#include <Expansion1D.h>

Inheritance diagram for Nektar::LocalRegions::Expansion1D:

Collaboration diagram for Nektar::LocalRegions::Expansion1D:

Public Member Functions
	Expansion1D (SpatialDomains::Geometry1DSharedPtr pGeom)
virtual	~Expansion1D ()
void	AddNormTraceInt (const int dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Expansion2DSharedPtr	GetLeftAdjacentElementExp () const
Expansion2DSharedPtr	GetRightAdjacentElementExp () const
int	GetLeftAdjacentElementEdge () const
int	GetRightAdjacentElementEdge () const
void	SetAdjacentElementExp (int edge, Expansion2DSharedPtr &e)
void	AddHDGHelmholtzTraceTerms (const NekDouble tau, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
SpatialDomains::Geometry1DSharedPtr	GetGeom1D () const
Public Member Functions inherited from Nektar::LocalRegions::Expansion
	Expansion (SpatialDomains::GeometrySharedPtr pGeom)
	Expansion (const Expansion &pSrc)
virtual	~Expansion ()
DNekScalMatSharedPtr	GetLocMatrix (const LocalRegions::MatrixKey &mkey)
DNekScalMatSharedPtr	GetLocMatrix (const StdRegions::MatrixType mtype, const StdRegions::ConstFactorMap &factors=StdRegions::NullConstFactorMap, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)
SpatialDomains::GeometrySharedPtr	GetGeom () const
virtual const SpatialDomains::GeomFactorsSharedPtr &	v_GetMetricInfo () const
DNekMatSharedPtr	BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
DNekMatSharedPtr	BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
void	AddEdgeNormBoundaryInt (const int edge, const boost::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 boost::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	AddFaceNormBoundaryInt (const int face, const boost::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)
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	GetNedges () const
	This function returns the number of edges of the expansion domain.
int	GetEdgeNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th edge.
int	GetTotalEdgeIntNcoeffs () const
int	GetEdgeNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th edge.
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.
int	GetFaceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th face.
int	GetFaceIntNcoeffs (const int i) const
int	GetTotalFaceIntNcoeffs () const
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.
int	GetNfaces () const
	This function returns the number of faces of the expansion domain.
int	GetNtrace () const
	Returns the number of trace elements connected to this element.
LibUtilities::ShapeType	DetShapeType () const
	This function returns the shape of the expansion domain.
int	GetShapeDimension () const
bool	IsBoundaryInteriorExpansion ()
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	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.
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)
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)
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, const Array< OneD, const 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)
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)
void	ExtractDataToCoeffs (const NekDouble data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble coeffs)
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	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)
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.
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).
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	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	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.
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.
void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta.
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.
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_ExtractDataToCoeffs (const NekDouble data, const std::vector< unsigned int > &nummodes, const int nmode_offset, NekDouble coeffs)
	Unpack data from input file assuming it comes from the same expansion type.
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
virtual void	v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
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.
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.
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.
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)
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)
	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.
template<class T >
boost::shared_ptr< T >	as ()
Public Member Functions inherited from Nektar::StdRegions::StdExpansion1D
	StdExpansion1D ()
	StdExpansion1D (int numcoeffs, const LibUtilities::BasisKey &Ba)
	StdExpansion1D (const StdExpansion1D &T)
virtual	~StdExpansion1D ()
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.

Protected Member Functions
virtual DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey)
virtual void	v_AddRobinMassMatrix (const int vert, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
virtual void	v_AddRobinEdgeContribution (const int vert, const Array< OneD, const NekDouble > &primCoeffs, Array< OneD, NekDouble > &coeffs)
Protected Member Functions inherited from Nektar::LocalRegions::Expansion
void	ComputeLaplacianMetric ()
void	ComputeQuadratureMetric ()
virtual void	v_MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_ComputeLaplacianMetric ()
virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3)
virtual DNekScalMatSharedPtr	v_GetLocMatrix (const LocalRegions::MatrixKey &mkey)
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 boost::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 boost::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_AddFaceNormBoundaryInt (const int face, const boost::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)
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.
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.
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	IProductWRTBase_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)
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion1D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)

Private Attributes
Expansion2DWeakPtr	m_elementLeft
Expansion2DWeakPtr	m_elementRight
int	m_elementEdgeLeft
int	m_elementEdgeRight

Additional Inherited Members
Protected Attributes inherited from Nektar::LocalRegions::Expansion
SpatialDomains::GeometrySharedPtr	m_geom
SpatialDomains::GeomFactorsSharedPtr	m_metricinfo
MetricMap	m_metrics
Protected Attributes inherited from Nektar::StdRegions::StdExpansion1D
std::map< int, NormalVector >	m_vertexNormals

Detailed Description

Definition at line 60 of file Expansion1D.h.

Constructor & Destructor Documentation

Nektar::LocalRegions::Expansion1D::Expansion1D ( SpatialDomains::Geometry1DSharedPtr pGeom )

inline

Definition at line 63 of file Expansion1D.h.

References m_elementEdgeLeft, and m_elementEdgeRight.

                                                                                          : Expansion(pGeom), StdExpansion1D()
                {
                    m_elementEdgeLeft = -1;
                    m_elementEdgeRight = -1;
                }

virtual Nektar::LocalRegions::Expansion1D::~Expansion1D ( )

inlinevirtual

Definition at line 69 of file Expansion1D.h.

{}

Member Function Documentation

void Nektar::LocalRegions::Expansion1D::AddHDGHelmholtzTraceTerms	(	const NekDouble	tau,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Definition at line 282 of file Expansion1D.cpp.

Referenced by v_GenMatrix().

        {
            int i,n;
            int nbndry  = NumBndryCoeffs();
            int nquad   = GetNumPoints(0);
            int ncoeffs = GetNcoeffs();
            int coordim = GetCoordim();
            Array<OneD, unsigned int> vmap;
            
            ASSERTL0(&inarray[0] != &outarray[0],"Input and output arrays use the same memory");
            const Array<OneD, const NekDouble> &Basis  = GetBasis(0)->GetBdata();
            DNekScalMat  &invMass = *GetLocMatrix(StdRegions::eInvMass);
            GetBoundaryMap(vmap);
            // Add F = \tau <phi_i,phi_j> (note phi_i is zero if phi_j is non-zero)
            for(i = 0; i < nbndry; ++i)
            {
                outarray[vmap[i]] += tau*Basis[(vmap[i]+1)*nquad-1]*Basis[(vmap[i]+1)*nquad-1]*inarray[vmap[i]];
                outarray[vmap[i]] += tau*Basis[vmap[i]*nquad]*Basis[vmap[i]*nquad]*inarray[vmap[i]];
            }
            
            //===============================================================
            // Add -\sum_i D_i^T M^{-1} G_i + E_i M^{-1} G_i = 
            //                         \sum_i D_i M^{-1} G_i term
            StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                                   StdRegions::eWeakDeriv1,
                                                   StdRegions::eWeakDeriv2};
            Array<OneD, NekDouble> tmpcoeff(ncoeffs,0.0);
            DNekVec                Coeffs  (ncoeffs,outarray,eWrapper);
            DNekVec                Tmpcoeff(ncoeffs,tmpcoeff,eWrapper);
            for(n = 0; n < coordim; ++n)
            {
                // evaluate M^{-1} G
                for(i = 0; i < ncoeffs; ++i)
                {
                    // lower boundary (negative normal) 
                    tmpcoeff[i] -= invMass(i,vmap[0])*Basis[vmap[0]*nquad]*Basis[vmap[0]*nquad]*inarray[vmap[0]];
                    
                    // upper boundary (positive normal) 
                    tmpcoeff[i] += invMass(i,vmap[1])*Basis[(vmap[1]+1)*nquad-1]*Basis[(vmap[1]+1)*nquad-1]*inarray[vmap[1]];
                    
                }
                
                DNekScalMat &Dmat = *GetLocMatrix(DerivType[n]);
                Coeffs = Coeffs  + Dmat*Tmpcoeff; 
            }
        }

void Nektar::LocalRegions::Expansion1D::AddNormTraceInt	(	const int	dir,
		Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Definition at line 261 of file Expansion1D.cpp.

References Nektar::StdRegions::StdExpansion::GetBasis(), Nektar::StdRegions::StdExpansion::GetBoundaryMap(), Nektar::StdRegions::StdExpansion::GetNumPoints(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

Referenced by v_GenMatrix().

        {
            
            int k;
            int nbndry = NumBndryCoeffs();
            int nquad  = GetNumPoints(0);
            const Array<OneD, const NekDouble> &Basis  = GetBasis(0)->GetBdata();
            Array<OneD, unsigned int> vmap;
            
            GetBoundaryMap(vmap);
            
            // add G \lambda term (can assume G is diagonal since one
            // of the basis is zero at boundary otherwise)
            for(k = 0; k < nbndry; ++k)
            {
                outarray[vmap[k]] += (Basis[(vmap[k]+1)*nquad-1]*Basis[(vmap[k]+1)*nquad-1] - Basis[vmap[k]*nquad]*Basis[vmap[k]*nquad])*inarray[vmap[k]];
            }
        }

SpatialDomains::Geometry1DSharedPtr Nektar::LocalRegions::Expansion1D::GetGeom1D ( ) const

inline

Definition at line 154 of file Expansion1D.h.

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

Referenced by Nektar::MultiRegions::AssemblyMapDG::SetUpUniversalDGMap().

        {
            return boost::dynamic_pointer_cast<SpatialDomains::Geometry1D>(m_geom);
        }

int Nektar::LocalRegions::Expansion1D::GetLeftAdjacentElementEdge ( ) const

inline

Definition at line 128 of file Expansion1D.h.

References m_elementEdgeLeft.

Referenced by Extractlayerdata(), and Nektar::LocalRegions::SegExp::v_NormVectorIProductWRTBase().

        {
            return m_elementEdgeLeft;
        }

Expansion2DSharedPtr Nektar::LocalRegions::Expansion1D::GetLeftAdjacentElementExp ( ) const

inline

Definition at line 116 of file Expansion1D.h.

References ASSERTL1, and m_elementLeft.

Referenced by Nektar::CoupledLocalToGlobalC0ContMap::CoupledLocalToGlobalC0ContMap(), Nektar::MultiRegions::ExpList1D::v_GetNormals(), and Nektar::LocalRegions::SegExp::v_NormVectorIProductWRTBase().

        {
            ASSERTL1(m_elementLeft.lock().get(), "Left adjacent element not set.");
            return m_elementLeft.lock();
        }

int Nektar::LocalRegions::Expansion1D::GetRightAdjacentElementEdge ( ) const

inline

Definition at line 133 of file Expansion1D.h.

References m_elementEdgeRight.

        {
            return m_elementEdgeRight;
        }

Expansion2DSharedPtr Nektar::LocalRegions::Expansion1D::GetRightAdjacentElementExp ( ) const

inline

Definition at line 122 of file Expansion1D.h.

References ASSERTL1, m_elementLeft, and m_elementRight.

        {
            ASSERTL1(m_elementLeft.lock().get(), "Right adjacent element not set.");
            return m_elementRight.lock();
        }

void Nektar::LocalRegions::Expansion1D::SetAdjacentElementExp	(	int	edge,
		Expansion2DSharedPtr &	e
	)

inline

Definition at line 138 of file Expansion1D.h.

References ASSERTL1, m_elementEdgeLeft, m_elementEdgeRight, m_elementLeft, and m_elementRight.

Referenced by Nektar::MultiRegions::DisContField2D::SetUpDG().

        {
            if (m_elementLeft.lock().get())
            {
                ASSERTL1(!m_elementRight.lock().get(),
                         "Both adjacent elements already set.");
                m_elementRight = e;
                m_elementEdgeRight = edge;
            }
            else
            {
                m_elementLeft = e;
                m_elementEdgeLeft = edge;
            }
        }

void Nektar::LocalRegions::Expansion1D::v_AddRobinEdgeContribution	(	const int	vert,
		const Array< OneD, const NekDouble > &	primCoeffs,
		Array< OneD, NekDouble > &	coeffs
	)

protectedvirtual

Given an edge and vector of element coefficients:

maps those elemental coefficients corresponding to the edge into an edge-vector.
resets the element coefficients
multiplies the edge vector by the edge mass matrix
maps the edge coefficients back onto the elemental coefficients

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 390 of file Expansion1D.cpp.

References ASSERTL1, Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetVertexMap(), Nektar::StdRegions::StdExpansion::IsBoundaryInteriorExpansion(), and Vmath::Zero().

        {
            ASSERTL1(IsBoundaryInteriorExpansion(),
                     "Not set up for non boundary-interior expansions");
            int map = GetVertexMap(vert);
            Vmath::Zero(GetNcoeffs(), coeffs, 1);
            coeffs[map] = primCoeffs[0];
        }

void Nektar::LocalRegions::Expansion1D::v_AddRobinMassMatrix	(	const int	vert,
		const Array< OneD, const NekDouble > &	primCoeffs,
		DNekMatSharedPtr &	inoutmat
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 337 of file Expansion1D.cpp.

References ASSERTL0, ASSERTL1, Nektar::StdRegions::StdExpansion::GetBoundaryMap(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetVertexMap(), Nektar::StdRegions::StdExpansion::IsBoundaryInteriorExpansion(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

        {
            ASSERTL0(IsBoundaryInteriorExpansion(),"Robin boundary conditions are only implemented for boundary-interior expanisons");
            ASSERTL1(inoutmat->GetRows() == inoutmat->GetColumns(),
                     "Assuming that input matrix was square");
            // Get local Element mapping for vertex point
            int map = GetVertexMap(vert);
            // Now need to identify a map which takes the local edge
            // mass matrix to the matrix stored in inoutmat;
            // This can currently be deduced from the size of the matrix       
            // - if inoutmat.m_rows() == v_NCoeffs() it is a full
            //   matrix system
            // - if inoutmat.m_rows() == v_NumBndCoeffs() it is a
            //  boundary CG system
             
             int rows = inoutmat->GetRows();
             
             if (rows == GetNcoeffs())
             {
                 // no need to do anything
             }
             else if(rows == NumBndryCoeffs())  // same as NumDGBndryCoeffs()
             {
                 int i;
                 Array<OneD,unsigned int> bmap;
                 GetBoundaryMap(bmap);
                 
                 for(i = 0; i < 2; ++i)
                 {
                     if(map == bmap[i])
                     {
                         map = i;
                         break;
                     }
                 }
                 ASSERTL1(i != 2,"Did not find number in map");
             }
             
             // assumes end points have unit magnitude
             (*inoutmat)(map,map) +=  primCoeffs[0];
        }

DNekMatSharedPtr Nektar::LocalRegions::Expansion1D::v_GenMatrix ( const StdRegions::StdMatrixKey & mkey )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::SegExp.

Definition at line 43 of file Expansion1D.cpp.

        {
            DNekMatSharedPtr returnval;
            
            switch(mkey.GetMatrixType())
            {
            case StdRegions::eHybridDGHelmholtz:
                {                    
                ASSERTL1(IsBoundaryInteriorExpansion(),
                         "HybridDGHelmholtz matrix not set up "
                         "for non boundary-interior expansions");
                    int       i;
                    NekDouble lambdaval = mkey.GetConstFactor(StdRegions::eFactorLambda);
                    NekDouble tau       = mkey.GetConstFactor(StdRegions::eFactorTau);
                    int       ncoeffs   = GetNcoeffs();
                    int       coordim = GetCoordim();
                    DNekScalMat  &invMass = *GetLocMatrix(StdRegions::eInvMass);
                    StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                                           StdRegions::eWeakDeriv1,
                                                           StdRegions::eWeakDeriv2};
                    DNekMat LocMat(ncoeffs,ncoeffs); 
                    returnval = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,ncoeffs);
                    DNekMat &Mat = *returnval;
                    Vmath::Zero(ncoeffs*ncoeffs,Mat.GetPtr(),1);
                    for(i=0;  i < coordim; ++i)
                    {
                        DNekScalMat &Dmat = *GetLocMatrix(DerivType[i]);
                        Mat = Mat + Dmat*invMass*Transpose(Dmat);
                    }
                    // Add end Mass Matrix Contribution
                    DNekScalMat  &Mass = *GetLocMatrix(StdRegions::eMass);
                    Mat = Mat + lambdaval*Mass;                    
                    Array<OneD,unsigned int> bmap;
                    GetBoundaryMap(bmap);
                    // Add tau*F_e using elemental mass matrices
                    for(i = 0; i < 2; ++i)
                    {
                        Mat(bmap[i],bmap[i]) = Mat(bmap[i],bmap[i]) +  tau; 
                    }
                }
                break;
            case StdRegions::eHybridDGLamToU:
                {
                    int j,k;
                    int nbndry = NumDGBndryCoeffs();
                    int ncoeffs = GetNcoeffs();
                    StdRegions::ConstFactorMap factors;
                    factors[StdRegions::eFactorLambda] = mkey.GetConstFactor(StdRegions::eFactorLambda);
                    factors[StdRegions::eFactorTau] = mkey.GetConstFactor(StdRegions::eFactorTau);
                    
                    Array<OneD,NekDouble> lambda(nbndry);
                    DNekVec Lambda(nbndry,lambda,eWrapper);                    
                    Array<OneD,NekDouble> ulam(ncoeffs);
                    DNekVec Ulam(ncoeffs,ulam,eWrapper);
                    Array<OneD,NekDouble> f(ncoeffs);
                    DNekVec F(ncoeffs,f,eWrapper);
                    
                    // declare matrix space
                    returnval  = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,nbndry); 
                    DNekMat &Umat = *returnval;
                    
                    // Helmholtz matrix
                    DNekScalMat  &invHmat = *GetLocMatrix(StdRegions::eInvHybridDGHelmholtz, factors);
                    
                    // for each degree of freedom of the lambda space
                    // calculate Umat entry 
                    // Generate Lambda to U_lambda matrix 
                    for(j = 0; j < nbndry; ++j)
                    {
                        Vmath::Zero(nbndry,&lambda[0],1);
                        Vmath::Zero(ncoeffs,&f[0],1);
                        lambda[j] = 1.0;
                        
                        AddHDGHelmholtzTraceTerms(factors[StdRegions::eFactorTau],lambda,f);
                        
                        Ulam = invHmat*F; // generate Ulam from lambda
                        
                        // fill column of matrix
                        for(k = 0; k < ncoeffs; ++k)
                        {
                            Umat(k,j) = Ulam[k]; 
                        }
                    }
                }
                break;
            case StdRegions::eHybridDGLamToQ0:
            case StdRegions::eHybridDGLamToQ1:
            case StdRegions::eHybridDGLamToQ2:
                {
                    int j,k,dir;
                    int nbndry = NumDGBndryCoeffs();
                    int ncoeffs = GetNcoeffs();
                    Array<OneD,NekDouble> lambda(nbndry);
                    DNekVec Lambda(nbndry,lambda,eWrapper);                    
                    
                    Array<OneD,NekDouble> ulam(ncoeffs);
                    DNekVec Ulam(ncoeffs,ulam,eWrapper);
                    Array<OneD,NekDouble> f(ncoeffs);
                    DNekVec F(ncoeffs,f,eWrapper);
                    StdRegions::ConstFactorMap factors;
                    factors[StdRegions::eFactorLambda] = mkey.GetConstFactor(StdRegions::eFactorLambda);
                    factors[StdRegions::eFactorTau] = mkey.GetConstFactor(StdRegions::eFactorTau);
                    // declare matrix space
                    returnval  = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,nbndry); 
                    DNekMat &Qmat = *returnval;
                    
                    // Lambda to U matrix
                    DNekScalMat &lamToU = *GetLocMatrix(StdRegions::eHybridDGLamToU, factors);
                    
                    // Inverse mass matrix 
                    DNekScalMat &invMass = *GetLocMatrix(StdRegions::eInvMass);
                    
                    //Weak Derivative matrix 
                    DNekScalMatSharedPtr Dmat;
                    switch(mkey.GetMatrixType())
                    {
                    case StdRegions::eHybridDGLamToQ0:
                        dir = 0;
                        Dmat = GetLocMatrix(StdRegions::eWeakDeriv0);
                        break;
                    case StdRegions::eHybridDGLamToQ1:
                        dir = 1;
                        Dmat = GetLocMatrix(StdRegions::eWeakDeriv1);
                        break;
                    case StdRegions::eHybridDGLamToQ2:
                        dir = 2;
                        Dmat = GetLocMatrix(StdRegions::eWeakDeriv2);
                        break;
                    default:
                        ASSERTL0(false,"Direction not known");
                        break;
                    }
                
                    // for each degree of freedom of the lambda space
                    // calculate Qmat entry 
                    // Generate Lambda to Q_lambda matrix 
                    for(j = 0; j < nbndry; ++j)
                    {
                        Vmath::Zero(nbndry,&lambda[0],1);
                        lambda[j] = 1.0;
                        
                        // for lambda[j] = 1 this is the solution to ulam
                        for(k = 0; k < ncoeffs; ++k)
                        {
                            Ulam[k] = lamToU(k,j);
                        }
                        
                        // -D^T ulam
                        Vmath::Neg(ncoeffs,&ulam[0],1);
                        F = Transpose(*Dmat)*Ulam; 
                        
                        // + \tilde{G} \lambda
                        AddNormTraceInt(dir,lambda,f); 
                        
                        // multiply by inverse mass matrix
                        Ulam = invMass*F; 
                        
                        // fill column of matrix (Qmat is in column major format)
                        Vmath::Vcopy(ncoeffs,&ulam[0],1,&(Qmat.GetPtr())[0]+j*ncoeffs,1);
                    }
                }
                break;            
            case StdRegions::eHybridDGHelmBndLam:
                {
                    int j;
                    int nbndry = NumBndryCoeffs();
                    StdRegions::ConstFactorMap factors;
                    factors[StdRegions::eFactorLambda] = mkey.GetConstFactor(StdRegions::eFactorLambda);
                    factors[StdRegions::eFactorTau] = mkey.GetConstFactor(StdRegions::eFactorTau);
                    Array<OneD,unsigned int> bmap;
                    Array<OneD, NekDouble>   lam(2);
                    GetBoundaryMap(bmap);
                    
                    // declare matrix space
                    returnval = MemoryManager<DNekMat>::AllocateSharedPtr(nbndry,  nbndry);
                    DNekMat &BndMat = *returnval;
                    
                    // Matrix to map Lambda to U
                    DNekScalMat &LamToU = *GetLocMatrix(StdRegions::eHybridDGLamToU, factors);
                
                    // Matrix to map Lambda to Q
                    DNekScalMat &LamToQ = *GetLocMatrix(StdRegions::eHybridDGLamToQ0, factors);
                    lam[0] = 1.0; lam[1] = 0.0;
                    for(j = 0; j < nbndry; ++j)
                    {
                        BndMat(0,j) = -LamToQ(bmap[0],j) - factors[StdRegions::eFactorTau]*(LamToU(bmap[0],j) - lam[j]);
                    }
                    lam[0] = 0.0; lam[1] = 1.0;
                    for(j = 0; j < nbndry; ++j)
                    {
                        BndMat(1,j) =  LamToQ(bmap[1],j) - factors[StdRegions::eFactorTau]*(LamToU(bmap[1],j) - lam[j]);
                    }
                }
                break;
            default:
                ASSERTL0(false,"This matrix type cannot be generated from this class");
                break;
            }
            
            return returnval;
        }