#include <Expansion2D.h>

Inheritance diagram for Nektar::LocalRegions::Expansion2D:

Public Member Functions
	Expansion2D (SpatialDomains::Geometry2DSharedPtr pGeom)

virtual	~Expansion2D () override=default

DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)

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

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

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

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

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

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

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

SpatialDomains::Geometry2DSharedPtr	GetGeom2D () const

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

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

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

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

	Expansion (const Expansion &pSrc)

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::StdExpansion2D
	StdExpansion2D ()

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

	StdExpansion2D (const StdExpansion2D &T)

virtual	~StdExpansion2D () override

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

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

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

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

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

Protected Member Functions
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) override

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) override

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

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

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

virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) override

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

virtual void	v_SetUpPhysNormals (const int edge) override

virtual NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble >> &vec) 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 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_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble >> &factors, Array< OneD, Array< OneD, NekDouble >> &d0factors, Array< OneD, Array< OneD, NekDouble >> &d1factors)

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

virtual StdRegions::Orientation	v_GetTraceOrient (int trace)

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

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

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

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

virtual void	v_ComputeTraceNormal (const int id)

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

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

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_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::StdExpansion2D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

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

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

virtual void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &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) override

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

virtual void	v_GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray) override

virtual void	v_GetElmtTraceToTraceMap (const unsigned int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q) override
	Determine the mapping to re-orientate the coefficients along the element trace (assumed to align with the standard element) into the orientation of the local trace given by edgeOrient. More...

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

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

Protected Attributes
std::vector< bool >	m_requireNeg

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

std::map< int, ExpansionWeakPtr >	m_traceExp

SpatialDomains::GeometrySharedPtr	m_geom

SpatialDomains::GeomFactorsSharedPtr	m_metricinfo

MetricMap	m_metrics

std::map< int, NormalVector >	m_traceNormals

ExpansionWeakPtr	m_elementLeft

ExpansionWeakPtr	m_elementRight

int	m_elementTraceLeft = -1

int	m_elementTraceRight = -1

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

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

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

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

Detailed Description

Definition at line 59 of file Expansion2D.h.

Constructor & Destructor Documentation

◆ Expansion2D()

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

Definition at line 54 of file Expansion2D.cpp.

     : StdExpansion(), Expansion(pGeom), StdExpansion2D()
 {
 }

◆ ~Expansion2D()

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

overridevirtualdefault

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 \tilde{F}_1j contributions

@TODO Variable coeffs

Definition at line 836 of file Expansion2D.cpp.

 {
     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);
  
     GetTraceToElementMap(edge, map, sign, v_GetTraceOrient(edge));
  
     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.GetValue(),
                                         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];
     }
 }

References Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, GetPhysEdgeVarCoeffsFromElement(), Nektar::StdRegions::StdExpansion::GetTraceToElementMap(), sign, Nektar::LocalRegions::Expansion::v_GetTraceOrient(), and Vmath::Vmul().

Referenced by AddNormTraceInt().

◆ 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

@TODO: What direction to use here??

@TODO: Document this (probably not needed)

Definition at line 907 of file Expansion2D.cpp.

 {
     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 =
         GetTraceNormal(edge);
  
     Array<OneD, unsigned int> emap;
     Array<OneD, int> sign;
  
     StdRegions::Orientation edgedir = GetTraceOrient(edge);
  
     DNekVec Coeffs(ncoeffs, outarray, eWrapper);
     DNekVec Tmpcoeff(ncoeffs, tmpcoeff, eWrapper);
  
     GetTraceToElementMap(edge, emap, sign, edgedir);
  
     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.GetValue(), 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] = GetMFMag(n, varcoeffs);
  
             MatrixKey invMasskey(StdRegions::eInvMass, DetShapeType(), *this,
                                  StdRegions::NullConstFactorMap, Weight);
  
             invMass = GetLocMatrix(invMasskey);
  
             Array<OneD, NekDouble> ncdotMF_e =
                 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);
         }
  
         // 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] =
                 GetMF(n, coordim, varcoeffs);
             VarCoeffDirDeriv[StdRegions::eVarCoeffMFDiv] =
                 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;
             }
         }
     }
 }

Referenced by AddHDGHelmholtzTraceTerms().

◆ 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 877 of file Expansion2D.cpp.

 {
     ASSERTL0(&inarray[0] != &outarray[0],
              "Input and output arrays use the same memory");
  
     int e, cnt, order_e, nedges = GetNtraces();
     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;
     }
 }

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

Referenced by v_GenMatrix().

◆ AddNormTraceInt() [1/2]

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.

@TODO: Document this

Definition at line 748 of file Expansion2D.cpp.

 {
     int i, e, cnt;
     int order_e, nquad_e;
     int nedges = GetNtraces();
  
     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 =
             GetTraceNormal(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 =
                 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);
         }
  
         AddEdgeBoundaryInt(e, EdgeExp[e], edgePhys, outarray, varcoeffs);
     }
 }

References AddEdgeBoundaryInt(), Nektar::StdRegions::eVarCoeffMF1x, GetnEdgecdotMF(), Nektar::StdRegions::StdExpansion::GetNtraces(), Nektar::LocalRegions::Expansion::GetTraceNormal(), and Vmath::Vmul().

◆ AddNormTraceInt() [2/2]

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 808 of file Expansion2D.cpp.

 {
     int e;
     int nquad_e;
     int nedges = GetNtraces();
  
     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 =
             GetTraceNormal(e);
  
         EdgeExp[e]->BwdTrans(edgeCoeffs[e], edgePhys);
  
         Vmath::Vmul(nquad_e, normals[dir], 1, edgePhys, 1, edgePhys, 1);
  
         AddEdgeBoundaryInt(e, EdgeExp[e], edgePhys, outarray);
     }
 }

References AddEdgeBoundaryInt(), Nektar::StdRegions::StdExpansion::GetNtraces(), Nektar::LocalRegions::Expansion::GetTraceNormal(), and Vmath::Vmul().

Referenced by v_DGDeriv(), and v_GenMatrix().

◆ CreateMatrix()

DNekScalMatSharedPtr Nektar::LocalRegions::Expansion2D::CreateMatrix ( const MatrixKey & mkey )

Definition at line 59 of file Expansion2D.cpp.

 {
     DNekScalMatSharedPtr returnval;
     LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
  
     ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,
              "Geometric information is not set up");
  
     switch (mkey.GetMatrixType())
     {
         case StdRegions::eMass:
         {
             if ((m_metricinfo->GetGtype() == SpatialDomains::eDeformed) ||
                 (mkey.GetNVarCoeff()))
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble jac        = (m_metricinfo->GetJac(ptsKeys))[0];
                 DNekMatSharedPtr mat = GetStdMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(jac, mat);
             }
         }
         break;
         case StdRegions::eMassGJP:
         {
             MatrixKey masskey(mkey, StdRegions::eMass);
             DNekScalMat &MassMat = *GetLocMatrix(masskey);
  
             // Generate a local copy of traceMat
             MatrixKey key(mkey, StdRegions::eNormDerivOnTrace);
             DNekMatSharedPtr NDTraceMat = Expansion2D::v_GenMatrix(key);
  
             ASSERTL1(mkey.ConstFactorExists(StdRegions::eFactorGJP),
                      "Need to specify eFactorGJP to construct "
                      "a HelmholtzGJP matrix");
  
             NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorGJP);
  
             factor /= MassMat.Scale();
  
             int ntot = MassMat.GetRows() * MassMat.GetColumns();
  
             Vmath::Svtvp(ntot, factor, &NDTraceMat->GetPtr()[0], 1,
                          MassMat.GetRawPtr(), 1, &NDTraceMat->GetPtr()[0], 1);
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(
                 MassMat.Scale(), NDTraceMat);
         }
         break;
         case StdRegions::eInvMass:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 NekDouble one = 1.0;
                 StdRegions::StdMatrixKey masskey(StdRegions::eMass,
                                                  DetShapeType(), *this);
                 DNekMatSharedPtr mat = GenMatrix(masskey);
                 mat->Invert();
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble fac        = 1.0 / (m_metricinfo->GetJac(ptsKeys))[0];
                 DNekMatSharedPtr mat = GetStdMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(fac, mat);
             }
         }
         break;
         case StdRegions::eWeakDeriv0:
         case StdRegions::eWeakDeriv1:
         case StdRegions::eWeakDeriv2:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
                 mkey.GetNVarCoeff())
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                 Array<TwoD, const NekDouble> df =
                     m_metricinfo->GetDerivFactors(ptsKeys);
                 int dir = 0;
                 if (mkey.GetMatrixType() == StdRegions::eWeakDeriv0)
                     dir = 0;
                 if (mkey.GetMatrixType() == StdRegions::eWeakDeriv1)
                     dir = 1;
                 if (mkey.GetMatrixType() == StdRegions::eWeakDeriv2)
                     dir = 2;
  
                 MatrixKey deriv0key(StdRegions::eWeakDeriv0,
                                     mkey.GetShapeType(), *this);
                 MatrixKey deriv1key(StdRegions::eWeakDeriv1,
                                     mkey.GetShapeType(), *this);
  
                 DNekMat &deriv0 = *GetStdMatrix(deriv0key);
                 DNekMat &deriv1 = *GetStdMatrix(deriv1key);
  
                 int rows = deriv0.GetRows();
                 int cols = deriv1.GetColumns();
  
                 DNekMatSharedPtr WeakDeriv =
                     MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
                 (*WeakDeriv) =
                     df[2 * dir][0] * deriv0 + df[2 * dir + 1][0] * deriv1;
  
                 returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(
                     jac, WeakDeriv);
             }
         }
         break;
         case StdRegions::eWeakDirectionalDeriv:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
                 mkey.GetNVarCoeff())
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 int shapedim = 2;
  
                 // dfdirxi = tan_{xi_x} * d \xi/dx
                 //         + tan_{xi_y} * d \xi/dy
                 //         + tan_{xi_z} * d \xi/dz
                 // dfdireta = tan_{eta_x} * d \eta/dx
                 //         + tan_{xi_y} * d \xi/dy
                 //         + tan_{xi_z} * d \xi/dz
                 NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                 Array<TwoD, const NekDouble> df =
                     m_metricinfo->GetDerivFactors(ptsKeys);
  
                 Array<OneD, NekDouble> direction =
                     mkey.GetVarCoeff(StdRegions::eVarCoeffMF);
  
                 // d / dx = df[0]*deriv0 + df[1]*deriv1
                 // d / dy = df[2]*deriv0 + df[3]*deriv1
                 // d / dz = df[4]*deriv0 + df[5]*deriv1
  
                 // dfdir[dir] = e \cdot (d/dx, d/dy, d/dz)
                 //            = (e^0 * df[0] + e^1 * df[2]
                 //                  + e^2 * df[4]) * deriv0
                 //            + (e^0 * df[1] + e^1 * df[3]
                 //                  + e^2 * df[5]) * deriv1
                 // dfdir[dir] = e^0 * df[2 * 0 + dir]
                 //            + e^1 * df[2 * 1 + dir]
                 //            + e^2 * df [ 2 * 2 + dir]
                 Array<OneD, Array<OneD, NekDouble>> dfdir(shapedim);
                 Expansion::ComputeGmatcdotMF(df, direction, dfdir);
  
                 StdRegions::VarCoeffMap dfdirxi;
                 StdRegions::VarCoeffMap dfdireta;
  
                 dfdirxi[StdRegions::eVarCoeffWeakDeriv]  = dfdir[0];
                 dfdireta[StdRegions::eVarCoeffWeakDeriv] = dfdir[1];
  
                 MatrixKey derivxikey(StdRegions::eWeakDeriv0,
                                      mkey.GetShapeType(), *this,
                                      StdRegions::NullConstFactorMap, dfdirxi);
                 MatrixKey derivetakey(StdRegions::eWeakDeriv1,
                                       mkey.GetShapeType(), *this,
                                       StdRegions::NullConstFactorMap, dfdireta);
  
                 DNekMat &derivxi  = *GetStdMatrix(derivxikey);
                 DNekMat &deriveta = *GetStdMatrix(derivetakey);
  
                 int rows = derivxi.GetRows();
                 int cols = deriveta.GetColumns();
  
                 DNekMatSharedPtr WeakDirDeriv =
                     MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
  
                 (*WeakDirDeriv) = derivxi + deriveta;
  
                 // Add (\nabla \cdot e^k ) Mass
                 StdRegions::VarCoeffMap DiveMass;
                 DiveMass[StdRegions::eVarCoeffMass] =
                     mkey.GetVarCoeff(StdRegions::eVarCoeffMFDiv);
                 StdRegions::StdMatrixKey stdmasskey(
                     StdRegions::eMass, mkey.GetShapeType(), *this,
                     StdRegions::NullConstFactorMap, DiveMass);
  
                 DNekMatSharedPtr DiveMassmat = GetStdMatrix(stdmasskey);
  
                 (*WeakDirDeriv) = (*WeakDirDeriv) + (*DiveMassmat);
  
                 returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(
                     jac, WeakDirDeriv);
             }
             break;
         }
         case StdRegions::eLaplacian:
         {
             if ((m_metricinfo->GetGtype() == SpatialDomains::eDeformed) ||
                 (mkey.GetNVarCoeff() > 0) ||
                 (mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio)))
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 MatrixKey lap00key(StdRegions::eLaplacian00,
                                    mkey.GetShapeType(), *this);
                 MatrixKey lap01key(StdRegions::eLaplacian01,
                                    mkey.GetShapeType(), *this);
                 MatrixKey lap11key(StdRegions::eLaplacian11,
                                    mkey.GetShapeType(), *this);
  
                 DNekMat &lap00 = *GetStdMatrix(lap00key);
                 DNekMat &lap01 = *GetStdMatrix(lap01key);
                 DNekMat &lap11 = *GetStdMatrix(lap11key);
  
                 NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                 Array<TwoD, const NekDouble> gmat =
                     m_metricinfo->GetGmat(ptsKeys);
  
                 int rows = lap00.GetRows();
                 int cols = lap00.GetColumns();
  
                 DNekMatSharedPtr lap =
                     MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
  
                 (*lap) = gmat[0][0] * lap00 +
                          gmat[1][0] * (lap01 + Transpose(lap01)) +
                          gmat[3][0] * lap11;
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(jac, lap);
             }
         }
         break;
         case StdRegions::eInvLaplacianWithUnityMean:
         {
             DNekMatSharedPtr mat = GenMatrix(mkey);
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, mat);
         }
         break;
         case StdRegions::eHelmholtz:
         {
             NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorLambda);
  
             MatrixKey masskey(mkey, StdRegions::eMass);
             DNekScalMat &MassMat = *GetLocMatrix(masskey);
  
             MatrixKey lapkey(mkey, StdRegions::eLaplacian);
             DNekScalMat &LapMat = *GetLocMatrix(lapkey);
  
             int rows = LapMat.GetRows();
             int cols = LapMat.GetColumns();
  
             DNekMatSharedPtr helm =
                 MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
  
             NekDouble one = 1.0;
             (*helm)       = LapMat + factor * MassMat;
  
             returnval =
                 MemoryManager<DNekScalMat>::AllocateSharedPtr(one, helm);
         }
         break;
         case StdRegions::eHelmholtzGJP:
         {
             MatrixKey helmkey(mkey, StdRegions::eHelmholtz);
             DNekScalMat &HelmMat = *GetLocMatrix(helmkey);
  
             // Generate a local copy of traceMat
             MatrixKey key(mkey, StdRegions::eNormDerivOnTrace);
             DNekMatSharedPtr NDTraceMat = Expansion2D::v_GenMatrix(key);
  
             ASSERTL1(mkey.ConstFactorExists(StdRegions::eFactorGJP),
                      "Need to specify eFactorGJP to construct "
                      "a HelmholtzGJP matrix");
  
             NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorGJP);
  
             factor /= HelmMat.Scale();
  
             int ntot = HelmMat.GetRows() * HelmMat.GetColumns();
  
             Vmath::Svtvp(ntot, factor, &NDTraceMat->GetPtr()[0], 1,
                          HelmMat.GetRawPtr(), 1, &NDTraceMat->GetPtr()[0], 1);
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(
                 HelmMat.Scale(), NDTraceMat);
         }
         break;
         case StdRegions::eIProductWRTBase:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble jac        = (m_metricinfo->GetJac(ptsKeys))[0];
                 DNekMatSharedPtr mat = GetStdMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(jac, mat);
             }
         }
         break;
         case StdRegions::eIProductWRTDerivBase0:
         case StdRegions::eIProductWRTDerivBase1:
         case StdRegions::eIProductWRTDerivBase2:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
  
                 const Array<TwoD, const NekDouble> &df =
                     m_metricinfo->GetDerivFactors(ptsKeys);
                 int dir = 0;
                 if (mkey.GetMatrixType() == StdRegions::eIProductWRTDerivBase0)
                     dir = 0;
                 if (mkey.GetMatrixType() == StdRegions::eIProductWRTDerivBase1)
                     dir = 1;
                 if (mkey.GetMatrixType() == StdRegions::eIProductWRTDerivBase2)
                     dir = 2;
  
                 MatrixKey iProdDeriv0Key(StdRegions::eIProductWRTDerivBase0,
                                          mkey.GetShapeType(), *this);
                 MatrixKey iProdDeriv1Key(StdRegions::eIProductWRTDerivBase1,
                                          mkey.GetShapeType(), *this);
  
                 DNekMat &stdiprod0 = *GetStdMatrix(iProdDeriv0Key);
                 DNekMat &stdiprod1 = *GetStdMatrix(iProdDeriv0Key);
  
                 int rows = stdiprod0.GetRows();
                 int cols = stdiprod1.GetColumns();
  
                 DNekMatSharedPtr mat =
                     MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
                 (*mat) =
                     df[2 * dir][0] * stdiprod0 + df[2 * dir + 1][0] * stdiprod1;
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(jac, mat);
             }
         }
         break;
  
         case StdRegions::eInvHybridDGHelmholtz:
         {
             NekDouble one = 1.0;
  
             MatrixKey hkey(StdRegions::eHybridDGHelmholtz, DetShapeType(),
                            *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
  
             DNekMatSharedPtr mat = GenMatrix(hkey);
  
             mat->Invert();
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
         }
         break;
         case StdRegions::eInterpGauss:
         {
             ASSERTL1(DetShapeType() == LibUtilities::eQuadrilateral,
                      "Matrix only setup for quad elements currently");
             DNekMatSharedPtr m_Ix;
             Array<OneD, NekDouble> coords(1, 0.0);
             StdRegions::ConstFactorMap factors = mkey.GetConstFactors();
             int edge = static_cast<int>(factors[StdRegions::eFactorGaussEdge]);
  
             coords[0] = (edge == 0 || edge == 3) ? -1.0 : 1.0;
  
             m_Ix = m_base[(edge + 1) % 2]->GetI(coords);
  
             returnval =
                 MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, m_Ix);
         }
         break;
         case StdRegions::ePreconLinearSpace:
         {
             NekDouble one = 1.0;
             MatrixKey helmkey(StdRegions::eHelmholtz, mkey.GetShapeType(),
                               *this, mkey.GetConstFactors(),
                               mkey.GetVarCoeffs());
             DNekScalBlkMatSharedPtr helmStatCond =
                 GetLocStaticCondMatrix(helmkey);
             DNekScalMatSharedPtr A = helmStatCond->GetBlock(0, 0);
             DNekMatSharedPtr R     = BuildVertexMatrix(A);
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, R);
         }
         break;
         default:
         {
             NekDouble one        = 1.0;
             DNekMatSharedPtr mat = GenMatrix(mkey);
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
         }
         break;
     }
  
     return returnval;
 }

◆ GetGeom2D()

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

inline

Definition at line 172 of file Expansion2D.h.

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

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

Referenced by GetTraceInverseBoundaryMap(), Nektar::LocalRegions::QuadExp::v_FwdTransBndConstrained(), Nektar::LocalRegions::TriExp::v_FwdTransBndConstrained(), and Nektar::LocalRegions::TriExp::v_GetTraceOrient().

◆ GetnEdgecdotMF()

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

private

Definition at line 2099 of file Expansion2D.cpp.

 {
     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.GetValue();
  
         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;
 }

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

◆ GetPhysEdgeVarCoeffsFromElement()

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

private

Extracts the variable coefficients along an edge

Definition at line 1054 of file Expansion2D.cpp.

 {
     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 = GetTraceOrient(edge);
     GetTraceToElementMap(edge, emap, sign, edgedir);
  
     for (unsigned int i = 0; i < EdgeExp->GetNcoeffs(); ++i)
     {
         edgetmp[i] = tmp[emap[i]];
     }
  
     // BwdTrans
     EdgeExp->BwdTrans(edgetmp, outarray);
 }

References Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::LocalRegions::Expansion::GetTraceOrient(), Nektar::StdRegions::StdExpansion::GetTraceToElementMap(), and sign.

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

◆ GetTraceInverseBoundaryMap()

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

Definition at line 2021 of file Expansion2D.cpp.

 {
     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 = GetTraceNcoeffs(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
     GetTraceInteriorToElementMap(eid, maparray, signarray, eOrient);
  
     for (n = 0; n < nEdgeCoeffs; ++n)
     {
         edgemaparray[n] = invmap[maparray[n]];
     }
  
     return edgemaparray;
 }

References Nektar::StdRegions::StdExpansion::GetBoundaryMap(), GetGeom2D(), Nektar::StdRegions::StdExpansion::GetTraceInteriorToElementMap(), Nektar::StdRegions::StdExpansion::GetTraceNcoeffs(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

◆ ReOrientEdgePhysMap()

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

◆ SetTraceToGeomOrientation()

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

Definition at line 729 of file Expansion2D.cpp.

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

References Nektar::StdRegions::StdExpansion::GetNtraces(), Nektar::StdRegions::StdExpansion::GetTraceNcoeffs(), and Nektar::LocalRegions::Expansion::GetTraceOrient().

Referenced by v_GenMatrix().

◆ v_AddEdgeNormBoundaryInt() [1/2]

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

overrideprotectedvirtual

Definition at line 554 of file Expansion2D.cpp.

 {
     int i;
  
     if (m_requireNeg.size() == 0)
     {
         int nedges = GetNtraces();
         m_requireNeg.resize(nedges);
  
         for (i = 0; i < nedges; ++i)
         {
             m_requireNeg[i] = false;
  
             ExpansionSharedPtr edgeExp = m_traceExp[i].lock();
  
             if (edgeExp->GetRightAdjacentElementExp())
             {
                 if (edgeExp->GetRightAdjacentElementExp()
                         ->GetGeom()
                         ->GetGlobalID() == GetGeom()->GetGlobalID())
                 {
                     m_requireNeg[i] = true;
                 }
             }
         }
     }
  
     IndexMapKey ikey(eEdgeToElement, DetShapeType(), GetBasisNumModes(0),
                      GetBasisNumModes(1), 0, edge, GetTraceOrient(edge));
  
     IndexMapValuesSharedPtr map = GetIndexMap(ikey);
  
     // Order of the element
     int order_e = map->size();
     // 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_AddEdgeNormBoundaryInt() [2/2]

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
	)

overrideprotectedvirtual

Definition at line 496 of file Expansion2D.cpp.

 {
     ASSERTL1(GetCoordim() == 2, "Routine only set up for two-dimensions");
  
     const Array<OneD, const Array<OneD, NekDouble>> normals =
         GetTraceNormal(edge);
  
     if (m_requireNeg.size() == 0)
     {
         int nedges = GetNtraces();
         m_requireNeg.resize(nedges);
  
         for (int i = 0; i < nedges; ++i)
         {
             m_requireNeg[i] = false;
  
             ExpansionSharedPtr edgeExp = m_traceExp[i].lock();
  
             if (edgeExp->GetRightAdjacentElementExp())
             {
                 if (edgeExp->GetRightAdjacentElementExp()
                         ->GetGeom()
                         ->GetGlobalID() == GetGeom()->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].size()));
  
     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_requireNeg[edge])
     {
         if (locExp->GetRightAdjacentElementExp()->GetGeom()->GetGlobalID() ==
             m_geom->GetGlobalID())
         {
             Vmath::Neg(nquad_e, edgePhys, 1);
         }
     }
  
     AddEdgeNormBoundaryInt(edge, EdgeExp, edgePhys, outarray);
 }

References Nektar::LocalRegions::Expansion::AddEdgeNormBoundaryInt(), ASSERTL1, Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::LocalRegions::Expansion::GetGeom(), Nektar::StdRegions::StdExpansion::GetNtraces(), Nektar::LocalRegions::Expansion::GetTraceNormal(), Nektar::LocalRegions::Expansion::m_geom, m_requireNeg, Nektar::LocalRegions::Expansion::m_traceExp, Vmath::Neg(), Vmath::Vmul(), and Vmath::Vvtvp().

◆ v_AddRobinMassMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1817 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_traceExp[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())
     {
         GetTraceToElementMap(edge, map, sign, v_GetTraceOrient(edge));
     }
     else if (rows == NumBndryCoeffs())
     {
         int nbndry = NumBndryCoeffs();
         Array<OneD, unsigned int> bmap(nbndry);
  
         GetTraceToElementMap(edge, map, sign, v_GetTraceOrient(edge));
  
         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 += GetTraceNcoeffs(i);
         }
  
         for (i = 0; i < order_e; ++i)
         {
             map[i] = cnt++;
         }
         // check for mapping reversal
         if (GetTraceOrient(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_AddRobinTraceContribution()

void Nektar::LocalRegions::Expansion2D::v_AddRobinTraceContribution	(	const int	edgeid,
		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 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::LocalRegions::Expansion.

Definition at line 1947 of file Expansion2D.cpp.

 {
     ASSERTL1(IsBoundaryInteriorExpansion(),
              "Not set up for non boundary-interior expansions");
     int i;
     ExpansionSharedPtr edgeExp = m_traceExp[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);
  
     GetTraceToElementMap(edgeid, map, sign, v_GetTraceOrient(edgeid));
  
     for (i = 0; i < order_e; ++i)
     {
         vEdgeCoeffs[i] = incoeffs[map[i]] * sign[i];
     }
  
     vEdgeCoeffs = edgemat * vEdgeCoeffs;
  
     for (i = 0; i < order_e; ++i)
     {
         coeffs[map[i]] += vEdgeCoeffs[i] * sign[i];
     }
 }

References ASSERTL1, Nektar::StdRegions::eMass, Nektar::LibUtilities::eSegment, Nektar::StdRegions::eVarCoeffMass, Nektar::StdRegions::StdExpansion::GetTraceToElementMap(), Nektar::StdRegions::StdExpansion::IsBoundaryInteriorExpansion(), Nektar::LocalRegions::Expansion::m_traceExp, Nektar::StdRegions::NullConstFactorMap, sign, and Nektar::LocalRegions::Expansion::v_GetTraceOrient().

◆ v_BuildVertexMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1985 of file Expansion2D.cpp.

 {
     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;
 }

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

◆ 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
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1780 of file Expansion2D.cpp.

 {
     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;
 }

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().

◆ v_GenMatrix()

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

overridevirtual

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 1087 of file Expansion2D.cpp.

 {
     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    = GetNtraces();
             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;
  
             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] =
                             GetMF(i, shapedim, varcoeffs);
                         VarCoeffDirDeriv[StdRegions::eVarCoeffMFDiv] =
                             GetMFDiv(i, varcoeffs);
  
                         MatrixKey Dmatkey(StdRegions::eWeakDirectionalDeriv,
                                           DetShapeType(), *this,
                                           StdRegions::NullConstFactorMap,
                                           VarCoeffDirDeriv);
  
                         DNekScalMat &Dmat = *GetLocMatrix(Dmatkey);
  
                         StdRegions::VarCoeffMap Weight;
                         Weight[StdRegions::eVarCoeffMass] =
                             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 = GetTraceExp(i);
                 order_e = EdgeExp->GetNcoeffs();
  
                 int nq = EdgeExp->GetNumPoints(0);
                 GetTraceToElementMap(i, emap, sign, edgedir);
  
                 // @TODO: Document
                 StdRegions::VarCoeffMap edgeVarCoeffs;
                 if (mkey.HasVarCoeff(StdRegions::eVarCoeffD00))
                 {
                     Array<OneD, NekDouble> mu(nq);
                     GetPhysEdgeVarCoeffsFromElement(
                         i, EdgeExp, 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    = GetNtraces();
             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] = GetTraceExp(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   = GetNtraces();
             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] = GetTraceExp(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] =
                     GetMF(dir, shapedim, varcoeffs);
                 VarCoeffDirDeriv[StdRegions::eVarCoeffMFDiv] =
                     GetMFDiv(dir, varcoeffs);
  
                 MatrixKey Dmatkey(
                     StdRegions::eWeakDirectionalDeriv, DetShapeType(), *this,
                     StdRegions::NullConstFactorMap, VarCoeffDirDeriv);
  
                 Dmat = GetLocMatrix(Dmatkey);
  
                 StdRegions::VarCoeffMap Weight;
                 Weight[StdRegions::eVarCoeffMass] =
                     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    = GetNtraces();
             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] = GetTraceExp(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 = GetTraceNormal(e);
                     edgedir = GetTraceOrient(e);
  
                     work          = Array<OneD, NekDouble>(nquad_e);
                     varcoeff_work = Array<OneD, NekDouble>(nquad_e);
  
                     GetTraceToElementMap(e, emap, sign, edgedir);
  
                     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 = 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 = 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);
                     }
  
                     // - 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.GetValue(), 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(edgedir, edgeCoeffs,
                                                        edgeCoeffs);
  
                     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;
         case StdRegions::eNormDerivOnTrace:
         {
             int ntraces = GetNtraces();
             int ncoords = GetCoordim();
             int nphys   = GetTotPoints();
             Array<OneD, const Array<OneD, NekDouble>> normals;
             Array<OneD, NekDouble> phys(nphys);
             returnval =
                 MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, m_ncoeffs);
             DNekMat &Mat = *returnval;
             Vmath::Zero(m_ncoeffs * m_ncoeffs, Mat.GetPtr(), 1);
  
             Array<OneD, Array<OneD, NekDouble>> Deriv(3, NullNekDouble1DArray);
  
             for (int d = 0; d < ncoords; ++d)
             {
                 Deriv[d] = Array<OneD, NekDouble>(nphys);
             }
  
             Array<OneD, int> tracepts(ntraces);
             Array<OneD, ExpansionSharedPtr> traceExp(ntraces);
             int maxtpts = 0;
             for (int t = 0; t < ntraces; ++t)
             {
                 traceExp[t] = GetTraceExp(t);
                 tracepts[t] = traceExp[t]->GetTotPoints();
                 maxtpts     = (maxtpts > tracepts[t]) ? maxtpts : tracepts[t];
             }
  
             Array<OneD, NekDouble> val(maxtpts), tmp, tmp1;
  
             Array<OneD, Array<OneD, NekDouble>> dphidn(ntraces);
             for (int t = 0; t < ntraces; ++t)
             {
                 dphidn[t] =
                     Array<OneD, NekDouble>(m_ncoeffs * tracepts[t], 0.0);
             }
  
             for (int i = 0; i < m_ncoeffs; ++i)
             {
                 FillMode(i, phys);
                 PhysDeriv(phys, Deriv[0], Deriv[1], Deriv[2]);
  
                 for (int t = 0; t < ntraces; ++t)
                 {
                     const NormalVector norm = GetTraceNormal(t);
  
                     LibUtilities::BasisKey fromkey = GetTraceBasisKey(t);
                     LibUtilities::BasisKey tokey =
                         traceExp[t]->GetBasis(0)->GetBasisKey();
                     bool DoInterp = (fromkey != tokey);
  
                     Array<OneD, NekDouble> n(tracepts[t]);
                     ;
                     for (int d = 0; d < ncoords; ++d)
                     {
                         // if variable p may need to interpolate
                         if (DoInterp)
                         {
                             LibUtilities::Interp1D(fromkey, norm[d], tokey, n);
                         }
                         else
                         {
                             n = norm[d];
                         }
  
                         GetTracePhysVals(t, traceExp[t], Deriv[d], val,
                                          v_GetTraceOrient(t));
  
                         Vmath::Vvtvp(tracepts[t], n, 1, val, 1,
                                      tmp  = dphidn[t] + i * tracepts[t], 1,
                                      tmp1 = dphidn[t] + i * tracepts[t], 1);
                     }
                 }
             }
  
             for (int t = 0; t < ntraces; ++t)
             {
                 int nt = tracepts[t];
                 NekDouble h, p;
                 TraceNormLen(t, h, p);
  
                 // scaling from GJP paper
                 NekDouble scale =
                     (p == 1) ? 0.02 * h * h : 0.8 * pow(p + 1, -4.0) * h * h;
  
                 for (int i = 0; i < m_ncoeffs; ++i)
                 {
                     for (int j = i; j < m_ncoeffs; ++j)
                     {
                         Vmath::Vmul(nt, dphidn[t] + i * nt, 1,
                                     dphidn[t] + j * nt, 1, val, 1);
                         Mat(i, j) =
                             Mat(i, j) + scale * traceExp[t]->Integral(val);
                     }
                 }
             }
  
             // fill in symmetric components.
             for (int i = 0; i < m_ncoeffs; ++i)
             {
                 for (int j = 0; j < i; ++j)
                 {
                     Mat(i, j) = Mat(j, i);
                 }
             }
         }
         break;
         default:
             ASSERTL0(false,
                      "This matrix type cannot be generated from this class");
             break;
     }
  
     return returnval;
 }

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

◆ v_GenTraceExp()

void Nektar::LocalRegions::Expansion2D::v_GenTraceExp	(	const int	traceid,
		ExpansionSharedPtr &	exp
	)

overridevirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2015 of file Expansion2D.cpp.

 {
     exp = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
         GetTraceBasisKey(traceid), m_geom->GetEdge(traceid));
 }

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdExpansion::GetTraceBasisKey(), and Nektar::LocalRegions::Expansion::m_geom.

◆ v_ReOrientTracePhysMap()

void Nektar::LocalRegions::Expansion2D::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 2064 of file Expansion2D.cpp.

 {
     boost::ignore_unused(nq1);
  
     if (idmap.size() != 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;
     }
 }

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

◆ v_SetUpPhysNormals()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2059 of file Expansion2D.cpp.

 {
     v_ComputeTraceNormal(edge);
 }

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

◆ v_TraceNormLen()

void Nektar::LocalRegions::Expansion2D::v_TraceNormLen	(	const int	traceid,
		NekDouble &	h,
		NekDouble &	p
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2154 of file Expansion2D.cpp.

 {
     SpatialDomains::GeometrySharedPtr geom = GetGeom();
  
     int nverts = geom->GetNumVerts();
  
     // vertices on edges
     SpatialDomains::PointGeom ev0 = *geom->GetVertex(traceid);
     SpatialDomains::PointGeom ev1 = *geom->GetVertex((traceid + 1) % nverts);
  
     // vertex on adjacent edge to ev0
     SpatialDomains::PointGeom vadj =
         *geom->GetVertex((traceid + (nverts - 1)) % nverts);
  
     // calculate perpendicular distance of normal length
     // from first vertex
     NekDouble h1 = ev0.dist(vadj);
     SpatialDomains::PointGeom Dx, Dx1;
  
     Dx.Sub(ev1, ev0);
     Dx1.Sub(vadj, ev0);
  
     NekDouble d1    = Dx.dot(Dx1);
     NekDouble lenDx = Dx.dot(Dx);
     h               = sqrt(h1 * h1 - d1 * d1 / lenDx);
  
     // perpendicular distanace from second vertex
     SpatialDomains::PointGeom vadj1 = *geom->GetVertex((traceid + 2) % nverts);
  
     h1 = ev1.dist(vadj1);
     Dx1.Sub(vadj1, ev1);
     d1 = Dx.dot(Dx1);
  
     h = (h + sqrt(h1 * h1 - d1 * d1 / lenDx)) * 0.5;
  
     int dirn = (geom->GetDir(traceid) == 0) ? 1 : 0;
  
     p = (NekDouble)(GetBasisNumModes(dirn) - 1);
 }

References Nektar::SpatialDomains::PointGeom::dist(), Nektar::SpatialDomains::PointGeom::dot(), Nektar::StdRegions::StdExpansion::GetBasisNumModes(), Nektar::LocalRegions::Expansion::GetGeom(), Nektar::SpatialDomains::Geometry::GetVertex(), CellMLToNektar.cellml_metadata::p, tinysimd::sqrt(), and Nektar::SpatialDomains::PointGeom::Sub().

◆ v_VectorFlux()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2138 of file Expansion2D.cpp.

 {
     const Array<OneD, const Array<OneD, NekDouble>> &normals =
         GetLeftAdjacentElementExp()->GetTraceNormal(
             GetLeftAdjacentElementTrace());
  
     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);
 }

References Nektar::LocalRegions::Expansion::GetLeftAdjacentElementExp(), Nektar::LocalRegions::Expansion::GetLeftAdjacentElementTrace(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Vmath::Vmul(), and Vmath::Vvtvp().

Member Data Documentation

◆ m_requireNeg

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

protected

Definition at line 118 of file Expansion2D.h.

Referenced by v_AddEdgeNormBoundaryInt().

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Expansion2D()

◆ ~Expansion2D()

Member Function Documentation

◆ AddEdgeBoundaryInt()

◆ AddHDGHelmholtzEdgeTerms()

◆ AddHDGHelmholtzTraceTerms()

◆ AddNormTraceInt() [1/2]

◆ AddNormTraceInt() [2/2]

◆ CreateMatrix()

◆ GetGeom2D()

◆ GetnEdgecdotMF()

◆ GetPhysEdgeVarCoeffsFromElement()

◆ GetTraceInverseBoundaryMap()

◆ ReOrientEdgePhysMap()

◆ SetTraceToGeomOrientation()

◆ v_AddEdgeNormBoundaryInt() [1/2]

◆ v_AddEdgeNormBoundaryInt() [2/2]

◆ v_AddRobinMassMatrix()

◆ v_AddRobinTraceContribution()

◆ v_BuildVertexMatrix()

◆ v_DGDeriv()

◆ v_GenMatrix()

◆ v_GenTraceExp()

◆ v_ReOrientTracePhysMap()

◆ v_SetUpPhysNormals()

◆ v_TraceNormLen()

◆ v_VectorFlux()

Member Data Documentation

◆ m_requireNeg