Nektar::StdRegions::StdTetExp Class Reference

#include <StdTetExp.h>

Inheritance diagram for Nektar::StdRegions::StdTetExp:

Public Member Functions
	StdTetExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)
	StdTetExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc, NekDouble *coeffs, NekDouble *phys)
	StdTetExp (const StdTetExp &T)=default
	~StdTetExp () override=default
LibUtilities::ShapeType	DetShapeType () const
Public Member Functions inherited from Nektar::StdRegions::StdExpansion3D
	StdExpansion3D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)
	StdExpansion3D ()=default
	StdExpansion3D (const StdExpansion3D &T)=default
	~StdExpansion3D () override=default
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, bool UseGLL=false) 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	NodalToModal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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	LinearAdvectionMatrixOp (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...
void	PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData)
	interpolate from one set of quadrature points available from FromExp to the set of quadrature points in the current expansion. If the points are the same this routine will just copy the data More...
virtual int	v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
virtual void	v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray)
virtual DNekScalBlkMatSharedPtr	v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
virtual void	v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
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)

Protected Member Functions
void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dx, Array< OneD, NekDouble > &out_dy, Array< OneD, NekDouble > &out_dz) override
	Calculate the derivative of the physical points. More...
void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
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_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
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_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true) 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_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) 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_GetCoords (Array< OneD, NekDouble > &coords_x, Array< OneD, NekDouble > &coords_y, Array< OneD, NekDouble > &coords_z) override
void	v_FillMode (const int mode, Array< OneD, NekDouble > &outarray) override
NekDouble	v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) final
NekDouble	v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
void	v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override
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
LibUtilities::PointsKey	v_GetTracePointsKey (const int i, const int j) 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, bool UseGLL=false) const override
bool	v_IsBoundaryInteriorExpansion () 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 tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1) 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
DNekMatSharedPtr	v_GenMatrix (const StdMatrixKey &mkey) override
DNekMatSharedPtr	v_CreateStdMatrix (const StdMatrixKey &mkey) override
void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey) override
void	v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
void	v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true) override
Protected Member Functions inherited from Nektar::StdRegions::StdExpansion3D
NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...
NekDouble	v_PhysEvaluateInterp (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) override
virtual void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0
virtual void	v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0
void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray) override
	Integrates the specified function over the domain. More...
virtual int	v_GetNedges (void) const
virtual int	v_GetEdgeNcoeffs (const int i) const
NekDouble	BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
virtual void	v_GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards)
void	v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient, int P, int Q) override
void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat) override
void	v_PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData) 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	LinearAdvectionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void	HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void	HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
virtual void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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)

Private Member Functions
int	GetMode (const int i, const int j, const int k)
	Compute the mode number in the expansion for a particular tensorial combination. More...

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

Detailed Description

Definition at line 43 of file StdTetExp.h.

Constructor & Destructor Documentation

StdTetExp() [1/3]

Nektar::StdRegions::StdTetExp::StdTetExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		const LibUtilities::BasisKey &	Bc
	)

Definition at line 42 of file StdTetExp.cpp.

    : StdExpansion(LibUtilities::StdTetData::getNumberOfCoefficients(
                       Ba.GetNumModes(), Bb.GetNumModes(), Bc.GetNumModes()),
                   3, Ba, Bb, Bc),
      StdExpansion3D(LibUtilities::StdTetData::getNumberOfCoefficients(
                         Ba.GetNumModes(), Bb.GetNumModes(), Bc.GetNumModes()),
                     Ba, Bb, Bc)
{
    ASSERTL0(Ba.GetNumModes() <= Bb.GetNumModes(),
             "order in 'a' direction is higher than order "
             "in 'b' direction");
    ASSERTL0(Ba.GetNumModes() <= Bc.GetNumModes(),
             "order in 'a' direction is higher than order "
             "in 'c' direction");
    ASSERTL0(Bb.GetNumModes() <= Bc.GetNumModes(),
             "order in 'b' direction is higher than order "
             "in 'c' direction");
}

References ASSERTL0, and Nektar::LibUtilities::BasisKey::GetNumModes().

StdTetExp() [2/3]

Nektar::StdRegions::StdTetExp::StdTetExp	(	const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb,
		const LibUtilities::BasisKey &	Bc,
		NekDouble *	coeffs,
		NekDouble *	phys
	)

StdTetExp() [3/3]

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

default

~StdTetExp()

Nektar::StdRegions::StdTetExp::~StdTetExp ( )

overridedefault

Member Function Documentation

DetShapeType()

LibUtilities::ShapeType Nektar::StdRegions::StdTetExp::DetShapeType ( ) const

inline

Definition at line 56 of file StdTetExp.h.

    {
        return LibUtilities::eTetrahedron;
    }

References Nektar::LibUtilities::eTetrahedron.

Referenced by Nektar::StdRegions::StdNodalTetExp::ModalToNodal(), Nektar::StdRegions::StdNodalTetExp::NodalToModal(), Nektar::StdRegions::StdNodalTetExp::NodalToModalTranspose(), Nektar::LocalRegions::TetExp::v_FwdTrans(), Nektar::StdRegions::StdNodalTetExp::v_FwdTrans(), and v_FwdTrans().

GetMode()

int Nektar::StdRegions::StdTetExp::GetMode ( const int  I, const int  J, const int  K  )

private

Compute the mode number in the expansion for a particular tensorial combination.

Modes are numbered with the r index travelling fastest, followed by q and then p, and each q-r plane is of size (Q+1)*(Q+2)/2+max(0,R-Q-p)*Q. For example, when P=2, Q=3 and R=4 (nm0=3, nm1 = 4, nm2 = 5) the indexing inside each q-r plane (with r increasing upwards and q to the right) is:

4 3 8 17 2 7 11 16 20 25 1 6 10 13 15 19 22 24 27 0 5 9 12 14 18 21 23 26

Geometrically they can be interpreted as

p = 0: p = 2: p = 1:

1 4 8 17 3 11 7 25 16 20 2 10 13 6 24 27 15 19 22 0 9 12 5 23 26 14 18 21

so we have the following breakdown

Vertices V[0,1,2,3] = [0, 14, 5, 1] Edges E[0,1,2,3,4,5,6] =[[23],[18, 21], [9, 12], [2,3,4], [15, 16, 17], [6,7,8]] Faces F[0.1,2,3] = [[26], [24,25], [19, 22, 20], [10, 13, 11] Interior [27] Note that in this element, we must have that \( P \leq Q \leq R\).

Definition at line 1921 of file StdTetExp.cpp.

{
    const int Q = m_base[1]->GetNumModes();
    const int R = m_base[2]->GetNumModes();
 
    int i, j, q_hat, k_hat;
    int cnt = 0;
 
    // Traverse to q-r plane number I
    for (i = 0; i < I; ++i)
    {
        // Size of triangle part
        q_hat = Q - i;
        // Size of rectangle part
        k_hat = R - Q;
        cnt += q_hat * (q_hat + 1) / 2 + k_hat * (Q - i);
    }
 
    // Traverse to q column J
    q_hat = R - I;
    for (j = 0; j < J; ++j)
    {
        cnt += q_hat;
        q_hat--;
    }
 
    // Traverse up stacks to K
    cnt += K;
 
    return cnt;
}

References Nektar::StdRegions::StdExpansion::m_base.

Referenced by v_GetBoundaryMap(), v_GetEdgeInteriorToElementMap(), v_GetInteriorMap(), v_GetTraceCoeffMap(), v_GetTraceInteriorToElementMap(), and v_GetVertexMap().

v_BwdTrans()

void Nektar::StdRegions::StdTetExp::v_BwdTrans ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Note

'r' (base[2]) runs fastest in this element

\( u^{\delta} (\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{m(pqr)} \hat u_{pqr} \phi_{pqr} (\xi_{1i}, \xi_{2j}, \xi_{3k})\)

Backward transformation is three dimensional tensorial expansion \( u (\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{p=0}^{Q_x} \psi_p^a (\xi_{1i}) \lbrace { \sum_{q=0}^{Q_y} \psi_{pq}^b (\xi_{2j}) \lbrace { \sum_{r=0}^{Q_z} \hat u_{pqr} \psi_{pqr}^c (\xi_{3k}) \rbrace} \rbrace}. \) And sumfactorizing step of the form is as:\

\( f_{pq} (\xi_{3k}) = \sum_{r=0}^{Q_z} \hat u_{pqr} \psi_{pqr}^c (\xi_{3k}),\\ g_{p} (\xi_{2j}, \xi_{3k}) = \sum_{r=0}^{Q_y} \psi_{pq}^b (\xi_{2j}) f_{pq} (\xi_{3k}),\\ u(\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{p=0}^{Q_x} \psi_{p}^a (\xi_{1i}) g_{p} (\xi_{2j}, \xi_{3k}). \)

Implements Nektar::StdRegions::StdExpansion.

Definition at line 266 of file StdTetExp.cpp.

{
    ASSERTL1((m_base[1]->GetBasisType() != LibUtilities::eOrtho_B) ||
                 (m_base[1]->GetBasisType() != LibUtilities::eModified_B),
             "Basis[1] is not a general tensor type");
 
    ASSERTL1((m_base[2]->GetBasisType() != LibUtilities::eOrtho_C) ||
                 (m_base[2]->GetBasisType() != LibUtilities::eModified_C),
             "Basis[2] is not a general tensor type");
 
    if (m_base[0]->Collocation() && m_base[1]->Collocation() &&
        m_base[2]->Collocation())
    {
        Vmath::Vcopy(m_base[0]->GetNumPoints() * m_base[1]->GetNumPoints() *
                         m_base[2]->GetNumPoints(),
                     inarray, 1, outarray, 1);
    }
    else
    {
        StdTetExp::v_BwdTrans_SumFac(inarray, outarray);
    }
}

References ASSERTL1, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::StdRegions::StdExpansion::m_base, v_BwdTrans_SumFac(), and Vmath::Vcopy().

Referenced by v_FillMode().

v_BwdTrans_SumFac()

void Nektar::StdRegions::StdTetExp::v_BwdTrans_SumFac ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Sum-factorisation implementation of the BwdTrans operation.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 293 of file StdTetExp.cpp.

{
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
    int order0 = m_base[0]->GetNumModes();
    int order1 = m_base[1]->GetNumModes();
 
    Array<OneD, NekDouble> wsp(nquad2 * order0 * (2 * order1 - order0 + 1) / 2 +
                               nquad2 * nquad1 * order0);
 
    BwdTrans_SumFacKernel(m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                          m_base[2]->GetBdata(), inarray, outarray, wsp, true,
                          true, true);
}

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

Referenced by v_BwdTrans(), and Nektar::StdRegions::StdNodalTetExp::v_BwdTrans_SumFac().

v_BwdTrans_SumFacKernel()

void Nektar::StdRegions::StdTetExp::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  )

overrideprotectedvirtual

Parameters

base0	x-dirn basis matrix
base1	y-dirn basis matrix
base2	z-dirn basis matrix
inarray	Input vector of modes.
outarray	Output vector of physical space data.
wsp	Workspace of size Q_x*P_z*(P_y+Q_y)
doCheckCollDir0	Check for collocation of basis.
doCheckCollDir1	Check for collocation of basis.
doCheckCollDir2	Check for collocation of basis.

Todo:

Account for some directions being collocated. See StdQuadExp as an example.

Implements Nektar::StdRegions::StdExpansion3D.

Definition at line 322 of file StdTetExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
 
    int order0 = m_base[0]->GetNumModes();
    int order1 = m_base[1]->GetNumModes();
    int order2 = m_base[2]->GetNumModes();
 
    Array<OneD, NekDouble> tmp = wsp;
    Array<OneD, NekDouble> tmp1 =
        tmp + nquad2 * order0 * (2 * order1 - order0 + 1) / 2;
 
    int i, j, mode, mode1, cnt;
 
    // Perform summation over '2' direction
    mode = mode1 = cnt = 0;
    for (i = 0; i < order0; ++i)
    {
        for (j = 0; j < order1 - i; ++j, ++cnt)
        {
            Blas::Dgemv('N', nquad2, order2 - i - j, 1.0,
                        base2.data() + mode * nquad2, nquad2,
                        inarray.data() + mode1, 1, 0.0,
                        tmp.data() + cnt * nquad2, 1);
            mode += order2 - i - j;
            mode1 += order2 - i - j;
        }
        // increment mode in case order1!=order2
        for (j = order1 - i; j < order2 - i; ++j)
        {
            mode += order2 - i - j;
        }
    }
 
    // fix for modified basis by adding split of top singular
    // vertex mode - currently (1+c)/2 x (1-b)/2 x (1-a)/2
    // component is evaluated
    if (m_base[0]->GetBasisType() == LibUtilities::eModified_A)
    {
        // top singular vertex - (1+c)/2 x (1+b)/2 x (1-a)/2 component
        Blas::Daxpy(nquad2, inarray[1], base2.data() + nquad2, 1,
                    &tmp[0] + nquad2, 1);
 
        // top singular vertex - (1+c)/2 x (1-b)/2 x (1+a)/2 component
        Blas::Daxpy(nquad2, inarray[1], base2.data() + nquad2, 1,
                    &tmp[0] + order1 * nquad2, 1);
    }
 
    // Perform summation over '1' direction
    mode = 0;
    for (i = 0; i < order0; ++i)
    {
        Blas::Dgemm('N', 'T', nquad1, nquad2, order1 - i, 1.0,
                    base1.data() + mode * nquad1, nquad1,
                    tmp.data() + mode * nquad2, nquad2, 0.0,
                    tmp1.data() + i * nquad1 * nquad2, nquad1);
        mode += order1 - i;
    }
 
    // fix for modified basis by adding additional split of
    // top and base singular vertex modes as well as singular
    // edge
    if (m_base[0]->GetBasisType() == LibUtilities::eModified_A)
    {
        // use tmp to sort out singular vertices and
        // singular edge components with (1+b)/2 (1+a)/2 form
        for (i = 0; i < nquad2; ++i)
        {
            Blas::Daxpy(nquad1, tmp[nquad2 + i], base1.data() + nquad1, 1,
                        &tmp1[nquad1 * nquad2] + i * nquad1, 1);
        }
    }
 
    // Perform summation over '0' direction
    Blas::Dgemm('N', 'T', nquad0, nquad1 * nquad2, order0, 1.0, base0.data(),
                nquad0, tmp1.data(), nquad1 * nquad2, 0.0, outarray.data(),
                nquad0);
}

References Blas::Daxpy(), Blas::Dgemm(), Blas::Dgemv(), Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

v_CalcNumberOfCoefficients()

int Nektar::StdRegions::StdTetExp::v_CalcNumberOfCoefficients ( const std::vector< unsigned int > &  nummodes, int &  modes_offset  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1123 of file StdTetExp.cpp.

{
    int nmodes = LibUtilities::StdTetData::getNumberOfCoefficients(
        nummodes[modes_offset], nummodes[modes_offset + 1],
        nummodes[modes_offset + 2]);
    modes_offset += 3;
 
    return nmodes;
}

References Nektar::LibUtilities::StdTetData::getNumberOfCoefficients().

v_CreateStdMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdTetExp::v_CreateStdMatrix ( const StdMatrixKey &  mkey )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 1877 of file StdTetExp.cpp.

{
    return v_GenMatrix(mkey);
}

References v_GenMatrix().

v_DetShapeType()

LibUtilities::ShapeType Nektar::StdRegions::StdTetExp::v_DetShapeType ( ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 972 of file StdTetExp.cpp.

{
    return LibUtilities::eTetrahedron;
}

References Nektar::LibUtilities::eTetrahedron.

v_FillMode()

void Nektar::StdRegions::StdTetExp::v_FillMode ( const int  mode, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 809 of file StdTetExp.cpp.

{
    Array<OneD, NekDouble> tmp(m_ncoeffs, 0.0);
    tmp[mode] = 1.0;
    StdTetExp::v_BwdTrans(tmp, outarray);
}

References Nektar::StdRegions::StdExpansion::m_ncoeffs, and v_BwdTrans().

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

v_FwdTrans()

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

overrideprotectedvirtual

Parameters

inarray	array of physical quadrature points to be transformed.
outarray	updated array of expansion coefficients.

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 416 of file StdTetExp.cpp.

{ // int       numMax  = nmodes0;
    v_IProductWRTBase(inarray, outarray);
 
    // get Mass matrix inverse
    StdMatrixKey masskey(eInvMass, DetShapeType(), *this);
    DNekMatSharedPtr matsys = GetStdMatrix(masskey);
 
    // copy inarray in case inarray == outarray
    DNekVec in(m_ncoeffs, outarray);
    DNekVec out(m_ncoeffs, outarray, eWrapper);
 
    out = (*matsys) * in;
}

References DetShapeType(), Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, and v_IProductWRTBase().

v_GenMatrix()

DNekMatSharedPtr Nektar::StdRegions::StdTetExp::v_GenMatrix ( const StdMatrixKey &  mkey )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 1789 of file StdTetExp.cpp.

{
 
    MatrixType mtype = mkey.GetMatrixType();
 
    DNekMatSharedPtr Mat;
 
    switch (mtype)
    {
        case ePhysInterpToEquiSpaced:
        {
            int nq0 = m_base[0]->GetNumPoints();
            int nq1 = m_base[1]->GetNumPoints();
            int nq2 = m_base[2]->GetNumPoints();
            int nq;
 
            // take definition from key
            if (mkey.ConstFactorExists(eFactorConst))
            {
                nq = (int)mkey.GetConstFactor(eFactorConst);
            }
            else
            {
                nq = max(nq0, max(nq1, nq2));
            }
 
            int neq =
                LibUtilities::StdTetData::getNumberOfCoefficients(nq, nq, nq);
            Array<OneD, Array<OneD, NekDouble>> coords(neq);
            Array<OneD, NekDouble> coll(3);
            Array<OneD, DNekMatSharedPtr> I(3);
            Array<OneD, NekDouble> tmp(nq0);
 
            Mat =
                MemoryManager<DNekMat>::AllocateSharedPtr(neq, nq0 * nq1 * nq2);
            int cnt = 0;
 
            for (int i = 0; i < nq; ++i)
            {
                for (int j = 0; j < nq - i; ++j)
                {
                    for (int k = 0; k < nq - i - j; ++k, ++cnt)
                    {
                        coords[cnt]    = Array<OneD, NekDouble>(3);
                        coords[cnt][0] = -1.0 + 2 * k / (NekDouble)(nq - 1);
                        coords[cnt][1] = -1.0 + 2 * j / (NekDouble)(nq - 1);
                        coords[cnt][2] = -1.0 + 2 * i / (NekDouble)(nq - 1);
                    }
                }
            }
 
            for (int i = 0; i < neq; ++i)
            {
                LocCoordToLocCollapsed(coords[i], coll);
 
                I[0] = m_base[0]->GetI(coll);
                I[1] = m_base[1]->GetI(coll + 1);
                I[2] = m_base[2]->GetI(coll + 2);
 
                // interpolate first coordinate direction
                NekDouble fac;
                for (int k = 0; k < nq2; ++k)
                {
                    for (int j = 0; j < nq1; ++j)
                    {
 
                        fac = (I[1]->GetPtr())[j] * (I[2]->GetPtr())[k];
                        Vmath::Smul(nq0, fac, I[0]->GetPtr(), 1, tmp, 1);
 
                        Vmath::Vcopy(nq0, &tmp[0], 1,
                                     Mat->GetRawPtr() + k * nq0 * nq1 * neq +
                                         j * nq0 * neq + i,
                                     neq);
                    }
                }
            }
        }
        break;
        default:
        {
            Mat = StdExpansion::CreateGeneralMatrix(mkey);
        }
        break;
    }
 
    return Mat;
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::StdExpansion::CreateGeneralMatrix(), Nektar::StdRegions::eFactorConst, Nektar::StdRegions::ePhysInterpToEquiSpaced, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetMatrixType(), Nektar::LibUtilities::StdTetData::getNumberOfCoefficients(), Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Smul(), and Vmath::Vcopy().

Referenced by v_CreateStdMatrix().

v_GetBoundaryMap()

void Nektar::StdRegions::StdTetExp::v_GetBoundaryMap ( Array< OneD, unsigned int > &  outarray )

overrideprotectedvirtual

List of all boundary modes in the the expansion.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1321 of file StdTetExp.cpp.

{
    ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                 GetBasisType(0) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(1) == LibUtilities::eModified_B ||
                 GetBasisType(1) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(2) == LibUtilities::eModified_C ||
                 GetBasisType(2) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
 
    int P = m_base[0]->GetNumModes();
    int Q = m_base[1]->GetNumModes();
    int R = m_base[2]->GetNumModes();
 
    int i, j, k;
    int idx = 0;
 
    int nBnd = NumBndryCoeffs();
 
    if (outarray.size() != nBnd)
    {
        outarray = Array<OneD, unsigned int>(nBnd);
    }
 
    for (i = 0; i < P; ++i)
    {
        // First two Q-R planes are entirely boundary modes
        if (i < 2)
        {
            for (j = 0; j < Q - i; j++)
            {
                for (k = 0; k < R - i - j; ++k)
                {
                    outarray[idx++] = GetMode(i, j, k);
                }
            }
        }
        // Remaining Q-R planes contain boundary modes on bottom and
        // left edge.
        else
        {
            for (k = 0; k < R - i; ++k)
            {
                outarray[idx++] = GetMode(i, 0, k);
            }
            for (j = 1; j < Q - i; ++j)
            {
                outarray[idx++] = GetMode(i, j, 0);
            }
        }
    }
}

References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::NumBndryCoeffs(), and Nektar::LibUtilities::P.

v_GetCoords()

void Nektar::StdRegions::StdTetExp::v_GetCoords ( Array< OneD, NekDouble > &  coords_x, Array< OneD, NekDouble > &  coords_y, Array< OneD, NekDouble > &  coords_z  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 1161 of file StdTetExp.cpp.

{
    Array<OneD, const NekDouble> eta_x = m_base[0]->GetZ();
    Array<OneD, const NekDouble> eta_y = m_base[1]->GetZ();
    Array<OneD, const NekDouble> eta_z = m_base[2]->GetZ();
    int Qx                             = GetNumPoints(0);
    int Qy                             = GetNumPoints(1);
    int Qz                             = GetNumPoints(2);
 
    // Convert collapsed coordinates into cartesian coordinates: eta
    // --> xi
    for (int k = 0; k < Qz; ++k)
    {
        for (int j = 0; j < Qy; ++j)
        {
            for (int i = 0; i < Qx; ++i)
            {
                int s = i + Qx * (j + Qy * k);
                xi_x[s] =
                    (eta_x[i] + 1.0) * (1.0 - eta_y[j]) * (1.0 - eta_z[k]) / 4 -
                    1.0;
                xi_y[s] = (eta_y[j] + 1.0) * (1.0 - eta_z[k]) / 2 - 1.0;
                xi_z[s] = eta_z[k];
            }
        }
    }
}

References Nektar::StdRegions::StdExpansion::GetNumPoints(), and Nektar::StdRegions::StdExpansion::m_base.

v_GetEdgeInteriorToElementMap()

void Nektar::StdRegions::StdTetExp::v_GetEdgeInteriorToElementMap ( const int  eid, Array< OneD, unsigned int > &  maparray, Array< OneD, int > &  signarray, const Orientation  edgeOrient = eDir1FwdDir1_Dir2FwdDir2  )

overrideprotectedvirtual

Maps interior modes of an edge to the elemental modes.

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 1583 of file StdTetExp.cpp.

{
    int i;
    const int P = m_base[0]->GetNumModes();
    const int Q = m_base[1]->GetNumModes();
    const int R = m_base[2]->GetNumModes();
 
    const int nEdgeIntCoeffs = v_GetEdgeNcoeffs(eid) - 2;
 
    if (maparray.size() != nEdgeIntCoeffs)
    {
        maparray = Array<OneD, unsigned int>(nEdgeIntCoeffs);
    }
    else
    {
        fill(maparray.data(), maparray.data() + nEdgeIntCoeffs, 0);
    }
 
    if (signarray.size() != nEdgeIntCoeffs)
    {
        signarray = Array<OneD, int>(nEdgeIntCoeffs, 1);
    }
    else
    {
        fill(signarray.data(), signarray.data() + nEdgeIntCoeffs, 1);
    }
 
    switch (eid)
    {
        case 0:
            for (i = 0; i < P - 2; ++i)
            {
                maparray[i] = GetMode(i + 2, 0, 0);
            }
            if (edgeOrient == eBackwards)
            {
                for (i = 1; i < nEdgeIntCoeffs; i += 2)
                {
                    signarray[i] = -1;
                }
            }
            break;
        case 1:
            for (i = 0; i < Q - 2; ++i)
            {
                maparray[i] = GetMode(1, i + 1, 0);
            }
            if (edgeOrient == eBackwards)
            {
                for (i = 1; i < nEdgeIntCoeffs; i += 2)
                {
                    signarray[i] = -1;
                }
            }
            break;
        case 2:
            for (i = 0; i < Q - 2; ++i)
            {
                maparray[i] = GetMode(0, i + 2, 0);
            }
            if (edgeOrient == eBackwards)
            {
                for (i = 1; i < nEdgeIntCoeffs; i += 2)
                {
                    signarray[i] = -1;
                }
            }
            break;
        case 3:
            for (i = 0; i < R - 2; ++i)
            {
                maparray[i] = GetMode(0, 0, i + 2);
            }
            if (edgeOrient == eBackwards)
            {
                for (i = 1; i < nEdgeIntCoeffs; i += 2)
                {
                    signarray[i] = -1;
                }
            }
            break;
        case 4:
            for (i = 0; i < R - 2; ++i)
            {
                maparray[i] = GetMode(1, 0, i + 1);
            }
            if (edgeOrient == eBackwards)
            {
                for (i = 1; i < nEdgeIntCoeffs; i += 2)
                {
                    signarray[i] = -1;
                }
            }
            break;
        case 5:
            for (i = 0; i < R - 2; ++i)
            {
                maparray[i] = GetMode(0, 1, i + 1);
            }
            if (edgeOrient == eBackwards)
            {
                for (i = 1; i < nEdgeIntCoeffs; i += 2)
                {
                    signarray[i] = -1;
                }
            }
            break;
        default:
            ASSERTL0(false, "Edge not defined.");
            break;
    }
}

References ASSERTL0, Nektar::StdRegions::eBackwards, GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LibUtilities::P, and v_GetEdgeNcoeffs().

v_GetEdgeNcoeffs()

int Nektar::StdRegions::StdTetExp::v_GetEdgeNcoeffs ( const int  i ) const

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 1082 of file StdTetExp.cpp.

{
    ASSERTL2((i >= 0) && (i <= 5), "edge id is out of range");
    int P = m_base[0]->GetNumModes();
    int Q = m_base[1]->GetNumModes();
    int R = m_base[2]->GetNumModes();
 
    if (i == 0)
    {
        return P;
    }
    else if (i == 1 || i == 2)
    {
        return Q;
    }
    else
    {
        return R;
    }
}

References ASSERTL2, Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.

Referenced by v_GetEdgeInteriorToElementMap().

v_GetElmtTraceToTraceMap()

void Nektar::StdRegions::StdTetExp::v_GetElmtTraceToTraceMap ( const unsigned int  tid, Array< OneD, unsigned int > &  maparray, Array< OneD, int > &  signarray, Orientation  traceOrient = eForwards, int  P = -1, int  Q = -1  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1468 of file StdTetExp.cpp.

{
    int nummodesA = 0, nummodesB = 0, i, j, k, idx;
 
    ASSERTL1(v_IsBoundaryInteriorExpansion(),
             "Method only implemented for Modified_A BasisType (x "
             "direction), Modified_B BasisType (y direction), and "
             "Modified_C BasisType(z direction)");
 
    int nFaceCoeffs = 0;
 
    switch (fid)
    {
        case 0:
            nummodesA = m_base[0]->GetNumModes();
            nummodesB = m_base[1]->GetNumModes();
            break;
        case 1:
            nummodesA = m_base[0]->GetNumModes();
            nummodesB = m_base[2]->GetNumModes();
            break;
        case 2:
        case 3:
            nummodesA = m_base[1]->GetNumModes();
            nummodesB = m_base[2]->GetNumModes();
            break;
        default:
            ASSERTL0(false, "fid must be between 0 and 3");
    }
 
    if (P == -1)
    {
        P = nummodesA;
        Q = nummodesB;
    }
 
    nFaceCoeffs = P * (2 * Q - P + 1) / 2;
 
    // Allocate the map array and sign array; set sign array to ones (+)
    if (maparray.size() != nFaceCoeffs)
    {
        maparray = Array<OneD, unsigned int>(nFaceCoeffs, 1);
    }
 
    if (signarray.size() != nFaceCoeffs)
    {
        signarray = Array<OneD, int>(nFaceCoeffs, 1);
    }
    else
    {
        fill(signarray.data(), signarray.data() + nFaceCoeffs, 1);
    }
 
    // zero signmap and set maparray to zero if elemental
    // modes are not as large as face modesl
    idx       = 0;
    int cnt   = 0;
    int minPA = min(nummodesA, P);
    int minQB = min(nummodesB, Q);
 
    for (j = 0; j < minPA; ++j)
    {
        // set maparray
        for (k = 0; k < minQB - j; ++k, ++cnt)
        {
            maparray[idx++] = cnt;
        }
 
        cnt += nummodesB - minQB;
 
        for (k = nummodesB - j; k < Q - j; ++k)
        {
            signarray[idx]  = 0.0;
            maparray[idx++] = maparray[0];
        }
    }
 
    for (j = nummodesA; j < P; ++j)
    {
        for (k = 0; k < Q - j; ++k)
        {
            signarray[idx]  = 0.0;
            maparray[idx++] = maparray[0];
        }
    }
 
    if (faceOrient == eDir1BwdDir1_Dir2FwdDir2)
    {
        idx = 0;
        for (i = 0; i < P; ++i)
        {
            for (j = 0; j < Q - i; ++j, idx++)
            {
                if (i > 1)
                {
                    signarray[idx] = (i % 2 ? -1 : 1);
                }
            }
        }
 
        swap(maparray[0], maparray[Q]);
 
        for (i = 1; i < Q - 1; ++i)
        {
            swap(maparray[i + 1], maparray[Q + i]);
        }
    }
}

References ASSERTL0, ASSERTL1, Nektar::StdRegions::eDir1BwdDir1_Dir2FwdDir2, Nektar::StdRegions::StdExpansion::m_base, Nektar::LibUtilities::P, and v_IsBoundaryInteriorExpansion().

v_GetInteriorMap()

void Nektar::StdRegions::StdTetExp::v_GetInteriorMap ( Array< OneD, unsigned int > &  outarray )

overrideprotectedvirtual

Maps interior modes of an edge to the elemental modes. List of all interior modes in the expansion.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1282 of file StdTetExp.cpp.

{
    ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                 GetBasisType(0) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(1) == LibUtilities::eModified_B ||
                 GetBasisType(1) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(2) == LibUtilities::eModified_C ||
                 GetBasisType(2) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
 
    int P = m_base[0]->GetNumModes();
    int Q = m_base[1]->GetNumModes();
    int R = m_base[2]->GetNumModes();
 
    int nIntCoeffs = m_ncoeffs - NumBndryCoeffs();
 
    if (outarray.size() != nIntCoeffs)
    {
        outarray = Array<OneD, unsigned int>(nIntCoeffs);
    }
 
    int idx = 0;
    for (int i = 2; i < P; ++i)
    {
        for (int j = 1; j < Q - i - 1; ++j)
        {
            for (int k = 1; k < R - i - j; ++k)
            {
                outarray[idx++] = GetMode(i, j, k);
            }
        }
    }
}

References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::NumBndryCoeffs(), and Nektar::LibUtilities::P.

v_GetNedges()

int Nektar::StdRegions::StdTetExp::v_GetNedges ( void  ) const

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion3D.

Definition at line 962 of file StdTetExp.cpp.

{
    return 6;
}

v_GetNtraces()

int Nektar::StdRegions::StdTetExp::v_GetNtraces ( ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 967 of file StdTetExp.cpp.

{
    return 4;
}

v_GetNverts()

int Nektar::StdRegions::StdTetExp::v_GetNverts ( ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 957 of file StdTetExp.cpp.

{
    return 4;
}

v_GetSimplexEquiSpacedConnectivity()

void Nektar::StdRegions::StdTetExp::v_GetSimplexEquiSpacedConnectivity ( Array< OneD, int > &  conn, bool  standard = true  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 2236 of file StdTetExp.cpp.

{
    int np0 = m_base[0]->GetNumPoints();
    int np1 = m_base[1]->GetNumPoints();
    int np2 = m_base[2]->GetNumPoints();
    int np  = max(np0, max(np1, np2));
 
    conn = Array<OneD, int>(4 * (np - 1) * (np - 1) * (np - 1));
 
    int row     = 0;
    int rowp1   = 0;
    int plane   = 0;
    int row1    = 0;
    int row1p1  = 0;
    int planep1 = 0;
    int cnt     = 0;
    for (int i = 0; i < np - 1; ++i)
    {
        planep1 += (np - i) * (np - i + 1) / 2;
        row    = 0; // current plane row offset
        rowp1  = 0; // current plane row plus one offset
        row1   = 0; // next plane row offset
        row1p1 = 0; // nex plane row plus one offset
        for (int j = 0; j < np - i - 1; ++j)
        {
            rowp1 += np - i - j;
            row1p1 += np - i - j - 1;
            for (int k = 0; k < np - i - j - 2; ++k)
            {
                conn[cnt++] = plane + row + k + 1;
                conn[cnt++] = plane + row + k;
                conn[cnt++] = plane + rowp1 + k;
                conn[cnt++] = planep1 + row1 + k;
 
                conn[cnt++] = plane + row + k + 1;
                conn[cnt++] = plane + rowp1 + k + 1;
                conn[cnt++] = planep1 + row1 + k + 1;
                conn[cnt++] = planep1 + row1 + k;
 
                conn[cnt++] = plane + rowp1 + k + 1;
                conn[cnt++] = plane + row + k + 1;
                conn[cnt++] = plane + rowp1 + k;
                conn[cnt++] = planep1 + row1 + k;
 
                conn[cnt++] = planep1 + row1 + k;
                conn[cnt++] = planep1 + row1p1 + k;
                conn[cnt++] = plane + rowp1 + k;
                conn[cnt++] = plane + rowp1 + k + 1;
 
                conn[cnt++] = planep1 + row1 + k;
                conn[cnt++] = planep1 + row1p1 + k;
                conn[cnt++] = planep1 + row1 + k + 1;
                conn[cnt++] = plane + rowp1 + k + 1;
 
                if (k < np - i - j - 3)
                {
                    conn[cnt++] = plane + rowp1 + k + 1;
                    conn[cnt++] = planep1 + row1p1 + k + 1;
                    conn[cnt++] = planep1 + row1 + k + 1;
                    conn[cnt++] = planep1 + row1p1 + k;
                }
            }
 
            conn[cnt++] = plane + row + np - i - j - 1;
            conn[cnt++] = plane + row + np - i - j - 2;
            conn[cnt++] = plane + rowp1 + np - i - j - 2;
            conn[cnt++] = planep1 + row1 + np - i - j - 2;
 
            row += np - i - j;
            row1 += np - i - j - 1;
        }
        plane += (np - i) * (np - i + 1) / 2;
    }
}

References Nektar::StdRegions::StdExpansion::m_base.

v_GetTraceBasisKey()

const LibUtilities::BasisKey Nektar::StdRegions::StdTetExp::v_GetTraceBasisKey ( const int  i, const int  k, bool  UseGLL = false  ) const

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1134 of file StdTetExp.cpp.

{
    ASSERTL2(i >= 0 && i <= 4, "face id is out of range");
    ASSERTL2(k == 0 || k == 1, "face direction out of range");
 
    int dir = k;
    switch (i)
    {
        case 0:
            dir = k;
            break;
        case 1:
            dir = 2 * k;
            break;
        case 2:
        case 3:
            dir = k + 1;
            break;
    }
 
    return EvaluateTriFaceBasisKey(k, m_base[dir]->GetBasisType(),
                                   m_base[dir]->GetNumPoints(),
                                   m_base[dir]->GetNumModes(), UseGLL);
}

References ASSERTL2, Nektar::StdRegions::EvaluateTriFaceBasisKey(), Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNumPoints(), and Nektar::StdRegions::StdExpansion::m_base.

v_GetTraceCoeffMap()

void Nektar::StdRegions::StdTetExp::v_GetTraceCoeffMap ( const unsigned int  fid, Array< OneD, unsigned int > &  maparray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1376 of file StdTetExp.cpp.

{
    int i, j, k;
    int P = 0, Q = 0, idx = 0;
    int nFaceCoeffs = 0;
 
    switch (fid)
    {
        case 0:
            P = m_base[0]->GetNumModes();
            Q = m_base[1]->GetNumModes();
            break;
        case 1:
            P = m_base[0]->GetNumModes();
            Q = m_base[2]->GetNumModes();
            break;
        case 2:
        case 3:
            P = m_base[1]->GetNumModes();
            Q = m_base[2]->GetNumModes();
            break;
        default:
            ASSERTL0(false, "fid must be between 0 and 3");
    }
 
    nFaceCoeffs = P * (2 * Q - P + 1) / 2;
 
    if (maparray.size() != nFaceCoeffs)
    {
        maparray = Array<OneD, unsigned int>(nFaceCoeffs);
    }
 
    switch (fid)
    {
        case 0:
            idx = 0;
            for (i = 0; i < P; ++i)
            {
                for (j = 0; j < Q - i; ++j)
                {
                    maparray[idx++] = GetMode(i, j, 0);
                }
            }
            break;
        case 1:
            idx = 0;
            for (i = 0; i < P; ++i)
            {
                for (k = 0; k < Q - i; ++k)
                {
                    maparray[idx++] = GetMode(i, 0, k);
                }
            }
            break;
        case 2:
            idx = 0;
            for (j = 0; j < P - 1; ++j)
            {
                for (k = 0; k < Q - 1 - j; ++k)
                {
                    maparray[idx++] = GetMode(1, j, k);
                    // Incorporate modes from zeroth plane where needed.
                    if (j == 0 && k == 0)
                    {
                        maparray[idx++] = GetMode(0, 0, 1);
                    }
                    if (j == 0 && k == Q - 2)
                    {
                        for (int r = 0; r < Q - 1; ++r)
                        {
                            maparray[idx++] = GetMode(0, 1, r);
                        }
                    }
                }
            }
            break;
        case 3:
            idx = 0;
            for (j = 0; j < P; ++j)
            {
                for (k = 0; k < Q - j; ++k)
                {
                    maparray[idx++] = GetMode(0, j, k);
                }
            }
            break;
        default:
            ASSERTL0(false, "Element map not available.");
    }
}

References ASSERTL0, GetMode(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.

v_GetTraceInteriorToElementMap()

void Nektar::StdRegions::StdTetExp::v_GetTraceInteriorToElementMap ( const int  tid, Array< OneD, unsigned int > &  maparray, Array< OneD, int > &  signarray, const Orientation  traceOrient = eDir1FwdDir1_Dir2FwdDir2  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1698 of file StdTetExp.cpp.

{
    int i, j, idx, k;
    const int P = m_base[0]->GetNumModes();
    const int Q = m_base[1]->GetNumModes();
    const int R = m_base[2]->GetNumModes();
 
    const int nFaceIntCoeffs = v_GetTraceIntNcoeffs(fid);
 
    if (maparray.size() != nFaceIntCoeffs)
    {
        maparray = Array<OneD, unsigned int>(nFaceIntCoeffs);
    }
 
    if (signarray.size() != nFaceIntCoeffs)
    {
        signarray = Array<OneD, int>(nFaceIntCoeffs, 1);
    }
    else
    {
        fill(signarray.data(), signarray.data() + nFaceIntCoeffs, 1);
    }
 
    switch (fid)
    {
        case 0:
            idx = 0;
            for (i = 2; i < P; ++i)
            {
                for (j = 1; j < Q - i; ++j)
                {
                    if ((int)faceOrient == 7)
                    {
                        signarray[idx] = (i % 2 ? -1 : 1);
                    }
                    maparray[idx++] = GetMode(i, j, 0);
                }
            }
            break;
        case 1:
            idx = 0;
            for (i = 2; i < P; ++i)
            {
                for (k = 1; k < R - i; ++k)
                {
                    if ((int)faceOrient == 7)
                    {
                        signarray[idx] = (i % 2 ? -1 : 1);
                    }
                    maparray[idx++] = GetMode(i, 0, k);
                }
            }
            break;
        case 2:
            idx = 0;
            for (j = 1; j < Q - 1; ++j)
            {
                for (k = 1; k < R - 1 - j; ++k)
                {
                    if ((int)faceOrient == 7)
                    {
                        signarray[idx] = ((j + 1) % 2 ? -1 : 1);
                    }
                    maparray[idx++] = GetMode(1, j, k);
                }
            }
            break;
        case 3:
            idx = 0;
            for (j = 2; j < Q; ++j)
            {
                for (k = 1; k < R - j; ++k)
                {
                    if ((int)faceOrient == 7)
                    {
                        signarray[idx] = (j % 2 ? -1 : 1);
                    }
                    maparray[idx++] = GetMode(0, j, k);
                }
            }
            break;
        default:
            ASSERTL0(false, "Face interior map not available.");
            break;
    }
}

References ASSERTL0, GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LibUtilities::P, and v_GetTraceIntNcoeffs().

v_GetTraceIntNcoeffs()

int Nektar::StdRegions::StdTetExp::v_GetTraceIntNcoeffs ( const int  i ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 1043 of file StdTetExp.cpp.

{
    ASSERTL2((i >= 0) && (i <= 3), "face id is out of range");
    int Pi = m_base[0]->GetNumModes() - 2;
    int Qi = m_base[1]->GetNumModes() - 2;
    int Ri = m_base[2]->GetNumModes() - 2;
 
    if ((i == 0))
    {
        return Pi * (2 * Qi - Pi - 1) / 2;
    }
    else if ((i == 1))
    {
        return Pi * (2 * Ri - Pi - 1) / 2;
    }
    else
    {
        return Qi * (2 * Ri - Qi - 1) / 2;
    }
}

References ASSERTL2, and Nektar::StdRegions::StdExpansion::m_base.

Referenced by v_GetTraceInteriorToElementMap().

v_GetTraceNcoeffs()

int Nektar::StdRegions::StdTetExp::v_GetTraceNcoeffs ( const int  i ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 1017 of file StdTetExp.cpp.

{
    ASSERTL2((i >= 0) && (i <= 3), "face id is out of range");
    int nFaceCoeffs = 0;
    int nummodesA, nummodesB, P, Q;
    if (i == 0)
    {
        nummodesA = GetBasisNumModes(0);
        nummodesB = GetBasisNumModes(1);
    }
    else if ((i == 1) || (i == 2))
    {
        nummodesA = GetBasisNumModes(0);
        nummodesB = GetBasisNumModes(2);
    }
    else
    {
        nummodesA = GetBasisNumModes(1);
        nummodesB = GetBasisNumModes(2);
    }
    P           = nummodesA - 1;
    Q           = nummodesB - 1;
    nFaceCoeffs = Q + 1 + (P * (1 + 2 * Q - P)) / 2;
    return nFaceCoeffs;
}

References ASSERTL2, Nektar::StdRegions::StdExpansion::GetBasisNumModes(), and Nektar::LibUtilities::P.

v_GetTraceNumModes()

void Nektar::StdRegions::StdTetExp::v_GetTraceNumModes ( const int  fid, int &  numModes0, int &  numModes1, Orientation  traceOrient = eDir1FwdDir1_Dir2FwdDir2  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 923 of file StdTetExp.cpp.

{
    int nummodes[3] = {m_base[0]->GetNumModes(), m_base[1]->GetNumModes(),
                       m_base[2]->GetNumModes()};
    switch (fid)
    {
        case 0:
        {
            numModes0 = nummodes[0];
            numModes1 = nummodes[1];
        }
        break;
        case 1:
        {
            numModes0 = nummodes[0];
            numModes1 = nummodes[2];
        }
        break;
        case 2:
        case 3:
        {
            numModes0 = nummodes[1];
            numModes1 = nummodes[2];
        }
        break;
    }
}

References Nektar::StdRegions::StdExpansion::m_base.

v_GetTraceNumPoints()

int Nektar::StdRegions::StdTetExp::v_GetTraceNumPoints ( const int  i ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 1064 of file StdTetExp.cpp.

{
    ASSERTL2(i >= 0 && i <= 3, "face id is out of range");
 
    if (i == 0)
    {
        return m_base[0]->GetNumPoints() * m_base[1]->GetNumPoints();
    }
    else if (i == 1)
    {
        return m_base[0]->GetNumPoints() * m_base[2]->GetNumPoints();
    }
    else
    {
        return m_base[1]->GetNumPoints() * m_base[2]->GetNumPoints();
    }
}

References ASSERTL2, and Nektar::StdRegions::StdExpansion::m_base.

v_GetTracePointsKey()

LibUtilities::PointsKey Nektar::StdRegions::StdTetExp::v_GetTracePointsKey ( const int  i, const int  j  ) const

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1103 of file StdTetExp.cpp.

{
    ASSERTL2(i >= 0 && i <= 3, "face id is out of range");
    ASSERTL2(j == 0 || j == 1, "face direction is out of range");
 
    if (i == 0)
    {
        return m_base[j]->GetPointsKey();
    }
    else if (i == 1)
    {
        return m_base[2 * j]->GetPointsKey();
    }
    else
    {
        return m_base[j + 1]->GetPointsKey();
    }
}

References ASSERTL2, and Nektar::StdRegions::StdExpansion::m_base.

v_GetVertexMap()

int Nektar::StdRegions::StdTetExp::v_GetVertexMap ( int  localVertexId, bool  useCoeffPacking = false  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1201 of file StdTetExp.cpp.

{
    ASSERTL0((GetBasisType(0) == LibUtilities::eModified_A) ||
                 (GetBasisType(1) == LibUtilities::eModified_B) ||
                 (GetBasisType(2) == LibUtilities::eModified_C),
             "Mapping not defined for this type of basis");
 
    int localDOF = 0;
    if (useCoeffPacking == true) // follow packing of coefficients i.e q,r,p
    {
        switch (localVertexId)
        {
            case 0:
            {
                localDOF = GetMode(0, 0, 0);
                break;
            }
            case 1:
            {
                localDOF = GetMode(0, 0, 1);
                break;
            }
            case 2:
            {
                localDOF = GetMode(0, 1, 0);
                break;
            }
            case 3:
            {
                localDOF = GetMode(1, 0, 0);
                break;
            }
            default:
            {
                ASSERTL0(false, "Vertex ID must be between 0 and 3");
                break;
            }
        }
    }
    else
    {
        switch (localVertexId)
        {
            case 0:
            {
                localDOF = GetMode(0, 0, 0);
                break;
            }
            case 1:
            {
                localDOF = GetMode(1, 0, 0);
                break;
            }
            case 2:
            {
                localDOF = GetMode(0, 1, 0);
                break;
            }
            case 3:
            {
                localDOF = GetMode(0, 0, 1);
                break;
            }
            default:
            {
                ASSERTL0(false, "Vertex ID must be between 0 and 3");
                break;
            }
        }
    }
 
    return localDOF;
}

References ASSERTL0, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), and GetMode().

v_IProductWRTBase()

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

overrideprotectedvirtual

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

\( \phi_{pqr} (\xi_1 , \xi_2 , \xi_3) = \psi_p^a (\eta_1) \psi_{pq}^b (\eta_2) \psi_{pqr}^c (\eta_3) \)

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

Parameters

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

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 466 of file StdTetExp.cpp.

{
    ASSERTL1((m_base[1]->GetBasisType() != LibUtilities::eOrtho_B) ||
                 (m_base[1]->GetBasisType() != LibUtilities::eModified_B),
             "Basis[1] is not a general tensor type");
 
    ASSERTL1((m_base[2]->GetBasisType() != LibUtilities::eOrtho_C) ||
                 (m_base[2]->GetBasisType() != LibUtilities::eModified_C),
             "Basis[2] is not a general tensor type");
 
    if (m_base[0]->Collocation() && m_base[1]->Collocation())
    {
        MultiplyByQuadratureMetric(inarray, outarray);
    }
    else
    {
        StdTetExp::v_IProductWRTBase_SumFac(inarray, outarray);
    }
}

References ASSERTL1, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), and v_IProductWRTBase_SumFac().

Referenced by v_FwdTrans().

v_IProductWRTBase_SumFac()

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

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::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 493 of file StdTetExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
    int order0 = m_base[0]->GetNumModes();
    int order1 = m_base[1]->GetNumModes();
 
    Array<OneD, NekDouble> wsp(nquad1 * nquad2 * order0 +
                               nquad2 * order0 * (2 * order1 - order0 + 1) / 2);
 
    if (multiplybyweights)
    {
        Array<OneD, NekDouble> tmp(nquad0 * nquad1 * nquad2);
        MultiplyByQuadratureMetric(inarray, tmp);
 
        StdTetExp::IProductWRTBase_SumFacKernel(
            m_base[0]->GetBdata(), m_base[1]->GetBdata(), m_base[2]->GetBdata(),
            tmp, outarray, wsp, true, true, true);
    }
    else
    {
        StdTetExp::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(), and Nektar::StdRegions::StdNodalTetExp::v_IProductWRTBase_SumFac().

v_IProductWRTBase_SumFacKernel()

void Nektar::StdRegions::StdTetExp::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  )

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion3D.

Definition at line 523 of file StdTetExp.cpp.

{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
 
    int order0 = m_base[0]->GetNumModes();
    int order1 = m_base[1]->GetNumModes();
    int order2 = m_base[2]->GetNumModes();
 
    Array<OneD, NekDouble> tmp1 = wsp;
    Array<OneD, NekDouble> tmp2 = wsp + nquad1 * nquad2 * order0;
 
    int i, j, mode, mode1, cnt;
 
    // Inner product with respect to the '0' direction
    Blas::Dgemm('T', 'N', nquad1 * nquad2, order0, nquad0, 1.0, inarray.data(),
                nquad0, base0.data(), nquad0, 0.0, tmp1.data(),
                nquad1 * nquad2);
 
    // Inner product with respect to the '1' direction
    for (mode = i = 0; i < order0; ++i)
    {
        Blas::Dgemm('T', 'N', nquad2, order1 - i, nquad1, 1.0,
                    tmp1.data() + i * nquad1 * nquad2, nquad1,
                    base1.data() + mode * nquad1, nquad1, 0.0,
                    tmp2.data() + mode * nquad2, nquad2);
        mode += order1 - i;
    }
 
    // fix for modified basis for base singular vertex
    if (m_base[0]->GetBasisType() == LibUtilities::eModified_A)
    {
        // base singular vertex and singular edge (1+b)/2
        //(1+a)/2 components (makes tmp[nquad2] entry into (1+b)/2)
        Blas::Dgemv('T', nquad1, nquad2, 1.0, tmp1.data() + nquad1 * nquad2,
                    nquad1, base1.data() + nquad1, 1, 1.0, tmp2.data() + nquad2,
                    1);
    }
 
    // Inner product with respect to the '2' direction
    mode = mode1 = cnt = 0;
    for (i = 0; i < order0; ++i)
    {
        for (j = 0; j < order1 - i; ++j, ++cnt)
        {
            Blas::Dgemv('T', nquad2, order2 - i - j, 1.0,
                        base2.data() + mode * nquad2, nquad2,
                        tmp2.data() + cnt * nquad2, 1, 0.0,
                        outarray.data() + mode1, 1);
            mode += order2 - i - j;
            mode1 += order2 - i - j;
        }
        // increment mode in case order1!=order2
        for (j = order1 - i; j < order2 - i; ++j)
        {
            mode += order2 - i - j;
        }
    }
 
    // fix for modified basis for top singular vertex component
    // Already have evaluated (1+c)/2 (1-b)/2 (1-a)/2
    if (m_base[0]->GetBasisType() == LibUtilities::eModified_A)
    {
        // add in (1+c)/2 (1+b)/2   component
        outarray[1] +=
            Blas::Ddot(nquad2, base2.data() + nquad2, 1, &tmp2[nquad2], 1);
 
        // add in (1+c)/2 (1-b)/2 (1+a)/2 component
        outarray[1] += Blas::Ddot(nquad2, base2.data() + nquad2, 1,
                                  &tmp2[nquad2 * order1], 1);
    }
}

References Blas::Ddot(), Blas::Dgemm(), Blas::Dgemv(), Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

v_IProductWRTDerivBase()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 605 of file StdTetExp.cpp.

{
    StdTetExp::v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
}

References v_IProductWRTDerivBase_SumFac().

v_IProductWRTDerivBase_SumFac()

void Nektar::StdRegions::StdTetExp::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::StdExpansion.

Definition at line 618 of file StdTetExp.cpp.

{
    int i;
    int nquad0  = m_base[0]->GetNumPoints();
    int nquad1  = m_base[1]->GetNumPoints();
    int nquad2  = m_base[2]->GetNumPoints();
    int nqtot   = nquad0 * nquad1 * nquad2;
    int nmodes0 = m_base[0]->GetNumModes();
    int nmodes1 = m_base[1]->GetNumModes();
    int wspsize = nquad0 + nquad1 + nquad2 + max(nqtot, m_ncoeffs) +
                  nquad1 * nquad2 * nmodes0 +
                  nquad2 * nmodes0 * (2 * nmodes1 - nmodes0 + 1) / 2;
 
    Array<OneD, NekDouble> gfac0(wspsize);
    Array<OneD, NekDouble> gfac1(gfac0 + nquad0);
    Array<OneD, NekDouble> gfac2(gfac1 + nquad1);
    Array<OneD, NekDouble> tmp0(gfac2 + nquad2);
    Array<OneD, NekDouble> wsp(tmp0 + max(nqtot, m_ncoeffs));
 
    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();
 
    // set up geometric factor: (1+z0)/2
    for (i = 0; i < nquad0; ++i)
    {
        gfac0[i] = 0.5 * (1 + z0[i]);
    }
 
    // set up geometric factor: 2/(1-z1)
    for (i = 0; i < nquad1; ++i)
    {
        gfac1[i] = 2.0 / (1 - z1[i]);
    }
 
    // Set up geometric factor: 2/(1-z2)
    for (i = 0; i < nquad2; ++i)
    {
        gfac2[i] = 2.0 / (1 - z2[i]);
    }
 
    // Derivative in first direction is always scaled as follows
    for (i = 0; i < nquad1 * nquad2; ++i)
    {
        Vmath::Smul(nquad0, gfac1[i % nquad1], &inarray[0] + i * nquad0, 1,
                    &tmp0[0] + i * nquad0, 1);
    }
    for (i = 0; i < nquad2; ++i)
    {
        Vmath::Smul(nquad0 * nquad1, gfac2[i], &tmp0[0] + i * nquad0 * nquad1,
                    1, &tmp0[0] + i * nquad0 * nquad1, 1);
    }
 
    MultiplyByQuadratureMetric(tmp0, tmp0);
 
    switch (dir)
    {
        case 0:
        {
            IProductWRTBase_SumFacKernel(
                m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                m_base[2]->GetBdata(), tmp0, outarray, wsp, false, true, true);
        }
        break;
        case 1:
        {
            Array<OneD, NekDouble> tmp3(m_ncoeffs);
 
            for (i = 0; i < nquad1 * nquad2; ++i)
            {
                Vmath::Vmul(nquad0, &gfac0[0], 1, &tmp0[0] + i * nquad0, 1,
                            &tmp0[0] + i * nquad0, 1);
            }
 
            IProductWRTBase_SumFacKernel(
                m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                m_base[2]->GetBdata(), tmp0, tmp3, wsp, false, true, true);
 
            for (i = 0; i < nquad2; ++i)
            {
                Vmath::Smul(nquad0 * nquad1, gfac2[i],
                            &inarray[0] + i * nquad0 * nquad1, 1,
                            &tmp0[0] + i * nquad0 * nquad1, 1);
            }
            MultiplyByQuadratureMetric(tmp0, tmp0);
            IProductWRTBase_SumFacKernel(
                m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                m_base[2]->GetBdata(), tmp0, outarray, wsp, true, false, true);
            Vmath::Vadd(m_ncoeffs, &tmp3[0], 1, &outarray[0], 1, &outarray[0],
                        1);
        }
        break;
        case 2:
        {
            Array<OneD, NekDouble> tmp3(m_ncoeffs);
            Array<OneD, NekDouble> tmp4(m_ncoeffs);
            for (i = 0; i < nquad1; ++i)
            {
                gfac1[i] = (1 + z1[i]) / 2;
            }
 
            for (i = 0; i < nquad1 * nquad2; ++i)
            {
                Vmath::Vmul(nquad0, &gfac0[0], 1, &tmp0[0] + i * nquad0, 1,
                            &tmp0[0] + i * nquad0, 1);
            }
            IProductWRTBase_SumFacKernel(
                m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                m_base[2]->GetBdata(), tmp0, tmp3, wsp, false, true, true);
 
            for (i = 0; i < nquad2; ++i)
            {
                Vmath::Smul(nquad0 * nquad1, gfac2[i],
                            &inarray[0] + i * nquad0 * nquad1, 1,
                            &tmp0[0] + i * nquad0 * nquad1, 1);
            }
            for (i = 0; i < nquad1 * nquad2; ++i)
            {
                Vmath::Smul(nquad0, gfac1[i % nquad1], &tmp0[0] + i * nquad0, 1,
                            &tmp0[0] + i * nquad0, 1);
            }
            MultiplyByQuadratureMetric(tmp0, tmp0);
            IProductWRTBase_SumFacKernel(
                m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                m_base[2]->GetBdata(), tmp0, tmp4, wsp, true, false, true);
 
            MultiplyByQuadratureMetric(inarray, tmp0);
            IProductWRTBase_SumFacKernel(
                m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                m_base[2]->GetDbdata(), tmp0, outarray, wsp, true, true, false);
 
            Vmath::Vadd(m_ncoeffs, &tmp3[0], 1, &outarray[0], 1, &outarray[0],
                        1);
            Vmath::Vadd(m_ncoeffs, &tmp4[0], 1, &outarray[0], 1, &outarray[0],
                        1);
        }
        break;
        default:
        {
            ASSERTL1(false, "input dir is out of range");
        }
        break;
    }
}

References ASSERTL1, Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().

Referenced by v_IProductWRTDerivBase(), and Nektar::StdRegions::StdNodalTetExp::v_IProductWRTDerivBase_SumFac().

v_IsBoundaryInteriorExpansion()

bool Nektar::StdRegions::StdTetExp::v_IsBoundaryInteriorExpansion ( ) const

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1191 of file StdTetExp.cpp.

{
    return (m_base[0]->GetBasisType() == LibUtilities::eModified_A) &&
           (m_base[1]->GetBasisType() == LibUtilities::eModified_B) &&
           (m_base[2]->GetBasisType() == LibUtilities::eModified_C);
}

References Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

Referenced by v_GetElmtTraceToTraceMap().

v_LocCollapsedToLocCoord()

void Nektar::StdRegions::StdTetExp::v_LocCollapsedToLocCoord ( const Array< OneD, const NekDouble > &  eta, Array< OneD, NekDouble > &  xi  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 801 of file StdTetExp.cpp.

{
    xi[2] = eta[2];
    xi[1] = (1.0 + eta[1]) * (1.0 - xi[2]) * 0.5 - 1.0;
    xi[0] = (1.0 + eta[0]) * (-xi[1] - xi[2]) * 0.5 - 1.0;
}

v_LocCoordToLocCollapsed()

void Nektar::StdRegions::StdTetExp::v_LocCoordToLocCollapsed ( const Array< OneD, const NekDouble > &  xi, Array< OneD, NekDouble > &  eta  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 769 of file StdTetExp.cpp.

{
    NekDouble d2  = 1.0 - xi[2];
    NekDouble d12 = -xi[1] - xi[2];
    if (fabs(d2) < NekConstants::kNekZeroTol)
    {
        if (d2 >= 0.)
        {
            d2 = NekConstants::kNekZeroTol;
        }
        else
        {
            d2 = -NekConstants::kNekZeroTol;
        }
    }
    if (fabs(d12) < NekConstants::kNekZeroTol)
    {
        if (d12 >= 0.)
        {
            d12 = NekConstants::kNekZeroTol;
        }
        else
        {
            d12 = -NekConstants::kNekZeroTol;
        }
    }
    eta[0] = 2.0 * (1.0 + xi[0]) / d12 - 1.0;
    eta[1] = 2.0 * (1.0 + xi[1]) / d2 - 1.0;
    eta[2] = xi[2];
}

References Nektar::NekConstants::kNekZeroTol.

v_MultiplyByStdQuadratureMetric()

void Nektar::StdRegions::StdTetExp::v_MultiplyByStdQuadratureMetric ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1953 of file StdTetExp.cpp.

{
    int i, j;
 
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
 
    const Array<OneD, const NekDouble> &w0 = m_base[0]->GetW();
    const Array<OneD, const NekDouble> &w1 = m_base[1]->GetW();
    const Array<OneD, const NekDouble> &w2 = m_base[2]->GetW();
 
    const Array<OneD, const NekDouble> &z1 = m_base[1]->GetZ();
    const Array<OneD, const NekDouble> &z2 = m_base[2]->GetZ();
 
    // multiply by integration constants
    for (i = 0; i < nquad1 * nquad2; ++i)
    {
        Vmath::Vmul(nquad0, (NekDouble *)&inarray[0] + i * nquad0, 1, w0.data(),
                    1, &outarray[0] + i * nquad0, 1);
    }
 
    switch (m_base[1]->GetPointsType())
    {
        // (1,0) Jacobi Inner product.
        case LibUtilities::eGaussRadauMAlpha1Beta0:
            for (j = 0; j < nquad2; ++j)
            {
                for (i = 0; i < nquad1; ++i)
                {
                    Blas::Dscal(nquad0, 0.5 * w1[i],
                                &outarray[0] + i * nquad0 + j * nquad0 * nquad1,
                                1);
                }
            }
            break;
 
        default:
            for (j = 0; j < nquad2; ++j)
            {
                for (i = 0; i < nquad1; ++i)
                {
                    Blas::Dscal(nquad0, 0.5 * (1 - z1[i]) * w1[i],
                                &outarray[0] + i * nquad0 + j * nquad0 * nquad1,
                                1);
                }
            }
            break;
    }
 
    switch (m_base[2]->GetPointsType())
    {
            // (2,0) Jacobi inner product.
        case LibUtilities::eGaussRadauMAlpha2Beta0:
            for (i = 0; i < nquad2; ++i)
            {
                Blas::Dscal(nquad0 * nquad1, 0.25 * w2[i],
                            &outarray[0] + i * nquad0 * nquad1, 1);
            }
            break;
            // (1,0) Jacobi inner product.
        case LibUtilities::eGaussRadauMAlpha1Beta0:
            for (i = 0; i < nquad2; ++i)
            {
                Blas::Dscal(nquad0 * nquad1, 0.25 * (1 - z2[i]) * w2[i],
                            &outarray[0] + i * nquad0 * nquad1, 1);
            }
            break;
        default:
            for (i = 0; i < nquad2; ++i)
            {
                Blas::Dscal(nquad0 * nquad1,
                            0.25 * (1 - z2[i]) * (1 - z2[i]) * w2[i],
                            &outarray[0] + i * nquad0 * nquad1, 1);
            }
            break;
    }
}

References Blas::Dscal(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vmul().

v_NumBndryCoeffs()

int Nektar::StdRegions::StdTetExp::v_NumBndryCoeffs ( ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 977 of file StdTetExp.cpp.

{
    ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                 GetBasisType(0) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(1) == LibUtilities::eModified_B ||
                 GetBasisType(1) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(2) == LibUtilities::eModified_C ||
                 GetBasisType(2) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
 
    int P = m_base[0]->GetNumModes();
    int Q = m_base[1]->GetNumModes();
    int R = m_base[2]->GetNumModes();
 
    return LibUtilities::StdTetData::getNumberOfBndCoefficients(P, Q, R);
}

References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::LibUtilities::StdTetData::getNumberOfBndCoefficients(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.

v_NumDGBndryCoeffs()

int Nektar::StdRegions::StdTetExp::v_NumDGBndryCoeffs ( ) const

overrideprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 996 of file StdTetExp.cpp.

{
    ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                 GetBasisType(0) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(1) == LibUtilities::eModified_B ||
                 GetBasisType(1) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
    ASSERTL1(GetBasisType(2) == LibUtilities::eModified_C ||
                 GetBasisType(2) == LibUtilities::eGLL_Lagrange,
             "BasisType is not a boundary interior form");
 
    int P = m_base[0]->GetNumModes() - 1;
    int Q = m_base[1]->GetNumModes() - 1;
    int R = m_base[2]->GetNumModes() - 1;
 
    return (Q + 1) + P * (1 + 2 * Q - P) / 2    // base face
           + (R + 1) + P * (1 + 2 * R - P) / 2  // front face
           + 2 * (R + 1) + Q * (1 + 2 * R - Q); // back two faces
}

References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.

v_PhysDeriv() [1/2]

void Nektar::StdRegions::StdTetExp::v_PhysDeriv ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  out_dxi0, Array< OneD, NekDouble > &  out_dxi1, Array< OneD, NekDouble > &  out_dxi2  )

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

\(\begin{Bmatrix} \frac {\partial} {\partial \xi_1} \\ \frac {\partial} {\partial \xi_2} \\ \frac {\partial} {\partial \xi_3} \end{Bmatrix} = \begin{Bmatrix} \frac 4 {(1-\eta_2)(1-\eta_3)} \frac \partial {\partial \eta_1} \ \ \frac {2(1+\eta_1)} {(1-\eta_2)(1-\eta_3)} \frac \partial {\partial \eta_1} + \frac 2 {1-\eta_3} \frac \partial {\partial \eta_3} \\ \frac {2(1 + \eta_1)} {2(1 - \eta_2)(1-\eta_3)} \frac \partial {\partial \eta_1} + \frac {1 + \eta_2} {1 - \eta_3} \frac \partial {\partial \eta_2} + \frac \partial {\partial \eta_3} \end{Bmatrix}\)

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 83 of file StdTetExp.cpp.

{
    int Q0   = m_base[0]->GetNumPoints();
    int Q1   = m_base[1]->GetNumPoints();
    int Q2   = m_base[2]->GetNumPoints();
    int Qtot = Q0 * Q1 * Q2;
 
    // Compute the physical derivative
    Array<OneD, NekDouble> out_dEta0(3 * Qtot, 0.0);
    Array<OneD, NekDouble> out_dEta1 = out_dEta0 + Qtot;
    Array<OneD, NekDouble> out_dEta2 = out_dEta1 + Qtot;
 
    bool Do_2 = (out_dxi2.size() > 0) ? true : false;
    bool Do_1 = (out_dxi1.size() > 0) ? true : false;
 
    if (Do_2) // Need all local derivatives
    {
        PhysTensorDeriv(inarray, out_dEta0, out_dEta1, out_dEta2);
    }
    else if (Do_1) // Need 0 and 1 derivatives
    {
        PhysTensorDeriv(inarray, out_dEta0, out_dEta1, NullNekDouble1DArray);
    }
    else // Only need Eta0 derivaitve
    {
        PhysTensorDeriv(inarray, out_dEta0, NullNekDouble1DArray,
                        NullNekDouble1DArray);
    }
 
    Array<OneD, const NekDouble> eta_0, eta_1, eta_2;
    eta_0 = m_base[0]->GetZ();
    eta_1 = m_base[1]->GetZ();
    eta_2 = m_base[2]->GetZ();
 
    // calculate 2.0/((1-eta_1)(1-eta_2)) Out_dEta0
 
    NekDouble *dEta0 = &out_dEta0[0];
    NekDouble fac;
    for (int k = 0; k < Q2; ++k)
    {
        for (int j = 0; j < Q1; ++j, dEta0 += Q0)
        {
            Vmath::Smul(Q0, 2.0 / (1.0 - eta_1[j]), dEta0, 1, dEta0, 1);
        }
        fac = 1.0 / (1.0 - eta_2[k]);
        Vmath::Smul(Q0 * Q1, fac, &out_dEta0[0] + k * Q0 * Q1, 1,
                    &out_dEta0[0] + k * Q0 * Q1, 1);
    }
 
    if (out_dxi0.size() > 0)
    {
        // out_dxi0 = 4.0/((1-eta_1)(1-eta_2)) Out_dEta0
        Vmath::Smul(Qtot, 2.0, out_dEta0, 1, out_dxi0, 1);
    }
 
    if (Do_1 || Do_2)
    {
        Array<OneD, NekDouble> Fac0(Q0);
        Vmath::Sadd(Q0, 1.0, eta_0, 1, Fac0, 1);
 
        // calculate 2.0*(1+eta_0)/((1-eta_1)(1-eta_2)) Out_dEta0
        for (int k = 0; k < Q1 * Q2; ++k)
        {
            Vmath::Vmul(Q0, &Fac0[0], 1, &out_dEta0[0] + k * Q0, 1,
                        &out_dEta0[0] + k * Q0, 1);
        }
        // calculate 2/(1.0-eta_2) out_dEta1
        for (int k = 0; k < Q2; ++k)
        {
            Vmath::Smul(Q0 * Q1, 2.0 / (1.0 - eta_2[k]),
                        &out_dEta1[0] + k * Q0 * Q1, 1,
                        &out_dEta1[0] + k * Q0 * Q1, 1);
        }
 
        if (Do_1)
        {
            // calculate out_dxi1 = 2.0(1+eta_0)/((1-eta_1)(1-eta_2)) Out_dEta0
            // + 2/(1.0-eta_2) out_dEta1
            Vmath::Vadd(Qtot, out_dEta0, 1, out_dEta1, 1, out_dxi1, 1);
        }
 
        if (Do_2)
        {
            // calculate (1 + eta_1)/(1 -eta_2)*out_dEta1
            NekDouble *dEta1 = &out_dEta1[0];
            for (int k = 0; k < Q2; ++k)
            {
                for (int j = 0; j < Q1; ++j, dEta1 += Q0)
                {
                    Vmath::Smul(Q0, (1.0 + eta_1[j]) / 2.0, dEta1, 1, dEta1, 1);
                }
            }
 
            // calculate out_dxi2 =
            // 2.0(1+eta_0)/((1-eta_1)(1-eta_2)) Out_dEta0 +
            // (1 + eta_1)/(1 -eta_2)*out_dEta1 + out_dEta2
            Vmath::Vadd(Qtot, out_dEta0, 1, out_dEta1, 1, out_dxi2, 1);
            Vmath::Vadd(Qtot, out_dEta2, 1, out_dxi2, 1, out_dxi2, 1);
        }
    }
}

References Nektar::StdRegions::StdExpansion::m_base, Nektar::NullNekDouble1DArray, Nektar::StdRegions::StdExpansion3D::PhysTensorDeriv(), Vmath::Sadd(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().

Referenced by v_PhysDeriv(), and v_StdPhysDeriv().

v_PhysDeriv() [2/2]

void Nektar::StdRegions::StdTetExp::v_PhysDeriv ( const int  dir, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Parameters

dir	Direction in which to compute derivative. Valid values are 0, 1, 2.
inarray	Input array.
outarray	Output array.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 194 of file StdTetExp.cpp.

{
    switch (dir)
    {
        case 0:
        {
            v_PhysDeriv(inarray, outarray, NullNekDouble1DArray,
                        NullNekDouble1DArray);
            break;
        }
        case 1:
        {
            v_PhysDeriv(inarray, NullNekDouble1DArray, outarray,
                        NullNekDouble1DArray);
            break;
        }
        case 2:
        {
            v_PhysDeriv(inarray, NullNekDouble1DArray, NullNekDouble1DArray,
                        outarray);
            break;
        }
        default:
        {
            ASSERTL1(false, "input dir is out of range");
        }
        break;
    }
}

References ASSERTL1, Nektar::NullNekDouble1DArray, and v_PhysDeriv().

v_PhysEvalFirstDeriv()

NekDouble Nektar::StdRegions::StdTetExp::v_PhysEvalFirstDeriv ( const Array< OneD, NekDouble > &  coord, const Array< OneD, const NekDouble > &  inarray, std::array< NekDouble, 3 > &  firstOrderDerivs  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 858 of file StdTetExp.cpp.

{
    // Collapse coordinates
    Array<OneD, NekDouble> coll(3, 0.0);
    LocCoordToLocCollapsed(coord, coll);
 
    // If near singularity do the old interpolation matrix method
    if ((1 - coll[1]) < 1e-5 || (1 - coll[2]) < 1e-5)
    {
        int totPoints = GetTotPoints();
        Array<OneD, NekDouble> EphysDeriv0(totPoints), EphysDeriv1(totPoints),
            EphysDeriv2(totPoints);
        PhysDeriv(inarray, EphysDeriv0, EphysDeriv1, EphysDeriv2);
 
        Array<OneD, DNekMatSharedPtr> I(3);
        I[0] = GetBase()[0]->GetI(coll);
        I[1] = GetBase()[1]->GetI(coll + 1);
        I[2] = GetBase()[2]->GetI(coll + 2);
 
        firstOrderDerivs[0] = PhysEvaluate(I, EphysDeriv0);
        firstOrderDerivs[1] = PhysEvaluate(I, EphysDeriv1);
        firstOrderDerivs[2] = PhysEvaluate(I, EphysDeriv2);
        return PhysEvaluate(I, inarray);
    }
 
    std::array<NekDouble, 3> interDeriv;
    NekDouble val = BaryTensorDeriv(coll, inarray, interDeriv);
 
    // calculate 2.0/((1-eta_1)(1-eta_2)) * Out_dEta0
    NekDouble temp = 2.0 / ((1 - coll[1]) * (1 - coll[2]));
    interDeriv[0] *= temp;
 
    // out_dxi0 = 4.0/((1-eta_1)(1-eta_2)) * Out_dEta0
    firstOrderDerivs[0] = 2 * interDeriv[0];
 
    // fac0 = 1 + eta_0
    NekDouble fac0;
    fac0 = 1 + coll[0];
 
    // calculate 2.0*(1+eta_0)/((1-eta_1)(1-eta_2)) * Out_dEta0
    interDeriv[0] *= fac0;
 
    // calculate 2/(1.0-eta_2) * out_dEta1
    fac0 = 2 / (1 - coll[2]);
    interDeriv[1] *= fac0;
 
    // calculate out_dxi1 = 2.0(1+eta_0)/((1-eta_1)(1-eta_2))
    //  * Out_dEta0 + 2/(1.0-eta_2) out_dEta1
    firstOrderDerivs[1] = interDeriv[0] + interDeriv[1];
 
    // calculate (1 + eta_1)/(1 -eta_2)*out_dEta1
    fac0 = (1 + coll[1]) / 2;
    interDeriv[1] *= fac0;
 
    // calculate out_dxi2 =
    // 2.0(1+eta_0)/((1-eta_1)(1-eta_2)) Out_dEta0 +
    // (1 + eta_1)/(1 -eta_2)*out_dEta1 + out_dEta2
    firstOrderDerivs[2] = interDeriv[0] + interDeriv[1] + interDeriv[2];
 
    return val;
}

References Nektar::StdRegions::StdExpansion3D::BaryTensorDeriv(), Nektar::StdRegions::StdExpansion::GetBase(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::PhysDeriv(), and Nektar::StdRegions::StdExpansion::PhysEvaluate().

v_PhysEvaluateBasis()

NekDouble Nektar::StdRegions::StdTetExp::v_PhysEvaluateBasis ( const Array< OneD, const NekDouble > &  coords, int  mode  )

finalprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 816 of file StdTetExp.cpp.

{
    Array<OneD, NekDouble> coll(3);
    LocCoordToLocCollapsed(coords, coll);
 
    const int nm1 = m_base[1]->GetNumModes();
    const int nm2 = m_base[2]->GetNumModes();
 
    const int b     = 2 * nm2 + 1;
    const int mode0 = floor(0.5 * (b - sqrt(b * b - 8.0 * mode / nm1)));
    const int tmp =
        mode - nm1 * (mode0 * (nm2 - 1) + 1 - (mode0 - 2) * (mode0 - 1) / 2);
    const int mode1 = tmp / (nm2 - mode0);
    const int mode2 = tmp % (nm2 - mode0);
 
    if (m_base[0]->GetBasisType() == LibUtilities::eModified_A)
    {
        // Handle the collapsed vertices and edges in the modified
        // basis.
        if (mode == 1)
        {
            // Collapsed top vertex
            return StdExpansion::BaryEvaluateBasis<2>(coll[2], 1);
        }
        else if (mode0 == 0 && mode2 == 1)
        {
            return StdExpansion::BaryEvaluateBasis<1>(coll[1], 0) *
                   StdExpansion::BaryEvaluateBasis<2>(coll[2], 1);
        }
        else if (mode0 == 1 && mode1 == 1 && mode2 == 0)
        {
            return StdExpansion::BaryEvaluateBasis<0>(coll[0], 0) *
                   StdExpansion::BaryEvaluateBasis<1>(coll[1], 1);
        }
    }
 
    return StdExpansion::BaryEvaluateBasis<0>(coll[0], mode0) *
           StdExpansion::BaryEvaluateBasis<1>(coll[1], mode1) *
           StdExpansion::BaryEvaluateBasis<2>(coll[2], mode2);
}

References Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::m_base, and tinysimd::sqrt().

v_ReduceOrderCoeffs()

void Nektar::StdRegions::StdTetExp::v_ReduceOrderCoeffs ( int  numMin, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 2176 of file StdTetExp.cpp.

{
    int nquad0  = m_base[0]->GetNumPoints();
    int nquad1  = m_base[1]->GetNumPoints();
    int nquad2  = m_base[2]->GetNumPoints();
    int nqtot   = nquad0 * nquad1 * nquad2;
    int nmodes0 = m_base[0]->GetNumModes();
    int nmodes1 = m_base[1]->GetNumModes();
    int nmodes2 = m_base[2]->GetNumModes();
    int numMax  = nmodes0;
 
    Array<OneD, NekDouble> coeff(m_ncoeffs);
    Array<OneD, NekDouble> coeff_tmp1(m_ncoeffs, 0.0);
    Array<OneD, NekDouble> coeff_tmp2(m_ncoeffs, 0.0);
    Array<OneD, NekDouble> phys_tmp(nqtot, 0.0);
    Array<OneD, NekDouble> tmp, tmp2, tmp3, tmp4;
 
    Vmath::Vcopy(m_ncoeffs, inarray, 1, coeff_tmp2, 1);
 
    const LibUtilities::PointsKey Pkey0 = m_base[0]->GetPointsKey();
    const LibUtilities::PointsKey Pkey1 = m_base[1]->GetPointsKey();
    const LibUtilities::PointsKey Pkey2 = m_base[2]->GetPointsKey();
 
    LibUtilities::BasisKey bortho0(LibUtilities::eOrtho_A, nmodes0, Pkey0);
    LibUtilities::BasisKey bortho1(LibUtilities::eOrtho_B, nmodes1, Pkey1);
    LibUtilities::BasisKey bortho2(LibUtilities::eOrtho_C, nmodes2, Pkey2);
 
    Vmath::Zero(m_ncoeffs, coeff_tmp2, 1);
 
    StdRegions::StdTetExpSharedPtr OrthoTetExp;
    OrthoTetExp = MemoryManager<StdRegions::StdTetExp>::AllocateSharedPtr(
        bortho0, bortho1, bortho2);
 
    BwdTrans(inarray, phys_tmp);
    OrthoTetExp->FwdTrans(phys_tmp, coeff);
 
    Vmath::Zero(m_ncoeffs, outarray, 1);
 
    // filtering
    int cnt = 0;
    for (int u = 0; u < numMin; ++u)
    {
        for (int i = 0; i < numMin - u; ++i)
        {
            Vmath::Vcopy(numMin - u - i, tmp = coeff + cnt, 1,
                         tmp2 = coeff_tmp1 + cnt, 1);
            cnt += numMax - u - i;
        }
        for (int i = numMin; i < numMax - u; ++i)
        {
            cnt += numMax - u - i;
        }
    }
 
    OrthoTetExp->BwdTrans(coeff_tmp1, phys_tmp);
    FwdTrans(phys_tmp, outarray);
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vcopy(), and Vmath::Zero().

v_StdPhysDeriv() [1/2]

void Nektar::StdRegions::StdTetExp::v_StdPhysDeriv ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  out_d0, Array< OneD, NekDouble > &  out_d1, Array< OneD, NekDouble > &  out_d2  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 226 of file StdTetExp.cpp.

{
    StdTetExp::v_PhysDeriv(inarray, out_d0, out_d1, out_d2);
}

References v_PhysDeriv().

v_StdPhysDeriv() [2/2]

void Nektar::StdRegions::StdTetExp::v_StdPhysDeriv ( const int  dir, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 234 of file StdTetExp.cpp.

{
    StdTetExp::v_PhysDeriv(dir, inarray, outarray);
}

References v_PhysDeriv().

v_SVVLaplacianFilter()

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

overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp.

Definition at line 2034 of file StdTetExp.cpp.

{
    // To do : 1) add a test to ensure 0 \leq SvvCutoff \leq 1.
    //        2) check if the transfer function needs an analytical
    //           Fourier transform.
    //        3) if it doesn't : find a transfer function that renders
    //           the if( cutoff_a ...) useless to reduce computational
    //           cost.
    //        4) add SVVDiffCoef to both models!!
 
    int qa       = m_base[0]->GetNumPoints();
    int qb       = m_base[1]->GetNumPoints();
    int qc       = m_base[2]->GetNumPoints();
    int nmodes_a = m_base[0]->GetNumModes();
    int nmodes_b = m_base[1]->GetNumModes();
    int nmodes_c = m_base[2]->GetNumModes();
 
    // Declare orthogonal basis.
    LibUtilities::PointsKey pa(qa, m_base[0]->GetPointsType());
    LibUtilities::PointsKey pb(qb, m_base[1]->GetPointsType());
    LibUtilities::PointsKey pc(qc, m_base[2]->GetPointsType());
 
    LibUtilities::BasisKey Ba(LibUtilities::eOrtho_A, nmodes_a, pa);
    LibUtilities::BasisKey Bb(LibUtilities::eOrtho_B, nmodes_b, pb);
    LibUtilities::BasisKey Bc(LibUtilities::eOrtho_C, nmodes_c, pc);
 
    StdTetExp OrthoExp(Ba, Bb, Bc);
 
    Array<OneD, NekDouble> orthocoeffs(OrthoExp.GetNcoeffs());
    int i, j, k, cnt = 0;
 
    // project onto physical space.
    OrthoExp.FwdTrans(array, orthocoeffs);
 
    if (mkey.ConstFactorExists(eFactorSVVPowerKerDiffCoeff))
    {
        // Rodrigo's power kernel
        NekDouble cutoff = mkey.GetConstFactor(eFactorSVVCutoffRatio);
        NekDouble SvvDiffCoeff =
            mkey.GetConstFactor(eFactorSVVPowerKerDiffCoeff) *
            mkey.GetConstFactor(eFactorSVVDiffCoeff);
 
        for (i = 0; i < nmodes_a; ++i)
        {
            for (j = 0; j < nmodes_b - j; ++j)
            {
                NekDouble fac1 = std::max(
                    pow((1.0 * i) / (nmodes_a - 1), cutoff * nmodes_a),
                    pow((1.0 * j) / (nmodes_b - 1), cutoff * nmodes_b));
 
                for (k = 0; k < nmodes_c - i - j; ++k)
                {
                    NekDouble fac =
                        std::max(fac1, pow((1.0 * k) / (nmodes_c - 1),
                                           cutoff * nmodes_c));
 
                    orthocoeffs[cnt] *= SvvDiffCoeff * fac;
                    cnt++;
                }
            }
        }
    }
    else if (mkey.ConstFactorExists(
                 eFactorSVVDGKerDiffCoeff)) // Rodrigo/Mansoor's DG Kernel
    {
        NekDouble SvvDiffCoeff = mkey.GetConstFactor(eFactorSVVDGKerDiffCoeff) *
                                 mkey.GetConstFactor(eFactorSVVDiffCoeff);
 
        int max_abc = max(nmodes_a - kSVVDGFiltermodesmin,
                          nmodes_b - kSVVDGFiltermodesmin);
        max_abc     = max(max_abc, nmodes_c - kSVVDGFiltermodesmin);
        // clamp max_abc
        max_abc = max(max_abc, 0);
        max_abc = min(max_abc, kSVVDGFiltermodesmax - kSVVDGFiltermodesmin);
 
        for (i = 0; i < nmodes_a; ++i)
        {
            for (j = 0; j < nmodes_b - j; ++j)
            {
                int maxij = max(i, j);
 
                for (k = 0; k < nmodes_c - i - j; ++k)
                {
                    int maxijk = max(maxij, k);
                    maxijk     = min(maxijk, kSVVDGFiltermodesmax - 1);
 
                    orthocoeffs[cnt] *=
                        SvvDiffCoeff * kSVVDGFilter[max_abc][maxijk];
                    cnt++;
                }
            }
        }
    }
    else
    {
 
        // SVV filter paramaters (how much added diffusion
        // relative to physical one and fraction of modes from
        // which you start applying this added diffusion)
 
        NekDouble SvvDiffCoeff =
            mkey.GetConstFactor(StdRegions::eFactorSVVDiffCoeff);
        NekDouble SVVCutOff =
            mkey.GetConstFactor(StdRegions::eFactorSVVCutoffRatio);
 
        // Defining the cut of mode
        int cutoff_a      = (int)(SVVCutOff * nmodes_a);
        int cutoff_b      = (int)(SVVCutOff * nmodes_b);
        int cutoff_c      = (int)(SVVCutOff * nmodes_c);
        int nmodes        = min(min(nmodes_a, nmodes_b), nmodes_c);
        NekDouble cutoff  = min(min(cutoff_a, cutoff_b), cutoff_c);
        NekDouble epsilon = 1;
 
        //------"New" Version August 22nd '13--------------------
        for (i = 0; i < nmodes_a; ++i)
        {
            for (j = 0; j < nmodes_b - i; ++j)
            {
                for (k = 0; k < nmodes_c - i - j; ++k)
                {
                    if (i + j + k >= cutoff)
                    {
                        orthocoeffs[cnt] *= ((SvvDiffCoeff)*exp(
                            -(i + j + k - nmodes) * (i + j + k - nmodes) /
                            ((NekDouble)((i + j + k - cutoff + epsilon) *
                                         (i + j + k - cutoff + epsilon)))));
                    }
                    else
                    {
                        orthocoeffs[cnt] *= 0.0;
                    }
                    cnt++;
                }
            }
        }
    }
 
    // backward transform to physical space
    OrthoExp.BwdTrans(orthocoeffs, array);
}

References Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::eFactorSVVDGKerDiffCoeff, Nektar::StdRegions::eFactorSVVDiffCoeff, Nektar::StdRegions::eFactorSVVPowerKerDiffCoeff, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::kSVVDGFilter, Nektar::StdRegions::kSVVDGFiltermodesmax, Nektar::StdRegions::kSVVDGFiltermodesmin, and Nektar::StdRegions::StdExpansion::m_base.