Nektar::LocalRegions::QuadExp Class Reference

#include <QuadExp.h>

Inheritance diagram for Nektar::LocalRegions::QuadExp:

Public Member Functions
	QuadExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, SpatialDomains::Geometry2D *geom)
	Constructor using BasisKey class for quadrature points and order definition.
	QuadExp (const QuadExp &T)
	~QuadExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdQuadExp
	StdQuadExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)
	Constructor using BasisKey class for quadrature points and order definition.
	StdQuadExp (const StdQuadExp &T)=default
	~StdQuadExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdExpansion2D
	StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)
	StdExpansion2D ()=default
	StdExpansion2D (const StdExpansion2D &T)=default
	~StdExpansion2D () override=default
NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
void	IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, NekDouble > &jac, const bool Deformed, bool CollDir0=false, bool CollDir1=false)
Public Member Functions inherited from Nektar::StdRegions::StdExpansion
	StdExpansion ()
	Default Constructor.
	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.
	StdExpansion (const StdExpansion &T)
	Copy Constructor.
virtual	~StdExpansion ()
	Destructor.
int	GetNumBases () const
	This function returns the number of 1D bases used in the expansion.
const Array< OneD, const LibUtilities::BasisSharedPtr > &	GetBase () const
	This function gets the shared point to basis.
const LibUtilities::BasisSharedPtr &	GetBasis (int dir) const
	This function gets the shared point to basis in the dir direction.
int	GetNcoeffs (void) const
	This function returns the total number of coefficients used in the expansion.
int	GetTotPoints () const
	This function returns the total number of quadrature points used in the element.
LibUtilities::BasisType	GetBasisType (const int dir) const
	This function returns the type of basis used in the dir direction.
int	GetBasisNumModes (const int dir) const
	This function returns the number of expansion modes in the dir direction.
int	EvalBasisNumModesMax (void) const
	This function returns the maximum number of expansion modes over all local directions.
LibUtilities::PointsType	GetPointsType (const int dir) const
	This function returns the type of quadrature points used in the dir direction.
int	GetNumPoints (const int dir) const
	This function returns the number of quadrature points in the dir direction.
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.
int	GetNverts () const
	This function returns the number of vertices of the expansion domain.
int	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th trace.
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.
const LibUtilities::BasisKey	GetTraceBasisKey (const int i, int k=-1, bool UseGLL=false) const
	This function returns the basis key belonging to the i-th trace.
LibUtilities::PointsKey	GetTracePointsKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace.
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.
int	GetNtraces () const
	Returns the number of trace elements connected to this element.
LibUtilities::ShapeType	DetShapeType () const
	This function returns the shape of the expansion domain.
int	GetShapeDimension () const
bool	IsBoundaryInteriorExpansion () const
bool	IsNodalNonTensorialExp ()
void	NodalToModal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Backward transformation from coefficient space to physical space.
void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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.
void	FillMode (const int mode, Array< OneD, NekDouble > &outarray)
	This function fills the array outarray with the mode-th mode of the expansion.
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
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.
void	SetElmtId (const int id)
	Set the element id of this expansion when used in a list by returning value of m_elmt_id.
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
Array< OneD, Array< OneD, NekDouble > >	GetCoords ()
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
DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)
Array< OneD, const NekDouble >	GetStdFac (const StdFacKey &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 \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\)
void	GeneralMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)
void	ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)
void	LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)
void	PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void	PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	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)
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.
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.
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.
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.
void	ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1, bool Forwards=true)
void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta.
void	LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
	Convert local collapsed coordinates eta into local cartesian coordinate xi.
void	PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData, bool Transpose=false)
	interpolate from one set of quadrature points available from FromExp to the set of quadrature points in the current expansion. If the points are the same this routine will just copy the data
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)
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.
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.
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.
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.
void	PhysInterpToGLL (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
void	PhysInterpToPoints (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset, MatrixType distrib)
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.
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.
void	EquiSpacedToPhys (const int nequi, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
template<class T >
std::shared_ptr< T >	as ()
void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
Public Member Functions inherited from Nektar::LocalRegions::Expansion2D
	Expansion2D (SpatialDomains::Geometry2D *pGeom)
	~Expansion2D () override=default
DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)
void	SetTraceToGeomOrientation (Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &inout)
Array< OneD, unsigned int >	GetTraceInverseBoundaryMap (int eid)
void	AddNormTraceInt (const int dir, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &edgeCoeffs, Array< OneD, NekDouble > &outarray)
void	AddNormTraceInt (const int dir, Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs)
void	AddEdgeBoundaryInt (const int edge, ExpansionSharedPtr &EdgeExp, Array< OneD, NekDouble > &edgePhys, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)
void	AddHDGHelmholtzEdgeTerms (const NekDouble tau, const int edge, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &edgePhys, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray)
void	AddHDGHelmholtzTraceTerms (const NekDouble tau, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray)
SpatialDomains::Geometry2D *	GetGeom2D () const
void	ReOrientEdgePhysMap (const int nvert, const StdRegions::Orientation orient, const int nq0, Array< OneD, int > &idmap)
void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors) override
	: This method gets all of the factors which are required as part of the Gradient Jump Penalty (GJP) stabilisation and involves the product of the normal and geometric factors along the element trace.
Public Member Functions inherited from Nektar::LocalRegions::Expansion
	Expansion (SpatialDomains::Geometry *pGeom)
	Expansion (const Expansion &pSrc)
	~Expansion () override
void	SetTraceExp (const int traceid, ExpansionSharedPtr &f)
ExpansionSharedPtr	GetTraceExp (const int traceid)
ExpansionSharedPtr	GetLocTraceExp (const int traceid)
StdRegions::StdExpansionSharedPtr	GetStdExp () const
StdRegions::StdExpansionSharedPtr	GetLinStdExp (void) const
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::Geometry *	GetGeom () const
void	Reset ()
IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)
DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)
SpatialDomains::GeomFactors *	GetGeomFactors () const
	Get the geometric factors for this object, generating them if required.
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.
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).
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	GetLocTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GetTracePhysMap (const int edge, Array< OneD, int > &outarray)
void	ReOrientTracePhysVals (const StdRegions::Orientation orient, const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const int nq0, const int nq1, bool Forwards=true)
const NormalVector &	GetTraceNormal (const int id)
const std::map< int, NormalVector > &	GetTraceNormals (void)
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)
void	PhysDerivBaseOnTraceMat (const int traceid, Array< OneD, DNekMatSharedPtr > &DerivMat)
void	PhysBaseOnTraceMat (const int traceid, DNekMatSharedPtr &BdataMat)
void	GenGeomFactors ()
	Handles generation of geometry factors.

Protected Member Functions
void	v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray) override
void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray) override
void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray) override
StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const override
StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const override
void	v_GetCoord (const Array< OneD, const NekDouble > &Lcoords, Array< OneD, NekDouble > &coords) override
void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override
NekDouble	v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
void	v_GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) override
void	v_GetLocTracePhysVals (const int edge, const StdRegions::StdExpansionSharedPtr &EdgeExp, const NekDouble *inarray, Array< OneD, NekDouble > &outarray) override
void	v_GetTraceQFactors (const int edge, Array< OneD, NekDouble > &outarray) override
void	v_ComputeTraceNormal (const int edge) override
void	v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int mode_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType) override
StdRegions::Orientation	v_GetTraceOrient (int edge) override
void	v_GetTracePhysMap (const int edge, Array< OneD, int > &outarray) override
DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override
DNekMatSharedPtr	v_CreateStdMatrix (const StdRegions::StdMatrixKey &mkey) override
DNekScalMatSharedPtr	v_GetLocMatrix (const MatrixKey &mkey) override
void	v_DropLocMatrix (const MatrixKey &mkey) override
DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const MatrixKey &mkey) override
void	v_DropLocStaticCondMatrix (const MatrixKey &mkey) override
void	v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp) override
void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_ComputeLaplacianMetric () override
void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdRegions::StdMatrixKey &mkey) override
void	GetEdgeInterpVals (const int edge, const NekDouble *inarray, Array< OneD, NekDouble > &outarray)
Protected Member Functions inherited from Nektar::StdRegions::StdQuadExp
void	v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray) override
	Calculate the derivative of the physical points.
void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, NekDouble > &jac, const bool Deformed, const bool CollDir0=false, const bool CollDir1=false) override
	Inner product of inarray over region with respect to the expansion basis (this)->m_base[0] and return in outarray.
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta) override
void	v_LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi) override
void	v_FillMode (const int mode, Array< OneD, NekDouble > &array) override
	Fill outarray with mode mode of expansion.
int	v_GetNverts () const final
int	v_GetNtraces () const final
int	v_GetTraceNcoeffs (const int i) const final
int	v_GetTraceIntNcoeffs (const int i) const final
int	v_GetTraceNumPoints (const int i) const final
int	v_NumBndryCoeffs () const final
int	v_NumDGBndryCoeffs () const final
int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset) override
const LibUtilities::BasisKey	v_GetTraceBasisKey (const int i, const int j, bool UseGLL=false) const final
LibUtilities::ShapeType	v_DetShapeType () const final
bool	v_IsBoundaryInteriorExpansion () const override
void	v_GetCoords (Array< OneD, NekDouble > &coords_0, Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2) override
NekDouble	v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) override
	This function evaluates the basis function mode mode at a point coords of the domain.
NekDouble	v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
void	v_GetBoundaryMap (Array< OneD, unsigned int > &outarray) override
void	v_GetInteriorMap (Array< OneD, unsigned int > &outarray) override
int	v_GetVertexMap (int localVertexId, bool useCoeffPacking=false) override
void	v_GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray) override
	Get the map of the coefficient location to teh local trace coefficients.
void	v_GetTraceInteriorToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation edgeOrient=eForwards) override
DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey) override
DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey) override
void	v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override
void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey) override
void	v_ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff) override
void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion2D
void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d0, Array< OneD, NekDouble > &outarray_d1)
	Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points.
void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the derivative of the physical points in a given direction.
NekDouble	v_StdPhysEvaluate (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.
NekDouble	v_PhysEvaluateInterp (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) override
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the inner product of inarray with respect to the basis B=base0*base1 and put into outarray.
void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_GetElmtTraceToTraceMap (const unsigned int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q) override
	Determine the mapping to re-orientate the coefficients along the element trace (assumed to align with the standard element) into the orientation of the local trace given by edgeOrient.
void	v_GetTraceToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient=eForwards, int P=-1, int Q=-1) override
void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat) override
void	v_PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData, bool Transpose) override
void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1, bool Forwards) override
int	v_GetShapeDimension () const final
bool	v_IsCollocatedBasis () const final
virtual void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2, Array< OneD, NekDouble > &out_d3)
	Calculate the derivative of the physical points.
virtual void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0)
	Calculate the derivative of the physical points in a given direction.
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr	CreateStdMatrix (const StdMatrixKey &mkey)
std::shared_ptr< Array< OneD, const NekDouble > >	CreateStdFac (const StdFacKey &mkey)
DNekBlkMatSharedPtr	CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
	Create the static condensation of a matrix when using a boundary interior decomposition.
void	GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
void	LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
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.
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.
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)
virtual LibUtilities::PointsKey	v_GetTracePointsKey (const int i, const int j) const
virtual const LibUtilities::PointsKey	v_GetNodalPointsKey () const
virtual bool	v_IsNodalNonTensorialExp ()
virtual void	v_NodalToModal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual NekDouble	v_PhysEvalFirstSecondDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)
virtual void	v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)
virtual void	v_GetVertexPhysVals (const int vertex, const Array< OneD, const NekDouble > &inarray, NekDouble &outarray)
virtual void	v_LinearAdvectionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void	v_LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
virtual DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
Protected Member Functions inherited from Nektar::LocalRegions::Expansion2D
void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the derivative of the physical points in a given direction.
void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray) override
	Calculate the derivative of the physical points.
void	v_PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &out) override
	Physical derivative along a direction vector.
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculates the inner product of a given function f with the different modes of the expansion.
void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &edgeCoeffs, Array< OneD, NekDouble > &out_d) override
void	v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp) override
void	v_AddEdgeNormBoundaryInt (const int edge, const ExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray) override
void	v_AddEdgeNormBoundaryInt (const int edge, const ExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) override
void	v_AddRobinMassMatrix (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) override
void	v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs) override
DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) override
void	v_ReOrientTracePhysVals (const StdRegions::Orientation orient, const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const int nq0, const int nq1, bool Forwards) override
void	v_SetUpPhysNormals (const int edge) override
NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec) override
void	v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) override
Protected Member Functions inherited from Nektar::LocalRegions::Expansion
void	ComputeLaplacianMetric ()
void	ComputeQuadratureMetric ()
void	ComputeGmatcdotMF (const Array< TwoD, const NekDouble > &df, const Array< OneD, const NekDouble > &direction, Array< OneD, Array< OneD, NekDouble > > &dfdir)
Array< OneD, NekDouble >	GetMF (const int dir, const int shapedim, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	GetMFDiv (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	GetMFMag (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in (this)->m_coeffs.
NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coord, const Array< OneD, const NekDouble > &physvals) override
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)
int	v_GetCoordim () const override
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
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)
void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual const Array< OneD, const NekDouble > &	v_GetPhysNormals ()
virtual void	v_SetPhysNormals (Array< OneD, const NekDouble > &normal)

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

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

Additional Inherited Members
Protected Attributes inherited from Nektar::StdRegions::StdExpansion
Array< OneD, LibUtilities::BasisSharedPtr >	m_base
int	m_elmt_id
int	m_ncoeffs
std::vector< Array< OneD, const NekDouble > >	m_weights
LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess >	m_stdMatrixManager
LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess >	m_stdStaticCondMatrixManager
LibUtilities::NekManager< StdFacKey, Array< OneD, const NekDouble > >	m_stdFacManager
Protected Attributes inherited from Nektar::LocalRegions::Expansion2D
std::vector< bool >	m_requireNeg
Protected Attributes inherited from Nektar::LocalRegions::Expansion
LibUtilities::NekManager< IndexMapKey, IndexMapValues, IndexMapKey::opLess >	m_indexMapManager
std::map< int, ExpansionWeakPtr >	m_traceExp
SpatialDomains::Geometry *	m_geom
SpatialDomains::GeomFactorsUniquePtr	m_geomFactors
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_geomFactors times the standard element length (which is 2.0)

Detailed Description

Definition at line 48 of file QuadExp.h.

Constructor & Destructor Documentation

QuadExp() [1/3]

Nektar::LocalRegions::QuadExp::QuadExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		SpatialDomains::Geometry2D *	geom
	)

Constructor using BasisKey class for quadrature points and order definition.

Definition at line 47 of file QuadExp.cpp.

    : StdExpansion(Ba.GetNumModes() * Bb.GetNumModes(), 2, Ba, Bb),
      StdExpansion2D(Ba.GetNumModes() * Bb.GetNumModes(), Ba, Bb),
      StdQuadExp(Ba, Bb), Expansion(geom), Expansion2D(geom),
      m_matrixManager(
          std::bind(&Expansion2D::CreateMatrix, this, std::placeholders::_1)),
      m_staticCondMatrixManager(std::bind(&Expansion::CreateStaticCondMatrix,
                                          this, std::placeholders::_1))
{
}

QuadExp() [2/3]

Nektar::LocalRegions::QuadExp::QuadExp

(

const QuadExp &

T

)

Definition at line 60 of file QuadExp.cpp.

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

~QuadExp()

Nektar::LocalRegions::QuadExp::~QuadExp ( )

overridedefault

QuadExp() [3/3]

Nektar::LocalRegions::QuadExp::QuadExp ( )

private

Member Function Documentation

GetEdgeInterpVals() [1/2]

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

private

Definition at line 397 of file QuadExp.cpp.

{
    GetEdgeInterpVals(edge, inarray.data(), outarray);
}

References GetEdgeInterpVals().

GetEdgeInterpVals() [2/2]

void Nektar::LocalRegions::QuadExp::GetEdgeInterpVals ( const int  edge, const NekDouble *  inarray, Array< OneD, NekDouble > &  outarray  )

protected

Definition at line 404 of file QuadExp.cpp.

{
    int i;
    int nq0 = m_base[0]->GetNumPoints();
    int nq1 = m_base[1]->GetNumPoints();
 
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorGaussEdge] = edge;
 
    StdRegions::StdMatrixKey key(StdRegions::eInterpGauss, DetShapeType(),
                                 *this, factors);
 
    DNekScalMatSharedPtr mat_gauss = m_matrixManager[key];
 
    switch (edge)
    {
        case 0:
        {
            for (i = 0; i < nq0; i++)
            {
                outarray[i] = Vmath::Dot(
                    nq1, mat_gauss->GetOwnedMatrix()->GetPtr().data(), 1,
                    &inarray[i], nq0);
            }
            break;
        }
        case 1:
        {
            for (i = 0; i < nq1; i++)
            {
                outarray[i] = Vmath::Dot(
                    nq0, mat_gauss->GetOwnedMatrix()->GetPtr().data(), 1,
                    &inarray[i * nq0], 1);
            }
            break;
        }
        case 2:
        {
            for (i = 0; i < nq0; i++)
            {
                outarray[i] = Vmath::Dot(
                    nq1, mat_gauss->GetOwnedMatrix()->GetPtr().data(), 1,
                    &inarray[i], nq0);
            }
            break;
        }
        case 3:
        {
            for (i = 0; i < nq1; i++)
            {
                outarray[i] = Vmath::Dot(
                    nq0, mat_gauss->GetOwnedMatrix()->GetPtr().data(), 1,
                    &inarray[i * nq0], 1);
            }
            break;
        }
        default:
            ASSERTL0(false, "edge value (< 3) is out of range");
            break;
    }
}

References ASSERTL0, Nektar::StdRegions::StdExpansion::DetShapeType(), Vmath::Dot(), Nektar::StdRegions::eFactorGaussEdge, Nektar::StdRegions::eInterpGauss, Nektar::StdRegions::StdExpansion::m_base, and m_matrixManager.

Referenced by GetEdgeInterpVals(), v_ComputeTraceNormal(), v_GetLocTracePhysVals(), and v_GetTraceQFactors().

v_AlignVectorToCollapsedDir()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 212 of file QuadExp.cpp.

{
    ASSERTL1((dir == 0) || (dir == 1) || (dir == 2), "Invalid direction.");
    ASSERTL1((dir == 2) ? (m_geom->GetCoordim() == 3) : true,
             "Invalid direction.");
 
    int nqtot = m_base[0]->GetNumPoints() * m_base[1]->GetNumPoints();
 
    const Array<TwoD, const NekDouble> &df = m_geomFactors->GetDerivFactors();
 
    Array<OneD, NekDouble> tmp1 = outarray[0];
    Array<OneD, NekDouble> tmp2 = outarray[1];
 
    if (m_geomFactors->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nqtot, &df[2 * dir][0], 1, inarray.data(), 1, tmp1.data(),
                    1);
        Vmath::Vmul(nqtot, &df[2 * dir + 1][0], 1, inarray.data(), 1,
                    tmp2.data(), 1);
    }
    else
    {
        Vmath::Smul(nqtot, df[2 * dir][0], inarray.data(), 1, tmp1.data(), 1);
        Vmath::Smul(nqtot, df[2 * dir + 1][0], inarray.data(), 1, tmp2.data(),
                    1);
    }
}

References ASSERTL1, Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::Geometry::GetCoordim(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_geomFactors, Vmath::Smul(), and Vmath::Vmul().

Referenced by v_IProductWRTDerivBase().

v_ComputeLaplacianMetric()

void Nektar::LocalRegions::QuadExp::v_ComputeLaplacianMetric ( )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1298 of file QuadExp.cpp.

{
    const SpatialDomains::GeomType type = m_geomFactors->GetGtype();
    const unsigned int nqtot            = GetTotPoints();
    const unsigned int dim              = 2;
    const MetricType m[3][3]            = {
        {eMetricLaplacian00, eMetricLaplacian01, eMetricLaplacian02},
        {eMetricLaplacian01, eMetricLaplacian11, eMetricLaplacian12},
        {eMetricLaplacian02, eMetricLaplacian12, eMetricLaplacian22}};
 
    const Array<TwoD, const NekDouble> gmat =
        m_geomFactors->GetGmat(GetPointsKeys());
    for (unsigned int i = 0; i < dim; ++i)
    {
        for (unsigned int j = i; j < dim; ++j)
        {
            m_metrics[m[i][j]] = Array<OneD, NekDouble>(nqtot);
            if (type == SpatialDomains::eDeformed)
            {
                Vmath::Vcopy(nqtot, &gmat[i * dim + j][0], 1,
                             &m_metrics[m[i][j]][0], 1);
            }
            else
            {
                Vmath::Fill(nqtot, gmat[i * dim + j][0], &m_metrics[m[i][j]][0],
                            1);
            }
        }
    }
}

References Nektar::SpatialDomains::eDeformed, Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::LocalRegions::Expansion::m_geomFactors, Nektar::LocalRegions::Expansion::m_metrics, and Vmath::Vcopy().

v_ComputeTraceNormal()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 722 of file QuadExp.cpp.

{
    int i;
    SpatialDomains::GeomType type = m_geomFactors->GetGtype();
 
    LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
    for (i = 0; i < ptsKeys.size(); ++i)
    {
        // Need at least 2 points for computing normals
        if (ptsKeys[i].GetNumPoints() == 1)
        {
            LibUtilities::PointsKey pKey(2, ptsKeys[i].GetPointsType());
            ptsKeys[i] = pKey;
        }
    }
 
    const Array<TwoD, const NekDouble> &df =
        m_geomFactors->ComputeDerivFactors(ptsKeys);
    const Array<OneD, const NekDouble> &jac =
        m_geomFactors->ComputeJac(ptsKeys);
 
    // The points of normals should follow trace basis, not local basis.
    LibUtilities::BasisKey tobasis = GetTraceBasisKey(edge);
 
    int nqe       = tobasis.GetNumPoints();
    int vCoordDim = GetCoordim();
 
    m_traceNormals[edge] = Array<OneD, Array<OneD, NekDouble>>(vCoordDim);
    Array<OneD, Array<OneD, NekDouble>> &normal = m_traceNormals[edge];
    for (i = 0; i < vCoordDim; ++i)
    {
        normal[i] = Array<OneD, NekDouble>(nqe);
    }
 
    size_t nqb                     = nqe;
    size_t nbnd                    = edge;
    m_elmtBndNormDirElmtLen[nbnd]  = Array<OneD, NekDouble>{nqb, 0.0};
    Array<OneD, NekDouble> &length = m_elmtBndNormDirElmtLen[nbnd];
 
    // Regular geometry case
    if ((type == SpatialDomains::eRegular) ||
        (type == SpatialDomains::eMovingRegular))
    {
        NekDouble fac;
        // Set up normals
        switch (edge)
        {
            case 0:
                for (i = 0; i < vCoordDim; ++i)
                {
                    Vmath::Fill(nqe, -df[2 * i + 1][0], normal[i], 1);
                }
                break;
            case 1:
                for (i = 0; i < vCoordDim; ++i)
                {
                    Vmath::Fill(nqe, df[2 * i][0], normal[i], 1);
                }
                break;
            case 2:
                for (i = 0; i < vCoordDim; ++i)
                {
                    Vmath::Fill(nqe, df[2 * i + 1][0], normal[i], 1);
                }
                break;
            case 3:
                for (i = 0; i < vCoordDim; ++i)
                {
                    Vmath::Fill(nqe, -df[2 * i][0], normal[i], 1);
                }
                break;
            default:
                ASSERTL0(false, "edge is out of range (edge < 4)");
        }
 
        // normalise
        fac = 0.0;
        for (i = 0; i < vCoordDim; ++i)
        {
            fac += normal[i][0] * normal[i][0];
        }
        fac = 1.0 / sqrt(fac);
 
        Vmath::Fill(nqb, fac, length, 1);
 
        for (i = 0; i < vCoordDim; ++i)
        {
            Vmath::Smul(nqe, fac, normal[i], 1, normal[i], 1);
        }
    }
    else // Set up deformed normals
    {
        int j;
 
        int nquad0 = ptsKeys[0].GetNumPoints();
        int nquad1 = ptsKeys[1].GetNumPoints();
 
        LibUtilities::PointsKey from_key;
 
        Array<OneD, NekDouble> normals(vCoordDim * max(nquad0, nquad1), 0.0);
        Array<OneD, NekDouble> edgejac(vCoordDim * max(nquad0, nquad1), 0.0);
 
        // Extract Jacobian along edges and recover local
        // derivates (dx/dr) for polynomial interpolation by
        // multiplying m_gmat by jacobian
 
        // Implementation for all the basis except Gauss points
        if (m_base[0]->GetPointsType() != LibUtilities::eGaussGaussLegendre &&
            m_base[1]->GetPointsType() != LibUtilities::eGaussGaussLegendre)
        {
            switch (edge)
            {
                case 0:
                    for (j = 0; j < nquad0; ++j)
                    {
                        edgejac[j] = jac[j];
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            normals[i * nquad0 + j] =
                                -df[2 * i + 1][j] * edgejac[j];
                        }
                    }
                    from_key = ptsKeys[0];
                    break;
                case 1:
                    for (j = 0; j < nquad1; ++j)
                    {
                        edgejac[j] = jac[nquad0 * j + nquad0 - 1];
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            normals[i * nquad1 + j] =
                                df[2 * i][nquad0 * j + nquad0 - 1] * edgejac[j];
                        }
                    }
                    from_key = ptsKeys[1];
                    break;
                case 2:
                    for (j = 0; j < nquad0; ++j)
                    {
                        edgejac[j] = jac[nquad0 * (nquad1 - 1) + j];
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            normals[i * nquad0 + j] =
                                (df[2 * i + 1][nquad0 * (nquad1 - 1) + j]) *
                                edgejac[j];
                        }
                    }
                    from_key = ptsKeys[0];
                    break;
                case 3:
                    for (j = 0; j < nquad1; ++j)
                    {
                        edgejac[j] = jac[nquad0 * j];
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            normals[i * nquad1 + j] =
                                -df[2 * i][nquad0 * j] * edgejac[j];
                        }
                    }
                    from_key = ptsKeys[1];
                    break;
                default:
                    ASSERTL0(false, "edge is out of range (edge < 3)");
            }
        }
        else
        {
            int nqtot = nquad0 * nquad1;
            Array<OneD, NekDouble> tmp_gmat(nqtot, 0.0);
            Array<OneD, NekDouble> tmp_gmat_edge(nqe, 0.0);
 
            switch (edge)
            {
                case 0:
                    for (j = 0; j < nquad0; ++j)
                    {
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            Vmath::Vmul(nqtot, &(df[2 * i + 1][0]), 1, &jac[0],
                                        1, &(tmp_gmat[0]), 1);
                            QuadExp::GetEdgeInterpVals(edge, tmp_gmat,
                                                       tmp_gmat_edge);
                            normals[i * nquad0 + j] = -tmp_gmat_edge[j];
                        }
                    }
                    from_key = ptsKeys[0];
                    break;
                case 1:
                    for (j = 0; j < nquad1; ++j)
                    {
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            Vmath::Vmul(nqtot, &(df[2 * i][0]), 1, &jac[0], 1,
                                        &(tmp_gmat[0]), 1);
                            QuadExp::GetEdgeInterpVals(edge, tmp_gmat,
                                                       tmp_gmat_edge);
                            normals[i * nquad1 + j] = tmp_gmat_edge[j];
                        }
                    }
                    from_key = ptsKeys[1];
                    break;
                case 2:
                    for (j = 0; j < nquad0; ++j)
                    {
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            Vmath::Vmul(nqtot, &(df[2 * i + 1][0]), 1, &jac[0],
                                        1, &(tmp_gmat[0]), 1);
                            QuadExp::GetEdgeInterpVals(edge, tmp_gmat,
                                                       tmp_gmat_edge);
                            normals[i * nquad0 + j] = tmp_gmat_edge[j];
                        }
                    }
                    from_key = ptsKeys[0];
                    break;
                case 3:
                    for (j = 0; j < nquad1; ++j)
                    {
                        for (i = 0; i < vCoordDim; ++i)
                        {
                            Vmath::Vmul(nqtot, &(df[2 * i][0]), 1, &jac[0], 1,
                                        &(tmp_gmat[0]), 1);
                            QuadExp::GetEdgeInterpVals(edge, tmp_gmat,
                                                       tmp_gmat_edge);
                            normals[i * nquad1 + j] = -tmp_gmat_edge[j];
                        }
                    }
                    from_key = ptsKeys[1];
                    break;
                default:
                    ASSERTL0(false, "edge is out of range (edge < 3)");
            }
        }
 
        int nq = from_key.GetNumPoints();
        Array<OneD, NekDouble> work(nqe, 0.0);
 
        // interpolate Jacobian and invert
        LibUtilities::Interp1D(from_key, jac, tobasis.GetPointsKey(), work);
        Vmath::Sdiv(nqe, 1.0, &work[0], 1, &work[0], 1);
 
        // interpolate
        for (i = 0; i < GetCoordim(); ++i)
        {
            LibUtilities::Interp1D(from_key, &normals[i * nq],
                                   tobasis.GetPointsKey(), &normal[i][0]);
            Vmath::Vmul(nqe, work, 1, normal[i], 1, normal[i], 1);
        }
 
        // normalise normal vectors
        Vmath::Zero(nqe, work, 1);
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vvtvp(nqe, normal[i], 1, normal[i], 1, work, 1, work, 1);
        }
 
        Vmath::Vsqrt(nqe, work, 1, work, 1);
        Vmath::Sdiv(nqe, 1.0, work, 1, work, 1);
 
        Vmath::Vcopy(nqb, work, 1, length, 1);
 
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vmul(nqe, normal[i], 1, work, 1, normal[i], 1);
        }
    }
    if (GetGeom()->GetEorient(edge) == StdRegions::eBackwards)
    {
        for (i = 0; i < vCoordDim; ++i)
        {
            if (m_geomFactors->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Reverse(nqe, normal[i], 1, normal[i], 1);
            }
        }
    }
}

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

v_CreateStdMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1115 of file QuadExp.cpp.

{
    LibUtilities::BasisKey bkey0 = m_base[0]->GetBasisKey();
    LibUtilities::BasisKey bkey1 = m_base[1]->GetBasisKey();
    StdRegions::StdQuadExpSharedPtr tmp =
        MemoryManager<StdQuadExp>::AllocateSharedPtr(bkey0, bkey1);
    return tmp->GetStdMatrix(mkey);
}

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

v_DropLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1130 of file QuadExp.cpp.

{
    m_matrixManager.DeleteObject(mkey);
}

References m_matrixManager.

v_DropLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1140 of file QuadExp.cpp.

{
    m_staticCondMatrixManager.DeleteObject(mkey);
}

References m_staticCondMatrixManager.

v_ExtractDataToCoeffs()

void Nektar::LocalRegions::QuadExp::v_ExtractDataToCoeffs ( const NekDouble *  data, const std::vector< unsigned int > &  nummodes, const int  mode_offset, NekDouble *  coeffs, std::vector< LibUtilities::BasisType > &  fromType  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1000 of file QuadExp.cpp.

{
    int data_order0 = nummodes[mode_offset];
    int fillorder0  = std::min(m_base[0]->GetNumModes(), data_order0);
 
    int data_order1 = nummodes[mode_offset + 1];
    int order1      = m_base[1]->GetNumModes();
    int fillorder1  = min(order1, data_order1);
 
    // Check if same basis
    if (fromType[0] != m_base[0]->GetBasisType() ||
        fromType[1] != m_base[1]->GetBasisType())
    {
        // Construct a quad with the appropriate basis type at our
        // quadrature points, and one more to do a forwards
        // transform. We can then copy the output to coeffs.
        StdRegions::StdQuadExp tmpQuad(
            LibUtilities::BasisKey(fromType[0], data_order0,
                                   m_base[0]->GetPointsKey()),
            LibUtilities::BasisKey(fromType[1], data_order1,
                                   m_base[1]->GetPointsKey()));
        StdRegions::StdQuadExp tmpQuad2(m_base[0]->GetBasisKey(),
                                        m_base[1]->GetBasisKey());
 
        Array<OneD, const NekDouble> tmpData(tmpQuad.GetNcoeffs(), data);
        Array<OneD, NekDouble> tmpBwd(tmpQuad2.GetTotPoints());
        Array<OneD, NekDouble> tmpOut(tmpQuad2.GetNcoeffs());
 
        tmpQuad.BwdTrans(tmpData, tmpBwd);
        tmpQuad2.FwdTrans(tmpBwd, tmpOut);
        Vmath::Vcopy(tmpOut.size(), &tmpOut[0], 1, coeffs, 1);
 
        return;
    }
 
    switch (m_base[0]->GetBasisType())
    {
        case LibUtilities::eModified_A:
        {
            int i;
            int cnt  = 0;
            int cnt1 = 0;
 
            ASSERTL1(m_base[1]->GetBasisType() == LibUtilities::eModified_A,
                     "Extraction routine not set up for this basis");
 
            Vmath::Zero(m_ncoeffs, coeffs, 1);
            for (i = 0; i < fillorder0; ++i)
            {
                Vmath::Vcopy(fillorder1, data + cnt, 1, coeffs + cnt1, 1);
                cnt += data_order1;
                cnt1 += order1;
            }
        }
        break;
        case LibUtilities::eGLL_Lagrange:
        {
            LibUtilities::PointsKey p0(nummodes[0],
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey p1(nummodes[1],
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey t0(m_base[0]->GetNumModes(),
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey t1(m_base[1]->GetNumModes(),
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::Interp2D(p0, p1, data, t0, t1, coeffs);
        }
        break;
        case LibUtilities::eGauss_Lagrange:
        {
            // Assume that input is also Gll_Lagrange but no way to check;
            LibUtilities::PointsKey p0(nummodes[0],
                                       LibUtilities::eGaussGaussLegendre);
            LibUtilities::PointsKey p1(nummodes[1],
                                       LibUtilities::eGaussGaussLegendre);
            LibUtilities::PointsKey t0(m_base[0]->GetNumModes(),
                                       LibUtilities::eGaussGaussLegendre);
            LibUtilities::PointsKey t1(m_base[1]->GetNumModes(),
                                       LibUtilities::eGaussGaussLegendre);
            LibUtilities::Interp2D(p0, p1, data, t0, t1, coeffs);
        }
        break;
        default:
            ASSERTL0(false, "basis is either not set up or not hierarchicial");
    }
}

References ASSERTL0, ASSERTL1, Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::LibUtilities::Interp2D(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, tinysimd::min(), Vmath::Vcopy(), and Vmath::Zero().

v_FwdTransBndConstrained()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 67 of file QuadExp.cpp.

{
    if ((m_base[0]->Collocation()) && (m_base[1]->Collocation()))
    {
        Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
    }
    else
    {
        int i, j;
        int npoints[2] = {m_base[0]->GetNumPoints(), m_base[1]->GetNumPoints()};
        int nmodes[2]  = {m_base[0]->GetNumModes(), m_base[1]->GetNumModes()};
 
        fill(outarray.data(), outarray.data() + m_ncoeffs, 0.0);
 
        if (nmodes[0] == 1 && nmodes[1] == 1)
        {
            outarray[0] = inarray[0];
            return;
        }
 
        Array<OneD, NekDouble> physEdge[4];
        Array<OneD, NekDouble> coeffEdge[4];
        for (i = 0; i < 4; i++)
        {
            physEdge[i]  = Array<OneD, NekDouble>(npoints[i % 2]);
            coeffEdge[i] = Array<OneD, NekDouble>(nmodes[i % 2]);
        }
 
        for (i = 0; i < npoints[0]; i++)
        {
            physEdge[0][i] = inarray[i];
            physEdge[2][i] = inarray[npoints[0] * (npoints[1] - 1) + i];
        }
 
        for (i = 0; i < npoints[1]; i++)
        {
            physEdge[1][i] = inarray[npoints[0] - 1 + i * npoints[0]];
            physEdge[3][i] = inarray[i * npoints[0]];
        }
 
        SegExpSharedPtr segexp[4];
        for (i = 0; i < 4; i++)
        {
            segexp[i] = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                m_base[i % 2]->GetBasisKey(), GetGeom2D()->GetEdge(i));
        }
 
        Array<OneD, unsigned int> mapArray;
        Array<OneD, int> signArray;
        NekDouble sign;
 
        for (i = 0; i < 4; i++)
        {
            segexp[i % 2]->FwdTransBndConstrained(physEdge[i], coeffEdge[i]);
 
            GetTraceToElementMap(i, mapArray, signArray);
            for (j = 0; j < nmodes[i % 2]; j++)
            {
                sign                  = (NekDouble)signArray[j];
                outarray[mapArray[j]] = sign * coeffEdge[i][j];
            }
        }
 
        int nBoundaryDofs = NumBndryCoeffs();
        int nInteriorDofs = m_ncoeffs - nBoundaryDofs;
 
        if (nInteriorDofs > 0)
        {
            Array<OneD, NekDouble> tmp0(m_ncoeffs);
            Array<OneD, NekDouble> tmp1(m_ncoeffs);
 
            StdRegions::StdMatrixKey stdmasskey(StdRegions::eMass,
                                                DetShapeType(), *this);
            MassMatrixOp(outarray, tmp0, stdmasskey);
            v_IProductWRTBase(inarray, tmp1);
 
            Vmath::Vsub(m_ncoeffs, tmp1, 1, tmp0, 1, tmp1, 1);
 
            // get Mass matrix inverse (only of interior DOF)
            // use block (1,1) of the static condensed system
            // note: this block alreay contains the inverse matrix
            MatrixKey masskey(StdRegions::eMass, DetShapeType(), *this);
            DNekScalMatSharedPtr matsys =
                (m_staticCondMatrixManager[masskey])->GetBlock(1, 1);
 
            Array<OneD, NekDouble> rhs(nInteriorDofs);
            Array<OneD, NekDouble> result(nInteriorDofs);
 
            GetInteriorMap(mapArray);
 
            for (i = 0; i < nInteriorDofs; i++)
            {
                rhs[i] = tmp1[mapArray[i]];
            }
 
            Blas::Dgemv('N', nInteriorDofs, nInteriorDofs, matsys->Scale(),
                        &((matsys->GetOwnedMatrix())->GetPtr())[0],
                        nInteriorDofs, rhs.data(), 1, 0.0, result.data(), 1);
 
            for (i = 0; i < nInteriorDofs; i++)
            {
                outarray[mapArray[i]] = result[i];
            }
        }
    }
}

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

v_GenMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1095 of file QuadExp.cpp.

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

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

v_GetCoord()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 301 of file QuadExp.cpp.

{
    int i;
 
    ASSERTL1(Lcoords[0] >= -1.0 && Lcoords[1] <= 1.0 && Lcoords[1] >= -1.0 &&
                 Lcoords[1] <= 1.0,
             "Local coordinates are not in region [-1,1]");
 
    m_geom->FillGeom();
    for (i = 0; i < m_geom->GetCoordim(); ++i)
    {
        coords[i] = m_geom->GetCoord(i, Lcoords);
    }
}

References ASSERTL1, Nektar::SpatialDomains::Geometry::FillGeom(), Nektar::SpatialDomains::Geometry::GetCoord(), Nektar::SpatialDomains::Geometry::GetCoordim(), and Nektar::LocalRegions::Expansion::m_geom.

v_GetCoords()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 294 of file QuadExp.cpp.

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

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

v_GetLinStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 283 of file QuadExp.cpp.

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

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

v_GetLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1125 of file QuadExp.cpp.

{
    return m_matrixManager[mkey];
}

References m_matrixManager.

v_GetLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1135 of file QuadExp.cpp.

{
    return m_staticCondMatrixManager[mkey];
}

References m_staticCondMatrixManager.

v_GetLocTracePhysVals()

void Nektar::LocalRegions::QuadExp::v_GetLocTracePhysVals ( const int  edge, const StdRegions::StdExpansionSharedPtr &  EdgeExp, const NekDouble *  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 347 of file QuadExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
 
    // Implementation for all the basis except Gauss points
    if (m_base[0]->GetPointsType() != LibUtilities::eGaussGaussLegendre &&
        m_base[1]->GetPointsType() != LibUtilities::eGaussGaussLegendre)
    {
        switch (edge)
        {
            case 0:
                Vmath::Vcopy(nquad0, &(inarray[0]), 1, &(outarray[0]), 1);
                break;
            case 1:
                Vmath::Vcopy(nquad1, &(inarray[0]) + (nquad0 - 1), nquad0,
                             &(outarray[0]), 1);
                break;
            case 2:
                Vmath::Vcopy(nquad0, &(inarray[0]) + nquad0 * (nquad1 - 1), 1,
                             &(outarray[0]), 1);
                break;
            case 3:
                Vmath::Vcopy(nquad1, &(inarray[0]), nquad0, &(outarray[0]), 1);
                break;
            default:
                ASSERTL0(false, "edge value (< 3) is out of range");
                break;
        }
    }
    else
    {
        QuadExp::GetEdgeInterpVals(edge, inarray, outarray);
    }
 
    // Interpolate if required
    if (m_base[edge % 2]->GetPointsKey() !=
        EdgeExp->GetBasis(0)->GetPointsKey())
    {
        Array<OneD, NekDouble> outtmp(max(nquad0, nquad1));
 
        outtmp = outarray;
 
        LibUtilities::Interp1D(m_base[edge % 2]->GetPointsKey(), outtmp,
                               EdgeExp->GetBasis(0)->GetPointsKey(), outarray);
    }
}

References ASSERTL0, Nektar::LibUtilities::eGaussGaussLegendre, GetEdgeInterpVals(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::m_base, tinysimd::max(), and Vmath::Vcopy().

Referenced by v_GetTracePhysVals().

v_GetStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 277 of file QuadExp.cpp.

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

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

v_GetTraceOrient()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1090 of file QuadExp.cpp.

{
    return m_geom->GetEorient(edge);
}

References Nektar::SpatialDomains::Geometry::GetEorient(), and Nektar::LocalRegions::Expansion::m_geom.

v_GetTracePhysMap()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 467 of file QuadExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
 
    // Get points in Cartesian orientation
    switch (edge)
    {
        case 0:
            outarray = Array<OneD, int>(nquad0);
            for (int i = 0; i < nquad0; ++i)
            {
                outarray[i] = i;
            }
            break;
        case 1:
            outarray = Array<OneD, int>(nquad1);
            for (int i = 0; i < nquad1; ++i)
            {
                outarray[i] = (nquad0 - 1) + i * nquad0;
            }
            break;
        case 2:
            outarray = Array<OneD, int>(nquad0);
            for (int i = 0; i < nquad0; ++i)
            {
                outarray[i] = i + nquad0 * (nquad1 - 1);
            }
            break;
        case 3:
            outarray = Array<OneD, int>(nquad1);
            for (int i = 0; i < nquad1; ++i)
            {
                outarray[i] = i * nquad0;
            }
            break;
        default:
            ASSERTL0(false, "edge value (< 3) is out of range");
            break;
    }
}

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

v_GetTracePhysVals()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 328 of file QuadExp.cpp.

{
    v_GetLocTracePhysVals(edge, EdgeExp, inarray.data(), outarray);
 
    if (orient == StdRegions::eNoOrientation)
    {
        orient = GetTraceOrient(edge);
    }
    // Reverse data if necessary
    if (orient == StdRegions::eBackwards)
    {
        Vmath::Reverse(EdgeExp->GetNumPoints(0), &outarray[0], 1, &outarray[0],
                       1);
    }
}

References Nektar::StdRegions::eBackwards, Nektar::StdRegions::eNoOrientation, Nektar::LocalRegions::Expansion::GetTraceOrient(), Vmath::Reverse(), and v_GetLocTracePhysVals().

v_GetTraceQFactors()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 509 of file QuadExp.cpp.

{
    int i;
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
 
    LibUtilities::PointsKeyVector ptsKeys   = GetPointsKeys();
    const Array<OneD, const NekDouble> &jac = m_geomFactors->GetJac();
    const Array<TwoD, const NekDouble> &df  = m_geomFactors->GetDerivFactors();
 
    Array<OneD, NekDouble> j(max(nquad0, nquad1), 0.0);
    Array<OneD, NekDouble> g0(max(nquad0, nquad1), 0.0);
    Array<OneD, NekDouble> g1(max(nquad0, nquad1), 0.0);
    Array<OneD, NekDouble> g2(max(nquad0, nquad1), 0.0);
    Array<OneD, NekDouble> g3(max(nquad0, nquad1), 0.0);
 
    if (m_geomFactors->GetGtype() == SpatialDomains::eDeformed)
    {
        // Implementation for all the basis except Gauss points
        if (m_base[0]->GetPointsType() != LibUtilities::eGaussGaussLegendre &&
            m_base[1]->GetPointsType() != LibUtilities::eGaussGaussLegendre)
        {
            switch (edge)
            {
                case 0:
                    Vmath::Vcopy(nquad0, &(df[1][0]), 1, &(g1[0]), 1);
                    Vmath::Vcopy(nquad0, &(df[3][0]), 1, &(g3[0]), 1);
                    Vmath::Vcopy(nquad0, &(jac[0]), 1, &(j[0]), 1);
 
                    for (i = 0; i < nquad0; ++i)
                    {
                        outarray[i] =
                            j[i] * sqrt(g1[i] * g1[i] + g3[i] * g3[i]);
                    }
                    break;
                case 1:
                    Vmath::Vcopy(nquad1, &(df[0][0]) + (nquad0 - 1), nquad0,
                                 &(g0[0]), 1);
 
                    Vmath::Vcopy(nquad1, &(df[2][0]) + (nquad0 - 1), nquad0,
                                 &(g2[0]), 1);
 
                    Vmath::Vcopy(nquad1, &(jac[0]) + (nquad0 - 1), nquad0,
                                 &(j[0]), 1);
 
                    for (i = 0; i < nquad1; ++i)
                    {
                        outarray[i] =
                            j[i] * sqrt(g0[i] * g0[i] + g2[i] * g2[i]);
                    }
                    break;
                case 2:
 
                    Vmath::Vcopy(nquad0, &(df[1][0]) + (nquad0 * (nquad1 - 1)),
                                 1, &(g1[0]), 1);
 
                    Vmath::Vcopy(nquad0, &(df[3][0]) + (nquad0 * (nquad1 - 1)),
                                 1, &(g3[0]), 1);
 
                    Vmath::Vcopy(nquad0, &(jac[0]) + (nquad0 * (nquad1 - 1)), 1,
                                 &(j[0]), 1);
 
                    for (i = 0; i < nquad0; ++i)
                    {
                        outarray[i] =
                            j[i] * sqrt(g1[i] * g1[i] + g3[i] * g3[i]);
                    }
                    break;
                case 3:
 
                    Vmath::Vcopy(nquad1, &(df[0][0]), nquad0, &(g0[0]), 1);
                    Vmath::Vcopy(nquad1, &(df[2][0]), nquad0, &(g2[0]), 1);
                    Vmath::Vcopy(nquad1, &(jac[0]), nquad0, &(j[0]), 1);
 
                    for (i = 0; i < nquad1; ++i)
                    {
                        outarray[i] =
                            j[i] * sqrt(g0[i] * g0[i] + g2[i] * g2[i]);
                    }
                    break;
                default:
                    ASSERTL0(false, "edge value (< 3) is out of range");
                    break;
            }
        }
        else
        {
            int nqtot = nquad0 * nquad1;
            Array<OneD, NekDouble> tmp_gmat0(nqtot, 0.0);
            Array<OneD, NekDouble> tmp_gmat1(nqtot, 0.0);
            Array<OneD, NekDouble> tmp_gmat2(nqtot, 0.0);
            Array<OneD, NekDouble> tmp_gmat3(nqtot, 0.0);
            Array<OneD, NekDouble> g0_edge(max(nquad0, nquad1), 0.0);
            Array<OneD, NekDouble> g1_edge(max(nquad0, nquad1), 0.0);
            Array<OneD, NekDouble> g2_edge(max(nquad0, nquad1), 0.0);
            Array<OneD, NekDouble> g3_edge(max(nquad0, nquad1), 0.0);
            Array<OneD, NekDouble> jac_edge(max(nquad0, nquad1), 0.0);
 
            switch (edge)
            {
                case 0:
                    Vmath::Vmul(nqtot, &(df[1][0]), 1, &jac[0], 1,
                                &(tmp_gmat1[0]), 1);
                    Vmath::Vmul(nqtot, &(df[3][0]), 1, &jac[0], 1,
                                &(tmp_gmat3[0]), 1);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat1, g1_edge);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat3, g3_edge);
 
                    for (i = 0; i < nquad0; ++i)
                    {
                        outarray[i] = sqrt(g1_edge[i] * g1_edge[i] +
                                           g3_edge[i] * g3_edge[i]);
                    }
                    break;
 
                case 1:
                    Vmath::Vmul(nqtot, &(df[0][0]), 1, &jac[0], 1,
                                &(tmp_gmat0[0]), 1);
                    Vmath::Vmul(nqtot, &(df[2][0]), 1, &jac[0], 1,
                                &(tmp_gmat2[0]), 1);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat0, g0_edge);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat2, g2_edge);
 
                    for (i = 0; i < nquad1; ++i)
                    {
                        outarray[i] = sqrt(g0_edge[i] * g0_edge[i] +
                                           g2_edge[i] * g2_edge[i]);
                    }
 
                    break;
                case 2:
 
                    Vmath::Vmul(nqtot, &(df[1][0]), 1, &jac[0], 1,
                                &(tmp_gmat1[0]), 1);
                    Vmath::Vmul(nqtot, &(df[3][0]), 1, &jac[0], 1,
                                &(tmp_gmat3[0]), 1);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat1, g1_edge);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat3, g3_edge);
 
                    for (i = 0; i < nquad0; ++i)
                    {
                        outarray[i] = sqrt(g1_edge[i] * g1_edge[i] +
                                           g3_edge[i] * g3_edge[i]);
                    }
 
                    Vmath::Reverse(nquad0, &outarray[0], 1, &outarray[0], 1);
 
                    break;
                case 3:
                    Vmath::Vmul(nqtot, &(df[0][0]), 1, &jac[0], 1,
                                &(tmp_gmat0[0]), 1);
                    Vmath::Vmul(nqtot, &(df[2][0]), 1, &jac[0], 1,
                                &(tmp_gmat2[0]), 1);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat0, g0_edge);
                    QuadExp::GetEdgeInterpVals(edge, tmp_gmat2, g2_edge);
 
                    for (i = 0; i < nquad1; ++i)
                    {
                        outarray[i] = sqrt(g0_edge[i] * g0_edge[i] +
                                           g2_edge[i] * g2_edge[i]);
                    }
 
                    Vmath::Reverse(nquad1, &outarray[0], 1, &outarray[0], 1);
 
                    break;
                default:
                    ASSERTL0(false, "edge value (< 3) is out of range");
                    break;
            }
        }
    }
    else
    {
 
        switch (edge)
        {
            case 0:
 
                for (i = 0; i < nquad0; ++i)
                {
                    outarray[i] = jac[0] * sqrt(df[1][0] * df[1][0] +
                                                df[3][0] * df[3][0]);
                }
                break;
            case 1:
                for (i = 0; i < nquad1; ++i)
                {
                    outarray[i] = jac[0] * sqrt(df[0][0] * df[0][0] +
                                                df[2][0] * df[2][0]);
                }
                break;
            case 2:
                for (i = 0; i < nquad0; ++i)
                {
                    outarray[i] = jac[0] * sqrt(df[1][0] * df[1][0] +
                                                df[3][0] * df[3][0]);
                }
                break;
            case 3:
                for (i = 0; i < nquad1; ++i)
                {
                    outarray[i] = jac[0] * sqrt(df[0][0] * df[0][0] +
                                                df[2][0] * df[2][0]);
                }
                break;
            default:
                ASSERTL0(false, "edge value (< 3) is out of range");
                break;
        }
    }
}

References ASSERTL0, Nektar::SpatialDomains::eDeformed, Nektar::LibUtilities::eGaussGaussLegendre, GetEdgeInterpVals(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geomFactors, tinysimd::max(), Vmath::Reverse(), tinysimd::sqrt(), Vmath::Vcopy(), and Vmath::Vmul().

v_HelmholtzMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1189 of file QuadExp.cpp.

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

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

v_IProductWRTDerivBase()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 176 of file QuadExp.cpp.

{
    ASSERTL1((dir == 0) || (dir == 1) || (dir == 2), "Invalid direction.");
    ASSERTL1((dir == 2) ? (m_geom->GetCoordim() == 3) : true,
             "Invalid direction.");
 
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nqtot  = nquad0 * nquad1;
 
    Array<OneD, NekDouble> tmp1(nqtot);
    Array<OneD, NekDouble> tmp2(nqtot);
    Array<OneD, NekDouble> tmp3(m_ncoeffs);
 
    Array<OneD, Array<OneD, NekDouble>> tmp2D{2};
    tmp2D[0] = tmp1;
    tmp2D[1] = tmp2;
 
    QuadExp::v_AlignVectorToCollapsedDir(dir, inarray, tmp2D);
 
    const Array<OneD, const NekDouble> &jac = m_geomFactors->GetJac();
    bool Deformed = (m_geomFactors->GetGtype() == SpatialDomains::eDeformed);
 
    v_IProductWRTBaseKernel(m_base[0]->GetDbdata(), m_base[1]->GetBdata(), tmp1,
                            tmp3, jac, Deformed, false,
                            m_base[1]->Collocation());
 
    v_IProductWRTBaseKernel(m_base[0]->GetBdata(), m_base[1]->GetDbdata(), tmp2,
                            outarray, jac, Deformed, m_base[0]->Collocation(),
                            false);
 
    Vmath::Vadd(m_ncoeffs, tmp3, 1, outarray, 1, outarray, 1);
}

References ASSERTL1, Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::Geometry::GetCoordim(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_geomFactors, Nektar::StdRegions::StdExpansion::m_ncoeffs, v_AlignVectorToCollapsedDir(), Nektar::StdRegions::StdQuadExp::v_IProductWRTBaseKernel(), and Vmath::Vadd().

v_LaplacianMatrixOp() [1/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1152 of file QuadExp.cpp.

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

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

v_LaplacianMatrixOp() [2/2]

void Nektar::LocalRegions::QuadExp::v_LaplacianMatrixOp ( const int  k1, const int  k2, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, const StdRegions::StdMatrixKey &  mkey  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1159 of file QuadExp.cpp.

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

v_LaplacianMatrixOp_MatFree_Kernel()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1236 of file QuadExp.cpp.

{
    if (m_metrics.count(eMetricLaplacian00) == 0)
    {
        ComputeLaplacianMetric();
    }
 
    int nquad0  = m_base[0]->GetNumPoints();
    int nquad1  = m_base[1]->GetNumPoints();
    int nqtot   = nquad0 * nquad1;
    int nmodes0 = m_base[0]->GetNumModes();
    int nmodes1 = m_base[1]->GetNumModes();
    int wspsize =
        max(max(max(nqtot, m_ncoeffs), nquad1 * nmodes0), nquad0 * nmodes1);
 
    ASSERTL1(wsp.size() >= 3 * wspsize, "Workspace is of insufficient size.");
 
    const Array<OneD, const NekDouble> &base0  = m_base[0]->GetBdata();
    const Array<OneD, const NekDouble> &base1  = m_base[1]->GetBdata();
    const Array<OneD, const NekDouble> &dbase0 = m_base[0]->GetDbdata();
    const Array<OneD, const NekDouble> &dbase1 = m_base[1]->GetDbdata();
    const Array<OneD, const NekDouble> &metric00 =
        m_metrics[eMetricLaplacian00];
    const Array<OneD, const NekDouble> &metric01 =
        m_metrics[eMetricLaplacian01];
    const Array<OneD, const NekDouble> &metric11 =
        m_metrics[eMetricLaplacian11];
 
    // Allocate temporary storage
    Array<OneD, NekDouble> wsp0(wsp);
    Array<OneD, NekDouble> wsp1(wsp + wspsize);
    Array<OneD, NekDouble> wsp2(wsp + 2 * wspsize);
 
    PhysTensorDeriv(inarray, wsp1, wsp2);
 
    // wsp0 = k = g0 * wsp1 + g1 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
    // wsp2 = l = g1 * wsp1 + g2 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
    // where g0, g1 and g2 are the metric terms set up in the GeomFactors class
    // especially for this purpose
    Vmath::Vvtvvtp(nqtot, &metric00[0], 1, &wsp1[0], 1, &metric01[0], 1,
                   &wsp2[0], 1, &wsp0[0], 1);
    Vmath::Vvtvvtp(nqtot, &metric01[0], 1, &wsp1[0], 1, &metric11[0], 1,
                   &wsp2[0], 1, &wsp2[0], 1);
 
    // outarray = m = (D_xi1 * B)^T * k
    // wsp1     = n = (D_xi2 * B)^T * l
    const Array<OneD, const NekDouble> &jac = m_geomFactors->GetJac();
    bool Deformed = (m_geomFactors->GetGtype() == SpatialDomains::eDeformed);
 
    v_IProductWRTBaseKernel(dbase0, base1, wsp0, outarray, jac, Deformed, false,
                            m_base[1]->Collocation());
    v_IProductWRTBaseKernel(base0, dbase1, wsp2, wsp1, jac, Deformed,
                            m_base[1]->Collocation(), false);
 
    // outarray = outarray + wsp1
    //          = L * u_hat
    Vmath::Vadd(m_ncoeffs, wsp1.data(), 1, outarray.data(), 1, outarray.data(),
                1);
}

References ASSERTL1, Nektar::LocalRegions::Expansion::ComputeLaplacianMetric(), Nektar::SpatialDomains::eDeformed, Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian11, Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geomFactors, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::m_ncoeffs, tinysimd::max(), Nektar::StdRegions::StdExpansion2D::PhysTensorDeriv(), Nektar::StdRegions::StdQuadExp::v_IProductWRTBaseKernel(), Vmath::Vadd(), and Vmath::Vvtvvtp().

v_MassLevelCurvatureMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1182 of file QuadExp.cpp.

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

v_MassMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1145 of file QuadExp.cpp.

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

v_NormVectorIProductWRTBase() [1/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 270 of file QuadExp.cpp.

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

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

v_NormVectorIProductWRTBase() [2/2]

void Nektar::LocalRegions::QuadExp::v_NormVectorIProductWRTBase ( const Array< OneD, const NekDouble > &  Fx, const Array< OneD, const NekDouble > &  Fy, const Array< OneD, const NekDouble > &  Fz, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 242 of file QuadExp.cpp.

{
    int nq = m_base[0]->GetNumPoints() * m_base[1]->GetNumPoints();
    Array<OneD, NekDouble> Fn(nq);
 
    const Array<OneD, const Array<OneD, NekDouble>> &normals =
        GetLeftAdjacentElementExp()->GetTraceNormal(
            GetLeftAdjacentElementTrace());
 
    if (m_geomFactors->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vvtvvtp(nq, &normals[0][0], 1, &Fx[0], 1, &normals[1][0], 1,
                       &Fy[0], 1, &Fn[0], 1);
        Vmath::Vvtvp(nq, &normals[2][0], 1, &Fz[0], 1, &Fn[0], 1, &Fn[0], 1);
    }
    else
    {
        Vmath::Svtsvtp(nq, normals[0][0], &Fx[0], 1, normals[1][0], &Fy[0], 1,
                       &Fn[0], 1);
        Vmath::Svtvp(nq, normals[2][0], &Fz[0], 1, &Fn[0], 1, &Fn[0], 1);
    }
 
    IProductWRTBase(Fn, outarray);
}

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

v_PhysEvalFirstDeriv()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 317 of file QuadExp.cpp.

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

References ASSERTL0, Nektar::SpatialDomains::Geometry::GetLocCoords(), and Nektar::LocalRegions::Expansion::m_geom.

v_ReduceOrderCoeffs()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1196 of file QuadExp.cpp.

{
    int n_coeffs = inarray.size();
 
    Array<OneD, NekDouble> coeff(n_coeffs);
    Array<OneD, NekDouble> coeff_tmp(n_coeffs, 0.0);
    Array<OneD, NekDouble> tmp, tmp2;
 
    int nmodes0 = m_base[0]->GetNumModes();
    int nmodes1 = m_base[1]->GetNumModes();
    int numMax  = nmodes0;
 
    Vmath::Vcopy(n_coeffs, inarray, 1, coeff_tmp, 1);
 
    const LibUtilities::PointsKey Pkey0(nmodes0,
                                        LibUtilities::eGaussLobattoLegendre);
    const LibUtilities::PointsKey Pkey1(nmodes1,
                                        LibUtilities::eGaussLobattoLegendre);
    LibUtilities::BasisKey b0(m_base[0]->GetBasisType(), nmodes0, Pkey0);
    LibUtilities::BasisKey b1(m_base[1]->GetBasisType(), nmodes1, Pkey1);
    LibUtilities::BasisKey bortho0(LibUtilities::eOrtho_A, nmodes0, Pkey0);
    LibUtilities::BasisKey bortho1(LibUtilities::eOrtho_A, nmodes1, Pkey1);
 
    LibUtilities::InterpCoeff2D(b0, b1, coeff_tmp, bortho0, bortho1, coeff);
 
    Vmath::Zero(n_coeffs, coeff_tmp, 1);
 
    int cnt = 0;
    for (int i = 0; i < numMin + 1; ++i)
    {
        Vmath::Vcopy(numMin, tmp = coeff + cnt, 1, tmp2 = coeff_tmp + cnt, 1);
 
        cnt = i * numMax;
    }
 
    LibUtilities::InterpCoeff2D(bortho0, bortho1, coeff_tmp, b0, b1, outarray);
}

References Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eOrtho_A, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::LibUtilities::InterpCoeff2D(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Vcopy(), and Vmath::Zero().

v_SVVLaplacianFilter()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1329 of file QuadExp.cpp.

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

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

v_WeakDerivMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1167 of file QuadExp.cpp.

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

v_WeakDirectionalDerivMatrixOp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1175 of file QuadExp.cpp.

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

Member Data Documentation

m_matrixManager

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

private

Definition at line 206 of file QuadExp.h.

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

m_staticCondMatrixManager

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

private

Definition at line 208 of file QuadExp.h.

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