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 68 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::eGaussKronrodLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, 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, 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 154 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::eGaussKronrodLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, 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::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 430 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 238 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::eGaussKronrodLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, 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::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 69 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::eGaussKronrodLegendre, Nektar::LibUtilities::eGaussLobattoChebyshev, Nektar::LibUtilities::eGaussLobattoKronrodLegendre, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauKronrodMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauKronrodMLegendre, 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::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 149 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 311 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 422 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 320 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 417 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 339 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 332 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 347 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 360 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 373 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 390 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

Initial value:

= {
                PointsManager().RegisterCreator(PointsKey(0, eGaussGaussLegendre),           GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauMLegendre),          GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauPLegendre),          GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussLobattoLegendre),         GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussGaussChebyshev),          GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauMChebyshev),         GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauPChebyshev),         GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussLobattoChebyshev),        GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauMAlpha0Beta1),       GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauMAlpha0Beta2),       GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauMAlpha1Beta0),       GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauMAlpha2Beta0),       GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussKronrodLegendre),         GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauKronrodMLegendre),   GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussRadauKronrodMAlpha1Beta0),GaussPoints::Create),
                PointsManager().RegisterCreator(PointsKey(0, eGaussLobattoKronrodLegendre),  GaussPoints::Create)
        }

Definition at line 155 of file GaussPoints.h.