#include <Expansion1D.h>

Inheritance diagram for Nektar::LocalRegions::Expansion1D:

Public Member Functions
	Expansion1D (SpatialDomains::Geometry1DSharedPtr pGeom)

virtual	~Expansion1D () override=default

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

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

SpatialDomains::Geometry1DSharedPtr	GetGeom1D () const

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

	Expansion (const Expansion &pSrc)

virtual	~Expansion ()

void	SetTraceExp (const int traceid, ExpansionSharedPtr &f)

ExpansionSharedPtr	GetTraceExp (const int traceid)

DNekScalMatSharedPtr	GetLocMatrix (const LocalRegions::MatrixKey &mkey)

void	DropLocMatrix (const LocalRegions::MatrixKey &mkey)

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

SpatialDomains::GeometrySharedPtr	GetGeom () const

void	Reset ()

IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)

DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)

const SpatialDomains::GeomFactorsSharedPtr &	GetMetricInfo () const

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

DNekMatSharedPtr	BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)

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

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

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

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

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

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

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

IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)

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

ExpansionSharedPtr	GetLeftAdjacentElementExp () const

ExpansionSharedPtr	GetRightAdjacentElementExp () const

int	GetLeftAdjacentElementTrace () const

int	GetRightAdjacentElementTrace () const

void	SetAdjacentElementExp (int traceid, ExpansionSharedPtr &e)

StdRegions::Orientation	GetTraceOrient (int trace)

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

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

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

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

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

void	ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1)

const NormalVector &	GetTraceNormal (const int id)

void	ComputeTraceNormal (const int id)

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

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

void	SetUpPhysNormals (const int trace)

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

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

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

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

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

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

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

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

virtual	~StdExpansion ()
	Destructor. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

int	GetTraceIntNcoeffs (const int i) const

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

const LibUtilities::BasisKey	GetTraceBasisKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...

LibUtilities::PointsKey	GetTracePointsKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...

int	NumBndryCoeffs (void) const

int	NumDGBndryCoeffs (void) const

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

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

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

std::shared_ptr< StdExpansion >	GetStdExp () const

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

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion () const

bool	IsNodalNonTensorialExp ()

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

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

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

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

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

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

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

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

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

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

void	SetElmtId (const int id)
	Set the element id of this expansion when used in a list by returning value of m_elmt_id. More...

void	GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
	this function returns the physical coordinates of the quadrature points of the expansion More...

void	GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
	given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point More...

DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)

DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)

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

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

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

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

DNekScalBlkMatSharedPtr	GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

void	DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

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

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

int	GetCoordim ()

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

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

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

void	GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)

void	GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray)

void	GetElmtTraceToTraceMap (const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)

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

void	GetTraceNumModes (const int tid, int &numModes0, int &numModes1, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)

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

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

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

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

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

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

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

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

NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
	This function evaluates the first derivative of the expansion at a single (arbitrary) point of the domain. More...

NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)

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

NekDouble	PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
	This function evaluates the basis function mode `mode` at a point `coords` of the domain. More...

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

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

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

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

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

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

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

virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

virtual void	v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)

NekDouble	Linf (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_\infty\) error \( \|\epsilon\|_\infty = \max \|u - u_{exact}\|\) where \( u_{exact}\) is given by the array sol. More...

NekDouble	L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_2\) error, \( \| \epsilon \|_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...

NekDouble	H1 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( H^1\) error, \( \| \epsilon \|^1_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u - u_{exact})\cdot dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...

const LibUtilities::PointsKeyVector	GetPointsKeys () const

DNekMatSharedPtr	BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)

void	PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
	This function performs an interpolation from the physical space points provided at input into an array of equispaced points which are not the collapsed coordinate. So for a tetrahedron you will only get a tetrahedral number of values. More...

void	GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
	This function provides the connectivity of local simplices (triangles or tets) to connect the equispaced data points provided by PhysInterpToSimplexEquiSpaced. More...

void	EquiSpacedToCoeffs (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs a projection/interpolation from the equispaced points sometimes used in post-processing onto the coefficient space. More...

template<class T >
std::shared_ptr< T >	as ()

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

void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)

Public Member Functions inherited from Nektar::StdRegions::StdExpansion1D
	StdExpansion1D ()

	StdExpansion1D (int numcoeffs, const LibUtilities::BasisKey &Ba)

	StdExpansion1D (const StdExpansion1D &T)

virtual	~StdExpansion1D () override

void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray. More...

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

NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)

Protected Member Functions
virtual DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override

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

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

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

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

virtual void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1) override

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

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

void	ComputeQuadratureMetric ()

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

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

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

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

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

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

virtual void	v_ComputeLaplacianMetric ()

virtual int	v_GetCoordim () const override

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

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

virtual void	v_DropLocMatrix (const LocalRegions::MatrixKey &mkey)

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

virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)

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

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

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

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

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

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

virtual StdRegions::Orientation	v_GetTraceOrient (int trace)

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

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

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

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

virtual void	v_ComputeTraceNormal (const int id)

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

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

virtual void	v_SetUpPhysNormals (const int id)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv, NekDouble &deriv2)
	This function performs the barycentric interpolation of the polynomial stored in `coord` at a point `physvals` using barycentric interpolation weights in direction. More...

template<int DIR>
NekDouble	BaryEvaluateBasis (const NekDouble &coord, const int &mode)

template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
	Helper function to pass an unused value by reference into BaryEvaluate. More...

template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)

Protected Member Functions inherited from Nektar::StdRegions::StdExpansion1D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override

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

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

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

std::map< int, ExpansionWeakPtr >	m_traceExp

SpatialDomains::GeometrySharedPtr	m_geom

SpatialDomains::GeomFactorsSharedPtr	m_metricinfo

MetricMap	m_metrics

std::map< int, NormalVector >	m_traceNormals

ExpansionWeakPtr	m_elementLeft

ExpansionWeakPtr	m_elementRight

int	m_elementTraceLeft = -1

int	m_elementTraceRight = -1

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

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

Detailed Description

Definition at line 56 of file Expansion1D.h.

Constructor & Destructor Documentation

◆ Expansion1D()

Nektar::LocalRegions::Expansion1D::Expansion1D ( SpatialDomains::Geometry1DSharedPtr pGeom )

inline

Definition at line 60 of file Expansion1D.h.

         : Expansion(pGeom), StdExpansion1D()
     {
     }

◆ ~Expansion1D()

virtual Nektar::LocalRegions::Expansion1D::~Expansion1D ( )

overridevirtualdefault

Member Function Documentation

◆ AddHDGHelmholtzTraceTerms()

void Nektar::LocalRegions::Expansion1D::AddHDGHelmholtzTraceTerms	(	const NekDouble	tau,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Definition at line 315 of file Expansion1D.cpp.

 {
     int i, n;
     int nbndry  = NumBndryCoeffs();
     int nquad   = GetNumPoints(0);
     int ncoeffs = GetNcoeffs();
     int coordim = GetCoordim();
     Array<OneD, unsigned int> vmap;
  
     ASSERTL0(&inarray[0] != &outarray[0],
              "Input and output arrays use the same memory");
  
     const Array<OneD, const NekDouble> &Basis = GetBasis(0)->GetBdata();
     DNekScalMat &invMass = *GetLocMatrix(StdRegions::eInvMass);
  
     GetBoundaryMap(vmap);
  
     // Add F = \tau <phi_i,phi_j> (note phi_i is zero if phi_j is non-zero)
     for (i = 0; i < nbndry; ++i)
     {
         outarray[vmap[i]] += tau * Basis[(vmap[i] + 1) * nquad - 1] *
                              Basis[(vmap[i] + 1) * nquad - 1] *
                              inarray[vmap[i]];
         outarray[vmap[i]] += tau * Basis[vmap[i] * nquad] *
                              Basis[vmap[i] * nquad] * inarray[vmap[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
  
     StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                            StdRegions::eWeakDeriv1,
                                            StdRegions::eWeakDeriv2};
     Array<OneD, NekDouble> tmpcoeff(ncoeffs, 0.0);
     DNekVec Coeffs(ncoeffs, outarray, eWrapper);
     DNekVec Tmpcoeff(ncoeffs, tmpcoeff, eWrapper);
  
     for (n = 0; n < coordim; ++n)
     {
         // evaluate M^{-1} G
         for (i = 0; i < ncoeffs; ++i)
         {
             // lower boundary (negative normal)
             tmpcoeff[i] -= invMass(i, vmap[0]) * Basis[vmap[0] * nquad] *
                            Basis[vmap[0] * nquad] * inarray[vmap[0]];
  
             // upper boundary (positive normal)
             tmpcoeff[i] += invMass(i, vmap[1]) *
                            Basis[(vmap[1] + 1) * nquad - 1] *
                            Basis[(vmap[1] + 1) * nquad - 1] * inarray[vmap[1]];
         }
  
         DNekScalMat &Dmat = *GetLocMatrix(DerivType[n]);
         Coeffs            = Coeffs + Dmat * Tmpcoeff;
     }
 }

References ASSERTL0, Nektar::StdRegions::eInvMass, Nektar::StdRegions::eWeakDeriv0, Nektar::StdRegions::eWeakDeriv1, Nektar::StdRegions::eWeakDeriv2, Nektar::eWrapper, and Nektar::LibUtilities::Basis::GetBdata().

◆ AddNormTraceInt()

void Nektar::LocalRegions::Expansion1D::AddNormTraceInt	(	const int	dir,
		Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Definition at line 290 of file Expansion1D.cpp.

 {
     boost::ignore_unused(dir);
  
     int k;
     int nbndry                                = NumBndryCoeffs();
     int nquad                                 = GetNumPoints(0);
     const Array<OneD, const NekDouble> &Basis = GetBasis(0)->GetBdata();
     Array<OneD, unsigned int> vmap;
  
     GetBoundaryMap(vmap);
  
     // add G \lambda term (can assume G is diagonal since one
     // of the basis is zero at boundary otherwise)
     for (k = 0; k < nbndry; ++k)
     {
         outarray[vmap[k]] += (Basis[(vmap[k] + 1) * nquad - 1] *
                                   Basis[(vmap[k] + 1) * nquad - 1] -
                               Basis[vmap[k] * nquad] * Basis[vmap[k] * nquad]) *
                              inarray[vmap[k]];
     }
 }

References Nektar::LibUtilities::Basis::GetBdata().

◆ GetGeom1D()

SpatialDomains::Geometry1DSharedPtr Nektar::LocalRegions::Expansion1D::GetGeom1D ( ) const

inline

Definition at line 108 of file Expansion1D.h.

 {
     return std::dynamic_pointer_cast<SpatialDomains ::Geometry1D>(m_geom);
 }

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

Referenced by Nektar::VariableConverter::SetElmtMinHP(), and Nektar::DiffusionLDGNS::v_InitObject().

◆ v_AddRobinMassMatrix()

void Nektar::LocalRegions::Expansion1D::v_AddRobinMassMatrix	(	const int	vert,
		const Array< OneD, const NekDouble > &	primCoeffs,
		DNekMatSharedPtr &	inoutmat
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 375 of file Expansion1D.cpp.

 {
     ASSERTL0(IsBoundaryInteriorExpansion(),
              "Robin boundary conditions are only implemented for "
              "boundary-interior expanisons");
     ASSERTL1(inoutmat->GetRows() == inoutmat->GetColumns(),
              "Assuming that input matrix was square");
  
     // Get local Element mapping for vertex point
     int map = GetVertexMap(vert);
  
     // 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
  
     int rows = inoutmat->GetRows();
  
     if (rows == GetNcoeffs())
     {
         // no need to do anything
     }
     else if (rows == NumBndryCoeffs()) // same as NumDGBndryCoeffs()
     {
         int i;
         Array<OneD, unsigned int> bmap;
         GetBoundaryMap(bmap);
  
         for (i = 0; i < 2; ++i)
         {
             if (map == bmap[i])
             {
                 map = i;
                 break;
             }
         }
         ASSERTL1(i != 2, "Did not find number in map");
     }
  
     // assumes end points have unit magnitude
     (*inoutmat)(map, map) += primCoeffs[0];
 }

References ASSERTL0, and ASSERTL1.

◆ v_AddRobinTraceContribution()

void Nektar::LocalRegions::Expansion1D::v_AddRobinTraceContribution	(	const int	vert,
		const Array< OneD, const NekDouble > &	primCoeffs,
		const Array< OneD, NekDouble > &	incoeffs,
		Array< OneD, NekDouble > &	coeffs
	)

overrideprotectedvirtual

Given an edge and vector of element coefficients:

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

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 431 of file Expansion1D.cpp.

 {
     ASSERTL1(IsBoundaryInteriorExpansion(),
              "Not set up for non boundary-interior expansions");
  
     int map = GetVertexMap(vert);
     coeffs[map] += primCoeffs[0] * incoeffs[map];
 }

References ASSERTL1.

◆ v_GenMatrix()

DNekMatSharedPtr Nektar::LocalRegions::Expansion1D::v_GenMatrix ( const StdRegions::StdMatrixKey & mkey )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 47 of file Expansion1D.cpp.

 {
     DNekMatSharedPtr returnval;
  
     switch (mkey.GetMatrixType())
     {
         case StdRegions::eHybridDGHelmholtz:
         {
             ASSERTL1(IsBoundaryInteriorExpansion(),
                      "HybridDGHelmholtz matrix not set up "
                      "for non boundary-interior expansions");
             int i;
             NekDouble lambdaval =
                 mkey.GetConstFactor(StdRegions::eFactorLambda);
             NekDouble tau = mkey.GetConstFactor(StdRegions::eFactorTau);
             int ncoeffs   = GetNcoeffs();
  
             int 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);
  
             for (i = 0; i < coordim; ++i)
             {
                 DNekScalMat &Dmat = *GetLocMatrix(DerivType[i]);
  
                 Mat = Mat + Dmat * invMass * Transpose(Dmat);
             }
  
             // Add end Mass Matrix Contribution
             DNekScalMat &Mass = *GetLocMatrix(StdRegions::eMass);
             Mat               = Mat + lambdaval * Mass;
  
             Array<OneD, unsigned int> bmap;
             GetBoundaryMap(bmap);
  
             // Add tau*F_e using elemental mass matrices
             for (i = 0; i < 2; ++i)
             {
                 Mat(bmap[i], bmap[i]) = Mat(bmap[i], bmap[i]) + tau;
             }
         }
         break;
         case StdRegions::eHybridDGLamToU:
         {
             int j, k;
             int nbndry  = NumDGBndryCoeffs();
             int ncoeffs = GetNcoeffs();
             StdRegions::ConstFactorMap factors;
             factors[StdRegions::eFactorLambda] =
                 mkey.GetConstFactor(StdRegions::eFactorLambda);
             factors[StdRegions::eFactorTau] =
                 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);
  
             // declare matrix space
             returnval =
                 MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs, nbndry);
             DNekMat &Umat = *returnval;
  
             // Helmholtz matrix
             DNekScalMat &invHmat =
                 *GetLocMatrix(StdRegions::eInvHybridDGHelmholtz, factors);
  
             // for each degree of freedom of the lambda space
             // calculate Umat entry
             // Generate Lambda to U_lambda matrix
             for (j = 0; j < nbndry; ++j)
             {
                 Vmath::Zero(nbndry, &lambda[0], 1);
                 Vmath::Zero(ncoeffs, &f[0], 1);
                 lambda[j] = 1.0;
  
                 AddHDGHelmholtzTraceTerms(factors[StdRegions::eFactorTau],
                                           lambda, f);
  
                 Ulam = invHmat * F; // generate Ulam from lambda
  
                 // fill column of matrix
                 for (k = 0; k < ncoeffs; ++k)
                 {
                     Umat(k, j) = Ulam[k];
                 }
             }
         }
         break;
         case StdRegions::eHybridDGLamToQ0:
         case StdRegions::eHybridDGLamToQ1:
         case StdRegions::eHybridDGLamToQ2:
         {
             int j       = 0;
             int k       = 0;
             int dir     = 0;
             int nbndry  = NumDGBndryCoeffs();
             int ncoeffs = GetNcoeffs();
  
             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);
             StdRegions::ConstFactorMap factors;
             factors[StdRegions::eFactorLambda] =
                 mkey.GetConstFactor(StdRegions::eFactorLambda);
             factors[StdRegions::eFactorTau] =
                 mkey.GetConstFactor(StdRegions::eFactorTau);
  
             // declare matrix space
             returnval =
                 MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs, nbndry);
             DNekMat &Qmat = *returnval;
  
             // Lambda to U matrix
             DNekScalMat &lamToU =
                 *GetLocMatrix(StdRegions::eHybridDGLamToU, factors);
  
             // Inverse mass matrix
             DNekScalMat &invMass = *GetLocMatrix(StdRegions::eInvMass);
  
             // 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;
             }
  
             // 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;
  
                 // + \tilde{G} \lambda
                 AddNormTraceInt(dir, lambda, f);
  
                 // 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;
         case StdRegions::eHybridDGHelmBndLam:
         {
             int j;
             int nbndry = NumBndryCoeffs();
  
             StdRegions::ConstFactorMap factors;
             factors[StdRegions::eFactorLambda] =
                 mkey.GetConstFactor(StdRegions::eFactorLambda);
             factors[StdRegions::eFactorTau] =
                 mkey.GetConstFactor(StdRegions::eFactorTau);
  
             Array<OneD, unsigned int> bmap;
             Array<OneD, NekDouble> lam(2);
             GetBoundaryMap(bmap);
  
             // declare matrix space
             returnval =
                 MemoryManager<DNekMat>::AllocateSharedPtr(nbndry, nbndry);
             DNekMat &BndMat = *returnval;
  
             // Matrix to map Lambda to U
             DNekScalMat &LamToU =
                 *GetLocMatrix(StdRegions::eHybridDGLamToU, factors);
  
             // Matrix to map Lambda to Q
             DNekScalMat &LamToQ =
                 *GetLocMatrix(StdRegions::eHybridDGLamToQ0, factors);
  
             lam[0] = 1.0;
             lam[1] = 0.0;
             for (j = 0; j < nbndry; ++j)
             {
                 BndMat(0, j) =
                     -LamToQ(bmap[0], j) - factors[StdRegions::eFactorTau] *
                                               (LamToU(bmap[0], j) - lam[j]);
             }
  
             lam[0] = 0.0;
             lam[1] = 1.0;
             for (j = 0; j < nbndry; ++j)
             {
                 BndMat(1, j) =
                     LamToQ(bmap[1], j) - factors[StdRegions::eFactorTau] *
                                              (LamToU(bmap[1], j) - lam[j]);
             }
         }
         break;
         default:
             ASSERTL0(false,
                      "This matrix type cannot be generated from this class");
             break;
     }
  
     return returnval;
 }

Referenced by Nektar::LocalRegions::SegExp::v_GenMatrix().

◆ v_NormalTraceDerivFactors()

void Nektar::LocalRegions::Expansion1D::v_NormalTraceDerivFactors	(	Array< OneD, Array< OneD, NekDouble >> &	factors,
		Array< OneD, Array< OneD, NekDouble >> &	d0factors,
		Array< OneD, Array< OneD, NekDouble >> &	d1factors
	)

overrideprotectedvirtual

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

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 462 of file Expansion1D.cpp.

 {
     boost::ignore_unused(d0factors, d1factors); // for 2D&3D shapes
     int nquad = GetNumPoints(0);
     Array<TwoD, const NekDouble> gmat =
         m_metricinfo->GetDerivFactors(GetPointsKeys());
  
     if (factors.size() <= 2)
     {
         factors    = Array<OneD, Array<OneD, NekDouble>>(2);
         factors[0] = Array<OneD, NekDouble>(1);
         factors[1] = Array<OneD, NekDouble>(1);
     }
  
     // Outwards normal
     const Array<OneD, const Array<OneD, NekDouble>> &normal_0 =
         GetTraceNormal(0);
     const Array<OneD, const Array<OneD, NekDouble>> &normal_1 =
         GetTraceNormal(1);
  
     if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
     {
         factors[0][0] = gmat[0][nquad - 1] * normal_0[0][0];
         factors[1][0] = gmat[0][0] * normal_1[0][0];
  
         for (int n = 1; n < normal_0.size(); ++n)
         {
             factors[0][0] += gmat[n][0] * normal_0[n][0];
             factors[1][0] += gmat[n][nquad - 1] * normal_1[n][0];
         }
     }
     else
     {
         factors[0][0] = gmat[0][0] * normal_0[0][0];
         factors[1][0] = gmat[0][0] * normal_1[0][0];
  
         for (int n = 1; n < normal_0.size(); ++n)
         {
             factors[0][0] += gmat[n][0] * normal_0[n][0];
             factors[1][0] += gmat[n][0] * normal_1[n][0];
         }
     }
 }

References Nektar::SpatialDomains::eDeformed.

◆ v_ReOrientTracePhysMap()

void Nektar::LocalRegions::Expansion1D::v_ReOrientTracePhysMap	(	const StdRegions::Orientation	orient,
		Array< OneD, int > &	idmap,
		const int	nq0,
		const int	nq1
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 509 of file Expansion1D.cpp.

 {
     boost::ignore_unused(orient, nq0, nq1);
  
     if (idmap.size() != 1)
     {
         idmap = Array<OneD, int>(1);
     }
  
     idmap[0] = 0;
 }

◆ v_TraceNormLen()

void Nektar::LocalRegions::Expansion1D::v_TraceNormLen	(	const int	traceid,
		NekDouble &	h,
		NekDouble &	p
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 523 of file Expansion1D.cpp.

 {
     boost::ignore_unused(traceid);
     h = GetGeom()->GetVertex(1)->dist(*GetGeom()->GetVertex(0));
     p = m_ncoeffs - 1;
 }

References CellMLToNektar.cellml_metadata::p.

◆ v_VectorFlux()

NekDouble Nektar::LocalRegions::Expansion1D::v_VectorFlux ( const Array< OneD, Array< OneD, NekDouble >> & vec )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 442 of file Expansion1D.cpp.

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

References Vmath::Vmul(), and Vmath::Vvtvp().

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Expansion1D()

◆ ~Expansion1D()

Member Function Documentation

◆ AddHDGHelmholtzTraceTerms()

◆ AddNormTraceInt()

◆ GetGeom1D()

◆ v_AddRobinMassMatrix()

◆ v_AddRobinTraceContribution()

◆ v_GenMatrix()

◆ v_NormalTraceDerivFactors()

◆ v_ReOrientTracePhysMap()

◆ v_TraceNormLen()

◆ v_VectorFlux()