Nektar::LocalRegions::PyrExp Class Reference

#include <PyrExp.h>

Inheritance diagram for Nektar::LocalRegions::PyrExp:

Public Member Functions
	PyrExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc, const SpatialDomains::PyrGeomSharedPtr &geom)
	Constructor using BasisKey class for quadrature points and order definition. More...
	PyrExp (const PyrExp &T)
	~PyrExp ()
Public Member Functions inherited from Nektar::StdRegions::StdPyrExp
	StdPyrExp ()
	StdPyrExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)
	StdPyrExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc, NekDouble *coeffs, NekDouble *phys)
	StdPyrExp (const StdPyrExp &T)
	~StdPyrExp ()
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. More...
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)
Public Member Functions inherited from Nektar::StdRegions::StdExpansion
	StdExpansion ()
	Default Constructor. More...
	StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey)
	Constructor. More...
	StdExpansion (const StdExpansion &T)
	Copy Constructor. More...
virtual	~StdExpansion ()
	Destructor. More...
int	GetNumBases () const
	This function returns the number of 1D bases used in the expansion. More...
const Array< OneD, const LibUtilities::BasisSharedPtr > &	GetBase () const
	This function gets the shared point to basis. More...
const LibUtilities::BasisSharedPtr &	GetBasis (int dir) const
	This function gets the shared point to basis in the dir direction. More...
int	GetNcoeffs (void) const
	This function returns the total number of coefficients used in the expansion. More...
int	GetTotPoints () const
	This function returns the total number of quadrature points used in the element. More...
LibUtilities::BasisType	GetBasisType (const int dir) const
	This function returns the type of basis used in the dir direction. More...
int	GetBasisNumModes (const int dir) const
	This function returns the number of expansion modes in the dir direction. More...
int	EvalBasisNumModesMax (void) const
	This function returns the maximum number of expansion modes over all local directions. More...
LibUtilities::PointsType	GetPointsType (const int dir) const
	This function returns the type of quadrature points used in the dir direction. More...
int	GetNumPoints (const int dir) const
	This function returns the number of quadrature points in the dir direction. More...
const Array< OneD, const NekDouble > &	GetPoints (const int dir) const
	This function returns a pointer to the array containing the quadrature points in dir direction. More...
int	GetNverts () const
	This function returns the number of vertices of the expansion domain. More...
int	GetNedges () const
	This function returns the number of edges of the expansion domain. More...
int	GetEdgeNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th edge. More...
int	GetTotalEdgeIntNcoeffs () const
int	GetEdgeNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th edge. More...
int	DetCartesianDirOfEdge (const int edge)
const LibUtilities::BasisKey	DetEdgeBasisKey (const int i) const
const LibUtilities::BasisKey	DetFaceBasisKey (const int i, const int k) const
int	GetFaceNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th face. More...
int	GetFaceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th face. More...
int	GetFaceIntNcoeffs (const int i) const
int	GetTotalFaceIntNcoeffs () const
int	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th edge/face. More...
LibUtilities::PointsKey	GetFacePointsKey (const int i, const int j) const
int	NumBndryCoeffs (void) const
int	NumDGBndryCoeffs (void) const
LibUtilities::BasisType	GetEdgeBasisType (const int i) const
	This function returns the type of expansion basis on the i-th edge. More...
const LibUtilities::PointsKey	GetNodalPointsKey () const
	This function returns the type of expansion Nodal point type if defined. More...
int	GetNfaces () const
	This function returns the number of faces of the expansion domain. More...
int	GetNtrace () const
	Returns the number of trace elements connected to this element. More...
LibUtilities::ShapeType	DetShapeType () const
	This function returns the shape of the expansion domain. More...
std::shared_ptr< StdExpansion >	GetStdExp (void) const
std::shared_ptr< StdExpansion >	GetLinStdExp (void) const
int	GetShapeDimension () const
bool	IsBoundaryInteriorExpansion ()
bool	IsNodalNonTensorialExp ()
void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Backward transformation from coefficient space to physical space. More...
void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Forward transformation from physical space to coefficient space. More...
void	FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)
	This function integrates the specified function over the domain. More...
void	FillMode (const int mode, Array< OneD, NekDouble > &outarray)
	This function fills the array outarray with the mode-th mode of the expansion. More...
void	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	this function calculates the inner product of a given function f with the different modes of the expansion More...
void	IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)
void	IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
int	GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id. More...
void	SetElmtId (const int id)
	Set the element id of this expansion when used in a list by returning value of m_elmt_id. More...
void	GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
	this function returns the physical coordinates of the quadrature points of the expansion More...
void	GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
	given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point More...
DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)
IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)
const Array< OneD, const NekDouble > &	GetPhysNormals (void)
void	SetPhysNormals (Array< OneD, const NekDouble > &normal)
virtual void	SetUpPhysNormals (const int edge)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray)
DNekScalBlkMatSharedPtr	GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
void	DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
StdRegions::Orientation	GetForient (int face)
StdRegions::Orientation	GetEorient (int edge)
void	SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)
void	SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
int	CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
NekDouble	StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
int	GetCoordim ()
void	GetBoundaryMap (Array< OneD, unsigned int > &outarray)
void	GetInteriorMap (Array< OneD, unsigned int > &outarray)
int	GetVertexMap (const int localVertexId, bool useCoeffPacking=false)
void	GetEdgeInteriorMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
void	GetFaceNumModes (const int fid, const Orientation faceOrient, int &numModes0, int &numModes1)
void	GetFaceInteriorMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
void	GetEdgeToElementMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int P=-1)
void	GetFaceToElementMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int nummodesA=-1, int nummodesB=-1)
void	GetEdgePhysVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Extract the physical values along edge edge from inarray into outarray following the local edge orientation and point distribution defined by defined in EdgeExp. More...
void	GetEdgePhysVals (const int edge, const std::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GetTracePhysVals (const int edge, const std::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GetVertexPhysVals (const int vertex, const Array< OneD, const NekDouble > &inarray, NekDouble &outarray)
void	GetEdgeInterpVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GetEdgeQFactors (const int edge, Array< OneD, NekDouble > &outarray)
	Extract the metric factors to compute the contravariant fluxes along edge edge and stores them into outarray following the local edge orientation (i.e. anticlockwise convention). More...
void	GetFacePhysVals (const int face, const std::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=eNoOrientation)
void	GetEdgePhysMap (const int edge, Array< OneD, int > &outarray)
void	GetFacePhysMap (const int face, Array< OneD, int > &outarray)
void	MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
DNekMatSharedPtr	CreateGeneralMatrix (const StdMatrixKey &mkey)
	this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) More...
void	GeneralMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)
void	ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)
void	LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)
void	PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void	PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	PhysDeriv_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds)
void	PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn)
void	PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)
void	StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void	StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	AddRobinMassMatrix (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
void	AddRobinEdgeContribution (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, Array< OneD, NekDouble > &coeffs)
NekDouble	PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta. More...
virtual int	v_GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id. More...
virtual const Array< OneD, const NekDouble > &	v_GetPhysNormals (void)
virtual void	v_SetPhysNormals (Array< OneD, const NekDouble > &normal)
virtual void	v_SetUpPhysNormals (const int edge)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
virtual StdRegions::Orientation	v_GetEorient (int edge)
NekDouble	Linf (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_\infty\) error \( |\epsilon|_\infty = \max |u - u_{exact}|\) where \( u_{exact}\) is given by the array sol. More...
NekDouble	L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( L_2\) error, \( | \epsilon |_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...
NekDouble	H1 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
	Function to evaluate the discrete \( H^1\) error, \( | \epsilon |^1_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u - u_{exact})\cdot dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol. More...
const NormalVector &	GetEdgeNormal (const int edge) const
void	ComputeEdgeNormal (const int edge)
void	NegateEdgeNormal (const int edge)
bool	EdgeNormalNegated (const int edge)
void	ComputeFaceNormal (const int face)
void	NegateFaceNormal (const int face)
bool	FaceNormalNegated (const int face)
void	ComputeVertexNormal (const int vertex)
void	NegateVertexNormal (const int vertex)
bool	VertexNormalNegated (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, int P1=-1, int P2=-1)
void	GetInverseBoundaryMaps (Array< OneD, unsigned int > &vmap, Array< OneD, Array< OneD, unsigned int > > &emap, Array< OneD, Array< OneD, unsigned int > > &fmap)
DNekMatSharedPtr	BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
void	PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
	This function performs an interpolation from the physical space points provided at input into an array of equispaced points which are not the collapsed coordinate. So for a tetrahedron you will only get a tetrahedral number of values. More...
void	GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
	This function provides the connectivity of local simplices (triangles or tets) to connect the equispaced data points provided by PhysInterpToSimplexEquiSpaced. More...
void	EquiSpacedToCoeffs (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs a projection/interpolation from the equispaced points sometimes used in post-processing onto the coefficient space. More...
template<class T >
std::shared_ptr< T >	as ()
void	IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)
Public Member Functions inherited from Nektar::LocalRegions::Expansion3D
	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. More...
void	SetFaceToGeomOrientation (const int face, Array< OneD, NekDouble > &inout)
	Align face orientation with the geometry orientation. More...
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, ExpansionSharedPtr > &FaceExp, Array< OneD, Array< OneD, NekDouble > > &faceCoeffs, Array< OneD, NekDouble > &outarray)
void	AddNormTraceInt (const int dir, Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &FaceExp, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs)
void	AddFaceBoundaryInt (const int face, ExpansionSharedPtr &FaceExp, Array< OneD, NekDouble > &facePhys, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)
SpatialDomains::Geometry3DSharedPtr	GetGeom3D () const
void	ReOrientFacePhysMap (const int nvert, const StdRegions::Orientation orient, const int nq0, const int nq1, Array< OneD, int > &idmap)
void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray)
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
void	Reset ()
const SpatialDomains::GeomFactorsSharedPtr &	GetMetricInfo () const
DNekMatSharedPtr	BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
DNekMatSharedPtr	BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
void	ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
NekDouble	VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)

Protected Member Functions
virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray)
	Integrate the physical point list inarray over pyramidic region and return the value. More...
virtual void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2)
	Calculate the derivative of the physical points. More...
virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in (this)->m_coeffs. More...
virtual void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Calculate the inner product of inarray with respect to the basis B=base0*base1*base2 and put into outarray: More...
virtual void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Calculates the inner product \( I_{pqr} = (u, \partial_{x_i} \phi_{pqr}) \). More...
void	v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const
virtual StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const
virtual void	v_GetCoord (const Array< OneD, const NekDouble > &Lcoords, Array< OneD, NekDouble > &coords)
virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3)
virtual void	v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int mode_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType)
NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coord, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
virtual int	v_GetCoordim ()
virtual void	v_GetFacePhysMap (const int face, Array< OneD, int > &outarray)
void	v_ComputeFaceNormal (const int face)
virtual void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdRegions::StdMatrixKey &mkey)
virtual DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey)
virtual DNekMatSharedPtr	v_CreateStdMatrix (const StdRegions::StdMatrixKey &mkey)
virtual DNekScalMatSharedPtr	v_GetLocMatrix (const MatrixKey &mkey)
virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const MatrixKey &mkey)
void	v_DropLocStaticCondMatrix (const MatrixKey &mkey)
DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)
DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)
virtual void	v_ComputeLaplacianMetric ()
Protected Member Functions inherited from Nektar::StdRegions::StdPyrExp
virtual void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Calculate the derivative of the physical points in a given direction. More...
virtual void	v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2)
virtual void	v_StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Backward transformation is evaluated at the quadrature points. More...
virtual void	v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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)
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)
virtual void	v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
virtual void	v_FillMode (const int mode, Array< OneD, NekDouble > &outarray)
virtual void	v_GetFaceNumModes (const int fid, const Orientation faceOrient, int &numModes0, int &numModes1)
virtual int	v_GetNverts () const
virtual int	v_GetNedges () const
virtual int	v_GetNfaces () const
virtual LibUtilities::ShapeType	v_DetShapeType () const
virtual int	v_NumBndryCoeffs () const
virtual int	v_NumDGBndryCoeffs () const
virtual int	v_GetEdgeNcoeffs (const int i) const
virtual int	v_GetFaceNcoeffs (const int i) const
virtual int	v_GetFaceIntNcoeffs (const int i) const
virtual int	v_GetFaceNumPoints (const int i) const
virtual int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
virtual const LibUtilities::BasisKey	v_DetFaceBasisKey (const int i, const int k) const
virtual LibUtilities::BasisType	v_GetEdgeBasisType (const int i) const
virtual void	v_GetFaceToElementMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int nummodesA=-1, int nummodesB=-1)
virtual int	v_GetVertexMap (int localVertexId, bool useCoeffPacking=false)
virtual void	v_GetEdgeInteriorMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
virtual void	v_GetFaceInteriorMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
virtual void	v_GetInteriorMap (Array< OneD, unsigned int > &outarray)
virtual void	v_GetBoundaryMap (Array< OneD, unsigned int > &outarray)
virtual void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion3D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
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 void	v_NegateFaceNormal (const int face)
virtual bool	v_FaceNormalNegated (const int face)
virtual int	v_GetTraceNcoeffs (const int i) const
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr	CreateStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
	Create the static condensation of a matrix when using a boundary interior decomposition. More...
IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)
	Create an IndexMap which contains mapping information linking any specific element shape with either its boundaries, edges, faces, verteces, etc. More...
void	BwdTrans_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
void	LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	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)
Protected Member Functions inherited from Nektar::LocalRegions::Expansion3D
virtual void	v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, ExpansionSharedPtr > &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). More...
virtual void	v_AddFaceNormBoundaryInt (const int face, const ExpansionSharedPtr &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 StdRegions::Orientation	v_GetForient (int face)
virtual void	v_GetTracePhysVals (const int face, const StdRegions::StdExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient)
	Returns the physical values at the quadrature points of a face Wrapper function to v_GetFacePhysVals. More...
virtual void	v_GetFacePhysVals (const int face, const StdRegions::StdExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient)
void	GetPhysFaceVarCoeffsFromElement (const int face, ExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &varcoeff, Array< OneD, NekDouble > &outarray)
virtual Array< OneD, NekDouble >	v_GetnFacecdotMF (const int dir, const int face, ExpansionSharedPtr &FaceExp_f, const Array< OneD, const Array< OneD, NekDouble > > &normals, const StdRegions::VarCoeffMap &varcoeffs)
virtual Array< OneD, unsigned int >	v_GetEdgeInverseBoundaryMap (int eid)
virtual Array< OneD, unsigned int >	v_GetFaceInverseBoundaryMap (int fid, StdRegions::Orientation faceOrient=StdRegions::eNoOrientation, int P1=-1, int P2=-1)
void	v_GetInverseBoundaryMaps (Array< OneD, unsigned int > &vmap, Array< OneD, Array< OneD, unsigned int > > &emap, Array< OneD, Array< OneD, unsigned int > > &fmap)
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
virtual DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &transformationmatrix)
	Build inverse and inverse transposed transformation matrix: \(\mathbf{R^{-1}}\) and \(\mathbf{R^{-T}}\). More...
virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
void	ReOrientTriFacePhysMap (const StdRegions::Orientation orient, const int nq0, const int nq1, Array< OneD, int > &idmap)
void	ReOrientQuadFacePhysMap (const StdRegions::Orientation orient, const int nq0, const int nq1, Array< OneD, int > &idmap)
Protected Member Functions inherited from Nektar::LocalRegions::Expansion
void	ComputeLaplacianMetric ()
void	ComputeQuadratureMetric ()
void	ComputeGmatcdotMF (const Array< TwoD, const NekDouble > &df, const Array< OneD, const NekDouble > &direction, Array< OneD, Array< OneD, NekDouble > > &dfdir)
virtual void	v_MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Array< OneD, NekDouble >	v_GetMF (const int dir, const int shapedim, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	v_GetMFDiv (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	v_GetMFMag (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void	v_AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual NekDouble	v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec)

Private Member Functions
virtual void	v_LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)

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

Additional Inherited Members
Protected Attributes inherited from Nektar::StdRegions::StdExpansion3D
std::map< int, NormalVector >	m_faceNormals
std::map< int, bool >	m_negatedNormals
Protected Attributes inherited from Nektar::StdRegions::StdExpansion
Array< OneD, LibUtilities::BasisSharedPtr >	m_base
int	m_elmt_id
int	m_ncoeffs
LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess >	m_stdMatrixManager
LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess >	m_stdStaticCondMatrixManager
LibUtilities::NekManager< IndexMapKey, IndexMapValues, IndexMapKey::opLess >	m_IndexMapManager
Protected Attributes inherited from Nektar::LocalRegions::Expansion
SpatialDomains::GeometrySharedPtr	m_geom
SpatialDomains::GeomFactorsSharedPtr	m_metricinfo
MetricMap	m_metrics

Detailed Description

Definition at line 50 of file PyrExp.h.

Constructor & Destructor Documentation

PyrExp() [1/2]

Nektar::LocalRegions::PyrExp::PyrExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		const LibUtilities::BasisKey &	Bc,
		const SpatialDomains::PyrGeomSharedPtr &	geom
	)

Constructor using BasisKey class for quadrature points and order definition.

Definition at line 45 of file PyrExp.cpp.

                                                                  :
            StdExpansion  (LibUtilities::StdPyrData::getNumberOfCoefficients(
                               Ba.GetNumModes(),
                               Bb.GetNumModes(),
                               Bc.GetNumModes()),
                           3, Ba, Bb, Bc),
            StdExpansion3D(LibUtilities::StdPyrData::getNumberOfCoefficients(
                               Ba.GetNumModes(),
                               Bb.GetNumModes(),
                               Bc.GetNumModes()),
                           Ba, Bb, Bc),
            StdPyrExp     (Ba,Bb,Bc),
            Expansion     (geom),
            Expansion3D   (geom),
            m_matrixManager(
                    std::bind(&PyrExp::CreateMatrix, this, std::placeholders::_1),
                    std::string("PyrExpMatrix")),
            m_staticCondMatrixManager(
                    std::bind(&PyrExp::CreateStaticCondMatrix, this, std::placeholders::_1),
                    std::string("PyrExpStaticCondMatrix"))
        {
        }

PyrExp() [2/2]

Nektar::LocalRegions::PyrExp::PyrExp

(

const PyrExp &

T

)

Definition at line 71 of file PyrExp.cpp.

                                     :
            StdExpansion  (T),
            StdExpansion3D(T),
            StdPyrExp     (T),
            Expansion     (T),
            Expansion3D   (T),
            m_matrixManager(T.m_matrixManager),
            m_staticCondMatrixManager(T.m_staticCondMatrixManager)
        {
        } 

~PyrExp()

Nektar::LocalRegions::PyrExp::~PyrExp

(

)

Definition at line 82 of file PyrExp.cpp.

        {
        }

Member Function Documentation

CreateMatrix()

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

protected

Definition at line 1083 of file PyrExp.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), ASSERTL2, Nektar::LocalRegions::Expansion::BuildVertexMatrix(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::ErrorUtil::efatal, Nektar::StdRegions::eHelmholtz, Nektar::StdRegions::eInvMass, Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eLaplacian00, Nektar::StdRegions::eLaplacian01, Nektar::StdRegions::eLaplacian02, Nektar::StdRegions::eLaplacian11, Nektar::StdRegions::eLaplacian12, Nektar::StdRegions::eLaplacian22, Nektar::StdRegions::eMass, Nektar::SpatialDomains::eNoGeomType, Nektar::StdRegions::ePreconLinearSpace, Nektar::StdRegions::ePreconLinearSpaceMass, Nektar::StdRegions::StdExpansion::GenMatrix(), Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetConstFactors(), Nektar::StdRegions::StdExpansion::GetLocStaticCondMatrix(), Nektar::StdRegions::StdMatrixKey::GetMatrixType(), Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdMatrixKey::GetShapeType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdMatrixKey::GetVarCoeffs(), m_matrixManager, Nektar::LocalRegions::Expansion::m_metricinfo, NEKERROR, and Nektar::Transpose().

        {
            DNekScalMatSharedPtr returnval;
            LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();

            ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,"Geometric information is not set up");

            switch(mkey.GetMatrixType())
            {
            case StdRegions::eMass:
                {
                    if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
                    {
                        NekDouble one = 1.0;
                        DNekMatSharedPtr mat = GenMatrix(mkey);
                        returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                    }
                    else
                    {
                        NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                        DNekMatSharedPtr mat = GetStdMatrix(mkey);
                        returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,mat);
                    }
                }
                break;
            case StdRegions::eInvMass:
                {
                    if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
                    {
                        NekDouble one = 1.0;
                        StdRegions::StdMatrixKey masskey(StdRegions::eMass,DetShapeType(),
                                                         *this);
                        DNekMatSharedPtr mat = GenMatrix(masskey);
                        mat->Invert();
                        returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                    }
                    else
                    {
                        NekDouble fac = 1.0/(m_metricinfo->GetJac(ptsKeys))[0];
                        DNekMatSharedPtr mat = GetStdMatrix(mkey);
                        returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(fac,mat);
                    }
                }
                break;
            case StdRegions::eLaplacian:
                {
                    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
                        mkey.GetNVarCoeff() > 0 ||
                        mkey.ConstFactorExists(
                                StdRegions::eFactorSVVCutoffRatio))
                    {
                        NekDouble one = 1.0;
                        DNekMatSharedPtr mat = GenMatrix(mkey);

                        returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
                    }
                    else
                    {
                        MatrixKey lap00key(StdRegions::eLaplacian00,
                                           mkey.GetShapeType(), *this);
                        MatrixKey lap01key(StdRegions::eLaplacian01,
                                           mkey.GetShapeType(), *this);
                        MatrixKey lap02key(StdRegions::eLaplacian02,
                                           mkey.GetShapeType(), *this);
                        MatrixKey lap11key(StdRegions::eLaplacian11,
                                           mkey.GetShapeType(), *this);
                        MatrixKey lap12key(StdRegions::eLaplacian12,
                                           mkey.GetShapeType(), *this);
                        MatrixKey lap22key(StdRegions::eLaplacian22,
                                           mkey.GetShapeType(), *this);

                        DNekMat &lap00 = *GetStdMatrix(lap00key);
                        DNekMat &lap01 = *GetStdMatrix(lap01key);
                        DNekMat &lap02 = *GetStdMatrix(lap02key);
                        DNekMat &lap11 = *GetStdMatrix(lap11key);
                        DNekMat &lap12 = *GetStdMatrix(lap12key);
                        DNekMat &lap22 = *GetStdMatrix(lap22key);

                        NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
                        Array<TwoD, const NekDouble> gmat =
                                            m_metricinfo->GetGmat(ptsKeys);

                        int rows = lap00.GetRows();
                        int cols = lap00.GetColumns();

                        DNekMatSharedPtr lap = MemoryManager<DNekMat>
                                                ::AllocateSharedPtr(rows,cols);

                        (*lap)  = gmat[0][0]*lap00
                                + gmat[4][0]*lap11
                                + gmat[8][0]*lap22
                                + gmat[3][0]*(lap01 + Transpose(lap01))
                                + gmat[6][0]*(lap02 + Transpose(lap02))
                                + gmat[7][0]*(lap12 + Transpose(lap12));

                        returnval = MemoryManager<DNekScalMat>
                                                ::AllocateSharedPtr(jac, lap);
                    }
                }
                break;
            case StdRegions::eHelmholtz:
                {
                    NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorLambda);
                    MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
                    DNekScalMat &MassMat = *(this->m_matrixManager[masskey]);
                    MatrixKey lapkey(StdRegions::eLaplacian, mkey.GetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    DNekScalMat &LapMat = *(this->m_matrixManager[lapkey]);

                    int rows = LapMat.GetRows();
                    int cols = LapMat.GetColumns();

                    DNekMatSharedPtr helm = MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);

                    (*helm) = LapMat + factor*MassMat;

                    returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, helm);
                }
                break;
            case StdRegions::ePreconLinearSpace:
                {
                    NekDouble one = 1.0;
                    MatrixKey helmkey(StdRegions::eHelmholtz, mkey.GetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
                    DNekScalBlkMatSharedPtr helmStatCond = GetLocStaticCondMatrix(helmkey);
                    DNekScalMatSharedPtr A =helmStatCond->GetBlock(0,0);
                    DNekMatSharedPtr R=BuildVertexMatrix(A);

                    returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,R);
                }
                break;
            case StdRegions::ePreconLinearSpaceMass:
                {
                    NekDouble one = 1.0;
                    MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
                    DNekScalBlkMatSharedPtr massStatCond = GetLocStaticCondMatrix(masskey);
                    DNekScalMatSharedPtr A =massStatCond->GetBlock(0,0);
                    DNekMatSharedPtr R=BuildVertexMatrix(A);

                    returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,R);
                }
                break;
            default:
                NEKERROR(ErrorUtil::efatal, "Matrix creation not defined");
                break;
            }

            return returnval;
        }

CreateStaticCondMatrix()

DNekScalBlkMatSharedPtr Nektar::LocalRegions::PyrExp::CreateStaticCondMatrix ( const MatrixKey &  mkey )

protected

Definition at line 1231 of file PyrExp.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), ASSERTL2, Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::eHelmholtz, Nektar::StdRegions::eLaplacian, Nektar::SpatialDomains::eNoGeomType, Nektar::StdRegions::StdExpansion::GetBoundaryMap(), Nektar::StdRegions::StdExpansion::GetInteriorMap(), Nektar::LocalRegions::Expansion::GetLocMatrix(), Nektar::StdRegions::StdMatrixKey::GetMatrixType(), Nektar::StdRegions::StdExpansion::GetStdStaticCondMatrix(), Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::m_ncoeffs, and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

        {
            DNekScalBlkMatSharedPtr returnval;

            ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,"Geometric information is not set up");

            // set up block matrix system
            unsigned int nbdry = NumBndryCoeffs();
            unsigned int nint = (unsigned int)(m_ncoeffs - nbdry);
            unsigned int exp_size[] = {nbdry, nint};
            unsigned int nblks = 2;
            returnval = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(nblks, nblks, exp_size, exp_size); //Really need a constructor which takes Arrays
            NekDouble factor = 1.0;

            switch(mkey.GetMatrixType())
            {
            case StdRegions::eLaplacian: 
            case StdRegions::eHelmholtz: // special case since Helmholtz not defined in StdRegions

                // use Deformed case for both regular and deformed geometries
                factor = 1.0;
                goto UseLocRegionsMatrix;
                break;
            default:
                if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
                {
                    factor = 1.0;
                    goto UseLocRegionsMatrix;
                }
                else
                {
                    DNekScalMatSharedPtr mat = GetLocMatrix(mkey);
                    factor = mat->Scale();
                    goto UseStdRegionsMatrix;
                }
                break;
            UseStdRegionsMatrix:
                {
                    NekDouble            invfactor = 1.0/factor;
                    NekDouble            one = 1.0;
                    DNekBlkMatSharedPtr  mat = GetStdStaticCondMatrix(mkey);
                    DNekScalMatSharedPtr Atmp;
                    DNekMatSharedPtr     Asubmat;

                    //TODO: check below
                    returnval->SetBlock(0,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,Asubmat = mat->GetBlock(0,0)));
                    returnval->SetBlock(0,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,Asubmat = mat->GetBlock(0,1)));
                    returnval->SetBlock(1,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,Asubmat = mat->GetBlock(1,0)));
                    returnval->SetBlock(1,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(invfactor,Asubmat = mat->GetBlock(1,1)));
                }
                break;
            UseLocRegionsMatrix:
                {
                    int i,j;
                    NekDouble            invfactor = 1.0/factor;
                    NekDouble            one = 1.0;
                    DNekScalMat &mat = *GetLocMatrix(mkey);
                    DNekMatSharedPtr A = MemoryManager<DNekMat>::AllocateSharedPtr(nbdry,nbdry);
                    DNekMatSharedPtr B = MemoryManager<DNekMat>::AllocateSharedPtr(nbdry,nint);
                    DNekMatSharedPtr C = MemoryManager<DNekMat>::AllocateSharedPtr(nint,nbdry);
                    DNekMatSharedPtr D = MemoryManager<DNekMat>::AllocateSharedPtr(nint,nint);

                    Array<OneD,unsigned int> bmap(nbdry);
                    Array<OneD,unsigned int> imap(nint);
                    GetBoundaryMap(bmap);
                    GetInteriorMap(imap);

                    for(i = 0; i < nbdry; ++i)
                    {
                        for(j = 0; j < nbdry; ++j)
                        {
                            (*A)(i,j) = mat(bmap[i],bmap[j]);
                        }

                        for(j = 0; j < nint; ++j)
                        {
                            (*B)(i,j) = mat(bmap[i],imap[j]);
                        }
                    }

                    for(i = 0; i < nint; ++i)
                    {
                        for(j = 0; j < nbdry; ++j)
                        {
                            (*C)(i,j) = mat(imap[i],bmap[j]);
                        }

                        for(j = 0; j < nint; ++j)
                        {
                            (*D)(i,j) = mat(imap[i],imap[j]);
                        }
                    }

                    // Calculate static condensed system
                    if(nint)
                    {
                        D->Invert();
                        (*B) = (*B)*(*D);
                        (*A) = (*A) - (*B)*(*C);
                    }

                    DNekScalMatSharedPtr     Atmp;

                    returnval->SetBlock(0,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,A));
                    returnval->SetBlock(0,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,B));
                    returnval->SetBlock(1,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,C));
                    returnval->SetBlock(1,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(invfactor,D));
                }
            }
            return returnval;
        }

v_ComputeFaceNormal()

void Nektar::LocalRegions::PyrExp::v_ComputeFaceNormal ( const int  face )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 723 of file PyrExp.cpp.

References ASSERTL0, Nektar::StdRegions::StdExpansion::DetFaceBasisKey(), Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::LocalRegions::Expansion::GetGeom(), Nektar::LibUtilities::BasisKey::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::LibUtilities::BasisKey::GetPointsKey(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::LibUtilities::Interp2D(), Nektar::StdRegions::StdExpansion3D::m_faceNormals, Vmath::Sdiv(), Vmath::Vmul(), Vmath::Vsqrt(), Vmath::Vvtvp(), and Vmath::Zero().

        {
            const SpatialDomains::GeomFactorsSharedPtr &geomFactors =
                GetGeom()->GetMetricInfo();

            LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
            for(int i = 0; i < ptsKeys.size(); ++i)
            {
                // Need at least 2 points for computing normals
                if (ptsKeys[i].GetNumPoints() == 1)
                {
                    LibUtilities::PointsKey pKey(2, ptsKeys[i].GetPointsType());
                    ptsKeys[i] = pKey;
                }
            }

            SpatialDomains::GeomType type            = geomFactors->GetGtype();
            const Array<TwoD, const NekDouble> &df   = geomFactors->GetDerivFactors(ptsKeys);
            const Array<OneD, const NekDouble> &jac  = geomFactors->GetJac(ptsKeys);

            LibUtilities::BasisKey tobasis0 = DetFaceBasisKey(face,0);
            LibUtilities::BasisKey tobasis1 = DetFaceBasisKey(face,1);

            // Number of quadrature points in face expansion.
            int nq_face = tobasis0.GetNumPoints()*tobasis1.GetNumPoints();

            int vCoordDim = GetCoordim();
            int i;

            m_faceNormals[face] = Array<OneD, Array<OneD, NekDouble> >(vCoordDim);
            Array<OneD, Array<OneD, NekDouble> > &normal = m_faceNormals[face];
            for (i = 0; i < vCoordDim; ++i)
            {
                normal[i] = Array<OneD, NekDouble>(nq_face);
            }

            // Regular geometry case
            if (type == SpatialDomains::eRegular      ||
                type == SpatialDomains::eMovingRegular)
            {
                NekDouble fac;
                // Set up normals
                switch(face)
                {
                    case 0:
                    {
                        for(i = 0; i < vCoordDim; ++i)
                        {
                            normal[i][0] = -df[3*i+2][0]; 
                        }
                        break;
                    }
                    case 1:
                    {
                        for(i = 0; i < vCoordDim; ++i)
                        {
                            normal[i][0] = -df[3*i+1][0]; 
                        }
                        break;
                    }
                    case 2:
                    {
                        for(i = 0; i < vCoordDim; ++i)
                        {
                            normal[i][0] = df[3*i][0]+df[3*i+2][0]; 
                        }
                        break;
                    }
                    case 3:
                    {
                        for(i = 0; i < vCoordDim; ++i)
                        {
                            normal[i][0] = df[3*i+1][0]+df[3*i+2][0];
                        }
                        break;
                    }
                    case 4:
                    {
                        for(i = 0; i < vCoordDim; ++i)
                        {
                            normal[i][0] = -df[3*i][0]; 
                        }
                        break;
                    }
                    default:
                        ASSERTL0(false,"face is out of range (face < 4)");
                }

                // Normalise resulting vector.
                fac = 0.0;
                for(i = 0; i < vCoordDim; ++i)
                {
                    fac += normal[i][0]*normal[i][0];
                }
                fac = 1.0/sqrt(fac);
                for (i = 0; i < vCoordDim; ++i)
                {
                    Vmath::Fill(nq_face,fac*normal[i][0],normal[i],1);
                }
            }
            else
            {
                // Set up deformed normals.
                int j, k;

                int nq0  = ptsKeys[0].GetNumPoints();
                int nq1  = ptsKeys[1].GetNumPoints();
                int nq2  = ptsKeys[2].GetNumPoints();
                int nq01 = nq0*nq1;
                int nqtot;

                // Determine number of quadrature points on the face.
                if (face == 0)
                {
                    nqtot = nq0*nq1;
                }
                else if (face == 1 || face == 3)
                {
                    nqtot = nq0*nq2;
                }
                else
                {
                    nqtot = nq1*nq2;
                }

                LibUtilities::PointsKey points0;
                LibUtilities::PointsKey points1;

                Array<OneD, NekDouble> faceJac(nqtot);
                Array<OneD, NekDouble> normals(vCoordDim*nqtot,0.0);

                // Extract Jacobian along face and recover local derivatives
                // (dx/dr) for polynomial interpolation by multiplying m_gmat by
                // jacobian
                switch(face)
                {
                    case 0:
                    {
                        for(j = 0; j < nq01; ++j)
                        {
                            normals[j]         = -df[2][j]*jac[j];
                            normals[nqtot+j]   = -df[5][j]*jac[j];
                            normals[2*nqtot+j] = -df[8][j]*jac[j];
                            faceJac[j]         = jac[j];
                        }

                        points0 = ptsKeys[0];
                        points1 = ptsKeys[1];
                        break;
                    }

                    case 1:
                    {
                        for (j = 0; j < nq0; ++j)
                        {
                            for(k = 0; k < nq2; ++k)
                            {
                                int tmp = j+nq01*k;
                                normals[j+k*nq0]          =
                                    -df[1][tmp]*jac[tmp];
                                normals[nqtot+j+k*nq0]    =
                                    -df[4][tmp]*jac[tmp];
                                normals[2*nqtot+j+k*nq0]  =
                                    -df[7][tmp]*jac[tmp];
                                faceJac[j+k*nq0] = jac[tmp];
                            }
                        }

                        points0 = ptsKeys[0];
                        points1 = ptsKeys[2];
                        break;
                    }

                    case 2:
                    {
                        for (j = 0; j < nq1; ++j)
                        {
                            for(k = 0; k < nq2; ++k)
                            {
                                int tmp = nq0-1+nq0*j+nq01*k;
                                normals[j+k*nq1]         =
                                    (df[0][tmp]+df[2][tmp])*jac[tmp];
                                normals[nqtot+j+k*nq1]   =
                                    (df[3][tmp]+df[5][tmp])*jac[tmp];
                                normals[2*nqtot+j+k*nq1] =
                                    (df[6][tmp]+df[8][tmp])*jac[tmp];
                                faceJac[j+k*nq1] = jac[tmp];
                            }
                        }

                        points0 = ptsKeys[1];
                        points1 = ptsKeys[2];
                        break;
                    }

                    case 3:
                    {
                        for (j = 0; j < nq0; ++j)
                        {
                            for(k = 0; k < nq2; ++k)
                            {
                                int tmp = nq0*(nq1-1) + j + nq01*k;
                                normals[j+k*nq0]         =
                                    (df[1][tmp]+df[2][tmp])*jac[tmp];
                                normals[nqtot+j+k*nq0]   =
                                    (df[4][tmp]+df[5][tmp])*jac[tmp];
                                normals[2*nqtot+j+k*nq0] =
                                    (df[7][tmp]+df[8][tmp])*jac[tmp];
                                faceJac[j+k*nq0] = jac[tmp];
                            }
                        }

                        points0 = ptsKeys[0];
                        points1 = ptsKeys[2];
                        break;
                    }

                    case 4:
                    {
                        for (j = 0; j < nq1; ++j)
                        {
                            for(k = 0; k < nq2; ++k)
                            {
                                int tmp = j*nq0+nq01*k;
                                normals[j+k*nq1]         =
                                    -df[0][tmp]*jac[tmp];
                                normals[nqtot+j+k*nq1]   =
                                    -df[3][tmp]*jac[tmp];
                                normals[2*nqtot+j+k*nq1] =
                                    -df[6][tmp]*jac[tmp];
                                faceJac[j+k*nq1] = jac[tmp];
                            }
                        }

                        points0 = ptsKeys[1];
                        points1 = ptsKeys[2];
                        break;
                    }

                    default:
                        ASSERTL0(false,"face is out of range (face < 4)");
                }

                Array<OneD, NekDouble> work   (nq_face, 0.0);
                // Interpolate Jacobian and invert
                LibUtilities::Interp2D(points0, points1, faceJac,
                                       tobasis0.GetPointsKey(),
                                       tobasis1.GetPointsKey(),
                                       work);
                Vmath::Sdiv(nq_face, 1.0, &work[0], 1, &work[0], 1);

                // Interpolate normal and multiply by inverse Jacobian.
                for(i = 0; i < vCoordDim; ++i)
                {
                    LibUtilities::Interp2D(points0, points1,
                                           &normals[i*nqtot],
                                           tobasis0.GetPointsKey(),
                                           tobasis1.GetPointsKey(),
                                           &normal[i][0]);
                    Vmath::Vmul(nq_face,work,1,normal[i],1,normal[i],1);
                }

                // Normalise to obtain unit normals.
                Vmath::Zero(nq_face,work,1);
                for(i = 0; i < GetCoordim(); ++i)
                {
                    Vmath::Vvtvp(nq_face,normal[i],1,normal[i],1,work,1,work,1);
                }

                Vmath::Vsqrt(nq_face,work,1,work,1);
                Vmath::Sdiv (nq_face,1.0,work,1,work,1);

                for(i = 0; i < GetCoordim(); ++i)
                {
                    Vmath::Vmul(nq_face,normal[i],1,work,1,normal[i],1);
                }
            }
        }

v_ComputeLaplacianMetric()

void Nektar::LocalRegions::PyrExp::v_ComputeLaplacianMetric ( )

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1343 of file PyrExp.cpp.

References Nektar::LocalRegions::Expansion::ComputeQuadratureMetric(), Blas::Dscal(), Nektar::SpatialDomains::eDeformed, Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Nektar::LocalRegions::eMetricQuadrature, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Svtsvtp(), Vmath::Svtvp(), Vmath::Vvtvp(), and Vmath::Vvtvvtp().

        {
            if (m_metrics.count(eMetricQuadrature) == 0)
            {
                ComputeQuadratureMetric();
            }

            int i, j;
            const unsigned int nqtot = GetTotPoints();
            const unsigned int dim = 3;
            const MetricType m[3][3] = {
                { eMetricLaplacian00, eMetricLaplacian01, eMetricLaplacian02 },
                { eMetricLaplacian01, eMetricLaplacian11, eMetricLaplacian12 },
                { eMetricLaplacian02, eMetricLaplacian12, eMetricLaplacian22 }
            };

            for (unsigned int i = 0; i < dim; ++i)
            {
                for (unsigned int j = i; j < dim; ++j)
                {
                    m_metrics[m[i][j]] = Array<OneD, NekDouble>(nqtot);
                }
            }

            // Define shorthand synonyms for m_metrics storage
            Array<OneD,NekDouble> g0   (m_metrics[m[0][0]]);
            Array<OneD,NekDouble> g1   (m_metrics[m[1][1]]);
            Array<OneD,NekDouble> g2   (m_metrics[m[2][2]]);
            Array<OneD,NekDouble> g3   (m_metrics[m[0][1]]);
            Array<OneD,NekDouble> g4   (m_metrics[m[0][2]]);
            Array<OneD,NekDouble> g5   (m_metrics[m[1][2]]);

            // Allocate temporary storage
            Array<OneD,NekDouble> alloc(9*nqtot,0.0);
            Array<OneD,NekDouble> h0   (nqtot, alloc);
            Array<OneD,NekDouble> h1   (nqtot, alloc+ 1*nqtot);
            Array<OneD,NekDouble> h2   (nqtot, alloc+ 2*nqtot);
            Array<OneD,NekDouble> wsp1 (nqtot, alloc+ 3*nqtot);
            Array<OneD,NekDouble> wsp2 (nqtot, alloc+ 4*nqtot);
            Array<OneD,NekDouble> wsp3 (nqtot, alloc+ 5*nqtot);
            Array<OneD,NekDouble> wsp4 (nqtot, alloc+ 6*nqtot);
            Array<OneD,NekDouble> wsp5 (nqtot, alloc+ 7*nqtot);
            Array<OneD,NekDouble> wsp6 (nqtot, alloc+ 8*nqtot);

            const Array<TwoD, const NekDouble>& df =
                                m_metricinfo->GetDerivFactors(GetPointsKeys());
            const Array<OneD, const NekDouble>& z0 = m_base[0]->GetZ();
            const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
            const Array<OneD, const NekDouble>& z2 = m_base[2]->GetZ();
            const unsigned int nquad0 = m_base[0]->GetNumPoints();
            const unsigned int nquad1 = m_base[1]->GetNumPoints();
            const unsigned int nquad2 = m_base[2]->GetNumPoints();

            // Populate collapsed coordinate arrays h0, h1 and h2.
            for(j = 0; j < nquad2; ++j)
            {
                for(i = 0; i < nquad1; ++i)
                {
                    Vmath::Fill(nquad0, 2.0/(1.0-z2[j]),         &h0[0]+i*nquad0 + j*nquad0*nquad1,1);
                    Vmath::Fill(nquad0, 1.0/(1.0-z2[j]),         &h1[0]+i*nquad0 + j*nquad0*nquad1,1);
                    Vmath::Fill(nquad0, (1.0+z1[i])/(1.0-z2[j]), &h2[0]+i*nquad0 + j*nquad0*nquad1,1);
                }
            }
            for(i = 0; i < nquad0; i++)
            {
                Blas::Dscal(nquad1*nquad2, 1+z0[i], &h1[0]+i, nquad0);
            }

            // Step 3. Construct combined metric terms for physical space to
            // collapsed coordinate system.
            // Order of construction optimised to minimise temporary storage
            if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                // f_{1k}
                Vmath::Vvtvvtp(nqtot, &df[0][0], 1, &h0[0], 1, &df[2][0], 1, &h1[0], 1, &wsp1[0], 1);
                Vmath::Vvtvvtp(nqtot, &df[3][0], 1, &h0[0], 1, &df[5][0], 1, &h1[0], 1, &wsp2[0], 1);
                Vmath::Vvtvvtp(nqtot, &df[6][0], 1, &h0[0], 1, &df[8][0], 1, &h1[0], 1, &wsp3[0], 1);

                // g0
                Vmath::Vvtvvtp(nqtot, &wsp1[0], 1, &wsp1[0], 1, &wsp2[0], 1, &wsp2[0], 1, &g0[0], 1);
                Vmath::Vvtvp  (nqtot, &wsp3[0], 1, &wsp3[0], 1, &g0[0],   1, &g0[0],   1);

                // g4
                Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &wsp1[0], 1, &df[5][0], 1, &wsp2[0], 1, &g4[0], 1);
                Vmath::Vvtvp  (nqtot, &df[8][0], 1, &wsp3[0], 1, &g4[0], 1, &g4[0], 1);

                // f_{2k}
                Vmath::Vvtvvtp(nqtot, &df[1][0], 1, &h0[0], 1, &df[2][0], 1, &h2[0], 1, &wsp4[0], 1);
                Vmath::Vvtvvtp(nqtot, &df[4][0], 1, &h0[0], 1, &df[5][0], 1, &h2[0], 1, &wsp5[0], 1);
                Vmath::Vvtvvtp(nqtot, &df[7][0], 1, &h0[0], 1, &df[8][0], 1, &h2[0], 1, &wsp6[0], 1);

                // g1
                Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp4[0], 1, &wsp5[0], 1, &wsp5[0], 1, &g1[0], 1);
                Vmath::Vvtvp  (nqtot, &wsp6[0], 1, &wsp6[0], 1, &g1[0],   1, &g1[0],   1);

                // g3
                Vmath::Vvtvvtp(nqtot, &wsp1[0], 1, &wsp4[0], 1, &wsp2[0], 1, &wsp5[0], 1, &g3[0], 1);
                Vmath::Vvtvp  (nqtot, &wsp3[0], 1, &wsp6[0], 1, &g3[0],   1, &g3[0],   1);

                // g5
                Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &wsp4[0], 1, &df[5][0], 1, &wsp5[0], 1, &g5[0], 1);
                Vmath::Vvtvp  (nqtot, &df[8][0], 1, &wsp6[0], 1, &g5[0], 1, &g5[0], 1);

                // g2
                Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &df[2][0], 1, &df[5][0], 1, &df[5][0], 1, &g2[0], 1);
                Vmath::Vvtvp  (nqtot, &df[8][0], 1, &df[8][0], 1, &g2[0], 1, &g2[0], 1);
            }
            else
            {
                // f_{1k}
                Vmath::Svtsvtp(nqtot, df[0][0], &h0[0], 1, df[2][0], &h1[0], 1, &wsp1[0], 1);
                Vmath::Svtsvtp(nqtot, df[3][0], &h0[0], 1, df[5][0], &h1[0], 1, &wsp2[0], 1);
                Vmath::Svtsvtp(nqtot, df[6][0], &h0[0], 1, df[8][0], &h1[0], 1, &wsp3[0], 1);

                // g0
                Vmath::Vvtvvtp(nqtot, &wsp1[0], 1, &wsp1[0], 1, &wsp2[0], 1, &wsp2[0], 1, &g0[0], 1);
                Vmath::Vvtvp  (nqtot, &wsp3[0], 1, &wsp3[0], 1, &g0[0],   1, &g0[0],   1);

                // g4
                Vmath::Svtsvtp(nqtot, df[2][0], &wsp1[0], 1, df[5][0], &wsp2[0], 1, &g4[0], 1);
                Vmath::Svtvp  (nqtot, df[8][0], &wsp3[0], 1, &g4[0], 1, &g4[0], 1);

                // f_{2k}
                Vmath::Svtsvtp(nqtot, df[1][0], &h0[0], 1, df[2][0], &h2[0], 1, &wsp4[0], 1);
                Vmath::Svtsvtp(nqtot, df[4][0], &h0[0], 1, df[5][0], &h2[0], 1, &wsp5[0], 1);
                Vmath::Svtsvtp(nqtot, df[7][0], &h0[0], 1, df[8][0], &h2[0], 1, &wsp6[0], 1);

                // g1
                Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp4[0], 1, &wsp5[0], 1, &wsp5[0], 1, &g1[0], 1);
                Vmath::Vvtvp  (nqtot, &wsp6[0], 1, &wsp6[0], 1, &g1[0],   1, &g1[0],   1);

                // g3
                Vmath::Vvtvvtp(nqtot, &wsp1[0], 1, &wsp4[0], 1, &wsp2[0], 1, &wsp5[0], 1, &g3[0], 1);
                Vmath::Vvtvp  (nqtot, &wsp3[0], 1, &wsp6[0], 1, &g3[0],   1, &g3[0],   1);

                // g5
                Vmath::Svtsvtp(nqtot, df[2][0], &wsp4[0], 1, df[5][0], &wsp5[0], 1, &g5[0], 1);
                Vmath::Svtvp  (nqtot, df[8][0], &wsp6[0], 1, &g5[0], 1, &g5[0], 1);

                // g2
                Vmath::Fill(nqtot, df[2][0]*df[2][0] + df[5][0]*df[5][0] + df[8][0]*df[8][0], &g2[0], 1);
            }

            for (unsigned int i = 0; i < dim; ++i)
            {
                for (unsigned int j = i; j < dim; ++j)
                {
                    MultiplyByQuadratureMetric(m_metrics[m[i][j]],
                                               m_metrics[m[i][j]]);

                }
            }
        }

v_CreateStdMatrix()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 1057 of file PyrExp.cpp.

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

        {
            LibUtilities::BasisKey bkey0 = m_base[0]->GetBasisKey();
            LibUtilities::BasisKey bkey1 = m_base[1]->GetBasisKey();
            LibUtilities::BasisKey bkey2 = m_base[2]->GetBasisKey();
            StdRegions::StdPyrExpSharedPtr tmp = 
                MemoryManager<StdPyrExp>::AllocateSharedPtr(bkey0, bkey1, bkey2);

            return tmp->GetStdMatrix(mkey);
        }

v_DropLocStaticCondMatrix()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1078 of file PyrExp.cpp.

References m_staticCondMatrixManager.

        {
            m_staticCondMatrixManager.DeleteObject(mkey);
        }

v_ExtractDataToCoeffs()

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

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 532 of file PyrExp.cpp.

References Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, and Vmath::Vcopy().

        {
            int data_order0 = nummodes[mode_offset];
            int fillorder0  = min(m_base[0]->GetNumModes(),data_order0);
            int data_order1 = nummodes[mode_offset+1];
            int order1      = m_base[1]->GetNumModes();
            int fillorder1  = min(order1,data_order1);
            int data_order2 = nummodes[mode_offset+2];
            int order2      = m_base[2]->GetNumModes();
            int fillorder2  = min(order2,data_order2);

            // Check if not same order or basis and if not make temp
            // element to read in data
            if (fromType[0] != m_base[0]->GetBasisType() ||
                fromType[1] != m_base[1]->GetBasisType() ||
                fromType[2] != m_base[2]->GetBasisType() || 
                data_order0 != fillorder0 ||
                data_order1 != fillorder1 ||
                data_order2 != fillorder2)
            {
                // Construct a pyr with the appropriate basis type at our
                // quadrature points, and one more to do a forwards
                // transform. We can then copy the output to coeffs.
                StdRegions::StdPyrExp tmpPyr(
                    LibUtilities::BasisKey(
                        fromType[0], data_order0, m_base[0]->GetPointsKey()),
                    LibUtilities::BasisKey(
                        fromType[1], data_order1, m_base[1]->GetPointsKey()),
                    LibUtilities::BasisKey(
                        fromType[2], data_order2, m_base[2]->GetPointsKey()));

                StdRegions::StdPyrExp tmpPyr2(m_base[0]->GetBasisKey(),
                                              m_base[1]->GetBasisKey(),
                                              m_base[2]->GetBasisKey());

                Array<OneD, const NekDouble> tmpData(tmpPyr.GetNcoeffs(), data);
                Array<OneD, NekDouble> tmpBwd(tmpPyr2.GetTotPoints());
                Array<OneD, NekDouble> tmpOut(tmpPyr2.GetNcoeffs());

                tmpPyr.BwdTrans(tmpData, tmpBwd);
                tmpPyr2.FwdTrans(tmpBwd, tmpOut);
                Vmath::Vcopy(tmpOut.num_elements(), &tmpOut[0], 1, coeffs, 1);

            }
            else
            {
                Vmath::Vcopy(m_ncoeffs,&data[0],1,coeffs,1);
            }
        }

v_FwdTrans()

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

protectedvirtual

Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in (this)->m_coeffs.

Inputs:

• inarray: array of physical quadrature points to be transformed

Outputs:

• (this)->_coeffs: updated array of expansion coefficients.

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 220 of file PyrExp.cpp.

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

        {
            if(m_base[0]->Collocation() && 
               m_base[1]->Collocation() && 
               m_base[2]->Collocation())
            {
                Vmath::Vcopy(GetNcoeffs(),&inarray[0],1,&outarray[0],1);
            }
            else
            {
                v_IProductWRTBase(inarray,outarray);

                // get Mass matrix inverse
                MatrixKey             masskey(StdRegions::eInvMass,
                                              DetShapeType(),*this);
                DNekScalMatSharedPtr  matsys = m_matrixManager[masskey];

                // copy inarray in case inarray == outarray
                DNekVec in (m_ncoeffs,outarray);
                DNekVec out(m_ncoeffs,outarray,eWrapper);

                out = (*matsys)*in;
            }
        }

v_GenMatrix()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 1036 of file PyrExp.cpp.

References Nektar::StdRegions::eHybridDGHelmBndLam, Nektar::StdRegions::eHybridDGHelmholtz, Nektar::StdRegions::eHybridDGLamToQ0, Nektar::StdRegions::eHybridDGLamToQ1, Nektar::StdRegions::eHybridDGLamToQ2, Nektar::StdRegions::eHybridDGLamToU, Nektar::StdRegions::StdMatrixKey::GetMatrixType(), and Nektar::LocalRegions::Expansion3D::v_GenMatrix().

        {
            DNekMatSharedPtr returnval;

            switch(mkey.GetMatrixType())
            {
            case StdRegions::eHybridDGHelmholtz:
            case StdRegions::eHybridDGLamToU:
            case StdRegions::eHybridDGLamToQ0:
            case StdRegions::eHybridDGLamToQ1:
            case StdRegions::eHybridDGLamToQ2:
            case StdRegions::eHybridDGHelmBndLam:
                returnval = Expansion3D::v_GenMatrix(mkey);
                break;
            default:
                returnval = StdPyrExp::v_GenMatrix(mkey);
            }
            
            return returnval;            
        }

v_GetCoord()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 505 of file PyrExp.cpp.

References ASSERTL1, and Nektar::LocalRegions::Expansion::m_geom.

        {
            int  i;
            
            ASSERTL1(Lcoords[0] <= -1.0 && Lcoords[0] >= 1.0 && 
                     Lcoords[1] <= -1.0 && Lcoords[1] >= 1.0 &&
                     Lcoords[2] <= -1.0 && Lcoords[2] >= 1.0,
                     "Local coordinates are not in region [-1,1]");
            
            // m_geom->FillGeom(); // TODO: implement FillGeom()
            
            for(i = 0; i < m_geom->GetCoordim(); ++i) 
            {
                coords[i] = m_geom->GetCoord(i,Lcoords);
            }
        }

v_GetCoordim()

int Nektar::LocalRegions::PyrExp::v_GetCoordim ( void  )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 618 of file PyrExp.cpp.

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

        {
            return m_geom->GetCoordim();
        }

v_GetCoords()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 523 of file PyrExp.cpp.

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

        {
            Expansion::v_GetCoords(coords_1, coords_2, coords_3);
        }

v_GetFacePhysMap()

void Nektar::LocalRegions::PyrExp::v_GetFacePhysMap ( const int  face, Array< OneD, int > &  outarray  )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 623 of file PyrExp.cpp.

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

        {
            int nquad0 = m_base[0]->GetNumPoints();
            int nquad1 = m_base[1]->GetNumPoints();
            int nquad2 = m_base[2]->GetNumPoints();
            
            int nq0 = 0; 
            int nq1 = 0; 

            switch(face)
            {
            case 0:
                nq0 = nquad0;
                nq1 = nquad1;
                if(outarray.num_elements()!=nq0*nq1)
                {
                    outarray = Array<OneD, int>(nq0*nq1);
                }
                
                //Directions A and B positive
                for(int i = 0; i < nquad0*nquad1; ++i)
                {
                    outarray[i] = i;
                }

                break;
              case 1:
                    nq0 = nquad0;
                    nq1 = nquad2;
                    if(outarray.num_elements()!=nq0*nq1)
                    {
                        outarray = Array<OneD, int>(nq0*nq1);
                    }
                    
                    //Direction A and B positive
                    for (int k=0; k<nquad2; k++)
                    {
                        for(int i = 0; i < nquad0; ++i)
                        {
                            outarray[k*nquad0+i] = (nquad0*nquad1*k)+i;
                        }
                    }

                    break; 
                case 2:
                    nq0 = nquad1;
                    nq1 = nquad2;
                    if(outarray.num_elements()!=nq0*nq1)
                    {
                        outarray = Array<OneD, int>(nq0*nq1);
                    }
                    
                    //Directions A and B positive
                    for(int j = 0; j < nquad1*nquad2; ++j)
                    {
                        outarray[j] = nquad0-1 + j*nquad0;
                        
                    }
                    break;
                case 3:
                
                    nq0 = nquad0;
                    nq1 = nquad2;
                    if(outarray.num_elements()!=nq0*nq1)
                    {
                        outarray = Array<OneD, int>(nq0*nq1);
                    }
                    
                    //Direction A and B positive
                    for (int k=0; k<nquad2; k++)
                    {
                        for(int i = 0; i < nquad0; ++i)
                        {
                            outarray[k*nquad0+i] = nquad0*(nquad1-1) + (nquad0*nquad1*k)+i;
                        }
                    }
                    break;
                case 4:
                    nq0 = nquad1;
                    nq1 = nquad2;

                    if(outarray.num_elements()!=nq0*nq1)
                    {
                        outarray = Array<OneD, int>(nq0*nq1);
                    }
                    
                    //Directions A and B positive
                    for(int j = 0; j < nquad1*nquad2; ++j)
                    {
                        outarray[j] = j*nquad0;
                        
                    }
                    break;
                default:
                    ASSERTL0(false,"face value (> 4) is out of range");
                    break;
            }
        }

v_GetLinStdExp()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 488 of file PyrExp.cpp.

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

        {
            LibUtilities::BasisKey bkey0(m_base[0]->GetBasisType(),
                           2, m_base[0]->GetPointsKey());
            LibUtilities::BasisKey bkey1(m_base[1]->GetBasisType(),
                           2, m_base[1]->GetPointsKey());
            LibUtilities::BasisKey bkey2(m_base[2]->GetBasisType(),
                           2, m_base[2]->GetPointsKey());
            
            return MemoryManager<StdRegions::StdPyrExp>
                ::AllocateSharedPtr( bkey0, bkey1, bkey2);
        }

v_GetLocMatrix()

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

protectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1068 of file PyrExp.cpp.

References m_matrixManager.

        {
            return m_matrixManager[mkey];
        }

v_GetLocStaticCondMatrix()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1073 of file PyrExp.cpp.

References m_staticCondMatrixManager.

        {
            return m_staticCondMatrixManager[mkey];
        }

v_GetStdExp()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 480 of file PyrExp.cpp.

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

        {
            return MemoryManager<StdRegions::StdPyrExp>
                ::AllocateSharedPtr(m_base[0]->GetBasisKey(),
                                    m_base[1]->GetBasisKey(),
                                    m_base[2]->GetBasisKey());
        }

v_Integral()

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

protectedvirtual

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

Inputs:

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

Outputs:

• returns \(\int^1_{-1}\int^1_{-1}\int^1_{-1} u(\bar \eta_1, \eta_2, \eta_3) J[i,j,k] d \bar \eta_1 d \eta_2 d \eta_3\)
  \(= \sum_{i=0}^{Q_1 - 1} \sum_{j=0}^{Q_2 - 1} \sum_{k=0}^{Q_3 - 1} u(\bar \eta_{1i}^{0,0}, \eta_{2j}^{0,0},\eta_{3k}^{2,0})w_{i}^{0,0} w_{j}^{0,0} \hat w_{k}^{2,0} \)
  where \(inarray[i,j, k] = u(\bar \eta_{1i},\eta_{2j}, \eta_{3k}) \),
  \(\hat w_{k}^{2,0} = \frac {w^{2,0}} {2} \)
  and \( J[i,j,k] \) is the Jacobian evaluated at the quadrature point.

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 111 of file PyrExp.cpp.

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

        {
            int nquad0 = m_base[0]->GetNumPoints();
            int nquad1 = m_base[1]->GetNumPoints();
            int nquad2 = m_base[2]->GetNumPoints();
            Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
            Array<OneD,       NekDouble> tmp(nquad0*nquad1*nquad2);

            // multiply inarray with Jacobian
            if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nquad0*nquad1*nquad2,&jac[0],1,(NekDouble*)&inarray[0],1, &tmp[0],1);
            }
            else
            {
                Vmath::Smul(nquad0*nquad1*nquad2,(NekDouble) jac[0], (NekDouble*)&inarray[0],1,&tmp[0],1);
            }

            // call StdPyrExp version;
            return StdPyrExp::v_Integral(tmp);
        }

v_IProductWRTBase()

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

protectedvirtual

Calculate the inner product of inarray with respect to the basis B=base0*base1*base2 and put into outarray:

\( \begin{array}{rcl} I_{pqr} = (\phi_{pqr}, u)_{\delta} & = & \sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \sum_{k=0}^{nq_2} \psi_{p}^{a} (\bar \eta_{1i}) \psi_{q}^{a} (\eta_{2j}) \psi_{pqr}^{c} (\eta_{3k}) w_i w_j w_k u(\bar \eta_{1,i} \eta_{2,j} \eta_{3,k}) J_{i,j,k}\\ & = & \sum_{i=0}^{nq_0} \psi_p^a(\bar \eta_{1,i}) \sum_{j=0}^{nq_1} \psi_{q}^a(\eta_{2,j}) \sum_{k=0}^{nq_2} \psi_{pqr}^c u(\bar \eta_{1i},\eta_{2j},\eta_{3k}) J_{i,j,k} \end{array} \)
where

\(\phi_{pqr} (\xi_1 , \xi_2 , \xi_3) = \psi_p^a (\bar \eta_1) \psi_{q}^a (\eta_2) \psi_{pqr}^c (\eta_3) \)
which can be implemented as
\(f_{pqr} (\xi_{3k}) = \sum_{k=0}^{nq_3} \psi_{pqr}^c u(\bar \eta_{1i},\eta_{2j},\eta_{3k}) J_{i,j,k} = {\bf B_3 U} \)
\( g_{pq} (\xi_{3k}) = \sum_{j=0}^{nq_1} \psi_{q}^a (\xi_{2j}) f_{pqr} (\xi_{3k}) = {\bf B_2 F} \)
\( (\phi_{pqr}, u)_{\delta} = \sum_{k=0}^{nq_0} \psi_{p}^a (\xi_{3k}) g_{pq} (\xi_{3k}) = {\bf B_1 G} \)

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 278 of file PyrExp.cpp.

References v_IProductWRTBase_SumFac().

Referenced by v_FwdTrans().

        {
            v_IProductWRTBase_SumFac(inarray, outarray);
        }

v_IProductWRTBase_SumFac()

void Nektar::LocalRegions::PyrExp::v_IProductWRTBase_SumFac ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, bool  multiplybyweights = true  )

protectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 285 of file PyrExp.cpp.

References Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric().

Referenced by v_IProductWRTBase().

        {
            const int nquad0 = m_base[0]->GetNumPoints();
            const int nquad1 = m_base[1]->GetNumPoints();
            const int nquad2 = m_base[2]->GetNumPoints();
            const int order0 = m_base[0]->GetNumModes();
            const int order1 = m_base[1]->GetNumModes();

            Array<OneD, NekDouble> wsp(order0*nquad2*(nquad1+order1));

            if(multiplybyweights)
            {
                Array<OneD, NekDouble> tmp(nquad0*nquad1*nquad2);
                
                MultiplyByQuadratureMetric(inarray, tmp);
                
                IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
                                             m_base[1]->GetBdata(),
                                             m_base[2]->GetBdata(),
                                             tmp,outarray,wsp,
                                             true,true,true);
            }
            else
            {
                IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
                                             m_base[1]->GetBdata(),
                                             m_base[2]->GetBdata(),
                                             inarray,outarray,wsp,
                                             true,true,true);
            }
        }

v_IProductWRTDerivBase()

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

protectedvirtual

Calculates the inner product \( I_{pqr} = (u, \partial_{x_i} \phi_{pqr}) \).

The derivative of the basis functions is performed using the chain rule in order to incorporate the geometric factors. Assuming that the basis functions are a tensor product \(\phi_{pqr}(\eta_1,\eta_2,\eta_3) = \phi_1(\eta_1)\phi_2(\eta_2)\phi_3(\eta_3)\), this yields the result

\[ I_{pqr} = \sum_{j=1}^3 \left(u, \frac{\partial u}{\partial \eta_j} \frac{\partial \eta_j}{\partial x_i}\right) \]

In the pyramid element, we must also incorporate a second set of geometric factors which incorporate the collapsed co-ordinate system, so that

\[ \frac{\partial\eta_j}{\partial x_i} = \sum_{k=1}^3 \frac{\partial\eta_j}{\partial\xi_k}\frac{\partial\xi_k}{\partial x_i} \]

These derivatives can be found on p152 of Sherwin & Karniadakis.

Parameters

dir	Direction in which to take the derivative.
inarray	The function \( u \).
outarray	Value of the inner product.

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 351 of file PyrExp.cpp.

References v_IProductWRTDerivBase_SumFac().

        {
            v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
        }

v_IProductWRTDerivBase_SumFac()

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

protectedvirtual

Parameters

inarray	Function evaluated at physical collocation points.
outarray	Inner product with respect to each basis function over the element.

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 359 of file PyrExp.cpp.

References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().

Referenced by v_IProductWRTDerivBase().

        {
            const int nquad0 = m_base[0]->GetNumPoints();
            const int nquad1 = m_base[1]->GetNumPoints();
            const int nquad2 = m_base[2]->GetNumPoints();
            const int order0 = m_base[0]->GetNumModes ();
            const int order1 = m_base[1]->GetNumModes ();
            const int nqtot  = nquad0*nquad1*nquad2;
            int i;

            const Array<OneD, const NekDouble> &z0 = m_base[0]->GetZ();
            const Array<OneD, const NekDouble> &z1 = m_base[1]->GetZ();
            const Array<OneD, const NekDouble> &z2 = m_base[2]->GetZ();

            Array<OneD, NekDouble> gfac0(nquad0   );
            Array<OneD, NekDouble> gfac1(nquad1   );
            Array<OneD, NekDouble> gfac2(nquad2   );
            Array<OneD, NekDouble> tmp1 (nqtot    );
            Array<OneD, NekDouble> tmp2 (nqtot    );
            Array<OneD, NekDouble> tmp3 (nqtot    );
            Array<OneD, NekDouble> tmp4 (nqtot    );
            Array<OneD, NekDouble> tmp5 (nqtot    );
            Array<OneD, NekDouble> tmp6 (m_ncoeffs);
            Array<OneD, NekDouble> wsp  (std::max(nqtot,order0*nquad2*(nquad1+order1)));

            const Array<TwoD, const NekDouble>& df =
                            m_metricinfo->GetDerivFactors(GetPointsKeys());

            MultiplyByQuadratureMetric(inarray, tmp1);

            if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                Vmath::Vmul(nqtot,&df[3*dir][0],  1,tmp1.get(),1,tmp2.get(),1);
                Vmath::Vmul(nqtot,&df[3*dir+1][0],1,tmp1.get(),1,tmp3.get(),1);
                Vmath::Vmul(nqtot,&df[3*dir+2][0],1,tmp1.get(),1,tmp4.get(),1);
            }
            else
            {
                Vmath::Smul(nqtot, df[3*dir][0],  tmp1.get(),1,tmp2.get(), 1);
                Vmath::Smul(nqtot, df[3*dir+1][0],tmp1.get(),1,tmp3.get(), 1);
                Vmath::Smul(nqtot, df[3*dir+2][0],tmp1.get(),1,tmp4.get(), 1);
            }

            // set up geometric factor: (1+z0)/2
            for (i = 0; i < nquad0; ++i)
            {
                gfac0[i] = 0.5*(1+z0[i]);
            }

            // set up geometric factor: (1+z1)/2
            for(i = 0; i < nquad1; ++i)
            {
                gfac1[i] = 0.5*(1+z1[i]);
            }

            // Set up geometric factor: 2/(1-z2)
            for (i = 0; i < nquad2; ++i)
            {
                gfac2[i] = 2.0/(1-z2[i]);
            }

            const int nq01 = nquad0*nquad1;

            for (i = 0; i < nquad2; ++i)
            {
                Vmath::Smul(nq01,gfac2[i],&tmp2[0]+i*nq01,1,&tmp2[0]+i*nq01,1); // 2/(1-z2) for d/dxi_0
                Vmath::Smul(nq01,gfac2[i],&tmp3[0]+i*nq01,1,&tmp3[0]+i*nq01,1); // 2/(1-z2) for d/dxi_1
                Vmath::Smul(nq01,gfac2[i],&tmp4[0]+i*nq01,1,&tmp5[0]+i*nq01,1); // 2/(1-z2) for d/dxi_2
            }

            // (1+z0)/(1-z2) for d/d eta_0
            for(i = 0; i < nquad1*nquad2; ++i)
            {
                Vmath::Vmul(nquad0,&gfac0[0],1,
                            &tmp5[0]+i*nquad0,1,
                             &wsp[0]+i*nquad0,1);
            }

            Vmath::Vadd(nqtot, &tmp2[0], 1, &wsp[0], 1, &tmp2[0], 1);
            
            // (1+z1)/(1-z2) for d/d eta_1
            for(i = 0; i < nquad1*nquad2; ++i)
            {
                Vmath::Smul(nquad0,gfac1[i%nquad1],
                            &tmp5[0]+i*nquad0,1,
                            &tmp5[0]+i*nquad0,1);
            }
            Vmath::Vadd(nqtot, &tmp3[0], 1, &tmp5[0], 1, &tmp3[0], 1);

            
            IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),
                                         m_base[1]->GetBdata (),
                                         m_base[2]->GetBdata (),
                                         tmp2,outarray,wsp,
                                         false,true,true);

            IProductWRTBase_SumFacKernel(m_base[0]->GetBdata (),
                                         m_base[1]->GetDbdata(),
                                         m_base[2]->GetBdata (),
                                         tmp3,tmp6,wsp,
                                         true,false,true);

            Vmath::Vadd(m_ncoeffs, tmp6, 1, outarray, 1, outarray, 1);

            IProductWRTBase_SumFacKernel(m_base[0]->GetBdata (),
                                         m_base[1]->GetBdata (),
                                         m_base[2]->GetDbdata(),
                                         tmp4,tmp6,wsp,
                                         true,true,false);

            Vmath::Vadd(m_ncoeffs, tmp6, 1, outarray, 1, outarray, 1);
        }

v_LaplacianMatrixOp_MatFree_Kernel()

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

privatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1497 of file PyrExp.cpp.

References ASSERTL1, Nektar::LocalRegions::Expansion::ComputeLaplacianMetric(), Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vadd(), Vmath::Vvtvp(), and Vmath::Vvtvvtp().

        {
            // This implementation is only valid when there are no coefficients
            // associated to the Laplacian operator
            if (m_metrics.count(eMetricLaplacian00) == 0)
            {
                ComputeLaplacianMetric();
            }

            int nquad0  = m_base[0]->GetNumPoints();
            int nquad1  = m_base[1]->GetNumPoints();
            int nq2  = m_base[2]->GetNumPoints();
            int nqtot   = nquad0*nquad1*nq2;

            ASSERTL1(wsp.num_elements() >= 6*nqtot,
                     "Insufficient workspace size.");
            ASSERTL1(m_ncoeffs <= nqtot,
                     "Workspace not set up for ncoeffs > nqtot");

            const Array<OneD, const NekDouble>& base0  = m_base[0]->GetBdata();
            const Array<OneD, const NekDouble>& base1  = m_base[1]->GetBdata();
            const Array<OneD, const NekDouble>& base2  = m_base[2]->GetBdata();
            const Array<OneD, const NekDouble>& dbase0 = m_base[0]->GetDbdata();
            const Array<OneD, const NekDouble>& dbase1 = m_base[1]->GetDbdata();
            const Array<OneD, const NekDouble>& dbase2 = m_base[2]->GetDbdata();
            const Array<OneD, const NekDouble>& metric00 = m_metrics[eMetricLaplacian00];
            const Array<OneD, const NekDouble>& metric01 = m_metrics[eMetricLaplacian01];
            const Array<OneD, const NekDouble>& metric02 = m_metrics[eMetricLaplacian02];
            const Array<OneD, const NekDouble>& metric11 = m_metrics[eMetricLaplacian11];
            const Array<OneD, const NekDouble>& metric12 = m_metrics[eMetricLaplacian12];
            const Array<OneD, const NekDouble>& metric22 = m_metrics[eMetricLaplacian22];

            // Allocate temporary storage
            Array<OneD,NekDouble> wsp0 (2*nqtot, wsp);
            Array<OneD,NekDouble> wsp1 (  nqtot, wsp+1*nqtot);
            Array<OneD,NekDouble> wsp2 (  nqtot, wsp+2*nqtot);
            Array<OneD,NekDouble> wsp3 (  nqtot, wsp+3*nqtot);
            Array<OneD,NekDouble> wsp4 (  nqtot, wsp+4*nqtot);
            Array<OneD,NekDouble> wsp5 (  nqtot, wsp+5*nqtot);

            // LAPLACIAN MATRIX OPERATION
            // wsp1 = du_dxi1 = D_xi1 * inarray = D_xi1 * u
            // wsp2 = du_dxi2 = D_xi2 * inarray = D_xi2 * u
            // wsp2 = du_dxi3 = D_xi3 * inarray = D_xi3 * u
            StdExpansion3D::PhysTensorDeriv(inarray,wsp0,wsp1,wsp2);

            // wsp0 = k = g0 * wsp1 + g1 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
            // wsp2 = l = g1 * wsp1 + g2 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
            // where g0, g1 and g2 are the metric terms set up in the GeomFactors class
            // especially for this purpose
            Vmath::Vvtvvtp(nqtot,&metric00[0],1,&wsp0[0],1,&metric01[0],1,&wsp1[0],1,&wsp3[0],1);
            Vmath::Vvtvp  (nqtot,&metric02[0],1,&wsp2[0],1,&wsp3[0],1,&wsp3[0],1);
            Vmath::Vvtvvtp(nqtot,&metric01[0],1,&wsp0[0],1,&metric11[0],1,&wsp1[0],1,&wsp4[0],1);
            Vmath::Vvtvp  (nqtot,&metric12[0],1,&wsp2[0],1,&wsp4[0],1,&wsp4[0],1);
            Vmath::Vvtvvtp(nqtot,&metric02[0],1,&wsp0[0],1,&metric12[0],1,&wsp1[0],1,&wsp5[0],1);
            Vmath::Vvtvp  (nqtot,&metric22[0],1,&wsp2[0],1,&wsp5[0],1,&wsp5[0],1);

            // outarray = m = (D_xi1 * B)^T * k
            // wsp1     = n = (D_xi2 * B)^T * l
            IProductWRTBase_SumFacKernel(dbase0,base1,base2,wsp3,outarray,wsp0,false,true,true);
            IProductWRTBase_SumFacKernel(base0,dbase1,base2,wsp4,wsp2,    wsp0,true,false,true);
            Vmath::Vadd(m_ncoeffs,wsp2.get(),1,outarray.get(),1,outarray.get(),1);
            IProductWRTBase_SumFacKernel(base0,base1,dbase2,wsp5,wsp2,    wsp0,true,true,false);
            Vmath::Vadd(m_ncoeffs,wsp2.get(),1,outarray.get(),1,outarray.get(),1);
        }

v_PhysDeriv()

void Nektar::LocalRegions::PyrExp::v_PhysDeriv ( const Array< OneD, const NekDouble > &  u_physical, Array< OneD, NekDouble > &  out_dxi1, Array< OneD, NekDouble > &  out_dxi2, Array< OneD, NekDouble > &  out_dxi3  )

protectedvirtual

Calculate the derivative of the physical points.

The derivative is evaluated at the nodal physical points. Derivatives with respect to the local Cartesian coordinates.

\(\begin{Bmatrix} \frac {\partial} {\partial \xi_1} \\ \frac {\partial} {\partial \xi_2} \\ \frac {\partial} {\partial \xi_3} \end{Bmatrix} = \begin{Bmatrix} \frac 2 {(1-\eta_3)} \frac \partial {\partial \bar \eta_1} \\ \frac {\partial} {\partial \xi_2} \ \ \frac {(1 + \bar \eta_1)} {(1 - \eta_3)} \frac \partial {\partial \bar \eta_1} + \frac {\partial} {\partial \eta_3} \end{Bmatrix}\)

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 138 of file PyrExp.cpp.

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

        {
            int    nquad0 = m_base[0]->GetNumPoints();
            int    nquad1 = m_base[1]->GetNumPoints();
            int    nquad2 = m_base[2]->GetNumPoints();
            Array<TwoD, const NekDouble> gmat =
                                m_metricinfo->GetDerivFactors(GetPointsKeys());
            Array<OneD,NekDouble> diff0(nquad0*nquad1*nquad2);
            Array<OneD,NekDouble> diff1(nquad0*nquad1*nquad2);
            Array<OneD,NekDouble> diff2(nquad0*nquad1*nquad2);

            StdPyrExp::v_PhysDeriv(inarray, diff0, diff1, diff2);

            if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
            {
                if(out_d0.num_elements())
                {
                    Vmath::Vmul  (nquad0*nquad1*nquad2,&gmat[0][0],1,&diff0[0],1, &out_d0[0], 1);
                    Vmath::Vvtvp (nquad0*nquad1*nquad2,&gmat[1][0],1,&diff1[0],1, &out_d0[0], 1,&out_d0[0],1);
                    Vmath::Vvtvp (nquad0*nquad1*nquad2,&gmat[2][0],1,&diff2[0],1, &out_d0[0], 1,&out_d0[0],1);
                }
                
                if(out_d1.num_elements())
                {
                    Vmath::Vmul  (nquad0*nquad1*nquad2,&gmat[3][0],1,&diff0[0],1, &out_d1[0], 1);
                    Vmath::Vvtvp (nquad0*nquad1*nquad2,&gmat[4][0],1,&diff1[0],1, &out_d1[0], 1,&out_d1[0],1);
                    Vmath::Vvtvp (nquad0*nquad1*nquad2,&gmat[5][0],1,&diff2[0],1, &out_d1[0], 1,&out_d1[0],1);
                }
                
                if(out_d2.num_elements())
                {
                    Vmath::Vmul  (nquad0*nquad1*nquad2,&gmat[6][0],1,&diff0[0],1, &out_d2[0], 1);
                    Vmath::Vvtvp (nquad0*nquad1*nquad2,&gmat[7][0],1,&diff1[0],1, &out_d2[0], 1, &out_d2[0],1);
                    Vmath::Vvtvp (nquad0*nquad1*nquad2,&gmat[8][0],1,&diff2[0],1, &out_d2[0], 1, &out_d2[0],1);
                }
            }
            else // regular geometry
            {
                if(out_d0.num_elements())
                {
                    Vmath::Smul  (nquad0*nquad1*nquad2,gmat[0][0],&diff0[0],1, &out_d0[0], 1);
                    Blas::Daxpy (nquad0*nquad1*nquad2,gmat[1][0],&diff1[0],1, &out_d0[0], 1);
                    Blas::Daxpy (nquad0*nquad1*nquad2,gmat[2][0],&diff2[0],1, &out_d0[0], 1);
                }
                
                if(out_d1.num_elements())
                {
                    Vmath::Smul  (nquad0*nquad1*nquad2,gmat[3][0],&diff0[0],1, &out_d1[0], 1);
                    Blas::Daxpy (nquad0*nquad1*nquad2,gmat[4][0],&diff1[0],1, &out_d1[0], 1);
                    Blas::Daxpy (nquad0*nquad1*nquad2,gmat[5][0],&diff2[0],1, &out_d1[0], 1);
                }
                
                if(out_d2.num_elements())
                {
                    Vmath::Smul  (nquad0*nquad1*nquad2,gmat[6][0],&diff0[0],1, &out_d2[0], 1);
                    Blas::Daxpy (nquad0*nquad1*nquad2,gmat[7][0],&diff1[0],1, &out_d2[0], 1);
                    Blas::Daxpy (nquad0*nquad1*nquad2,gmat[8][0],&diff2[0],1, &out_d2[0], 1);
                }
            }
        }

v_PhysEvaluate()

NekDouble Nektar::LocalRegions::PyrExp::v_PhysEvaluate ( const Array< OneD, const NekDouble > &  coords, const Array< OneD, const NekDouble > &  physvals  )

protectedvirtual

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

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

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

is evaluated using Lagrangian interpolants through the quadrature points:

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

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

Parameters

coords

the coordinates of the single point

Returns

returns the value of the expansion at the single point

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 600 of file PyrExp.cpp.

References ASSERTL0, and Nektar::LocalRegions::Expansion::m_geom.

        {
            Array<OneD,NekDouble> Lcoord(3);

            ASSERTL0(m_geom,"m_geom not defined");
    
            //TODO: check GetLocCoords()
            m_geom->GetLocCoords(coord, Lcoord);
            
            return StdPyrExp::v_PhysEvaluate(Lcoord, physvals);
        }

v_StdPhysEvaluate()

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

protectedvirtual

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 592 of file PyrExp.cpp.

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

v_SVVLaplacianFilter()

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

protectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 1002 of file PyrExp.cpp.

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

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

Member Data Documentation

m_matrixManager

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

private

Definition at line 182 of file PyrExp.h.

Referenced by CreateMatrix(), v_FwdTrans(), and v_GetLocMatrix().

m_staticCondMatrixManager

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

private

Definition at line 183 of file PyrExp.h.

Referenced by v_DropLocStaticCondMatrix(), and v_GetLocStaticCondMatrix().