NodalTriEvenlySpaced.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: NodalTriEvenlySpaced.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
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// DEALINGS IN THE SOFTWARE.
//
// Description: 2D Nodal Triangle Evenly Spaced Point Definitions
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/Foundations/NodalTriEvenlySpaced.h>
#include <vector>
 
namespace Nektar::LibUtilities
{
bool NodalTriEvenlySpaced::initPointsManager[] = {
    PointsManager().RegisterCreator(PointsKey(0, eNodalTriEvenlySpaced),
                                    NodalTriEvenlySpaced::Create)};
 
namespace
{
// construct the geometory and set the coordinate of triangle
// edges and vertices are ordered as anticlockwise
bool isVertex(size_t i, size_t j, size_t npts)
{
    return (i == 0 && j == 0) || (i == (npts - 1) && j == 0) ||
           (i == 0 && j == (npts - 1));
}
 
bool isEdge(size_t i, size_t j, size_t npts)
{
    return i == 0 || j == 0 || i + j == npts - 1; // i+j=tot num of steps
}
 
bool isEdge_1(size_t i, [[maybe_unused]] size_t j, [[maybe_unused]] size_t npts)
{
    return i == 0;
}
 
bool isEdge_2(size_t i, size_t j, size_t npts)
{
    return i + j == npts - 1;
}
} // namespace
 
void NodalTriEvenlySpaced::v_CalculatePoints()
{
    // Allocate the storage for points
    PointsBaseType::v_CalculatePoints();
 
    // Populate m_points
    size_t npts     = GetNumPoints();
    NekDouble delta = 2.0 / (npts - 1.0);
    for (size_t i = 0, index = 0; i < npts; ++i)
    { // y-direction
        for (size_t j = 0; j < npts - i; ++j, ++index)
        { // x-direction
            NekDouble x        = -1.0 + j * delta;
            NekDouble y        = -1.0 + i * delta;
            m_points[0][index] = x;
            m_points[1][index] = y;
        }
    }
 
    NodalPointReorder2d();
 
    m_util = MemoryManager<NodalUtilTriangle>::AllocateSharedPtr(
        npts - 1, m_points[0], m_points[1]);
}
 
void NodalTriEvenlySpaced::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 NodalTriEvenlySpaced::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 NodalTriEvenlySpaced::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> NodalTriEvenlySpaced::Create(
    const PointsKey &key)
{
    std::shared_ptr<PointsBaseType> returnval(
        MemoryManager<NodalTriEvenlySpaced>::AllocateSharedPtr(key));
 
    returnval->Initialize();
 
    return returnval;
}
 
void NodalTriEvenlySpaced::NodalPointReorder2d()
{
    size_t npts = GetNumPoints();
    using std::vector;
    vector<int> vertex;
    vector<int> iEdge_1; // interior edge points on the bottom triangle edge
    vector<int> iEdge_2; // interior edge points on the right triangle edge
    vector<int> iEdge_3; // interior edge points on the left triangle edge
    vector<int> interiorPoints;
    vector<int> map;
 
    // Build the lattice triangle left to right - bottom to top
    for (size_t i = 0, index = 0; i < npts; ++i)
    { // y-direction
        for (size_t j = 0; j < npts - i; ++j, ++index)
        { // x-direction
 
            if (isVertex(i, j, npts))
            {
 
                vertex.push_back(index);
            }
            else if (isEdge(i, j, npts))
            { // interior edge
 
                if (isEdge_1(i, j, npts))
                { // bottom edge
 
                    iEdge_1.push_back(index);
                }
                else if (isEdge_2(i, j, npts))
                { // right edge
 
                    iEdge_2.push_back(index);
                }
                else // left edge
                {
                    // Add backwards.  This is because of counter clockwise.
                    iEdge_3.insert(iEdge_3.begin(), index);
                }
            }
            else
            { // Interior points
 
                interiorPoints.push_back(index);
            }
        }
    }
 
    // Mapping the vertex, edges, and interior points using the permutation
    // matrix, so the points are ordered anticlockwise.
    for (size_t k = 0; k < vertex.size(); ++k)
    {
 
        map.push_back(vertex[k]);
    }
 
    for (size_t k = 0; k < iEdge_1.size(); ++k)
    {
 
        map.push_back(iEdge_1[k]);
    }
 
    for (size_t k = 0; k < iEdge_2.size(); ++k)
    {
 
        map.push_back(iEdge_2[k]);
    }
 
    for (size_t k = 0; k < iEdge_3.size(); ++k)
    {
 
        map.push_back(iEdge_3[k]);
    }
 
    for (size_t k = 0; k < interiorPoints.size(); ++k)
    {
 
        map.push_back(interiorPoints[k]);
    }
 
    Array<OneD, NekDouble> points[2];
    points[0] = Array<OneD, NekDouble>(GetTotNumPoints());
    points[1] = Array<OneD, NekDouble>(GetTotNumPoints());
    for (size_t index = 0; index < map.size(); ++index)
    {
        points[0][index] = m_points[0][index];
        points[1][index] = m_points[1][index];
    }
 
    for (size_t index = 0; index < map.size(); ++index)
    {
        m_points[0][index] = points[0][map[index]];
        m_points[1][index] = points[1][map[index]];
    }
}
 
} // namespace Nektar::LibUtilities