#include <Expansion3D.h>

Inheritance diagram for Nektar::LocalRegions::Expansion3D:

Collaboration diagram for Nektar::LocalRegions::Expansion3D:

Public Member Functions
	Expansion3D (SpatialDomains::Geometry3DSharedPtr pGeom)
virtual	~Expansion3D ()
void	SetFaceExp (const int face, Expansion2DSharedPtr &f)
Expansion2DSharedPtr	GetFaceExp (const int face)
void	SetTraceToGeomOrientation (Array< OneD, NekDouble > &inout)
	Align trace orientation with the geometry orientation.
void	SetFaceToGeomOrientation (const int face, Array< OneD, NekDouble > &inout)
	Align face orientation with the geometry orientation.
void	AddHDGHelmholtzFaceTerms (const NekDouble tau, const int edge, Array< OneD, NekDouble > &facePhys, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray)
void	AddNormTraceInt (const int dir, Array< OneD, StdRegions::StdExpansionSharedPtr > &FaceExp, Array< OneD, Array< OneD, NekDouble > > &faceCoeffs, Array< OneD, NekDouble > &outarray)
void	AddNormTraceInt (const int dir, Array< OneD, const NekDouble > &inarray, Array< OneD, StdRegions::StdExpansionSharedPtr > &FaceExp, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs)
void	AddFaceBoundaryInt (const int face, StdRegions::StdExpansionSharedPtr &FaceExp, Array< OneD, NekDouble > &facePhys, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)
SpatialDomains::Geometry3DSharedPtr	GetGeom3D () 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)
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.
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	GetFaceOrient (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)
void	AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	AddEdgeNormBoundaryBiInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray)
void	AddFaceNormBoundaryInt (const int face, boost::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
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)
void	DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, boost::shared_ptr< StdExpansion > > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
NekDouble	PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain.
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_GetFaceOrient (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)
template<class T >
boost::shared_ptr< T >	as ()
Public Member Functions inherited from Nektar::StdRegions::StdExpansion3D
	StdExpansion3D ()
	StdExpansion3D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)
	StdExpansion3D (const StdExpansion3D &T)
virtual	~StdExpansion3D ()
void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d1, Array< OneD, NekDouble > &outarray_d2, Array< OneD, NekDouble > &outarray_d3)
	Calculate the 3D derivative in the local tensor/collapsed coordinate at the physical points.
void	BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
void	IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)

Protected Member Functions
virtual void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, StdRegions::StdExpansionSharedPtr > &FaceExp, Array< OneD, Array< OneD, NekDouble > > &faceCoeffs, Array< OneD, NekDouble > &out_d)
	Evaluate coefficients of weak deriviative in the direction dir given the input coefficicents incoeffs and the imposed boundary values in EdgeExp (which will have its phys space updated).
virtual DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey)
virtual void	v_AddFaceNormBoundaryInt (const int face, StdRegions::StdExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_AddRobinMassMatrix (const int face, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
virtual NekDouble	v_Integrate (const Array< OneD, const NekDouble > &inarray)
virtual Array< OneD, unsigned int >	v_GetEdgeInverseBoundaryMap (int eid)
virtual Array< OneD, unsigned int >	v_GetFaceInverseBoundaryMap (int fid, StdRegions::Orientation faceOrient=StdRegions::eNoOrientation)
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
virtual DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
	Build inverse and inverse transposed transformation matrix: $\mathbf{R^{-1}}$ and $\mathbf{R^{-T}}$ .
virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
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)
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)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_AddFaceNormBoundaryInt (const int face, boost::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion3D
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.
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 > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0
virtual void	v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0
virtual void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)
virtual void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)
virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray)
	Integrates the specified function over the domain.
virtual void	v_NegateFaceNormal (const int face)

Private Attributes
std::vector< Expansion2DWeakPtr >	m_faceExp
std::vector< bool >	m_requireNeg

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::StdExpansion3D
std::map< int, NormalVector >	m_faceNormals
std::map< int, bool >	m_negatedNormals

Detailed Description

Definition at line 59 of file Expansion3D.h.

Constructor & Destructor Documentation

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

inline

Definition at line 63 of file Expansion3D.h.

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

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

inlinevirtual

Definition at line 64 of file Expansion3D.h.

{}

Member Function Documentation

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

inline

For a given face add the {F}_1j contributions

Definition at line 267 of file Expansion3D.cpp.

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eFaceToElement, Nektar::StdRegions::StdExpansion::GetBasisNumModes(), Nektar::StdRegions::StdExpansion::GetFaceOrient(), and Nektar::StdRegions::StdExpansion::GetIndexMap().

Referenced by AddNormTraceInt().

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

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

inline

Definition at line 48 of file Expansion3D.cpp.

Referenced by v_GenMatrix().

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

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

inline

Definition at line 230 of file Expansion3D.cpp.

References AddFaceBoundaryInt(), Nektar::StdRegions::StdExpansion::GetFaceNormal(), Nektar::StdRegions::StdExpansion::GetNfaces(), Nektar::StdRegions::StdExpansion3D::m_negatedNormals, Vmath::Neg(), and Vmath::Vmul().

Referenced by v_DGDeriv(), and v_GenMatrix().

        {
            int f, cnt;
            int order_f, nquad_f;
            int nfaces = GetNfaces();
            cnt = 0;
            for(f = 0; f < nfaces; ++f)
            {
                order_f = FaceExp[f]->GetNcoeffs();
                nquad_f = FaceExp[f]->GetNumPoints(0)*FaceExp[f]->GetNumPoints(1);
                const Array<OneD, const Array<OneD, NekDouble> > &normals = GetFaceNormal(f);
                Array<OneD, NekDouble> facePhys(nquad_f);
                
                cnt += order_f;
                
                FaceExp[f]->BwdTrans(faceCoeffs[f], facePhys);
                
                Vmath::Vmul(nquad_f, normals[dir], 1, facePhys, 1, facePhys, 1);
                
                if (m_negatedNormals[f])
                {
                    Vmath::Neg(nquad_f, facePhys, 1);
                }
                AddFaceBoundaryInt(f, FaceExp[f], facePhys, outarray);
            }
        }

void Nektar::LocalRegions::Expansion3D::AddNormTraceInt	(	const int	dir,
		Array< OneD, const NekDouble > &	inarray,
		Array< OneD, StdRegions::StdExpansionSharedPtr > &	FaceExp,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::VarCoeffMap &	varcoeffs
	)

inline

Computes the C matrix entries due to the presence of the identity matrix in Eqn. 32.

: Document this

Definition at line 175 of file Expansion3D.cpp.

References AddFaceBoundaryInt(), Nektar::StdRegions::StdExpansion::GetFaceNormal(), Nektar::StdRegions::StdExpansion::GetNfaces(), Nektar::StdRegions::StdExpansion3D::m_negatedNormals, Vmath::Neg(), and Vmath::Vmul().

        {
            int i,f,cnt;
            int order_f,nquad_f;
            int nfaces = GetNfaces();
            cnt = 0;
            for(f = 0; f < nfaces; ++f)
            {
                order_f = FaceExp[f]->GetNcoeffs();
                nquad_f = FaceExp[f]->GetNumPoints(0)*FaceExp[f]->GetNumPoints(1);
                const Array<OneD, const Array<OneD, NekDouble> > &normals = GetFaceNormal(f);
                Array<OneD, NekDouble> faceCoeffs(order_f);
                Array<OneD, NekDouble> facePhys  (nquad_f);
                for(i = 0; i < order_f; ++i)
                {
                    faceCoeffs[i] = inarray[i+cnt];
                }
                cnt += order_f;
                FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
                // Multiply by variable coefficient
                /// @TODO: Document this
//                StdRegions::VarCoeffType VarCoeff[3] = {StdRegions::eVarCoeffD00,
//                                                        StdRegions::eVarCoeffD11,
//                                                        StdRegions::eVarCoeffD22};
//                StdRegions::VarCoeffMap::const_iterator x;
//                Array<OneD, NekDouble> varcoeff_work(nquad_e);
//                if ((x = varcoeffs.find(VarCoeff[dir])) != varcoeffs.end())
//                {
//                    GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
//                    Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
//                }
                Vmath::Vmul(nquad_f, normals[dir], 1, facePhys, 1, facePhys, 1);
                
                if (m_negatedNormals[f])
                {
                    Vmath::Neg(nquad_f, facePhys, 1);
                }
                AddFaceBoundaryInt(f, FaceExp[f], facePhys, outarray, varcoeffs);
            }
        }

Expansion2DSharedPtr Nektar::LocalRegions::Expansion3D::GetFaceExp ( const int face )

Definition at line 913 of file Expansion3D.cpp.

References m_faceExp.

Referenced by AddHDGHelmholtzFaceTerms(), and v_GenMatrix().

        {
            return m_faceExp[face].lock();
        }

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

inline

Definition at line 150 of file Expansion3D.h.

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

Referenced by Nektar::MultiRegions::ExpList2D::ExpList2D(), Nektar::MultiRegions::AssemblyMapCG3D::SetUp3DExpansionC0ContMap(), Nektar::MultiRegions::DisContField3D::SetUpDG(), v_AddFaceNormBoundaryInt(), v_BuildTransformationMatrix(), v_GetEdgeInverseBoundaryMap(), Nektar::LocalRegions::HexExp::v_GetFaceDGForwards(), Nektar::LocalRegions::PyrExp::v_GetFaceOrient(), Nektar::LocalRegions::TetExp::v_GetFaceOrient(), Nektar::LocalRegions::PrismExp::v_GetFaceOrient(), and Nektar::LocalRegions::HexExp::v_GetFaceOrient().

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

void Nektar::LocalRegions::Expansion3D::SetFaceExp	(	const int	face,
		Expansion2DSharedPtr &	f
	)

Definition at line 902 of file Expansion3D.cpp.

References ASSERTL1, Nektar::StdRegions::StdExpansion::GetNfaces(), and m_faceExp.

        {
            int nFaces = GetNfaces();
            ASSERTL1(face < nFaces, "Face is out of range.");
            if (m_faceExp.size() < nFaces)
            {
                m_faceExp.resize(nFaces);
            }
            m_faceExp[face] = f;
        }

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

Align face orientation with the geometry orientation.

Definition at line 310 of file Expansion3D.cpp.

References ASSERTL1, Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eDir1FwdDir1_Dir2FwdDir2, Nektar::StdRegions::eFaceToElement, Nektar::StdRegions::StdExpansion::GetBasisNumModes(), Nektar::StdRegions::StdExpansion::GetFaceNcoeffs(), Nektar::StdRegions::StdExpansion::GetFaceOrient(), Nektar::StdRegions::StdExpansion::GetIndexMap(), and Vmath::Vcopy().

Referenced by SetTraceToGeomOrientation(), and v_GenMatrix().

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

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

Align trace orientation with the geometry orientation.

Definition at line 357 of file Expansion3D.cpp.

References Nektar::StdRegions::StdExpansion::GetFaceNcoeffs(), Nektar::StdRegions::StdExpansion::GetNfaces(), and SetFaceToGeomOrientation().

Referenced by v_GenMatrix().

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

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

protectedvirtual

Definition at line 918 of file Expansion3D.cpp.

        {
            int i, j;
            
            /*
             * Coming into this routine, the velocity V will have been
             * multiplied by the trace normals to give the input vector Vn. By
             * convention, these normals are inwards facing for elements which
             * have FaceExp as their right-adjacent face.  This conditional
             * statement therefore determines whether the normals must be
             * negated, since the integral being performed here requires an
             * outwards facing normal.
             */
            if (m_requireNeg.size() == 0)
            {
                m_requireNeg.resize(GetNfaces());
                
                for (i = 0; i < GetNfaces(); ++i)
                {
                    m_requireNeg[i] = false;
                    if (m_negatedNormals[i])
                    {
                        m_requireNeg[i] = true;
                        continue;
                    }
                    
                    Expansion2DSharedPtr faceExp = m_faceExp[i].lock();
                    if (faceExp->GetRightAdjacentElementExp())
                    {
                        if (faceExp->GetRightAdjacentElementExp()->GetGeom3D()
                            ->GetGlobalID() == GetGeom3D()->GetGlobalID())
                        {
                            m_requireNeg[i] = true;
                        }
                    }
                }
            }
            StdRegions::IndexMapKey ikey(
                StdRegions::eFaceToElement, DetShapeType(),
                GetBasisNumModes(0), GetBasisNumModes(1), GetBasisNumModes(2),
                face, GetFaceOrient(face));
            StdRegions::IndexMapValuesSharedPtr map =
            StdExpansion::GetIndexMap(ikey);
            int order_e  = (*map).num_elements(); // Order of the element
            int n_coeffs = FaceExp->GetNcoeffs();
            Array<OneD, NekDouble> faceCoeffs(n_coeffs);
            if (n_coeffs != order_e) // Going to orthogonal space
            {
                Array<OneD, NekDouble> coeff(n_coeffs);
                Array<OneD, NekDouble> array(n_coeffs);
                FaceExp->FwdTrans(Fn, faceCoeffs);
                int NumModesElementMax  = FaceExp->GetBasis(0)->GetNumModes();
                int NumModesElementMin  = m_base[0]->GetNumModes();
                FaceExp->ReduceOrderCoeffs(NumModesElementMin,
                                           faceCoeffs,
                                           faceCoeffs);
                StdRegions::StdMatrixKey masskey(
                    StdRegions::eMass, FaceExp->DetShapeType(), *FaceExp);
                FaceExp->MassMatrixOp(
                                      faceCoeffs,faceCoeffs,masskey);
                // Reorder coefficients for the lower degree face.
                int offset1 = 0, offset2 = 0;
                if (FaceExp->DetShapeType() == LibUtilities::eQuadrilateral)
                {
                    for (i = 0; i < NumModesElementMin; ++i)
                    {
                        for (j = 0; j < NumModesElementMin; ++j)
                        {
                            faceCoeffs[offset1+j] =
                            faceCoeffs[offset2+j];
                        }
                        offset1 += NumModesElementMin;
                        offset2 += NumModesElementMax;
                    }
                    // Extract lower degree modes. TODO: Check this is correct.
                    for (i = NumModesElementMin; i < NumModesElementMax; ++i)
                    {
                        for (j = NumModesElementMin; j < NumModesElementMax; ++j)
                        {
                            faceCoeffs[i*NumModesElementMax+j] = 0.0;
                        }
                    }
                }
                if (FaceExp->DetShapeType() == LibUtilities::eTriangle)
                {
                    // Reorder coefficients for the lower degree face.
                    int offset1 = 0, offset2 = 0;
                    for (i = 0; i < NumModesElementMin; ++i)
                    {
                        for (j = 0; j < NumModesElementMin-i; ++j)
                        {
                            faceCoeffs[offset1+j] =
                            faceCoeffs[offset2+j];
                        }
                        offset1 += NumModesElementMin-i;
                        offset2 += NumModesElementMax-i;
                    }
                }
            }
            else
            {
                FaceExp->IProductWRTBase(Fn, faceCoeffs);
            }
            if (m_requireNeg[face])
            {
                for (i = 0; i < order_e; ++i)
                {
                    outarray[(*map)[i].index] -= (*map)[i].sign * faceCoeffs[i];
                }
            }
            else
            {
                for (i = 0; i < order_e; ++i)
                {
                    outarray[(*map)[i].index] += (*map)[i].sign * faceCoeffs[i];
                }
            }
        }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1094 of file Expansion3D.cpp.

        {
            ASSERTL1(IsBoundaryInteriorExpansion(),
                     "Not set up for non boundary-interior expansions");
            ASSERTL1(inoutmat->GetRows() == inoutmat->GetColumns(),
                     "Assuming that input matrix was square");
            
            int i,j;
            int id1,id2;
            Expansion2DSharedPtr faceExp = m_faceExp[face].lock();
            int order_f = faceExp->GetNcoeffs();
         
            Array<OneD, unsigned int> map;
            Array<OneD,          int> sign;
            
            StdRegions::VarCoeffMap varcoeffs;
            varcoeffs[StdRegions::eVarCoeffMass] = primCoeffs;
            LibUtilities::ShapeType shapeType = 
                faceExp->DetShapeType();
            LocalRegions::MatrixKey mkey(
                StdRegions::eMass,
                shapeType, 
                *faceExp, 
                StdRegions::NullConstFactorMap, 
                varcoeffs);
            DNekScalMat &facemat = *faceExp->GetLocMatrix(mkey);
            // Now need to identify a map which takes the local face
            // mass matrix to the matrix stored in inoutmat;
            // This can currently be deduced from the size of the matrix
            
            // - if inoutmat.m_rows() == v_NCoeffs() it is a full
            //   matrix system
            
            // - if inoutmat.m_rows() == v_NumBndCoeffs() it is a
            //  boundary CG system
            // - if inoutmat.m_rows() == v_NumDGBndCoeffs() it is a
            //  trace DG system; still needs implementing.
            int rows = inoutmat->GetRows();
            if (rows == GetNcoeffs())
            {
                GetFaceToElementMap(face,GetFaceOrient(face),map,sign);
            }
            else if(rows == NumBndryCoeffs())
            {
                int nbndry = NumBndryCoeffs();
                Array<OneD,unsigned int> bmap(nbndry);
                GetFaceToElementMap(face,GetFaceOrient(face),map,sign);
                GetBoundaryMap(bmap);
                
                for(i = 0; i < order_f; ++i)
                {
                    for(j = 0; j < nbndry; ++j)
                    {
                        if(map[i] == bmap[j])
                        {
                            map[i] = j;
                            break;
                        }
                    }
                    ASSERTL1(j != nbndry,"Did not find number in map");
                }
            }
            else if (rows == NumDGBndryCoeffs())
            {
                // possibly this should be a separate method
                int cnt = 0; 
                map  = Array<OneD, unsigned int> (order_f);
                sign = Array<OneD,          int> (order_f,1);
                
                StdRegions::IndexMapKey ikey1(
                    StdRegions::eFaceToElement, DetShapeType(), 
                    GetBasisNumModes(0), GetBasisNumModes(1), GetBasisNumModes(2),
                    face, GetFaceOrient(face));
                StdRegions::IndexMapValuesSharedPtr map1 = 
                    StdExpansion::GetIndexMap(ikey1);
                StdRegions::IndexMapKey ikey2(
                    StdRegions::eFaceToElement, DetShapeType(), 
                    GetBasisNumModes(0), GetBasisNumModes(1), GetBasisNumModes(2),
                    face, StdRegions::eDir1FwdDir1_Dir2FwdDir2);
                StdRegions::IndexMapValuesSharedPtr map2 = 
                    StdExpansion::GetIndexMap(ikey2);
                
                ASSERTL1((*map1).num_elements() == (*map2).num_elements(),
                         "There is an error with the GetFaceToElementMap");
                
                for (i = 0; i < face; ++i)
                {
                    cnt += GetFaceNcoeffs(i);
                }
                for(i = 0; i < (*map1).num_elements(); ++i)
                {
                    int idx = -1;
                    for(j = 0; j < (*map2).num_elements(); ++j)
                    {
                        if((*map1)[i].index == (*map2)[j].index)
                        {
                            idx = j;
                            break;
                        }
                    }
                    
                    ASSERTL2(idx >= 0, "Index not found");
                    map [i] = idx + cnt;
                    sign[i] = (*map2)[idx].sign;
                }
            }
            else
            {
                ASSERTL0(false,"Could not identify matrix type from dimension");
            }
            for(i = 0; i < order_f; ++i)
            {
                id1 = map[i];
                for(j = 0; j < order_f; ++j)
                {
                    id2 = map[j];
                    (*inoutmat)(id1,id2) += facemat(i,j)*sign[i]*sign[j];
                }
            }
        }

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

protectedvirtual

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

{R^{-T}}=[[{array}{ccc} {I} & -{R}_{ef} & -{R}_{ve}+{R}_{ve}{R}_{vf} \ 0 & {I} & {R}_{ef} \ 0 & 0 & {I}} {array}]]

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1680 of file Expansion3D.cpp.

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

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

protectedvirtual

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

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

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

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1259 of file Expansion3D.cpp.

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

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

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1228 of file Expansion3D.cpp.

References Nektar::eFULL, Nektar::StdRegions::StdExpansion::GetNverts(), and Nektar::StdRegions::StdExpansion::GetVertexMap().

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

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

protectedvirtual

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

Definition at line 1064 of file Expansion3D.cpp.

References AddNormTraceInt(), Nektar::StdRegions::eInvMass, Nektar::StdRegions::eWeakDeriv0, Nektar::StdRegions::eWeakDeriv1, Nektar::StdRegions::eWeakDeriv2, Nektar::eWrapper, Nektar::LocalRegions::Expansion::GetLocMatrix(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Vmath::Neg(), and Nektar::Transpose().

        {
            int ncoeffs = GetNcoeffs();
            StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                                   StdRegions::eWeakDeriv1,
                                                   StdRegions::eWeakDeriv2};
            DNekScalMat &InvMass = *GetLocMatrix(StdRegions::eInvMass);
            DNekScalMat &Dmat    = *GetLocMatrix(DerivType[dir]);
            Array<OneD, NekDouble> coeffs = incoeffs;
            DNekVec     Coeffs  (ncoeffs,coeffs, eWrapper);
            Coeffs = Transpose(Dmat)*Coeffs;
            Vmath::Neg(ncoeffs, coeffs,1);
            // Add the boundary integral including the relevant part of
            // the normal
            AddNormTraceInt(dir, FaceExp, faceCoeffs, coeffs);
            DNekVec Out_d (ncoeffs,out_d,eWrapper);
            Out_d  = InvMass*Coeffs;
        }

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

protectedvirtual

Computes matrices needed for the HDG formulation. References to equations relate to the following paper (with a suitable changes in formulation to adapt to 3D): R. M. Kirby, S. J. Sherwin, B. Cockburn, To CG or to HDG: A Comparative Study, J. Sci. Comp P1-30 DOI 10.1007/s10915-011-9501-7 NOTE: VARIABLE COEFFICIENTS CASE IS NOT IMPLEMENTED

Reimplemented from Nektar::StdRegions::StdExpansion.

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

Definition at line 380 of file Expansion3D.cpp.

        {
            //Variable coefficients are not implemented/////////
            ASSERTL1(!mkey.HasVarCoeff(StdRegions::eVarCoeffD00),
                     "Matrix construction is not implemented for variable "
                     "coefficients at the moment");
            ////////////////////////////////////////////////////
            DNekMatSharedPtr returnval;
            
            switch(mkey.GetMatrixType())
            {
                // (Z^e)^{-1} (Eqn. 33, P22)
                case StdRegions::eHybridDGHelmholtz:
                {
                    ASSERTL1(IsBoundaryInteriorExpansion(),
                             "HybridDGHelmholtz matrix not set up "
                             "for non boundary-interior expansions");
                    
                    int       i,j,k;
                    NekDouble lambdaval = mkey.GetConstFactor(StdRegions::eFactorLambda);
                    NekDouble tau       = mkey.GetConstFactor(StdRegions::eFactorTau);
                    int       ncoeffs   = GetNcoeffs();
                    int       nfaces    = GetNfaces();
                    Array<OneD,unsigned int> fmap;
                    Array<OneD,int> sign;
                    ExpansionSharedPtr FaceExp;
                    StdRegions::StdExpansionSharedPtr FaceExp2;
                    int order_f, coordim = GetCoordim();
                    DNekScalMat  &invMass = *GetLocMatrix(StdRegions::eInvMass);
                    StdRegions::MatrixType DerivType[3] = {StdRegions::eWeakDeriv0,
                                                           StdRegions::eWeakDeriv1,
                                                           StdRegions::eWeakDeriv2};
                    returnval = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,ncoeffs);
                    DNekMat &Mat = *returnval;
                    Vmath::Zero(ncoeffs*ncoeffs,Mat.GetPtr(),1);
                    // StdRegions::VarCoeffType Coeffs[3] = {StdRegions::eVarCoeffD00,
                    //                                       StdRegions::eVarCoeffD11,
                    //                                       StdRegions::eVarCoeffD22};
                    for(i=0;  i < coordim; ++i)
                    {
                        DNekScalMat &Dmat = *GetLocMatrix(DerivType[i]);
                        Mat = Mat + Dmat*invMass*Transpose(Dmat);
                        
                        /*
                        if(mkey.HasVarCoeff(Coeffs[i]))
                        {
                            MatrixKey DmatkeyL(DerivType[i], DetExpansionType(), *this, 
                                               StdRegions::NullConstFactorMap,
                                               mkey.GetVarCoeffAsMap(Coeffs[i]));
                            MatrixKey DmatkeyR(DerivType[i], DetExpansionType(), *this);
                            DNekScalMat &DmatL = *GetLocMatrix(DmatkeyL);
                            DNekScalMat &DmatR = *GetLocMatrix(DmatkeyR);
                            Mat = Mat + DmatL*invMass*Transpose(DmatR);
                        }
                        else
                        {
                            DNekScalMat &Dmat = *GetLocMatrix(DerivType[i]);
                            Mat = Mat + Dmat*invMass*Transpose(Dmat);
                        }
                        */
                    }
                    // Add Mass Matrix Contribution for Helmholtz problem
                    DNekScalMat  &Mass = *GetLocMatrix(StdRegions::eMass);
                    Mat = Mat + lambdaval*Mass;
                    // Add tau*E_l using elemental mass matrices on each edge
                    for(i = 0; i < nfaces; ++i)
                    {
                        FaceExp = GetFaceExp(i);
                        order_f = FaceExp->GetNcoeffs();  
                        StdRegions::IndexMapKey ikey(
                            StdRegions::eFaceToElement, DetShapeType(), 
                            GetBasisNumModes(0), GetBasisNumModes(1), 
                            GetBasisNumModes(2), i, GetFaceOrient(i));
                        StdRegions::IndexMapValuesSharedPtr map = 
                            StdExpansion::GetIndexMap(ikey);
                        // @TODO: Document
                        /*
                        StdRegions::VarCoeffMap edgeVarCoeffs;
                        if (mkey.HasVarCoeff(StdRegions::eVarCoeffD00))
                        {
                            Array<OneD, NekDouble> mu(nq);
                            GetPhysEdgeVarCoeffsFromElement(
                                i, EdgeExp2, 
                                mkey.GetVarCoeff(StdRegions::eVarCoeffD00), mu);
                            edgeVarCoeffs[StdRegions::eVarCoeffMass] = mu;
                        }
                        DNekScalMat &eMass = *EdgeExp->GetLocMatrix(
                            StdRegions::eMass, 
                            StdRegions::NullConstFactorMap, edgeVarCoeffs);
                        */
                        DNekScalMat &eMass = *FaceExp->GetLocMatrix(StdRegions::eMass);
                        for(j = 0; j < order_f; ++j)
                        {
                            for(k = 0; k < order_f; ++k)
                            {
                                Mat((*map)[j].index,(*map)[k].index) += 
                                    tau*(*map)[j].sign*(*map)[k].sign*eMass(j,k);
                            }
                        }
                    }
                    break;
                }
                // U^e (P22)
                case StdRegions::eHybridDGLamToU:
                {
                    int       i,j,k;
                    int       nbndry  = NumDGBndryCoeffs();
                    int       ncoeffs = GetNcoeffs();
                    int       nfaces  = GetNfaces();
                    NekDouble tau     = mkey.GetConstFactor(StdRegions::eFactorTau);
                    
                    Array<OneD,NekDouble> lambda(nbndry);
                    DNekVec Lambda(nbndry,lambda,eWrapper);
                    Array<OneD,NekDouble> ulam(ncoeffs);
                    DNekVec Ulam(ncoeffs,ulam,eWrapper);
                    Array<OneD,NekDouble> f(ncoeffs);
                    DNekVec F(ncoeffs,f,eWrapper);
                    
                    StdRegions::StdExpansionSharedPtr FaceExp;
                    // declare matrix space
                    returnval = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,nbndry); 
                    DNekMat &Umat = *returnval;
                    
                    // Z^e matrix
                    MatrixKey newkey(StdRegions::eInvHybridDGHelmholtz, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    DNekScalMat  &invHmat = *GetLocMatrix(newkey);
                    Array<OneD,unsigned int> fmap;
                    Array<OneD,int> sign;
                    
                    //alternative way to add boundary terms contribution
                    int bndry_cnt = 0;
                    for(i = 0; i < nfaces; ++i)
                    {
                        FaceExp = GetFaceExp(i);//temporary, need to rewrite AddHDGHelmholtzFaceTerms
                        int nface = GetFaceNcoeffs(i);
                        Array<OneD, NekDouble> face_lambda(nface);
            
                        const Array<OneD, const Array<OneD, NekDouble> > normals
                            = GetFaceNormal(i);
                        for(j = 0; j < nface; ++j)
                        {
                            Vmath::Zero(nface,&face_lambda[0],1);
                            Vmath::Zero(ncoeffs,&f[0],1);
                            face_lambda[j] = 1.0;
                            SetFaceToGeomOrientation(i, face_lambda);
                            Array<OneD, NekDouble> tmp(FaceExp->GetTotPoints());
                            FaceExp->BwdTrans(face_lambda, tmp);
                            AddHDGHelmholtzFaceTerms(tau, i, tmp, mkey.GetVarCoeffs(), f);
                            
                            Ulam = invHmat*F; // generate Ulam from lambda
                            // fill column of matrix
                            for(k = 0; k < ncoeffs; ++k)
                            {
                                Umat(k,bndry_cnt) = Ulam[k]; 
                            }
                            
                            ++bndry_cnt;
                        }
                    }
                    //// Set up face expansions from local geom info
                    //for(i = 0; i < nfaces; ++i)
                    //{
                    //    FaceExp[i] = GetFaceExp(i);
                    //}
                    //
                    //// for each degree of freedom of the lambda space
                    //// calculate Umat entry 
                    //// Generate Lambda to U_lambda matrix 
                    //for(j = 0; j < nbndry; ++j)
                    //{
                    //    // standard basis vectors e_j
                    //    Vmath::Zero(nbndry,&lambda[0],1);
                    //    Vmath::Zero(ncoeffs,&f[0],1);
                    //    lambda[j] = 1.0;
                    //    
                    //  //cout << Lambda;
                    //    SetTraceToGeomOrientation(lambda);
                    //  //cout << Lambda << endl;
                    //    
                    //    // Compute F = [I   D_1 M^{-1}   D_2 M^{-1}] C e_j
                    //    AddHDGHelmholtzTraceTerms(tau, lambda, FaceExp, mkey.GetVarCoeffs(), f);
                    //    
                    //    // Compute U^e_j
                    //    Ulam = invHmat*F; // generate Ulam from lambda
                    //    
                    //    // fill column of matrix
                    //    for(k = 0; k < ncoeffs; ++k)
                    //    {
                    //        Umat(k,j) = Ulam[k]; 
                    //    }
                    //}
                }
                break;
            // Q_0, Q_1, Q_2 matrices (P23)
            // Each are a product of a row of Eqn 32 with the C matrix.
            // Rather than explicitly computing all of Eqn 32, we note each
            // row is almost a multiple of U^e, so use that as our starting
            // point.
            case StdRegions::eHybridDGLamToQ0:
            case StdRegions::eHybridDGLamToQ1:
            case StdRegions::eHybridDGLamToQ2:
                {
                    int i,j,k,dir;
                    int nbndry = NumDGBndryCoeffs();
                    //int nquad  = GetNumPoints(0);
                    int ncoeffs = GetNcoeffs();
                    int nfaces  = GetNfaces();
                    Array<OneD,NekDouble> lambda(nbndry);
                    DNekVec Lambda(nbndry,lambda,eWrapper);                    
                    Array<OneD,StdRegions::StdExpansionSharedPtr>  FaceExp(nfaces);
                    
                    Array<OneD,NekDouble> ulam(ncoeffs);
                    DNekVec Ulam(ncoeffs,ulam,eWrapper);
                    Array<OneD,NekDouble> f(ncoeffs);
                    DNekVec F(ncoeffs,f,eWrapper);
                    
                    // declare matrix space
                    returnval  = MemoryManager<DNekMat>::AllocateSharedPtr(ncoeffs,nbndry); 
                    DNekMat &Qmat = *returnval;
                    
                    // Lambda to U matrix
                    MatrixKey lamToUkey(StdRegions::eHybridDGLamToU, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    DNekScalMat &lamToU = *GetLocMatrix(lamToUkey);
                    // Inverse mass matrix 
                    DNekScalMat &invMass = *GetLocMatrix(StdRegions::eInvMass);
                    
                    for(i = 0; i < nfaces; ++i)
                    {
                        FaceExp[i] = GetFaceExp(i);
                    }
                    //Weak Derivative matrix 
                    DNekScalMatSharedPtr Dmat;
                    switch(mkey.GetMatrixType())
                    {
                    case StdRegions::eHybridDGLamToQ0:
                        dir = 0;
                        Dmat = GetLocMatrix(StdRegions::eWeakDeriv0);
                        break;
                    case StdRegions::eHybridDGLamToQ1:
                        dir = 1;
                        Dmat = GetLocMatrix(StdRegions::eWeakDeriv1);
                        break;
                    case StdRegions::eHybridDGLamToQ2:
                        dir = 2;
                        Dmat = GetLocMatrix(StdRegions::eWeakDeriv2);
                        break;
                    default:
                        ASSERTL0(false,"Direction not known");
                        break;
                    }
                
                    // for each degree of freedom of the lambda space
                    // calculate Qmat entry 
                    // Generate Lambda to Q_lambda matrix 
                    for(j = 0; j < nbndry; ++j)
                    {
                        Vmath::Zero(nbndry,&lambda[0],1);
                        lambda[j] = 1.0;
                        
                        // for lambda[j] = 1 this is the solution to ulam
                        for(k = 0; k < ncoeffs; ++k)
                        {
                            Ulam[k] = lamToU(k,j);
                        }
                        
                        // -D^T ulam
                        Vmath::Neg(ncoeffs,&ulam[0],1);
                        F = Transpose(*Dmat)*Ulam; 
                        
                        SetTraceToGeomOrientation(lambda);
                        
                        // Add the C terms resulting from the I's on the
                        // diagonals of Eqn 32
                        AddNormTraceInt(dir,lambda,FaceExp,f,mkey.GetVarCoeffs());
                        
                        // finally multiply by inverse mass matrix
                        Ulam = invMass*F; 
                        
                        // fill column of matrix (Qmat is in column major format)
                        Vmath::Vcopy(ncoeffs,&ulam[0],1,&(Qmat.GetPtr())[0]+j*ncoeffs,1);
                    }
                }
                break;            
            // Matrix K (P23)
            case StdRegions::eHybridDGHelmBndLam:
                {
                    int i,j,f,cnt;
                    int order_f, nquad_f;
                    int nbndry  = NumDGBndryCoeffs();
                    int nfaces  = GetNfaces();
                    NekDouble tau = mkey.GetConstFactor(StdRegions::eFactorTau);
                    Array<OneD,NekDouble>       work, varcoeff_work;
                    Array<OneD,const Array<OneD, NekDouble> > normals; 
                    Array<OneD,StdRegions::StdExpansionSharedPtr>  FaceExp(nfaces);
                    Array<OneD, NekDouble> lam(nbndry); 
                    
                    Array<OneD,unsigned int>    fmap;
                    Array<OneD, int>            sign;
                    
                    // declare matrix space
                    returnval = MemoryManager<DNekMat>::AllocateSharedPtr(nbndry, nbndry);
                    DNekMat &BndMat = *returnval;
                    
                    DNekScalMatSharedPtr LamToQ[3];
                    
                    // Matrix to map Lambda to U
                    MatrixKey LamToUkey(StdRegions::eHybridDGLamToU, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    DNekScalMat &LamToU = *GetLocMatrix(LamToUkey);
                    // Matrix to map Lambda to Q0
                    MatrixKey LamToQ0key(StdRegions::eHybridDGLamToQ0, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    LamToQ[0] = GetLocMatrix(LamToQ0key);
 
                    // Matrix to map Lambda to Q1
                    MatrixKey LamToQ1key(StdRegions::eHybridDGLamToQ1, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    LamToQ[1] = GetLocMatrix(LamToQ1key);
                    // Matrix to map Lambda to Q2
                    MatrixKey LamToQ2key(StdRegions::eHybridDGLamToQ2, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    LamToQ[2] = GetLocMatrix(LamToQ2key);
                    // Set up edge segment expansions from local geom info
                    for(i = 0; i < nfaces; ++i)
                    {
                        FaceExp[i] = GetFaceExp(i);
                    }
                    // Set up matrix derived from <mu, Q_lam.n - \tau (U_lam - Lam) > 
                    for(i = 0; i < nbndry; ++i)
                    {
                        cnt = 0;
                        
                        Vmath::Zero(nbndry,lam,1);
                        lam[i] = 1.0;
                        SetTraceToGeomOrientation(lam);
                        for(f = 0; f < nfaces; ++f)
                        {
                            order_f = FaceExp[f]->GetNcoeffs();  
                            nquad_f = FaceExp[f]->GetNumPoints(0)*FaceExp[f]->GetNumPoints(1);    
                            normals = GetFaceNormal(f);
                            
                            work = Array<OneD,NekDouble>(nquad_f);
                            varcoeff_work = Array<OneD, NekDouble>(nquad_f);
                            StdRegions::IndexMapKey ikey(
                                StdRegions::eFaceToElement, DetShapeType(), 
                                GetBasisNumModes(0), GetBasisNumModes(1), 
                                GetBasisNumModes(2), f, GetFaceOrient(f));
                            StdRegions::IndexMapValuesSharedPtr map = 
                                StdExpansion::GetIndexMap(ikey);
                            // @TODO Variable coefficients
                            /*
                            StdRegions::VarCoeffType VarCoeff[3] = {StdRegions::eVarCoeffD00,
                                                                    StdRegions::eVarCoeffD11,
                                                                    StdRegions::eVarCoeffD22};
                            const StdRegions::VarCoeffMap &varcoeffs = mkey.GetVarCoeffs();
                            StdRegions::VarCoeffMap::const_iterator x;
                            */
                            // Q0 * n0 (BQ_0 terms)
                            Array<OneD, NekDouble> faceCoeffs(order_f);
                            Array<OneD, NekDouble> facePhys  (nquad_f);
                            for(j = 0; j < order_f; ++j)
                            {
                                faceCoeffs[j] = (*map)[j].sign*(*LamToQ[0])((*map)[j].index,i);
                            }
                            
                            FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
                            // @TODO Variable coefficients
                            // Multiply by variable coefficient
                            /*
                            if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
                            {
                                GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
                                Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
                            }
                            */
          
                            Vmath::Vmul(nquad_f, normals[0], 1, facePhys, 1, work, 1);
                            
                            // Q1 * n1 (BQ_1 terms)
                            for(j = 0; j < order_f; ++j)
                            {
                                faceCoeffs[j] = (*map)[j].sign*(*LamToQ[1])((*map)[j].index,i);
                            }
                            
                            FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
                            // @TODO Variable coefficients
                            // Multiply by variable coefficients
                            /*
                            if ((x = varcoeffs.find(VarCoeff[1])) != varcoeffs.end())
                            {
                                GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
                                Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
                            }
                            */
                            Vmath::Vvtvp(nquad_f, normals[1], 1, facePhys, 1, work, 1, work, 1);
                            
                            // Q2 * n2 (BQ_2 terms)
                            for(j = 0; j < order_f; ++j)
                            {
                                faceCoeffs[j] = (*map)[j].sign*(*LamToQ[2])((*map)[j].index,i);
                            }
                            
                            FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
                            // @TODO Variable coefficients
                            // Multiply by variable coefficients
                            /*
                            if ((x = varcoeffs.find(VarCoeff[2])) != varcoeffs.end())
                            {
                                GetPhysEdgeVarCoeffsFromElement(e,EdgeExp[e],x->second,varcoeff_work);
                                Vmath::Vmul(nquad_e,varcoeff_work,1,EdgeExp[e]->GetPhys(),1,EdgeExp[e]->UpdatePhys(),1);
                            }
                            */
                            Vmath::Vvtvp(nquad_f, normals[2], 1, facePhys, 1,
                                                  work,       1, work,     1);
                            if (m_negatedNormals[f])
                            {
                                Vmath::Neg(nquad_f, work, 1);
                            }
                            // - tau (ulam - lam)
                            // Corresponds to the G and BU terms.
                            for(j = 0; j < order_f; ++j)
                            {
                                faceCoeffs[j] = (*map)[j].sign*LamToU((*map)[j].index,i) - lam[cnt+j];
                            }
                            
                            FaceExp[f]->BwdTrans(faceCoeffs, facePhys);
                            // @TODO Variable coefficients
                            // Multiply by variable coefficients
                            /*
                            if ((x = varcoeffs.find(VarCoeff[0])) != varcoeffs.end())
                            {
                                GetPhysEdgeVarCoeffsFromElement(e,FaceExp[f],x->second,varcoeff_work);
                                Vmath::Vmul(nquad_f,varcoeff_work,1,FaceExp[f]->GetPhys(),1,FaceExp[f]->UpdatePhys(),1);
                            }
                            */
                            Vmath::Svtvp(nquad_f, -tau, facePhys, 1,
                                         work, 1, work, 1);
                            // @TODO Add variable coefficients
                            FaceExp[f]->IProductWRTBase(work, faceCoeffs);
                            
                            SetFaceToGeomOrientation(f, faceCoeffs);
                            for(j = 0; j < order_f; ++j)
                            {
                                BndMat(cnt+j,i) = faceCoeffs[j];
                            }
                            cnt += order_f;
                        }
                    }
                }
                break;
            //HDG postprocessing
            case StdRegions::eInvLaplacianWithUnityMean:
                {
                    MatrixKey lapkey(StdRegions::eLaplacian, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    DNekScalMat  &LapMat = *GetLocMatrix(lapkey);
                    
                    returnval = MemoryManager<DNekMat>::AllocateSharedPtr(LapMat.GetRows(),LapMat.GetColumns());
                    DNekMatSharedPtr lmat = returnval;
                    
                    (*lmat) = LapMat;
                    // replace first column with inner product wrt 1
                    int nq = GetTotPoints();
                    Array<OneD, NekDouble> tmp(nq);
                    Array<OneD, NekDouble> outarray(m_ncoeffs);
                    Vmath::Fill(nq,1.0,tmp,1);
                    IProductWRTBase(tmp, outarray);
                    Vmath::Vcopy(m_ncoeffs,&outarray[0],1,
                                 &(lmat->GetPtr())[0],1);
                    //cout << endl << *lmat << endl;
                    lmat->Invert();
                }
                break;
            default:
                ASSERTL0(false,"This matrix type cannot be generated from this class");
                break;
            }
            
            return returnval;
        }

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1806 of file Expansion3D.cpp.

References Nektar::StdRegions::StdExpansion::GetBoundaryMap(), Nektar::StdRegions::StdExpansion::GetEdgeInteriorMap(), Nektar::StdRegions::StdExpansion::GetEdgeNcoeffs(), GetGeom3D(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

        {
            int n, j;
            int nEdgeCoeffs;
            int nBndCoeffs = NumBndryCoeffs();
            Array<OneD, unsigned int> bmap(nBndCoeffs);
            GetBoundaryMap(bmap);
            // Map from full system to statically condensed system (i.e reverse
            // GetBoundaryMap)
            map<int, int> invmap;
            for (j = 0; j < nBndCoeffs; ++j)
            {
                invmap[bmap[j]] = j;
            }
            // Number of interior edge coefficients
            nEdgeCoeffs = GetEdgeNcoeffs(eid) - 2;
            const SpatialDomains::Geometry3DSharedPtr &geom = GetGeom3D();
            Array<OneD, unsigned int> edgemaparray(nEdgeCoeffs);
            StdRegions::Orientation   eOrient  =
                geom->GetEorient(eid);
            Array<OneD, unsigned int> maparray =
                Array<OneD, unsigned int>(nEdgeCoeffs);
            Array<OneD, int> signarray         =
                Array<OneD, int>(nEdgeCoeffs, 1);
            // maparray is the location of the edge within the matrix
            GetEdgeInteriorMap(eid, eOrient, maparray, signarray);
            for (n = 0; n < nEdgeCoeffs; ++n)
            {
                edgemaparray[n] = invmap[maparray[n]];
            }
            return edgemaparray;
        }

Array< OneD, unsigned int > Nektar::LocalRegions::Expansion3D::v_GetFaceInverseBoundaryMap	(	int	fid,
		StdRegions::Orientation	faceOrient = `StdRegions::eNoOrientation`
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1849 of file Expansion3D.cpp.

References Nektar::StdRegions::eNoOrientation, Nektar::StdRegions::StdExpansion::GetBoundaryMap(), Nektar::StdRegions::StdExpansion::GetFaceInteriorMap(), Nektar::StdRegions::StdExpansion::GetFaceIntNcoeffs(), Nektar::StdRegions::StdExpansion::GetFaceOrient(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

        {
            int n, j;
            int nFaceCoeffs;
            int nBndCoeffs = NumBndryCoeffs();
            Array<OneD, unsigned int> bmap(nBndCoeffs);
            GetBoundaryMap(bmap);
            // Map from full system to statically condensed system (i.e reverse
            // GetBoundaryMap)
            map<int, int> reversemap;
            for (j = 0; j < bmap.num_elements(); ++j)
            {
                reversemap[bmap[j]] = j;
            }
            // Number of interior face coefficients
            nFaceCoeffs = GetFaceIntNcoeffs(fid);
            Array<OneD, unsigned int> facemaparray(nFaceCoeffs);
            StdRegions::Orientation   fOrient; 
            Array<OneD, unsigned int> maparray  =
                Array<OneD, unsigned int>(nFaceCoeffs);
            Array<OneD, int>          signarray =
                Array<OneD, int>(nFaceCoeffs, 1);
            if(faceOrient == StdRegions::eNoOrientation)
            {
                fOrient = GetFaceOrient(fid);
            }
            else
            {
                fOrient = faceOrient; 
            }
            
            // maparray is the location of the face within the matrix
            GetFaceInteriorMap(fid, fOrient, maparray, signarray);
            for (n = 0; n < nFaceCoeffs; ++n)
            {
                facemaparray[n] = reversemap[maparray[n]];
            }
            return facemaparray;
        }

NekDouble Nektar::LocalRegions::Expansion3D::v_Integrate ( const Array< OneD, const NekDouble > & inarray )

protectedvirtual

Definition at line 1897 of file Expansion3D.cpp.

References ErrorUtil::efatal, and NEKERROR.

        {
            NEKERROR(ErrorUtil::efatal, 
                     "This function is not implemented here. It is shape "
                     "specific");
            return 0.0;
        }

Member Data Documentation

std::vector<Expansion2DWeakPtr> Nektar::LocalRegions::Expansion3D::m_faceExp

private

Definition at line 146 of file Expansion3D.h.

Referenced by GetFaceExp(), SetFaceExp(), v_AddFaceNormBoundaryInt(), and v_AddRobinMassMatrix().

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

private

Definition at line 147 of file Expansion3D.h.

Referenced by v_AddFaceNormBoundaryInt().

Public Member Functions

Protected Member Functions

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Constructor & Destructor Documentation

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