quadrilateral_interface_2d_4.h

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//    |  /           |
//    ' /   __| _` | __|  _ \   __|
//    . \  |   (   | |   (   |\__ `
//   _|\_\_|  \__,_|\__|\___/ ____/
//                   Multi-Physics
//
//  License:         BSD License
//                   Kratos default license: kratos/license.txt
//
//  Main authors:    Ignasi de Pouplana
//
 
#if !defined(KRATOS_QUADRILATERAL_INTERFACE_2D_4_H_INCLUDED )
#define  KRATOS_QUADRILATERAL_INTERFACE_2D_4_H_INCLUDED
 
// System includes
 
// External includes
 
// Project includes
#include "geometries/line_2d_2.h"
#include "integration/quadrilateral_gauss_lobatto_integration_points.h"
 
 
namespace Kratos
{
 
 
 
 
 
template<class TPointType> class QuadrilateralInterface2D4
    : public Geometry<TPointType>
{
public:
 
    typedef Geometry<TPointType> BaseType;
 
    typedef Line2D2<TPointType> EdgeType;
 
    KRATOS_CLASS_POINTER_DEFINITION( QuadrilateralInterface2D4 );
 
    typedef GeometryData::IntegrationMethod IntegrationMethod;
 
    typedef typename BaseType::GeometriesArrayType GeometriesArrayType;
 
    typedef TPointType PointType;
 
    typedef typename BaseType::IndexType IndexType;
 
    typedef typename BaseType::SizeType SizeType;
 
    typedef  typename BaseType::PointsArrayType PointsArrayType;
 
    typedef typename BaseType::CoordinatesArrayType CoordinatesArrayType;
 
    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;
 
 
//     QuadrilateralInterface2D4( const PointType& FirstPoint,
//                       const PointType& SecondPoint,
//                       const PointType& ThirdPoint,
//                       const PointType& FourthPoint )
//         : BaseType( PointsArrayType(), &msGeometryData )
//     {
//         double p2_p1_X = (ThirdPoint->X() + FourthPoint->X() - FirstPoint->X() - SecondPoint->X())*0.5;
//         double p2_p1_Y = (ThirdPoint->Y() + FourthPoint->Y() - FirstPoint->Y() - SecondPoint->Y())*0.5;
//         double p4_p3_X = (ThirdPoint->X() + SecondPoint->X() - FirstPoint->X() - FourthPoint->X())*0.5;
//         double p4_p3_Y = (ThirdPoint->Y() + SecondPoint->Y() - FirstPoint->Y() - FourthPoint->Y())*0.5;
//
//         double lx = std::sqrt(p4_p3_X*p4_p3_X + p4_p3_Y*p4_p3_Y);
//         double ly = std::sqrt(p2_p1_X*p2_p1_X + p2_p1_Y*p2_p1_Y);
//      if(lx > ly)
//      {
//          this->Points().push_back( typename PointType::Pointer( new PointType( FirstPoint ) ) );
//          this->Points().push_back( typename PointType::Pointer( new PointType( SecondPoint ) ) );
//          this->Points().push_back( typename PointType::Pointer( new PointType( ThirdPoint ) ) );
//          this->Points().push_back( typename PointType::Pointer( new PointType( FourthPoint ) ) );
//      }
//      else
//      {
//          this->Points().push_back( typename PointType::Pointer( new PointType( FourthPoint ) ) );
//          this->Points().push_back( typename PointType::Pointer( new PointType( FirstPoint ) ) );
//          this->Points().push_back( typename PointType::Pointer( new PointType( SecondPoint ) ) );
//          this->Points().push_back( typename PointType::Pointer( new PointType( ThirdPoint ) ) );
//      }
//     }
 
    QuadrilateralInterface2D4( typename PointType::Pointer pFirstPoint,
                      typename PointType::Pointer pSecondPoint,
                      typename PointType::Pointer pThirdPoint,
                      typename PointType::Pointer pFourthPoint )
        : BaseType( PointsArrayType(), &msGeometryData )
    {
        double p2_p1_X = (pThirdPoint->X() + pFourthPoint->X() - pFirstPoint->X() - pSecondPoint->X())*0.5;
        double p2_p1_Y = (pThirdPoint->Y() + pFourthPoint->Y() - pFirstPoint->Y() - pSecondPoint->Y())*0.5;
        double p4_p3_X = (pThirdPoint->X() + pSecondPoint->X() - pFirstPoint->X() - pFourthPoint->X())*0.5;
        double p4_p3_Y = (pThirdPoint->Y() + pSecondPoint->Y() - pFirstPoint->Y() - pFourthPoint->Y())*0.5;
 
        double lx = std::sqrt(p4_p3_X*p4_p3_X + p4_p3_Y*p4_p3_Y);
        double ly = std::sqrt(p2_p1_X*p2_p1_X + p2_p1_Y*p2_p1_Y);
 
        if(ly < lx)
        {
            this->Points().push_back( pFirstPoint );
            this->Points().push_back( pSecondPoint );
            this->Points().push_back( pThirdPoint );
            this->Points().push_back( pFourthPoint );
        }
        else
        {
            this->Points().push_back( pFourthPoint );
            this->Points().push_back( pFirstPoint );
            this->Points().push_back( pSecondPoint );
            this->Points().push_back( pThirdPoint );
        }
    }
 
    QuadrilateralInterface2D4( const PointsArrayType& ThisPoints )
        : BaseType( ThisPoints, &msGeometryData )
    {
        if ( this->PointsNumber() != 4 )
            KRATOS_ERROR << "Invalid points number. Expected 4, given " << this->PointsNumber() << std::endl;
    }
 
    QuadrilateralInterface2D4( QuadrilateralInterface2D4 const& rOther )
        : BaseType( rOther )
    {
    }
 
    template<class TOtherPointType> QuadrilateralInterface2D4( QuadrilateralInterface2D4<TOtherPointType> const& rOther )
        : BaseType( rOther )
    {
    }
 
    virtual ~QuadrilateralInterface2D4() {}
 
    GeometryData::KratosGeometryFamily GetGeometryFamily() const override
    {
        return GeometryData::KratosGeometryFamily::Kratos_Quadrilateral;
    }
 
    GeometryData::KratosGeometryType GetGeometryType() const override
    {
        return GeometryData::KratosGeometryType::Kratos_Quadrilateral2D4;
    }
 
 
    QuadrilateralInterface2D4& operator=( const QuadrilateralInterface2D4& rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
    template<class TOtherPointType>
    QuadrilateralInterface2D4& operator=( QuadrilateralInterface2D4<TOtherPointType> const & rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
 
    typename BaseType::Pointer Create( PointsArrayType const& ThisPoints ) const override
    {
        return typename BaseType::Pointer( new QuadrilateralInterface2D4( ThisPoints ) );
    }
 
    Matrix& PointsLocalCoordinates( Matrix& rResult ) const override
    {
        noalias( rResult ) = ZeroMatrix( 4, 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;
        return rResult;
    }
 
 
    double Length() const override
    {
        array_1d<double, 3> p0 = 0.5 * (BaseType::GetPoint( 0 ) + BaseType::GetPoint( 3 ));
        array_1d<double, 3> p1 = 0.5 * (BaseType::GetPoint( 1 ) + BaseType::GetPoint( 2 ));
 
        array_1d<double, 3> v( p1 - p0 );
        return std::sqrt( v[0]*v[0] + v[1]*v[1] );
    }
 
    double Area() const override
    {
        return Length();
    }
 
 
    double DomainSize() const override
    {
        return Length();
    }
 
    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;
    }
 
    // TODO: Check if correct
    CoordinatesArrayType& PointLocalCoordinates(
        CoordinatesArrayType& rResult,
        const CoordinatesArrayType& rPoint
        ) const override
    {
        rResult.clear();
 
        array_1d<double, 3> FirstPoint;
        noalias(FirstPoint) = 0.5 * (BaseType::GetPoint( 0 ) + BaseType::GetPoint( 3 ));
        array_1d<double, 3> SecondPoint;
        noalias(SecondPoint) = 0.5 * (BaseType::GetPoint( 1 ) + BaseType::GetPoint( 2 ));
 
        // Project point
        double tol = 1e-14; // Tolerance
 
        // Normal
        array_1d<double,2> Normal = ZeroVector(2);
        Normal[0] = SecondPoint[1] -  FirstPoint[1];
        Normal[1] =  FirstPoint[0] - SecondPoint[0];
        double norm = std::sqrt(Normal[0] * Normal[0] + Normal[1] * Normal[1]);
        Normal /= norm;
 
        // Vector point and distance
        array_1d<double,2> VectorPoint = ZeroVector(2);
        VectorPoint[0] = rPoint[0] - FirstPoint[0];
        VectorPoint[1] = rPoint[1] - FirstPoint[1];
        double dist_proy = VectorPoint[0] * Normal[0] + VectorPoint[1] * Normal[1];
 
        if (dist_proy < tol)
        {
            double L  = Length();
 
            double l1 = (rPoint[0] - FirstPoint[0]) * (rPoint[0] - FirstPoint[0])
                      + (rPoint[1] - FirstPoint[1]) * (rPoint[1] - FirstPoint[1]);
            l1 = std::sqrt(l1);
 
            double l2 = (rPoint[0] - SecondPoint[0]) * (rPoint[0] - SecondPoint[0])
                      + (rPoint[1] - SecondPoint[1]) * (rPoint[1] - SecondPoint[1]);
            l2 = std::sqrt(l2);
 
//            std::cout << "L: " << L << " l1: " << l1 << " l2: " << l2 << std::endl;
 
            if (l1 <= (L + tol)  && l2 <= (L + tol))
            {
                rResult[0] = 2.0 * l1/(L + tol) - 1.0;
            }
            else
            {
                rResult[0] = 2.0; // Out of the line!!! TODO: Check if this value gives problems
            }
        }
        else
        {
            rResult[0] = 2.0; // Out of the line!!!
        }
 
        return( rResult );
    }
 
    Matrix& Jacobian( Matrix& rResult,
                      IndexType IntegrationPointIndex,
                      IntegrationMethod ThisMethod ) const override
    {
        array_1d<double, 3> p0 = 0.5 * (BaseType::GetPoint( 0 ) + BaseType::GetPoint( 3 ));
        array_1d<double, 3> p1 = 0.5 * (BaseType::GetPoint( 1 ) + BaseType::GetPoint( 2 ));
        if(rResult.size1() != 2 || rResult.size2() != 1)
            rResult.resize(2, 1, false);
        rResult( 0, 0 ) = ( p1[0] - p0[0] ) * 0.5;
        rResult( 1, 0 ) = ( p1[1] - p0[1] ) * 0.5;
        return rResult;
    }
 
    Matrix& Jacobian( Matrix& rResult,
                      IndexType IntegrationPointIndex,
                      IntegrationMethod ThisMethod,
                      const Matrix& DeltaPosition ) const override
    {
        array_1d<double, 3> p0 = 0.5 * (BaseType::GetPoint( 0 ) + BaseType::GetPoint( 3 ));
        array_1d<double, 3> p1 = 0.5 * (BaseType::GetPoint( 1 ) + BaseType::GetPoint( 2 ));
 
        array_1d<double, 2> dp0;
        array_1d<double, 2> dp1;
        dp0[0] = (DeltaPosition(0,0) + DeltaPosition(3,0))*0.5;
        dp0[1] = (DeltaPosition(0,1) + DeltaPosition(3,1))*0.5;
        dp1[0] = (DeltaPosition(1,0) + DeltaPosition(2,0))*0.5;
        dp1[1] = (DeltaPosition(1,1) + DeltaPosition(2,1))*0.5;
 
        if(rResult.size1() != 2 || rResult.size2() != 1)
            rResult.resize(2, 1, false);
        rResult( 0, 0 ) = ( (p1[0]-dp1[0]) - (p0[0]-dp0[0]) ) * 0.5;
        rResult( 1, 0 ) = ( (p1[1]-dp1[1]) - (p0[1]-dp0[1]) ) * 0.5;
 
        return rResult;
    }
 
    Matrix& Jacobian( Matrix& rResult, const CoordinatesArrayType& rPoint ) const override
    {
        array_1d<double, 3> p0 = 0.5 * (BaseType::GetPoint( 0 ) + BaseType::GetPoint( 3 ));
        array_1d<double, 3> p1 = 0.5 * (BaseType::GetPoint( 1 ) + BaseType::GetPoint( 2 ));
        if(rResult.size1() != 2 || rResult.size2() != 1)
            rResult.resize(2, 1, false);
        rResult( 0, 0 ) = ( p1[0] - p0[0] ) * 0.5;
        rResult( 1, 0 ) = ( p1[1] - p0[1] ) * 0.5;
        return rResult;
    }
 
    Vector& DeterminantOfJacobian( Vector& rResult,
                                   IntegrationMethod ThisMethod ) const override
    {
        //workaround by riccardo
        if ( rResult.size() != this->IntegrationPointsNumber( ThisMethod ) )
            rResult.resize( this->IntegrationPointsNumber( ThisMethod ), false );
 
        //for all integration points
        double detJ = Length()*0.5;
        for ( unsigned int pnt = 0; pnt < this->IntegrationPointsNumber( ThisMethod ); pnt++ )
            rResult[pnt] = detJ;
 
        return rResult;
    }
 
    double DeterminantOfJacobian( IndexType IntegrationPointIndex,
                                  IntegrationMethod ThisMethod ) const override
    {
        return Length()*0.5;
    }
 
    double DeterminantOfJacobian( const CoordinatesArrayType& rPoint ) const override
    {
        return Length()*0.5;
    }
 
    JacobiansType& InverseOfJacobian( JacobiansType& rResult,
                                      IntegrationMethod ThisMethod ) const override
    {
        KRATOS_ERROR << "Jacobian is not square" << std::endl;
        return rResult;
    }
 
    Matrix& InverseOfJacobian( Matrix& rResult,
                               IndexType IntegrationPointIndex,
                               IntegrationMethod ThisMethod ) const override
    {
        KRATOS_ERROR << "Jacobian is not square" << std::endl;
        return rResult;
    }
 
    Matrix& InverseOfJacobian( Matrix& rResult,
                               const CoordinatesArrayType& rPoint ) const override
    {
        KRATOS_ERROR << "Jacobian is not square" << std::endl;
        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 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 1 ), this->pGetPoint( 2 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 2 ), this->pGetPoint( 3 ) ) );
        edges.push_back( Kratos::make_shared<EdgeType>( this->pGetPoint( 3 ), this->pGetPoint( 0 ) ) );
        return edges;
    }
 
 
    double ShapeFunctionValue( IndexType ShapeFunctionIndex,
                               const CoordinatesArrayType& rPoint ) const override
    {
        switch ( ShapeFunctionIndex )
        {
        case 0:
            return( 0.25*( 1.0 - rPoint[0] )*( 1.0 - rPoint[1] ) );
        case 1:
            return( 0.25*( 1.0 + rPoint[0] )*( 1.0 - rPoint[1] ) );
        case 2:
            return( 0.25*( 1.0 + rPoint[0] )*( 1.0 + rPoint[1] ) );
        case 3:
            return( 0.25*( 1.0 - rPoint[0] )*( 1.0 + rPoint[1] ) );
        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() != 4) rResult.resize(4,false);
      rResult[0] =  0.25*( 1.0 - rCoordinates[0] )*( 1.0 - rCoordinates[1] );
      rResult[1] =  0.25*( 1.0 + rCoordinates[0] )*( 1.0 - rCoordinates[1] );
      rResult[2] =  0.25*( 1.0 + rCoordinates[0] )*( 1.0 + rCoordinates[1] );
      rResult[3] =  0.25*( 1.0 - rCoordinates[0] )*( 1.0 + rCoordinates[1] );
 
        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 ( int i = 0; i < 4; i++ )
            {
                for ( 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 four nodes in 2D space";
    }
 
    void PrintInfo( std::ostream& rOStream ) const override
    {
        rOStream << "2 dimensional quadrilateral with four 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;
        }
    }
 
    Matrix& ShapeFunctionsLocalGradients( Matrix& rResult, const CoordinatesArrayType& rPoint ) const override
    {
        rResult.resize( 4, 2 ,false);
        noalias( rResult ) = ZeroMatrix( 4, 2 );
        rResult( 0, 0 ) = -0.25 * ( 1.0 - rPoint[1] );
        rResult( 0, 1 ) = -0.25 * ( 1.0 - rPoint[0] );
        rResult( 1, 0 ) = 0.25 * ( 1.0 - rPoint[1] );
        rResult( 1, 1 ) = -0.25 * ( 1.0 + rPoint[0] );
        rResult( 2, 0 ) = 0.25 * ( 1.0 + rPoint[1] );
        rResult( 2, 1 ) = 0.25 * ( 1.0 + rPoint[0] );
        rResult( 3, 0 ) = -0.25 * ( 1.0 + rPoint[1] );
        rResult( 3, 1 ) = 0.25 * ( 1.0 - rPoint[0] );
        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 );
        }
 
        rResult[0].resize( 2, 2 ,false);
 
        rResult[1].resize( 2, 2 ,false);
        rResult[2].resize( 2, 2 ,false);
        rResult[3].resize( 2, 2 ,false);
        rResult[0]( 0, 0 ) = 0.0;
        rResult[0]( 0, 1 ) = 0.25;
        rResult[0]( 1, 0 ) = 0.25;
        rResult[0]( 1, 1 ) = 0.0;
        rResult[1]( 0, 0 ) = 0.0;
        rResult[1]( 0, 1 ) = -0.25;
        rResult[1]( 1, 0 ) = -0.25;
        rResult[1]( 1, 1 ) = 0.0;
        rResult[2]( 0, 0 ) = 0.0;
        rResult[2]( 0, 1 ) = 0.25;
        rResult[2]( 1, 0 ) = 0.25;
        rResult[2]( 1, 1 ) = 0.0;
        rResult[3]( 0, 0 ) = 0.0;
        rResult[3]( 0, 1 ) = -0.25;
        rResult[3]( 1, 0 ) = -0.25;
        rResult[3]( 1, 1 ) = 0.0;
        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 ( unsigned int j = 0; j < 2; j++ )
            {
                rResult[i][j].resize( 2, 2, false );
                noalias( rResult[i][j] ) = ZeroMatrix( 2, 2 );
            }
        }
 
//             rResult(0,0).resize( 2, 2);
//             rResult(0,1).resize( 2, 2);
//             rResult(1,0).resize( 2, 2);
//             rResult(1,1).resize( 2, 2);
//             rResult(2,0).resize( 2, 2);
//             rResult(2,1).resize( 2, 2);
//             rResult(3,0).resize( 2, 2);
//             rResult(3,0).resize( 2, 2);
 
        for ( int i = 0; i < 4; i++ )
        {
            rResult[i][0]( 0, 0 ) = 0.0;
            rResult[i][0]( 0, 1 ) = 0.0;
            rResult[i][0]( 1, 0 ) = 0.0;
            rResult[i][0]( 1, 1 ) = 0.0;
            rResult[i][1]( 0, 0 ) = 0.0;
            rResult[i][1]( 0, 1 ) = 0.0;
            rResult[i][1]( 1, 0 ) = 0.0;
            rResult[i][1]( 1, 1 ) = 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 );
    }
 
    QuadrilateralInterface2D4(): 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 int integration_points_number = integration_points.size();
        //number of nodes in current geometry
        const int points_number = 4;
        //setting up return matrix
        Matrix shape_function_values( integration_points_number, points_number );
        //loop over all integration points
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            shape_function_values( pnt, 0 ) =
                0.25 * ( 1.0 - integration_points[pnt].X() )
                * ( 1.0 - integration_points[pnt].Y() );
            shape_function_values( pnt, 1 ) =
                0.25 * ( 1.0 + integration_points[pnt].X() )
                * ( 1.0 - integration_points[pnt].Y() );
            shape_function_values( pnt, 2 ) =
                0.25 * ( 1.0 + integration_points[pnt].X() )
                * ( 1.0 + integration_points[pnt].Y() );
            shape_function_values( pnt, 3 ) =
                0.25 * ( 1.0 - integration_points[pnt].X() )
                * ( 1.0 + integration_points[pnt].Y() );
        }
        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 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 ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Matrix result( 4, 2 );
            result( 0, 0 ) = -0.25 * ( 1.0 - integration_points[pnt].Y() );
            result( 0, 1 ) = -0.25 * ( 1.0 - integration_points[pnt].X() );
            result( 1, 0 ) = 0.25 * ( 1.0 - integration_points[pnt].Y() );
            result( 1, 1 ) = -0.25 * ( 1.0 + integration_points[pnt].X() );
            result( 2, 0 ) = 0.25 * ( 1.0 + integration_points[pnt].Y() );
            result( 2, 1 ) = 0.25 * ( 1.0 + integration_points[pnt].X() );
            result( 3, 0 ) = -0.25 * ( 1.0 + integration_points[pnt].Y() );
            result( 3, 1 ) = 0.25 * ( 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 < QuadrilateralGaussLobattoIntegrationPoints1,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature < QuadrilateralGaussLobattoIntegrationPoints2,
                2, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                IntegrationPointsArrayType(),
                IntegrationPointsArrayType()
            }
        };
        return integration_points;
    }
 
    static const ShapeFunctionsValuesContainerType AllShapeFunctionsValues()
    {
        ShapeFunctionsValuesContainerType shape_functions_values =
        {
            {
                QuadrilateralInterface2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                QuadrilateralInterface2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Matrix(),
                Matrix()
            }
        };
        return shape_functions_values;
    }
 
    static const ShapeFunctionsLocalGradientsContainerType
    AllShapeFunctionsLocalGradients()
    {
        ShapeFunctionsLocalGradientsContainerType shape_functions_local_gradients =
        {
            {
                QuadrilateralInterface2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                QuadrilateralInterface2D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                ShapeFunctionsGradientsType(),
                ShapeFunctionsGradientsType(),
            }
        };
        return shape_functions_local_gradients;
    }
 
 
 
 
 
 
    template<class TOtherPointType> friend class QuadrilateralInterface2D4;
 
 
 
}; // Class Geometry
 
 
 
 
template<class TPointType> inline std::istream& operator >> (
    std::istream& rIStream,
    QuadrilateralInterface2D4<TPointType>& rThis );
template<class TPointType> inline std::ostream& operator << (
    std::ostream& rOStream,
    const QuadrilateralInterface2D4<TPointType>& rThis )
{
    rThis.PrintInfo( rOStream );
    rOStream << std::endl;
    rThis.PrintData( rOStream );
    return rOStream;
}
 
 
template<class TPointType> const
GeometryData QuadrilateralInterface2D4<TPointType>::msGeometryData(
    &msGeometryDimension,
    GeometryData::IntegrationMethod::GI_GAUSS_2,
    QuadrilateralInterface2D4<TPointType>::AllIntegrationPoints(),
    QuadrilateralInterface2D4<TPointType>::AllShapeFunctionsValues(),
    AllShapeFunctionsLocalGradients()
);
 
template<class TPointType>
const GeometryDimension QuadrilateralInterface2D4<TPointType>::msGeometryDimension(2, 2);
 
}// namespace Kratos.
 
#endif // KRATOS_QUADRILATERAL_INTERFACE_2D_4_H_INCLUDED  defined