quadrilateral_2d_8.h

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//    |  /           |
//    ' /   __| _` | __|  _ \   __|
//    . \  |   (   | |   (   |\__ `
//   _|\_\_|  \__,_|\__|\___/ ____/
//                   Multi-Physics
//
//  License:         BSD License
//                   Kratos default license: kratos/license.txt
//
//  Main authors:    Riccardo Rossi
//                   Janosch Stascheit
//                   Felix Nagel
//  contributors:    Hoang Giang Bui
//                   Josep Maria Carbonell
//
 
#pragma once
 
// System includes
 
// External includes
 
// Project includes
#include "geometries/line_2d_3.h"
#include "utilities/integration_utilities.h"
#include "integration/quadrilateral_gauss_legendre_integration_points.h"
 
namespace Kratos
{
template<class TPointType> class Quadrilateral2D8
    : public Geometry<TPointType>
{
public:
    typedef Geometry<TPointType> BaseType;
 
    typedef Line2D3<TPointType> EdgeType;
 
    KRATOS_CLASS_POINTER_DEFINITION( Quadrilateral2D8 );
 
    typedef GeometryData::IntegrationMethod IntegrationMethod;
 
    typedef typename BaseType::GeometriesArrayType GeometriesArrayType;
 
    typedef TPointType PointType;
 
    //typedef typename BaseType::CoordinatesArrayType CoordinatesArrayType;
 
 
    typedef typename BaseType::IndexType IndexType;
 
    typedef typename BaseType::SizeType SizeType;
 
    typedef  typename BaseType::PointsArrayType PointsArrayType;
 
    typedef typename BaseType::IntegrationPointType IntegrationPointType;
 
    typedef typename BaseType::IntegrationPointsArrayType IntegrationPointsArrayType;
 
    typedef typename BaseType::IntegrationPointsContainerType IntegrationPointsContainerType;
 
    typedef typename BaseType::ShapeFunctionsValuesContainerType
    ShapeFunctionsValuesContainerType;
 
    typedef typename BaseType::ShapeFunctionsLocalGradientsContainerType
    ShapeFunctionsLocalGradientsContainerType;
 
    typedef typename BaseType::JacobiansType JacobiansType;
 
    typedef typename BaseType::ShapeFunctionsGradientsType ShapeFunctionsGradientsType;
 
    typedef typename BaseType::ShapeFunctionsSecondDerivativesType
    ShapeFunctionsSecondDerivativesType;
 
 
    typedef typename BaseType::ShapeFunctionsThirdDerivativesType
    ShapeFunctionsThirdDerivativesType;
 
    typedef typename BaseType::NormalType NormalType;
 
    typedef typename BaseType::CoordinatesArrayType CoordinatesArrayType;
 
 
    Quadrilateral2D8( const PointType& Point1, const PointType& Point2,
                      const PointType& Point3, const PointType& Point4,
                      const PointType& Point5, const PointType& Point6,
                      const PointType& Point7, const PointType& Point8
                    )
        : BaseType( PointsArrayType(), &msGeometryData )
    {
        this->Points().push_back( typename PointType::Pointer( new PointType( Point1 ) ) );
        this->Points().push_back( typename PointType::Pointer( new PointType( Point2 ) ) );
        this->Points().push_back( typename PointType::Pointer( new PointType( Point3 ) ) );
        this->Points().push_back( typename PointType::Pointer( new PointType( Point4 ) ) );
        this->Points().push_back( typename PointType::Pointer( new PointType( Point5 ) ) );
        this->Points().push_back( typename PointType::Pointer( new PointType( Point6 ) ) );
        this->Points().push_back( typename PointType::Pointer( new PointType( Point7 ) ) );
        this->Points().push_back( typename PointType::Pointer( new PointType( Point8 ) ) );
    }
 
    Quadrilateral2D8( typename PointType::Pointer pPoint1, typename PointType::Pointer pPoint2,
                      typename PointType::Pointer pPoint3, typename PointType::Pointer pPoint4,
                      typename PointType::Pointer pPoint5, typename PointType::Pointer pPoint6,
                      typename PointType::Pointer pPoint7, typename PointType::Pointer pPoint8 )
        : BaseType( PointsArrayType(), &msGeometryData )
    {
        this->Points().push_back( pPoint1 );
        this->Points().push_back( pPoint2 );
        this->Points().push_back( pPoint3 );
        this->Points().push_back( pPoint4 );
        this->Points().push_back( pPoint5 );
        this->Points().push_back( pPoint6 );
        this->Points().push_back( pPoint7 );
        this->Points().push_back( pPoint8 );
    }
 
    Quadrilateral2D8( const PointsArrayType& ThisPoints )
        : BaseType( ThisPoints, &msGeometryData )
    {
        if ( this->PointsNumber() != 8 )
            KRATOS_ERROR << "Invalid points number. Expected 8, given " << this->PointsNumber() << std::endl;
    }
 
    explicit Quadrilateral2D8(
        const IndexType GeometryId,
        const PointsArrayType& rThisPoints
    ) : BaseType(GeometryId, rThisPoints, &msGeometryData)
    {
        KRATOS_ERROR_IF( this->PointsNumber() != 8 ) << "Invalid points number. Expected 8, given " << this->PointsNumber() << std::endl;
    }
 
    explicit Quadrilateral2D8(
        const std::string& rGeometryName,
        const PointsArrayType& rThisPoints
    ) : BaseType(rGeometryName, rThisPoints, &msGeometryData)
    {
        KRATOS_ERROR_IF(this->PointsNumber() != 8) << "Invalid points number. Expected 8, given " << this->PointsNumber() << std::endl;
    }
 
    Quadrilateral2D8( Quadrilateral2D8 const& rOther )
        : BaseType( rOther )
    {
    }
 
    template<class TOtherPointType> Quadrilateral2D8( Quadrilateral2D8<TOtherPointType> const& rOther )
        : BaseType( rOther )
    {
    }
 
    ~Quadrilateral2D8() override {}
 
    GeometryData::KratosGeometryFamily GetGeometryFamily() const override
    {
        return GeometryData::KratosGeometryFamily::Kratos_Quadrilateral;
    }
 
    GeometryData::KratosGeometryType GetGeometryType() const override
    {
        return GeometryData::KratosGeometryType::Kratos_Quadrilateral2D8;
    }
 
    Quadrilateral2D8& operator=( const Quadrilateral2D8& rOther )
    {
        BaseType::operator=( rOther );
 
        return *this;
    }
 
    template<class TOtherPointType>
    Quadrilateral2D8& operator=( Quadrilateral2D8<TOtherPointType> const & rOther )
    {
        BaseType::operator=( rOther );
 
        return *this;
    }
 
    typename BaseType::Pointer Create(
        const IndexType NewGeometryId,
        PointsArrayType const& rThisPoints
        ) const override
    {
        return typename BaseType::Pointer( new Quadrilateral2D8( NewGeometryId, rThisPoints ) );
    }
 
    typename BaseType::Pointer Create(
        const IndexType NewGeometryId,
        const BaseType& rGeometry
        ) const override
    {
        auto p_geometry = typename BaseType::Pointer( new Quadrilateral2D8( NewGeometryId, rGeometry.Points() ) );
        p_geometry->SetData(rGeometry.GetData());
        return p_geometry;
    }
 
    SizeType PointsNumberInDirection(IndexType LocalDirectionIndex) const override
    {
        if ((LocalDirectionIndex == 0) || (LocalDirectionIndex == 1)) {
            return 3;
        }
        KRATOS_ERROR << "Possible direction index reaches from 0-1. Given direction index: "
            << LocalDirectionIndex << std::endl;
    }
 
    double Length() const override
    {
        array_1d<double,3> point;
        point[0] = 1.0/3.0; point[1] = 1.0/3.0; point[2] = 1.0/3.0;
        return sqrt( fabs( DeterminantOfJacobian( point ) ) );
    }
 
    double Area() const override
    {
        return IntegrationUtilities::ComputeArea2DGeometry(*this);
    }
 
    // TODO: Code activated in June 2023
    // /**
    //  * @brief This method calculates and returns the volume of this geometry.
    //  * @return Error, the volume of a 2D geometry is not defined
    //  * @see Length()
    //  * @see Area()
    //  * @see Volume()
    //  */
    // double Volume() const override
    // {
    //     KRATOS_ERROR << "Quadrilateral2D8:: Method not well defined. Replace with DomainSize() instead." << std::endl;
    //     return 0.0;
    // }
 
    double DomainSize() const override
    {
        return Area();
    }
 
    bool IsInside(
        const CoordinatesArrayType& rPoint,
        CoordinatesArrayType& rResult,
        const double Tolerance = std::numeric_limits<double>::epsilon()
        ) const override
    {
        this->PointLocalCoordinates( rResult, rPoint );
 
        if ( std::abs( rResult[0] ) <= (1.0 + Tolerance) )
        {
            if ( std::abs( rResult[1] ) <= (1.0 + Tolerance) )
            {
                return true;
            }
        }
 
        return false;
    }
 
    JacobiansType& Jacobian( JacobiansType& rResult,
                                     IntegrationMethod ThisMethod ) const override
    {
        //getting derivatives of shape functions
        ShapeFunctionsGradientsType shape_functions_gradients =
            CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        //getting values of shape functions
        Matrix shape_functions_values =
            CalculateShapeFunctionsIntegrationPointsValues( ThisMethod );
        //workaround by riccardo...
 
        if ( rResult.size() != this->IntegrationPointsNumber( ThisMethod ) )
        {
            // KLUDGE: While there is a bug in ublas
            // vector resize, I have to put this beside resizing!!
            JacobiansType temp( this->IntegrationPointsNumber( ThisMethod ) );
            rResult.swap( temp );
        }
 
        //loop over all integration points
        for ( unsigned int pnt = 0; pnt < this->IntegrationPointsNumber( ThisMethod ); pnt++ )
        {
            //defining single jacobian matrix
            Matrix jacobian = ZeroMatrix( 2, 2 );
            //loop over all nodes
 
            for ( unsigned int i = 0; i < this->PointsNumber(); i++ )
            {
                jacobian( 0, 0 ) += ( this->GetPoint( i ).X() ) * ( shape_functions_gradients[pnt]( i, 0 ) );
                jacobian( 0, 1 ) += ( this->GetPoint( i ).X() ) * ( shape_functions_gradients[pnt]( i, 1 ) );
                jacobian( 1, 0 ) += ( this->GetPoint( i ).Y() ) * ( shape_functions_gradients[pnt]( i, 0 ) );
                jacobian( 1, 1 ) += ( this->GetPoint( i ).Y() ) * ( shape_functions_gradients[pnt]( i, 1 ) );
            }
 
            rResult[pnt] = jacobian;
        }//end of loop over all integration points
 
        return rResult;
    }
 
    JacobiansType& Jacobian( JacobiansType& rResult,
                                     IntegrationMethod ThisMethod,
                     Matrix & DeltaPosition ) const override
    {
        //getting derivatives of shape functions
        ShapeFunctionsGradientsType shape_functions_gradients =
            CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        //getting values of shape functions
        Matrix shape_functions_values =
            CalculateShapeFunctionsIntegrationPointsValues( ThisMethod );
        //workaround by riccardo...
 
        if ( rResult.size() != this->IntegrationPointsNumber( ThisMethod ) )
        {
            // KLUDGE: While there is a bug in ublas
            // vector resize, I have to put this beside resizing!!
            JacobiansType temp( this->IntegrationPointsNumber( ThisMethod ) );
            rResult.swap( temp );
        }
 
        //loop over all integration points
        for ( unsigned int pnt = 0; pnt < this->IntegrationPointsNumber( ThisMethod ); pnt++ )
        {
            //defining single jacobian matrix
            Matrix jacobian = ZeroMatrix( 2, 2 );
            //loop over all nodes
 
            for ( unsigned int i = 0; i < this->PointsNumber(); i++ )
            {
                jacobian( 0, 0 ) += ( this->GetPoint( i ).X() - DeltaPosition(i,0) ) * ( shape_functions_gradients[pnt]( i, 0 ) );
                jacobian( 0, 1 ) += ( this->GetPoint( i ).X() - DeltaPosition(i,0) ) * ( shape_functions_gradients[pnt]( i, 1 ) );
                jacobian( 1, 0 ) += ( this->GetPoint( i ).Y() - DeltaPosition(i,1) ) * ( shape_functions_gradients[pnt]( i, 0 ) );
                jacobian( 1, 1 ) += ( this->GetPoint( i ).Y() - DeltaPosition(i,1) ) * ( shape_functions_gradients[pnt]( i, 1 ) );
            }
 
            rResult[pnt] = jacobian;
        }//end of loop over all integration points
 
        return rResult;
    }
 
    Matrix& Jacobian( Matrix& rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod ) const override
    {
        // Setting up size of jacobian matrix
        if (rResult.size1() != 2 || rResult.size2() != 2)
            rResult.resize( 2, 2 , false);
        rResult.clear();
        //derivatives of shape functions
        ShapeFunctionsGradientsType shape_functions_gradients = CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        Matrix ShapeFunctionsGradientInIntegrationPoint = shape_functions_gradients( IntegrationPointIndex );
        //values of shape functions in integration points
        DenseVector<double> ShapeFunctionsValuesInIntegrationPoint = ZeroVector( 8 );
        ShapeFunctionsValuesInIntegrationPoint =row( CalculateShapeFunctionsIntegrationPointsValues( ThisMethod ), IntegrationPointIndex );
 
        //Elements of jacobian matrix (e.g. J(1,1) = dX1/dXi1)
        // Loop over all nodes
        for ( unsigned int i = 0; i < this->PointsNumber(); i++ )
        {
            rResult( 0, 0 ) +=
                ( this->GetPoint( i ).X() ) * ( ShapeFunctionsGradientInIntegrationPoint( i, 0 ) );
            rResult( 0, 1 ) +=
                ( this->GetPoint( i ).X() ) * ( ShapeFunctionsGradientInIntegrationPoint( i, 1 ) );
            rResult( 1, 0 ) +=
                ( this->GetPoint( i ).Y() ) * ( ShapeFunctionsGradientInIntegrationPoint( i, 0 ) );
            rResult( 1, 1 ) +=
                ( this->GetPoint( i ).Y() ) * ( ShapeFunctionsGradientInIntegrationPoint( i, 1 ) );
        }
 
        return rResult;
    }
 
    Matrix& Jacobian( Matrix& rResult, const CoordinatesArrayType& rPoint ) const override
    {
        // Setting up size of jacobian matrix
        if (rResult.size1() != 2 || rResult.size2() != 2)
            rResult.resize( 2, 2 , false);
        rResult.clear();
        //derivatives of shape functions
        Matrix shape_functions_gradients;
        shape_functions_gradients = ShapeFunctionsLocalGradients( shape_functions_gradients, rPoint );
        //Elements of jacobian matrix (e.g. J(1,1) = dX1/dXi1)
        //loop over all nodes
 
        for ( unsigned int i = 0; i < this->PointsNumber(); i++ )
        {
            rResult( 0, 0 ) += ( this->GetPoint( i ).X() ) * ( shape_functions_gradients( i, 0 ) );
            rResult( 0, 1 ) += ( this->GetPoint( i ).X() ) * ( shape_functions_gradients( i, 1 ) );
            rResult( 1, 0 ) += ( this->GetPoint( i ).Y() ) * ( shape_functions_gradients( i, 0 ) );
            rResult( 1, 1 ) += ( this->GetPoint( i ).Y() ) * ( shape_functions_gradients( i, 1 ) );
        }
 
        return rResult;
    }
 
    Vector& DeterminantOfJacobian(
        Vector& rResult,
        IntegrationMethod ThisMethod
        ) const override
    {
        if( rResult.size() != this->IntegrationPointsNumber( ThisMethod ) )
            rResult.resize( this->IntegrationPointsNumber( ThisMethod ), false );
 
        Matrix J( this->WorkingSpaceDimension(), this->LocalSpaceDimension());
        for ( unsigned int pnt = 0; pnt < this->IntegrationPointsNumber( ThisMethod ); pnt++ ) {
            this->Jacobian( J, pnt, ThisMethod);
            rResult[pnt] = (( J( 0, 0 )*J( 1, 1 ) ) - ( J( 0, 1 )*J( 1, 0 ) ) );
        }
        return rResult;
    }
 
    double DeterminantOfJacobian( IndexType IntegrationPointIndex, IntegrationMethod ThisMethod ) const override
    {
        Matrix jacobian( 2, 2 );
        jacobian = Jacobian( jacobian, IntegrationPointIndex, ThisMethod );
        return(( jacobian( 0, 0 )*jacobian( 1, 1 ) ) - ( jacobian( 0, 1 )*jacobian( 1, 0 ) ) );
    }
 
    double DeterminantOfJacobian( const CoordinatesArrayType& rPoint ) const override
    {
        Matrix jacobian( 2, 2 );
        jacobian = Jacobian( jacobian, rPoint );
        return(( jacobian( 0, 0 )*jacobian( 1, 1 ) ) - ( jacobian( 0, 1 )*jacobian( 1, 0 ) ) );
    }
 
    JacobiansType& InverseOfJacobian( JacobiansType& rResult, IntegrationMethod ThisMethod ) const override
    {
        //workaround by riccardo
        if ( rResult.size() != this->IntegrationPointsNumber( ThisMethod ) )
        {
            // KLUDGE: While there is a bug in ublas
            // vector resize, I have to put this beside resizing!!
            JacobiansType temp( this->IntegrationPointsNumber( ThisMethod ) );
            rResult.swap( temp );
        }
 
        //loop over all integration points
        for ( unsigned int pnt = 0; pnt < this->IntegrationPointsNumber( ThisMethod ); pnt++ )
        {
            Matrix tempMatrix( 2, 2 );
            rResult[pnt] = InverseOfJacobian( tempMatrix, pnt, ThisMethod );
        }
 
        return rResult;
    }
 
    Matrix& InverseOfJacobian( Matrix& rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod ) const override
    {
        // Current jacobian
        Matrix tempMatrix = ZeroMatrix( 2, 2 );
        tempMatrix = Jacobian( tempMatrix, IntegrationPointIndex, ThisMethod );
 
        // Determinant of jacobian
        const double det_j = DeterminantOfJacobian( IntegrationPointIndex, ThisMethod );
 
        // Checking for singularity
        if ( det_j == 0.00 )
        {
            KRATOS_ERROR << "Zero determinant of jacobian." << *this << std::endl;
        }
 
        // Setting up result matrix
        rResult.resize( 2, 2 , false);
 
        // Filling matrix
        rResult( 0, 0 ) = ( tempMatrix( 1, 1 ) ) / ( det_j );
 
        rResult( 1, 0 ) = -( tempMatrix( 1, 0 ) ) / ( det_j );
 
        rResult( 0, 1 ) = -( tempMatrix( 0, 1 ) ) / ( det_j );
 
        return rResult;
    }
 
    Matrix& InverseOfJacobian( Matrix& rResult, const CoordinatesArrayType& rPoint ) const override
    {
        //current jacobian
        Matrix tempMatrix;
        tempMatrix.resize( 2, 2, false );
        tempMatrix = this->Jacobian( tempMatrix, rPoint );
        //deteminant of Jacobian
        double det_j = DeterminantOfJacobian( rPoint );
        //checking for singularity
 
        if ( det_j == 0.0 )
        {
            KRATOS_ERROR << "Zero determinant of jacobian." << *this << std::endl;
        }
 
        //setting up result matrix
        rResult.resize( 2, 2 , false);
 
        //filling matrix
        rResult( 0, 0 ) = ( tempMatrix( 1, 1 ) ) / ( det_j );
 
        rResult( 1, 0 ) = -( tempMatrix( 1, 0 ) ) / ( det_j );
 
        rResult( 0, 1 ) = -( tempMatrix( 0, 1 ) ) / ( det_j );
 
        rResult( 1, 1 ) = ( tempMatrix( 0, 0 ) ) / ( det_j );
 
        return rResult;
    }
 
 
    SizeType EdgesNumber() const override
    {
        return 4;
    }
 
    GeometriesArrayType GenerateEdges() const override
    {
        GeometriesArrayType edges = GeometriesArrayType();
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 0 ), this->pGetPoint( 1 ), this->pGetPoint( 4 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 1 ), this->pGetPoint( 2 ), this->pGetPoint( 5 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 2 ), this->pGetPoint( 3 ), this->pGetPoint( 6 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 3 ), this->pGetPoint( 0 ), this->pGetPoint( 7 ) ) );
        return edges;
    }
 
    double ShapeFunctionValue( IndexType ShapeFunctionIndex,
                                       const CoordinatesArrayType& rPoint ) const override
    {
        switch ( ShapeFunctionIndex )
        {
            // Primary nodes
            case 0:
                return -(( 1.0 - rPoint[0] )*( 1.0 - rPoint[1] )
                        *( 1.0 + rPoint[0] + rPoint[1] ) ) / 4.0;
            case 1:
                return -(( 1.0 + rPoint[0] )*( 1.0 - rPoint[1] )
                        *( 1.0 - rPoint[0] + rPoint[1] ) ) / 4.0;
            case 2:
                return -(( 1.0 + rPoint[0] )*( 1.0 + rPoint[1] )
                        *( 1.0 - rPoint[0] - rPoint[1] ) ) / 4.0;
            case 3:
                return -(( 1.0 - rPoint[0] )*( 1.0 + rPoint[1] )
                        *( 1.0 + rPoint[0] - rPoint[1] ) ) / 4.0;
            // Secondary nodes
            case 4:
                return  (( 1.0 -rPoint[0]*rPoint[0] )
                        *( 1.0 - rPoint[1] ) ) / 2.0;
            case 5:
                return  (( 1.0 + rPoint[0] )
                        *( 1.0 - rPoint[1]*rPoint[1] ) ) / 2.0 ;
            case 6:
                return  (( 1.0 -rPoint[0]*rPoint[0] )
                        *( 1.0 + rPoint[1] ) ) / 2.0 ;
            case 7:
                return  (( 1.0 -rPoint[0] )
                        *( 1.0 - rPoint[1]*rPoint[1] ) ) / 2.0 ;
            default:
                KRATOS_ERROR << "Wrong index of shape function!" << *this << std::endl;
        }
 
        return 0;
    }
 
    Vector& ShapeFunctionsValues (
        Vector &rResult,
        const CoordinatesArrayType& rCoordinates
        ) const override
    {
        if(rResult.size() != 8)
        {
            rResult.resize(8,false);
        }
 
        // Primary nodes
        rResult[0] = -(( 1.0 - rCoordinates[0] )*( 1.0 - rCoordinates[1] )
                     *( 1.0 + rCoordinates[0] + rCoordinates[1] ) ) / 4.0;
        rResult[1] = -(( 1.0 + rCoordinates[0] )*( 1.0 - rCoordinates[1] )
                     *( 1.0 - rCoordinates[0] + rCoordinates[1] ) ) / 4.0;
        rResult[2] = -(( 1.0 + rCoordinates[0] )*( 1.0 + rCoordinates[1] )
                     *( 1.0 - rCoordinates[0] - rCoordinates[1] ) ) / 4.0;
        rResult[3] = -(( 1.0 - rCoordinates[0] )*( 1.0 + rCoordinates[1] )
                     *( 1.0 + rCoordinates[0] - rCoordinates[1] ) ) / 4.0;
 
        // Secondary nodes
        rResult[4] =  (( 1.0 -rCoordinates[0]*rCoordinates[0] )
                     *( 1.0 - rCoordinates[1] ) ) / 2.0;
        rResult[5] =  (( 1.0 + rCoordinates[0] )
                     *( 1.0 - rCoordinates[1]*rCoordinates[1] ) ) / 2.0 ;
        rResult[6] =  (( 1.0 -rCoordinates[0]*rCoordinates[0] )
                     *( 1.0 + rCoordinates[1] ) ) / 2.0 ;
        rResult[7] =  (( 1.0 -rCoordinates[0] )
                     *( 1.0 - rCoordinates[1]*rCoordinates[1] ) ) / 2.0 ;
 
        return rResult;
    }
    void ShapeFunctionsIntegrationPointsGradients(
        ShapeFunctionsGradientsType& rResult,
        IntegrationMethod ThisMethod ) const override
    {
        const unsigned int integration_points_number =
            msGeometryData.IntegrationPointsNumber( ThisMethod );
 
        if ( integration_points_number == 0 )
        {
            KRATOS_ERROR << "This integration method is not supported" << *this << std::endl;
        }
 
        //workaround by riccardo
        if ( rResult.size() != integration_points_number )
        {
            // KLUDGE: While there is a bug in ublas
            // vector resize, I have to put this beside resizing!!
            ShapeFunctionsGradientsType temp( integration_points_number );
            rResult.swap( temp );
        }
 
        //calculating the local gradients
        ShapeFunctionsGradientsType locG =
            CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
 
        //getting the inverse jacobian matrices
        JacobiansType temp( integration_points_number );
 
        JacobiansType invJ = InverseOfJacobian( temp, ThisMethod );
 
        //loop over all integration points
        for ( unsigned int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            rResult[pnt].resize( 4, 2, false );
 
            for ( unsigned int i = 0; i < 4; i++ )
            {
                for ( unsigned int j = 0; j < 2; j++ )
                {
                    rResult[pnt]( i, j ) =
                        ( locG[pnt]( i, 0 ) * invJ[pnt]( j, 0 ) )
                        + ( locG[pnt]( i, 1 ) * invJ[pnt]( j, 1 ) );
                }
            }
        }//end of loop over integration points
    }
 
    std::string Info() const override
    {
        return "2 dimensional quadrilateral with eight nodes in 2D space";
    }
 
    void PrintInfo( std::ostream& rOStream ) const override
    {
        rOStream << "2 dimensional quadrilateral with eight nodes in 2D space";
    }
 
    void PrintData( std::ostream& rOStream ) const override
    {
        // Base Geometry class PrintData call
        BaseType::PrintData( rOStream );
        std::cout << std::endl;
 
        // If the geometry has valid points, calculate and output its data
        if (this->AllPointsAreValid()) {
            Matrix jacobian;
            this->Jacobian( jacobian, PointType() );
            rOStream << "    Jacobian in the origin\t : " << jacobian;
        }
    }
 
    virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients(
        IntegrationMethod ThisMethod )
    {
        ShapeFunctionsGradientsType localGradients
        = CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        const int integration_points_number
        = msGeometryData.IntegrationPointsNumber( ThisMethod );
        ShapeFunctionsGradientsType Result( integration_points_number );
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Result[pnt] = localGradients[pnt];
        }
 
        return Result;
    }
 
    virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients()
    {
        IntegrationMethod ThisMethod = msGeometryData.DefaultIntegrationMethod();
        ShapeFunctionsGradientsType localGradients
        = CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        const int integration_points_number
        = msGeometryData.IntegrationPointsNumber( ThisMethod );
        ShapeFunctionsGradientsType Result( integration_points_number );
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Result[pnt] = localGradients[pnt];
        }
 
        return Result;
    }
 
    Matrix& ShapeFunctionsLocalGradients(
        Matrix& rResult,
        const CoordinatesArrayType& rPoint
        ) const override
    {
        // Setting up result matrix
        rResult.resize( 8, 2 , false);
        noalias( rResult ) = ZeroMatrix( 8, 2 );
 
        // Primary nodes
        rResult( 0, 0 ) = - ((-1.0 + rPoint[1])*( 2.0 * rPoint[0] + rPoint[1])) / 4.0;
        rResult( 0, 1 ) = - ((-1.0 + rPoint[0])*( 2.0 * rPoint[1] + rPoint[0])) / 4.0;
 
        rResult( 1, 0 ) =   ((-1.0 + rPoint[1])*(-2.0 * rPoint[0] + rPoint[1])) / 4.0;
        rResult( 1, 1 ) =   (( 1.0 + rPoint[0])*( 2.0 * rPoint[1] - rPoint[0])) / 4.0;
 
        rResult( 2, 0 ) =   (( 1.0 + rPoint[1])*( 2.0 * rPoint[0] + rPoint[1])) / 4.0;
        rResult( 2, 1 ) =   (( 1.0 + rPoint[0])*( 2.0 * rPoint[1] + rPoint[0])) / 4.0;
 
        rResult( 3, 0 ) = - (( 1.0 + rPoint[1])*(-2.0 * rPoint[0] + rPoint[1])) / 4.0;
        rResult( 3, 1 ) = - ((-1.0 + rPoint[0])*( 2.0 * rPoint[1] - rPoint[0])) / 4.0;
 
        // Secondary nodes
        rResult( 4, 0 ) =   rPoint[0] * (-1.0 + rPoint[1]);
        rResult( 4, 1 ) =   ((1.0 + rPoint[0]) * (-1.0 + rPoint[0])) / 2.0;
 
        rResult( 5, 0 ) = - ((1.0 + rPoint[1]) * (-1.0 + rPoint[1])) / 2.0;
        rResult( 5, 1 ) = - rPoint[1] * ( 1.0 + rPoint[0]);
 
        rResult( 6, 0 ) = - rPoint[0] * ( 1.0 + rPoint[1]);
        rResult( 6, 1 ) = - ((1.0 + rPoint[0]) * (-1.0 + rPoint[0])) / 2.0;
 
        rResult( 7, 0 ) =   ((1.0 + rPoint[1]) * (-1.0 + rPoint[1])) / 2.0;
        rResult( 7, 1 ) =   rPoint[1] * (-1.0 + rPoint[0]);
 
        return( rResult );
    }
 
    Matrix& PointsLocalCoordinates( Matrix& rResult ) const override
    {
        rResult.resize( 8, 2 , false);
        noalias( rResult ) = ZeroMatrix( 8, 2 );
        rResult( 0, 0 ) = -1.0;
        rResult( 0, 1 ) = -1.0;
        rResult( 1, 0 ) =  1.0;
        rResult( 1, 1 ) = -1.0;
        rResult( 2, 0 ) =  1.0;
        rResult( 2, 1 ) =  1.0;
        rResult( 3, 0 ) = -1.0;
        rResult( 3, 1 ) =  1.0;
        rResult( 4, 0 ) =  0.0;
        rResult( 4, 1 ) = -1.0;
        rResult( 5, 0 ) =  1.0;
        rResult( 5, 1 ) =  0.0;
        rResult( 6, 0 ) =  0.0;
        rResult( 6, 1 ) =  1.0;
        rResult( 7, 0 ) = -1.0;
        rResult( 7, 1 ) =  0.0;
        return rResult;
    }
 
    virtual Matrix& ShapeFunctionsGradients( Matrix& rResult, PointType& rPoint )
    {
        rResult.resize( 8, 2 , false);
        noalias( rResult ) = ZeroMatrix( 8, 2 );
 
        const CoordinatesArrayType& Coords = rPoint.Coordinates();
 
        rResult = ShapeFunctionsLocalGradients(rResult, Coords);
 
        return rResult;
    }
 
    ShapeFunctionsSecondDerivativesType& ShapeFunctionsSecondDerivatives( ShapeFunctionsSecondDerivativesType& rResult, const CoordinatesArrayType& rPoint ) const override
    {
        if ( rResult.size() != this->PointsNumber() )
        {
            // KLUDGE: While there is a bug in ublas
            // vector resize, I have to put this beside resizing!!
            ShapeFunctionsGradientsType temp( this->PointsNumber() );
            rResult.swap( temp );
        }
 
        for ( unsigned  int i = 0; i < this->PointsNumber(); i++ )
        {
            rResult[i].resize( 2, 2 , false);
            noalias( rResult[i] ) = ZeroMatrix( 2, 2 );
        }
 
        rResult[0]( 0, 0 ) = ( 4.0 - 4 * rPoint[1] ) / 8.0;
 
        rResult[0]( 0, 1 ) = ( -2.0 ) * ( 1.0 + 2.0 * rPoint[0] + rPoint[1] - 1.0 ) / 8.0
                             + (( -1.0 + rPoint[1] ) * ( -2.0 ) ) / 8.0;
        rResult[0]( 1, 0 ) = ( -2.0 ) * ( 1.0 + rPoint[0] + 2.0 * rPoint[1] - 1.0 ) / 8.0
                             + (( -1.0 + rPoint[0] ) * ( -2.0 ) ) / 8.0;
        rResult[0]( 1, 1 ) = (( -1.0 + rPoint[0] ) * ( -2.0 ) * ( 2.0 ) ) / 8.0;
 
        rResult[1]( 0, 0 ) = -(( -1.0 + rPoint[1] ) * ( -2.0 ) * ( -2.0 ) ) / 8.0;
        rResult[1]( 0, 1 ) = ( 2.0 ) * ( 1.0 - 2.0 * rPoint[0] + rPoint[1] - 1.0 ) / 8.0
                             - (( -1.0 + rPoint[1] ) * ( -2.0 ) ) / 8.0;
        rResult[1]( 1, 0 ) = ( -1.0 + rPoint[0] - 2.0 * rPoint[1] + 1.0 ) * ( -2.0 ) / 8.0
                             + (( 1.0 + rPoint[0] ) * ( -2.0 ) ) / 8.0;
        rResult[1]( 1, 1 ) = (( 1.0 + rPoint[0] ) * ( -2.0 ) * ( -2.0 ) ) / 8.0;
 
        rResult[2]( 0, 0 ) = -(( 1.0 + rPoint[1] ) * ( 2.0 ) * ( -2.0 ) ) / 8.0;
        rResult[2]( 0, 1 ) = -(( 1.0 ) * ( -1.0 + 2.0 * rPoint[0] + rPoint[1] + 1.0 ) * ( -2.0 ) ) / 8.0
                             - (( 1.0 + rPoint[1] ) * ( -2.0 ) ) / 8.0;
        rResult[2]( 1, 0 ) = -(( 1.0 ) * ( -1.0 + rPoint[0] + 2.0 * rPoint[1] + 1.0 ) * ( -2.0 ) ) / 8.0
                             - (( 1.0 + rPoint[0] ) * ( -2.0 ) ) / 8.0;
        rResult[2]( 1, 1 ) = -(( 1.0 + rPoint[0] ) * ( 2.0 ) * ( -2.0 ) ) / 8.0;
 
        rResult[3]( 0, 0 ) = (( 1.0 + rPoint[1] ) * ( -2.0 ) * ( -2.0 ) ) / 8.0;
        rResult[3]( 0, 1 ) = (( 1.0 ) * ( -1.0 - 2.0 * rPoint[0] + rPoint[1] + 1.0 ) * ( -2.0 ) ) / 8.0
                             + (( 1.0 + rPoint[1] ) * ( -2.0 ) ) / 8.0;
        rResult[3]( 1, 0 ) = -(( -2.0 ) * ( 1.0 + rPoint[0] - 2.0 * rPoint[1] - 1.0 ) ) / 8.0
                             - (( -1.0 + rPoint[0] ) * ( -2.0 ) ) / 8.0;
        rResult[3]( 1, 1 ) = -(( -1.0 + rPoint[0] ) * ( -2.0 ) * ( -2.0 ) ) / 8.0;
 
        rResult[4]( 0, 0 ) = -(( -1.0 + rPoint[1] ) * ( -2.0 ) ) / 2.0;
        rResult[4]( 0, 1 ) = -( rPoint[0] * ( -2.0 ) ) / 2.0;
        rResult[4]( 1, 0 ) = -(( 2.0 * rPoint[0] ) * ( -2.0 ) ) / 4.0;
        rResult[4]( 1, 1 ) = 0.0;
 
        rResult[5]( 0, 0 ) = 0.0;
        rResult[5]( 0, 1 ) = (( 2.0 * rPoint[1] ) * ( -2.0 ) ) / 4.0;
        rResult[5]( 1, 0 ) = ( rPoint[1] * ( -2.0 ) ) / 2.0;
        rResult[5]( 1, 1 ) = (( 1.0 + rPoint[0] ) * ( -2.0 ) ) / 2.0;
 
        rResult[6]( 0, 0 ) = (( 1.0 + rPoint[1] ) * ( -2.0 ) ) / 2.0;
        rResult[6]( 0, 1 ) = ( rPoint[0] * ( -2.0 ) ) / 2.0;
        rResult[6]( 1, 0 ) = (( 2.0 * rPoint[0] ) * ( -2.0 ) ) / 4.0;
        rResult[6]( 1, 1 ) = 0.0;
 
        rResult[7]( 0, 0 ) = 0.0;
        rResult[7]( 0, 1 ) = -(( 2.0 * rPoint[1] ) * ( -2.0 ) ) / 4.0;
        rResult[7]( 1, 0 ) = -( rPoint[1] * ( -2.0 ) ) / 2.0;
        rResult[7]( 1, 1 ) = -(( -1.0 + rPoint[0] ) * ( -2.0 ) ) / 2.0;
 
        return rResult;
    }
 
    ShapeFunctionsThirdDerivativesType& ShapeFunctionsThirdDerivatives(
        ShapeFunctionsThirdDerivativesType& rResult,
        const CoordinatesArrayType& rPoint
        ) const override
    {
 
        if ( rResult.size() != this->PointsNumber() )
        {
            // KLUDGE: While there is a bug in
            // ublas vector resize, I have to put this beside resizing!!
//                 ShapeFunctionsGradientsType
            ShapeFunctionsThirdDerivativesType temp( this->PointsNumber() );
            rResult.swap( temp );
        }
 
        for ( IndexType i = 0; i < rResult.size(); i++ )
        {
            DenseVector<Matrix> temp( this->PointsNumber() );
            rResult[i].swap( temp );
        }
 
        for ( unsigned int i = 0; i < this->PointsNumber(); i++ )
        {
            for ( int j = 0; j < 2; j++ )
            {
                rResult[i][j].resize( 2, 2 , false);
                noalias( rResult[i][j] ) = ZeroMatrix( 2, 2);
            }
        }
 
        rResult[0][0]( 0, 0 ) = 0.0;
 
        rResult[0][0]( 0, 1 ) = -0.5;
        rResult[0][0]( 1, 0 ) = -0.5;
        rResult[0][0]( 1, 1 ) = -0.5;
        rResult[0][1]( 0, 0 ) = -0.5;
        rResult[0][1]( 0, 1 ) = -0.5;
        rResult[0][1]( 1, 0 ) = -0.5;
        rResult[0][1]( 1, 1 ) = 0.0;
        rResult[1][0]( 0, 0 ) = 0.0;
        rResult[1][0]( 0, 1 ) = -0.5;
        rResult[1][0]( 1, 0 ) = -0.5;
        rResult[1][0]( 1, 1 ) = 0.5;
        rResult[1][1]( 0, 0 ) = -0.5;
        rResult[1][1]( 0, 1 ) = 0.5;
        rResult[1][1]( 1, 0 ) = 0.5;
        rResult[1][1]( 1, 1 ) = 0.0;
        rResult[2][0]( 0, 0 ) = 0.0;
        rResult[2][0]( 0, 1 ) = 0.5;
        rResult[2][0]( 1, 0 ) = 0.5;
        rResult[2][0]( 1, 1 ) = 0.5;
        rResult[2][1]( 0, 0 ) = 0.5;
        rResult[2][1]( 0, 1 ) = 0.5;
        rResult[2][1]( 1, 0 ) = 0.5;
        rResult[2][1]( 1, 1 ) = 0.0;
        rResult[3][0]( 0, 0 ) = 0.0;
        rResult[3][0]( 0, 1 ) = 0.5;
        rResult[3][0]( 1, 0 ) = 0.5;
        rResult[3][0]( 1, 1 ) = -0.5;
        rResult[3][1]( 0, 0 ) = 0.5;
        rResult[3][1]( 0, 1 ) = -0.5;
        rResult[3][1]( 1, 0 ) = -0.5;
        rResult[3][1]( 1, 1 ) = 0.0;
        rResult[4][0]( 0, 0 ) = 0.0;
        rResult[4][0]( 0, 1 ) = 1.0;
        rResult[4][0]( 1, 0 ) = 1.0;
        rResult[4][0]( 1, 1 ) = 0.0;
        rResult[4][1]( 0, 0 ) = 1.0;
        rResult[4][1]( 0, 1 ) = 0.0;
        rResult[4][1]( 1, 0 ) = 0.0;
        rResult[4][1]( 1, 1 ) = 0.0;
        rResult[5][0]( 0, 0 ) = 0.0;
        rResult[5][0]( 0, 1 ) = 0.0;
        rResult[5][0]( 1, 0 ) = 0.0;
        rResult[5][0]( 1, 1 ) = -1.0;
        rResult[5][1]( 0, 0 ) = 0.0;
        rResult[5][1]( 0, 1 ) = -1.0;
        rResult[5][1]( 1, 0 ) = 1.0;
        rResult[5][1]( 1, 1 ) = 0.0;
        rResult[6][0]( 0, 0 ) = 0.0;
        rResult[6][0]( 0, 1 ) = -1.0;
        rResult[6][0]( 1, 0 ) = -1.0;
        rResult[6][0]( 1, 1 ) = 0.0;
        rResult[6][1]( 0, 0 ) = -1.0;
        rResult[6][1]( 0, 1 ) = 0.0;
        rResult[6][1]( 1, 0 ) = 0.0;
        rResult[6][1]( 1, 1 ) = 0.0;
        rResult[7][0]( 0, 0 ) = 0.0;
        rResult[7][0]( 0, 1 ) = 0.0;
        rResult[7][0]( 1, 0 ) = 0.0;
        rResult[7][0]( 1, 1 ) = 1.0;
        rResult[7][1]( 0, 0 ) = 0.0;
        rResult[7][1]( 0, 1 ) = 1.0;
        rResult[7][1]( 1, 0 ) = -1.0;
        rResult[7][1]( 1, 0 ) = 0.0;
 
        return rResult;
    }
 
protected:
 
private:
 
    static const GeometryData msGeometryData;
 
    static const GeometryDimension msGeometryDimension;
 
 
 
    friend class Serializer;
 
    void save( Serializer& rSerializer ) const override
    {
        KRATOS_SERIALIZE_SAVE_BASE_CLASS( rSerializer, BaseType );
    }
 
    void load( Serializer& rSerializer ) override
    {
        KRATOS_SERIALIZE_LOAD_BASE_CLASS( rSerializer, BaseType );
    }
 
    Quadrilateral2D8(): BaseType( PointsArrayType(), &msGeometryData ) {}
 
    static Matrix CalculateShapeFunctionsIntegrationPointsValues( typename BaseType::IntegrationMethod ThisMethod )
    {
        IntegrationPointsContainerType all_integration_points = AllIntegrationPoints();
        IntegrationPointsArrayType integration_points = all_integration_points[static_cast<int>(ThisMethod)];
 
        // Number of integration points
        const unsigned int integration_points_number = integration_points.size();
 
        // Number of nodes in current geometry
        const unsigned int points_number = 8;
 
        // Setting up return matrix
        Matrix shape_function_values( integration_points_number, points_number );
 
        // Loop over all integration points
        for ( unsigned int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            // Primary nodes
            row( shape_function_values, pnt )[0] =
                -(( 1.0 - integration_points[pnt].X() )
                  * ( 1.0 - integration_points[pnt].Y() )
                  * ( 1.0 + integration_points[pnt].X()
                      + integration_points[pnt].Y() ) ) / 4.0;
            row( shape_function_values, pnt )[1] =
                -(( 1.0 + integration_points[pnt].X() )
                  * ( 1.0 - integration_points[pnt].Y() ) * ( 1.0
                          - integration_points[pnt].X()
                          + integration_points[pnt].Y() ) ) / 4.0;
            row( shape_function_values, pnt )[2] =
                -(( 1.0 + integration_points[pnt].X() )
                  * ( 1.0 + integration_points[pnt].Y() ) * ( 1.0
                          - integration_points[pnt].X()
                          - integration_points[pnt].Y() ) ) / 4.0;
            row( shape_function_values, pnt )[3] =
                -(( 1.0 - integration_points[pnt].X() ) * ( 1.0
                        + integration_points[pnt].Y() ) * ( 1.0 ) * ( 1.0
                        + integration_points[pnt].X()
                        - integration_points[pnt].Y() ) ) / 4.0;
 
            // Secondary nodes
            row( shape_function_values, pnt )[4] =
                (( 1.0 - integration_points[pnt].X()
                   * integration_points[pnt].X() )
                 * ( 1.0 - integration_points[pnt].Y() ) ) / 2.0;
            row( shape_function_values, pnt )[5] =
                (( 1.0 + integration_points[pnt].X() )
                 * ( 1.0 - integration_points[pnt].Y()
                     * integration_points[pnt].Y() ) ) / 2.0 ;
            row( shape_function_values, pnt )[6] =
                (( 1.0 - integration_points[pnt].X()
                   * integration_points[pnt].X() )
                 * ( 1.0 + integration_points[pnt].Y() ) ) / 2.0 ;
            row( shape_function_values, pnt )[7] =
                (( 1.0 - integration_points[pnt].X() )
                 * ( 1.0 - integration_points[pnt].Y()
                     * integration_points[pnt].Y() ) ) / 2.0 ;
        }
 
        return shape_function_values;
    }
 
    static ShapeFunctionsGradientsType
    CalculateShapeFunctionsIntegrationPointsLocalGradients(typename BaseType::IntegrationMethod ThisMethod )
    {
        IntegrationPointsContainerType all_integration_points = AllIntegrationPoints();
        IntegrationPointsArrayType integration_points = all_integration_points[static_cast<int>(ThisMethod)];
        // Number of integration points
        const unsigned int integration_points_number = integration_points.size();
        ShapeFunctionsGradientsType d_shape_f_values( integration_points_number );
        // Initialising container
        //std::fill(d_shape_f_values.begin(), d_shape_f_values.end(), Matrix(4,2));
 
        // Loop over all integration points
        for ( unsigned int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Matrix result = ZeroMatrix( 8, 2 );
 
            // Primary nodes
            result( 0, 0 ) = - ((-1.0 + integration_points[pnt].Y())*( 2.0 * integration_points[pnt].X() + integration_points[pnt].Y())) / 4.0;
            result( 0, 1 ) = - ((-1.0 + integration_points[pnt].X())*( 2.0 * integration_points[pnt].Y() + integration_points[pnt].X())) / 4.0;
 
            result( 1, 0 ) =   ((-1.0 + integration_points[pnt].Y())*(-2.0 * integration_points[pnt].X() + integration_points[pnt].Y())) / 4.0;
            result( 1, 1 ) =   (( 1.0 + integration_points[pnt].X())*( 2.0 * integration_points[pnt].Y() - integration_points[pnt].X())) / 4.0;
 
            result( 2, 0 ) =   (( 1.0 + integration_points[pnt].Y())*( 2.0 * integration_points[pnt].X() + integration_points[pnt].Y())) / 4.0;
            result( 2, 1 ) =   (( 1.0 + integration_points[pnt].X())*( 2.0 * integration_points[pnt].Y() + integration_points[pnt].X())) / 4.0;
 
            result( 3, 0 ) = - (( 1.0 + integration_points[pnt].Y())*(-2.0 * integration_points[pnt].X() + integration_points[pnt].Y())) / 4.0;
            result( 3, 1 ) = - ((-1.0 + integration_points[pnt].X())*( 2.0 * integration_points[pnt].Y() - integration_points[pnt].X())) / 4.0;
 
            // Secondary nodes
            result( 4, 0 ) =   integration_points[pnt].X() * (-1.0 + integration_points[pnt].Y());
            result( 4, 1 ) =   ((1.0 + integration_points[pnt].X()) * (-1.0 + integration_points[pnt].X())) / 2.0;
 
            result( 5, 0 ) = - ((1.0 + integration_points[pnt].Y()) * (-1.0 + integration_points[pnt].Y())) / 2.0;
            result( 5, 1 ) = - integration_points[pnt].Y() * ( 1.0 + integration_points[pnt].X());
 
            result( 6, 0 ) = - integration_points[pnt].X() * ( 1.0 + integration_points[pnt].Y());
            result( 6, 1 ) = - ((1.0 + integration_points[pnt].X()) * (-1.0 + integration_points[pnt].X())) / 2.0;
 
            result( 7, 0 ) =   ((1.0 + integration_points[pnt].Y()) * (-1.0 + integration_points[pnt].Y())) / 2.0;
            result( 7, 1 ) =   integration_points[pnt].Y() * (-1.0 + integration_points[pnt].X());
 
            d_shape_f_values[pnt] = result;
        }
 
        return d_shape_f_values;
    }
 
    static const IntegrationPointsContainerType AllIntegrationPoints()
    {
        IntegrationPointsContainerType integration_points =
        {
            {
                //Quadrature< QuadrilateralGaussLegendreIntegrationPointsNeu1,
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints1,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints2,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints3,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints4,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLegendreIntegrationPoints5,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints()
            }
        };
        return integration_points;
    }
 
    static const ShapeFunctionsValuesContainerType AllShapeFunctionsValues()
    {
        ShapeFunctionsValuesContainerType shape_functions_values =
        {
            {
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_3 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_4 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_5 )
            }
        };
        return shape_functions_values;
    }
 
    static const ShapeFunctionsLocalGradientsContainerType
    AllShapeFunctionsLocalGradients()
    {
        ShapeFunctionsLocalGradientsContainerType shape_functions_local_gradients =
        {
            {
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
                    GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
                    GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
                    GeometryData::IntegrationMethod::GI_GAUSS_3 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
                    GeometryData::IntegrationMethod::GI_GAUSS_4 ),
                Quadrilateral2D8<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
                    GeometryData::IntegrationMethod::GI_GAUSS_5 )
            }
        };
        return shape_functions_local_gradients;
    }
 
    template<class TOtherPointType> friend class Quadrilateral2D8;
 
}; // Class Geometry
 
template< class TPointType > inline std::istream& operator >> (
    std::istream& rIStream,
    Quadrilateral2D8<TPointType>& rThis );
 
template<class TPointType> inline std::ostream& operator << (
    std::ostream& rOStream,
    const Quadrilateral2D8<TPointType>& rThis )
{
    rThis.PrintInfo( rOStream );
    rOStream << std::endl;
    rThis.PrintData( rOStream );
    return rOStream;
}
 
template<class TPointType>
const GeometryData Quadrilateral2D8<TPointType>::msGeometryData(
        &msGeometryDimension,
        GeometryData::IntegrationMethod::GI_GAUSS_3,
        Quadrilateral2D8<TPointType>::AllIntegrationPoints(),
        Quadrilateral2D8<TPointType>::AllShapeFunctionsValues(),
        AllShapeFunctionsLocalGradients()
);
 
template<class TPointType>
const GeometryDimension Quadrilateral2D8<TPointType>::msGeometryDimension(2, 2);
 
}  // namespace Kratos.