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).
//
// 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.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// 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
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: 2D Nodal Triangle Fekete Point Definitions
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/Foundations/NodalTriFekete.h>
#include <LibUtilities/Foundations/NodalTriFeketeData.h>
 
namespace Nektar
{
namespace LibUtilities
{
bool NodalTriFekete::initPointsManager[] = {PointsManager().RegisterCreator(
    PointsKey(0, eNodalTriFekete), NodalTriFekete::Create)};
 
// ////////////////////////////////////////////////////////
//  Coordinate the nodal trianlge Fekete points
void NodalTriFekete::v_CalculatePoints()
{
    // Allocate the storage for points
    PointsBaseType::v_CalculatePoints();
 
    size_t index = 0, isum = 0;
    const size_t offset = 3; // offset to match Datafile
    NekDouble b, c;
    size_t numPoints = GetNumPoints();
 
    // initialize values
    for (size_t i = 0; i < numPoints - 2; ++i)
    {
        index += NodalTriFeketeNPTS[i];
    }
 
    for (size_t 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 (size_t 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 (size_t 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 (size_t 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<size_t>(isum) == m_pointsKey.GetTotNumPoints()),
             "sum not equal to npts");
 
    m_util = MemoryManager<NodalUtilTriangle>::AllocateSharedPtr(
        numPoints - 1, m_points[0], m_points[1]);
}
 
void NodalTriFekete::v_CalculateWeights()
{
    // Allocate the storage for points
    PointsBaseType::v_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;
 
    std::shared_ptr<NekMatrix<NekDouble>> mat =
        m_util->GetInterpolationMatrix(xi);
    Vmath::Vcopy(mat->GetRows() * mat->GetColumns(), mat->GetRawPtr(), 1,
                 &interp[0], 1);
}
 
// ////////////////////////////////////////
//        CalculateDerivMatrix()
void NodalTriFekete::v_CalculateDerivMatrix()
{
    // Allocate the derivative matrix.
    PointsBaseType::v_CalculateDerivMatrix();
 
    m_derivmatrix[0] = m_util->GetDerivMatrix(0);
    m_derivmatrix[1] = m_util->GetDerivMatrix(1);
}
 
std::shared_ptr<PointsBaseType> NodalTriFekete::Create(const PointsKey &key)
{
    std::shared_ptr<PointsBaseType> returnval(
        MemoryManager<NodalTriFekete>::AllocateSharedPtr(key));
    returnval->Initialize();
    return returnval;
}
 
void NodalTriFekete::NodalPointReorder2d()
{
    size_t i, j;
    size_t cnt;
    size_t istart, iend;
 
    const size_t nVerts              = 3;
    const size_t nEdgeInteriorPoints = GetNumPoints() - 2;
    const size_t 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].size() - iend);
    Array<OneD, NekDouble> yc(m_points[0].size() - iend);
    size_t ct = 0;
    for (i = iend; i < m_points[0].size(); 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.size() - 1; i++)
        {
            if (yc[i] > yc[i + 1])
            {
                std::swap(xc[i], xc[i + 1]);
                std::swap(yc[i], yc[i + 1]);
                repeat = true;
            }
        }
    }
 
    size_t offset = 0;
    size_t 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].size(); i++, ct++)
    {
        m_points[0][i] = xc[ct];
        m_points[1][i] = yc[ct];
    }
    return;
}
 
} // namespace LibUtilities
} // namespace Nektar