NodalTriFekete.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File NodalTriFekete.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// License for the specific language governing rights and limitations under
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// DEALINGS IN THE SOFTWARE.
//
// Description: 2D Nodal Triangle Fekete Point Definitions
//
///////////////////////////////////////////////////////////////////////////////

#include <LibUtilities/Foundations/NodalTriFekete.h>
#include <LibUtilities/Foundations/Points.h>
#include <LibUtilities/Foundations/NodalTriFeketeData.h>
#include <LibUtilities/Foundations/NodalUtil.h>
#include <LibUtilities/BasicUtils/ErrorUtil.hpp>
#include <LibUtilities/BasicUtils/SharedArray.hpp>
#include <LibUtilities/BasicConst/NektarUnivConsts.hpp>
#include <LibUtilities/LinearAlgebra/NekMatrix.hpp>
#include <LibUtilities/LinearAlgebra/NekVector.hpp>


namespace Nektar
{
    namespace LibUtilities
    {


        // ////////////////////////////////////////////////////////
        //  Coordinate the nodal trianlge Fekete points
        void NodalTriFekete::CalculatePoints()
        {
            // Allocate the storage for points
            PointsBaseType::CalculatePoints();

            int index=0,isum=0;
            const int offset = 3; //offset to match Datafile
            NekDouble b,c;
            unsigned int numPoints = GetNumPoints();

            // initialize values
            for(unsigned int i=0; i < numPoints-2; ++i)
            {
                index += NodalTriFeketeNPTS[i];
            }

            for(unsigned int i=0; i < NodalTriFeketeNPTS[numPoints-2]; ++i, ++index)
            {
                if(int(NodalTriFeketeData[index][0]))
                {
                    b = NodalTriFeketeData[index][4];
                    c = NodalTriFeketeData[index][5];

                    m_points[0][isum] = 2.0*b - 1.0;
                    m_points[1][isum] = 2.0*c - 1.0;
                    isum++;
                    continue;
                }//end symmetry1


                if(int(NodalTriFeketeData[index][1]) == 1)
                {
                    for(unsigned int j=0; j < 3; ++j)
                    {
                        b = NodalTriFeketeData[index][offset+perm3A_2d[j][1]];
                        c = NodalTriFeketeData[index][offset+perm3A_2d[j][2]];
                        m_points[0][isum] = 2.0*b - 1.0;
                        m_points[1][isum] = 2.0*c - 1.0;
                        isum++;
                    }//end j
                    continue;
                }//end symmetry3a

                if(int(NodalTriFeketeData[index][1]) == 2)
                {
                    for(unsigned int j=0; j < 3; ++j)
                    {
                        b = NodalTriFeketeData[index][offset+perm3B_2d[j][1]];
                        c = NodalTriFeketeData[index][offset+perm3B_2d[j][2]];
                        m_points[0][isum] = 2.0*b - 1.0;
                        m_points[1][isum] = 2.0*c - 1.0;
                        isum++;
                    }//end j
                    continue;
                }//end symmetry3b


                if(int(NodalTriFeketeData[index][2]))
                {
                    for(unsigned int j=0; j < 6; ++j)
                    {
                        b = NodalTriFeketeData[index][offset+perm6_2d[j][1]];
                        c = NodalTriFeketeData[index][offset+perm6_2d[j][2]];
                        m_points[0][isum] = 2.0*b - 1.0;
                        m_points[1][isum] = 2.0*c - 1.0;
                        isum++;
                    }//end j
                    continue;
                }//end symmetry6
            }//end npts

            NodalPointReorder2d();

            ASSERTL1((static_cast<unsigned int>(isum)==m_pointsKey.GetTotNumPoints()),"sum not equal to npts");

            m_util = MemoryManager<NodalUtilTriangle>::AllocateSharedPtr(
                numPoints - 1, m_points[0], m_points[1]);
        }

        void NodalTriFekete::CalculateWeights()
        {
            // Allocate the storage for points
            PointsBaseType::CalculateWeights();

            typedef DataType T;

            // Solve the Vandermonde system of integrals for the weight vector
            NekVector<T> w = m_util->GetWeights();
            m_weights = Array<OneD,T>( w.GetRows(), w.GetPtr() );

        }

        // ////////////////////////////////////////
        //        CalculateInterpMatrix()
        void NodalTriFekete::CalculateInterpMatrix(const Array<OneD, const NekDouble>& xia, const Array<OneD, const NekDouble>& yia,
                                                   Array<OneD, NekDouble>& interp)
        {
             Array<OneD, Array<OneD, NekDouble> > xi(2);
             xi[0] = xia;
             xi[1] = yia;

             boost::shared_ptr<NekMatrix<NekDouble> > mat =
                 m_util->GetInterpolationMatrix(xi);
             Vmath::Vcopy(mat->GetRows() * mat->GetColumns(), mat->GetRawPtr(),
                          1, &interp[0], 1);
         }

         // ////////////////////////////////////////
        //        CalculateDerivMatrix()
        void NodalTriFekete::CalculateDerivMatrix()
        {
            // Allocate the derivative matrix.
            PointsBaseType::CalculateDerivMatrix();

            m_derivmatrix[0] = m_util->GetDerivMatrix(0);
            m_derivmatrix[1] = m_util->GetDerivMatrix(1);
        }

        boost::shared_ptr<PointsBaseType> NodalTriFekete::Create(const PointsKey &key)
        {
            boost::shared_ptr<PointsBaseType> returnval(MemoryManager<NodalTriFekete>::AllocateSharedPtr(key));
            returnval->Initialize();
            return returnval;
        }

        void NodalTriFekete::NodalPointReorder2d()
        {
            int i,j;
            int cnt;
            int istart,iend;

            const int nVerts = 3;
            const int nEdgeInteriorPoints = GetNumPoints()-2;
            const int nBoundaryPoints = 3*nEdgeInteriorPoints + 3;

            if(nEdgeInteriorPoints==0)
            {
                return;
            }

            // group the points of edge 1 together;
            istart = nVerts;
            for(i = cnt = istart; i < nBoundaryPoints; i++)
            {
                if( fabs(m_points[1][i] + 1.0) < NekConstants::kNekZeroTol)
                {
                    std::swap(m_points[0][cnt], m_points[0][i]);
                    std::swap(m_points[1][cnt], m_points[1][i]);
                    cnt++;
                }
            }

            // bubble sort edge 1 (counterclockwise numbering)
            iend = istart + nEdgeInteriorPoints;
            for(i = istart; i < iend; i++)
            {
                for(j = istart+1; j < iend; j++)
                {
                    if(m_points[0][j] < m_points[0][j-1])
                    {
                        std::swap(m_points[0][j], m_points[0][j-1]);
                        std::swap(m_points[1][j], m_points[1][j-1]);
                    }
                }
            }

            // group the points of edge 2 together;
            istart = iend;
            for(i = cnt = istart; i < nBoundaryPoints; i++)
            {
                if( fabs(m_points[1][i]+m_points[0][i]) < NekConstants::kNekZeroTol)
                {
                    std::swap(m_points[0][cnt], m_points[0][i]);
                    std::swap(m_points[1][cnt], m_points[1][i]);
                    cnt++;
                }
            }

            // bubble sort edge 2 (counterclockwise numbering)
            iend = istart + nEdgeInteriorPoints;
            for(i = istart; i < iend; i++)
            {
                for(j = istart+1; j < iend; j++)
                {
                    if(m_points[1][j] < m_points[1][j-1])
                    {
                        std::swap(m_points[0][j], m_points[0][j-1]);
                        std::swap(m_points[1][j], m_points[1][j-1]);
                    }
                }
            }

            // group the points of edge 3 together;
            istart = iend;
            for(i = cnt = istart; i < nBoundaryPoints; i++)
            {
                if( fabs(m_points[0][i]+1.0) < NekConstants::kNekZeroTol)
                {
                    std::swap(m_points[0][cnt], m_points[0][i]);
                    std::swap(m_points[1][cnt], m_points[1][i]);
                    cnt++;
                }
            }
            // bubble sort edge 3 (counterclockwise numbering)
            iend = istart + nEdgeInteriorPoints;
            for(i = istart; i < iend; i++)
            {
                for(j = istart+1; j < iend; j++)
                {
                    if(m_points[1][j] > m_points[1][j-1])
                    {
                        std::swap(m_points[0][j], m_points[0][j-1]);
                        std::swap(m_points[1][j], m_points[1][j-1]);
                    }
                }
            }

            if(GetNumPoints() < 5)
            {
                //at numpoints = 4 there is only one interior point so doesnt
                //need sorting
                return;
            }

            //someone forgot to finish this piece of code and tell anyone
            //that they didnt
            //face interior nodes needs to be considered
            //make a copy of the unsorted nodes
            //bubble sort by smallest y
            //which will put them into sets of ever decreasing size
            //which can be bubble sorted by x to obtain the distrobution

            Array<OneD, NekDouble> xc(m_points[0].num_elements() - iend);
            Array<OneD, NekDouble> yc(m_points[0].num_elements() - iend);
            int ct = 0;
            for(i = iend; i < m_points[0].num_elements(); i++, ct++)
            {
                xc[ct] = m_points[0][i];
                yc[ct] = m_points[1][i];
            }

            //sort smallest first
            bool repeat = true;
            while(repeat)
            {
                repeat = false;
                for(i = 0; i < xc.num_elements() - 1; i++)
                {
                    if(yc[i] > yc[i+1])
                    {
                        std::swap(xc[i],xc[i+1]);
                        std::swap(yc[i],yc[i+1]);
                        repeat = true;
                    }
                }
            }

            int offset = 0;
            int npl = GetNumPoints() - 3;
            while(npl > 1)
            {
                repeat = true;
                while(repeat)
                {
                    repeat = false;
                    for(i = offset; i < offset + npl - 1; i++)
                    {
                        if(xc[i] > xc[i+1])
                        {
                            std::swap(xc[i],xc[i+1]);
                            std::swap(yc[i],yc[i+1]);
                            repeat = true;
                        }
                    }
                }
                offset += npl;
                npl--;
            }

            //copy back in
            ct = 0;
            for(i = iend; i < m_points[0].num_elements(); i++, ct++)
            {
                m_points[0][i] = xc[ct];
                m_points[1][i] = yc[ct];
            }
            return;
        }


    } // end of namespace stdregion
} // end of namespace stdregion