#include <Expansion3D.h>

Inheritance diagram for Nektar::LocalRegions::Expansion3D:

Public Member Functions
	Expansion3D (SpatialDomains::Geometry3DSharedPtr pGeom)

virtual	~Expansion3D () override=default

void	SetTraceToGeomOrientation (Array< OneD, NekDouble > &inout)
	Align trace orientation with the geometry orientation. More...

void	SetFaceToGeomOrientation (const int face, Array< OneD, NekDouble > &inout)
	Align face orientation with the geometry orientation. More...

void	AddHDGHelmholtzFaceTerms (const NekDouble tau, const int edge, Array< OneD, NekDouble > &facePhys, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray)

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

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

void	AddFaceBoundaryInt (const int face, ExpansionSharedPtr &FaceExp, Array< OneD, NekDouble > &facePhys, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)

SpatialDomains::Geometry3DSharedPtr	GetGeom3D () const

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

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

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

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

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

DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)

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 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::StdExpansion3D
	StdExpansion3D ()

	StdExpansion3D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)

	StdExpansion3D (const StdExpansion3D &T)

virtual	~StdExpansion3D () override

void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d1, Array< OneD, NekDouble > &outarray_d2, Array< OneD, NekDouble > &outarray_d3)
	Calculate the 3D derivative in the local tensor/collapsed coordinate at the physical points. More...

void	BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)

void	IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)

int	GetNedges () const
	return the number of edges in 3D expansion More...

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

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

Protected Member Functions
virtual void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, ExpansionSharedPtr > &FaceExp, Array< OneD, Array< OneD, NekDouble >> &faceCoeffs, Array< OneD, NekDouble > &out_d) override
	Evaluate coefficients of weak deriviative in the direction dir given the input coefficicents incoeffs and the imposed boundary values in EdgeExp (which will have its phys space updated). More...

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

virtual void	v_AddFaceNormBoundaryInt (const int face, const ExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) override

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

virtual StdRegions::Orientation	v_GetTraceOrient (int face) override

virtual void	v_GetTracePhysVals (const int face, const StdRegions::StdExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) override
	Extract the physical values along face face from inarray into outarray following the local face orientation and point distribution defined by defined in FaceExp. More...

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

void	GetPhysFaceVarCoeffsFromElement (const int face, ExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &varcoeff, Array< OneD, NekDouble > &outarray)

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

virtual DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &transformationmatrix) override
	Build inverse and inverse transposed transformation matrix: \(\mathbf{R^{-1}}\) and \(\mathbf{R^{-T}}\). More...

virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) 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 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 NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble >> &vec)

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

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

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

virtual void	v_ComputeTraceNormal (const int id)

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

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

virtual void	v_SetUpPhysNormals (const int id)

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

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::StdExpansion3D
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 > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0

virtual void	v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=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 NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrates the specified function over the domain. More...

virtual int	v_GetNedges (void) const

virtual int	v_GetEdgeNcoeffs (const int i) const

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

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

virtual void	v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient, int P, int Q) override

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

Protected Attributes
std::map< int, NormalVector >	m_faceNormals

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
Array< OneD, NekDouble >	GetnFacecdotMF (const int dir, const int face, ExpansionSharedPtr &FaceExp_f, const Array< OneD, const Array< OneD, NekDouble >> &normals, const StdRegions::VarCoeffMap &varcoeffs)

Private Attributes
std::vector< bool >	m_requireNeg

Detailed Description

Definition at line 57 of file Expansion3D.h.

Constructor & Destructor Documentation

◆ Expansion3D()

Nektar::LocalRegions::Expansion3D::Expansion3D ( SpatialDomains::Geometry3DSharedPtr pGeom )

inline

Definition at line 61 of file Expansion3D.h.

         : Expansion(pGeom), StdExpansion3D(), m_requireNeg()
     {
     }

◆ ~Expansion3D()

virtual Nektar::LocalRegions::Expansion3D::~Expansion3D ( )

overridevirtualdefault

Member Function Documentation

◆ AddFaceBoundaryInt()

void Nektar::LocalRegions::Expansion3D::AddFaceBoundaryInt	(	const int	face,
		ExpansionSharedPtr &	FaceExp,
		Array< OneD, NekDouble > &	facePhys,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::VarCoeffMap &	varcoeffs = `StdRegions::NullVarCoeffMap`
	)

inline

For a given face add the \tilde{F}_1j contributions

Definition at line 326 of file Expansion3D.cpp.

 {
     boost::ignore_unused(varcoeffs);
  
     int i;
     int order_f = FaceExp->GetNcoeffs();
     Array<OneD, NekDouble> coeff(order_f);
  
     IndexMapKey ikey(eFaceToElement, DetShapeType(), GetBasisNumModes(0),
                      GetBasisNumModes(1), GetBasisNumModes(2), face,
                      GetTraceOrient(face));
     IndexMapValuesSharedPtr map = GetIndexMap(ikey);
  
     //            StdRegions::VarCoeffType VarCoeff[3] =
     //            {StdRegions::eVarCoeffD00,
     //                                                    StdRegions::eVarCoeffD11,
     //                                                    StdRegions::eVarCoeffD22};
     //            StdRegions::VarCoeffMap::const_iterator x;
     //            Array<OneD, NekDouble> varcoeff_work(nquad_e);
     //
     ///// @TODO Variable coeffs
     //            if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
     //            {
     //                GetPhysEdgeVarCoeffsFromElement(edge,EdgeExp,x->second,varcoeff_work);
     //                Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp->GetPhys(),1,EdgeExp->UpdatePhys(),1);
     //            }
  
     FaceExp->IProductWRTBase(facePhys, coeff);
  
     // add data to out array
     for (i = 0; i < order_f; ++i)
     {
         outarray[(*map)[i].index] += (*map)[i].sign * coeff[i];
     }
 }

References Nektar::LocalRegions::eFaceToElement.

◆ AddHDGHelmholtzFaceTerms()

void Nektar::LocalRegions::Expansion3D::AddHDGHelmholtzFaceTerms	(	const NekDouble	tau,
		const int	edge,
		Array< OneD, NekDouble > &	facePhys,
		const StdRegions::VarCoeffMap &	dirForcing,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 54 of file Expansion3D.cpp.

 {
     ExpansionSharedPtr FaceExp = GetTraceExp(face);
     int i, j, n;
     int nquad_f = FaceExp->GetNumPoints(0) * FaceExp->GetNumPoints(1);
     int order_f = FaceExp->GetNcoeffs();
     int coordim = GetCoordim();
     int ncoeffs = GetNcoeffs();
     bool mmf = (varcoeffs.find(StdRegions::eVarCoeffMF1x) != varcoeffs.end());
  
     Array<OneD, NekDouble> inval(nquad_f);
     Array<OneD, NekDouble> outcoeff(order_f);
     Array<OneD, NekDouble> tmpcoeff(ncoeffs);
  
     const Array<OneD, const Array<OneD, NekDouble>> &normals =
         GetTraceNormal(face);
  
     DNekScalMat &invMass = *GetLocMatrix(StdRegions::eInvMass);
  
     DNekVec Coeffs(ncoeffs, outarray, eWrapper);
     DNekVec Tmpcoeff(ncoeffs, tmpcoeff, eWrapper);
  
     IndexMapKey ikey(eFaceToElement, DetShapeType(), GetBasisNumModes(0),
                      GetBasisNumModes(1), GetBasisNumModes(2), face,
                      GetTraceOrient(face));
     IndexMapValuesSharedPtr map = GetIndexMap(ikey);
  
     StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                            StdRegions::eWeakDeriv1,
                                            StdRegions::eWeakDeriv2};
  
     // @TODO Variable coefficients
     /*
     StdRegions::VarCoeffType VarCoeff[3] = {StdRegions::eVarCoeffD00,
                                             StdRegions::eVarCoeffD11,
                                             StdRegions::eVarCoeffD22};
     Array<OneD, NekDouble> varcoeff_work(nquad_f);
     StdRegions::VarCoeffMap::const_iterator x;
     ///// @TODO: What direction to use here??
     if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
     {
         GetPhysFaceVarCoeffsFromElement(face,FaceExp,x->second,varcoeff_work);
         Vmath::Vmul(nquad_f,varcoeff_work,1,FaceExp->GetPhys(),1,FaceExp->UpdatePhys(),1);
     }
     */
  
     //================================================================
     // Add F = \tau <phi_i,in_phys>
     // Fill face and take inner product
     FaceExp->IProductWRTBase(facePhys, outcoeff);
  
     for (i = 0; i < order_f; ++i)
     {
         outarray[(*map)[i].index] += (*map)[i].sign * 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
  
     // Three independent direction
     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_f =
                 GetnFacecdotMF(n, face, FaceExp, normals, varcoeffs);
  
             Vmath::Vmul(nquad_f, ncdotMF_f, 1, facePhys, 1, inval, 1);
         }
         else
         {
             Vmath::Vmul(nquad_f, normals[n], 1, facePhys, 1, inval, 1);
         }
  
         NekDouble scale       = invMass.Scale();
         const NekDouble *data = invMass.GetRawPtr();
  
         // @TODO Multiply by variable coefficients
         // @TODO: Document this (probably not needed)
         /*
         StdRegions::VarCoeffMap::const_iterator x;
         if ((x = varcoeffs.find(VarCoeff[n])) != varcoeffs.end())
         {
             GetPhysEdgeVarCoeffsFromElement(edge,FaceExp,x->second,varcoeff_work);
             Vmath::Vmul(nquad_f,varcoeff_work,1,FaceExp->GetPhys(),1,FaceExp->UpdatePhys(),1);
         }
         */
  
         FaceExp->IProductWRTBase(inval, outcoeff);
  
         // M^{-1} G
         for (i = 0; i < ncoeffs; ++i)
         {
             tmpcoeff[i] = 0;
             for (j = 0; j < order_f; ++j)
             {
                 tmpcoeff[i] += scale * data[i + (*map)[j].index * ncoeffs] *
                                (*map)[j].sign * 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
         {
             DNekScalMat &Dmat = *GetLocMatrix(DerivType[n]);
             Coeffs            = Coeffs + Dmat * Tmpcoeff;
         }
  
         /*
         if(varcoeffs.find(VarCoeff[n]) != varcoeffs.end())
         {
             MatrixKey mkey(DerivType[n], DetExpansionType(), *this,
         StdRegions::NullConstFactorMap, varcoeffs); DNekScalMat &Dmat =
         *GetLocMatrix(mkey); Coeffs = Coeffs  + Dmat*Tmpcoeff;
         }
  
         else
         {
             DNekScalMat &Dmat = *GetLocMatrix(DerivType[n]);
             Coeffs = Coeffs  + Dmat*Tmpcoeff;
         }
         */
     }
 }

References Nektar::LocalRegions::eFaceToElement, Nektar::StdRegions::eInvMass, Nektar::StdRegions::eVarCoeffMass, Nektar::StdRegions::eVarCoeffMF, Nektar::StdRegions::eVarCoeffMF1x, Nektar::StdRegions::eVarCoeffMFDiv, Nektar::StdRegions::eWeakDeriv0, Nektar::StdRegions::eWeakDeriv1, Nektar::StdRegions::eWeakDeriv2, Nektar::StdRegions::eWeakDirectionalDeriv, Nektar::eWrapper, Nektar::StdRegions::NullConstFactorMap, and Vmath::Vmul().

◆ AddNormTraceInt() [1/2]

void Nektar::LocalRegions::Expansion3D::AddNormTraceInt	(	const int	dir,
		Array< OneD, const NekDouble > &	inarray,
		Array< OneD, ExpansionSharedPtr > &	FaceExp,
		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 236 of file Expansion3D.cpp.

 {
     int i, f, cnt;
     int order_f, nquad_f;
     int nfaces = GetNtraces();
  
     cnt = 0;
     for (f = 0; f < nfaces; ++f)
     {
         order_f = FaceExp[f]->GetNcoeffs();
         nquad_f = FaceExp[f]->GetNumPoints(0) * FaceExp[f]->GetNumPoints(1);
  
         const Array<OneD, const Array<OneD, NekDouble>> &normals =
             GetTraceNormal(f);
         Array<OneD, NekDouble> faceCoeffs(order_f);
         Array<OneD, NekDouble> facePhys(nquad_f);
  
         for (i = 0; i < order_f; ++i)
         {
             faceCoeffs[i] = inarray[i + cnt];
         }
         cnt += order_f;
  
         FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
  
         // 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);
         //                }
         StdRegions::VarCoeffMap::const_iterator x;
         if ((x = varcoeffs.find(StdRegions::eVarCoeffMF1x)) != varcoeffs.end())
         {
             Array<OneD, NekDouble> ncdotMF_f =
                 GetnFacecdotMF(dir, f, FaceExp[f], normals, varcoeffs);
  
             Vmath::Vmul(nquad_f, ncdotMF_f, 1, facePhys, 1, facePhys, 1);
         }
         else
         {
             Vmath::Vmul(nquad_f, normals[dir], 1, facePhys, 1, facePhys, 1);
         }
  
         AddFaceBoundaryInt(f, FaceExp[f], facePhys, outarray, varcoeffs);
     }
 }

References Nektar::StdRegions::eVarCoeffMF1x, and Vmath::Vmul().

◆ AddNormTraceInt() [2/2]

void Nektar::LocalRegions::Expansion3D::AddNormTraceInt	(	const int	dir,
		Array< OneD, ExpansionSharedPtr > &	FaceExp,
		Array< OneD, Array< OneD, NekDouble >> &	faceCoeffs,
		Array< OneD, NekDouble > &	outarray
	)

inline

Definition at line 298 of file Expansion3D.cpp.

 {
     int f;
     int nquad_f;
     int nfaces = GetNtraces();
  
     for (f = 0; f < nfaces; ++f)
     {
         nquad_f = FaceExp[f]->GetNumPoints(0) * FaceExp[f]->GetNumPoints(1);
  
         const Array<OneD, const Array<OneD, NekDouble>> &normals =
             GetTraceNormal(f);
         Array<OneD, NekDouble> facePhys(nquad_f);
  
         FaceExp[f]->BwdTrans(faceCoeffs[f], facePhys);
  
         Vmath::Vmul(nquad_f, normals[dir], 1, facePhys, 1, facePhys, 1);
  
         AddFaceBoundaryInt(f, FaceExp[f], facePhys, outarray);
     }
 }

References Vmath::Vmul().

◆ CreateMatrix()

DNekScalMatSharedPtr Nektar::LocalRegions::Expansion3D::CreateMatrix ( const MatrixKey & mkey )

Definition at line 426 of file Expansion3D.cpp.

 {
     DNekScalMatSharedPtr returnval;
     LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
  
     ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,
              "Geometric information is not set up");
  
     switch (mkey.GetMatrixType())
     {
         case StdRegions::eMass:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
                 mkey.GetNVarCoeff())
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble jac        = (m_metricinfo->GetJac(ptsKeys))[0];
                 DNekMatSharedPtr mat = GetStdMatrix(mkey);
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(jac, mat);
             }
         }
         break;
         case StdRegions::eInvMass:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
             {
                 NekDouble one = 1.0;
                 StdRegions::StdMatrixKey masskey(StdRegions::eMass,
                                                  DetShapeType(), *this);
                 DNekMatSharedPtr mat = GenMatrix(masskey);
                 mat->Invert();
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble fac        = 1.0 / (m_metricinfo->GetJac(ptsKeys))[0];
                 DNekMatSharedPtr mat = GetStdMatrix(mkey);
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(fac, mat);
             }
         }
         break;
         case StdRegions::eWeakDeriv0:
         case StdRegions::eWeakDeriv1:
         case StdRegions::eWeakDeriv2:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
                 mkey.GetNVarCoeff())
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                 Array<TwoD, const NekDouble> df =
                     m_metricinfo->GetDerivFactors(ptsKeys);
                 int dir = 0;
                 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);
                 MatrixKey deriv2key(StdRegions::eWeakDeriv2,
                                     mkey.GetShapeType(), *this);
  
                 DNekMat &deriv0 = *GetStdMatrix(deriv0key);
                 DNekMat &deriv1 = *GetStdMatrix(deriv1key);
                 DNekMat &deriv2 = *GetStdMatrix(deriv2key);
  
                 int rows = deriv0.GetRows();
                 int cols = deriv1.GetColumns();
  
                 DNekMatSharedPtr WeakDeriv =
                     MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
                 (*WeakDeriv) = df[3 * dir][0] * deriv0 +
                                df[3 * dir + 1][0] * deriv1 +
                                df[3 * dir + 2][0] * deriv2;
  
                 returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(
                     jac, WeakDeriv);
             }
         }
         break;
         case StdRegions::eLaplacian:
         {
             if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
                 (mkey.GetNVarCoeff() > 0) ||
                 (mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio)))
             {
                 NekDouble one        = 1.0;
                 DNekMatSharedPtr mat = GenMatrix(mkey);
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
             }
             else
             {
                 MatrixKey lap00key(StdRegions::eLaplacian00,
                                    mkey.GetShapeType(), *this);
                 MatrixKey lap01key(StdRegions::eLaplacian01,
                                    mkey.GetShapeType(), *this);
                 MatrixKey lap02key(StdRegions::eLaplacian02,
                                    mkey.GetShapeType(), *this);
                 MatrixKey lap11key(StdRegions::eLaplacian11,
                                    mkey.GetShapeType(), *this);
                 MatrixKey lap12key(StdRegions::eLaplacian12,
                                    mkey.GetShapeType(), *this);
                 MatrixKey lap22key(StdRegions::eLaplacian22,
                                    mkey.GetShapeType(), *this);
  
                 DNekMat &lap00 = *GetStdMatrix(lap00key);
                 DNekMat &lap01 = *GetStdMatrix(lap01key);
                 DNekMat &lap02 = *GetStdMatrix(lap02key);
                 DNekMat &lap11 = *GetStdMatrix(lap11key);
                 DNekMat &lap12 = *GetStdMatrix(lap12key);
                 DNekMat &lap22 = *GetStdMatrix(lap22key);
  
                 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[4][0] * lap11 +
                          gmat[8][0] * lap22 +
                          gmat[3][0] * (lap01 + Transpose(lap01)) +
                          gmat[6][0] * (lap02 + Transpose(lap02)) +
                          gmat[7][0] * (lap12 + Transpose(lap12));
  
                 returnval =
                     MemoryManager<DNekScalMat>::AllocateSharedPtr(jac, lap);
             }
         }
         break;
         case StdRegions::eHelmholtz:
         {
             NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorLambda);
             MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
             DNekScalMat &MassMat = *GetLocMatrix(masskey);
             MatrixKey lapkey(StdRegions::eLaplacian, mkey.GetShapeType(), *this,
                              mkey.GetConstFactors(), mkey.GetVarCoeffs());
             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 = Expansion3D::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::eInvHybridDGHelmholtz:
         {
             NekDouble one = 1.0;
  
             MatrixKey hkey(StdRegions::eHybridDGHelmholtz, DetShapeType(),
                            *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
             DNekMatSharedPtr mat = GenMatrix(hkey);
  
             mat->Invert();
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
         }
         break;
         case StdRegions::ePreconLinearSpace:
         {
             NekDouble one = 1.0;
             MatrixKey helmkey(StdRegions::eHelmholtz, mkey.GetShapeType(),
                               *this, mkey.GetConstFactors(),
                               mkey.GetVarCoeffs());
             DNekScalBlkMatSharedPtr helmStatCond =
                 GetLocStaticCondMatrix(helmkey);
             DNekScalMatSharedPtr A = helmStatCond->GetBlock(0, 0);
             DNekMatSharedPtr R     = BuildVertexMatrix(A);
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, R);
         }
         break;
         case StdRegions::ePreconLinearSpaceMass:
         {
             NekDouble one = 1.0;
             MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
             DNekScalBlkMatSharedPtr massStatCond =
                 GetLocStaticCondMatrix(masskey);
             DNekScalMatSharedPtr A = massStatCond->GetBlock(0, 0);
             DNekMatSharedPtr R     = BuildVertexMatrix(A);
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, R);
         }
         break;
         case StdRegions::ePreconR:
         {
             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);
  
             DNekScalMatSharedPtr Atmp;
             DNekMatSharedPtr R =
                 BuildTransformationMatrix(A, mkey.GetMatrixType());
  
             returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, R);
         }
         break;
         case StdRegions::ePreconRMass:
         {
             NekDouble one = 1.0;
             MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
             DNekScalBlkMatSharedPtr StatCond = GetLocStaticCondMatrix(masskey);
             DNekScalMatSharedPtr A           = StatCond->GetBlock(0, 0);
  
             DNekScalMatSharedPtr Atmp;
             DNekMatSharedPtr R =
                 BuildTransformationMatrix(A, mkey.GetMatrixType());
  
             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;
 }

◆ GetEdgeInverseBoundaryMap()

Array< OneD, unsigned int > Nektar::LocalRegions::Expansion3D::GetEdgeInverseBoundaryMap ( int eid )

Definition at line 2349 of file Expansion3D.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 = GetEdgeNcoeffs(eid) - 2;
  
     const SpatialDomains::Geometry3DSharedPtr &geom = GetGeom3D();
  
     Array<OneD, unsigned int> edgemaparray(nEdgeCoeffs);
     StdRegions::Orientation eOrient    = geom->GetEorient(eid);
     Array<OneD, unsigned int> maparray = Array<OneD, unsigned int>(nEdgeCoeffs);
     Array<OneD, int> signarray         = Array<OneD, int>(nEdgeCoeffs, 1);
  
     // maparray is the location of the edge within the matrix
     GetEdgeInteriorToElementMap(eid, maparray, signarray, eOrient);
  
     for (n = 0; n < nEdgeCoeffs; ++n)
     {
         edgemaparray[n] = invmap[maparray[n]];
     }
  
     return edgemaparray;
 }

◆ GetGeom3D()

SpatialDomains::Geometry3DSharedPtr Nektar::LocalRegions::Expansion3D::GetGeom3D ( ) const

inline

Definition at line 182 of file Expansion3D.h.

 {
     return std::dynamic_pointer_cast<SpatialDomains::Geometry3D>(m_geom);
 }

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

◆ GetInverseBoundaryMaps()

void Nektar::LocalRegions::Expansion3D::GetInverseBoundaryMaps	(	Array< OneD, unsigned int > &	vmap,
		Array< OneD, Array< OneD, unsigned int >> &	emap,
		Array< OneD, Array< OneD, unsigned int >> &	fmap
	)

Definition at line 2501 of file Expansion3D.cpp.

 {
     int n, j;
     int nEdgeCoeffs;
     int nFaceCoeffs;
  
     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> reversemap;
     for (j = 0; j < bmap.size(); ++j)
     {
         reversemap[bmap[j]] = j;
     }
  
     int nverts = GetNverts();
     vmap       = Array<OneD, unsigned int>(nverts);
     for (n = 0; n < nverts; ++n)
     {
         int id  = GetVertexMap(n);
         vmap[n] = reversemap[id]; // not sure what should be true here.
     }
  
     int nedges = GetNedges();
     emap       = Array<OneD, Array<OneD, unsigned int>>(nedges);
  
     for (int eid = 0; eid < nedges; ++eid)
     {
         // Number of interior edge coefficients
         nEdgeCoeffs = GetEdgeNcoeffs(eid) - 2;
  
         Array<OneD, unsigned int> edgemaparray(nEdgeCoeffs);
         Array<OneD, unsigned int> maparray =
             Array<OneD, unsigned int>(nEdgeCoeffs);
         Array<OneD, int> signarray = Array<OneD, int>(nEdgeCoeffs, 1);
  
         // maparray is the location of the edge within the matrix
         GetEdgeInteriorToElementMap(eid, maparray, signarray,
                                     StdRegions::eForwards);
  
         for (n = 0; n < nEdgeCoeffs; ++n)
         {
             edgemaparray[n] = reversemap[maparray[n]];
         }
         emap[eid] = edgemaparray;
     }
  
     int nfaces = GetNtraces();
     fmap       = Array<OneD, Array<OneD, unsigned int>>(nfaces);
  
     for (int fid = 0; fid < nfaces; ++fid)
     {
         // Number of interior face coefficients
         nFaceCoeffs = GetTraceIntNcoeffs(fid);
  
         Array<OneD, unsigned int> facemaparray(nFaceCoeffs);
         Array<OneD, unsigned int> maparray =
             Array<OneD, unsigned int>(nFaceCoeffs);
         Array<OneD, int> signarray = Array<OneD, int>(nFaceCoeffs, 1);
  
         // maparray is the location of the face within the matrix
         GetTraceInteriorToElementMap(fid, maparray, signarray,
                                      StdRegions::eDir1FwdDir1_Dir2FwdDir2);
  
         for (n = 0; n < nFaceCoeffs; ++n)
         {
             facemaparray[n] = reversemap[maparray[n]];
         }
  
         fmap[fid] = facemaparray;
     }
 }

References Nektar::StdRegions::eDir1FwdDir1_Dir2FwdDir2, and Nektar::StdRegions::eForwards.

◆ GetnFacecdotMF()

Array< OneD, NekDouble > Nektar::LocalRegions::Expansion3D::GetnFacecdotMF	(	const int	dir,
		const int	face,
		ExpansionSharedPtr &	FaceExp_f,
		const Array< OneD, const Array< OneD, NekDouble >> &	normals,
		const StdRegions::VarCoeffMap &	varcoeffs
	)

private

Definition at line 2806 of file Expansion3D.cpp.

 {
     int nquad_f = FaceExp_f->GetNumPoints(0) * FaceExp_f->GetNumPoints(1);
     int coordim = GetCoordim();
  
     int nquad0 = m_base[0]->GetNumPoints();
     int nquad1 = m_base[1]->GetNumPoints();
     int nquad2 = m_base[2]->GetNumPoints();
     int nqtot  = nquad0 * nquad1 * nquad2;
  
     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> nFacecdotMF(nqtot, 0.0);
     Array<OneD, NekDouble> tmp(nqtot);
     Array<OneD, NekDouble> tmp_f(nquad_f);
     for (int k = 0; k < coordim; k++)
     {
         MFdir = varcoeffs.find(MMFCoeffs[dir * 5 + k]);
         tmp   = MFdir->second.GetValue();
  
         GetPhysFaceVarCoeffsFromElement(face, FaceExp_f, tmp, tmp_f);
  
         Vmath::Vvtvp(nquad_f, &tmp_f[0], 1, &normals[k][0], 1, &nFacecdotMF[0],
                      1, &nFacecdotMF[0], 1);
     }
  
     return nFacecdotMF;
 }

◆ GetPhysFaceVarCoeffsFromElement()

void Nektar::LocalRegions::Expansion3D::GetPhysFaceVarCoeffsFromElement	(	const int	face,
		ExpansionSharedPtr &	FaceExp,
		const Array< OneD, const NekDouble > &	varcoeff,
		Array< OneD, NekDouble > &	outarray
	)

protected

Definition at line 206 of file Expansion3D.cpp.

 {
     Array<OneD, NekDouble> tmp(GetNcoeffs());
     Array<OneD, NekDouble> facetmp(FaceExp->GetNcoeffs());
  
     // FwdTrans varcoeffs
     FwdTrans(varcoeff, tmp);
  
     // Map to edge
     Array<OneD, unsigned int> emap;
     Array<OneD, int> sign;
  
     GetTraceToElementMap(face, emap, sign, GetTraceOrient(face));
  
     for (unsigned int i = 0; i < FaceExp->GetNcoeffs(); ++i)
     {
         facetmp[i] = tmp[emap[i]];
     }
  
     // BwdTrans
     FaceExp->BwdTrans(facetmp, outarray);
 }

References sign.

◆ GetTraceInverseBoundaryMap()

Array< OneD, unsigned int > Nektar::LocalRegions::Expansion3D::GetTraceInverseBoundaryMap	(	int	fid,
		StdRegions::Orientation	faceOrient = `StdRegions::eNoOrientation`,
		int	P1 = `-1`,
		int	P2 = `-1`
	)

Definition at line 2387 of file Expansion3D.cpp.

 {
     int n, j;
     int nFaceCoeffs;
  
     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> reversemap;
     for (j = 0; j < bmap.size(); ++j)
     {
         reversemap[bmap[j]] = j;
     }
  
     // Number of interior face coefficients
     nFaceCoeffs = GetTraceIntNcoeffs(fid);
  
     StdRegions::Orientation fOrient;
     Array<OneD, unsigned int> maparray = Array<OneD, unsigned int>(nFaceCoeffs);
     Array<OneD, int> signarray         = Array<OneD, int>(nFaceCoeffs, 1);
  
     if (faceOrient == StdRegions::eNoOrientation)
     {
         fOrient = GetTraceOrient(fid);
     }
     else
     {
         fOrient = faceOrient;
     }
  
     // maparray is the location of the face within the matrix
     GetTraceInteriorToElementMap(fid, maparray, signarray, fOrient);
  
     Array<OneD, unsigned int> facemaparray;
     int locP1, locP2;
     GetTraceNumModes(fid, locP1, locP2, fOrient);
  
     if (P1 == -1)
     {
         P1 = locP1;
     }
     else
     {
         ASSERTL1(P1 <= locP1, "Expect value of passed P1 to "
                               "be lower or equal to face num modes");
     }
  
     if (P2 == -1)
     {
         P2 = locP2;
     }
     else
     {
         ASSERTL1(P2 <= locP2, "Expect value of passed P2 to "
                               "be lower or equal to face num modes");
     }
  
     switch (GetGeom3D()->GetFace(fid)->GetShapeType())
     {
         case LibUtilities::eTriangle:
         {
             if (((P1 - 3) > 0) && ((P2 - 3) > 0))
             {
                 facemaparray = Array<OneD, unsigned int>(
                     LibUtilities::StdTriData::getNumberOfCoefficients(P1 - 3,
                                                                       P2 - 3));
                 int cnt  = 0;
                 int cnt1 = 0;
                 for (n = 0; n < P1 - 3; ++n)
                 {
                     for (int m = 0; m < P2 - 3 - n; ++m, ++cnt)
                     {
                         facemaparray[cnt] = reversemap[maparray[cnt1 + m]];
                     }
                     cnt1 += locP2 - 3 - n;
                 }
             }
         }
         break;
         case LibUtilities::eQuadrilateral:
         {
             if (((P1 - 2) > 0) && ((P2 - 2) > 0))
             {
                 facemaparray = Array<OneD, unsigned int>(
                     LibUtilities::StdQuadData::getNumberOfCoefficients(P1 - 2,
                                                                        P2 - 2));
                 int cnt  = 0;
                 int cnt1 = 0;
                 for (n = 0; n < P2 - 2; ++n)
                 {
                     for (int m = 0; m < P1 - 2; ++m, ++cnt)
                     {
                         facemaparray[cnt] = reversemap[maparray[cnt1 + m]];
                     }
                     cnt1 += locP1 - 2;
                 }
             }
         }
         break;
         default:
         {
             ASSERTL0(false, "Invalid shape type.");
         }
         break;
     }
  
     return facemaparray;
 }

References ASSERTL0, ASSERTL1, Nektar::StdRegions::eNoOrientation, Nektar::LibUtilities::eQuadrilateral, Nektar::LibUtilities::eTriangle, and Nektar::LibUtilities::StdSegData::getNumberOfCoefficients().

◆ SetFaceToGeomOrientation()

void Nektar::LocalRegions::Expansion3D::SetFaceToGeomOrientation	(	const int	face,
		Array< OneD, NekDouble > &	inout
	)

Align face orientation with the geometry orientation.

Definition at line 369 of file Expansion3D.cpp.

 {
     int j, k;
     int nface = GetTraceNcoeffs(face);
     Array<OneD, NekDouble> f_in(nface);
     Vmath::Vcopy(nface, &inout[0], 1, &f_in[0], 1);
  
     // retreiving face to element map for standard face orientation and
     // for actual face orientation
     IndexMapKey ikey1(eFaceToElement, DetShapeType(), GetBasisNumModes(0),
                       GetBasisNumModes(1), GetBasisNumModes(2), face,
                       StdRegions::eDir1FwdDir1_Dir2FwdDir2);
     IndexMapValuesSharedPtr map1 = GetIndexMap(ikey1);
     IndexMapKey ikey2(eFaceToElement, DetShapeType(), GetBasisNumModes(0),
                       GetBasisNumModes(1), GetBasisNumModes(2), face,
                       GetTraceOrient(face));
     IndexMapValuesSharedPtr map2 = GetIndexMap(ikey2);
  
     ASSERTL1((*map1).size() == (*map2).size(),
              "There is an error with the GetTraceToElementMap");
  
     for (j = 0; j < (*map1).size(); ++j)
     {
         // j = index in the standard orientation
         for (k = 0; k < (*map2).size(); ++k)
         {
             // k = index in the actual orientation
             if ((*map1)[j].index == (*map2)[k].index && k != j)
             {
                 inout[k] = f_in[j];
                 // checking if sign is changing
                 if ((*map1)[j].sign != (*map2)[k].sign)
                     inout[k] *= -1.0;
                 break;
             }
         }
     }
 }

References ASSERTL1, Nektar::StdRegions::eDir1FwdDir1_Dir2FwdDir2, Nektar::LocalRegions::eFaceToElement, sign, and Vmath::Vcopy().

◆ SetTraceToGeomOrientation()

void Nektar::LocalRegions::Expansion3D::SetTraceToGeomOrientation ( Array< OneD, NekDouble > & inout )

Align trace orientation with the geometry orientation.

Definition at line 412 of file Expansion3D.cpp.

 {
     int i, cnt = 0;
     int nfaces = GetNtraces();
  
     Array<OneD, NekDouble> f_tmp;
  
     for (i = 0; i < nfaces; ++i)
     {
         SetFaceToGeomOrientation(i, f_tmp = inout + cnt);
         cnt += GetTraceNcoeffs(i);
     }
 }

◆ v_AddFaceNormBoundaryInt()

void Nektar::LocalRegions::Expansion3D::v_AddFaceNormBoundaryInt	(	const int	face,
		const ExpansionSharedPtr &	FaceExp,
		const Array< OneD, const NekDouble > &	Fn,
		Array< OneD, NekDouble > &	outarray
	)

overrideprotectedvirtual

Definition at line 1506 of file Expansion3D.cpp.

 {
     int i, j;
  
     /*
      * Coming into this routine, the velocity V will have been
      * multiplied by the trace normals to give the input vector Vn. By
      * convention, these normals are inwards facing for elements which
      * have FaceExp as their right-adjacent face.  This conditional
      * statement therefore determines whether the normals must be
      * negated, since the integral being performed here requires an
      * outwards facing normal.
      */
     if (m_requireNeg.size() == 0)
     {
         m_requireNeg.resize(GetNtraces());
  
         for (i = 0; i < GetNtraces(); ++i)
         {
             m_requireNeg[i] = false;
  
             ExpansionSharedPtr faceExp = m_traceExp[i].lock();
  
             if (faceExp->GetRightAdjacentElementExp())
             {
                 if (faceExp->GetRightAdjacentElementExp()
                         ->GetGeom()
                         ->GetGlobalID() == GetGeom()->GetGlobalID())
                 {
                     m_requireNeg[i] = true;
                 }
             }
         }
     }
  
     IndexMapKey ikey(eFaceToElement, DetShapeType(), GetBasisNumModes(0),
                      GetBasisNumModes(1), GetBasisNumModes(2), face,
                      GetTraceOrient(face));
     IndexMapValuesSharedPtr map = GetIndexMap(ikey);
  
     int order_e  = (*map).size(); // Order of the element
     int n_coeffs = FaceExp->GetNcoeffs();
  
     Array<OneD, NekDouble> faceCoeffs(n_coeffs);
  
     if (n_coeffs != order_e) // Going to orthogonal space
     {
         Array<OneD, NekDouble> coeff(n_coeffs);
         Array<OneD, NekDouble> array(n_coeffs);
  
         FaceExp->FwdTrans(Fn, faceCoeffs);
  
         int NumModesElementMax = FaceExp->GetBasis(0)->GetNumModes();
         int NumModesElementMin = m_base[0]->GetNumModes();
  
         FaceExp->ReduceOrderCoeffs(NumModesElementMin, faceCoeffs, faceCoeffs);
  
         StdRegions::StdMatrixKey masskey(StdRegions::eMass,
                                          FaceExp->DetShapeType(), *FaceExp);
         FaceExp->MassMatrixOp(faceCoeffs, faceCoeffs, masskey);
  
         // Reorder coefficients for the lower degree face.
         int offset1 = 0, offset2 = 0;
  
         if (FaceExp->DetShapeType() == LibUtilities::eQuadrilateral)
         {
             for (i = 0; i < NumModesElementMin; ++i)
             {
                 for (j = 0; j < NumModesElementMin; ++j)
                 {
                     faceCoeffs[offset1 + j] = faceCoeffs[offset2 + j];
                 }
                 offset1 += NumModesElementMin;
                 offset2 += NumModesElementMax;
             }
  
             // Extract lower degree modes. TODO: Check this is correct.
             for (i = NumModesElementMin; i < NumModesElementMax; ++i)
             {
                 for (j = NumModesElementMin; j < NumModesElementMax; ++j)
                 {
                     faceCoeffs[i * NumModesElementMax + j] = 0.0;
                 }
             }
         }
  
         if (FaceExp->DetShapeType() == LibUtilities::eTriangle)
         {
  
             // Reorder coefficients for the lower degree face.
             int offset1 = 0, offset2 = 0;
  
             for (i = 0; i < NumModesElementMin; ++i)
             {
                 for (j = 0; j < NumModesElementMin - i; ++j)
                 {
                     faceCoeffs[offset1 + j] = faceCoeffs[offset2 + j];
                 }
                 offset1 += NumModesElementMin - i;
                 offset2 += NumModesElementMax - i;
             }
         }
     }
     else
     {
         FaceExp->IProductWRTBase(Fn, faceCoeffs);
     }
  
     if (m_requireNeg[face])
     {
         for (i = 0; i < order_e; ++i)
         {
             outarray[(*map)[i].index] -= (*map)[i].sign * faceCoeffs[i];
         }
     }
     else
     {
         for (i = 0; i < order_e; ++i)
         {
             outarray[(*map)[i].index] += (*map)[i].sign * faceCoeffs[i];
         }
     }
 }

References Nektar::LocalRegions::eFaceToElement, Nektar::StdRegions::eMass, Nektar::LibUtilities::eQuadrilateral, and Nektar::LibUtilities::eTriangle.

◆ v_AddRobinMassMatrix()

void Nektar::LocalRegions::Expansion3D::v_AddRobinMassMatrix	(	const int	face,
		const Array< OneD, const NekDouble > &	primCoeffs,
		DNekMatSharedPtr &	inoutmat
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1666 of file Expansion3D.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 faceExp = m_traceExp[face].lock();
     int order_f                = faceExp->GetNcoeffs();
  
     Array<OneD, unsigned int> map;
     Array<OneD, int> sign;
  
     StdRegions::VarCoeffMap varcoeffs;
     varcoeffs[StdRegions::eVarCoeffMass] = primCoeffs;
  
     LibUtilities::ShapeType shapeType = faceExp->DetShapeType();
  
     LocalRegions::MatrixKey mkey(StdRegions::eMass, shapeType, *faceExp,
                                  StdRegions::NullConstFactorMap, varcoeffs);
  
     DNekScalMat &facemat = *faceExp->GetLocMatrix(mkey);
  
     // Now need to identify a map which takes the local face
     // 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_GetNverts() it is a vertex space
     //  preconditioner.
  
     // - if inoutmat.m_rows() == v_NumBndCoeffs() it is a
     //  boundary CG system
  
     // - if inoutmat.m_rows() == v_NumDGBndCoeffs() it is a
     //  trace DG system; still needs implementing.
     int rows = inoutmat->GetRows();
  
     if (rows == GetNcoeffs())
     {
         GetTraceToElementMap(face, map, sign, GetTraceOrient(face));
     }
     else if (rows == GetNverts())
     {
         int nfvert = faceExp->GetNverts();
  
         // Need to find where linear vertices are in facemat
         Array<OneD, unsigned int> linmap;
         Array<OneD, int> linsign;
  
         // Use a linear expansion to get correct mapping
         GetLinStdExp()->GetTraceToElementMap(face, linmap, linsign,
                                              GetTraceOrient(face));
  
         // zero out sign map to remove all other modes
         sign = Array<OneD, int>(order_f, 0);
         map  = Array<OneD, unsigned int>(order_f, (unsigned int)0);
  
         int fmap;
         // Reset sign map to only have contribution from vertices
         for (i = 0; i < nfvert; ++i)
         {
             fmap       = faceExp->GetVertexMap(i, true);
             sign[fmap] = 1;
  
             // need to reset map
             map[fmap] = linmap[i];
         }
     }
     else if (rows == NumBndryCoeffs())
     {
         int nbndry = NumBndryCoeffs();
         Array<OneD, unsigned int> bmap(nbndry);
  
         GetTraceToElementMap(face, map, sign, GetTraceOrient(face));
         GetBoundaryMap(bmap);
  
         for (i = 0; i < order_f; ++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_f);
         sign    = Array<OneD, int>(order_f, 1);
  
         IndexMapKey ikey1(eFaceToElement, DetShapeType(), GetBasisNumModes(0),
                           GetBasisNumModes(1), GetBasisNumModes(2), face,
                           GetTraceOrient(face));
         IndexMapValuesSharedPtr map1 = GetIndexMap(ikey1);
         IndexMapKey ikey2(eFaceToElement, DetShapeType(), GetBasisNumModes(0),
                           GetBasisNumModes(1), GetBasisNumModes(2), face,
                           StdRegions::eDir1FwdDir1_Dir2FwdDir2);
         IndexMapValuesSharedPtr map2 = GetIndexMap(ikey2);
  
         ASSERTL1((*map1).size() == (*map2).size(),
                  "There is an error with the GetTraceToElementMap");
  
         for (i = 0; i < face; ++i)
         {
             cnt += GetTraceNcoeffs(i);
         }
  
         for (i = 0; i < (*map1).size(); ++i)
         {
             int idx = -1;
  
             for (j = 0; j < (*map2).size(); ++j)
             {
                 if ((*map1)[i].index == (*map2)[j].index)
                 {
                     idx = j;
                     break;
                 }
             }
  
             ASSERTL2(idx >= 0, "Index not found");
             map[i]  = idx + cnt;
             sign[i] = (*map2)[idx].sign;
         }
     }
     else
     {
         ASSERTL0(false, "Could not identify matrix type from dimension");
     }
  
     for (i = 0; i < order_f; ++i)
     {
         id1 = map[i];
         for (j = 0; j < order_f; ++j)
         {
             id2 = map[j];
             (*inoutmat)(id1, id2) += facemat(i, j) * sign[i] * sign[j];
         }
     }
 }

References ASSERTL0, ASSERTL1, ASSERTL2, Nektar::StdRegions::eDir1FwdDir1_Dir2FwdDir2, Nektar::LocalRegions::eFaceToElement, Nektar::StdRegions::eMass, Nektar::StdRegions::eVarCoeffMass, Nektar::StdRegions::NullConstFactorMap, and sign.

◆ v_BuildInverseTransformationMatrix()

DNekMatSharedPtr Nektar::LocalRegions::Expansion3D::v_BuildInverseTransformationMatrix ( const DNekScalMatSharedPtr & transformationmatrix )

overrideprotectedvirtual

Build inverse and inverse transposed transformation matrix: \(\mathbf{R^{-1}}\) and \(\mathbf{R^{-T}}\).

\f\mathbf{R^{-T}}=[\left[\begin{array}{ccc} \mathbf{I} & -\mathbf{R}_{ef} & -\mathbf{R}_{ve}+\mathbf{R}_{ve}\mathbf{R}_{vf} \ 0 & \mathbf{I} & \mathbf{R}_{ef} \ 0 & 0 & \mathbf{I}} \end{array}\right]\f]

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 2232 of file Expansion3D.cpp.

 {
     int i, j, n, eid = 0, fid = 0;
     int nCoeffs = NumBndryCoeffs();
     NekDouble MatrixValue;
     DNekScalMat &R = (*transformationmatrix);
  
     // Define storage for vertex transpose matrix and zero all entries
     MatrixStorage storage = eFULL;
  
     // Inverse transformation matrix
     DNekMatSharedPtr inversetransformationmatrix =
         MemoryManager<DNekMat>::AllocateSharedPtr(nCoeffs, nCoeffs, 0.0,
                                                   storage);
     DNekMat &InvR = (*inversetransformationmatrix);
  
     int nVerts = GetNverts();
     int nEdges = GetNedges();
     int nFaces = GetNtraces();
  
     int nedgemodes      = 0;
     int nfacemodes      = 0;
     int nedgemodestotal = 0;
     int nfacemodestotal = 0;
  
     for (eid = 0; eid < nEdges; ++eid)
     {
         nedgemodes = GetEdgeNcoeffs(eid) - 2;
         nedgemodestotal += nedgemodes;
     }
  
     for (fid = 0; fid < nFaces; ++fid)
     {
         nfacemodes = GetTraceIntNcoeffs(fid);
         nfacemodestotal += nfacemodes;
     }
  
     Array<OneD, unsigned int> edgemodearray(nedgemodestotal);
     Array<OneD, unsigned int> facemodearray(nfacemodestotal);
  
     int offset = 0;
  
     // Create array of edge modes
     for (eid = 0; eid < nEdges; ++eid)
     {
         Array<OneD, unsigned int> edgearray = GetEdgeInverseBoundaryMap(eid);
         nedgemodes                          = GetEdgeNcoeffs(eid) - 2;
  
         // Only copy if there are edge modes
         if (nedgemodes)
         {
             Vmath::Vcopy(nedgemodes, &edgearray[0], 1, &edgemodearray[offset],
                          1);
         }
  
         offset += nedgemodes;
     }
  
     offset = 0;
  
     // Create array of face modes
     for (fid = 0; fid < nFaces; ++fid)
     {
         Array<OneD, unsigned int> facearray = GetTraceInverseBoundaryMap(fid);
         nfacemodes                          = GetTraceIntNcoeffs(fid);
  
         // Only copy if there are face modes
         if (nfacemodes)
         {
             Vmath::Vcopy(nfacemodes, &facearray[0], 1, &facemodearray[offset],
                          1);
         }
  
         offset += nfacemodes;
     }
  
     // Vertex-edge/face
     for (i = 0; i < nVerts; ++i)
     {
         for (j = 0; j < nedgemodestotal; ++j)
         {
             InvR.SetValue(GetVertexMap(i), edgemodearray[j],
                           -R(GetVertexMap(i), edgemodearray[j]));
         }
         for (j = 0; j < nfacemodestotal; ++j)
         {
             InvR.SetValue(GetVertexMap(i), facemodearray[j],
                           -R(GetVertexMap(i), facemodearray[j]));
             for (n = 0; n < nedgemodestotal; ++n)
             {
                 MatrixValue = InvR.GetValue(GetVertexMap(i), facemodearray[j]) +
                               R(GetVertexMap(i), edgemodearray[n]) *
                                   R(edgemodearray[n], facemodearray[j]);
                 InvR.SetValue(GetVertexMap(i), facemodearray[j], MatrixValue);
             }
         }
     }
  
     // Edge-face contributions
     for (i = 0; i < nedgemodestotal; ++i)
     {
         for (j = 0; j < nfacemodestotal; ++j)
         {
             InvR.SetValue(edgemodearray[i], facemodearray[j],
                           -R(edgemodearray[i], facemodearray[j]));
         }
     }
  
     for (i = 0; i < nCoeffs; ++i)
     {
         InvR.SetValue(i, i, 1.0);
     }
  
     return inversetransformationmatrix;
 }

References Nektar::eFULL, and Vmath::Vcopy().

◆ v_BuildTransformationMatrix()

DNekMatSharedPtr Nektar::LocalRegions::Expansion3D::v_BuildTransformationMatrix	(	const DNekScalMatSharedPtr &	r_bnd,
		const StdRegions::MatrixType	matrixType
	)

overrideprotectedvirtual

The matrix component of \(\mathbf{R}\) is given by

\[ \mathbf{R^{T}_{v}}= -\mathbf{S}^{-1}_{ef,ef}\mathbf{S}^{T}_{v,ef}\]

For every vertex mode we extract the submatrices from statically condensed matrix \(\mathbf{S}\) corresponding to the coupling between the attached edges and faces of a vertex ( \(\mathbf{S_{ef,ef}}\)). This matrix is then inverted and multiplied by the submatrix representing the coupling between a vertex and the attached edges and faces ( \(\mathbf{S_{v,ef}}\)).

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1850 of file Expansion3D.cpp.

 {
     int nVerts, nEdges;
     int eid, fid, vid, n, i;
  
     int nBndCoeffs = NumBndryCoeffs();
  
     const SpatialDomains::Geometry3DSharedPtr &geom = GetGeom3D();
  
     // Get geometric information about this element
     nVerts = GetNverts();
     nEdges = GetNedges();
  
     /*************************************/
     /* Vetex-edge & vertex-face matrices */
     /*************************************/
  
     /**
      * The matrix component of \f$\mathbf{R}\f$ is given by \f[
      * \mathbf{R^{T}_{v}}=
      * -\mathbf{S}^{-1}_{ef,ef}\mathbf{S}^{T}_{v,ef}\f]
      *
      * For every vertex mode we extract the submatrices from statically
      * condensed matrix \f$\mathbf{S}\f$ corresponding to the coupling
      * between the attached edges and faces of a vertex
      * (\f$\mathbf{S_{ef,ef}}\f$). This matrix is then inverted and
      * multiplied by the submatrix representing the coupling between a
      * vertex and the attached edges and faces
      * (\f$\mathbf{S_{v,ef}}\f$).
      */
  
     int nmodes;
     int m;
     NekDouble VertexEdgeFaceValue;
  
     // The number of connected edges/faces is 3 (for all elements)
     int nConnectedEdges = 3;
     int nConnectedFaces = 3;
  
     // Location in the matrix
     Array<OneD, Array<OneD, unsigned int>> MatEdgeLocation(nConnectedEdges);
     Array<OneD, Array<OneD, unsigned int>> MatFaceLocation(nConnectedFaces);
  
     // Define storage for vertex transpose matrix and zero all entries
     MatrixStorage storage = eFULL;
     DNekMatSharedPtr transformationmatrix;
  
     transformationmatrix = MemoryManager<DNekMat>::AllocateSharedPtr(
         nBndCoeffs, nBndCoeffs, 0.0, storage);
  
     DNekMat &R = (*transformationmatrix);
  
     // Build the vertex-edge/face transform matrix: This matrix is
     // constructed from the submatrices corresponding to the couping
     // between each vertex and the attached edges/faces
     for (vid = 0; vid < nVerts; ++vid)
     {
         // Row and column size of the vertex-edge/face matrix
         int efRow = GetEdgeNcoeffs(geom->GetVertexEdgeMap(vid, 0)) +
                     GetEdgeNcoeffs(geom->GetVertexEdgeMap(vid, 1)) +
                     GetEdgeNcoeffs(geom->GetVertexEdgeMap(vid, 2)) +
                     GetTraceIntNcoeffs(geom->GetVertexFaceMap(vid, 0)) +
                     GetTraceIntNcoeffs(geom->GetVertexFaceMap(vid, 1)) +
                     GetTraceIntNcoeffs(geom->GetVertexFaceMap(vid, 2)) - 6;
  
         int nedgemodesconnected =
             GetEdgeNcoeffs(geom->GetVertexEdgeMap(vid, 0)) +
             GetEdgeNcoeffs(geom->GetVertexEdgeMap(vid, 1)) +
             GetEdgeNcoeffs(geom->GetVertexEdgeMap(vid, 2)) - 6;
         Array<OneD, unsigned int> edgemodearray(nedgemodesconnected);
  
         int nfacemodesconnected =
             GetTraceIntNcoeffs(geom->GetVertexFaceMap(vid, 0)) +
             GetTraceIntNcoeffs(geom->GetVertexFaceMap(vid, 1)) +
             GetTraceIntNcoeffs(geom->GetVertexFaceMap(vid, 2));
         Array<OneD, unsigned int> facemodearray(nfacemodesconnected);
  
         int offset = 0;
  
         // Create array of edge modes
         for (eid = 0; eid < nConnectedEdges; ++eid)
         {
             MatEdgeLocation[eid] =
                 GetEdgeInverseBoundaryMap(geom->GetVertexEdgeMap(vid, eid));
             nmodes = MatEdgeLocation[eid].size();
  
             if (nmodes)
             {
                 Vmath::Vcopy(nmodes, &MatEdgeLocation[eid][0], 1,
                              &edgemodearray[offset], 1);
             }
  
             offset += nmodes;
         }
  
         offset = 0;
  
         // Create array of face modes
         for (fid = 0; fid < nConnectedFaces; ++fid)
         {
             MatFaceLocation[fid] =
                 GetTraceInverseBoundaryMap(geom->GetVertexFaceMap(vid, fid));
             nmodes = MatFaceLocation[fid].size();
  
             if (nmodes)
             {
                 Vmath::Vcopy(nmodes, &MatFaceLocation[fid][0], 1,
                              &facemodearray[offset], 1);
             }
             offset += nmodes;
         }
  
         DNekMatSharedPtr vertexedgefacetransformmatrix =
             MemoryManager<DNekMat>::AllocateSharedPtr(1, efRow, 0.0, storage);
         DNekMat &Sveft = (*vertexedgefacetransformmatrix);
  
         DNekMatSharedPtr vertexedgefacecoupling =
             MemoryManager<DNekMat>::AllocateSharedPtr(1, efRow, 0.0, storage);
         DNekMat &Svef = (*vertexedgefacecoupling);
  
         // Vertex-edge coupling
         for (n = 0; n < nedgemodesconnected; ++n)
         {
             // Matrix value for each coefficient location
             VertexEdgeFaceValue = (*r_bnd)(GetVertexMap(vid), edgemodearray[n]);
  
             // Set the value in the vertex edge/face matrix
             Svef.SetValue(0, n, VertexEdgeFaceValue);
         }
  
         // Vertex-face coupling
         for (n = 0; n < nfacemodesconnected; ++n)
         {
             // Matrix value for each coefficient location
             VertexEdgeFaceValue = (*r_bnd)(GetVertexMap(vid), facemodearray[n]);
  
             // Set the value in the vertex edge/face matrix
             Svef.SetValue(0, n + nedgemodesconnected, VertexEdgeFaceValue);
         }
  
         /*
          * Build the edge-face transform matrix: This matrix is
          * constructed from the submatrices corresponding to the couping
          * between the edges and faces on the attached faces/edges of a
          * vertex.
          */
  
         // Allocation of matrix to store edge/face-edge/face coupling
         DNekMatSharedPtr edgefacecoupling =
             MemoryManager<DNekMat>::AllocateSharedPtr(efRow, efRow, 0.0,
                                                       storage);
         DNekMat &Sefef = (*edgefacecoupling);
  
         NekDouble EdgeEdgeValue, FaceFaceValue;
  
         // Edge-edge coupling (S_{ee})
         for (m = 0; m < nedgemodesconnected; ++m)
         {
             for (n = 0; n < nedgemodesconnected; ++n)
             {
                 // Matrix value for each coefficient location
                 EdgeEdgeValue = (*r_bnd)(edgemodearray[n], edgemodearray[m]);
  
                 // Set the value in the vertex edge/face matrix
                 Sefef.SetValue(n, m, EdgeEdgeValue);
             }
         }
  
         // Face-face coupling (S_{ff})
         for (n = 0; n < nfacemodesconnected; ++n)
         {
             for (m = 0; m < nfacemodesconnected; ++m)
             {
                 // Matrix value for each coefficient location
                 FaceFaceValue = (*r_bnd)(facemodearray[n], facemodearray[m]);
                 // Set the value in the vertex edge/face matrix
                 Sefef.SetValue(nedgemodesconnected + n, nedgemodesconnected + m,
                                FaceFaceValue);
             }
         }
  
         // Edge-face coupling (S_{ef} and trans(S_{ef}))
         for (n = 0; n < nedgemodesconnected; ++n)
         {
             for (m = 0; m < nfacemodesconnected; ++m)
             {
                 // Matrix value for each coefficient location
                 FaceFaceValue = (*r_bnd)(edgemodearray[n], facemodearray[m]);
  
                 // Set the value in the vertex edge/face matrix
                 Sefef.SetValue(n, nedgemodesconnected + m, FaceFaceValue);
  
                 FaceFaceValue = (*r_bnd)(facemodearray[m], edgemodearray[n]);
  
                 // and transpose
                 Sefef.SetValue(nedgemodesconnected + m, n, FaceFaceValue);
             }
         }
  
         // Invert edge-face coupling matrix
         if (efRow)
         {
             Sefef.Invert();
  
             // R_{v}=-S_{v,ef}inv(S_{ef,ef})
             Sveft = -Svef * Sefef;
         }
  
         // Populate R with R_{ve} components
         for (n = 0; n < edgemodearray.size(); ++n)
         {
             R.SetValue(GetVertexMap(vid), edgemodearray[n], Sveft(0, n));
         }
  
         // Populate R with R_{vf} components
         for (n = 0; n < facemodearray.size(); ++n)
         {
             R.SetValue(GetVertexMap(vid), facemodearray[n],
                        Sveft(0, n + nedgemodesconnected));
         }
     }
  
     /********************/
     /* edge-face matrix */
     /********************/
  
     /*
      * The matrix component of \f$\mathbf{R}\f$ is given by \f[
      * \mathbf{R^{T}_{ef}}=-\mathbf{S}^{-1}_{ff}\mathbf{S}^{T}_{ef}\f]
      *
      * For each edge extract the submatrices from statically condensed
      * matrix \f$\mathbf{S}\f$ corresponding to inner products of modes
      * on the two attached faces within themselves as well as the
      * coupling matrix between the two faces
      * (\f$\mathbf{S}_{ff}\f$). This matrix of face coupling is then
      * inverted and multiplied by the submatrices of corresponding to
      * the coupling between the edge and attached faces
      * (\f$\mathbf{S}_{ef}\f$).
      */
  
     NekDouble EdgeFaceValue, FaceFaceValue;
     int efCol, efRow, nedgemodes;
  
     // Number of attached faces is always 2
     nConnectedFaces = 2;
  
     // Location in the matrix
     MatEdgeLocation = Array<OneD, Array<OneD, unsigned int>>(nEdges);
     MatFaceLocation = Array<OneD, Array<OneD, unsigned int>>(nConnectedFaces);
  
     // Build the edge/face transform matrix: This matrix is constructed
     // from the submatrices corresponding to the couping between a
     // specific edge and the two attached faces.
     for (eid = 0; eid < nEdges; ++eid)
     {
         // Row and column size of the vertex-edge/face matrix
         efCol = GetTraceIntNcoeffs(geom->GetEdgeFaceMap(eid, 0)) +
                 GetTraceIntNcoeffs(geom->GetEdgeFaceMap(eid, 1));
         efRow = GetEdgeNcoeffs(eid) - 2;
  
         // Edge-face coupling matrix
         DNekMatSharedPtr efedgefacecoupling =
             MemoryManager<DNekMat>::AllocateSharedPtr(efRow, efCol, 0.0,
                                                       storage);
         DNekMat &Mef = (*efedgefacecoupling);
  
         // Face-face coupling matrix
         DNekMatSharedPtr effacefacecoupling =
             MemoryManager<DNekMat>::AllocateSharedPtr(efCol, efCol, 0.0,
                                                       storage);
         DNekMat &Meff = (*effacefacecoupling);
  
         // Edge-face transformation matrix
         DNekMatSharedPtr edgefacetransformmatrix =
             MemoryManager<DNekMat>::AllocateSharedPtr(efRow, efCol, 0.0,
                                                       storage);
         DNekMat &Meft = (*edgefacetransformmatrix);
  
         int nfacemodesconnected =
             GetTraceIntNcoeffs(geom->GetEdgeFaceMap(eid, 0)) +
             GetTraceIntNcoeffs(geom->GetEdgeFaceMap(eid, 1));
         Array<OneD, unsigned int> facemodearray(nfacemodesconnected);
  
         // Create array of edge modes
         Array<OneD, unsigned int> inedgearray = GetEdgeInverseBoundaryMap(eid);
         nedgemodes                            = GetEdgeNcoeffs(eid) - 2;
         Array<OneD, unsigned int> edgemodearray(nedgemodes);
  
         if (nedgemodes)
         {
             Vmath::Vcopy(nedgemodes, &inedgearray[0], 1, &edgemodearray[0], 1);
         }
  
         int offset = 0;
  
         // Create array of face modes
         for (fid = 0; fid < nConnectedFaces; ++fid)
         {
             MatFaceLocation[fid] =
                 GetTraceInverseBoundaryMap(geom->GetEdgeFaceMap(eid, fid));
             nmodes = MatFaceLocation[fid].size();
  
             if (nmodes)
             {
                 Vmath::Vcopy(nmodes, &MatFaceLocation[fid][0], 1,
                              &facemodearray[offset], 1);
             }
             offset += nmodes;
         }
  
         // Edge-face coupling
         for (n = 0; n < nedgemodes; ++n)
         {
             for (m = 0; m < nfacemodesconnected; ++m)
             {
                 // Matrix value for each coefficient location
                 EdgeFaceValue = (*r_bnd)(edgemodearray[n], facemodearray[m]);
  
                 // Set the value in the edge/face matrix
                 Mef.SetValue(n, m, EdgeFaceValue);
             }
         }
  
         // Face-face coupling
         for (n = 0; n < nfacemodesconnected; ++n)
         {
             for (m = 0; m < nfacemodesconnected; ++m)
             {
                 // Matrix value for each coefficient location
                 FaceFaceValue = (*r_bnd)(facemodearray[n], facemodearray[m]);
  
                 // Set the value in the vertex edge/face matrix
                 Meff.SetValue(n, m, FaceFaceValue);
             }
         }
  
         if (efCol)
         {
             // Invert edge-face coupling matrix
             Meff.Invert();
  
             // trans(R_{ef})=-S_{ef}*(inv(S_{ff})
             Meft = -Mef * Meff;
         }
  
         // Populate transformation matrix with Meft
         for (n = 0; n < Meft.GetRows(); ++n)
         {
             for (m = 0; m < Meft.GetColumns(); ++m)
             {
                 R.SetValue(edgemodearray[n], facemodearray[m], Meft(n, m));
             }
         }
     }
  
     for (i = 0; i < R.GetRows(); ++i)
     {
         R.SetValue(i, i, 1.0);
     }
  
     if ((matrixType == StdRegions::ePreconR) ||
         (matrixType == StdRegions::ePreconRMass))
     {
         return transformationmatrix;
     }
     else
     {
         NEKERROR(ErrorUtil::efatal, "unkown matrix type");
         return NullDNekMatSharedPtr;
     }
 }

References Nektar::eFULL, Nektar::StdRegions::ePreconR, Nektar::StdRegions::ePreconRMass, NEKERROR, Nektar::NullDNekMatSharedPtr, and Vmath::Vcopy().

◆ v_BuildVertexMatrix()

DNekMatSharedPtr Nektar::LocalRegions::Expansion3D::v_BuildVertexMatrix ( const DNekScalMatSharedPtr & r_bnd )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1820 of file Expansion3D.cpp.

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

References Nektar::eFULL.

◆ v_DGDeriv()

void Nektar::LocalRegions::Expansion3D::v_DGDeriv	(	const int	dir,
		const Array< OneD, const NekDouble > &	incoeffs,
		Array< OneD, ExpansionSharedPtr > &	FaceExp,
		Array< OneD, Array< OneD, NekDouble >> &	faceCoeffs,
		Array< OneD, NekDouble > &	out_d
	)

overrideprotectedvirtual

Evaluate coefficients of weak deriviative in the direction dir given the input coefficicents incoeffs and the imposed boundary values in EdgeExp (which will have its phys space updated).

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1637 of file Expansion3D.cpp.

 {
     int ncoeffs                         = GetNcoeffs();
     StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                            StdRegions::eWeakDeriv1,
                                            StdRegions::eWeakDeriv2};
  
     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, FaceExp, faceCoeffs, coeffs);
  
     DNekVec Out_d(ncoeffs, out_d, eWrapper);
  
     Out_d = InvMass * Coeffs;
 }

References Nektar::StdRegions::eInvMass, Nektar::StdRegions::eWeakDeriv0, Nektar::StdRegions::eWeakDeriv1, Nektar::StdRegions::eWeakDeriv2, Nektar::eWrapper, Vmath::Neg(), and Nektar::Transpose().

◆ v_GenMatrix()

DNekMatSharedPtr Nektar::LocalRegions::Expansion3D::v_GenMatrix ( const StdRegions::StdMatrixKey & mkey )

overrideprotectedvirtual

Computes matrices needed for the HDG formulation. References to equations relate to the following paper (with a suitable changes in formulation to adapt to 3D): 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 NOTE: VARIABLE COEFFICIENTS CASE IS NOT IMPLEMENTED

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::PrismExp, and Nektar::LocalRegions::HexExp.

Definition at line 739 of file Expansion3D.cpp.

 {
     // Variable coefficients are not implemented/////////
     ASSERTL1(!mkey.HasVarCoeff(StdRegions::eVarCoeffD00),
              "Matrix construction is not implemented for variable "
              "coefficients at the moment");
     ////////////////////////////////////////////////////
  
     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 nfaces    = GetNtraces();
  
             Array<OneD, unsigned int> fmap;
             Array<OneD, int> sign;
             ExpansionSharedPtr FaceExp;
             ExpansionSharedPtr FaceExp2;
  
             int order_f, coordim = GetCoordim();
             DNekScalMat &invMass = *GetLocMatrix(StdRegions::eInvMass);
             StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                                    StdRegions::eWeakDeriv1,
                                                    StdRegions::eWeakDeriv2};
  
             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;
             const StdRegions::VarCoeffMap &varcoeffs = mkey.GetVarCoeffs();
  
             for (i = 0; i < coordim; ++i)
             {
                 if ((x = varcoeffs.find(StdRegions::eVarCoeffMF1x)) !=
                     varcoeffs.end())
                 {
                     StdRegions::VarCoeffMap VarCoeffDirDeriv;
                     VarCoeffDirDeriv[StdRegions::eVarCoeffMF] =
                         GetMF(i, coordim, 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
                 {
                     DNekScalMat &Dmat = *GetLocMatrix(DerivType[i]);
                     Mat               = Mat + Dmat * invMass * Transpose(Dmat);
                 }
  
                 /*
                 if(mkey.HasVarCoeff(Coeffs[i]))
                 {
                     MatrixKey DmatkeyL(DerivType[i], DetExpansionType(), *this,
                                        StdRegions::NullConstFactorMap,
                                        mkey.GetVarCoeffAsMap(Coeffs[i]));
                     MatrixKey DmatkeyR(DerivType[i], DetExpansionType(), *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 < nfaces; ++i)
             {
                 FaceExp = GetTraceExp(i);
                 order_f = FaceExp->GetNcoeffs();
  
                 IndexMapKey ikey(eFaceToElement, DetShapeType(),
                                  GetBasisNumModes(0), GetBasisNumModes(1),
                                  GetBasisNumModes(2), i, GetTraceOrient(i));
                 IndexMapValuesSharedPtr map = GetIndexMap(ikey);
  
                 // @TODO: Document
                 /*
                 StdRegions::VarCoeffMap edgeVarCoeffs;
                 if (mkey.HasVarCoeff(StdRegions::eVarCoeffD00))
                 {
                     Array<OneD, NekDouble> mu(nq);
                     GetPhysEdgeVarCoeffsFromElement(
                         i, EdgeExp2,
                         mkey.GetVarCoeff(StdRegions::eVarCoeffD00), mu);
                     edgeVarCoeffs[StdRegions::eVarCoeffMass] = mu;
                 }
                 DNekScalMat &eMass = *EdgeExp->GetLocMatrix(
                     StdRegions::eMass,
                     StdRegions::NullConstFactorMap, edgeVarCoeffs);
                 */
  
                 DNekScalMat &eMass = *FaceExp->GetLocMatrix(StdRegions::eMass);
  
                 for (j = 0; j < order_f; ++j)
                 {
                     for (k = 0; k < order_f; ++k)
                     {
                         Mat((*map)[j].index, (*map)[k].index) +=
                             tau * (*map)[j].sign * (*map)[k].sign * eMass(j, k);
                     }
                 }
             }
             break;
         }
  
         // U^e (P22)
         case StdRegions::eHybridDGLamToU:
         {
             int i, j, k;
             int nbndry    = NumDGBndryCoeffs();
             int ncoeffs   = GetNcoeffs();
             int nfaces    = 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);
  
             ExpansionSharedPtr FaceExp;
             // 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> fmap;
             Array<OneD, int> sign;
  
             // alternative way to add boundary terms contribution
             int bndry_cnt = 0;
             for (i = 0; i < nfaces; ++i)
             {
                 FaceExp = GetTraceExp(
                     i); // temporary, need to rewrite AddHDGHelmholtzFaceTerms
                 int nface = GetTraceNcoeffs(i);
                 Array<OneD, NekDouble> face_lambda(nface);
  
                 const Array<OneD, const Array<OneD, NekDouble>> normals =
                     GetTraceNormal(i);
  
                 for (j = 0; j < nface; ++j)
                 {
                     Vmath::Zero(nface, &face_lambda[0], 1);
                     Vmath::Zero(ncoeffs, &f[0], 1);
                     face_lambda[j] = 1.0;
  
                     SetFaceToGeomOrientation(i, face_lambda);
  
                     Array<OneD, NekDouble> tmp(FaceExp->GetTotPoints());
                     FaceExp->BwdTrans(face_lambda, tmp);
                     AddHDGHelmholtzFaceTerms(tau, i, tmp, mkey.GetVarCoeffs(),
                                              f);
  
                     Ulam = invHmat * F; // generate Ulam from lambda
  
                     // fill column of matrix
                     for (k = 0; k < ncoeffs; ++k)
                     {
                         Umat(k, bndry_cnt) = Ulam[k];
                     }
  
                     ++bndry_cnt;
                 }
             }
  
             //// Set up face expansions from local geom info
             // for(i = 0; i < nfaces; ++i)
             //{
             //    FaceExp[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;
             //
             //  //cout << Lambda;
             //    SetTraceToGeomOrientation(lambda);
             //  //cout << Lambda << endl;
             //
             //    // Compute F = [I   D_1 M^{-1}   D_2 M^{-1}] C e_j
             //    AddHDGHelmholtzTraceTerms(tau, lambda, FaceExp,
             //    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 coordim = GetCoordim();
             int ncoeffs = GetNcoeffs();
             int nfaces  = GetNtraces();
  
             Array<OneD, NekDouble> lambda(nbndry);
             DNekVec Lambda(nbndry, lambda, eWrapper);
             Array<OneD, ExpansionSharedPtr> FaceExp(nfaces);
  
             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 < nfaces; ++i)
             {
                 FaceExp[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;
             }
  
             // DNekScalMatSharedPtr Dmat;
             // DNekScalMatSharedPtr &invMass;
             StdRegions::VarCoeffMap::const_iterator x;
             const StdRegions::VarCoeffMap &varcoeffs = mkey.GetVarCoeffs();
             if ((x = varcoeffs.find(StdRegions::eVarCoeffMF1x)) !=
                 varcoeffs.end())
             {
                 StdRegions::VarCoeffMap VarCoeffDirDeriv;
                 VarCoeffDirDeriv[StdRegions::eVarCoeffMF] =
                     GetMF(dir, coordim, 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
             {
                 // Inverse mass matrix
                 invMass = *GetLocMatrix(StdRegions::eInvMass);
             }
  
             // 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(lambda);
  
                 // Add the C terms resulting from the I's on the
                 // diagonals of Eqn 32
                 AddNormTraceInt(dir, lambda, FaceExp, 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, f, cnt;
             int order_f, nquad_f;
             int nbndry    = NumDGBndryCoeffs();
             int nfaces    = GetNtraces();
             NekDouble tau = mkey.GetConstFactor(StdRegions::eFactorTau);
  
             Array<OneD, NekDouble> work, varcoeff_work;
             Array<OneD, const Array<OneD, NekDouble>> normals;
             Array<OneD, ExpansionSharedPtr> FaceExp(nfaces);
             Array<OneD, NekDouble> lam(nbndry);
  
             Array<OneD, unsigned int> fmap;
             Array<OneD, int> sign;
  
             // 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
             MatrixKey LamToQ2key(StdRegions::eHybridDGLamToQ2, DetShapeType(),
                                  *this, mkey.GetConstFactors(),
                                  mkey.GetVarCoeffs());
             LamToQ[2] = GetLocMatrix(LamToQ2key);
  
             // Set up edge segment expansions from local geom info
             const StdRegions::VarCoeffMap &varcoeffs = mkey.GetVarCoeffs();
             for (i = 0; i < nfaces; ++i)
             {
                 FaceExp[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(lam);
  
                 for (f = 0; f < nfaces; ++f)
                 {
                     order_f = FaceExp[f]->GetNcoeffs();
                     nquad_f = FaceExp[f]->GetNumPoints(0) *
                               FaceExp[f]->GetNumPoints(1);
                     normals = GetTraceNormal(f);
  
                     work          = Array<OneD, NekDouble>(nquad_f);
                     varcoeff_work = Array<OneD, NekDouble>(nquad_f);
  
                     IndexMapKey ikey(eFaceToElement, DetShapeType(),
                                      GetBasisNumModes(0), GetBasisNumModes(1),
                                      GetBasisNumModes(2), f, GetTraceOrient(f));
                     IndexMapValuesSharedPtr map = GetIndexMap(ikey);
  
                     // @TODO Variable coefficients
                     /*
                     StdRegions::VarCoeffType VarCoeff[3] =
                     {StdRegions::eVarCoeffD00, StdRegions::eVarCoeffD11,
                                                             StdRegions::eVarCoeffD22};
                     const StdRegions::VarCoeffMap &varcoeffs =
                     mkey.GetVarCoeffs(); StdRegions::VarCoeffMap::const_iterator
                     x;
                     */
  
                     // Q0 * n0 (BQ_0 terms)
                     Array<OneD, NekDouble> faceCoeffs(order_f);
                     Array<OneD, NekDouble> facePhys(nquad_f);
                     for (j = 0; j < order_f; ++j)
                     {
                         faceCoeffs[j] =
                             (*map)[j].sign * (*LamToQ[0])((*map)[j].index, i);
                     }
  
                     FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
  
                     // @TODO Variable coefficients
                     // 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 (varcoeffs.find(StdRegions::eVarCoeffMF1x) !=
                         varcoeffs.end())
                     {
                         Array<OneD, NekDouble> ncdotMF = GetnFacecdotMF(
                             0, f, FaceExp[f], normals, varcoeffs);
  
                         Vmath::Vmul(nquad_f, ncdotMF, 1, facePhys, 1, work, 1);
                     }
                     else
                     {
                         Vmath::Vmul(nquad_f, normals[0], 1, facePhys, 1, work,
                                     1);
                     }
  
                     // Q1 * n1 (BQ_1 terms)
                     for (j = 0; j < order_f; ++j)
                     {
                         faceCoeffs[j] =
                             (*map)[j].sign * (*LamToQ[1])((*map)[j].index, i);
                     }
  
                     FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
  
                     // @TODO Variable coefficients
                     // 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 ((varcoeffs.find(StdRegions::eVarCoeffMF1x)) !=
                         varcoeffs.end())
                     {
                         Array<OneD, NekDouble> ncdotMF = GetnFacecdotMF(
                             1, f, FaceExp[f], normals, varcoeffs);
  
                         Vmath::Vvtvp(nquad_f, ncdotMF, 1, facePhys, 1, work, 1,
                                      work, 1);
                     }
                     else
                     {
                         Vmath::Vvtvp(nquad_f, normals[1], 1, facePhys, 1, work,
                                      1, work, 1);
                     }
  
                     // Q2 * n2 (BQ_2 terms)
                     for (j = 0; j < order_f; ++j)
                     {
                         faceCoeffs[j] =
                             (*map)[j].sign * (*LamToQ[2])((*map)[j].index, i);
                     }
  
                     FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
  
                     // @TODO Variable coefficients
                     // 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);
                     }
                     */
  
                     if (varcoeffs.find(StdRegions::eVarCoeffMF1x) !=
                         varcoeffs.end())
                     {
                         Array<OneD, NekDouble> ncdotMF = GetnFacecdotMF(
                             2, f, FaceExp[f], normals, varcoeffs);
  
                         Vmath::Vvtvp(nquad_f, ncdotMF, 1, facePhys, 1, work, 1,
                                      work, 1);
                     }
                     else
                     {
                         Vmath::Vvtvp(nquad_f, normals[2], 1, facePhys, 1, work,
                                      1, work, 1);
                     }
  
                     // - tau (ulam - lam)
                     // Corresponds to the G and BU terms.
                     for (j = 0; j < order_f; ++j)
                     {
                         faceCoeffs[j] =
                             (*map)[j].sign * LamToU((*map)[j].index, i) -
                             lam[cnt + j];
                     }
  
                     FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
  
                     // @TODO Variable coefficients
                     // Multiply by variable coefficients
                     /*
                     if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
                     {
                         GetPhysEdgeVarCoeffsFromElement(e,FaceExp[f],x->second,varcoeff_work);
                         Vmath::Vmul(nquad_f,varcoeff_work,1,FaceExp[f]->GetPhys(),1,FaceExp[f]->UpdatePhys(),1);
                     }
                     */
  
                     Vmath::Svtvp(nquad_f, -tau, facePhys, 1, work, 1, work, 1);
  
                     // @TODO Add variable coefficients
                     FaceExp[f]->IProductWRTBase(work, faceCoeffs);
  
                     SetFaceToGeomOrientation(f, faceCoeffs);
  
                     for (j = 0; j < order_f; ++j)
                     {
                         BndMat(cnt + j, i) = faceCoeffs[j];
                     }
  
                     cnt += order_f;
                 }
             }
         }
         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 fromkey0 = GetTraceBasisKey(t, 0);
                     LibUtilities::BasisKey fromkey1 = GetTraceBasisKey(t, 1);
                     LibUtilities::BasisKey tokey0 =
                         traceExp[t]->GetBasis(0)->GetBasisKey();
                     LibUtilities::BasisKey tokey1 =
                         traceExp[t]->GetBasis(1)->GetBasisKey();
                     bool DoInterp =
                         (fromkey0 != tokey0) || (fromkey1 != tokey1);
  
                     // for variable p need add check and
                     // interpolation here.
  
                     Array<OneD, NekDouble> n(tracepts[t]);
                     ;
                     for (int d = 0; d < ncoords; ++d)
                     {
                         // if variable p may need to interpolate
                         if (DoInterp)
                         {
                             LibUtilities::Interp2D(fromkey0, fromkey1, norm[d],
                                                    tokey0, tokey1, 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 Nektar::LocalRegions::HexExp::v_GenMatrix(), Nektar::LocalRegions::PrismExp::v_GenMatrix(), Nektar::LocalRegions::PyrExp::v_GenMatrix(), and Nektar::LocalRegions::TetExp::v_GenMatrix().

◆ v_GenTraceExp()

void Nektar::LocalRegions::Expansion3D::v_GenTraceExp	(	const int	traceid,
		ExpansionSharedPtr &	exp
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2643 of file Expansion3D.cpp.

 {
     SpatialDomains::GeometrySharedPtr faceGeom = m_geom->GetFace(traceid);
     if (faceGeom->GetNumVerts() == 3)
     {
         exp = MemoryManager<LocalRegions::TriExp>::AllocateSharedPtr(
             GetTraceBasisKey(traceid, 0), GetTraceBasisKey(traceid, 1),
             m_geom->GetFace(traceid));
     }
     else
     {
         exp = MemoryManager<LocalRegions::QuadExp>::AllocateSharedPtr(
             GetTraceBasisKey(traceid, 0), GetTraceBasisKey(traceid, 1),
             m_geom->GetFace(traceid));
     }
 }

◆ v_GetTraceOrient()

StdRegions::Orientation Nektar::LocalRegions::Expansion3D::v_GetTraceOrient ( int face )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2581 of file Expansion3D.cpp.

 {
     return m_geom->GetForient(face);
 }

◆ v_GetTracePhysVals()

void Nektar::LocalRegions::Expansion3D::v_GetTracePhysVals	(	const int	face,
		const StdRegions::StdExpansionSharedPtr &	FaceExp,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		StdRegions::Orientation	orient
	)

overrideprotectedvirtual

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

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2591 of file Expansion3D.cpp.

 {
     if (orient == StdRegions::eNoOrientation)
     {
         orient = GetTraceOrient(face);
     }
  
     int nq0 = FaceExp->GetNumPoints(0);
     int nq1 = FaceExp->GetNumPoints(1);
  
     int nfacepts = GetTraceNumPoints(face);
     int dir0     = GetGeom3D()->GetDir(face, 0);
     int dir1     = GetGeom3D()->GetDir(face, 1);
  
     Array<OneD, NekDouble> o_tmp(nfacepts);
     Array<OneD, NekDouble> o_tmp2(FaceExp->GetTotPoints());
     Array<OneD, int> faceids;
  
     // Get local face pts and put into o_tmp
     GetTracePhysMap(face, faceids);
     // The static cast is necessary because faceids should be
     // Array<OneD, size_t> faceids ... or at leaste the same type as
     // faceids.size() ...
     Vmath::Gathr(static_cast<int>(faceids.size()), inarray, faceids, o_tmp);
  
     int to_id0, to_id1;
  
     if (orient < StdRegions::eDir1FwdDir2_Dir2FwdDir1)
     {
         to_id0 = 0;
         to_id1 = 1;
     }
     else // transpose points key evaluation
     {
         to_id0 = 1;
         to_id1 = 0;
     }
  
     // interpolate to points distrbution given in FaceExp
     LibUtilities::Interp2D(
         m_base[dir0]->GetPointsKey(), m_base[dir1]->GetPointsKey(), o_tmp.get(),
         FaceExp->GetBasis(to_id0)->GetPointsKey(),
         FaceExp->GetBasis(to_id1)->GetPointsKey(), o_tmp2.get());
  
     // Reshuffule points as required and put into outarray.
     v_ReOrientTracePhysMap(orient, faceids, nq0, nq1);
     Vmath::Scatr(nq0 * nq1, o_tmp2, faceids, outarray);
 }

References Nektar::StdRegions::eDir1FwdDir2_Dir2FwdDir1, Nektar::StdRegions::eNoOrientation, Vmath::Gathr(), Nektar::LibUtilities::Interp2D(), and Vmath::Scatr().

◆ v_NormVectorIProductWRTBase()

void Nektar::LocalRegions::Expansion3D::v_NormVectorIProductWRTBase	(	const Array< OneD, const Array< OneD, NekDouble >> &	Fvec,
		Array< OneD, NekDouble > &	outarray
	)

overridevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 2798 of file Expansion3D.cpp.

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

◆ v_ReOrientTracePhysMap()

void Nektar::LocalRegions::Expansion3D::v_ReOrientTracePhysMap	(	const StdRegions::Orientation	orient,
		Array< OneD, int > &	idmap,
		const int	nq0,
		const int	nq1
	)

overridevirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2660 of file Expansion3D.cpp.

 {
  
     if (idmap.size() != nq0 * nq1)
     {
         idmap = Array<OneD, int>(nq0 * nq1);
     }
  
     if (GetNverts() == 3) // Tri face
     {
         switch (orient)
         {
             case StdRegions::eDir1FwdDir1_Dir2FwdDir2:
                 // eseentially straight copy
                 for (int i = 0; i < nq0 * nq1; ++i)
                 {
                     idmap[i] = i;
                 }
                 break;
             case StdRegions::eDir1BwdDir1_Dir2FwdDir2:
                 // reverse
                 for (int j = 0; j < nq1; ++j)
                 {
                     for (int i = 0; i < nq0; ++i)
                     {
                         idmap[j * nq0 + i] = nq0 - 1 - i + j * nq0;
                     }
                 }
                 break;
             default:
                 ASSERTL0(false,
                          "Case not supposed to be used in this function");
         }
     }
     else
     {
         switch (orient)
         {
             case StdRegions::eDir1FwdDir1_Dir2FwdDir2:
                 // eseentially straight copy
                 for (int i = 0; i < nq0 * nq1; ++i)
                 {
                     idmap[i] = i;
                 }
                 break;
             case StdRegions::eDir1BwdDir1_Dir2FwdDir2:
             {
                 // Direction A negative and B positive
                 for (int j = 0; j < nq1; j++)
                 {
                     for (int i = 0; i < nq0; ++i)
                     {
                         idmap[j * nq0 + i] = nq0 - 1 - i + j * nq0;
                     }
                 }
             }
             break;
             case StdRegions::eDir1FwdDir1_Dir2BwdDir2:
             {
                 // Direction A positive and B negative
                 for (int j = 0; j < nq1; j++)
                 {
                     for (int i = 0; i < nq0; ++i)
                     {
                         idmap[j * nq0 + i] = nq0 * (nq1 - 1 - j) + i;
                     }
                 }
             }
             break;
             case StdRegions::eDir1BwdDir1_Dir2BwdDir2:
             {
                 // Direction A negative and B negative
                 for (int j = 0; j < nq1; j++)
                 {
                     for (int i = 0; i < nq0; ++i)
                     {
                         idmap[j * nq0 + i] = nq0 * nq1 - 1 - j * nq0 - i;
                     }
                 }
             }
             break;
             case StdRegions::eDir1FwdDir2_Dir2FwdDir1:
             {
                 // Transposed, Direction A and B positive
                 for (int i = 0; i < nq0; ++i)
                 {
                     for (int j = 0; j < nq1; ++j)
                     {
                         idmap[i * nq1 + j] = i + j * nq0;
                     }
                 }
             }
             break;
             case StdRegions::eDir1FwdDir2_Dir2BwdDir1:
             {
                 // Transposed, Direction A positive and B negative
                 for (int i = 0; i < nq0; ++i)
                 {
                     for (int j = 0; j < nq1; ++j)
                     {
                         idmap[i * nq1 + j] = nq0 - 1 - i + j * nq0;
                     }
                 }
             }
             break;
             case StdRegions::eDir1BwdDir2_Dir2FwdDir1:
             {
                 // Transposed, Direction A negative and B positive
                 for (int i = 0; i < nq0; ++i)
                 {
                     for (int j = 0; j < nq1; ++j)
                     {
                         idmap[i * nq1 + j] = i + nq0 * (nq1 - 1) - j * nq0;
                     }
                 }
             }
             break;
             case StdRegions::eDir1BwdDir2_Dir2BwdDir1:
             {
                 // Transposed, Direction A and B negative
                 for (int i = 0; i < nq0; ++i)
                 {
                     for (int j = 0; j < nq1; ++j)
                     {
                         idmap[i * nq1 + j] = nq0 * nq1 - 1 - i - j * nq0;
                     }
                 }
             }
             break;
             default:
                 ASSERTL0(false, "Unknow orientation");
                 break;
         }
     }
 }

References ASSERTL0, Nektar::StdRegions::eDir1BwdDir1_Dir2BwdDir2, Nektar::StdRegions::eDir1BwdDir1_Dir2FwdDir2, Nektar::StdRegions::eDir1BwdDir2_Dir2BwdDir1, Nektar::StdRegions::eDir1BwdDir2_Dir2FwdDir1, Nektar::StdRegions::eDir1FwdDir1_Dir2BwdDir2, Nektar::StdRegions::eDir1FwdDir1_Dir2FwdDir2, Nektar::StdRegions::eDir1FwdDir2_Dir2BwdDir1, and Nektar::StdRegions::eDir1FwdDir2_Dir2FwdDir1.

◆ v_TraceNormLen()

void Nektar::LocalRegions::Expansion3D::v_TraceNormLen	(	const int	traceid,
		NekDouble &	h,
		NekDouble &	p
	)

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 2848 of file Expansion3D.cpp.

 {
     SpatialDomains::GeometrySharedPtr geom = GetGeom();
  
     int nverts = geom->GetFace(traceid)->GetNumVerts();
  
     SpatialDomains::PointGeom tn1, tn2, normal;
     tn1.Sub(*(geom->GetFace(traceid)->GetVertex(1)),
             *(geom->GetFace(traceid)->GetVertex(0)));
  
     tn2.Sub(*(geom->GetFace(traceid)->GetVertex(nverts - 1)),
             *(geom->GetFace(traceid)->GetVertex(0)));
  
     normal.Mult(tn1, tn2);
  
     // normalise normal
     NekDouble mag = normal.dot(normal);
     mag           = 1.0 / sqrt(mag);
     normal.UpdatePosition(normal.x() * mag, normal.y() * mag, normal.z() * mag);
  
     SpatialDomains::PointGeom Dx;
     h = 0.0;
     p = 0.0;
     for (int i = 0; i < nverts; ++i)
     {
         // vertices on edges
         int edgid = geom->GetEdgeNormalToFaceVert(traceid, i);
  
         // vector along noramal edge to each vertex
         Dx.Sub(*(geom->GetEdge(edgid)->GetVertex(0)),
                *(geom->GetEdge(edgid)->GetVertex(1)));
  
         // calculate perpendicular distance of normal length
         // from first vertex
         h += fabs(normal.dot(Dx));
     }
  
     h /= static_cast<NekDouble>(nverts);
  
     // find normal basis direction
     int dir0 = geom->GetDir(traceid, 0);
     int dir1 = geom->GetDir(traceid, 1);
     int dirn;
     for (dirn = 0; dirn < 3; ++dirn)
     {
         if ((dirn != dir0) && (dirn != dir1))
         {
             break;
         }
     }
     p = (NekDouble)(GetBasisNumModes(dirn) - 1);
 }

References Nektar::SpatialDomains::PointGeom::dot(), Nektar::SpatialDomains::PointGeom::Mult(), CellMLToNektar.cellml_metadata::p, tinysimd::sqrt(), Nektar::SpatialDomains::PointGeom::Sub(), Nektar::SpatialDomains::PointGeom::UpdatePosition(), Nektar::NekPoint< data_type >::x(), Nektar::NekPoint< data_type >::y(), and Nektar::NekPoint< data_type >::z().

Member Data Documentation

◆ m_faceNormals

std::map<int, NormalVector> Nektar::LocalRegions::Expansion3D::m_faceNormals

protected

Definition at line 119 of file Expansion3D.h.

◆ m_requireNeg

std::vector<bool> Nektar::LocalRegions::Expansion3D::m_requireNeg

private

Definition at line 174 of file Expansion3D.h.

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Expansion3D()

◆ ~Expansion3D()

Member Function Documentation

◆ AddFaceBoundaryInt()

◆ AddHDGHelmholtzFaceTerms()

◆ AddNormTraceInt() [1/2]

◆ AddNormTraceInt() [2/2]

◆ CreateMatrix()

◆ GetEdgeInverseBoundaryMap()

◆ GetGeom3D()

◆ GetInverseBoundaryMaps()

◆ GetnFacecdotMF()

◆ GetPhysFaceVarCoeffsFromElement()

◆ GetTraceInverseBoundaryMap()

◆ SetFaceToGeomOrientation()

◆ SetTraceToGeomOrientation()

◆ v_AddFaceNormBoundaryInt()

◆ v_AddRobinMassMatrix()

◆ v_BuildInverseTransformationMatrix()

◆ v_BuildTransformationMatrix()

◆ v_BuildVertexMatrix()

◆ v_DGDeriv()

◆ v_GenMatrix()

◆ v_GenTraceExp()

◆ v_GetTraceOrient()

◆ v_GetTracePhysVals()

◆ v_NormVectorIProductWRTBase()

◆ v_ReOrientTracePhysMap()

◆ v_TraceNormLen()

Member Data Documentation

◆ m_faceNormals

◆ m_requireNeg