Nektar::LibUtilities::FourierPoints Class Reference

#include <FourierPoints.h>

Inheritance diagram for Nektar::LibUtilities::FourierPoints:

Collaboration diagram for Nektar::LibUtilities::FourierPoints:

Public Member Functions
virtual	~FourierPoints ()
boost::shared_ptr< NekMatrix < NekDouble > >	CreateMatrix (const PointsKey &pkey)
const MatrixSharedPtrType	GetI (const PointsKey &pkey)
const MatrixSharedPtrType	GetI (const Array< OneD, const NekDouble > &x)
const MatrixSharedPtrType	GetI (unsigned int numpoints, const Array< OneD, const NekDouble > &x)
	FourierPoints (const PointsKey &key)
Public Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual	~Points ()
virtual void	Initialize (void)
unsigned int	GetPointsDim () const
unsigned int	GetNumPoints () const
unsigned int	GetTotNumPoints () const
PointsType	GetPointsType () const
const Array< OneD, const DataType > &	GetZ () const
const Array< OneD, const DataType > &	GetW () const
void	GetZW (Array< OneD, const DataType > &z, Array< OneD, const DataType > &w) const
void	GetPoints (Array< OneD, const DataType > &x) const
void	GetPoints (Array< OneD, const DataType > &x, Array< OneD, const DataType > &y) const
void	GetPoints (Array< OneD, const DataType > &x, Array< OneD, const DataType > &y, Array< OneD, const DataType > &z) const
const MatrixSharedPtrType &	GetD (Direction dir=xDir) const
virtual const MatrixSharedPtrType	GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y)
virtual const MatrixSharedPtrType	GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y, const Array< OneD, const DataType > &z)
virtual const MatrixSharedPtrType	GetGalerkinProjection (const PointsKey &pkey)

Static Public Member Functions
static boost::shared_ptr < PointsBaseType >	Create (const PointsKey &key)

Private Member Functions
	FourierPoints ()
	Default constructor should not be called except by Create method. More...
	FourierPoints (const FourierPoints &points)
	Copy constructor should not be called. More...
void	CalculatePoints ()
void	CalculateWeights ()
void	CalculateDerivMatrix ()
void	CalculateInterpMatrix (unsigned int npts, const Array< OneD, const NekDouble > &xpoints, Array< OneD, NekDouble > &interp)
NekDouble	PeriodicSincFunction (const NekDouble x, const NekDouble h)

Additional Inherited Members
Public Types inherited from Nektar::LibUtilities::Points< NekDouble >
typedef NekDouble	DataType
typedef boost::shared_ptr < NekMatrix< DataType > >	MatrixSharedPtrType
Protected Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
	Points (const PointsKey &key)
Protected Attributes inherited from Nektar::LibUtilities::Points< NekDouble >
PointsKey	m_pointsKey
Array< OneD, DataType >	m_points [3]
Array< OneD, DataType >	m_weights
MatrixSharedPtrType	m_derivmatrix [3]
NekManager< PointsKey, NekMatrix< DataType > , PointsKey::opLess >	m_InterpManager
NekManager< PointsKey, NekMatrix< DataType > , PointsKey::opLess >	m_GalerkinProjectionManager

Detailed Description

Definition at line 51 of file FourierPoints.h.

Constructor & Destructor Documentation

virtual Nektar::LibUtilities::FourierPoints::~FourierPoints ( )

inlinevirtual

Definition at line 54 of file FourierPoints.h.

                {
                }            

Nektar::LibUtilities::FourierPoints::FourierPoints ( const PointsKey &  key )

inline

Definition at line 65 of file FourierPoints.h.

References CreateMatrix(), Nektar::LibUtilities::eFourierEvenlySpaced, Nektar::LibUtilities::eGaussGaussChebyshev, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauMAlpha0Beta1, Nektar::LibUtilities::eGaussRadauMAlpha0Beta2, Nektar::LibUtilities::eGaussRadauMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauMAlpha2Beta0, Nektar::LibUtilities::eGaussRadauMChebyshev, Nektar::LibUtilities::eGaussRadauMLegendre, Nektar::LibUtilities::eGaussRadauPChebyshev, Nektar::LibUtilities::eGaussRadauPLegendre, Nektar::LibUtilities::ePolyEvenlySpaced, and Nektar::LibUtilities::Points< NekDouble >::m_InterpManager.

                                                   :PointsBaseType(key)
                {
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussGaussLegendre),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauMLegendre),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauPLegendre),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussLobattoLegendre),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussGaussChebyshev),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauMChebyshev),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauPChebyshev),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussLobattoChebyshev),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauMAlpha0Beta1),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauMAlpha0Beta2),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauMAlpha1Beta0),
                                                                    boost::bind(&FourierPoints::CreateMatrix, this, _1));
                                    m_InterpManager.RegisterCreator(PointsKey(0, eGaussRadauMAlpha2Beta0),
                                                                    boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, ePolyEvenlySpaced),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                    m_InterpManager.RegisterCreator(PointsKey(0, eFourierEvenlySpaced),
                        boost::bind(&FourierPoints::CreateMatrix, this, _1));
                }

Nektar::LibUtilities::FourierPoints::FourierPoints ( )

private

Default constructor should not be called except by Create method.

Nektar::LibUtilities::FourierPoints::FourierPoints ( const FourierPoints &  points )

private

Copy constructor should not be called.

Member Function Documentation

void Nektar::LibUtilities::FourierPoints::CalculateDerivMatrix ( )

privatevirtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 90 of file FourierPoints.cpp.

References Nektar::LibUtilities::Points< DataT >::CalculateDerivMatrix(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::Points< NekDouble >::m_derivmatrix, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, and npts.

        {
            //// Allocate the derivative matrix.
            Points<NekDouble>::CalculateDerivMatrix();

            unsigned int npts = m_pointsKey.GetNumPoints();

            for(unsigned int i=1;i<npts;++i)
            {
                m_derivmatrix[0]->SetValue(i,i, 0.0);
            }

            for(unsigned int i=1;i<npts;++i)
            {
                m_derivmatrix[0]->SetValue(0,i, -0.5*M_PI*pow(-1.0,NekDouble(i))*cos(M_PI*i/npts)/sin(M_PI*i/npts));
            }

            for(unsigned int i=1;i<npts;++i)
            {
                for(unsigned int j=0;j<npts;++j)
                {
                    m_derivmatrix[0]->SetValue(i,j, (*m_derivmatrix[0])(0,(j-i+npts)%npts));
                }
            }           
        }

void Nektar::LibUtilities::FourierPoints::CalculateInterpMatrix ( unsigned int  npts, const Array< OneD, const NekDouble > &  xpoints, Array< OneD, NekDouble > &  interp  )

private

Definition at line 165 of file FourierPoints.cpp.

References Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, npts, and PeriodicSincFunction().

Referenced by GetI().

        {
            const NekDouble h = 2.0/m_pointsKey.GetNumPoints();
            for(unsigned int i=0;i<npts;++i)
            {
                for(unsigned int j=0;j<m_pointsKey.GetNumPoints();++j)
                {
                    interp[i*m_pointsKey.GetNumPoints()+j] = PeriodicSincFunction(M_PI*(xpoints[i]-m_points[0][j]),h);
                }
            }
        }

void Nektar::LibUtilities::FourierPoints::CalculatePoints ( )

privatevirtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 49 of file FourierPoints.cpp.

References ASSERTL0, Nektar::LibUtilities::Points< NekDouble >::CalculatePoints(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, and npts.

        {
            // Allocate the storage for points
            PointsBaseType::CalculatePoints();

            unsigned int npts = m_pointsKey.GetNumPoints();
            ASSERTL0(!(npts%2), "Fourier points need to be of even order");

            if(npts==1)
            {
                m_points[0][0] = 0.0;
            }
            else
            {
                NekDouble dx = 2.0/(NekDouble)(npts);
                for(unsigned int i=0;i<npts;++i)
                {
                    m_points[0][i] = -1.0 + i*dx;
                }
            }
        }

void Nektar::LibUtilities::FourierPoints::CalculateWeights ( )

privatevirtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 71 of file FourierPoints.cpp.

References Nektar::LibUtilities::Points< NekDouble >::CalculateWeights(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, Nektar::LibUtilities::Points< NekDouble >::m_weights, and npts.

        {
            // Allocate the storage for points
            PointsBaseType::CalculateWeights();

            unsigned int npts = m_pointsKey.GetNumPoints();
            if(npts==1)
            {
                m_weights[0] = 1.0; //midpoint rule
            }
            else
            {
                for(unsigned int i=0; i<npts; ++i)
                {
                    m_weights[i] =  1.0/(NekDouble)npts;
                }
            }
        }

boost::shared_ptr< Points< NekDouble > > Nektar::LibUtilities::FourierPoints::Create ( const PointsKey &  key )

static

Definition at line 116 of file FourierPoints.cpp.

        {
            boost::shared_ptr<Points<NekDouble> > returnval(MemoryManager<FourierPoints>::AllocateSharedPtr(key));

            returnval->Initialize();

            return returnval;
        }

boost::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::FourierPoints::CreateMatrix

(

const PointsKey &

pkey

)

Delegate to function below.

Definition at line 126 of file FourierPoints.cpp.

References GetI(), Nektar::LibUtilities::PointsKey::GetNumPoints(), and Nektar::LibUtilities::PointsManager().

Referenced by FourierPoints().

        {
            int numpoints = pkey.GetNumPoints();
            Array<OneD, const NekDouble> xpoints;

            PointsManager()[pkey]->GetPoints(xpoints);

            /// Delegate to function below.
            return GetI(numpoints, xpoints);
        }

const boost::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::FourierPoints::GetI ( const PointsKey &  pkey )

virtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 137 of file FourierPoints.cpp.

References ASSERTL0, Nektar::LibUtilities::PointsKey::GetPointsDim(), and Nektar::LibUtilities::Points< NekDouble >::m_InterpManager.

Referenced by CreateMatrix(), and GetI().

        {
            ASSERTL0(pkey.GetPointsDim()==1, "Fourier Points can only interp to other 1d point distributions");

            return m_InterpManager[pkey];
        }

const boost::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::FourierPoints::GetI ( const Array< OneD, const NekDouble > &  x )

virtual

Delegate to function below.

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 144 of file FourierPoints.cpp.

References GetI().

        {
            int numpoints = 1;

            /// Delegate to function below.
            return GetI(numpoints, x);
        }

const boost::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::FourierPoints::GetI ( unsigned int  numpoints, const Array< OneD, const NekDouble > &  x  )

virtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 152 of file FourierPoints.cpp.

References CalculateInterpMatrix(), and Nektar::LibUtilities::Points< NekDouble >::GetNumPoints().

        {
            Array<OneD, NekDouble> interp(GetNumPoints()*numpoints);

            CalculateInterpMatrix(numpoints, x, interp);

            NekDouble* t = interp.data();
            unsigned int np = GetNumPoints();
            boost::shared_ptr< NekMatrix<NekDouble> > returnval(MemoryManager<NekMatrix<NekDouble> >::AllocateSharedPtr(numpoints,np,t));

            return returnval;
        }

NekDouble Nektar::LibUtilities::FourierPoints::PeriodicSincFunction ( const NekDouble  x, const NekDouble  h  )

private

Definition at line 177 of file FourierPoints.cpp.

Referenced by CalculateInterpMatrix().

        {
            // This formula is based upon a mapped version of 
            // the periodic sinc presented in Trefethen's "Spectral Methods
            // in Matlab"

            NekDouble y = 1.0;
            
            if(fabs(x)>1.0e-12)
            {
                y = sin(M_PI*x/(M_PI*h))/((2.0/h)*tan(0.5*x));
            }

            return y;
        }