Nektar::LibUtilities::FourierPoints Class Reference

#include <FourierPoints.h>

Inheritance diagram for Nektar::LibUtilities::FourierPoints:

Public Member Functions
virtual	~FourierPoints ()
std::shared_ptr< NekMatrix< NekDouble > >	CreateMatrix (const PointsKey &pkey)
	FourierPoints (const PointsKey &key)
Public Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual	~Points ()
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
const Array< OneD, const NekDouble > &	GetBaryWeights () 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
const MatrixSharedPtrType	GetI (const PointsKey &key)
const MatrixSharedPtrType	GetI (const Array< OneD, const DataType > &x)
const MatrixSharedPtrType	GetI (unsigned int uint, const Array< OneD, const DataType > &x)
const MatrixSharedPtrType	GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y)
const MatrixSharedPtrType	GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y, const Array< OneD, const DataType > &z)
const MatrixSharedPtrType	GetGalerkinProjection (const PointsKey &pkey)

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

Protected Member Functions
virtual const MatrixSharedPtrType	v_GetI (const PointsKey &pkey) override
virtual const MatrixSharedPtrType	v_GetI (const Array< OneD, const NekDouble > &x) override
virtual const MatrixSharedPtrType	v_GetI (unsigned int numpoints, const Array< OneD, const NekDouble > &x) override
Protected Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual void	v_Initialize (void)
virtual void	v_CalculateBaryWeights ()
	This function calculates the barycentric weights used for enhanced interpolation speed. More...
	Points (const PointsKey &key)
virtual const MatrixSharedPtrType	v_GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y)
virtual const MatrixSharedPtrType	v_GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y, const Array< OneD, const DataType > &z)
virtual const MatrixSharedPtrType	v_GetGalerkinProjection (const PointsKey &pkey)

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...
virtual void	v_CalculatePoints () override
virtual void	v_CalculateWeights () override
virtual void	v_CalculateDerivMatrix () override
void	CalculateInterpMatrix (unsigned int npts, const Array< OneD, const NekDouble > &xpoints, Array< OneD, NekDouble > &interp)
NekDouble	PeriodicSincFunction (const NekDouble x, const NekDouble h)

Static Private Attributes
static bool	initPointsManager []

Additional Inherited Members
Public Types inherited from Nektar::LibUtilities::Points< NekDouble >
typedef NekDouble	DataType
typedef std::shared_ptr< NekMatrix< DataType > >	MatrixSharedPtrType
Protected Attributes inherited from Nektar::LibUtilities::Points< NekDouble >
PointsKey	m_pointsKey
	Points type for this points distributions. More...
Array< OneD, DataType >	m_points [3]
	Storage for the point locations, allowing for up to a 3D points storage. More...
Array< OneD, DataType >	m_weights
	Quadrature weights for the weights. More...
Array< OneD, DataType >	m_bcweights
	Barycentric weights. More...
MatrixSharedPtrType	m_derivmatrix [3]
	Derivative matrices. More...
NekManager< PointsKey, NekMatrix< DataType >, PointsKey::opLess >	m_InterpManager
NekManager< PointsKey, NekMatrix< DataType >, PointsKey::opLess >	m_GalerkinProjectionManager

Detailed Description

Definition at line 47 of file FourierPoints.h.

Constructor & Destructor Documentation

~FourierPoints()

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

inlinevirtual

Definition at line 50 of file FourierPoints.h.

    {
    }

FourierPoints() [1/3]

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

inline

Definition at line 59 of file FourierPoints.h.

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

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

FourierPoints() [2/3]

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

private

Default constructor should not be called except by Create method.

FourierPoints() [3/3]

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

private

Copy constructor should not be called.

Member Function Documentation

CalculateInterpMatrix()

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

private

Definition at line 176 of file FourierPoints.cpp.

{
    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);
        }
    }
}

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

Referenced by v_GetI().

Create()

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

static

Definition at line 120 of file FourierPoints.cpp.

{
    std::shared_ptr<Points<NekDouble>> returnval(
        MemoryManager<FourierPoints>::AllocateSharedPtr(key));
 
    returnval->Initialize();
 
    return returnval;
}

CreateMatrix()

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

(

const PointsKey &

pkey

)

Delegate to function below.

Definition at line 130 of file FourierPoints.cpp.

{
    int numpoints = pkey.GetNumPoints();
    Array<OneD, const NekDouble> xpoints;
 
    PointsManager()[pkey]->GetPoints(xpoints);
 
    /// Delegate to function below.
    return GetI(numpoints, xpoints);
}

References Nektar::LibUtilities::Points< NekDouble >::GetI(), Nektar::LibUtilities::PointsKey::GetNumPoints(), and Nektar::LibUtilities::PointsManager().

Referenced by FourierPoints().

PeriodicSincFunction()

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

private

Definition at line 191 of file FourierPoints.cpp.

{
    // 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;
}

Referenced by CalculateInterpMatrix().

v_CalculateDerivMatrix()

void Nektar::LibUtilities::FourierPoints::v_CalculateDerivMatrix ( )

overrideprivatevirtual

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

Definition at line 90 of file FourierPoints.cpp.

{
    //// Allocate the derivative matrix.
    Points<NekDouble>::v_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));
        }
    }
}

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

v_CalculatePoints()

void Nektar::LibUtilities::FourierPoints::v_CalculatePoints ( )

overrideprivatevirtual

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

Definition at line 49 of file FourierPoints.cpp.

{
    // Allocate the storage for points
    PointsBaseType::v_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;
        }
    }
}

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

v_CalculateWeights()

void Nektar::LibUtilities::FourierPoints::v_CalculateWeights ( )

overrideprivatevirtual

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

Definition at line 71 of file FourierPoints.cpp.

{
    // Allocate the storage for points
    PointsBaseType::v_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;
        }
    }
}

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

v_GetI() [1/3]

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

overrideprotectedvirtual

Delegate to function below.

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

Definition at line 151 of file FourierPoints.cpp.

{
    int numpoints = 1;
 
    /// Delegate to function below.
    return GetI(numpoints, x);
}

References Nektar::LibUtilities::Points< NekDouble >::GetI().

v_GetI() [2/3]

const std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::FourierPoints::v_GetI ( const PointsKey &  pkey )

overrideprotectedvirtual

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

Definition at line 142 of file FourierPoints.cpp.

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

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

v_GetI() [3/3]

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

overrideprotectedvirtual

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

Definition at line 160 of file FourierPoints.cpp.

{
    Array<OneD, NekDouble> interp(GetNumPoints() * numpoints);
 
    CalculateInterpMatrix(numpoints, x, interp);
 
    NekDouble *t    = interp.data();
    unsigned int np = GetNumPoints();
    std::shared_ptr<NekMatrix<NekDouble>> returnval(
        MemoryManager<NekMatrix<NekDouble>>::AllocateSharedPtr(numpoints, np,
                                                               t));
 
    return returnval;
}

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

Member Data Documentation

initPointsManager

bool Nektar::LibUtilities::FourierPoints::initPointsManager

staticprivate

Initial value:

= {PointsManager().RegisterCreator(
    PointsKey(0, eFourierEvenlySpaced), FourierPoints::Create)}

Definition at line 115 of file FourierPoints.h.