quadrilateral_interface_3d_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_3D_4_H_INCLUDED )
#define  KRATOS_QUADRILATERAL_INTERFACE_3D_4_H_INCLUDED
 
// System includes
 
// External includes
 
// Project includes
#include "geometries/line_3d_2.h"
#include "integration/quadrilateral_gauss_lobatto_integration_points.h"
 
 
namespace Kratos
{
 
 
 
 
 
template<class TPointType> class QuadrilateralInterface3D4
    : public Geometry<TPointType>
{
public:
 
    typedef Geometry<TPointType> BaseType;
 
    typedef Line3D2<TPointType> EdgeType;
 
    KRATOS_CLASS_POINTER_DEFINITION( QuadrilateralInterface3D4 );
 
    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;
 
 
 
//     QuadrilateralInterface3D4( const PointType& FirstPoint,
//                       const PointType& SecondPoint,
//                       const PointType& ThirdPoint,
//                       const PointType& FourthPoint )
//         : BaseType( PointsArrayType(), &msGeometryData )
//     {
//         array_1d< double , 3 > vx;
//         vx.clear();
//         vx = SecondPoint + ThirdPoint - FirstPoint - FourthPoint;
//         vx *= 0.5;
//
//         array_1d< double , 3 > vy;
//         vy.clear();
//         vy = ThirdPoint + FourthPoint - FirstPoint - SecondPoint;
//         vy *= 0.5;
//
//         double lx = MathUtils<double>::Norm3(vx);
//         double ly = MathUtils<double>::Norm3(vy);
//
//      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 ) ) );
//      }
//     }
 
    QuadrilateralInterface3D4( typename PointType::Pointer pFirstPoint,
                      typename PointType::Pointer pSecondPoint,
                      typename PointType::Pointer pThirdPoint,
                      typename PointType::Pointer pFourthPoint )
        : BaseType( PointsArrayType(), &msGeometryData )
    {
        array_1d< double , 3 > vx;
        noalias(vx) = (*pSecondPoint + *pThirdPoint - *pFirstPoint - *pFourthPoint)*0.5;
 
        array_1d< double , 3 > vy;
        noalias(vy) = (*pThirdPoint + *pFourthPoint - *pFirstPoint - *pSecondPoint)*0.5;
 
        double lx = MathUtils<double>::Norm3(vx);
        double ly = MathUtils<double>::Norm3(vy);
 
        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 );
        }
    }
 
    QuadrilateralInterface3D4( const PointsArrayType& ThisPoints )
        : BaseType( ThisPoints, &msGeometryData )
    {
        if ( this->PointsNumber() != 4 )
            KRATOS_ERROR << "Invalid points number. Expected 4, given " << this->PointsNumber() << std::endl;
    }
 
    QuadrilateralInterface3D4( QuadrilateralInterface3D4 const& rOther )
        : BaseType( rOther )
    {
    }
 
    template<class TOtherPointType> QuadrilateralInterface3D4( QuadrilateralInterface3D4<TOtherPointType> const& rOther )
        : BaseType( rOther )
    {
    }
 
    virtual ~QuadrilateralInterface3D4() {}
 
    GeometryData::KratosGeometryFamily GetGeometryFamily() const override
    {
        return GeometryData::KratosGeometryFamily::Kratos_Quadrilateral;
    }
 
    GeometryData::KratosGeometryType GetGeometryType() const override
    {
        return GeometryData::KratosGeometryType::Kratos_Quadrilateral3D4;
    }
 
 
    QuadrilateralInterface3D4& operator=( const QuadrilateralInterface3D4& rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
    template<class TOtherPointType>
    QuadrilateralInterface3D4& operator=( QuadrilateralInterface3D4<TOtherPointType> const & rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
 
    typename BaseType::Pointer Create( PointsArrayType const& ThisPoints ) const override
    {
        return typename BaseType::Pointer( new QuadrilateralInterface3D4( 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> vx( p1 - p0 );
 
        return MathUtils<double>::Norm3(vx);
    }
 
    double Area() const override
    {
        return Length();
    }
 
    double DomainSize() const override
    {
        return Area();
    }
 
    double Volume() const override
    {
        KRATOS_WARNING("QuadrilateralInterface3D4") << "Method not well defined. Replace with DomainSize() instead. This method preserves current behaviour but will be changed in June 2023 (returning error instead)" << std::endl;
        return Area();
        // TODO: Replace in June 2023
        // KRATOS_ERROR << "QuadrilateralInterface3D4:: Method not well defined. Replace with DomainSize() instead." << std::endl;
        // return 0.0;
    }
 
    bool IsInside(
        const CoordinatesArrayType& rPoint,
        CoordinatesArrayType& rResult,
        const double Tolerance = std::numeric_limits<double>::epsilon()
        ) const override
    {
        PointLocalCoordinates( rResult, rPoint );
 
        if ( (rResult[0] >= (-1.0 - Tolerance)) && (rResult[0] <= (1.0 + Tolerance)) )
        {
            if ( (rResult[1] >= (-1.0 - Tolerance)) && (rResult[1] <= (1.0 + Tolerance)) )
            {
                return true;
            }
        }
 
        return false;
    }
 
    CoordinatesArrayType& PointLocalCoordinates(
        CoordinatesArrayType& rResult,
        const CoordinatesArrayType& rPoint
        ) const  override
    {
        BoundedMatrix<double,3,4> X;
        BoundedMatrix<double,3,2> DN;
        for(unsigned int i=0; i<this->size();i++) {
            X(0,i ) = this->GetPoint( i ).X();
            X(1,i ) = this->GetPoint( i ).Y();
            X(2,i ) = this->GetPoint( i ).Z();
        }
 
        double tol = 1.0e-8;
        int maxiter = 1000;
 
        Matrix J = ZeroMatrix( 2, 2 );
        Matrix invJ = ZeroMatrix( 2, 2 );
 
        //starting with xi = 0
        rResult = ZeroVector( 3 );
        Vector DeltaXi = ZeroVector( 2 );
        array_1d<double,3> CurrentGlobalCoords;
 
 
        //Newton iteration:
        for ( int k = 0; k < maxiter; k++ )
        {
            noalias(CurrentGlobalCoords) = ZeroVector( 3 );
            this->GlobalCoordinates( CurrentGlobalCoords, rResult );
 
            noalias( CurrentGlobalCoords ) = rPoint - CurrentGlobalCoords;
 
 
            //derivatives of shape functions
            Matrix shape_functions_gradients;
            shape_functions_gradients = ShapeFunctionsLocalGradients(shape_functions_gradients, rResult );
            noalias(DN) = prod(X,shape_functions_gradients);
 
            noalias(J) = prod(trans(DN),DN);
            Vector res = prod(trans(DN),CurrentGlobalCoords);
 
            //deteminant of Jacobian
            const double det_j = J( 0, 0 ) * J( 1, 1 ) - J( 0, 1 ) * J( 1, 0 );
 
            //filling matrix
            invJ( 0, 0 ) = ( J( 1, 1 ) ) / ( det_j );
            invJ( 1, 0 ) = -( J( 1, 0 ) ) / ( det_j );
            invJ( 0, 1 ) = -( J( 0, 1 ) ) / ( det_j );
            invJ( 1, 1 ) = ( J( 0, 0 ) ) / ( det_j );
 
 
            DeltaXi( 0 ) = invJ( 0, 0 ) * res[0] + invJ( 0, 1 ) * res[1];
            DeltaXi( 1 ) = invJ( 1, 0 ) * res[0] + invJ( 1, 1 ) * res[1];
 
            rResult[0] += DeltaXi[0];
            rResult[1] += DeltaXi[1];
            rResult[2] = 0.0;
 
            if ( norm_2( DeltaXi ) > 300 )
            {
                res[0] = 0.0;
                res[1] = 0.0;
                std::cout << "detJ =" << det_j << "DeltaX = " << DeltaXi << " stopping calculation and assigning the baricenter" << std::endl;
                break;
                //KRATOS_ERROR << "Computation of local coordinates failed at iteration" << k << std::endl;
            }
 
            if ( norm_2( DeltaXi ) < tol )
            {
                break;
            }
        }
 
        return( rResult );
    }
 
    JacobiansType& Jacobian( JacobiansType& rResult,
                             IntegrationMethod ThisMethod,
                             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, 3> dp0;
        array_1d<double, 3> dp1;
        dp0[0] = (DeltaPosition(0,0) + DeltaPosition(3,0))*0.5;
        dp0[1] = (DeltaPosition(0,1) + DeltaPosition(3,1))*0.5;
        dp0[2] = (DeltaPosition(0,2) + DeltaPosition(3,2))*0.5;
        dp1[0] = (DeltaPosition(1,0) + DeltaPosition(2,0))*0.5;
        dp1[1] = (DeltaPosition(1,1) + DeltaPosition(2,1))*0.5;
        dp1[2] = (DeltaPosition(1,2) + DeltaPosition(2,2))*0.5;
 
        Matrix jacobian( 3, 1 );
        jacobian( 0, 0 ) = ( p1[0]-dp1[0] - (p0[0]-dp0[0]) ) * 0.5; //on the Gauss points (J is constant at each element)
        jacobian( 1, 0 ) = ( p1[1]-dp1[1] - (p0[1]-dp0[1]) ) * 0.5;
        jacobian( 2, 0 ) = ( p1[2]-dp1[2] - (p0[2]-dp0[2]) ) * 0.5;
 
        if ( rResult.size() != BaseType::IntegrationPointsNumber( ThisMethod ) )
        {
            // KLUDGE: While there is a bug in ublas vector resize, I have to put this beside resizing!!
            JacobiansType temp( BaseType::IntegrationPointsNumber( ThisMethod ) );
            rResult.swap( temp );
        }
 
        std::fill( rResult.begin(), rResult.end(), jacobian );
 
        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() != 3 || rResult.size2() != 1)
            rResult.resize(3, 1, false);
 
        rResult( 0, 0 ) = ( p1[0] - p0[0] ) * 0.5;
        rResult( 1, 0 ) = ( p1[1] - p0[1] ) * 0.5;
        rResult( 2, 0 ) = ( p1[2] - p0[2] ) * 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() != 3 || rResult.size2() != 1)
            rResult.resize(3, 1, false);
 
        rResult( 0, 0 ) = ( p1[0] - p0[0] ) * 0.5;
        rResult( 1, 0 ) = ( p1[1] - p0[1] ) * 0.5;
        rResult( 2, 0 ) = ( p1[2] - p0[2] ) * 0.5;
 
        return rResult;
    }
 
    Vector& DeterminantOfJacobian( Vector& rResult,
                                   IntegrationMethod ThisMethod ) const override
    {
        KRATOS_ERROR << "QuadrilateralInterface3D4::DeterminantOfJacobian" <<"Jacobian is not square" << std::endl;
        return rResult;
    }
 
    double DeterminantOfJacobian( IndexType IntegrationPointIndex,
                                  IntegrationMethod ThisMethod ) const override
    {
        KRATOS_ERROR << "QuadrilateralInterface3D4::DeterminantOfJacobian" << "Jacobian is not square" << std::endl;
        return 0.0;
    }
 
    double DeterminantOfJacobian( const CoordinatesArrayType& rPoint ) const override
    {
        KRATOS_ERROR << "QuadrilateralInterface3D4::DeterminantOfJacobian" << "Jacobian is not square"  << std::endl;
        return 0.0;
    }
 
    JacobiansType& InverseOfJacobian( JacobiansType& rResult,
                                      IntegrationMethod ThisMethod ) const override
    {
        KRATOS_ERROR << "QuadrilateralInterface3D4::DeterminantOfJacobian" << "Jacobian is not square"  << std::endl;
        return rResult;
    }
 
    Matrix& InverseOfJacobian( Matrix& rResult,
                               IndexType IntegrationPointIndex,
                               IntegrationMethod ThisMethod ) const override
    {
        KRATOS_ERROR << "QuadrilateralInterface3D4::DeterminantOfJacobian" << "Jacobian is not square"  << std::endl;
        return rResult;
    }
 
    Matrix& InverseOfJacobian( Matrix& rResult,
                               const CoordinatesArrayType& rPoint ) const override
    {
        KRATOS_ERROR << "QuadrilateralInterface3D4::DeterminantOfJacobian" << "Jacobian is not square"  << std::endl;
        return rResult;
    }
 
 
 
    SizeType EdgesNumber() const override
    {
        return 4;
    }
 
    GeometriesArrayType GenerateEdges() const override
    {
        GeometriesArrayType edges = GeometriesArrayType();
        typedef typename Geometry<TPointType>::Pointer EdgePointerType;
        edges.push_back( EdgePointerType( new EdgeType( this->pGetPoint( 0 ), this->pGetPoint( 1 ) ) ) );
        edges.push_back( EdgePointerType( new EdgeType( this->pGetPoint( 1 ), this->pGetPoint( 2 ) ) ) );
        edges.push_back( EdgePointerType( new EdgeType( this->pGetPoint( 2 ), this->pGetPoint( 3 ) ) ) );
        edges.push_back( EdgePointerType( new 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 "3 dimensional quadrilateral with four nodes in 3D space";
    }
 
    void PrintInfo( std::ostream& rOStream ) const override
    {
        rOStream << "3 dimensional quadrilateral with four nodes in 3D 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 );
        }
 
        rResult[0][0].resize( 2, 2 , false);
 
        rResult[0][1].resize( 2, 2 , false);
        rResult[1][0].resize( 2, 2 , false);
        rResult[1][1].resize( 2, 2 , false);
        rResult[2][0].resize( 2, 2 , false);
        rResult[2][1].resize( 2, 2 , false);
        rResult[3][0].resize( 2, 2 , false);
        rResult[3][1].resize( 2, 2 , false);
 
        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 );
    }
 
    QuadrilateralInterface3D4(): 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 =
        {
            {
                QuadrilateralInterface3D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                QuadrilateralInterface3D4<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
                    GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Matrix(),
                Matrix()
            }
        };
        return shape_functions_values;
    }
 
    static const ShapeFunctionsLocalGradientsContainerType
    AllShapeFunctionsLocalGradients()
    {
        ShapeFunctionsLocalGradientsContainerType shape_functions_local_gradients =
        {
            {
                QuadrilateralInterface3D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                QuadrilateralInterface3D4<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                ShapeFunctionsGradientsType(),
                ShapeFunctionsGradientsType(),
            }
        };
        return shape_functions_local_gradients;
    }
 
 
 
 
 
 
    template<class TOtherPointType> friend class QuadrilateralInterface3D4;
 
 
 
}; // Class Geometry
 
 
 
 
template<class TPointType> inline std::istream& operator >> (
    std::istream& rIStream,
    QuadrilateralInterface3D4<TPointType>& rThis );
template<class TPointType> inline std::ostream& operator << (
    std::ostream& rOStream,
    const QuadrilateralInterface3D4<TPointType>& rThis )
{
    rThis.PrintInfo( rOStream );
    rOStream << std::endl;
    rThis.PrintData( rOStream );
    return rOStream;
}
 
 
template<class TPointType> const
GeometryData QuadrilateralInterface3D4<TPointType>::msGeometryData(
    &msGeometryDimension,
    GeometryData::IntegrationMethod::GI_GAUSS_2,
    QuadrilateralInterface3D4<TPointType>::AllIntegrationPoints(),
    QuadrilateralInterface3D4<TPointType>::AllShapeFunctionsValues(),
    AllShapeFunctionsLocalGradients()
);
 
template<class TPointType>
const GeometryDimension QuadrilateralInterface3D4<TPointType>::msGeometryDimension(3, 1);
 
}// namespace Kratos.
 
#endif // KRATOS_QUADRILATERAL_INTERFACE_3D_4_H_INCLUDED  defined