeffs();
                     int       nedges  = GetNedges();
                     NekDouble tau     = mkey.GetConstFactor(StdRegions::eFactorTau);
                     
                     Array<OneD,NekDouble> lambda(nbndry);
                     DNekVec Lambda(nbndry,lambda,eWrapper);                    
                     Array<OneD,NekDouble> ulam(ncoeffs);
                     DNekVec Ulam(ncoeffs,ulam,eWrapper);
                     Array<OneD,NekDouble> f(ncoeffs);
                     DNekVec F(ncoeffs,f,eWrapper);
                     
                     Array<OneD, ExpansionSharedPtr>  EdgeExp(nedges);
                     // declare matrix space
                     returnval  = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,nbndry); 
                     DNekMat &Umat = *returnval;
                     
                     // Z^e matrix
                     MatrixKey newkey(StdRegions::eInvHybridDGHelmholtz, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                     DNekScalMat  &invHmat = *GetLocMatrix(newkey);
 
                     Array<OneD,unsigned int> emap;
                     Array<OneD,int> sign;
                     
                     for(i = 0; i < nedges; ++i)
                     {
                         EdgeExp[i] = GetEdgeExp(i);
                     }
 
                     // for each degree of freedom of the lambda space
                     // calculate Umat entry 
                     // Generate Lambda to U_lambda matrix 
                     for(j = 0; j < nbndry; ++j)
                     {
                         // standard basis vectors e_j
                         Vmath::Zero(nbndry,&lambda[0],1);
                         Vmath::Zero(ncoeffs,&f[0],1);
                         lambda[j] = 1.0;
                         
                         SetTraceToGeomOrientation(EdgeExp,lambda);
                         
                         // Compute F = [I   D_1 M^{-1}   D_2 M^{-1}] C e_j
                         AddHDGHelmholtzTraceTerms(
                             tau, lambda, EdgeExp, mkey.GetVarCoeffs(), f);
                         
                         // Compute U^e_j
                         Ulam = invHmat*F; // generate Ulam from lambda
                         
                         // fill column of matrix
                         for(k = 0; k < ncoeffs; ++k)
                         {
                             Umat(k,j) = Ulam[k]; 
                         }
                     }
                 }
                 break;
             // Q_0, Q_1, Q_2 matrices (P23)
             // Each are a product of a row of Eqn 32 with the C matrix.
             // Rather than explicitly computing all of Eqn 32, we note each
             // row is almost a multiple of U^e, so use that as our starting
             // point.
             case StdRegions::eHybridDGLamToQ0:
             case StdRegions::eHybridDGLamToQ1:
             case StdRegions::eHybridDGLamToQ2:
                 {
                     int i        = 0;
                     int j        = 0;
                     int k        = 0;
                     int dir      = 0;
                     int nbndry   = NumDGBndryCoeffs();
                     int ncoeffs  = GetNcoeffs();
                     int nedges   = GetNedges();
                     int shapedim = 2;
 
                     Array<OneD,NekDouble> lambda(nbndry);
                     DNekVec Lambda(nbndry,lambda,eWrapper);                    
                     Array<OneD, ExpansionSharedPtr>  EdgeExp(nedges);
                     
                     Array<OneD,NekDouble> ulam(ncoeffs);
                     DNekVec Ulam(ncoeffs,ulam,eWrapper);
                     Array<OneD,NekDouble> f(ncoeffs);
                     DNekVec F(ncoeffs,f,eWrapper);
                     
                     // declare matrix space
                     returnval  = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,nbndry); 
                     DNekMat &Qmat = *returnval;
                     
                     // Lambda to U matrix
                     MatrixKey lamToUkey(StdRegions::eHybridDGLamToU, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                     DNekScalMat &lamToU = *GetLocMatrix(lamToUkey);
 
                     // Inverse mass matrix 
                     DNekScalMat &invMass = *GetLocMatrix(StdRegions::eInvMass);
                     
                     
                     for(i = 0; i < nedges; ++i)
                     {
                         EdgeExp[i] = GetEdgeExp(i);
                     }
 
                     //Weak Derivative matrix 
                     DNekScalMatSharedPtr Dmat;
                     switch(mkey.GetMatrixType())
                     {
                     case StdRegions::eHybridDGLamToQ0:
                         dir = 0;
                         Dmat = GetLocMatrix(StdRegions::eWeakDeriv0);
                         break;
                     case StdRegions::eHybridDGLamToQ1:
                         dir = 1;
                         Dmat = GetLocMatrix(StdRegions::eWeakDeriv1);
                         break;
                     case StdRegions::eHybridDGLamToQ2:
                         dir = 2;
                         Dmat = GetLocMatrix(StdRegions::eWeakDeriv2);
                         break;
                     default:
                         ASSERTL0(false,"Direction not known");
                         break;
                     }
 
                     const StdRegions::VarCoeffMap &varcoeffs =
                             mkey.GetVarCoeffs();
                     if (varcoeffs.find(StdRegions::eVarCoeffMF1x) !=
                             varcoeffs.end())
                     {
                         StdRegions::VarCoeffMap VarCoeffDirDeriv;
                         VarCoeffDirDeriv[StdRegions::eVarCoeffMF] =
                                 v_GetMF(dir,shapedim,varcoeffs);
                         VarCoeffDirDeriv[StdRegions::eVarCoeffMFDiv] =
                                 v_GetMFDiv(dir,varcoeffs);
 
                         MatrixKey Dmatkey( StdRegions::eWeakDirectionalDeriv,
                                            DetShapeType(), *this,
                                            StdRegions::NullConstFactorMap,
                                            VarCoeffDirDeriv);
 
                         Dmat = GetLocMatrix(Dmatkey);
 
                         StdRegions::VarCoeffMap Weight;
                         Weight[StdRegions::eVarCoeffMass] =
                                 v_GetMFMag(dir,mkey.GetVarCoeffs());
 
                         MatrixKey invMasskey( StdRegions::eInvMass,
                                               DetShapeType(), *this,
                                               StdRegions::NullConstFactorMap,
                                               Weight);
 
                         invMass = *GetLocMatrix(invMasskey);
                     }
                     else
                     {
                         StdRegions::MatrixType DerivType[3] = {
                             StdRegions::eWeakDeriv0,
                             StdRegions::eWeakDeriv1,
                             StdRegions::eWeakDeriv2};
 
                         Dmat = GetLocMatrix(DerivType[dir]);
 
                         MatrixKey invMasskey( StdRegions::eInvMass,
                                               DetShapeType(), *this);
                         invMass = *GetLocMatrix(invMasskey);
                     }
 
                     // for each degree of freedom of the lambda space
                     // calculate Qmat entry 
                     // Generate Lambda to Q_lambda matrix 
                     for(j = 0; j < nbndry; ++j)
                     {
                         Vmath::Zero(nbndry,&lambda[0],1);
                         lambda[j] = 1.0;
                         
                         // for lambda[j] = 1 this is the solution to ulam
                         for(k = 0; k < ncoeffs; ++k)
                         {
                             Ulam[k] = lamToU(k,j);
                         }
                         
                         // -D^T ulam
                         Vmath::Neg(ncoeffs,&ulam[0],1);
                         F = Transpose(*Dmat)*Ulam; 
                         
                         SetTraceToGeomOrientation(EdgeExp,lambda);
                         
                         // Add the C terms resulting from the I's on the
                         // diagonals of Eqn 32
                         AddNormTraceInt(dir,lambda,EdgeExp,f,mkey.GetVarCoeffs());
                         
                         // finally multiply by inverse mass matrix
                         Ulam = invMass*F; 
                         
                         // fill column of matrix (Qmat is in column major format)
                         Vmath::Vcopy(ncoeffs,&ulam[0],1,&(Qmat.GetPtr())[0]+j*ncoeffs,1);
                     }
                 }
                 break;
                         // Matrix K (P23)
             case StdRegions::eHybridDGHelmBndLam:
                 {
                     int i,j,e,cnt;
                     int order_e, nquad_e;
                     int nbndry  = NumDGBndryCoeffs();
                     int coordim = GetCoordim();
                     int nedges  = GetNedges();
                     NekDouble tau = mkey.GetConstFactor(StdRegions::eFactorTau);
                     StdRegions::VarCoeffMap::const_iterator x;
                     const StdRegions::VarCoeffMap &varcoeffs
                                 = mkey.GetVarCoeffs();
                     bool mmf    =
                         (varcoeffs.find(StdRegions::eVarCoeffMF1x) !=
                          varcoeffs.end());
 
                     Array<OneD,NekDouble>       work, varcoeff_work;
                     Array<OneD,const Array<OneD, NekDouble> > normals; 
                     Array<OneD, ExpansionSharedPtr>  EdgeExp(nedges);
                     Array<OneD, NekDouble> lam(nbndry); 
                     
                     Array<OneD,unsigned int>    emap;
                     Array<OneD, int>            sign;
                     StdRegions::Orientation edgedir;
                     
                     // declare matrix space
                     returnval = MemoryManager<DNekMat>::AllocateSharedPtr(nbndry, nbndry);
                     DNekMat &BndMat = *returnval;
                     
                     DNekScalMatSharedPtr LamToQ[3];
                     
                     // Matrix to map Lambda to U
                     MatrixKey LamToUkey(StdRegions::eHybridDGLamToU, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                     DNekScalMat &LamToU = *GetLocMatrix(LamToUkey);
 
                     // Matrix to map Lambda to Q0
                     MatrixKey LamToQ0key(StdRegions::eHybridDGLamToQ0, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                     LamToQ[0] = GetLocMatrix(LamToQ0key);
  
                     // Matrix to map Lambda to Q1
                     MatrixKey LamToQ1key(StdRegions::eHybridDGLamToQ1, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                     LamToQ[1] = GetLocMatrix(LamToQ1key);
 
                     // Matrix to map Lambda to Q2 for 3D coordinates
                     if (coordim == 3)
                     {
                         MatrixKey LamToQ2key(StdRegions::eHybridDGLamToQ2, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                         LamToQ[2] = GetLocMatrix(LamToQ2key);
                     }
 
                     // Set up edge segment expansions from local geom info
                     for(i = 0; i < nedges; ++i)
                     {
                         EdgeExp[i] = GetEdgeExp(i);
                     }
 
                     // Set up matrix derived from <mu, Q_lam.n - \tau (U_lam - Lam) > 
                     for(i = 0; i < nbndry; ++i)
                     {
                         cnt = 0;
                         
                         Vmath::Zero(nbndry,lam,1);
                         lam[i] = 1.0;
                         SetTraceToGeomOrientation(EdgeExp,lam);
 
                         for(e = 0; e < nedges; ++e)
                         {
                             order_e = EdgeExp[e]->GetNcoeffs();  
                             nquad_e = EdgeExp[e]->GetNumPoints(0);    
 
                             normals = GetEdgeNormal(e);
                             edgedir = GetEorient(e);
                             
                             work = Array<OneD,NekDouble>(nquad_e);
                             varcoeff_work = Array<OneD, NekDouble>(nquad_e);
 
                             GetEdgeToElementMap(e,edgedir,emap,sign);
 
 
                             StdRegions::VarCoeffType VarCoeff[3] = {StdRegions::eVarCoeffD00,
                                                                     StdRegions::eVarCoeffD11,
                                                                     StdRegions::eVarCoeffD22};
 
                             // Q0 * n0 (BQ_0 terms)
                             Array<OneD, NekDouble> edgeCoeffs(order_e);
                             Array<OneD, NekDouble> edgePhys  (nquad_e);
                             for(j = 0; j < order_e; ++j)
                             {
                                 edgeCoeffs[j] = sign[j]*(*LamToQ[0])(emap[j],i);
                             }
                             
                             EdgeExp[e]->BwdTrans(edgeCoeffs, edgePhys);
 // @TODO Var coeffs
                             // Multiply by variable coefficient
 //                            if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
 //                            {
 //                                GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
 //                                Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
 //                            }
                             if (mmf)
                             {
                                 Array<OneD, NekDouble> ncdotMF =
                                         v_GetnEdgecdotMF(0, e, EdgeExp[e],
                                                          normals, varcoeffs);
                                 Vmath::Vmul(nquad_e, ncdotMF,  1,
                                                      edgePhys, 1,
                                                      work,     1);
                             }
                             else
                             {
                                 Vmath::Vmul(nquad_e, normals[0], 1,
                                                      edgePhys,   1,
                                                      work,       1);
                             }
 
                             // Q1 * n1 (BQ_1 terms)
                             for(j = 0; j < order_e; ++j)
                             {
                                 edgeCoeffs[j] = sign[j]*(*LamToQ[1])(emap[j],i);
                             }
                             
                             EdgeExp[e]->BwdTrans(edgeCoeffs, edgePhys);
 
 // @TODO var coeffs
                             // Multiply by variable coefficients
 //                            if ((x = varcoeffs.find(VarCoeff[1])) != varcoeffs.end())
 //                            {
 //                                GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
 //                                Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
 //                            }
                             
                             if (mmf)
                             {
                                 Array<OneD, NekDouble> ncdotMF =
                                         v_GetnEdgecdotMF(1, e, EdgeExp[e],
                                                          normals, varcoeffs);
                                 Vmath::Vvtvp(nquad_e, ncdotMF,  1,
                                                       edgePhys, 1,
                                                       work,     1,
                                                       work,     1);
                             }
                             else
                             {
                                 Vmath::Vvtvp(nquad_e, normals[1], 1,
                                                       edgePhys,   1,
                                                       work,       1,
                                                       work,       1);
                             }
 
                             // Q2 * n2 (BQ_2 terms)
                             if (coordim == 3)
                             {
                                 for(j = 0; j < order_e; ++j)
                                 {
                                     edgeCoeffs[j] = sign[j]*(*LamToQ[2])(emap[j],i);
                                 }
                                 
                                 EdgeExp[e]->BwdTrans(edgeCoeffs, edgePhys);
 // @TODO var coeffs
                                 // Multiply by variable coefficients
 //                                if ((x = varcoeffs.find(VarCoeff[2])) != varcoeffs.end())
 //                                {
 //                                    GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
 //                                    Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
 //                                }
 
                                 Vmath::Vvtvp(nquad_e, normals[2], 1, edgePhys, 1,
                                                       work,       1, work,     1);
                             }
 
                             if (m_negatedNormals[e])
                             {
                                 Vmath::Neg(nquad_e, work, 1);
                             }
 
                             // - tau (ulam - lam)
                             // Corresponds to the G and BU terms.
                             for(j = 0; j < order_e; ++j)
                             {
                                 edgeCoeffs[j] = sign[j]*LamToU(emap[j],i) - lam[cnt+j];
                             }
                             
                             EdgeExp[e]->BwdTrans(edgeCoeffs, edgePhys);
 
                             // Multiply by variable coefficients
                             if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
                             {
                                 GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
                                 Vmath::Vmul(nquad_e,varcoeff_work,1,edgePhys,1,edgePhys,1);
                             }
 
                             Vmath::Svtvp(nquad_e,-tau,edgePhys,1,
                                          work,1,work,1);
 /// TODO: Add variable coeffs
                             EdgeExp[e]->IProductWRTBase(work, edgeCoeffs);
                             
                             EdgeExp[e]->SetCoeffsToOrientation(edgeCoeffs, edgedir);
                             
                             for(j = 0; j < order_e; ++j)
                             {
                                 BndMat(cnt+j,i) = edgeCoeffs[j];
                             }
                             
                             cnt += order_e;
                         }
                     }
                 }
                 break;
             //HDG postprocessing
             case StdRegions::eInvLaplacianWithUnityMean:
                 {
                     MatrixKey lapkey(StdRegions::eLaplacian, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                     DNekScalMat  &LapMat = *GetLocMatrix(lapkey);
                     
                     returnval = MemoryManager<DNekMat>::AllocateSharedPtr(LapMat.GetRows(),LapMat.GetColumns());
                     DNekMatSharedPtr lmat = returnval;
 
                     (*lmat) = LapMat;
 
                     // replace first column with inner product wrt 1
                     int nq = GetTotPoints();
                     Array<OneD, NekDouble> tmp(nq);
                     Array<OneD, NekDouble> outarray(m_ncoeffs);
                     Vmath::Fill(nq,1.0,tmp,1);
                     IProductWRTBase(tmp, outarray);
 
                     Vmath::Vcopy(m_ncoeffs,&outarray[0],1,
                                  &(lmat->GetPtr())[0],1);
 
                     lmat->Invert();
                 }
                 break;
             default:
                 ASSERTL0(false,"This matrix type cannot be generated from this class");
                 break;
             }
             
             return returnval;
         }

◆ v_GetEdgeInverseBoundaryMap()

Array< OneD, unsigned int > Nektar::LocalRegions::Expansion2D::v_GetEdgeInverseBoundaryMap ( int eid )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1527 of file Expansion2D.cpp.

References Nektar::StdRegions::StdExpansion::GetBoundaryMap(), Nektar::StdRegions::StdExpansion::GetEdgeInteriorMap(), Nektar::StdRegions::StdExpansion::GetEdgeNcoeffs(), GetGeom2D(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

         {
             int n, j;
             int nEdgeCoeffs;
             int nBndCoeffs = NumBndryCoeffs();
 
             Array<OneD, unsigned int> bmap(nBndCoeffs);
             GetBoundaryMap(bmap);
 
             // Map from full system to statically condensed system (i.e reverse
             // GetBoundaryMap)
             map<int, int> invmap;
             for (j = 0; j < nBndCoeffs; ++j)
             {
                 invmap[bmap[j]] = j;
             }
 
             // Number of interior edge coefficients
             nEdgeCoeffs = GetEdgeNcoeffs(eid) - 2;
 
             const SpatialDomains::Geometry2DSharedPtr &geom = GetGeom2D();
 
             Array<OneD, unsigned int> edgemaparray(nEdgeCoeffs);
             Array<OneD, unsigned int> maparray    (nEdgeCoeffs);
             Array<OneD, int>          signarray   (nEdgeCoeffs, 1);
             StdRegions::Orientation eOrient      = geom->GetEorient(eid);
 
             // maparray is the location of the edge within the matrix
             GetEdgeInteriorMap(eid, eOrient, maparray, signarray);
 
             for (n = 0; n < nEdgeCoeffs; ++n)
             {
                 edgemaparray[n] = invmap[maparray[n]];
             }
 
             return edgemaparray;
         }

◆ v_GetEdgeNormal()

const StdRegions::NormalVector & Nektar::LocalRegions::Expansion2D::v_GetEdgeNormal ( const int edge ) const

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1571 of file Expansion2D.cpp.

References ASSERTL0, and m_edgeNormals.

Referenced by v_GetSurfaceNormal().

         {
             std::map<int, StdRegions::NormalVector>::const_iterator x;
             x = m_edgeNormals.find(edge);
             ASSERTL0 (x != m_edgeNormals.end(),
                         "Edge normal not computed.");
             return x->second;
         }

◆ v_GetMF()

Array< OneD, NekDouble > Nektar::LocalRegions::Expansion2D::v_GetMF	(	const int	dir,
		const int	shapedim,
		const StdRegions::VarCoeffMap &	varcoeffs
	)

protectedvirtual

Definition at line 1637 of file Expansion2D.cpp.

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

Referenced by AddHDGHelmholtzEdgeTerms(), and v_GenMatrix().

         {
             return Expansion::v_GetMF(dir,shapedim,varcoeffs);
         }

◆ v_GetMFDiv()

Array< OneD, NekDouble > Nektar::LocalRegions::Expansion2D::v_GetMFDiv	(	const int	dir,
		const StdRegions::VarCoeffMap &	varcoeffs
	)

protectedvirtual

Definition at line 1645 of file Expansion2D.cpp.

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

Referenced by AddHDGHelmholtzEdgeTerms(), and v_GenMatrix().

         {
             return Expansion::v_GetMFDiv(dir,varcoeffs);
         }

◆ v_GetMFMag()

Array< OneD, NekDouble > Nektar::LocalRegions::Expansion2D::v_GetMFMag	(	const int	dir,
		const StdRegions::VarCoeffMap &	varcoeffs
	)

protectedvirtual

Definition at line 1652 of file Expansion2D.cpp.

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

Referenced by AddHDGHelmholtzEdgeTerms(), and v_GenMatrix().

         {
             return Expansion::v_GetMFMag(dir,varcoeffs);
         }

◆ v_GetnEdgecdotMF()

Array< OneD, NekDouble > Nektar::LocalRegions::Expansion2D::v_GetnEdgecdotMF	(	const int	dir,
		const int	edge,
		ExpansionSharedPtr &	EdgeExp_e,
		const Array< OneD, const Array< OneD, NekDouble > > &	normals,
		const StdRegions::VarCoeffMap &	varcoeffs
	)

protected

Definition at line 1660 of file Expansion2D.cpp.

Referenced by AddHDGHelmholtzEdgeTerms(), AddNormTraceInt(), and v_GenMatrix().

         {
             int nquad_e = EdgeExp_e->GetNumPoints(0);
             int coordim = GetCoordim();
             int nquad0  = m_base[0]->GetNumPoints();
             int nquad1  = m_base[1]->GetNumPoints();
             int nqtot   = nquad0*nquad1;
 
             StdRegions::VarCoeffType MMFCoeffs[15] =
             {
                 StdRegions::eVarCoeffMF1x,
                 StdRegions::eVarCoeffMF1y,
                 StdRegions::eVarCoeffMF1z,
                 StdRegions::eVarCoeffMF1Div,
                 StdRegions::eVarCoeffMF1Mag,
                 StdRegions::eVarCoeffMF2x,
                 StdRegions::eVarCoeffMF2y,
                 StdRegions::eVarCoeffMF2z,
                 StdRegions::eVarCoeffMF2Div,
                 StdRegions::eVarCoeffMF2Mag,
                 StdRegions::eVarCoeffMF3x,
                 StdRegions::eVarCoeffMF3y,
                 StdRegions::eVarCoeffMF3z,
                 StdRegions::eVarCoeffMF3Div,
                 StdRegions::eVarCoeffMF3Mag
             };
 
             StdRegions::VarCoeffMap::const_iterator MFdir;
 
             Array<OneD, NekDouble> ncdotMF(nqtot,0.0);
             Array<OneD, NekDouble> tmp(nqtot);
             Array<OneD, NekDouble> tmp_e(nquad_e);
             for (int k=0; k<coordim; k++)
             {
                 MFdir = varcoeffs.find(MMFCoeffs[dir*5+k]);
                 tmp = MFdir->second;
 
                 GetPhysEdgeVarCoeffsFromElement(edge, EdgeExp_e, tmp, tmp_e);
 
                 Vmath::Vvtvp(nquad_e,
                              &tmp_e[0],      1,
                              &normals[k][0], 1,
                              &ncdotMF[0],    1,
                              &ncdotMF[0],    1);
             }
             return ncdotMF;
         }

◆ v_GetSurfaceNormal()

const StdRegions::NormalVector & Nektar::LocalRegions::Expansion2D::v_GetSurfaceNormal ( const int id ) const

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1580 of file Expansion2D.cpp.

References v_GetEdgeNormal().

         {
             return v_GetEdgeNormal(id);
         }

◆ v_NegateEdgeNormal()

void Nektar::LocalRegions::Expansion2D::v_NegateEdgeNormal ( const int edge )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1586 of file Expansion2D.cpp.

References Nektar::StdRegions::StdExpansion::GetCoordim(), m_edgeNormals, m_negatedNormals, and Vmath::Neg().

         {
             m_negatedNormals[edge] = true;
             for (int i = 0; i < GetCoordim(); ++i)
             {
                 Vmath::Neg(m_edgeNormals[edge][i].num_elements(), 
                            m_edgeNormals[edge][i], 1);
             }
         }

◆ v_SetUpPhysNormals()

void Nektar::LocalRegions::Expansion2D::v_SetUpPhysNormals ( const int edge )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1566 of file Expansion2D.cpp.

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

         {
             ComputeEdgeNormal(edge);
         }

◆ v_VectorFlux()

NekDouble Nektar::LocalRegions::Expansion2D::v_VectorFlux ( const Array< OneD, Array< OneD, NekDouble > > & vec )

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1713 of file Expansion2D.cpp.

References Nektar::StdRegions::StdExpansion::GetFaceNormal(), GetLeftAdjacentElementExp(), GetLeftAdjacentElementFace(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Vmath::Vmul(), and Vmath::Vvtvp().

         {
             const Array<OneD, const Array<OneD, NekDouble> >
                 &normals = GetLeftAdjacentElementExp()->
                 GetFaceNormal(GetLeftAdjacentElementFace());
 
             int nq = GetTotPoints();
             Array<OneD, NekDouble > Fn(nq);
             Vmath::Vmul (nq, &vec[0][0], 1, &normals[0][0], 1, &Fn[0], 1);
             Vmath::Vvtvp(nq, &vec[1][0], 1, &normals[1][0], 1, &Fn[0], 1, &Fn[0], 1);
             Vmath::Vvtvp(nq, &vec[2][0], 1, &normals[2][0], 1, &Fn[0], 1, &Fn[0], 1);
 
             return StdExpansion::Integral(Fn);
         }

Member Data Documentation

◆ m_edgeExp

std::vector<Expansion1DWeakPtr> Nektar::LocalRegions::Expansion2D::m_edgeExp

protected

Definition at line 132 of file Expansion2D.h.

Referenced by GetEdgeExp(), SetEdgeExp(), v_AddEdgeNormBoundaryInt(), v_AddRobinEdgeContribution(), and v_AddRobinMassMatrix().

◆ m_edgeNormals

std::map<int, StdRegions::NormalVector> Nektar::LocalRegions::Expansion2D::m_edgeNormals

protected

Definition at line 134 of file Expansion2D.h.

Referenced by Nektar::LocalRegions::QuadExp::v_ComputeEdgeNormal(), Nektar::LocalRegions::TriExp::v_ComputeEdgeNormal(), Nektar::LocalRegions::NodalTriExp::v_ComputeEdgeNormal(), v_GetEdgeNormal(), and v_NegateEdgeNormal().

◆ m_elementFaceLeft

int Nektar::LocalRegions::Expansion2D::m_elementFaceLeft

protected

Definition at line 138 of file Expansion2D.h.

Referenced by Expansion2D(), GetLeftAdjacentElementFace(), and SetAdjacentElementExp().

◆ m_elementFaceRight

int Nektar::LocalRegions::Expansion2D::m_elementFaceRight

protected

Definition at line 139 of file Expansion2D.h.

Referenced by Expansion2D(), GetRightAdjacentElementFace(), and SetAdjacentElementExp().

◆ m_elementLeft

Expansion3DWeakPtr Nektar::LocalRegions::Expansion2D::m_elementLeft

protected

Definition at line 136 of file Expansion2D.h.

Referenced by GetLeftAdjacentElementExp(), GetRightAdjacentElementExp(), and SetAdjacentElementExp().

◆ m_elementRight

Expansion3DWeakPtr Nektar::LocalRegions::Expansion2D::m_elementRight

protected

Definition at line 137 of file Expansion2D.h.

Referenced by GetRightAdjacentElementExp(), and SetAdjacentElementExp().

◆ m_negatedNormals

std::map<int, bool> Nektar::LocalRegions::Expansion2D::m_negatedNormals

protected

Definition at line 135 of file Expansion2D.h.

Referenced by AddHDGHelmholtzEdgeTerms(), AddNormTraceInt(), v_AddEdgeNormBoundaryInt(), v_EdgeNormalNegated(), v_GenMatrix(), and v_NegateEdgeNormal().

◆ m_requireNeg

std::vector<bool> Nektar::LocalRegions::Expansion2D::m_requireNeg

protected

Definition at line 133 of file Expansion2D.h.

Referenced by v_AddEdgeNormBoundaryInt().

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Expansion2D()

◆ ~Expansion2D()

Member Function Documentation

◆ AddEdgeBoundaryInt()

◆ AddHDGHelmholtzEdgeTerms()

◆ AddHDGHelmholtzTraceTerms()

◆ AddNormTraceInt() [1/2]

◆ AddNormTraceInt() [2/2]

◆ GetEdgeExp()

◆ GetGeom2D()

◆ GetLeftAdjacentElementExp()

◆ GetLeftAdjacentElementFace()

◆ GetPhysEdgeVarCoeffsFromElement()

◆ GetRightAdjacentElementExp()

◆ GetRightAdjacentElementFace()

◆ ReOrientEdgePhysMap()

◆ ReOrientQuadEdgePhysMap()

◆ SetAdjacentElementExp()

◆ SetEdgeExp()

◆ SetTraceToGeomOrientation()

◆ v_AddEdgeNormBoundaryInt() [1/2]

◆ v_AddEdgeNormBoundaryInt() [2/2]

◆ v_AddRobinEdgeContribution()

◆ v_AddRobinMassMatrix()

◆ v_BuildVertexMatrix()

◆ v_DGDeriv()

◆ v_EdgeNormalNegated()

◆ v_GenMatrix()

◆ v_GetEdgeInverseBoundaryMap()

◆ v_GetEdgeNormal()

◆ v_GetMF()

◆ v_GetMFDiv()

◆ v_GetMFMag()

◆ v_GetnEdgecdotMF()

◆ v_GetSurfaceNormal()

◆ v_NegateEdgeNormal()

◆ v_SetUpPhysNormals()

◆ v_VectorFlux()

Member Data Documentation

◆ m_edgeExp

◆ m_edgeNormals

◆ m_elementFaceLeft

◆ m_elementFaceRight

◆ m_elementLeft

◆ m_elementRight

◆ m_negatedNormals

◆ m_requireNeg