#include <StdExpansion2D.h>

Inheritance diagram for Nektar::StdRegions::StdExpansion2D:

Public Member Functions
	StdExpansion2D ()

	StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)

	StdExpansion2D (const StdExpansion2D &T)

virtual	~StdExpansion2D ()

void	PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d0, Array< OneD, NekDouble > &outarray_d1)
	Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points. More...

NekDouble	Integral (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &w0, const Array< OneD, const NekDouble > &w1)

void	BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)

void	IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)

Public Member Functions inherited from Nektar::StdRegions::StdExpansion
	StdExpansion ()
	Default Constructor. More...

	StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey)
	Constructor. More...

	StdExpansion (const StdExpansion &T)
	Copy Constructor. More...

virtual	~StdExpansion ()
	Destructor. More...

int	GetNumBases () const
	This function returns the number of 1D bases used in the expansion. More...

const Array< OneD, const LibUtilities::BasisSharedPtr > &	GetBase () const
	This function gets the shared point to basis. More...

const LibUtilities::BasisSharedPtr &	GetBasis (int dir) const
	This function gets the shared point to basis in the dir direction. More...

int	GetNcoeffs (void) const
	This function returns the total number of coefficients used in the expansion. More...

int	GetTotPoints () const
	This function returns the total number of quadrature points used in the element. More...

LibUtilities::BasisType	GetBasisType (const int dir) const
	This function returns the type of basis used in the dir direction. More...

int	GetBasisNumModes (const int dir) const
	This function returns the number of expansion modes in the dir direction. More...

int	EvalBasisNumModesMax (void) const
	This function returns the maximum number of expansion modes over all local directions. More...

LibUtilities::PointsType	GetPointsType (const int dir) const
	This function returns the type of quadrature points used in the dir direction. More...

int	GetNumPoints (const int dir) const
	This function returns the number of quadrature points in the dir direction. More...

const Array< OneD, const NekDouble > &	GetPoints (const int dir) const
	This function returns a pointer to the array containing the quadrature points in dir direction. More...

int	GetNverts () const
	This function returns the number of vertices of the expansion domain. More...

int	GetTraceNcoeffs (const int i) const
	This function returns the number of expansion coefficients belonging to the i-th trace. More...

int	GetTraceIntNcoeffs (const int i) const

int	GetTraceNumPoints (const int i) const
	This function returns the number of quadrature points belonging to the i-th trace. More...

const LibUtilities::BasisKey	GetTraceBasisKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...

LibUtilities::PointsKey	GetTracePointsKey (const int i, int k=-1) const
	This function returns the basis key belonging to the i-th trace. More...

int	NumBndryCoeffs (void) const

int	NumDGBndryCoeffs (void) const

const LibUtilities::PointsKey	GetNodalPointsKey () const
	This function returns the type of expansion Nodal point type if defined. More...

int	GetNtraces () const
	Returns the number of trace elements connected to this element. More...

LibUtilities::ShapeType	DetShapeType () const
	This function returns the shape of the expansion domain. More...

std::shared_ptr< StdExpansion >	GetStdExp (void) const

std::shared_ptr< StdExpansion >	GetLinStdExp (void) const

int	GetShapeDimension () const

bool	IsBoundaryInteriorExpansion ()

bool	IsNodalNonTensorialExp ()

void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Backward transformation from coefficient space to physical space. More...

void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function performs the Forward transformation from physical space to coefficient space. More...

void	FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)
	This function integrates the specified function over the domain. More...

void	FillMode (const int mode, Array< OneD, NekDouble > &outarray)
	This function fills the array outarray with the mode-th mode of the expansion. More...

void	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	this function calculates the inner product of a given function f with the different modes of the expansion More...

void	IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)

void	IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

int	GetElmtId ()
	Get the element id of this expansion when used in a list by returning value of m_elmt_id. More...

void	SetElmtId (const int id)
	Set the element id of this expansion when used in a list by returning value of m_elmt_id. More...

void	GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
	this function returns the physical coordinates of the quadrature points of the expansion More...

void	GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
	given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point More...

DNekMatSharedPtr	GetStdMatrix (const StdMatrixKey &mkey)

DNekBlkMatSharedPtr	GetStdStaticCondMatrix (const StdMatrixKey &mkey)

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	GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eForwards)

void	GetTraceNumModes (const int tid, int &numModes0, int &numModes1, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)

void	MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

DNekMatSharedPtr	CreateGeneralMatrix (const StdMatrixKey &mkey)
	this function generates the mass matrix \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) More...

void	GeneralMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)

void	ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)

void	LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)

void	HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

DNekMatSharedPtr	GenMatrix (const StdMatrixKey &mkey)

void	PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)

void	PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	PhysDeriv_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds)

void	PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn)

void	PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)

void	StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)

void	StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

NekDouble	PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

NekDouble	PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

NekDouble	PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
	This function evaluates the basis function mode `mode` at a point `coords` of the domain. More...

void	LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
	Convert local cartesian coordinate xi into local collapsed coordinates eta. More...

void	LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
	Convert local collapsed coordinates eta into local cartesian coordinate xi. More...

virtual 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
virtual NekDouble	v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
	This function evaluates the expansion at a single (arbitrary) point of the domain. More...

virtual NekDouble	v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)

virtual void	v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0

virtual void	v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0

virtual void	v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)

virtual void	v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)

virtual void	v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)

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_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)

void	LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)

void	HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

void	HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)

virtual void	v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)

virtual NekDouble	v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)

virtual void	v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

template<int DIR>
NekDouble	BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
	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)

Private Member Functions
virtual int	v_GetShapeDimension () const

virtual int	v_GetCoordim (void)

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 48 of file StdExpansion2D.h.

Constructor & Destructor Documentation

◆ StdExpansion2D() [1/3]

Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( )

Definition at line 48 of file StdExpansion2D.cpp.

49 {

50 }

◆ StdExpansion2D() [2/3]

Nektar::StdRegions::StdExpansion2D::StdExpansion2D	(	int	numcoeffs,
		const LibUtilities::BasisKey &	Ba,
		const LibUtilities::BasisKey &	Bb
	)

Definition at line 52 of file StdExpansion2D.cpp.

                                                                       :
         StdExpansion(numcoeffs,2, Ba, Bb)
         {
         }

◆ StdExpansion2D() [3/3]

Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( const StdExpansion2D & T )

Definition at line 59 of file StdExpansion2D.cpp.

                                                              :
                 StdExpansion(T)
         {
         }

◆ ~StdExpansion2D()

Nektar::StdRegions::StdExpansion2D::~StdExpansion2D ( )

virtual

Definition at line 64 of file StdExpansion2D.cpp.

65 {

66 }

Member Function Documentation

◆ BwdTrans_SumFacKernel()

void Nektar::StdRegions::StdExpansion2D::BwdTrans_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0 = `true`,
		bool	doCheckCollDir1 = `true`
	)

Definition at line 198 of file StdExpansion2D.cpp.

         {
             v_BwdTrans_SumFacKernel(base0, base1, inarray, outarray, wsp, doCheckCollDir0, doCheckCollDir1);
         }

References v_BwdTrans_SumFacKernel().

Referenced by Nektar::StdRegions::StdQuadExp::v_BwdTrans_SumFac(), Nektar::StdRegions::StdTriExp::v_BwdTrans_SumFac(), v_HelmholtzMatrixOp_MatFree(), and v_LaplacianMatrixOp_MatFree().

◆ Integral()

NekDouble Nektar::StdRegions::StdExpansion2D::Integral	(	const Array< OneD, const NekDouble > &	inarray,
		const Array< OneD, const NekDouble > &	w0,
		const Array< OneD, const NekDouble > &	w1
	)

Definition at line 171 of file StdExpansion2D.cpp.

         {
             int i;
             NekDouble Int = 0.0;
             int nquad0 = m_base[0]->GetNumPoints();
             int nquad1 = m_base[1]->GetNumPoints();
             Array<OneD, NekDouble> tmp(nquad0 * nquad1);
  
             // multiply by integration constants
             for (i = 0; i < nquad1; ++i)
             {
                 Vmath::Vmul(nquad0, &inarray[0] + i*nquad0, 1, w0.get(),
                             1, &tmp[0] + i*nquad0, 1);
             }
  
             for (i = 0; i < nquad0; ++i)
             {
                 Vmath::Vmul(nquad1, &tmp[0]+ i, nquad0, w1.get(), 1,
                             &tmp[0] + i, nquad0);
             }
             Int = Vmath::Vsum(nquad0 * nquad1, tmp, 1);
  
             return Int;
         }

References Nektar::StdRegions::StdExpansion::m_base, Vmath::Vmul(), and Vmath::Vsum().

Referenced by Nektar::StdRegions::StdQuadExp::v_Integral(), and Nektar::StdRegions::StdTriExp::v_Integral().

◆ IProductWRTBase_SumFacKernel()

void Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0 = `true`,
		bool	doCheckCollDir1 = `true`
	)

Definition at line 210 of file StdExpansion2D.cpp.

         {
             v_IProductWRTBase_SumFacKernel(base0, base1, inarray, outarray, wsp, doCheckCollDir0, doCheckCollDir1);
         }

References v_IProductWRTBase_SumFacKernel().

◆ PhysTensorDeriv()

void Nektar::StdRegions::StdExpansion2D::PhysTensorDeriv	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray_d0,
		Array< OneD, NekDouble > &	outarray_d1
	)

Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points.

This function is independent of the expansion basis and can therefore be defined for all tensor product distribution of quadrature points in a generic manner. The key operations are:

\( \frac{d}{d\eta_1} \rightarrow {\bf D^T_0 u } \)
\( \frac{d}{d\eta_2} \rightarrow {\bf D_1 u } \)

Parameters

inarray	array of physical points to be differentiated
outarray_d0	the resulting array of derivative in the \(\eta_1\) direction will be stored in outarray_d0 as output of the function
outarray_d1	the resulting array of derivative in the \(\eta_2\) direction will be stored in outarray_d1 as output of the function

Recall that: \( \hspace{1cm} \begin{array}{llll} \mbox{Shape} & \mbox{Cartesian coordinate range} & \mbox{Collapsed coord.} & \mbox{Collapsed coordinate definition}\\ \mbox{Quadrilateral} & -1 \leq \xi_1,\xi_2 \leq 1 & -1 \leq \eta_1,\eta_2 \leq 1 & \eta_1 = \xi_1, \eta_2 = \xi_2\\ \mbox{Triangle} & -1 \leq \xi_1,\xi_2; \xi_1+\xi_2 \leq 0 & -1 \leq \eta_1,\eta_2 \leq 1 & \eta_1 = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \eta_2 = \xi_2 \\ \end{array} \)

Definition at line 71 of file StdExpansion2D.cpp.

         {
             int nquad0 = m_base[0]->GetNumPoints();
             int nquad1 = m_base[1]->GetNumPoints();
  
             if (outarray_d0.size() > 0) // calculate du/dx_0
             {
                 DNekMatSharedPtr D0 = m_base[0]->GetD();
                 if(inarray.data() == outarray_d0.data())
                 {
                     Array<OneD, NekDouble> wsp(nquad0 * nquad1);
                     Vmath::Vcopy(nquad0 * nquad1,inarray.get(),1,wsp.get(),1);
                     Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
                                 &(D0->GetPtr())[0], nquad0, &wsp[0], nquad0, 0.0,
                                 &outarray_d0[0], nquad0);
                 }
                 else
                 {
                     Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
                                 &(D0->GetPtr())[0], nquad0, &inarray[0], nquad0, 0.0,
                                 &outarray_d0[0], nquad0);
                 }
             }
  
             if (outarray_d1.size() > 0) // calculate du/dx_1
             {
                 DNekMatSharedPtr D1 = m_base[1]->GetD();
                 if(inarray.data() == outarray_d1.data())
                 {
                     Array<OneD, NekDouble> wsp(nquad0 * nquad1);
                     Vmath::Vcopy(nquad0 * nquad1,inarray.get(),1,wsp.get(),1);
                     Blas:: Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &wsp[0], nquad0,
                                  &(D1->GetPtr())[0], nquad1, 0.0, &outarray_d1[0], nquad0);
                 }
                 else
                 {
                     Blas:: Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &inarray[0], nquad0,
                                  &(D1->GetPtr())[0], nquad1, 0.0, &outarray_d1[0], nquad0);
                 }
             }
         }

References Blas::Dgemm(), Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vcopy().

Referenced by Nektar::StdRegions::StdQuadExp::v_PhysDeriv(), and Nektar::StdRegions::StdTriExp::v_PhysDeriv().

◆ v_BwdTrans_SumFacKernel()

virtual void Nektar::StdRegions::StdExpansion2D::v_BwdTrans_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0,
		bool	doCheckCollDir1
	)

protectedpure virtual

Implemented in Nektar::StdRegions::StdTriExp, and Nektar::StdRegions::StdQuadExp.

Referenced by BwdTrans_SumFacKernel().

◆ v_GenStdMatBwdDeriv()

void Nektar::StdRegions::StdExpansion2D::v_GenStdMatBwdDeriv	(	const int	dir,
		DNekMatSharedPtr &	mat
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 222 of file StdExpansion2D.cpp.

         {
             ASSERTL1((dir==0) || (dir==1),
                      "Invalid direction.");
  
             int    nquad0  = m_base[0]->GetNumPoints();
             int    nquad1  = m_base[1]->GetNumPoints();
             int    nqtot   = nquad0*nquad1;
             int    nmodes0 = m_base[0]->GetNumModes();
  
             Array<OneD, NekDouble> tmp1(2*nqtot+m_ncoeffs+nmodes0*nquad1,0.0);
             Array<OneD, NekDouble> tmp3(tmp1 + 2*nqtot);
             Array<OneD, NekDouble> tmp4(tmp1 + 2*nqtot+m_ncoeffs);
  
             switch(dir)
             {
             case 0:
                 for(int i=0; i<nqtot;i++)
                 {
                     tmp1[i] =   1.0;
                     IProductWRTBase_SumFacKernel(
                         m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                         tmp1, tmp3, tmp4, false, true);
                     tmp1[i] =   0.0;
                     
                     for(int j=0; j<m_ncoeffs;j++)
                     {
                         (*mat)(j,i) =   tmp3[j];
                     }
                 }
                 break;
             case 1:
                 for(int i=0; i<nqtot;i++)
                 {
                     tmp1[i] =   1.0;
                     IProductWRTBase_SumFacKernel(
                         m_base[0]->GetBdata() , m_base[1]->GetDbdata(),
                         tmp1, tmp3, tmp4, true, false);
                     tmp1[i] =   0.0;
                     
                     for(int j=0; j<m_ncoeffs;j++)
                     {
                         (*mat)(j,i) =   tmp3[j];
                     }
                 }
                 break;
             default:
                 NEKERROR(ErrorUtil::efatal, "Not a 2D expansion.");
                 break;
             }
         }

References ASSERTL1, Nektar::ErrorUtil::efatal, IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, and NEKERROR.

◆ v_GetCoordim()

virtual int Nektar::StdRegions::StdExpansion2D::v_GetCoordim ( void )

inlineprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::LocalRegions::QuadExp.

Definition at line 189 of file StdExpansion2D.h.

             {
                 return 2;
             }

◆ v_GetShapeDimension()

virtual int Nektar::StdRegions::StdExpansion2D::v_GetShapeDimension ( ) const

inlineprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 184 of file StdExpansion2D.h.

             {
                 return 2;
             }

◆ v_HelmholtzMatrixOp_MatFree()

void Nektar::StdRegions::StdExpansion2D::v_HelmholtzMatrixOp_MatFree	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 325 of file StdExpansion2D.cpp.

         {
             if (mkey.GetNVarCoeff() == 0 && !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00)
                 &&!mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
             {
                 using std::max;
  
                 int       nquad0  = m_base[0]->GetNumPoints();
                 int       nquad1  = m_base[1]->GetNumPoints();
                 int       nqtot   = nquad0*nquad1;
                 int       nmodes0 = m_base[0]->GetNumModes();
                 int       nmodes1 = m_base[1]->GetNumModes();
                 int       wspsize = max(max(max(nqtot,m_ncoeffs),nquad1*nmodes0),
                                         nquad0*nmodes1);
                 NekDouble lambda  =
                     mkey.GetConstFactor(StdRegions::eFactorLambda);
  
                 const Array<OneD, const NekDouble>& base0 = m_base[0]->GetBdata();
                 const Array<OneD, const NekDouble>& base1 = m_base[1]->GetBdata();
  
                 // Allocate temporary storage
                 Array<OneD,NekDouble> wsp0(5*wspsize);      // size wspsize
                 Array<OneD,NekDouble> wsp1(wsp0 + wspsize);  // size wspsize
                 Array<OneD,NekDouble> wsp2(wsp0 + 2*wspsize);// size 3*wspsize
  
                 if (!(m_base[0]->Collocation() && m_base[1]->Collocation()))
                 {
                     // MASS MATRIX OPERATION
                     // The following is being calculated:
                     // wsp0     = B   * u_hat = u
                     // wsp1     = W   * wsp0
                     // outarray = B^T * wsp1  = B^T * W * B * u_hat = M * u_hat
                     BwdTrans_SumFacKernel       (base0, base1, inarray,
                                                  wsp0, wsp2,true,true);
                     MultiplyByQuadratureMetric  (wsp0, wsp1);
                     IProductWRTBase_SumFacKernel(base0, base1, wsp1, outarray,
                                                  wsp2, true, true);
  
                     LaplacianMatrixOp_MatFree_Kernel(wsp0, wsp1, wsp2);
                 }
                 else
                 {
                     MultiplyByQuadratureMetric(inarray,outarray);
                     LaplacianMatrixOp_MatFree_Kernel(inarray, wsp1, wsp2);
                 }
  
                 // outarray = lambda * outarray + wsp1
                 //          = (lambda * M + L ) * u_hat
                 Vmath::Svtvp(m_ncoeffs, lambda, &outarray[0], 1,
                               &wsp1[0], 1, &outarray[0], 1);
             }
             else
             {
                 StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(
                     inarray,outarray,mkey);
             }
         }

Referenced by Nektar::StdRegions::StdQuadExp::v_HelmholtzMatrixOp(), and Nektar::StdRegions::StdTriExp::v_HelmholtzMatrixOp().

◆ v_IProductWRTBase_SumFacKernel()

virtual void Nektar::StdRegions::StdExpansion2D::v_IProductWRTBase_SumFacKernel	(	const Array< OneD, const NekDouble > &	base0,
		const Array< OneD, const NekDouble > &	base1,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		Array< OneD, NekDouble > &	wsp,
		bool	doCheckCollDir0,
		bool	doCheckCollDir1
	)

protectedpure virtual

Implemented in Nektar::StdRegions::StdTriExp, and Nektar::StdRegions::StdQuadExp.

Referenced by IProductWRTBase_SumFacKernel().

◆ v_LaplacianMatrixOp_MatFree()

void Nektar::StdRegions::StdExpansion2D::v_LaplacianMatrixOp_MatFree	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const StdRegions::StdMatrixKey &	mkey
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 276 of file StdExpansion2D.cpp.

         {
             if (mkey.GetNVarCoeff() == 0 && !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00)
                 &&!mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
             {
                 using std::max;
  
                 // This implementation is only valid when there are no
                 // coefficients associated to the Laplacian operator
                 int       nquad0  = m_base[0]->GetNumPoints();
                 int       nquad1  = m_base[1]->GetNumPoints();
                 int       nqtot   = nquad0*nquad1;
                 int       nmodes0 = m_base[0]->GetNumModes();
                 int       nmodes1 = m_base[1]->GetNumModes();
                 int       wspsize = max(max(max(nqtot,m_ncoeffs),nquad1*nmodes0),nquad0*nmodes1);
  
                 const Array<OneD, const NekDouble>& base0  = m_base[0]->GetBdata();
                 const Array<OneD, const NekDouble>& base1  = m_base[1]->GetBdata();
  
                 // Allocate temporary storage
                 Array<OneD,NekDouble> wsp0(4*wspsize);      // size wspsize
                 Array<OneD,NekDouble> wsp1(wsp0+wspsize);   // size 3*wspsize
  
                 if(!(m_base[0]->Collocation() && m_base[1]->Collocation()))
                 {
                     // LAPLACIAN MATRIX OPERATION
                     // wsp0 = u       = B   * u_hat
                     // wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
                     // wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
                     BwdTrans_SumFacKernel(base0,base1,inarray,wsp0,wsp1,true,true);
                     LaplacianMatrixOp_MatFree_Kernel(wsp0, outarray, wsp1);
                 }
                 else
                 {
                     LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp1);
                 }
             }
             else
             {
                 StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(
                     inarray,outarray,mkey);
             }
         }

References BwdTrans_SumFacKernel(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorCoeffD00, Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::m_ncoeffs.

Referenced by Nektar::StdRegions::StdQuadExp::v_LaplacianMatrixOp(), and Nektar::StdRegions::StdTriExp::v_LaplacianMatrixOp().

◆ v_PhysEvaluate() [1/2]

NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate	(	const Array< OneD, const NekDouble > &	coords,
		const Array< OneD, const NekDouble > &	physvals
	)

protectedvirtual

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

This function is a wrapper around the virtual function v_PhysEvaluate()

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

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

is evaluated using Lagrangian interpolants through the quadrature points:

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

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

Parameters

coords the coordinates of the single point

Returns: returns the value of the expansion at the single point

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::NodalTriExp.

Definition at line 115 of file StdExpansion2D.cpp.

         {
             ASSERTL2(coords[0] > -1 - NekConstants::kNekZeroTol,
                      "coord[0] < -1");
             ASSERTL2(coords[0] <  1 + NekConstants::kNekZeroTol,
                      "coord[0] >  1");
             ASSERTL2(coords[1] > -1 - NekConstants::kNekZeroTol,
                      "coord[1] < -1");
             ASSERTL2(coords[1] <  1 + NekConstants::kNekZeroTol,
                      "coord[1] >  1");
  
             Array<OneD, NekDouble> coll(2);
             LocCoordToLocCollapsed(coords,coll);
  
             const int nq0 = m_base[0]->GetNumPoints();
             const int nq1 = m_base[1]->GetNumPoints();
  
             Array<OneD, NekDouble> wsp(nq1);
             for (int i = 0; i < nq1; ++i)
             {
                 wsp[i] = StdExpansion::BaryEvaluate<0>(
                     coll[0], &physvals[0] + i * nq0);
             }
  
             return StdExpansion::BaryEvaluate<1>(coll[1], &wsp[0]);
         }

References ASSERTL2, Nektar::NekConstants::kNekZeroTol, Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), and Nektar::StdRegions::StdExpansion::m_base.

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

◆ v_PhysEvaluate() [2/2]

NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate	(	const Array< OneD, DNekMatSharedPtr > &	I,
		const Array< OneD, const NekDouble > &	physvals
	)

protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 144 of file StdExpansion2D.cpp.

         {
             NekDouble val;
             int i;
             int nq0 = m_base[0]->GetNumPoints();
             int nq1 = m_base[1]->GetNumPoints();
             Array<OneD, NekDouble> wsp1(nq1);
  
             // interpolate first coordinate direction
             for (i = 0; i < nq1;++i)
             {
                 wsp1[i] = Blas::Ddot(nq0, &(I[0]->GetPtr())[0], 1,
                                      &physvals[i * nq0], 1);
             }
  
             // interpolate in second coordinate direction
             val = Blas::Ddot(nq1, I[1]->GetPtr(), 1, wsp1, 1);
  
             return val;
         }

References Blas::Ddot(), and Nektar::StdRegions::StdExpansion::m_base.

Public Member Functions

Protected Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ StdExpansion2D() [1/3]

◆ StdExpansion2D() [2/3]

◆ StdExpansion2D() [3/3]

◆ ~StdExpansion2D()

Member Function Documentation

◆ BwdTrans_SumFacKernel()

◆ Integral()

◆ IProductWRTBase_SumFacKernel()

◆ PhysTensorDeriv()

◆ v_BwdTrans_SumFacKernel()

◆ v_GenStdMatBwdDeriv()

◆ v_GetCoordim()

◆ v_GetShapeDimension()

◆ v_HelmholtzMatrixOp_MatFree()

◆ v_IProductWRTBase_SumFacKernel()

◆ v_LaplacianMatrixOp_MatFree()

◆ v_PhysEvaluate() [1/2]

◆ v_PhysEvaluate() [2/2]