Nektar::LibUtilities::GaussPoints Class Reference

#include <GaussPoints.h>

Inheritance diagram for Nektar::LibUtilities::GaussPoints:

Public Member Functions
virtual	~GaussPoints ()
std::shared_ptr< NekMatrix< NekDouble > >	CreateMatrix (const PointsKey &pkey)
const std::shared_ptr< NekMatrix< NekDouble > >	GetI (const PointsKey &pkey)
const std::shared_ptr< NekMatrix< NekDouble > >	GetI (const Array< OneD, const NekDouble > &x)
const std::shared_ptr< NekMatrix< NekDouble > >	GetI (unsigned int numpoints, const Array< OneD, const NekDouble > &x)
std::shared_ptr< NekMatrix< NekDouble > >	CreateGPMatrix (const PointsKey &pkey)
const std::shared_ptr< NekMatrix< NekDouble > >	GetGalerkinProjection (const PointsKey &pkey)
	GaussPoints (const PointsKey &pkey)
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
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
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)

Static Public Member Functions
static std::shared_ptr< Points< NekDouble > >	Create (const PointsKey &pkey)

Private Member Functions
	GaussPoints ()
	These should not be called. All creation is done using the constructor requiring the key, declared above. More...
	GaussPoints (const GaussPoints &points)
void	CalculatePoints ()
void	CalculateWeights ()
void	CalculateDerivMatrix ()
void	CalculateInterpMatrix (unsigned int npts, const Array< OneD, const NekDouble > &xpoints, Array< OneD, NekDouble > &interp)
std::shared_ptr< NekMatrix< NekDouble > >	CalculateGalerkinProjectionMatrix (const PointsKey &pkey)
NekDouble	LagrangeInterpolant (NekDouble x, int npts, const Array< OneD, const NekDouble > &xpts, const Array< OneD, const NekDouble > &funcvals)
	functions used by the Kronrod points More...
NekDouble	LagrangePoly (NekDouble x, int pt, int npts, const Array< OneD, const NekDouble > &xpts)
NekDouble	LagrangePolyDeriv (NekDouble x, int pt, int npts, const Array< OneD, const NekDouble > &xpts)

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 Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual void	CalculateBaryWeights ()
	This function calculates the barycentric weights used for enhanced interpolation speed. More...
	Points (const PointsKey &key)
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 GaussPoints.h.

Constructor & Destructor Documentation

~GaussPoints()

virtual Nektar::LibUtilities::GaussPoints::~GaussPoints ( )

inlinevirtual

Definition at line 50 of file GaussPoints.h.

    {
    }

GaussPoints() [1/3]

Nektar::LibUtilities::GaussPoints::GaussPoints ( const PointsKey &  pkey )

inline

Definition at line 73 of file GaussPoints.h.

                                       : PointsBaseType(pkey)
    {
        namespace pl = std::placeholders;
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussGaussLegendre),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauMLegendre),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauPLegendre),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussLobattoLegendre),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussGaussChebyshev),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauMChebyshev),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauPChebyshev),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussLobattoChebyshev),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha0Beta1),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha0Beta2),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha1Beta0),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha2Beta0),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussKronrodLegendre),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauKronrodMLegendre),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussRadauKronrodMAlpha1Beta0),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eGaussLobattoKronrodLegendre),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eFourierEvenlySpaced),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, ePolyEvenlySpaced),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eBoundaryLayerPoints),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_InterpManager.RegisterCreator(
            PointsKey(0, eBoundaryLayerPointsRev),
            std::bind(&GaussPoints::CreateMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussGaussLegendre),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauMLegendre),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauPLegendre),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussLobattoLegendre),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussGaussChebyshev),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauMChebyshev),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauPChebyshev),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussLobattoChebyshev),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha0Beta1),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha0Beta2),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha1Beta0),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauMAlpha2Beta0),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussKronrodLegendre),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauKronrodMLegendre),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussRadauKronrodMAlpha1Beta0),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eGaussLobattoKronrodLegendre),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eFourierEvenlySpaced),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, ePolyEvenlySpaced),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eBoundaryLayerPoints),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
        m_GalerkinProjectionManager.RegisterCreator(
            PointsKey(0, eBoundaryLayerPointsRev),
            std::bind(&GaussPoints::CreateGPMatrix, this, pl::_1));
    }

References CreateGPMatrix(), CreateMatrix(), Nektar::LibUtilities::eBoundaryLayerPoints, Nektar::LibUtilities::eBoundaryLayerPointsRev, Nektar::LibUtilities::eFourierEvenlySpaced, Nektar::LibUtilities::eGaussGaussChebyshev, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, Nektar::LibUtilities::eGaussRadauMAlpha0Beta1, Nektar::LibUtilities::eGaussRadauMChebyshev, Nektar::LibUtilities::eGaussRadauMLegendre, Nektar::LibUtilities::eGaussRadauPChebyshev, Nektar::LibUtilities::eGaussRadauPLegendre, Nektar::LibUtilities::ePolyEvenlySpaced, Nektar::LibUtilities::Points< NekDouble >::m_GalerkinProjectionManager, and Nektar::LibUtilities::Points< NekDouble >::m_InterpManager.

GaussPoints() [2/3]

Nektar::LibUtilities::GaussPoints::GaussPoints ( )

private

These should not be called. All creation is done using the constructor requiring the key, declared above.

GaussPoints() [3/3]

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

private

Member Function Documentation

CalculateDerivMatrix()

void Nektar::LibUtilities::GaussPoints::CalculateDerivMatrix ( )

privatevirtual

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

Definition at line 184 of file GaussPoints.cpp.

{
    // Allocate the derivative matrix
    PointsBaseType::CalculateDerivMatrix();
 
    int numpoints = m_pointsKey.GetNumPoints();
    int totpoints = m_pointsKey.GetTotNumPoints();
    Array<OneD, NekDouble> dmtempSharedArray =
        Array<OneD, NekDouble>(totpoints * totpoints);
    NekDouble *dmtemp = dmtempSharedArray.data();
 
    switch (m_pointsKey.GetPointsType())
    {
        case eGaussGaussLegendre:
            Polylib::Dgj(dmtemp, m_points[0].data(), numpoints, 0.0, 0.0);
            break;
 
        case eGaussRadauMLegendre:
            Polylib::Dgrjm(dmtemp, m_points[0].data(), numpoints, 0.0, 0.0);
            break;
 
        case eGaussRadauPLegendre:
            Polylib::Dgrjp(dmtemp, m_points[0].data(), numpoints, 0.0, 0.0);
            break;
 
        case eGaussLobattoLegendre:
            Polylib::Dglj(dmtemp, m_points[0].data(), numpoints, 0.0, 0.0);
            break;
 
        case eGaussGaussChebyshev:
            Polylib::Dgj(dmtemp, m_points[0].data(), numpoints, -0.5, -0.5);
            break;
 
        case eGaussRadauMChebyshev:
            Polylib::Dgrjm(dmtemp, m_points[0].data(), numpoints, -0.5, -0.5);
            break;
 
        case eGaussRadauPChebyshev:
            Polylib::Dgrjp(dmtemp, m_points[0].data(), numpoints, -0.5, -0.5);
            break;
 
        case eGaussLobattoChebyshev:
            Polylib::Dglj(dmtemp, m_points[0].data(), numpoints, -0.5, -0.5);
            break;
 
        case eGaussRadauMAlpha0Beta1:
            Polylib::Dgrjm(dmtemp, m_points[0].data(), numpoints, 0.0, 1.0);
            break;
 
        case eGaussRadauMAlpha0Beta2:
            Polylib::Dgrjm(dmtemp, m_points[0].data(), numpoints, 0.0, 2.0);
            break;
 
        case eGaussRadauMAlpha1Beta0:
            Polylib::Dgrjm(dmtemp, m_points[0].data(), numpoints, 1.0, 0.0);
            break;
 
        case eGaussRadauMAlpha2Beta0:
            Polylib::Dgrjm(dmtemp, m_points[0].data(), numpoints, 2.0, 0.0);
            break;
 
        case eGaussKronrodLegendre:
        case eGaussRadauKronrodMLegendre:
        case eGaussRadauKronrodMAlpha1Beta0:
        case eGaussLobattoKronrodLegendre:
        {
            for (unsigned int i = 0; i < m_pointsKey.GetNumPoints(); ++i)
            {
                for (unsigned int j = 0; j < m_pointsKey.GetNumPoints(); ++j)
                {
                    (*m_derivmatrix[0])(i, j) = LagrangePolyDeriv(
                        m_points[0][i], j, m_pointsKey.GetNumPoints(),
                        m_points[0]);
                }
            }
            return;
        }
        break;
 
        default:
            NEKERROR(ErrorUtil::efatal,
                     "Unknown Gauss quadrature point distribution requested");
    }
 
    std::copy(dmtemp, dmtemp + totpoints * totpoints,
              m_derivmatrix[0]->begin());
}

References Nektar::LibUtilities::Points< NekDouble >::CalculateDerivMatrix(), CellMLToNektar.pycml::copy(), Polylib::Dgj(), Polylib::Dglj(), Polylib::Dgrjm(), Polylib::Dgrjp(), Nektar::ErrorUtil::efatal, Nektar::LibUtilities::eGaussGaussChebyshev, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, Nektar::LibUtilities::eGaussRadauMAlpha0Beta1, Nektar::LibUtilities::eGaussRadauMChebyshev, Nektar::LibUtilities::eGaussRadauMLegendre, Nektar::LibUtilities::eGaussRadauPChebyshev, Nektar::LibUtilities::eGaussRadauPLegendre, Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::LibUtilities::PointsKey::GetTotNumPoints(), LagrangePolyDeriv(), Nektar::LibUtilities::Points< NekDouble >::m_derivmatrix, Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, and NEKERROR.

CalculateGalerkinProjectionMatrix()

std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::GaussPoints::CalculateGalerkinProjectionMatrix ( const PointsKey &  pkey )

private

Definition at line 491 of file GaussPoints.cpp.

{
    int numpointsfrom = pkey.GetNumPoints();
    int numpointsto   = GetNumPoints();
 
    Array<OneD, const NekDouble> weightsfrom;
 
    weightsfrom = PointsManager()[pkey]->GetW();
 
    std::shared_ptr<NekMatrix<NekDouble>> Interp = GetI(pkey);
 
    Array<OneD, NekDouble> GalProj(numpointsfrom * numpointsto);
 
    // set up inner product matrix and multiply by inverse of
    // diagaonal mass matrix
    for (int i = 0; i < numpointsto; ++i)
    {
        Vmath::Vmul(numpointsfrom, Interp->GetPtr().get() + i * numpointsfrom,
                    1, &weightsfrom[0], 1, &GalProj[0] + i, numpointsto);
        Vmath::Smul(numpointsfrom, 1.0 / m_weights[i], &GalProj[0] + i,
                    numpointsto, &GalProj[0] + i, numpointsto);
    }
 
    NekDouble *t = GalProj.data();
    std::shared_ptr<NekMatrix<NekDouble>> returnval(
        MemoryManager<NekMatrix<NekDouble>>::AllocateSharedPtr(
            numpointsto, numpointsfrom, t));
 
    return returnval;
}

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

Referenced by CreateGPMatrix().

CalculateInterpMatrix()

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

private

Definition at line 272 of file GaussPoints.cpp.

{
    switch (m_pointsKey.GetPointsType())
    {
        case eGaussGaussLegendre:
            Polylib::Imgj(interp.data(), m_points[0].data(), xpoints.data(),
                          GetNumPoints(), npts, 0.0, 0.0);
            break;
 
        case eGaussRadauMLegendre:
            Polylib::Imgrjm(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, 0.0, 0.0);
            break;
 
        case eGaussRadauPLegendre:
            Polylib::Imgrjp(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, 0.0, 0.0);
            break;
 
        case eGaussLobattoLegendre:
            Polylib::Imglj(interp.data(), m_points[0].data(), xpoints.data(),
                           GetNumPoints(), npts, 0.0, 0.0);
            break;
 
        case eGaussGaussChebyshev:
            Polylib::Imgj(interp.data(), m_points[0].data(), xpoints.data(),
                          GetNumPoints(), npts, -0.5, -0.5);
            break;
 
        case eGaussRadauMChebyshev:
            Polylib::Imgrjm(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, -0.5, -0.5);
            break;
 
        case eGaussRadauPChebyshev:
            Polylib::Imgrjp(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, -0.5, -0.5);
            break;
 
        case eGaussLobattoChebyshev:
            Polylib::Imglj(interp.data(), m_points[0].data(), xpoints.data(),
                           GetNumPoints(), npts, -0.5, -0.5);
            break;
 
        case eGaussRadauMAlpha0Beta1:
            Polylib::Imgrjm(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, 0.0, 1.0);
            break;
 
        case eGaussRadauMAlpha0Beta2:
            Polylib::Imgrjm(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, 0.0, 2.0);
            break;
 
        case eGaussRadauMAlpha1Beta0:
            Polylib::Imgrjm(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, 1.0, 0.0);
            break;
 
        case eGaussRadauMAlpha2Beta0:
            Polylib::Imgrjm(interp.data(), m_points[0].data(), xpoints.data(),
                            GetNumPoints(), npts, 2.0, 0.0);
            break;
 
        case eGaussKronrodLegendre:
        case eGaussRadauKronrodMLegendre:
        case eGaussRadauKronrodMAlpha1Beta0:
        case eGaussLobattoKronrodLegendre:
        {
            for (unsigned int i = 0; i < npts; ++i)
            {
                for (unsigned int j = 0; j < m_pointsKey.GetNumPoints(); ++j)
                {
                    interp[i + j * npts] = LagrangePoly(
                        xpoints[i], j, m_pointsKey.GetNumPoints(), m_points[0]);
                }
            }
        }
        break;
 
        default:
            NEKERROR(ErrorUtil::efatal,
                     "Unknown Gauss quadrature point distribution requested");
    }
}

References Nektar::Array< OneD, DataType >::data(), Nektar::ErrorUtil::efatal, Nektar::LibUtilities::eGaussGaussChebyshev, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, Nektar::LibUtilities::eGaussRadauMAlpha0Beta1, Nektar::LibUtilities::eGaussRadauMChebyshev, Nektar::LibUtilities::eGaussRadauMLegendre, Nektar::LibUtilities::eGaussRadauPChebyshev, Nektar::LibUtilities::eGaussRadauPLegendre, Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::Points< NekDouble >::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetPointsType(), Polylib::Imgj(), Polylib::Imglj(), Polylib::Imgrjm(), Polylib::Imgrjp(), LagrangePoly(), Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, and NEKERROR.

Referenced by GetI().

CalculatePoints()

void Nektar::LibUtilities::GaussPoints::CalculatePoints ( )

privatevirtual

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

Definition at line 83 of file GaussPoints.cpp.

{
    // Allocate the storage for points and weights
    PointsBaseType::CalculatePoints();
    PointsBaseType::CalculateWeights();
 
    int numpoints = m_pointsKey.GetNumPoints();
 
    switch (m_pointsKey.GetPointsType())
    {
        case eGaussGaussLegendre:
            Polylib::zwgj(m_points[0].data(), m_weights.data(), numpoints, 0.0,
                          0.0);
            break;
 
        case eGaussRadauMLegendre:
            Polylib::zwgrjm(m_points[0].data(), m_weights.data(), numpoints,
                            0.0, 0.0);
            break;
 
        case eGaussRadauPLegendre:
            Polylib::zwgrjp(m_points[0].data(), m_weights.data(), numpoints,
                            0.0, 0.0);
            break;
 
        case eGaussLobattoLegendre:
            Polylib::zwglj(m_points[0].data(), m_weights.data(), numpoints, 0.0,
                           0.0);
            break;
 
        case eGaussGaussChebyshev:
            Polylib::zwgj(m_points[0].data(), m_weights.data(), numpoints, -0.5,
                          -0.5);
            break;
 
        case eGaussRadauMChebyshev:
            Polylib::zwgrjm(m_points[0].data(), m_weights.data(), numpoints,
                            -0.5, -0.5);
            break;
 
        case eGaussRadauPChebyshev:
            Polylib::zwgrjp(m_points[0].data(), m_weights.data(), numpoints,
                            -0.5, -0.5);
            break;
 
        case eGaussLobattoChebyshev:
            Polylib::zwglj(m_points[0].data(), m_weights.data(), numpoints,
                           -0.5, -0.5);
            break;
 
        case eGaussRadauMAlpha0Beta1:
            Polylib::zwgrjm(m_points[0].data(), m_weights.data(), numpoints,
                            0.0, 1.0);
            break;
 
        case eGaussRadauMAlpha0Beta2:
            Polylib::zwgrjm(m_points[0].data(), m_weights.data(), numpoints,
                            0.0, 2.0);
            break;
 
        case eGaussRadauMAlpha1Beta0:
            Polylib::zwgrjm(m_points[0].data(), m_weights.data(), numpoints,
                            1.0, 0.0);
            break;
 
        case eGaussRadauMAlpha2Beta0:
            Polylib::zwgrjm(m_points[0].data(), m_weights.data(), numpoints,
                            2.0, 0.0);
            break;
 
        case eGaussKronrodLegendre:
            Polylib::zwgk(m_points[0].data(), m_weights.data(), numpoints, 0.0,
                          0.0);
            break;
 
        case eGaussRadauKronrodMLegendre:
            Polylib::zwrk(m_points[0].data(), m_weights.data(), numpoints, 0.0,
                          0.0);
            break;
 
        case eGaussRadauKronrodMAlpha1Beta0:
            Polylib::zwrk(m_points[0].data(), m_weights.data(), numpoints, 1.0,
                          0.0);
            break;
 
        case eGaussLobattoKronrodLegendre:
            Polylib::zwlk(m_points[0].data(), m_weights.data(), numpoints, 0.0,
                          0.0);
            break;
 
        default:
            NEKERROR(ErrorUtil::efatal,
                     "Unknown Gauss quadrature point distribution requested");
    }
}

References Nektar::LibUtilities::Points< NekDouble >::CalculatePoints(), Nektar::LibUtilities::Points< NekDouble >::CalculateWeights(), Nektar::Array< OneD, DataType >::data(), Nektar::ErrorUtil::efatal, Nektar::LibUtilities::eGaussGaussChebyshev, Nektar::LibUtilities::eGaussGaussLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, Nektar::LibUtilities::eGaussRadauMAlpha0Beta1, Nektar::LibUtilities::eGaussRadauMChebyshev, Nektar::LibUtilities::eGaussRadauMLegendre, Nektar::LibUtilities::eGaussRadauPChebyshev, Nektar::LibUtilities::eGaussRadauPLegendre, Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, Nektar::LibUtilities::Points< NekDouble >::m_weights, NEKERROR, Polylib::zwgj(), Polylib::zwgk(), Polylib::zwglj(), Polylib::zwgrjm(), Polylib::zwgrjp(), Polylib::zwlk(), and Polylib::zwrk().

CalculateWeights()

void Nektar::LibUtilities::GaussPoints::CalculateWeights ( )

privatevirtual

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

Definition at line 179 of file GaussPoints.cpp.

{
    // For Gauss Quadrature, this is done as part of the points computation
}

Create()

std::shared_ptr< Points< NekDouble > > Nektar::LibUtilities::GaussPoints::Create ( const PointsKey &  pkey )

static

Definition at line 360 of file GaussPoints.cpp.

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

CreateGPMatrix()

std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::GaussPoints::CreateGPMatrix

(

const PointsKey &

pkey

)

Definition at line 481 of file GaussPoints.cpp.

{
    std::shared_ptr<NekMatrix<NekDouble>> returnval =
        CalculateGalerkinProjectionMatrix(pkey);
 
    // Delegate to function below
    return returnval;
}

References CalculateGalerkinProjectionMatrix().

Referenced by GaussPoints().

CreateMatrix()

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

(

const PointsKey &

pkey

)

Definition at line 370 of file GaussPoints.cpp.

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

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

Referenced by GaussPoints().

GetGalerkinProjection()

const std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::GaussPoints::GetGalerkinProjection ( const PointsKey &  pkey )

virtual

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

Definition at line 475 of file GaussPoints.cpp.

{
    return m_GalerkinProjectionManager[pkey];
}

References Nektar::LibUtilities::Points< NekDouble >::m_GalerkinProjectionManager.

GetI() [1/3]

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

virtual

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

Definition at line 391 of file GaussPoints.cpp.

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

References GetI().

GetI() [2/3]

const std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::GaussPoints::GetI ( const PointsKey &  pkey )

virtual

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

Definition at line 382 of file GaussPoints.cpp.

{
    ASSERTL0(pkey.GetPointsDim() == 1,
             "Gauss 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.

Referenced by CalculateGalerkinProjectionMatrix(), CreateMatrix(), and GetI().

GetI() [3/3]

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

virtual

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

Definition at line 400 of file GaussPoints.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().

LagrangeInterpolant()

NekDouble Nektar::LibUtilities::GaussPoints::LagrangeInterpolant ( NekDouble  x, int  npts, const Array< OneD, const NekDouble > &  xpts, const Array< OneD, const NekDouble > &  funcvals  )

private

functions used by the Kronrod points

Definition at line 416 of file GaussPoints.cpp.

{
    NekDouble sum = 0.0;
 
    for (int i = 0; i < npts; ++i)
    {
        sum += funcvals[i] * LagrangePoly(x, i, npts, xpts);
    }
    return sum;
}

References LagrangePoly().

LagrangePoly()

NekDouble Nektar::LibUtilities::GaussPoints::LagrangePoly ( NekDouble  x, int  pt, int  npts, const Array< OneD, const NekDouble > &  xpts  )

private

Definition at line 429 of file GaussPoints.cpp.

{
    NekDouble h = 1.0;
 
    for (int i = 0; i < pt; ++i)
    {
        h = h * (x - xpts[i]) / (xpts[pt] - xpts[i]);
    }
 
    for (int i = pt + 1; i < npts; ++i)
    {
        h = h * (x - xpts[i]) / (xpts[pt] - xpts[i]);
    }
 
    return h;
}

Referenced by CalculateInterpMatrix(), and LagrangeInterpolant().

LagrangePolyDeriv()

NekDouble Nektar::LibUtilities::GaussPoints::LagrangePolyDeriv ( NekDouble  x, int  pt, int  npts, const Array< OneD, const NekDouble > &  xpts  )

private

Definition at line 447 of file GaussPoints.cpp.

{
    NekDouble h;
    NekDouble y = 0.0;
 
    for (int j = 0; j < npts; ++j)
    {
        if (j != pt)
        {
            h = 1.0;
            for (int i = 0; i < npts; ++i)
            {
                if (i != pt)
                {
                    if (i != j)
                    {
                        h = h * (x - xpts[i]);
                    }
                    h = h / (xpts[pt] - xpts[i]);
                }
            }
            y = y + h;
        }
    }
    return y;
}

Referenced by CalculateDerivMatrix().

Member Data Documentation

initPointsManager

bool Nektar::LibUtilities::GaussPoints::initPointsManager

staticprivate

Definition at line 199 of file GaussPoints.h.