NodalTetElec.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: NodalTetElec.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: 3D Nodal Tet Electrostatic Point Definitions
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/BasicUtils/ErrorUtil.hpp>
#include <LibUtilities/Foundations/NodalTetElec.h>
#include <LibUtilities/Foundations/NodalTetElecData.h>
#include <LibUtilities/Foundations/NodalUtil.h>
#include <LibUtilities/LinearAlgebra/NekMatrix.hpp>
#include <LibUtilities/LinearAlgebra/NekVector.hpp>
 
namespace Nektar
{
namespace LibUtilities
{
bool NodalTetElec::initPointsManager[] = {PointsManager().RegisterCreator(
    PointsKey(0, eNodalTetElec), NodalTetElec::Create)};
 
// ////////////////////////////////////////////////////////
//  Coordinate the nodal tetrahedron electrostatic points
 
void NodalTetElec::v_CalculatePoints()
{
    // Allocate the storage for points
    Points<NekDouble>::v_CalculatePoints();
 
    int index = 0, isum = 0;
    const int offset = 5; // offset to match Datafile
    NekDouble b, c, d;
    unsigned int numPoints = GetNumPoints();
 
    // initialize values
    for (unsigned int i = 0; i < numPoints - 2; ++i)
    {
        index += NodalTetElecNPTS[i];
    }
 
    for (unsigned int i = 0; i < NodalTetElecNPTS[numPoints - 2]; ++i, ++index)
    {
        // 1 Point Symmetry: aaaa
        if (int(NodalTetElecData[index][0]))
        {
            b = NodalTetElecData[index][6];
            c = NodalTetElecData[index][7];
            d = NodalTetElecData[index][8];
 
            m_points[0][isum] = 2.0 * b - 1.0;
            m_points[1][isum] = 2.0 * c - 1.0;
            m_points[2][isum] = 2.0 * d - 1.0;
            isum++;
            continue;
        } // end symmetry 1
 
        // 4 Point symmetry: aaab or abbb
        if (int(NodalTetElecData[index][1]))
        {
            for (unsigned int j = 0; j < 4; ++j)
            {
                b = NodalTetElecData[index][offset + perm4_3d[j][1]];
                c = NodalTetElecData[index][offset + perm4_3d[j][2]];
                d = NodalTetElecData[index][offset + perm4_3d[j][3]];
 
                m_points[0][isum] = 2.0 * b - 1.0;
                m_points[1][isum] = 2.0 * c - 1.0;
                m_points[2][isum] = 2.0 * d - 1.0;
                isum++;
            } // end j
            continue;
        } // end symmetry 4
 
        // 6 Point symmetry: aabb
        if (int(NodalTetElecData[index][2]))
        {
            for (unsigned int j = 0; j < 6; ++j)
            {
                b = NodalTetElecData[index][offset + perm6_3d[j][1]];
                c = NodalTetElecData[index][offset + perm6_3d[j][2]];
                d = NodalTetElecData[index][offset + perm6_3d[j][3]];
 
                m_points[0][isum] = 2.0 * b - 1.0;
                m_points[1][isum] = 2.0 * c - 1.0;
                m_points[2][isum] = 2.0 * d - 1.0;
                isum++;
            } // end j
            continue;
        } // end symmetry6
 
        // 12 Point symmetry: case aabc
        if (int(NodalTetElecData[index][3]) == 1)
        {
            for (unsigned int j = 0; j < 12; ++j)
            {
                b = NodalTetElecData[index][offset + perm12A_3d[j][1]];
                c = NodalTetElecData[index][offset + perm12A_3d[j][2]];
                d = NodalTetElecData[index][offset + perm12A_3d[j][3]];
 
                m_points[0][isum] = 2.0 * b - 1.0;
                m_points[1][isum] = 2.0 * c - 1.0;
                m_points[2][isum] = 2.0 * d - 1.0;
                isum++;
            } // end j
            continue;
        } // end symmetry 12 aabc
 
        // 12 Point symmetry: case abcc
        if (int(NodalTetElecData[index][3]) == 2)
        {
            for (unsigned int j = 0; j < 12; ++j)
            {
                b = NodalTetElecData[index][offset + perm12B_3d[j][1]];
                c = NodalTetElecData[index][offset + perm12B_3d[j][2]];
                d = NodalTetElecData[index][offset + perm12B_3d[j][3]];
 
                m_points[0][isum] = 2.0 * b - 1.0;
                m_points[1][isum] = 2.0 * c - 1.0;
                m_points[2][isum] = 2.0 * d - 1.0;
                isum++;
            } // end j
            continue;
        } // end symmetry 12 abcc
 
        // 12 Point symmetry: case abbc
        if (int(NodalTetElecData[index][3]) == 3)
        {
            for (unsigned int j = 0; j < 12; ++j)
            {
                b = NodalTetElecData[index][offset + perm12C_3d[j][1]];
                c = NodalTetElecData[index][offset + perm12C_3d[j][2]];
                d = NodalTetElecData[index][offset + perm12C_3d[j][3]];
 
                m_points[0][isum] = 2.0 * b - 1.0;
                m_points[1][isum] = 2.0 * c - 1.0;
                m_points[2][isum] = 2.0 * d - 1.0;
                isum++;
            } // end j
            continue;
        } // end symmetry 12 abbc
 
        // 24 Point symmetry: case abcd
        if (int(NodalTetElecData[index][4]))
        {
            for (unsigned int j = 0; j < 24; ++j)
            {
                b = NodalTetElecData[index][offset + perm24_3d[j][1]];
                c = NodalTetElecData[index][offset + perm24_3d[j][2]];
                d = NodalTetElecData[index][offset + perm24_3d[j][3]];
 
                m_points[0][isum] = 2.0 * b - 1.0;
                m_points[1][isum] = 2.0 * c - 1.0;
                m_points[2][isum] = 2.0 * d - 1.0;
                isum++;
            } // end j
            continue;
        } // end symmetry24abcd
 
    } // end npts
 
    NodalPointReorder3d();
 
    ASSERTL1((static_cast<unsigned int>(isum) == m_pointsKey.GetTotNumPoints()),
             "sum not equal to npts");
 
    m_util = MemoryManager<NodalUtilTetrahedron>::AllocateSharedPtr(
        numPoints - 1, m_points[0], m_points[1], m_points[2]);
}
 
void NodalTetElec::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 NodalTetElec::CalculateInterpMatrix(
    const Array<OneD, const NekDouble> &xia,
    const Array<OneD, const NekDouble> &yia,
    const Array<OneD, const NekDouble> &zia, Array<OneD, NekDouble> &interp)
 
{
    Array<OneD, Array<OneD, NekDouble>> xi(3);
    xi[0] = xia;
    xi[1] = yia;
    xi[2] = zia;
 
    std::shared_ptr<NekMatrix<NekDouble>> mat =
        m_util->GetInterpolationMatrix(xi);
    Vmath::Vcopy(mat->GetRows() * mat->GetColumns(), mat->GetRawPtr(), 1,
                 &interp[0], 1);
}
 
void NodalTetElec::v_CalculateDerivMatrix()
{
    // Allocate the derivative matrix.
    PointsBaseType::v_CalculateDerivMatrix();
 
    m_derivmatrix[0] = m_util->GetDerivMatrix(0);
    m_derivmatrix[1] = m_util->GetDerivMatrix(1);
    m_derivmatrix[2] = m_util->GetDerivMatrix(2);
}
 
std::shared_ptr<PointsBaseType> NodalTetElec::Create(const PointsKey &key)
{
    std::shared_ptr<PointsBaseType> returnval(
        MemoryManager<NodalTetElec>::AllocateSharedPtr(key));
    returnval->Initialize();
    return returnval;
}
 
void NodalTetElec::NodalPointReorder3d()
{
    int cnt;
    int istart, iend;
 
    const int nVerts              = 4;
    const int nEdgeInteriorPoints = GetNumPoints() - 2;
    const int nFaceInteriorPoints =
        (GetNumPoints() - 3) * (GetNumPoints() - 2) / 2;
    // const int nBoundaryPoints = 4 + 6*nEdgeInteriorPoints +
    // 4*nFaceInteriorPoints;
    const int nAllPoints =
        GetNumPoints() * (GetNumPoints() + 1) * (GetNumPoints() + 2) / 6;
    if (nEdgeInteriorPoints == 0)
    {
        return;
    }
 
    // group all edge 1 points
    istart = nVerts;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[1][i] + 1.0) < NekConstants::kNekZeroTol &&
            fabs(m_points[2][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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort edge 1 (counterclockwise numbering)
    iend = istart + nEdgeInteriorPoints;
    for (int i = istart; i < iend; i++)
    {
        for (int 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]);
                std::swap(m_points[2][j], m_points[2][j - 1]);
            }
        }
    }
 
    // group the points of edge 2 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[1][i] + m_points[0][i]) < NekConstants::kNekZeroTol &&
            fabs(m_points[2][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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort edge 2 (counterclockwise numbering)
    iend = istart + nEdgeInteriorPoints;
    for (int i = istart; i < iend; i++)
    {
        for (int 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]);
                std::swap(m_points[2][j], m_points[2][j - 1]);
            }
        }
    }
 
    // group the points of edge 3 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[0][i] + 1.0) < NekConstants::kNekZeroTol &&
            fabs(m_points[2][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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort edge 3 (counterclockwise numbering)
    iend = istart + nEdgeInteriorPoints;
    for (int i = istart; i < iend; i++)
    {
        for (int 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]);
                std::swap(m_points[2][j], m_points[2][j - 1]);
            }
        }
    }
 
    // group the points of edge 4 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[0][i] + 1.0) < NekConstants::kNekZeroTol &&
            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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort edge 3 (counterclockwise numbering)
    iend = istart + nEdgeInteriorPoints;
    for (int i = istart; i < iend; i++)
    {
        for (int j = istart + 1; j < iend; j++)
        {
            if (m_points[2][j] < m_points[2][j - 1])
            {
                std::swap(m_points[0][j], m_points[0][j - 1]);
                std::swap(m_points[1][j], m_points[1][j - 1]);
                std::swap(m_points[2][j], m_points[2][j - 1]);
            }
        }
    }
 
    // group the points of edge 5 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[0][i] + m_points[2][i]) < NekConstants::kNekZeroTol &&
            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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort edge 5 (counterclockwise numbering)
    iend = istart + nEdgeInteriorPoints;
    for (int i = istart; i < iend; i++)
    {
        for (int j = istart + 1; j < iend; j++)
        {
            if (m_points[2][j] < m_points[2][j - 1])
            {
                std::swap(m_points[0][j], m_points[0][j - 1]);
                std::swap(m_points[1][j], m_points[1][j - 1]);
                std::swap(m_points[2][j], m_points[2][j - 1]);
            }
        }
    }
 
    // group the points of edge 6 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[1][i] + m_points[2][i]) < NekConstants::kNekZeroTol &&
            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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort edge 6 (counterclockwise numbering)
    iend = istart + nEdgeInteriorPoints;
    for (int i = istart; i < iend; i++)
    {
        for (int j = istart + 1; j < iend; j++)
        {
            if (m_points[2][j] < m_points[2][j - 1])
            {
                std::swap(m_points[0][j], m_points[0][j - 1]);
                std::swap(m_points[1][j], m_points[1][j - 1]);
                std::swap(m_points[2][j], m_points[2][j - 1]);
            }
        }
    }
 
    if (GetNumPoints() < 4)
    {
        // no face points
        return;
    }
 
    // group the points of face 1 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[2][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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort face1 (tensor numbering)
    iend        = istart + nFaceInteriorPoints;
    bool repeat = true;
    while (repeat)
    {
        repeat = false;
        for (int i = istart; i < iend - 1; i++)
        {
            if (m_points[1][i] > m_points[1][i + 1])
            {
                std::swap(m_points[0][i + 1], m_points[0][i]);
                std::swap(m_points[1][i + 1], m_points[1][i]);
                std::swap(m_points[2][i + 1], m_points[2][i]);
                repeat = true;
            }
        }
    }
    int offset = 0;
    int npl    = GetNumPoints() - 3;
    while (npl > 1)
    {
        repeat = true;
        while (repeat)
        {
            repeat = false;
            for (int i = offset + istart; i < offset + istart + npl - 1; i++)
            {
                if (m_points[0][i] > m_points[0][i + 1])
                {
                    std::swap(m_points[0][i + 1], m_points[0][i]);
                    std::swap(m_points[1][i + 1], m_points[1][i]);
                    std::swap(m_points[2][i + 1], m_points[2][i]);
                    repeat = true;
                }
            }
        }
        offset += npl;
        npl--;
    }
 
    // group the points of face 2 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; 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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort face2 (tensor numbering)
    iend   = istart + nFaceInteriorPoints;
    repeat = true;
    while (repeat)
    {
        repeat = false;
        for (int i = istart; i < iend - 1; i++)
        {
            if (m_points[2][i] > m_points[2][i + 1])
            {
                std::swap(m_points[0][i + 1], m_points[0][i]);
                std::swap(m_points[1][i + 1], m_points[1][i]);
                std::swap(m_points[2][i + 1], m_points[2][i]);
                repeat = true;
            }
        }
    }
    offset = 0;
    npl    = GetNumPoints() - 3;
    while (npl > 1)
    {
        repeat = true;
        while (repeat)
        {
            repeat = false;
            for (int i = offset + istart; i < offset + istart + npl - 1; i++)
            {
                if (m_points[0][i] > m_points[0][i + 1])
                {
                    std::swap(m_points[0][i + 1], m_points[0][i]);
                    std::swap(m_points[1][i + 1], m_points[1][i]);
                    std::swap(m_points[2][i + 1], m_points[2][i]);
                    repeat = true;
                }
            }
        }
        offset += npl;
        npl--;
    }
 
    // group the points of face 3 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; i++)
    {
        if (fabs(m_points[1][i] + m_points[0][i] + m_points[2][i] + 1.0) <
            1E-9) // nek zero tol too small
        {
            std::swap(m_points[0][cnt], m_points[0][i]);
            std::swap(m_points[1][cnt], m_points[1][i]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort face3 (tensor numbering)
    iend   = istart + nFaceInteriorPoints;
    repeat = true;
    while (repeat)
    {
        repeat = false;
        for (int i = istart; i < iend - 1; i++)
        {
            if (m_points[2][i] > m_points[2][i + 1])
            {
                std::swap(m_points[0][i + 1], m_points[0][i]);
                std::swap(m_points[1][i + 1], m_points[1][i]);
                std::swap(m_points[2][i + 1], m_points[2][i]);
                repeat = true;
            }
        }
    }
    offset = 0;
    npl    = GetNumPoints() - 3;
    while (npl > 1)
    {
        repeat = true;
        while (repeat)
        {
            repeat = false;
            for (int i = offset + istart; i < offset + istart + npl - 1; i++)
            {
                if (m_points[1][i] > m_points[1][i + 1])
                {
                    std::swap(m_points[0][i + 1], m_points[0][i]);
                    std::swap(m_points[1][i + 1], m_points[1][i]);
                    std::swap(m_points[2][i + 1], m_points[2][i]);
                    repeat = true;
                }
            }
        }
        offset += npl;
        npl--;
    }
 
    // group the points of face 4 together;
    istart = iend;
    for (int i = cnt = istart; i < nAllPoints; 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]);
            std::swap(m_points[2][cnt], m_points[2][i]);
            cnt++;
        }
    }
 
    // bubble sort face4 (tensor numbering)
    iend   = istart + nFaceInteriorPoints;
    repeat = true;
    while (repeat)
    {
        repeat = false;
        for (int i = istart; i < iend - 1; i++)
        {
            if (m_points[2][i] > m_points[2][i + 1])
            {
                std::swap(m_points[0][i + 1], m_points[0][i]);
                std::swap(m_points[1][i + 1], m_points[1][i]);
                std::swap(m_points[2][i + 1], m_points[2][i]);
                repeat = true;
            }
        }
    }
    offset = 0;
    npl    = GetNumPoints() - 3;
    while (npl > 1)
    {
        repeat = true;
        while (repeat)
        {
            repeat = false;
            for (int i = offset + istart; i < offset + istart + npl - 1; i++)
            {
                if (m_points[1][i] > m_points[1][i + 1])
                {
                    std::swap(m_points[0][i + 1], m_points[0][i]);
                    std::swap(m_points[1][i + 1], m_points[1][i]);
                    std::swap(m_points[2][i + 1], m_points[2][i]);
                    repeat = true;
                }
            }
        }
        offset += npl;
        npl--;
    }
}
 
} // namespace LibUtilities
} // namespace Nektar