Nektar::LocalRegions::SegExp Class Reference

#include <SegExp.h>

Inheritance diagram for Nektar::LocalRegions::SegExp:

Public Member Functions
	SegExp (const LibUtilities::BasisKey &Ba, SpatialDomains::Geometry1D *geom)
	Constructor using BasisKey class for quadrature points and order definition.
	SegExp (const SegExp &S)
	Copy Constructor.
	~SegExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdSegExp
	StdSegExp (const LibUtilities::BasisKey &Ba)
	Constructor using BasisKey class for quadrature points and order definition.
	StdSegExp (const StdSegExp &T)=default
	~StdSegExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdExpansion1D
	StdExpansion1D (int numcoeffs, const LibUtilities::BasisKey &Ba)
	StdExpansion1D ()=default
	StdExpansion1D (const StdExpansion1D &T)=default
	~StdExpansion1D () override=default
void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray.
NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)
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.
std::shared_ptr< StdExpansion >	GetStdExp () const
std::shared_ptr< StdExpansion >	GetLinStdExp (void) const
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)
	This function performs the Forward transformation from physical space to coefficient space.
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	IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)
void	IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
int	GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id.
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
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)
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	PhysDeriv_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds)
void	PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn)
void	PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)
void	StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
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	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)
	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, const Array< OneD, const NekDouble > &Fz, 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	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.
template<class T >
std::shared_ptr< T >	as ()
void	IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)
void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
Public Member Functions inherited from Nektar::LocalRegions::Expansion1D
	Expansion1D (SpatialDomains::Geometry1D *pGeom)
	~Expansion1D () override=default
void	AddNormTraceInt (const int dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	AddHDGHelmholtzTraceTerms (const NekDouble tau, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
SpatialDomains::Geometry1D *	GetGeom1D () const
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)
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)
const SpatialDomains::GeomFactorsSharedPtr &	GetMetricInfo () const
DNekMatSharedPtr	BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
DNekMatSharedPtr	BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
void	ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
NekDouble	VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)
void	NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors)
IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)
void	AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray)
ExpansionSharedPtr	GetLeftAdjacentElementExp () const
ExpansionSharedPtr	GetRightAdjacentElementExp () const
int	GetLeftAdjacentElementTrace () const
int	GetRightAdjacentElementTrace () const
void	SetAdjacentElementExp (int traceid, ExpansionSharedPtr &e)
StdRegions::Orientation	GetTraceOrient (int trace)
void	SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Divided by the metric jacobi and quadrature weights.
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	GetTracePhysMap (const int edge, Array< OneD, int > &outarray)
void	ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1)
const NormalVector &	GetTraceNormal (const int id)
void	ComputeTraceNormal (const int id)
const Array< OneD, const NekDouble > &	GetPhysNormals (void)
void	SetPhysNormals (Array< OneD, const NekDouble > &normal)
void	SetUpPhysNormals (const int trace)
void	AddRobinMassMatrix (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
void	TraceNormLen (const int traceid, NekDouble &h, NekDouble &p)
void	AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)
const Array< OneD, const NekDouble > &	GetElmtBndNormDirElmtLen (const int nbnd) const
void	StdDerivBaseOnTraceMat (Array< OneD, DNekMatSharedPtr > &DerivMat)
void	PhysDerivBaseOnTraceMat (const int traceid, Array< OneD, DNekMatSharedPtr > &DerivMat)
void	PhysBaseOnTraceMat (const int traceid, DNekMatSharedPtr &BdataMat)

Protected Member Functions
NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrate the physical point list inarray over region and return the value.
void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray) override
	Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray.
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_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds) override
	Evaluate the derivative along a line: \( d/ds=\frac{spacedim}{||tangent||}d/d{\xi} \). The derivative is calculated performing the product \( du/d{s}=\nabla u \cdot tangent \).
void	v_PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn) override
	Evaluate the derivative normal to a line: \( d/dn=\frac{spacedim}{||normal||}d/d{\xi} \). The derivative is calculated performing the product \( du/d{s}=\nabla u \cdot normal \).
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 outarray.
void	v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Inner product of inarray over region with respect to the expansion basis (this)->_Base[0] and return in outarray.
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check) override
	Inner product of inarray over region with respect to expansion basis base and return in outarray.
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray) override
void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray) override
NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals) override
NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coord, const Array< OneD, const NekDouble > &physvals) override
NekDouble	v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
NekDouble	v_PhysEvalFirstSecondDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs) 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
void	v_GetVertexPhysVals (const int vertex, const Array< OneD, const NekDouble > &inarray, NekDouble &outarray) override
void	v_GetTracePhysVals (const int edge, const StdRegions::StdExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) override
void	v_GetTracePhysMap (const int vertex, Array< OneD, int > &map) override
StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const override
StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const override
void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
int	v_NumBndryCoeffs () const override
int	v_NumDGBndryCoeffs () const override
void	v_ComputeTraceNormal (const int vertex) 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
	Unpack data from input file assuming it comes from.
const Array< OneD, const NekDouble > &	v_GetPhysNormals () 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_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override
DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)
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
Protected Member Functions inherited from Nektar::StdRegions::StdSegExp
NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrate the physical point list inarray over region and return the value.
void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray) override
	Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray.
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_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray) override
void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Backward transform from coefficient space given in inarray and evaluate at the physical quadrature points outarray.
void	v_BwdTrans_SumFac (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_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 outarray.
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Inner product of inarray over region with respect to the expansion basis (this)->m_base[0] and return in outarray.
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check) override
	Inner product of inarray over region with respect to expansion basis base and return in outarray.
void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true) override
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTDerivBase_SumFac (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
NekDouble	v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) final
NekDouble	v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
NekDouble	v_PhysEvalFirstSecondDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs) 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_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_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_FillMode (const int mode, Array< OneD, NekDouble > &outarray) override
void	v_GetCoords (Array< OneD, NekDouble > &coords_0, Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2) 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
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 override
int	v_NumDGBndryCoeffs () const override
bool	v_IsBoundaryInteriorExpansion () const override
int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset) override
LibUtilities::ShapeType	v_DetShapeType () const override
	Return Shape of region, using ShapeType enum list. i.e. Segment.
DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey) override
DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey) override
void	v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true) override
void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) 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_GetElmtTraceToTraceMap (const unsigned int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q) override
void	v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion1D
NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override
void	v_PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr	CreateStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
	Create the static condensation of a matrix when using a boundary interior decomposition.
void	BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
void	LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	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)
virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
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)
Protected Member Functions inherited from Nektar::LocalRegions::Expansion1D
void	v_AddRobinMassMatrix (const int vert, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) override
void	v_AddRobinTraceContribution (const int vert, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs) override
NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec) override
void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors) override
	: This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace.
void	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1) 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_MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_ComputeLaplacianMetric ()
int	v_GetCoordim () const override
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
virtual void	v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray)
virtual StdRegions::Orientation	v_GetTraceOrient (int trace)
virtual void	v_GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray)
virtual void	v_SetPhysNormals (Array< OneD, const NekDouble > &normal)
virtual void	v_SetUpPhysNormals (const int id)
virtual void	v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp)

Private Member Functions
void	ReverseCoeffsAndSign (const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Reverse the coefficients in a boundary interior expansion this routine is of use when we need the segment coefficients corresponding to a expansion in the reverse coordinate direction.
void	MultiplyByElmtInvMass (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

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
LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess >	m_stdMatrixManager
LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess >	m_stdStaticCondMatrixManager
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::GeomFactorsSharedPtr	m_metricinfo
MetricMap	m_metrics
std::map< int, NormalVector >	m_traceNormals
ExpansionWeakPtr	m_elementLeft
ExpansionWeakPtr	m_elementRight
int	m_elementTraceLeft = -1
int	m_elementTraceRight = -1
std::map< int, Array< OneD, NekDouble > >	m_elmtBndNormDirElmtLen
	the element length in each element boundary(Vertex, edge or face) normal direction calculated based on the local m_metricinfo times the standard element length (which is 2.0)

Detailed Description

Defines a Segment local expansion.

Definition at line 49 of file SegExp.h.

Constructor & Destructor Documentation

SegExp() [1/2]

Nektar::LocalRegions::SegExp::SegExp	(	const LibUtilities::BasisKey &	Ba,
		SpatialDomains::Geometry1D *	geom
	)

Constructor using BasisKey class for quadrature points and order definition.

Parameters

Ba	Basis key of segment expansion.
geom	Description of geometry.

Definition at line 55 of file SegExp.cpp.

    : StdExpansion(Ba.GetNumModes(), 1, Ba),
      StdExpansion1D(Ba.GetNumModes(), Ba), StdRegions::StdSegExp(Ba),
      Expansion(geom), Expansion1D(geom),
      m_matrixManager(
          std::bind(&SegExp::CreateMatrix, this, std::placeholders::_1),
          std::string("SegExpMatrix")),
      m_staticCondMatrixManager(std::bind(&Expansion::CreateStaticCondMatrix,
                                          this, std::placeholders::_1),
                                std::string("SegExpStaticCondMatrix"))
{
}

SegExp() [2/2]

Nektar::LocalRegions::SegExp::SegExp

(

const SegExp &

S

)

Copy Constructor.

Parameters

S	Existing segment to duplicate.

Definition at line 73 of file SegExp.cpp.

    : StdExpansion(S), StdExpansion1D(S), StdRegions::StdSegExp(S),
      Expansion(S), Expansion1D(S), m_matrixManager(S.m_matrixManager),
      m_staticCondMatrixManager(S.m_staticCondMatrixManager)
{
}

~SegExp()

Nektar::LocalRegions::SegExp::~SegExp ( )

overridedefault

Member Function Documentation

CreateMatrix()

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

protected

Definition at line 1127 of file SegExp.cpp.

{
    DNekScalMatSharedPtr returnval;
    NekDouble fac;
    LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
 
    ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,
             "Geometric information is not set up");
 
    switch (mkey.GetMatrixType())
    {
        case StdRegions::eMass:
        {
            if ((m_metricinfo->GetGtype() == SpatialDomains::eDeformed) ||
                (mkey.GetNVarCoeff()))
            {
                fac = 1.0;
                goto UseLocRegionsMatrix;
            }
            else
            {
                fac = (m_metricinfo->GetJac(ptsKeys))[0];
                goto UseStdRegionsMatrix;
            }
        }
        break;
        case StdRegions::eInvMass:
        {
            if ((m_metricinfo->GetGtype() == SpatialDomains::eDeformed) ||
                (mkey.GetNVarCoeff()))
            {
                NekDouble one = 1.0;
                StdRegions::StdMatrixKey masskey(StdRegions::eMass,
                                                 DetShapeType(), *this);
                DNekMatSharedPtr mat = GenMatrix(masskey);
                mat->Invert();
 
                returnval =
                    MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
            }
            else
            {
                fac = 1.0 / (m_metricinfo->GetJac(ptsKeys))[0];
                goto UseStdRegionsMatrix;
            }
        }
        break;
        case StdRegions::eWeakDeriv0:
        case StdRegions::eWeakDeriv1:
        case StdRegions::eWeakDeriv2:
        {
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
                mkey.GetNVarCoeff())
            {
                fac = 1.0;
                goto UseLocRegionsMatrix;
            }
            else
            {
                int dir = 0;
                switch (mkey.GetMatrixType())
                {
                    case StdRegions::eWeakDeriv0:
                        dir = 0;
                        break;
                    case StdRegions::eWeakDeriv1:
                        ASSERTL1(m_geom->GetCoordim() >= 2,
                                 "Cannot call eWeakDeriv2 in a "
                                 "coordinate system which is not at "
                                 "least two-dimensional");
                        dir = 1;
                        break;
                    case StdRegions::eWeakDeriv2:
                        ASSERTL1(m_geom->GetCoordim() == 3,
                                 "Cannot call eWeakDeriv2 in a "
                                 "coordinate system which is not "
                                 "three-dimensional");
                        dir = 2;
                        break;
                    default:
                        break;
                }
 
                MatrixKey deriv0key(StdRegions::eWeakDeriv0,
                                    mkey.GetShapeType(), *this);
 
                DNekMatSharedPtr WeakDerivStd = GetStdMatrix(deriv0key);
                fac = m_metricinfo->GetDerivFactors(ptsKeys)[dir][0] *
                      m_metricinfo->GetJac(ptsKeys)[0];
 
                returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(
                    fac, WeakDerivStd);
            }
        }
        break;
        case StdRegions::eLaplacian:
        {
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                fac = 1.0;
                goto UseLocRegionsMatrix;
            }
            else
            {
                int coordim = m_geom->GetCoordim();
                fac         = 0.0;
                for (int i = 0; i < coordim; ++i)
                {
                    fac += m_metricinfo->GetDerivFactors(ptsKeys)[i][0] *
                           m_metricinfo->GetDerivFactors(ptsKeys)[i][0];
                }
                fac *= m_metricinfo->GetJac(ptsKeys)[0];
                goto UseStdRegionsMatrix;
            }
        }
        break;
        case StdRegions::eLinearAdvection:
        {
            if ((m_metricinfo->GetGtype() == SpatialDomains::eDeformed) ||
                (mkey.GetNVarCoeff()))
            {
                fac = 1.0;
                goto UseLocRegionsMatrix;
            }
            else
            {
                fac = (m_metricinfo->GetJac(ptsKeys))[0];
                goto UseStdRegionsMatrix;
            }
        }
        break;
        case StdRegions::eHelmholtz:
        {
            NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorLambda);
            MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
            DNekScalMat &MassMat = *(this->m_matrixManager[masskey]);
            MatrixKey lapkey(StdRegions::eLaplacian, mkey.GetShapeType(), *this,
                             mkey.GetConstFactors(), mkey.GetVarCoeffs());
            DNekScalMat &LapMat = *(this->m_matrixManager[lapkey]);
 
            int rows = LapMat.GetRows();
            int cols = LapMat.GetColumns();
 
            DNekMatSharedPtr helm =
                MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
 
            NekDouble one = 1.0;
            (*helm)       = LapMat + factor * MassMat;
 
            returnval =
                MemoryManager<DNekScalMat>::AllocateSharedPtr(one, helm);
        }
        break;
        case StdRegions::eLinearAdvectionReaction:
        {
            NekDouble lambda = mkey.GetConstFactor(StdRegions::eFactorLambda);
 
            // Construct mass matrix
            // Check for mass-specific varcoeffs to avoid unncessary
            // re-computation of the elemental matrix every time step
            StdRegions::VarCoeffMap massVarcoeffs = StdRegions::NullVarCoeffMap;
            if (mkey.HasVarCoeff(StdRegions::eVarCoeffMass))
            {
                massVarcoeffs[StdRegions::eVarCoeffMass] =
                    mkey.GetVarCoeff(StdRegions::eVarCoeffMass);
            }
            MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this,
                              mkey.GetConstFactors(), massVarcoeffs);
            DNekScalMat &MassMat = *GetLocMatrix(masskey);
 
            // Construct advection matrix
            // Check for varcoeffs not required;
            // assume advection velocity is always time-dependent
            MatrixKey advkey(mkey, StdRegions::eLinearAdvection);
            DNekScalMat &AdvMat = *GetLocMatrix(advkey);
 
            int rows = MassMat.GetRows();
            int cols = MassMat.GetColumns();
 
            DNekMatSharedPtr adr =
                MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
 
            NekDouble one = 1.0;
            (*adr)        = -lambda * MassMat + AdvMat;
 
            returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, adr);
 
            // Clear memory for time-dependent matrices
            DropLocMatrix(advkey);
            if (!massVarcoeffs.empty())
            {
                DropLocMatrix(masskey);
            }
        }
        break;
        case StdRegions::eLinearAdvectionDiffusionReaction:
        {
            NekDouble lambda = mkey.GetConstFactor(StdRegions::eFactorLambda);
 
            // Construct mass matrix
            // Check for mass-specific varcoeffs to avoid unncessary
            // re-computation of the elemental matrix every time step
            StdRegions::VarCoeffMap massVarcoeffs = StdRegions::NullVarCoeffMap;
            if (mkey.HasVarCoeff(StdRegions::eVarCoeffMass))
            {
                massVarcoeffs[StdRegions::eVarCoeffMass] =
                    mkey.GetVarCoeff(StdRegions::eVarCoeffMass);
            }
            MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this,
                              mkey.GetConstFactors(), massVarcoeffs);
            DNekScalMat &MassMat = *GetLocMatrix(masskey);
 
            // Construct laplacian matrix (Check for varcoeffs)
            // Take all varcoeffs if one or more are detected
            // TODO We might want to have a map
            // from MatrixType to Vector of Varcoeffs and vice-versa
            StdRegions::VarCoeffMap lapVarcoeffs = StdRegions::NullVarCoeffMap;
            if ((mkey.HasVarCoeff(StdRegions::eVarCoeffLaplacian)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD00)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD01)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD10)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD02)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD20)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD11)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD12)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD21)) ||
                (mkey.HasVarCoeff(StdRegions::eVarCoeffD22)))
            {
                lapVarcoeffs = mkey.GetVarCoeffs();
            }
            MatrixKey lapkey(StdRegions::eLaplacian, mkey.GetShapeType(), *this,
                             mkey.GetConstFactors(), lapVarcoeffs);
            DNekScalMat &LapMat = *GetLocMatrix(lapkey);
 
            // Construct advection matrix
            // Check for varcoeffs not required;
            // assume advection velocity is always time-dependent
            MatrixKey advkey(mkey, StdRegions::eLinearAdvection);
            DNekScalMat &AdvMat = *GetLocMatrix(advkey);
 
            int rows = LapMat.GetRows();
            int cols = LapMat.GetColumns();
 
            DNekMatSharedPtr adr =
                MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
 
            NekDouble one = 1.0;
            (*adr)        = LapMat - lambda * MassMat + AdvMat;
 
            returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, adr);
 
            // Clear memory for time-dependent matrices
            DropLocMatrix(advkey);
            if (!massVarcoeffs.empty())
            {
                DropLocMatrix(masskey);
            }
            if (!lapVarcoeffs.empty())
            {
                DropLocMatrix(lapkey);
            }
        }
        break;
        case StdRegions::eHybridDGHelmholtz:
        case StdRegions::eHybridDGLamToU:
        case StdRegions::eHybridDGLamToQ0:
        case StdRegions::eHybridDGHelmBndLam:
        {
            NekDouble one = 1.0;
 
            DNekMatSharedPtr mat = GenMatrix(mkey);
            returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
        }
        break;
        case StdRegions::eInvHybridDGHelmholtz:
        {
            NekDouble one = 1.0;
 
            //                  StdRegions::StdMatrixKey
            //                  hkey(StdRegions::eHybridDGHelmholtz,
            //                                                DetShapeType(),*this,
            //                                                mkey.GetConstant(0),
            //                                                mkey.GetConstant(1));
            MatrixKey hkey(StdRegions::eHybridDGHelmholtz, DetShapeType(),
                           *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
            DNekMatSharedPtr mat = GenMatrix(hkey);
 
            mat->Invert();
            returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
        }
        break;
        case StdRegions::eInterpGauss:
        {
            DNekMatSharedPtr m_Ix;
            Array<OneD, NekDouble> coords(1, 0.0);
            StdRegions::ConstFactorMap factors = mkey.GetConstFactors();
            int vertex = (int)factors[StdRegions::eFactorGaussVertex];
 
            coords[0] = (vertex == 0) ? -1.0 : 1.0;
 
            m_Ix = m_base[0]->GetI(coords);
            returnval =
                MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, m_Ix);
        }
        break;
 
        UseLocRegionsMatrix:
        {
            DNekMatSharedPtr mat = GenMatrix(mkey);
            returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(fac, mat);
        }
        break;
        UseStdRegionsMatrix:
        {
            DNekMatSharedPtr mat = GetStdMatrix(mkey);
            returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(fac, mat);
        }
        break;
        default:
        {
            NekDouble one        = 1.0;
            DNekMatSharedPtr mat = GenMatrix(mkey);
 
            returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, mat);
        }
        break;
    }
 
    return returnval;
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), ASSERTL1, ASSERTL2, Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::LocalRegions::Expansion::DropLocMatrix(), Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::eFactorGaussVertex, Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eHelmholtz, Nektar::StdRegions::eHybridDGHelmBndLam, Nektar::StdRegions::eHybridDGHelmholtz, Nektar::StdRegions::eHybridDGLamToQ0, Nektar::StdRegions::eHybridDGLamToU, Nektar::StdRegions::eInterpGauss, Nektar::StdRegions::eInvHybridDGHelmholtz, Nektar::StdRegions::eInvMass, Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eLinearAdvection, Nektar::StdRegions::eLinearAdvectionDiffusionReaction, Nektar::StdRegions::eLinearAdvectionReaction, Nektar::StdRegions::eMass, Nektar::SpatialDomains::eNoGeomType, Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD01, Nektar::StdRegions::eVarCoeffD02, Nektar::StdRegions::eVarCoeffD10, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD12, Nektar::StdRegions::eVarCoeffD20, Nektar::StdRegions::eVarCoeffD21, Nektar::StdRegions::eVarCoeffD22, Nektar::StdRegions::eVarCoeffLaplacian, Nektar::StdRegions::eVarCoeffMass, Nektar::StdRegions::eWeakDeriv0, Nektar::StdRegions::eWeakDeriv1, Nektar::StdRegions::eWeakDeriv2, Nektar::StdRegions::StdExpansion::GenMatrix(), Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetConstFactors(), Nektar::SpatialDomains::Geometry::GetCoordim(), Nektar::LocalRegions::Expansion::GetLocMatrix(), Nektar::StdRegions::StdMatrixKey::GetMatrixType(), Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdMatrixKey::GetShapeType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdMatrixKey::GetVarCoeff(), Nektar::StdRegions::StdMatrixKey::GetVarCoeffs(), Nektar::StdRegions::StdMatrixKey::HasVarCoeff(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, m_matrixManager, Nektar::LocalRegions::Expansion::m_metricinfo, and Nektar::StdRegions::NullVarCoeffMap.

MultiplyByElmtInvMass()

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

private

Todo:

Same method exists in ExpList and everyone references ExpList::MultiplyByElmtInvMass. Remove this one?

Definition at line 1529 of file SegExp.cpp.

{
    // get Mass matrix inverse
    MatrixKey masskey(StdRegions::eInvMass, DetShapeType(), *this);
    DNekScalMatSharedPtr matsys = m_matrixManager[masskey];
 
    NekVector<NekDouble> in(m_ncoeffs, inarray, eCopy);
    NekVector<NekDouble> out(m_ncoeffs, outarray, eWrapper);
 
    out = (*matsys) * in;
}

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, m_matrixManager, and Nektar::StdRegions::StdExpansion::m_ncoeffs.

ReverseCoeffsAndSign()

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

private

Reverse the coefficients in a boundary interior expansion this routine is of use when we need the segment coefficients corresponding to a expansion in the reverse coordinate direction.

Definition at line 1488 of file SegExp.cpp.

{
 
    int m;
    NekDouble sgn = 1;
 
    ASSERTL1(&inarray[0] != &outarray[0],
             "inarray and outarray can not be the same");
    switch (GetBasisType(0))
    {
        case LibUtilities::eModified_A:
            // Swap vertices
            outarray[0] = inarray[1];
            outarray[1] = inarray[0];
            // negate odd modes
            for (m = 2; m < m_ncoeffs; ++m)
            {
                outarray[m] = sgn * inarray[m];
                sgn         = -sgn;
            }
            break;
        case LibUtilities::eGLL_Lagrange:
        case LibUtilities::eGauss_Lagrange:
            for (m = 0; m < m_ncoeffs; ++m)
            {
                outarray[m_ncoeffs - 1 - m] = inarray[m];
            }
            break;
        default:
            ASSERTL0(false, "This basis is not allowed in this method");
            break;
    }
}

References ASSERTL0, ASSERTL1, Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_ncoeffs.

Referenced by v_SetCoeffsToOrientation().

v_ComputeTraceNormal()

void Nektar::LocalRegions::SegExp::v_ComputeTraceNormal ( const int  vertex )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 833 of file SegExp.cpp.

{
    int i;
    const SpatialDomains::GeomFactorsSharedPtr &geomFactors =
        GetGeom()->GetMetricInfo();
    SpatialDomains::GeomType type = geomFactors->GetGtype();
    const Array<TwoD, const NekDouble> &gmat =
        geomFactors->GetDerivFactors(GetPointsKeys());
    int nqe       = 1;
    int vCoordDim = GetCoordim();
 
    m_traceNormals[vertex] = Array<OneD, Array<OneD, NekDouble>>(vCoordDim);
    Array<OneD, Array<OneD, NekDouble>> &normal = m_traceNormals[vertex];
    for (i = 0; i < vCoordDim; ++i)
    {
        normal[i] = Array<OneD, NekDouble>(nqe);
    }
 
    size_t nqb                     = nqe;
    size_t nbnd                    = vertex;
    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 vert;
        // Set up normals
        switch (vertex)
        {
            case 0:
                for (i = 0; i < vCoordDim; ++i)
                {
                    Vmath::Fill(nqe, -gmat[i][0], normal[i], 1);
                }
                break;
            case 1:
                for (i = 0; i < vCoordDim; ++i)
                {
                    Vmath::Fill(nqe, gmat[i][0], normal[i], 1);
                }
                break;
            default:
                ASSERTL0(false, "point is out of range (point < 2)");
        }
 
        // normalise
        vert = 0.0;
        for (i = 0; i < vCoordDim; ++i)
        {
            vert += normal[i][0] * normal[i][0];
        }
        vert = 1.0 / sqrt(vert);
 
        Vmath::Fill(nqb, vert, length, 1);
 
        for (i = 0; i < vCoordDim; ++i)
        {
            Vmath::Smul(nqe, vert, normal[i], 1, normal[i], 1);
        }
    }
}

References ASSERTL0, Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::LocalRegions::Expansion::GetGeom(), Nektar::SpatialDomains::Geometry::GetMetricInfo(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::LocalRegions::Expansion::m_elmtBndNormDirElmtLen, Nektar::LocalRegions::Expansion::m_traceNormals, Vmath::Smul(), and tinysimd::sqrt().

v_CreateStdMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1118 of file SegExp.cpp.

{
    LibUtilities::BasisKey bkey = m_base[0]->GetBasisKey();
    StdRegions::StdSegExpSharedPtr tmp =
        MemoryManager<StdSegExp>::AllocateSharedPtr(bkey);
 
    return tmp->GetStdMatrix(mkey);
}

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

v_DropLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1113 of file SegExp.cpp.

{
    m_matrixManager.DeleteObject(mkey);
}

References m_matrixManager.

v_DropLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1103 of file SegExp.cpp.

{
    m_staticCondMatrixManager.DeleteObject(mkey);
}

References m_staticCondMatrixManager.

v_ExtractDataToCoeffs()

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

overrideprotectedvirtual

Unpack data from input file assuming it comes from.

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 791 of file SegExp.cpp.

{
    switch (m_base[0]->GetBasisType())
    {
        case LibUtilities::eModified_A:
        {
            int fillorder = min((int)nummodes[mode_offset], m_ncoeffs);
 
            Vmath::Zero(m_ncoeffs, coeffs, 1);
            Vmath::Vcopy(fillorder, &data[0], 1, &coeffs[0], 1);
        }
        break;
        case LibUtilities::eGLL_Lagrange:
        {
            // Assume that input is also Gll_Lagrange
            // but no way to check;
            LibUtilities::PointsKey f0(nummodes[mode_offset],
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::PointsKey t0(m_base[0]->GetNumModes(),
                                       LibUtilities::eGaussLobattoLegendre);
            LibUtilities::Interp1D(f0, data, t0, coeffs);
        }
        break;
        case LibUtilities::eGauss_Lagrange:
        {
            // Assume that input is also Gauss_Lagrange
            // but no way to check;
            LibUtilities::PointsKey f0(nummodes[mode_offset],
                                       LibUtilities::eGaussGaussLegendre);
            LibUtilities::PointsKey t0(m_base[0]->GetNumModes(),
                                       LibUtilities::eGaussGaussLegendre);
            LibUtilities::Interp1D(f0, data, t0, coeffs);
        }
        break;
        default:
            ASSERTL0(false, "basis is either not set up or not hierarchicial");
    }
}

References ASSERTL0, Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, tinysimd::min(), Vmath::Vcopy(), and Vmath::Zero().

v_FwdTrans()

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

overrideprotectedvirtual

Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in outarray.

Perform a forward transform using a Galerkin projection by taking the inner product of the physical points and multiplying by the inverse of the mass matrix using the Solve method of the standard matrix container holding the local mass matrix, i.e. \( {\bf \hat{u}} = {\bf M}^{-1} {\bf I} \) where \( {\bf I}[p] = \int^1_{-1} \phi_p(\xi_1) u(\xi_1) d\xi_1 \)

Inputs:

• inarray: array of physical quadrature points to be transformed

Outputs:

• outarray: updated array of expansion coefficients.

Implements Nektar::StdRegions::StdExpansion.

Definition at line 346 of file SegExp.cpp.

{
    if (m_base[0]->Collocation())
    {
        Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
    }
    else
    {
        v_IProductWRTBase(inarray, outarray);
 
        // get Mass matrix inverse
        MatrixKey masskey(StdRegions::eInvMass, DetShapeType(), *this);
        DNekScalMatSharedPtr matsys = m_matrixManager[masskey];
 
        // copy inarray in case inarray == outarray
        NekVector<NekDouble> in(m_ncoeffs, outarray, eCopy);
        NekVector<NekDouble> out(m_ncoeffs, outarray, eWrapper);
 
        out = (*matsys) * in;
    }
}

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::m_base, m_matrixManager, Nektar::StdRegions::StdExpansion::m_ncoeffs, v_IProductWRTBase(), and Vmath::Vcopy().

Referenced by v_FwdTransBndConstrained().

v_FwdTransBndConstrained()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 369 of file SegExp.cpp.

{
    if (m_base[0]->Collocation())
    {
        Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
    }
    else
    {
        int nInteriorDofs = m_ncoeffs - 2;
        int offset        = 0;
        bool hasEndPoints = true;
        bool hasEndModes  = true;
 
        switch (m_base[0]->GetBasisType())
        {
            case LibUtilities::eGLL_Lagrange:
            {
                nInteriorDofs = m_ncoeffs - 2;
                offset        = 1;
                hasEndModes   = true;
            }
            break;
            case LibUtilities::eOrtho_A:
            case LibUtilities::eGauss_Lagrange:
            {
                nInteriorDofs = m_ncoeffs;
                offset        = 0;
                hasEndModes   = false;
            }
            break;
            case LibUtilities::eModified_A:
            case LibUtilities::eModified_B:
            {
                nInteriorDofs = m_ncoeffs - 2;
                offset        = 2;
                hasEndModes   = true;
            }
            break;
            default:
                ASSERTL0(false, "This type of FwdTrans is not defined"
                                "for this expansion type");
        }
 
        switch (m_base[0]->GetPointsType())
        {
            case LibUtilities::eGaussGaussLegendre:
            case LibUtilities::eGaussGaussChebyshev:
            case LibUtilities::eGaussKronrodLegendre:
            {
                hasEndPoints = false;
            }
            break;
            case LibUtilities::eGaussLegendreWithMP:
            case LibUtilities::eGaussLobattoLegendre:
            case LibUtilities::eGaussLobattoChebyshev:
            case LibUtilities::eGaussLobattoKronrodLegendre:
            case LibUtilities::ePolyEvenlySpaced:
            case LibUtilities::eFourierEvenlySpaced:
            {
                hasEndPoints = true;
            }
            break;
            default:
                ASSERTL0(false, "FwdTransBndConstrained cannot be used "
                                "with this point type");
        }
 
        fill(outarray.data(), outarray.data() + m_ncoeffs, 0.0);
 
        if (hasEndPoints && hasEndModes)
        {
 
            outarray[GetVertexMap(0)] = inarray[0];
            outarray[GetVertexMap(1)] = inarray[m_base[0]->GetNumPoints() - 1];
 
            if (m_ncoeffs > 2)
            {
                // ideally, we would like to have tmp0 to be replaced
                // by outarray (currently MassMatrixOp does not allow
                // aliasing)
                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)
                MatrixKey masskey(StdRegions::eMass, DetShapeType(), *this);
                DNekScalMatSharedPtr matsys =
                    (m_staticCondMatrixManager[masskey])->GetBlock(1, 1);
 
                Blas::Dgemv('N', nInteriorDofs, nInteriorDofs, matsys->Scale(),
                            &((matsys->GetOwnedMatrix())->GetPtr())[0],
                            nInteriorDofs, tmp1.data() + offset, 1, 0.0,
                            outarray.data() + offset, 1);
            }
        }
        else
        {
            SegExp::v_FwdTrans(inarray, outarray);
        }
    }
}

References ASSERTL0, Nektar::StdRegions::StdExpansion::DetShapeType(), Blas::Dgemv(), Nektar::LibUtilities::eFourierEvenlySpaced, Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGaussGaussChebyshev, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLegendreWithMP, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGLL_Lagrange, Nektar::StdRegions::eMass, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::ePolyEvenlySpaced, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::GetVertexMap(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, m_staticCondMatrixManager, Nektar::StdRegions::StdExpansion::MassMatrixOp(), v_FwdTrans(), v_IProductWRTBase(), Vmath::Vcopy(), and Vmath::Vsub().

v_GenMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1458 of file SegExp.cpp.

{
    DNekMatSharedPtr returnval;
 
    switch (mkey.GetMatrixType())
    {
        case StdRegions::eHybridDGHelmholtz:
        case StdRegions::eHybridDGLamToU:
        case StdRegions::eHybridDGLamToQ0:
        case StdRegions::eHybridDGLamToQ1:
        case StdRegions::eHybridDGLamToQ2:
        case StdRegions::eHybridDGHelmBndLam:
            returnval = Expansion1D::v_GenMatrix(mkey);
            break;
        default:
            returnval = StdSegExp::v_GenMatrix(mkey);
            break;
    }
 
    return returnval;
}

References Nektar::StdRegions::eHybridDGHelmBndLam, Nektar::StdRegions::eHybridDGHelmholtz, Nektar::StdRegions::eHybridDGLamToQ0, Nektar::StdRegions::eHybridDGLamToQ1, Nektar::StdRegions::eHybridDGLamToQ2, Nektar::StdRegions::eHybridDGLamToU, Nektar::StdRegions::StdMatrixKey::GetMatrixType(), and Nektar::LocalRegions::Expansion1D::v_GenMatrix().

v_GetCoord()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 654 of file SegExp.cpp.

{
    int i;
 
    ASSERTL1(Lcoords[0] >= -1.0 && Lcoords[0] <= 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::SegExp::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 669 of file SegExp.cpp.

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

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

v_GetLinStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 765 of file SegExp.cpp.

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

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

v_GetLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1108 of file SegExp.cpp.

{
    return m_matrixManager[mkey];
}

References m_matrixManager.

v_GetLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1098 of file SegExp.cpp.

{
    return m_staticCondMatrixManager[mkey];
}

References m_staticCondMatrixManager.

v_GetPhysNormals()

const Array< OneD, const NekDouble > & Nektar::LocalRegions::SegExp::v_GetPhysNormals ( void  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 773 of file SegExp.cpp.

{
    NEKERROR(ErrorUtil::efatal, "Got to SegExp");
    return NullNekDouble1DArray;
}

References Nektar::ErrorUtil::efatal, NEKERROR, and Nektar::NullNekDouble1DArray.

v_GetStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 759 of file SegExp.cpp.

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

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

v_GetTracePhysMap()

void Nektar::LocalRegions::SegExp::v_GetTracePhysMap ( const int  vertex, Array< OneD, int > &  map  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 725 of file SegExp.cpp.

{
    int nquad = m_base[0]->GetNumPoints();
 
    ASSERTL1(vertex == 0 || vertex == 1, "Vertex value should be 0 or 1");
 
    map = Array<OneD, int>(1);
 
    map[0] = vertex == 0 ? 0 : nquad - 1;
}

References ASSERTL1, and Nektar::StdRegions::StdExpansion::m_base.

v_GetTracePhysVals()

void Nektar::LocalRegions::SegExp::v_GetTracePhysVals ( const int  edge, const StdRegions::StdExpansionSharedPtr &  EdgeExp, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, StdRegions::Orientation  orient  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 712 of file SegExp.cpp.

{
    NekDouble result;
    v_GetVertexPhysVals(edge, inarray, result);
    outarray[0] = result;
}

References v_GetVertexPhysVals().

v_GetVertexPhysVals()

void Nektar::LocalRegions::SegExp::v_GetVertexPhysVals ( const int  vertex, const Array< OneD, const NekDouble > &  inarray, NekDouble &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 677 of file SegExp.cpp.

{
    int nquad = m_base[0]->GetNumPoints();
 
    if (m_base[0]->GetPointsType() != LibUtilities::eGaussGaussLegendre)
    {
        switch (vertex)
        {
            case 0:
                outarray = inarray[0];
                break;
            case 1:
                outarray = inarray[nquad - 1];
                break;
        }
    }
    else
    {
        StdRegions::ConstFactorMap factors;
        factors[StdRegions::eFactorGaussVertex] = vertex;
 
        StdRegions::StdMatrixKey key(StdRegions::eInterpGauss, DetShapeType(),
                                     *this, factors);
 
        DNekScalMatSharedPtr mat_gauss = m_matrixManager[key];
 
        outarray =
            Blas::Ddot(nquad, mat_gauss->GetOwnedMatrix()->GetPtr().data(), 1,
                       &inarray[0], 1);
    }
}

References Blas::Ddot(), Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eFactorGaussVertex, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::StdRegions::eInterpGauss, Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::m_base, and m_matrixManager.

Referenced by v_GetTracePhysVals().

v_HelmholtzMatrixOp()

void Nektar::LocalRegions::SegExp::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 999 of file SegExp.cpp.

{
    int nquad = m_base[0]->GetNumPoints();
    const Array<TwoD, const NekDouble> &gmat =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
    const NekDouble lambda = mkey.GetConstFactor(StdRegions::eFactorLambda);
 
    Array<OneD, NekDouble> physValues(nquad);
    Array<OneD, NekDouble> dPhysValuesdx(nquad);
    Array<OneD, NekDouble> wsp(m_ncoeffs);
 
    BwdTrans(inarray, physValues);
 
    // mass matrix operation
    v_IProductWRTBase((m_base[0]->GetBdata()), physValues, wsp, 1);
 
    // Laplacian matrix operation
    switch (m_geom->GetCoordim())
    {
        case 1:
        {
            PhysDeriv(physValues, dPhysValuesdx);
 
            // multiply with the proper geometric factors
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nquad, &gmat[0][0], 1, dPhysValuesdx.data(), 1,
                            dPhysValuesdx.data(), 1);
            }
            else
            {
                Blas::Dscal(nquad, gmat[0][0], dPhysValuesdx.data(), 1);
            }
        }
        break;
        case 2:
        {
            Array<OneD, NekDouble> dPhysValuesdy(nquad);
 
            PhysDeriv(physValues, dPhysValuesdx, dPhysValuesdy);
 
            // multiply with the proper geometric factors
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nquad, &gmat[0][0], 1, dPhysValuesdx.data(), 1,
                            dPhysValuesdx.data(), 1);
                Vmath::Vvtvp(nquad, &gmat[1][0], 1, dPhysValuesdy.data(), 1,
                             dPhysValuesdx.data(), 1, dPhysValuesdx.data(), 1);
            }
            else
            {
                Blas::Dscal(nquad, gmat[0][0], dPhysValuesdx.data(), 1);
                Blas::Daxpy(nquad, gmat[1][0], dPhysValuesdy.data(), 1,
                            dPhysValuesdx.data(), 1);
            }
        }
        break;
        case 3:
        {
            Array<OneD, NekDouble> dPhysValuesdy(nquad);
            Array<OneD, NekDouble> dPhysValuesdz(nquad);
 
            PhysDeriv(physValues, dPhysValuesdx, dPhysValuesdy, dPhysValuesdz);
 
            // multiply with the proper geometric factors
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nquad, &gmat[0][0], 1, dPhysValuesdx.data(), 1,
                            dPhysValuesdx.data(), 1);
                Vmath::Vvtvp(nquad, &gmat[1][0], 1, dPhysValuesdy.data(), 1,
                             dPhysValuesdx.data(), 1, dPhysValuesdx.data(), 1);
                Vmath::Vvtvp(nquad, &gmat[2][0], 1, dPhysValuesdz.data(), 1,
                             dPhysValuesdx.data(), 1, dPhysValuesdx.data(), 1);
            }
            else
            {
                Blas::Dscal(nquad, gmat[0][0], dPhysValuesdx.data(), 1);
                Blas::Daxpy(nquad, gmat[1][0], dPhysValuesdy.data(), 1,
                            dPhysValuesdx.data(), 1);
                Blas::Daxpy(nquad, gmat[2][0], dPhysValuesdz.data(), 1,
                            dPhysValuesdx.data(), 1);
            }
        }
        break;
        default:
            ASSERTL0(false, "Wrong number of dimensions");
            break;
    }
 
    v_IProductWRTBase(m_base[0]->GetDbdata(), dPhysValuesdx, outarray, 1);
    Blas::Daxpy(m_ncoeffs, lambda, wsp.data(), 1, outarray.data(), 1);
}

References ASSERTL0, Nektar::StdRegions::StdExpansion::BwdTrans(), Blas::Daxpy(), Blas::Dscal(), Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::SpatialDomains::Geometry::GetCoordim(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::PhysDeriv(), v_IProductWRTBase(), Vmath::Vmul(), and Vmath::Vvtvp().

v_Integral()

NekDouble Nektar::LocalRegions::SegExp::v_Integral ( const Array< OneD, const NekDouble > &  inarray )

overrideprotectedvirtual

Integrate the physical point list inarray over region and return the value.

Inputs:

• inarray: definition of function to be returned at quadrature point of expansion.

Outputs:

• returns \(\int^1_{-1} u(\xi_1)d \xi_1 \) where \(inarray[i] = u(\xi_{1i}) \)

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 98 of file SegExp.cpp.

{
    int nquad0                       = m_base[0]->GetNumPoints();
    Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
    NekDouble ival;
    Array<OneD, NekDouble> tmp(nquad0);
 
    // multiply inarray with Jacobian
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nquad0, jac, 1, inarray, 1, tmp, 1);
    }
    else
    {
        Vmath::Smul(nquad0, jac[0], inarray, 1, tmp, 1);
    }
 
    // call StdSegExp version;
    ival = StdSegExp::v_Integral(tmp);
    // ival = StdSegExp::Integral(tmp);
    return ival;
}

References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Smul(), and Vmath::Vmul().

v_IProductWRTBase() [1/2]

void Nektar::LocalRegions::SegExp::v_IProductWRTBase ( const Array< OneD, const NekDouble > &  base, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, int  coll_check  )

overrideprotectedvirtual

Inner product of inarray over region with respect to expansion basis base and return in outarray.

Calculate \( I[p] = \int^{1}_{-1} \phi_p(\xi_1) u(\xi_1) d\xi_1 = \sum_{i=0}^{nq-1} \phi_p(\xi_{1i}) u(\xi_{1i}) w_i \) where \( outarray[p] = I[p], inarray[i] = u(\xi_{1i}), base[p*nq+i] = \phi_p(\xi_{1i}) \).

Inputs:

• base: an array definiing the local basis for the inner product usually passed from Basis->get_bdata() or Basis->get_Dbdata()
• inarray: physical point array of function to be integrated \( u(\xi_1) \)
• coll_check: Flag to identify when a Basis->collocation() call should be performed to see if this is a GLL_Lagrange basis with a collocation property. (should be set to 0 if taking the inner product with respect to the derivative of basis)

Output:

• outarray: array of coefficients representing the inner product of function with ever mode in the exapnsion

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 531 of file SegExp.cpp.

{
    int nquad0                       = m_base[0]->GetNumPoints();
    Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
    Array<OneD, NekDouble> tmp(nquad0);
 
    // multiply inarray with Jacobian
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nquad0, jac, 1, inarray, 1, tmp, 1);
    }
    else
    {
        Vmath::Smul(nquad0, jac[0], inarray, 1, tmp, 1);
    }
    StdSegExp::v_IProductWRTBase(base, tmp, outarray, coll_check);
}

References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Smul(), and Vmath::Vmul().

v_IProductWRTBase() [2/2]

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

overrideprotectedvirtual

Inner product of inarray over region with respect to the expansion basis (this)->_Base[0] and return in outarray.

Wrapper call to SegExp::IProduct_WRT_B

Input:

• inarray: array of function evaluated at the physical collocation points

Output:

• outarray: array of inner product with respect to each basis over region

Implements Nektar::StdRegions::StdExpansion.

Definition at line 498 of file SegExp.cpp.

{
    v_IProductWRTBase(m_base[0]->GetBdata(), inarray, outarray, 1);
}

References Nektar::StdRegions::StdExpansion::m_base, and v_IProductWRTBase().

Referenced by v_FwdTrans(), v_FwdTransBndConstrained(), v_HelmholtzMatrixOp(), v_IProductWRTBase(), v_IProductWRTDerivBase(), v_LaplacianMatrixOp(), and v_NormVectorIProductWRTBase().

v_IProductWRTDerivBase()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 551 of file SegExp.cpp.

{
    ASSERTL1(dir < 3, "input dir is out of range");
    ASSERTL1((dir == 2) ? m_geom->GetCoordim() == 3 : true,
             "input dir is out of range");
 
    int nquad = m_base[0]->GetNumPoints();
    const Array<TwoD, const NekDouble> &gmat =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    Array<OneD, NekDouble> tmp1(nquad);
 
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nquad, gmat[dir], 1, inarray, 1, tmp1, 1);
    }
    else
    {
        Vmath::Smul(nquad, gmat[dir][0], inarray, 1, tmp1, 1);
    }
 
    v_IProductWRTBase(m_base[0]->GetDbdata(), tmp1, outarray, 1);
}

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

v_LaplacianMatrixOp() [1/2]

void Nektar::LocalRegions::SegExp::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 901 of file SegExp.cpp.

{
    int nquad = m_base[0]->GetNumPoints();
    const Array<TwoD, const NekDouble> &gmat =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    Array<OneD, NekDouble> physValues(nquad);
    Array<OneD, NekDouble> dPhysValuesdx(nquad);
 
    BwdTrans(inarray, physValues);
 
    // Laplacian matrix operation
    switch (m_geom->GetCoordim())
    {
        case 1:
        {
            PhysDeriv(physValues, dPhysValuesdx);
 
            // multiply with the proper geometric factors
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nquad, &gmat[0][0], 1, dPhysValuesdx.data(), 1,
                            dPhysValuesdx.data(), 1);
            }
            else
            {
                Blas::Dscal(nquad, gmat[0][0], dPhysValuesdx.data(), 1);
            }
        }
        break;
        case 2:
        {
            Array<OneD, NekDouble> dPhysValuesdy(nquad);
 
            PhysDeriv(physValues, dPhysValuesdx, dPhysValuesdy);
 
            // multiply with the proper geometric factors
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nquad, &gmat[0][0], 1, dPhysValuesdx.data(), 1,
                            dPhysValuesdx.data(), 1);
                Vmath::Vvtvp(nquad, &gmat[1][0], 1, dPhysValuesdy.data(), 1,
                             dPhysValuesdx.data(), 1, dPhysValuesdx.data(), 1);
            }
            else
            {
                Blas::Dscal(nquad, gmat[0][0], dPhysValuesdx.data(), 1);
                Blas::Daxpy(nquad, gmat[1][0], dPhysValuesdy.data(), 1,
                            dPhysValuesdx.data(), 1);
            }
        }
        break;
        case 3:
        {
            Array<OneD, NekDouble> dPhysValuesdy(nquad);
            Array<OneD, NekDouble> dPhysValuesdz(nquad);
 
            PhysDeriv(physValues, dPhysValuesdx, dPhysValuesdy, dPhysValuesdz);
 
            // multiply with the proper geometric factors
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nquad, &gmat[0][0], 1, dPhysValuesdx.data(), 1,
                            dPhysValuesdx.data(), 1);
                Vmath::Vvtvp(nquad, &gmat[1][0], 1, dPhysValuesdy.data(), 1,
                             dPhysValuesdx.data(), 1, dPhysValuesdx.data(), 1);
                Vmath::Vvtvp(nquad, &gmat[2][0], 1, dPhysValuesdz.data(), 1,
                             dPhysValuesdx.data(), 1, dPhysValuesdx.data(), 1);
            }
            else
            {
                Blas::Dscal(nquad, gmat[0][0], dPhysValuesdx.data(), 1);
                Blas::Daxpy(nquad, gmat[1][0], dPhysValuesdy.data(), 1,
                            dPhysValuesdx.data(), 1);
                Blas::Daxpy(nquad, gmat[2][0], dPhysValuesdz.data(), 1,
                            dPhysValuesdx.data(), 1);
            }
        }
        break;
        default:
            ASSERTL0(false, "Wrong number of dimensions");
            break;
    }
 
    v_IProductWRTBase(m_base[0]->GetDbdata(), dPhysValuesdx, outarray, 1);
}

References ASSERTL0, Nektar::StdRegions::StdExpansion::BwdTrans(), Blas::Daxpy(), Blas::Dscal(), Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::Geometry::GetCoordim(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::PhysDeriv(), v_IProductWRTBase(), Vmath::Vmul(), and Vmath::Vvtvp().

v_LaplacianMatrixOp() [2/2]

void Nektar::LocalRegions::SegExp::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 991 of file SegExp.cpp.

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

v_NormVectorIProductWRTBase() [1/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 595 of file SegExp.cpp.

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

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

v_NormVectorIProductWRTBase() [2/2]

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 577 of file SegExp.cpp.

{
    int nq = m_base[0]->GetNumPoints();
    Array<OneD, NekDouble> Fn(nq);
 
    // @TODO: This routine no longer makes sense as a normal is not unique to an
    // edge
    const Array<OneD, const Array<OneD, NekDouble>> &normals =
        GetLeftAdjacentElementExp()->GetTraceNormal(
            GetLeftAdjacentElementTrace());
    Vmath::Vmul(nq, &Fx[0], 1, &normals[0][0], 1, &Fn[0], 1);
    Vmath::Vvtvp(nq, &Fy[0], 1, &normals[1][0], 1, &Fn[0], 1, &Fn[0], 1);
 
    v_IProductWRTBase(Fn, outarray);
}

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

v_NumBndryCoeffs()

int Nektar::LocalRegions::SegExp::v_NumBndryCoeffs ( ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 779 of file SegExp.cpp.

{
    return 2;
}

v_NumDGBndryCoeffs()

int Nektar::LocalRegions::SegExp::v_NumDGBndryCoeffs ( ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 784 of file SegExp.cpp.

{
    return 2;
}

v_PhysDeriv() [1/2]

void Nektar::LocalRegions::SegExp::v_PhysDeriv ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  out_d0, Array< OneD, NekDouble > &  out_d1 = NullNekDouble1DArray, Array< OneD, NekDouble > &  out_d2 = NullNekDouble1DArray  )

overrideprotectedvirtual

Evaluate the derivative \( d/d{\xi_1} \) at the physical quadrature points given by inarray and return in outarray.

This is a wrapper around StdExpansion1D::Tensor_Deriv

Input:

• n: number of derivatives to be evaluated where \( n \leq dim\)
• inarray: array of function evaluated at the quadrature points

Output:

• outarray: array of the derivatives \( du/d_{\xi_1}|_{\xi_{1i}} d\xi_1/dx, du/d_{\xi_1}|_{\xi_{1i}} d\xi_1/dy, du/d_{\xi_1}|_{\xi_{1i}} d\xi_1/dz, \) depending on value of dim

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 145 of file SegExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    Array<TwoD, const NekDouble> gmat =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
    Array<OneD, NekDouble> diff(nquad0);
 
    // StdExpansion1D::PhysTensorDeriv(inarray,diff);
    PhysTensorDeriv(inarray, diff);
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        if (out_d0.size())
        {
            Vmath::Vmul(nquad0, &gmat[0][0], 1, &diff[0], 1, &out_d0[0], 1);
        }
 
        if (out_d1.size())
        {
            Vmath::Vmul(nquad0, &gmat[1][0], 1, &diff[0], 1, &out_d1[0], 1);
        }
 
        if (out_d2.size())
        {
            Vmath::Vmul(nquad0, &gmat[2][0], 1, &diff[0], 1, &out_d2[0], 1);
        }
    }
    else
    {
        if (out_d0.size())
        {
            Vmath::Smul(nquad0, gmat[0][0], diff, 1, out_d0, 1);
        }
 
        if (out_d1.size())
        {
            Vmath::Smul(nquad0, gmat[1][0], diff, 1, out_d1, 1);
        }
 
        if (out_d2.size())
        {
            Vmath::Smul(nquad0, gmat[2][0], diff, 1, out_d2, 1);
        }
    }
}

References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion1D::PhysTensorDeriv(), Vmath::Smul(), and Vmath::Vmul().

Referenced by v_PhysDeriv_n().

v_PhysDeriv() [2/2]

void Nektar::LocalRegions::SegExp::v_PhysDeriv ( const int  dir, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  out_d0  )

overrideprotectedvirtual

Calculate the derivative of the physical points in a given direction.

See also

StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 289 of file SegExp.cpp.

{
    switch (dir)
    {
        case 0:
        {
            PhysDeriv(inarray, outarray, NullNekDouble1DArray,
                      NullNekDouble1DArray);
        }
        break;
        case 1:
        {
            PhysDeriv(inarray, NullNekDouble1DArray, outarray,
                      NullNekDouble1DArray);
        }
        break;
        case 2:
        {
            PhysDeriv(inarray, NullNekDouble1DArray, NullNekDouble1DArray,
                      outarray);
        }
        break;
        default:
        {
            ASSERTL1(false, "input dir is out of range");
        }
        break;
    }
}

References ASSERTL1, Nektar::NullNekDouble1DArray, and Nektar::StdRegions::StdExpansion::PhysDeriv().

v_PhysDeriv_n()

void Nektar::LocalRegions::SegExp::v_PhysDeriv_n ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  out_dn  )

overrideprotectedvirtual

Evaluate the derivative normal to a line: \( d/dn=\frac{spacedim}{||normal||}d/d{\xi} \). The derivative is calculated performing the product \( du/d{s}=\nabla u \cdot normal \).

Parameters

inarray	function to derive
out_dn	result of the derivative operation

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 240 of file SegExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    Array<TwoD, const NekDouble> gmat =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
    int coordim = m_geom->GetCoordim();
    Array<OneD, NekDouble> out_dn_tmp(nquad0, 0.0);
    switch (coordim)
    {
        case 2:
 
            Array<OneD, NekDouble> inarray_d0(nquad0);
            Array<OneD, NekDouble> inarray_d1(nquad0);
 
            v_PhysDeriv(inarray, inarray_d0, inarray_d1);
            Array<OneD, Array<OneD, NekDouble>> normals;
            normals = Array<OneD, Array<OneD, NekDouble>>(coordim);
            cout << "der_n" << endl;
            for (int k = 0; k < coordim; ++k)
            {
                normals[k] = Array<OneD, NekDouble>(nquad0);
            }
            // @TODO: this routine no longer makes sense, since normals are not
            // unique on
            //        an edge
            //        normals = GetMetricInfo()->GetNormal();
            for (int i = 0; i < nquad0; i++)
            {
                cout << "nx= " << normals[0][i] << "  ny=" << normals[1][i]
                     << endl;
            }
            ASSERTL0(normals != NullNekDoubleArrayOfArray,
                     "normal vectors do not exist: check if a"
                     "boundary region is defined as I ");
            // \nabla u \cdot normal
            Vmath::Vmul(nquad0, normals[0], 1, inarray_d0, 1, out_dn_tmp, 1);
            Vmath::Vadd(nquad0, out_dn_tmp, 1, out_dn, 1, out_dn, 1);
            Vmath::Zero(nquad0, out_dn_tmp, 1);
            Vmath::Vmul(nquad0, normals[1], 1, inarray_d1, 1, out_dn_tmp, 1);
            Vmath::Vadd(nquad0, out_dn_tmp, 1, out_dn, 1, out_dn, 1);
 
            for (int i = 0; i < nquad0; i++)
            {
                cout << "deps/dx =" << inarray_d0[i]
                     << "  deps/dy=" << inarray_d1[i] << endl;
            }
    }
}

References ASSERTL0, Nektar::SpatialDomains::Geometry::GetCoordim(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::NullNekDoubleArrayOfArray, v_PhysDeriv(), Vmath::Vadd(), Vmath::Vmul(), and Vmath::Zero().

v_PhysDeriv_s()

void Nektar::LocalRegions::SegExp::v_PhysDeriv_s ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  out_ds  )

overrideprotectedvirtual

Evaluate the derivative along a line: \( d/ds=\frac{spacedim}{||tangent||}d/d{\xi} \). The derivative is calculated performing the product \( du/d{s}=\nabla u \cdot tangent \).

Parameters

inarray	function to derive
out_ds	result of the derivative operation

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 201 of file SegExp.cpp.

{
    int nquad0  = m_base[0]->GetNumPoints();
    int coordim = m_geom->GetCoordim();
    Array<OneD, NekDouble> diff(nquad0);
    // this operation is needed if you put out_ds==inarray
    Vmath::Zero(nquad0, out_ds, 1);
    switch (coordim)
    {
        case 2:
            // diff= dU/de
            Array<OneD, NekDouble> diff(nquad0);
 
            PhysTensorDeriv(inarray, diff);
 
            // get dS/de= (Jac)^-1
            Array<OneD, NekDouble> Jac = m_metricinfo->GetJac(GetPointsKeys());
            if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                // calculate the derivative as (dU/de)*(Jac)^-1
                Vmath::Vdiv(nquad0, diff, 1, Jac, 1, out_ds, 1);
            }
            else
            {
                NekDouble invJac = 1 / Jac[0];
                Vmath::Smul(nquad0, invJac, diff, 1, out_ds, 1);
            }
    }
}

References Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::Geometry::GetCoordim(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion1D::PhysTensorDeriv(), Vmath::Smul(), Vmath::Vdiv(), and Vmath::Zero().

v_PhysEvalFirstDeriv()

NekDouble Nektar::LocalRegions::SegExp::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 630 of file SegExp.cpp.

{
    Array<OneD, NekDouble> Lcoord(1);
    ASSERTL0(m_geom, "m_geom not defined");
    m_geom->GetLocCoords(coord, Lcoord);
    return StdSegExp::v_PhysEvalFirstDeriv(Lcoord, inarray, firstOrderDerivs);
}

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

v_PhysEvalFirstSecondDeriv()

NekDouble Nektar::LocalRegions::SegExp::v_PhysEvalFirstSecondDeriv ( const Array< OneD, NekDouble > &  coord, const Array< OneD, const NekDouble > &  inarray, std::array< NekDouble, 3 > &  firstOrderDerivs, std::array< NekDouble, 6 > &  secondOrderDerivs  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 641 of file SegExp.cpp.

{
    Array<OneD, NekDouble> Lcoord(1);
    ASSERTL0(m_geom, "m_geom not defined");
    m_geom->GetLocCoords(coord, Lcoord);
    return StdSegExp::v_PhysEvalFirstSecondDeriv(
        Lcoord, inarray, firstOrderDerivs, secondOrderDerivs);
}

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

v_PhysEvaluate()

NekDouble Nektar::LocalRegions::SegExp::v_PhysEvaluate ( const Array< OneD, const NekDouble > &  coord, const Array< OneD, const NekDouble > &  physvals  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 619 of file SegExp.cpp.

{
    Array<OneD, NekDouble> Lcoord = Array<OneD, NekDouble>(1);
 
    ASSERTL0(m_geom, "m_geom not defined");
    m_geom->GetLocCoords(coord, Lcoord);
 
    return StdExpansion1D::v_PhysEvaluate(Lcoord, physvals);
}

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

v_SetCoeffsToOrientation()

void Nektar::LocalRegions::SegExp::v_SetCoeffsToOrientation ( StdRegions::Orientation  dir, Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 740 of file SegExp.cpp.

{
 
    if (dir == StdRegions::eBackwards)
    {
        if (&inarray[0] != &outarray[0])
        {
            Array<OneD, NekDouble> intmp(inarray);
            ReverseCoeffsAndSign(intmp, outarray);
        }
        else
        {
            ReverseCoeffsAndSign(inarray, outarray);
        }
    }
}

References Nektar::StdRegions::eBackwards, and ReverseCoeffsAndSign().

v_StdPhysEvaluate()

NekDouble Nektar::LocalRegions::SegExp::v_StdPhysEvaluate ( const Array< OneD, const NekDouble > &  Lcoord, const Array< OneD, const NekDouble > &  physvals  )

overrideprotectedvirtual

Given the local cartesian coordinate Lcoord evaluate the value of physvals at this point by calling through to the StdExpansion method

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 611 of file SegExp.cpp.

{
    // Evaluate point in local (eta) coordinates.
    return StdExpansion1D::v_PhysEvaluate(Lcoord, physvals);
}

Member Data Documentation

m_matrixManager

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

private

Definition at line 237 of file SegExp.h.

Referenced by CreateMatrix(), MultiplyByElmtInvMass(), v_DropLocMatrix(), v_FwdTrans(), v_GetLocMatrix(), and v_GetVertexPhysVals().

m_staticCondMatrixManager

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

private

Definition at line 239 of file SegExp.h.

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