#include <StdExpansion2D.h>

Inheritance diagram for Nektar::StdRegions::StdExpansion2D:

Collaboration diagram for Nektar::StdRegions::StdExpansion2D:

Public Member Functions
	StdExpansion2D ()

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

	StdExpansion2D (const StdExpansion2D &T)

virtual	~StdExpansion2D ()

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

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

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

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

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

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

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

virtual	~StdExpansion ()
	Destructor. More...

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

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

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

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

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

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

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

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

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

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

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

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

int	GetNedges () const
	This function returns the number of edges of the expansion domain. More...

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

int	GetTotalEdgeIntNcoeffs () const

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

int	DetCartesianDirOfEdge (const int edge)

const LibUtilities::BasisKey	DetEdgeBasisKey (const int i) const

const LibUtilities::BasisKey	DetFaceBasisKey (const int i, const int k) const

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

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

int	GetFaceIntNcoeffs (const int i) const

int	GetTotalFaceIntNcoeffs () const

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

LibUtilities::PointsKey	GetFacePointsKey (const int i, const int j) const

int	NumBndryCoeffs (void) const

int	NumDGBndryCoeffs (void) const

LibUtilities::BasisType	GetEdgeBasisType (const int i) const
	This function returns the type of expansion basis on the i-th edge. More...

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

int	GetNfaces () const
	This function returns the number of faces of the expansion domain. More...

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

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

boost::shared_ptr< StdExpansion >	GetStdExp (void) const

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

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion ()

bool	IsNodalNonTensorialExp ()

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

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

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

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

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

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

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

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

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

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

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

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

DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)

DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)

IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)

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

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

virtual void	SetUpPhysNormals (const int edge)

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)

StdRegions::Orientation	GetForient (int face)

StdRegions::Orientation	GetEorient (int edge)

StdRegions::Orientation	GetPorient (int point)

StdRegions::Orientation	GetCartesianEorient (int edge)

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

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

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	GetEdgeInteriorMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)

void	GetFaceNumModes (const int fid, const Orientation faceOrient, int &numModes0, int &numModes1)

void	GetFaceInteriorMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)

void	GetEdgeToElementMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int P=-1)

void	GetFaceToElementMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int nummodesA=-1, int nummodesB=-1)

void	GetEdgePhysVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Extract the physical values along edge edge from inarray into outarray following the local edge orientation and point distribution defined by defined in EdgeExp. More...

void	GetEdgePhysVals (const int edge, const boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GetTracePhysVals (const int edge, const boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GetVertexPhysVals (const int vertex, const Array< OneD, const NekDouble > &inarray, NekDouble &outarray)

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

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

void	GetFacePhysVals (const int face, const boost::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=eNoOrientation)

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

void	GetFacePhysMap (const int face, Array< OneD, int > &outarray)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)

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

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

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

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

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

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

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

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

void	AddRobinEdgeContribution (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, Array< OneD, NekDouble > &coeffs)

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

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

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

const boost::shared_ptr < SpatialDomains::GeomFactors > &	GetMetricInfo (void) const

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

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

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

virtual void	v_SetUpPhysNormals (const int edge)

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

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

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

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

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

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

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

virtual StdRegions::Orientation	v_GetForient (int face)

virtual StdRegions::Orientation	v_GetEorient (int edge)

virtual StdRegions::Orientation	v_GetCartesianEorient (int edge)

virtual StdRegions::Orientation	v_GetPorient (int point)

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

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

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

const NormalVector &	GetEdgeNormal (const int edge) const

void	ComputeEdgeNormal (const int edge)

void	NegateEdgeNormal (const int edge)

bool	EdgeNormalNegated (const int edge)

void	ComputeFaceNormal (const int face)

void	NegateFaceNormal (const int face)

bool	FaceNormalNegated (const int face)

void	ComputeVertexNormal (const int vertex)

const NormalVector &	GetFaceNormal (const int face) const

const NormalVector &	GetVertexNormal (const int vertex) const

const NormalVector &	GetSurfaceNormal (const int id) const

const LibUtilities::PointsKeyVector	GetPointsKeys () const

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

Array< OneD, unsigned int >	GetFaceInverseBoundaryMap (int fid, StdRegions::Orientation faceOrient=eNoOrientation)

DNekMatSharedPtr	BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)

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

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

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

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

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

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

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

virtual void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0

virtual void	v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0

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

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

virtual int	v_GetTraceNcoeffs (const int i) const

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

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

IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)
	Create an IndexMap which contains mapping information linking any specific element shape with either its boundaries, edges, faces, verteces, etc. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Private Member Functions
virtual int	v_GetShapeDimension () const

virtual int	v_GetNfaces () const

virtual int	v_GetCoordim (void)

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

LibUtilities::NekManager < IndexMapKey, IndexMapValues, IndexMapKey::opLess >	m_IndexMapManager

Detailed Description

Definition at line 49 of file StdExpansion2D.h.

Constructor & Destructor Documentation

Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( )

Definition at line 49 of file StdExpansion2D.cpp.

50 {

51 }

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

Definition at line 53 of file StdExpansion2D.cpp.

                                                                       :
         StdExpansion(numcoeffs,2, Ba, Bb)
         {
         }

Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( const StdExpansion2D & T )

Definition at line 60 of file StdExpansion2D.cpp.

                                                              :
                 StdExpansion(T)
         {
         }

Nektar::StdRegions::StdExpansion2D::~StdExpansion2D ( )

virtual

Definition at line 65 of file StdExpansion2D.cpp.

66 {

67 }

Member Function Documentation

void Nektar::StdRegions::StdExpansion2D::BwdTrans_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0 = `true`,
		bool	doCheckCollDir1 = `true`
	)

Definition at line 188 of file StdExpansion2D.cpp.

References v_BwdTrans_SumFacKernel().

Referenced by Nektar::StdRegions::StdTriExp::v_BwdTrans_SumFac(), Nektar::StdRegions::StdQuadExp::v_BwdTrans_SumFac(), v_HelmholtzMatrixOp_MatFree(), and v_LaplacianMatrixOp_MatFree().

         {
             v_BwdTrans_SumFacKernel(base0, base1, inarray, outarray, wsp, doCheckCollDir0, doCheckCollDir1);
         }

NekDouble Nektar::StdRegions::StdExpansion2D::Integral	(	const Array< OneD, const NekDouble > &	inarray,
		const Array< OneD, const NekDouble > &	w0,
		const Array< OneD, const NekDouble > &	w1
	)

Definition at line 161 of file StdExpansion2D.cpp.

References Nektar::StdRegions::StdExpansion::m_base, Vmath::Vmul(), and Vmath::Vsum().

Referenced by Nektar::StdRegions::StdTriExp::v_Integral(), and Nektar::StdRegions::StdQuadExp::v_Integral().

         {
             int i;
             NekDouble Int = 0.0;
             int nquad0 = m_base[0]->GetNumPoints();
             int nquad1 = m_base[1]->GetNumPoints();
             Array<OneD, NekDouble> tmp(nquad0 * nquad1);
 
             // multiply by integration constants
             for (i = 0; i < nquad1; ++i)
             {
                 Vmath::Vmul(nquad0, &inarray[0] + i*nquad0, 1, w0.get(),
                             1, &tmp[0] + i*nquad0, 1);
             }
 
             for (i = 0; i < nquad0; ++i)
             {
                 Vmath::Vmul(nquad1, &tmp[0]+ i, nquad0, w1.get(), 1,
                             &tmp[0] + i, nquad0);
             }
             Int = Vmath::Vsum(nquad0 * nquad1, tmp, 1);
 
             return Int;
         }

void Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0 = `true`,
		bool	doCheckCollDir1 = `true`
	)

Definition at line 200 of file StdExpansion2D.cpp.

References v_IProductWRTBase_SumFacKernel().

Referenced by Nektar::LocalRegions::NodalTriExp::IProductWRTDerivBase_SumFac(), v_HelmholtzMatrixOp_MatFree(), Nektar::LocalRegions::TriExp::v_IProductWRTBase_SumFac(), Nektar::StdRegions::StdQuadExp::v_IProductWRTBase_SumFac(), Nektar::StdRegions::StdTriExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::TriExp::v_IProductWRTDerivBase_SumFac(), Nektar::LocalRegions::QuadExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdQuadExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdTriExp::v_IProductWRTDerivBase_SumFac(), Nektar::LocalRegions::TriExp::v_LaplacianMatrixOp_MatFree_Kernel(), and Nektar::LocalRegions::QuadExp::v_LaplacianMatrixOp_MatFree_Kernel().

         {
             v_IProductWRTBase_SumFacKernel(base0, base1, inarray, outarray, wsp, doCheckCollDir0, doCheckCollDir1);
         }

void Nektar::StdRegions::StdExpansion2D::PhysTensorDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray_d0,
		Array< OneD, NekDouble > &	outarray_d1
	)

Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points.

This function is independent of the expansion basis and can therefore be defined for all tensor product distribution of quadrature points in a generic manner. The key operations are:

$\frac{d}{d\eta_1} \rightarrow {\bf D^T_0 u }$
$\frac{d}{d\eta_2} \rightarrow {\bf D_1 u }$

Parameters

inarray	array of physical points to be differentiated
outarray_d0	the resulting array of derivative in the $\eta_1$ direction will be stored in outarray_d0 as output of the function
outarray_d1	the resulting array of derivative in the $\eta_2$ direction will be stored in outarray_d1 as output of the function

Recall that: $\hspace{1cm} \begin{array}{llll} \mbox{Shape} & \mbox{Cartesian coordinate range} & \mbox{Collapsed coord.} & \mbox{Collapsed coordinate definition}\\ \mbox{Quadrilateral} & -1 \leq \xi_1,\xi_2 \leq 1 & -1 \leq \eta_1,\eta_2 \leq 1 & \eta_1 = \xi_1, \eta_2 = \xi_2\\ \mbox{Triangle} & -1 \leq \xi_1,\xi_2; \xi_1+\xi_2 \leq 0 & -1 \leq \eta_1,\eta_2 \leq 1 & \eta_1 = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \eta_2 = \xi_2 \\ \end{array}$

Definition at line 72 of file StdExpansion2D.cpp.

References Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vcopy().

Referenced by Nektar::StdRegions::StdTriExp::v_PhysDeriv(), and Nektar::StdRegions::StdQuadExp::v_PhysDeriv().

         {
             int nquad0 = m_base[0]->GetNumPoints();
             int nquad1 = m_base[1]->GetNumPoints();
 
             if (outarray_d0.num_elements() > 0) // calculate du/dx_0
             {
                 DNekMatSharedPtr D0 = m_base[0]->GetD();
                 if(inarray.data() == outarray_d0.data())
                 {
                     Array<OneD, NekDouble> wsp(nquad0 * nquad1);
                     Vmath::Vcopy(nquad0 * nquad1,inarray.get(),1,wsp.get(),1);
                     Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
                                 &(D0->GetPtr())[0], nquad0, &wsp[0], nquad0, 0.0,
                                 &outarray_d0[0], nquad0);
                 }
                 else
                 {
                     Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
                                 &(D0->GetPtr())[0], nquad0, &inarray[0], nquad0, 0.0,
                                 &outarray_d0[0], nquad0);
                 }
             }
 
             if (outarray_d1.num_elements() > 0) // calculate du/dx_1
             {
                 DNekMatSharedPtr D1 = m_base[1]->GetD();
                 if(inarray.data() == outarray_d1.data())
                 {
                     Array<OneD, NekDouble> wsp(nquad0 * nquad1);
                     Vmath::Vcopy(nquad0 * nquad1,inarray.get(),1,wsp.get(),1);
                     Blas:: Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &wsp[0], nquad0,
                                  &(D1->GetPtr())[0], nquad1, 0.0, &outarray_d1[0], nquad0);
                 }
                 else
                 {
                     Blas:: Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &inarray[0], nquad0,
                                  &(D1->GetPtr())[0], nquad1, 0.0, &outarray_d1[0], nquad0);
                 }
             }
         }

virtual void Nektar::StdRegions::StdExpansion2D::v_BwdTrans_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0,
		bool	doCheckCollDir1
	)

protectedpure virtual

Implemented in Nektar::StdRegions::StdQuadExp, and Nektar::StdRegions::StdTriExp.

Referenced by BwdTrans_SumFacKernel().

virtual int Nektar::StdRegions::StdExpansion2D::v_GetCoordim ( void )

inlineprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 197 of file StdExpansion2D.h.

             {
                 return 2;
             }

virtual int Nektar::StdRegions::StdExpansion2D::v_GetNfaces ( ) const

inlineprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 192 of file StdExpansion2D.h.

             {
                 return 0;
             }

virtual int Nektar::StdRegions::StdExpansion2D::v_GetShapeDimension ( ) const

inlineprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 187 of file StdExpansion2D.h.

             {
                 return 2;
             }

virtual int Nektar::StdRegions::StdExpansion2D::v_GetTraceNcoeffs ( const int i ) const

inlineprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 179 of file StdExpansion2D.h.

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

             {
                 return GetEdgeNcoeffs(i);
             }

void Nektar::StdRegions::StdExpansion2D::v_HelmholtzMatrixOp_MatFree	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 261 of file StdExpansion2D.cpp.

Referenced by Nektar::StdRegions::StdQuadExp::v_HelmholtzMatrixOp(), and Nektar::StdRegions::StdTriExp::v_HelmholtzMatrixOp().

         {
             if (mkey.GetNVarCoeff() == 0
                 &&!mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
             {
                 using std::max;
 
                 int       nquad0  = m_base[0]->GetNumPoints();
                 int       nquad1  = m_base[1]->GetNumPoints();
                 int       nqtot   = nquad0*nquad1;
                 int       nmodes0 = m_base[0]->GetNumModes();
                 int       nmodes1 = m_base[1]->GetNumModes();
                 int       wspsize = max(max(max(nqtot,m_ncoeffs),nquad1*nmodes0),
                                         nquad0*nmodes1);
                 NekDouble lambda  =
                     mkey.GetConstFactor(StdRegions::eFactorLambda);
 
                 const Array<OneD, const NekDouble>& base0 = m_base[0]->GetBdata();
                 const Array<OneD, const NekDouble>& base1 = m_base[1]->GetBdata();
 
                 // Allocate temporary storage
                 Array<OneD,NekDouble> wsp0(5*wspsize);      // size wspsize
                 Array<OneD,NekDouble> wsp1(wsp0 + wspsize);  // size wspsize
                 Array<OneD,NekDouble> wsp2(wsp0 + 2*wspsize);// size 3*wspsize
 
                 if (!(m_base[0]->Collocation() && m_base[1]->Collocation()))
                 {
                     // MASS MATRIX OPERATION
                     // The following is being calculated:
                     // wsp0     = B   * u_hat = u
                     // wsp1     = W   * wsp0
                     // outarray = B^T * wsp1  = B^T * W * B * u_hat = M * u_hat
                     BwdTrans_SumFacKernel       (base0, base1, inarray,
                                                  wsp0, wsp2,true,true);
                     MultiplyByQuadratureMetric  (wsp0, wsp1);
                     IProductWRTBase_SumFacKernel(base0, base1, wsp1, outarray,
                                                  wsp2, true, true);
 
                     LaplacianMatrixOp_MatFree_Kernel(wsp0, wsp1, wsp2);
                 }
                 else
                 {
                     MultiplyByQuadratureMetric(inarray,outarray);
                     LaplacianMatrixOp_MatFree_Kernel(inarray, wsp1, wsp2);
                 }
 
                 // outarray = lambda * outarray + wsp1
                 //          = (lambda * M + L ) * u_hat
                 Vmath::Svtvp(m_ncoeffs, lambda, &outarray[0], 1,
                               &wsp1[0], 1, &outarray[0], 1);
             }
             else
             {
                 StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(
                     inarray,outarray,mkey);
             }
         }

virtual void Nektar::StdRegions::StdExpansion2D::v_IProductWRTBase_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0,
		bool	doCheckCollDir1
	)

protectedpure virtual

Implemented in Nektar::StdRegions::StdQuadExp, and Nektar::StdRegions::StdTriExp.

Referenced by IProductWRTBase_SumFacKernel().

void Nektar::StdRegions::StdExpansion2D::v_LaplacianMatrixOp_MatFree	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 212 of file StdExpansion2D.cpp.

References BwdTrans_SumFacKernel(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::m_ncoeffs.

Referenced by Nektar::StdRegions::StdQuadExp::v_LaplacianMatrixOp(), and Nektar::StdRegions::StdTriExp::v_LaplacianMatrixOp().

         {
             if (mkey.GetNVarCoeff() == 0
                 &&!mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
             {
                 using std::max;
 
                 // This implementation is only valid when there are no
                 // coefficients associated to the Laplacian operator
                 int       nquad0  = m_base[0]->GetNumPoints();
                 int       nquad1  = m_base[1]->GetNumPoints();
                 int       nqtot   = nquad0*nquad1;
                 int       nmodes0 = m_base[0]->GetNumModes();
                 int       nmodes1 = m_base[1]->GetNumModes();
                 int       wspsize = max(max(max(nqtot,m_ncoeffs),nquad1*nmodes0),nquad0*nmodes1);
 
                 const Array<OneD, const NekDouble>& base0  = m_base[0]->GetBdata();
                 const Array<OneD, const NekDouble>& base1  = m_base[1]->GetBdata();
 
                 // Allocate temporary storage
                 Array<OneD,NekDouble> wsp0(4*wspsize);      // size wspsize
                 Array<OneD,NekDouble> wsp1(wsp0+wspsize);   // size 3*wspsize
 
                 if(!(m_base[0]->Collocation() && m_base[1]->Collocation()))
                 {
                     // LAPLACIAN MATRIX OPERATION
                     // wsp0 = u       = B   * u_hat
                     // wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
                     // wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
                     BwdTrans_SumFacKernel(base0,base1,inarray,wsp0,wsp1,true,true);
                     LaplacianMatrixOp_MatFree_Kernel(wsp0, outarray, wsp1);
                 }
                 else
                 {
                     LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp1);
                 }
             }
             else
             {
                 StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(
                     inarray,outarray,mkey);
             }
         }

NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate	(	const Array< OneD, const NekDouble > &	coords,
		const Array< OneD, const NekDouble > &	physvals
	)

protectedvirtual

This function evaluates the expansion at a single (arbitrary) point of the domain.

This function is a wrapper around the virtual function v_PhysEvaluate()

Based on the value of the expansion at the quadrature points, this function calculates the value of the expansion at an arbitrary single points (with coordinates $\mathbf{x_c}$ given by the pointer coords). This operation, equivalent to

$u(\mathbf{x_c}) = \sum_p \phi_p(\mathbf{x_c}) \hat{u}_p$

is evaluated using Lagrangian interpolants through the quadrature points:

$u(\mathbf{x_c}) = \sum_p h_p(\mathbf{x_c}) u_p$

This function requires that the physical value array $\mathbf{u}$ (implemented as the attribute #m_phys) is set.

Parameters

coords the coordinates of the single point

Returns: returns the value of the expansion at the single point

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::TriExp, and Nektar::LocalRegions::QuadExp.

Definition at line 116 of file StdExpansion2D.cpp.

References ASSERTL2, Nektar::NekConstants::kNekZeroTol, Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), and Nektar::StdRegions::StdExpansion::m_base.

Referenced by Nektar::StdRegions::StdNodalTriExp::GenNBasisTransMatrix().

         {
             Array<OneD, NekDouble> coll(2);
             Array<OneD, DNekMatSharedPtr>  I(2);
 
             ASSERTL2(coords[0] > -1 - NekConstants::kNekZeroTol, "coord[0] < -1");
             ASSERTL2(coords[0] <  1 + NekConstants::kNekZeroTol, "coord[0] >  1");
             ASSERTL2(coords[1] > -1 - NekConstants::kNekZeroTol, "coord[1] < -1");
             ASSERTL2(coords[1] <  1 + NekConstants::kNekZeroTol, "coord[1] >  1");
 
             LocCoordToLocCollapsed(coords,coll);
             
             I[0] = m_base[0]->GetI(coll);
             I[1] = m_base[1]->GetI(coll+1);
 
             return v_PhysEvaluate(I,physvals);
         }

NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate	(	const Array< OneD, DNekMatSharedPtr > &	I,
		const Array< OneD, const NekDouble > &	physvals
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 134 of file StdExpansion2D.cpp.

References Vmath::Ddot(), and Nektar::StdRegions::StdExpansion::m_base.

         {
             NekDouble val;
             int i;
             int nq0 = m_base[0]->GetNumPoints();
             int nq1 = m_base[1]->GetNumPoints();
             Array<OneD, NekDouble> wsp1(nq1);
 
             // interpolate first coordinate direction
             for (i = 0; i < nq1;++i)
             {
                 wsp1[i] = Blas::Ddot(nq0, &(I[0]->GetPtr())[0], 1,
                                      &physvals[i * nq0], 1);
             }
 
             // interpolate in second coordinate direction
             val = Blas::Ddot(nq1, I[1]->GetPtr(), 1, wsp1, 1);
 
             return val;
         }

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