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)
virtual	~PyrExp () override=default
Public Member Functions inherited from Nektar::StdRegions::StdPyrExp
	StdPyrExp ()=default
	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 () override=default
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 () override
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)
int	GetNedges () const
	return the number of edges in 3D expansion More...
int	GetEdgeNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th edge. More...
void	GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards)
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	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th trace. More...
int	GetTraceIntNcoeffs (const int i) const
int	GetTraceNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th trace. More...
const LibUtilities::BasisKey	GetTraceBasisKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...
LibUtilities::PointsKey	GetTracePointsKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...
int	NumBndryCoeffs (void) const
int	NumDGBndryCoeffs (void) const
const LibUtilities::PointsKey	GetNodalPointsKey () const
	This function returns the type of expansion Nodal point type if defined. More...
int	GetNtraces () 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 () const
std::shared_ptr< StdExpansion >	GetLinStdExp (void) const
int	GetShapeDimension () const
bool	IsBoundaryInteriorExpansion () const
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	FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)
	This function integrates the specified function over the domain. 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)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
void	NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble >> &Fvec, Array< OneD, NekDouble > &outarray)
DNekScalBlkMatSharedPtr	GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
void	DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
int	CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
NekDouble	StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
int	GetCoordim ()
void	GetBoundaryMap (Array< OneD, unsigned int > &outarray)
void	GetInteriorMap (Array< OneD, unsigned int > &outarray)
int	GetVertexMap (const int localVertexId, bool useCoeffPacking=false)
void	GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
void	GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray)
void	GetElmtTraceToTraceMap (const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
void	GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eForwards)
void	GetTraceNumModes (const int tid, int &numModes0, int &numModes1, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)
void	MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
DNekMatSharedPtr	CreateGeneralMatrix (const StdMatrixKey &mkey)
	this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) 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)
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, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
	This function evaluates the first derivative of the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)
NekDouble	PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
	This function evaluates the basis function mode mode at a point coords of the domain. More...
void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta. More...
void	LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
	Convert local collapsed coordinates eta into local cartesian coordinate xi. More...
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)
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 LibUtilities::PointsKeyVector	GetPointsKeys () const
DNekMatSharedPtr	BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
void	PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
	This function performs an interpolation from the physical space points provided at input into an array of equispaced points which are not the collapsed coordinate. So for a tetrahedron you will only get a tetrahedral number of values. 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)
void	GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
Public Member Functions inherited from Nektar::LocalRegions::Expansion3D
	Expansion3D (SpatialDomains::Geometry3DSharedPtr pGeom)
virtual	~Expansion3D () override=default
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	v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1) override
void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble >> &Fvec, Array< OneD, NekDouble > &outarray) override
Array< OneD, unsigned int >	GetEdgeInverseBoundaryMap (int eid)
Array< OneD, unsigned int >	GetTraceInverseBoundaryMap (int fid, StdRegions::Orientation faceOrient=StdRegions::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)
DNekScalMatSharedPtr	CreateMatrix (const MatrixKey &mkey)
Public Member Functions inherited from Nektar::LocalRegions::Expansion
	Expansion (SpatialDomains::GeometrySharedPtr pGeom)
	Expansion (const Expansion &pSrc)
virtual	~Expansion ()
void	SetTraceExp (const int traceid, ExpansionSharedPtr &f)
ExpansionSharedPtr	GetTraceExp (const int traceid)
DNekScalMatSharedPtr	GetLocMatrix (const LocalRegions::MatrixKey &mkey)
void	DropLocMatrix (const LocalRegions::MatrixKey &mkey)
DNekScalMatSharedPtr	GetLocMatrix (const StdRegions::MatrixType mtype, const StdRegions::ConstFactorMap &factors=StdRegions::NullConstFactorMap, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap)
SpatialDomains::GeometrySharedPtr	GetGeom () const
void	Reset ()
IndexMapValuesSharedPtr	CreateIndexMap (const IndexMapKey &ikey)
DNekScalBlkMatSharedPtr	CreateStaticCondMatrix (const MatrixKey &mkey)
const SpatialDomains::GeomFactorsSharedPtr &	GetMetricInfo () const
DNekMatSharedPtr	BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType)
DNekMatSharedPtr	BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd)
void	ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void	AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void	DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble >> &coeffs, Array< OneD, NekDouble > &outarray)
NekDouble	VectorFlux (const Array< OneD, Array< OneD, NekDouble >> &vec)
void	NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble >> &factors, Array< OneD, Array< OneD, NekDouble >> &d0factors, Array< OneD, Array< OneD, NekDouble >> &d1factors)
IndexMapValuesSharedPtr	GetIndexMap (const IndexMapKey &ikey)
void	AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble >> &outarray)
ExpansionSharedPtr	GetLeftAdjacentElementExp () const
ExpansionSharedPtr	GetRightAdjacentElementExp () const
int	GetLeftAdjacentElementTrace () const
int	GetRightAdjacentElementTrace () const
void	SetAdjacentElementExp (int traceid, ExpansionSharedPtr &e)
StdRegions::Orientation	GetTraceOrient (int trace)
void	SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Divided by the metric jacobi and quadrature weights. More...
void	GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray)
	Extract the metric factors to compute the contravariant fluxes along edge edge and stores them into outarray following the local edge orientation (i.e. anticlockwise convention). More...
void	GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=StdRegions::eNoOrientation)
void	GetTracePhysMap (const int edge, Array< OneD, int > &outarray)
void	ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1)
const NormalVector &	GetTraceNormal (const int id)
void	ComputeTraceNormal (const int id)
const Array< OneD, const NekDouble > &	GetPhysNormals (void)
void	SetPhysNormals (Array< OneD, const NekDouble > &normal)
void	SetUpPhysNormals (const int trace)
void	AddRobinMassMatrix (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
void	TraceNormLen (const int traceid, NekDouble &h, NekDouble &p)
void	AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)
const Array< OneD, const NekDouble > &	GetElmtBndNormDirElmtLen (const int nbnd) const
void	StdDerivBaseOnTraceMat (Array< OneD, DNekMatSharedPtr > &DerivMat)

Protected Member Functions
virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	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) override
	Calculate the derivative of the physical points. More...
virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in (this)->m_coeffs. More...
virtual void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	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) override
void	v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	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) override
virtual void	v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble >> &outarray) override
virtual StdRegions::StdExpansionSharedPtr	v_GetStdExp (void) const override
virtual StdRegions::StdExpansionSharedPtr	v_GetLinStdExp (void) const override
virtual void	v_GetCoord (const Array< OneD, const NekDouble > &Lcoords, Array< OneD, NekDouble > &coords) override
virtual void	v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override
virtual void	v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int mode_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType) override
NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals) override
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coord, const Array< OneD, const NekDouble > &physvals) override
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
virtual NekDouble	v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
virtual void	v_GetTracePhysMap (const int face, Array< OneD, int > &outarray) override
void	v_ComputeTraceNormal (const int face) override
virtual void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdRegions::StdMatrixKey &mkey) override
virtual DNekMatSharedPtr	v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override
virtual DNekMatSharedPtr	v_CreateStdMatrix (const StdRegions::StdMatrixKey &mkey) override
virtual DNekScalMatSharedPtr	v_GetLocMatrix (const MatrixKey &mkey) override
virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const MatrixKey &mkey) override
void	v_DropLocMatrix (const MatrixKey &mkey) override
void	v_DropLocStaticCondMatrix (const MatrixKey &mkey) override
virtual void	v_ComputeLaplacianMetric () override
virtual void	v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble >> &d0factors, Array< OneD, Array< OneD, NekDouble >> &d1factors, Array< OneD, Array< OneD, NekDouble >> &d2factors) override
	: This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace. More...
Protected Member Functions inherited from Nektar::StdRegions::StdPyrExp
void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Calculate the derivative of the physical points in a given direction. More...
void	v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2) override
void	v_StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
	Backward transformation is evaluated at the quadrature points. More...
void	v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
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) override
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) override
void	v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta) override
void	v_LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi) override
void	v_FillMode (const int mode, Array< OneD, NekDouble > &outarray) override
void	v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation faceOrient=eDir1FwdDir1_Dir2FwdDir2) override
NekDouble	v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) final
int	v_GetNverts () const override
int	v_GetNedges () const override
int	v_GetNtraces () const override
LibUtilities::ShapeType	v_DetShapeType () const override
int	v_NumBndryCoeffs () const override
int	v_NumDGBndryCoeffs () const override
int	v_GetTraceNcoeffs (const int i) const override
int	v_GetTraceIntNcoeffs (const int i) const override
int	v_GetTraceNumPoints (const int i) const override
int	v_GetEdgeNcoeffs (const int i) const override
int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset) override
const LibUtilities::BasisKey	v_GetTraceBasisKey (const int i, const int k) const override
int	v_GetVertexMap (int localVertexId, bool useCoeffPacking=false) override
void	v_GetInteriorMap (Array< OneD, unsigned int > &outarray) override
void	v_GetBoundaryMap (Array< OneD, unsigned int > &outarray) override
void	v_GetTraceCoeffMap (const unsigned int fid, Array< OneD, unsigned int > &maparray) override
void	v_GetElmtTraceToTraceMap (const unsigned int fid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation faceOrient, int P, int Q) override
void	v_GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override
void	v_GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override
void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion3D
virtual NekDouble	v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) override
virtual void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
virtual void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
virtual void	v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient, int P, int Q) override
virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr	CreateStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr	CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
	Create the static condensation of a matrix when using a boundary interior decomposition. More...
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 (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv, NekDouble &deriv2)
	This function performs the barycentric interpolation of the polynomial stored in coord at a point physvals using barycentric interpolation weights in direction. More...
template<int DIR>
NekDouble	BaryEvaluateBasis (const NekDouble &coord, const int &mode)
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
	Helper function to pass an unused value by reference into BaryEvaluate. More...
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)
Protected Member Functions inherited from Nektar::LocalRegions::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) override
	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) override
virtual void	v_AddRobinMassMatrix (const int face, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) override
virtual StdRegions::Orientation	v_GetTraceOrient (int face) override
virtual void	v_GetTracePhysVals (const int face, const StdRegions::StdExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) override
	Extract the physical values along face face from inarray into outarray following the local face orientation and point distribution defined by defined in FaceExp. More...
virtual void	v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp) override
void	GetPhysFaceVarCoeffsFromElement (const int face, ExpansionSharedPtr &FaceExp, const Array< OneD, const NekDouble > &varcoeff, Array< OneD, NekDouble > &outarray)
virtual DNekMatSharedPtr	v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType) override
virtual DNekMatSharedPtr	v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &transformationmatrix) override
	Build inverse and inverse transposed transformation matrix: \(\mathbf{R^{-1}}\) and \(\mathbf{R^{-T}}\). More...
virtual DNekMatSharedPtr	v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) override
virtual void	v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) override
Protected Member Functions inherited from Nektar::LocalRegions::Expansion
void	ComputeLaplacianMetric ()
void	ComputeQuadratureMetric ()
void	ComputeGmatcdotMF (const Array< TwoD, const NekDouble > &df, const Array< OneD, const NekDouble > &direction, Array< OneD, Array< OneD, NekDouble >> &dfdir)
Array< OneD, NekDouble >	GetMF (const int dir, const int shapedim, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	GetMFDiv (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
Array< OneD, NekDouble >	GetMFMag (const int dir, const StdRegions::VarCoeffMap &varcoeffs)
virtual void	v_MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual int	v_GetCoordim () const override
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)
virtual void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
virtual void	v_GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray)
virtual const Array< OneD, const NekDouble > &	v_GetPhysNormals ()
virtual void	v_SetPhysNormals (Array< OneD, const NekDouble > &normal)
virtual void	v_SetUpPhysNormals (const int id)
virtual void	v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs)

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

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

Additional Inherited Members
Protected Attributes inherited from Nektar::StdRegions::StdExpansion
Array< OneD, LibUtilities::BasisSharedPtr >	m_base
int	m_elmt_id
int	m_ncoeffs
LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess >	m_stdMatrixManager
LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess >	m_stdStaticCondMatrixManager
Protected Attributes inherited from Nektar::LocalRegions::Expansion3D
std::map< int, NormalVector >	m_faceNormals
Protected Attributes inherited from Nektar::LocalRegions::Expansion
LibUtilities::NekManager< IndexMapKey, IndexMapValues, IndexMapKey::opLess >	m_indexMapManager
std::map< int, ExpansionWeakPtr >	m_traceExp
SpatialDomains::GeometrySharedPtr	m_geom
SpatialDomains::GeomFactorsSharedPtr	m_metricinfo
MetricMap	m_metrics
std::map< int, NormalVector >	m_traceNormals
ExpansionWeakPtr	m_elementLeft
ExpansionWeakPtr	m_elementRight
int	m_elementTraceLeft = -1
int	m_elementTraceRight = -1
std::map< int, Array< OneD, NekDouble > >	m_elmtBndNormDirElmtLen
	the element length in each element boundary(Vertex, edge or face) normal direction calculated based on the local m_metricinfo times the standard element length (which is 2.0) More...

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(&Expansion3D::CreateMatrix, this, std::placeholders::_1),
          std::string("PyrExpMatrix")),
      m_staticCondMatrixManager(std::bind(&Expansion::CreateStaticCondMatrix,
                                          this, std::placeholders::_1),
                                std::string("PyrExpStaticCondMatrix"))
{
}

PyrExp() [2/2]

Nektar::LocalRegions::PyrExp::PyrExp

(

const PyrExp &

T

)

Definition at line 65 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()

virtual Nektar::LocalRegions::PyrExp::~PyrExp ( )

overridevirtualdefault

Member Function Documentation

v_AlignVectorToCollapsedDir()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 396 of file PyrExp.cpp.

{
    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;
 
    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> tmp5(nqtot);
    Array<OneD, NekDouble> wsp(
        std::max(nqtot, order0 * nquad2 * (nquad1 + order1)));
 
    Array<OneD, NekDouble> tmp2 = outarray[0];
    Array<OneD, NekDouble> tmp3 = outarray[1];
    Array<OneD, NekDouble> tmp4 = outarray[2];
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    Array<OneD, NekDouble> tmp1;
    tmp1 = inarray;
 
    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 (int i = 0; i < nquad0; ++i)
    {
        gfac0[i] = 0.5 * (1 + z0[i]);
    }
 
    // set up geometric factor: (1+z1)/2
    for (int i = 0; i < nquad1; ++i)
    {
        gfac1[i] = 0.5 * (1 + z1[i]);
    }
 
    // Set up geometric factor: 2/(1-z2)
    for (int i = 0; i < nquad2; ++i)
    {
        gfac2[i] = 2.0 / (1 - z2[i]);
    }
 
    const int nq01 = nquad0 * nquad1;
 
    for (int 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 (int 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 (int 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);
}

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

Referenced by v_IProductWRTDerivBase_SumFac().

v_ComputeLaplacianMetric()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1097 of file PyrExp.cpp.

{
    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]]);
        }
    }
}

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().

v_ComputeTraceNormal()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 731 of file PyrExp.cpp.

{
    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 = GetTraceBasisKey(face, 0);
    LibUtilities::BasisKey tobasis1 = GetTraceBasisKey(face, 1);
 
    // Number of quadrature points in face expansion.
    int nq_face = tobasis0.GetNumPoints() * tobasis1.GetNumPoints();
 
    int vCoordDim = GetCoordim();
    int i;
 
    m_traceNormals[face] = Array<OneD, Array<OneD, NekDouble>>(vCoordDim);
    Array<OneD, Array<OneD, NekDouble>> &normal = m_traceNormals[face];
    for (i = 0; i < vCoordDim; ++i)
    {
        normal[i] = Array<OneD, NekDouble>(nq_face);
    }
 
    size_t nqb                     = nq_face;
    size_t nbnd                    = face;
    m_elmtBndNormDirElmtLen[nbnd]  = Array<OneD, NekDouble>{nqb, 0.0};
    Array<OneD, NekDouble> &length = m_elmtBndNormDirElmtLen[nbnd];
 
    // Regular geometry case
    if (type == SpatialDomains::eRegular ||
        type == SpatialDomains::eMovingRegular)
    {
        NekDouble 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);
 
        Vmath::Fill(nqb, fac, length, 1);
 
        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);
 
        Vmath::Vcopy(nqb, work, 1, length, 1);
 
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vmul(nq_face, normal[i], 1, work, 1, normal[i], 1);
        }
    }
}

References ASSERTL0, 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::StdRegions::StdExpansion::GetTraceBasisKey(), Nektar::LibUtilities::Interp2D(), Nektar::LocalRegions::Expansion::m_elmtBndNormDirElmtLen, Nektar::LocalRegions::Expansion::m_traceNormals, Vmath::Sdiv(), tinysimd::sqrt(), Vmath::Vcopy(), Vmath::Vmul(), Vmath::Vsqrt(), Vmath::Vvtvp(), and Vmath::Zero().

v_CreateStdMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 1066 of file PyrExp.cpp.

{
    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);
}

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

v_DropLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1082 of file PyrExp.cpp.

{
    m_matrixManager.DeleteObject(mkey);
}

References m_matrixManager.

v_DropLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1092 of file PyrExp.cpp.

{
    m_staticCondMatrixManager.DeleteObject(mkey);
}

References m_staticCondMatrixManager.

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  )

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 543 of file PyrExp.cpp.

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

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().

v_FwdTrans()

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

overrideprotectedvirtual

Forward transform from physical quadrature space stored in inarray and evaluate the expansion coefficients and store in (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 223 of file PyrExp.cpp.

{
    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;
    }
}

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().

v_GenMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 1045 of file PyrExp.cpp.

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

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

v_GetCoord()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 519 of file PyrExp.cpp.

{
    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);
    }
}

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

v_GetCoords()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 536 of file PyrExp.cpp.

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

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

v_GetLinStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 502 of file PyrExp.cpp.

{
    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);
}

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

v_GetLocMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1077 of file PyrExp.cpp.

{
    return m_matrixManager[mkey];
}

References m_matrixManager.

v_GetLocStaticCondMatrix()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1087 of file PyrExp.cpp.

{
    return m_staticCondMatrixManager[mkey];
}

References m_staticCondMatrixManager.

v_GetStdExp()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 495 of file PyrExp.cpp.

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

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

v_GetTracePhysMap()

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

overrideprotectedvirtual

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 633 of file PyrExp.cpp.

{
    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.size() != 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.size() != 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.size() != 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.size() != 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.size() != 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;
    }
}

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

v_Integral()

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

overrideprotectedvirtual

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 96 of file PyrExp.cpp.

{
    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);
}

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

v_IProductWRTBase()

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

overrideprotectedvirtual

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.

{
    v_IProductWRTBase_SumFac(inarray, outarray);
}

References v_IProductWRTBase_SumFac().

Referenced by v_FwdTrans().

v_IProductWRTBase_SumFac()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 284 of file PyrExp.cpp.

{
    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);
    }
}

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

Referenced by v_IProductWRTBase().

v_IProductWRTDerivBase()

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

overrideprotectedvirtual

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 344 of file PyrExp.cpp.

{
    v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
}

References v_IProductWRTDerivBase_SumFac().

v_IProductWRTDerivBase_SumFac()

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

overrideprotectedvirtual

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 351 of file PyrExp.cpp.

{
    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;
 
    Array<OneD, NekDouble> tmp1(nqtot);
    Array<OneD, NekDouble> tmp2(nqtot);
    Array<OneD, NekDouble> tmp3(nqtot);
    Array<OneD, NekDouble> tmp4(nqtot);
    Array<OneD, NekDouble> tmp6(m_ncoeffs);
    Array<OneD, NekDouble> wsp(
        std::max(nqtot, order0 * nquad2 * (nquad1 + order1)));
 
    MultiplyByQuadratureMetric(inarray, tmp1);
 
    Array<OneD, Array<OneD, NekDouble>> tmp2D{3};
    tmp2D[0] = tmp2;
    tmp2D[1] = tmp3;
    tmp2D[2] = tmp4;
 
    PyrExp::v_AlignVectorToCollapsedDir(dir, tmp1, tmp2D);
 
    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);
}

References Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), v_AlignVectorToCollapsedDir(), and Vmath::Vadd().

Referenced by v_IProductWRTDerivBase().

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  )

overrideprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1277 of file PyrExp.cpp.

{
    // 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.size() >= 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);
}

References ASSERTL1, Nektar::LocalRegions::Expansion::ComputeLaplacianMetric(), Nektar::LocalRegions::eMetricLaplacian00, Nektar::StdRegions::StdExpansion::m_base, and Nektar::LocalRegions::Expansion::m_metrics.

v_NormalTraceDerivFactors()

void Nektar::LocalRegions::PyrExp::v_NormalTraceDerivFactors ( Array< OneD, Array< OneD, NekDouble >> &  d0factors, Array< OneD, Array< OneD, NekDouble >> &  d1factors, Array< OneD, Array< OneD, NekDouble >> &  d2factors  )

overrideprotectedvirtual

: This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace.

Reimplemented from Nektar::LocalRegions::Expansion.

Definition at line 1360 of file PyrExp.cpp.

{
    int nquad0 = GetNumPoints(0);
    int nquad1 = GetNumPoints(1);
    int nquad2 = GetNumPoints(2);
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    if (d0factors.size() != 5)
    {
        d0factors = Array<OneD, Array<OneD, NekDouble>>(5);
        d1factors = Array<OneD, Array<OneD, NekDouble>>(5);
        d2factors = Array<OneD, Array<OneD, NekDouble>>(5);
    }
 
    if (d0factors[0].size() != nquad0 * nquad1)
    {
        d0factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d1factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d2factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
    }
 
    if (d0factors[1].size() != nquad0 * nquad2)
    {
        d0factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d0factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d1factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d1factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d2factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d2factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
    }
 
    if (d0factors[2].size() != nquad1 * nquad2)
    {
        d0factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d0factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d1factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d1factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d2factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d2factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
    }
 
    // Outwards normals
    const Array<OneD, const Array<OneD, NekDouble>> &normal_0 =
        GetTraceNormal(0);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_1 =
        GetTraceNormal(1);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_2 =
        GetTraceNormal(2);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_3 =
        GetTraceNormal(3);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_4 =
        GetTraceNormal(4);
 
    int ncoords = normal_0.size();
 
    // first gather together standard cartesian inner products
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        // face 0
        for (int i = 0; i < nquad0 * nquad1; ++i)
        {
            d0factors[0][i] = df[0][i] * normal_0[0][i];
            d1factors[0][i] = df[1][i] * normal_0[0][i];
            d2factors[0][i] = df[2][i] * normal_0[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                d0factors[0][i] += df[3 * n][i] * normal_0[n][i];
                d1factors[0][i] += df[3 * n + 1][i] * normal_0[n][i];
                d2factors[0][i] += df[3 * n + 2][i] * normal_0[n][i];
            }
        }
 
        // faces 1 and 3
        for (int j = 0; j < nquad2; ++j)
        {
            for (int i = 0; i < nquad0; ++i)
            {
                d0factors[1][i] = df[0][j * nquad0 * nquad1 + i] *
                                  normal_1[0][j * nquad0 + i];
                d0factors[3][i] =
                    df[0][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
                d1factors[1][i] = df[1][j * nquad0 * nquad1 + i] *
                                  normal_1[0][j * nquad0 + i];
                d1factors[3][i] =
                    df[1][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
                d2factors[1][i] = df[2][j * nquad0 * nquad1 + i] *
                                  normal_1[0][j * nquad0 + i];
                d2factors[3][i] =
                    df[2][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
            }
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int j = 0; j < nquad2; ++j)
            {
                for (int i = 0; i < nquad0; ++i)
                {
                    d0factors[1][i] = df[3 * n][j * nquad0 * nquad1 + i] *
                                      normal_1[0][j * nquad0 + i];
                    d0factors[3][i] =
                        df[3 * n][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                    d1factors[1][i] = df[3 * n + 1][j * nquad0 * nquad1 + i] *
                                      normal_1[0][j * nquad0 + i];
                    d1factors[3][i] =
                        df[3 * n + 1][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                    d2factors[1][i] = df[3 * n + 2][j * nquad0 * nquad1 + i] *
                                      normal_1[0][j * nquad0 + i];
                    d2factors[3][i] =
                        df[3 * n + 2][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                }
            }
        }
 
        // faces 2 and 4
        for (int j = 0; j < nquad2; ++j)
        {
            for (int i = 0; i < nquad1; ++i)
            {
                d0factors[2][j * nquad1 + i] =
                    df[0][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d0factors[4][j * nquad1 + i] =
                    df[0][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
                d1factors[2][j * nquad1 + i] =
                    df[1][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d1factors[4][j * nquad1 + i] =
                    df[1][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
                d2factors[2][j * nquad1 + i] =
                    df[2][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d2factors[4][j * nquad1 + i] =
                    df[2][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
            }
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int j = 0; j < nquad2; ++j)
            {
                for (int i = 0; i < nquad1; ++i)
                {
                    d0factors[2][j * nquad1 + i] +=
                        df[3 * n][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad0 + i];
                    d0factors[4][j * nquad0 + i] +=
                        df[3 * n][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad0 + i];
                    d1factors[2][j * nquad1 + i] +=
                        df[3 * n + 1]
                          [j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad0 + i];
                    d1factors[4][j * nquad0 + i] +=
                        df[3 * n + 1][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad0 + i];
                    d2factors[2][j * nquad1 + i] +=
                        df[3 * n + 2]
                          [j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad0 + i];
                    d2factors[4][j * nquad0 + i] +=
                        df[3 * n + 2][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad0 + i];
                }
            }
        }
    }
    else
    {
        // Face 0
        for (int i = 0; i < nquad0 * nquad1; ++i)
        {
            d0factors[0][i] = df[0][0] * normal_0[0][i];
            d1factors[0][i] = df[1][0] * normal_0[0][i];
            d2factors[0][i] = df[2][0] * normal_0[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                d0factors[0][i] += df[3 * n][0] * normal_0[n][i];
                d1factors[0][i] += df[3 * n + 1][0] * normal_0[n][i];
                d2factors[0][i] += df[3 * n + 2][0] * normal_0[n][i];
            }
        }
 
        // faces 1 and 3
        for (int i = 0; i < nquad0 * nquad2; ++i)
        {
            d0factors[1][i] = df[0][0] * normal_1[0][i];
            d0factors[3][i] = df[0][0] * normal_3[0][i];
 
            d1factors[1][i] = df[1][0] * normal_1[0][i];
            d1factors[3][i] = df[1][0] * normal_3[0][i];
 
            d2factors[1][i] = df[2][0] * normal_1[0][i];
            d2factors[3][i] = df[2][0] * normal_3[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad2; ++i)
            {
                d0factors[1][i] += df[3 * n][0] * normal_1[n][i];
                d0factors[3][i] += df[3 * n][0] * normal_3[n][i];
 
                d1factors[1][i] += df[3 * n + 1][0] * normal_1[n][i];
                d1factors[3][i] += df[3 * n + 1][0] * normal_3[n][i];
 
                d2factors[1][i] += df[3 * n + 2][0] * normal_1[n][i];
                d2factors[3][i] += df[3 * n + 2][0] * normal_3[n][i];
            }
        }
 
        // faces 2 and 4
        for (int i = 0; i < nquad1 * nquad2; ++i)
        {
            d0factors[2][i] = df[0][0] * normal_2[0][i];
            d0factors[4][i] = df[0][0] * normal_4[0][i];
 
            d1factors[2][i] = df[1][0] * normal_2[0][i];
            d1factors[4][i] = df[1][0] * normal_4[0][i];
 
            d2factors[2][i] = df[2][0] * normal_2[0][i];
            d2factors[4][i] = df[2][0] * normal_4[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad1 * nquad2; ++i)
            {
                d0factors[2][i] += df[3 * n][0] * normal_2[n][i];
                d0factors[4][i] += df[3 * n][0] * normal_4[n][i];
 
                d1factors[2][i] += df[3 * n + 1][0] * normal_2[n][i];
                d1factors[4][i] += df[3 * n + 1][0] * normal_4[n][i];
 
                d2factors[2][i] += df[3 * n + 2][0] * normal_2[n][i];
                d2factors[4][i] += df[3 * n + 2][0] * normal_4[n][i];
            }
        }
    }
}

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  )

overrideprotectedvirtual

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 124 of file PyrExp.cpp.

{
    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.size())
        {
            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.size())
        {
            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.size())
        {
            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.size())
        {
            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.size())
        {
            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.size())
        {
            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);
        }
    }
}

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().

v_PhysEvaluate() [1/2]

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

overrideprotectedvirtual

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 606 of file PyrExp.cpp.

{
    Array<OneD, NekDouble> Lcoord(3);
 
    ASSERTL0(m_geom, "m_geom not defined");
 
    // TODO: check GetLocCoords()
    m_geom->GetLocCoords(coord, Lcoord);
 
    return StdExpansion3D::v_PhysEvaluate(Lcoord, physvals);
}

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

v_PhysEvaluate() [2/2]

NekDouble Nektar::LocalRegions::PyrExp::v_PhysEvaluate ( const Array< OneD, NekDouble > &  coord, const Array< OneD, const NekDouble > &  inarray, std::array< NekDouble, 3 > &  firstOrderDerivs  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 619 of file PyrExp.cpp.

{
    Array<OneD, NekDouble> Lcoord(3);
    ASSERTL0(m_geom, "m_geom not defined");
    m_geom->GetLocCoords(coord, Lcoord);
    return StdPyrExp::v_PhysEvaluate(Lcoord, inarray, firstOrderDerivs);
}

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

v_StdPhysEvaluate()

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

overrideprotectedvirtual

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 598 of file PyrExp.cpp.

{
    // Evaluate point in local coordinates.
    return StdExpansion3D::v_PhysEvaluate(Lcoord, physvals);
}

v_SVVLaplacianFilter()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdPyrExp.

Definition at line 1014 of file PyrExp.cpp.

{
    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);
}

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

Member Data Documentation

m_matrixManager

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

private

Definition at line 176 of file PyrExp.h.

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

m_staticCondMatrixManager

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

private

Definition at line 178 of file PyrExp.h.

Referenced by v_DropLocStaticCondMatrix(), and v_GetLocStaticCondMatrix().