SegGeom.cpp

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////////////////////////////////////////////////////////////////////////////////
//
//  File: SegGeom.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
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//  Description:
//
//
////////////////////////////////////////////////////////////////////////////////
 
#include <SpatialDomains/GeomFactors.h>
#include <SpatialDomains/SegGeom.h>
 
#include <LibUtilities/Foundations/ManagerAccess.h> // for PointsManager, etc
#include <StdRegions/StdRegions.hpp>
#include <StdRegions/StdSegExp.h>
 
namespace Nektar
{
namespace SpatialDomains
{
SegGeom::SegGeom()
{
    m_shapeType = LibUtilities::eSegment;
}
 
SegGeom::SegGeom(int id, const int coordim, const PointGeomSharedPtr vertex[],
                 const CurveSharedPtr curve)
    : Geometry1D(coordim)
{
    m_shapeType = LibUtilities::eSegment;
    m_globalID  = id;
    m_state     = eNotFilled;
    m_curve     = curve;
 
    m_verts[0] = vertex[0];
    m_verts[1] = vertex[1];
}
 
SegGeom::SegGeom(const SegGeom &in) : Geometry1D(in)
{
    // From Geometry class
    m_shapeType = in.m_shapeType;
 
    // info from EdgeComponent class
    m_globalID = in.m_globalID;
    m_xmap     = in.m_xmap;
    SetUpCoeffs(m_xmap->GetNcoeffs());
 
    // info from SegGeom class
    m_coordim  = in.m_coordim;
    m_verts[0] = in.m_verts[0];
    m_verts[1] = in.m_verts[1];
 
    m_state = in.m_state;
}
 
void SegGeom::SetUpXmap()
{
    if (m_curve)
    {
        int npts = m_curve->m_points.size();
        LibUtilities::PointsKey pkey(npts + 1,
                                     LibUtilities::eGaussLobattoLegendre);
        const LibUtilities::BasisKey B(LibUtilities::eModified_A, npts, pkey);
        m_xmap = MemoryManager<StdRegions::StdSegExp>::AllocateSharedPtr(B);
    }
    else
    {
        const LibUtilities::BasisKey B(
            LibUtilities::eModified_A, 2,
            LibUtilities::PointsKey(2, LibUtilities::eGaussLobattoLegendre));
        m_xmap = MemoryManager<StdRegions::StdSegExp>::AllocateSharedPtr(B);
    }
}
 
/**
 * \brief Generate a one dimensional space segment geometry where the vert[0]
 * has the same x value and vert[1] is set to vert[0] plus the length of the
 * original segment
 **/
SegGeomSharedPtr SegGeom::GenerateOneSpaceDimGeom(void)
{
    SegGeomSharedPtr returnval = MemoryManager<SegGeom>::AllocateSharedPtr();
 
    // info about numbering
    returnval->m_globalID = m_globalID;
 
    // geometric information.
    returnval->m_coordim     = 1;
    NekDouble x0             = (*m_verts[0])[0];
    PointGeomSharedPtr vert0 = MemoryManager<PointGeom>::AllocateSharedPtr(
        1, m_verts[0]->GetGlobalID(), x0, 0.0, 0.0);
    vert0->SetGlobalID(vert0->GetGlobalID());
    returnval->m_verts[0] = vert0;
 
    // Get information to calculate length.
    const Array<OneD, const LibUtilities::BasisSharedPtr> base =
        m_xmap->GetBase();
    LibUtilities::PointsKeyVector v;
    v.push_back(base[0]->GetPointsKey());
    v_GenGeomFactors();
 
    const Array<OneD, const NekDouble> jac = m_geomFactors->GetJac(v);
 
    NekDouble len = 0.0;
    if (jac.size() == 1)
    {
        len = jac[0] * 2.0;
    }
    else
    {
        Array<OneD, const NekDouble> w0 = base[0]->GetW();
        len                             = 0.0;
 
        for (int i = 0; i < jac.size(); ++i)
        {
            len += jac[i] * w0[i];
        }
    }
    // Set up second vertex.
    PointGeomSharedPtr vert1 = MemoryManager<PointGeom>::AllocateSharedPtr(
        1, m_verts[1]->GetGlobalID(), x0 + len, 0.0, 0.0);
    vert1->SetGlobalID(vert1->GetGlobalID());
 
    returnval->m_verts[1] = vert1;
 
    // at present just use previous m_xmap[0];
    returnval->m_xmap = m_xmap;
    returnval->SetUpCoeffs(m_xmap->GetNcoeffs());
    returnval->m_state = eNotFilled;
 
    return returnval;
}
 
SegGeom::~SegGeom()
{
}
 
LibUtilities::ShapeType SegGeom::v_GetShapeType() const
{
    return LibUtilities::eSegment;
}
 
NekDouble SegGeom::v_GetCoord(const int i,
                              const Array<OneD, const NekDouble> &Lcoord)
{
    ASSERTL1(m_state == ePtsFilled, "Geometry is not in physical space");
 
    Array<OneD, NekDouble> tmp(m_xmap->GetTotPoints());
    m_xmap->BwdTrans(m_coeffs[i], tmp);
 
    return m_xmap->PhysEvaluate(Lcoord, tmp);
}
 
/**
 * @brief Get the orientation of @p edge1.
 *
 * If @p edge1 is connected to @p edge2 in the same direction as the points
 * comprising @p edge1 then it is forward, otherwise it is backward.
 *
 * For example, assume @p edge1 is comprised of points 1 and 2, and @p edge2 is
 * comprised of points 2 and 3, then @p edge1 is forward.
 *
 * If @p edge1 is comprised of points 2 and 1 and @p edge2 is comprised of
 * points 3 and 2, then @p edge1 is backward.
 *
 * Since both edges are passed, it does not need any information from the
 * EdgeComponent instance.
 */
StdRegions::Orientation SegGeom::GetEdgeOrientation(const SegGeom &edge1,
                                                    const SegGeom &edge2)
{
    StdRegions::Orientation returnval = StdRegions::eForwards;
 
    if ((*edge1.GetVertex(0) == *edge2.GetVertex(0)) ||
        (*edge1.GetVertex(0) == *edge2.GetVertex(1)))
    {
        // Backward direction.  Vertex 0 is connected to edge 2.
        returnval = StdRegions::eBackwards;
    }
    else if ((*edge1.GetVertex(1) != *edge2.GetVertex(0)) &&
             (*edge1.GetVertex(1) != *edge2.GetVertex(1)))
    {
        // Not forward either, then we have a problem.
        std::ostringstream errstrm;
        errstrm << "Connected edges do not share a vertex. Edges ";
        errstrm << edge1.GetGlobalID() << ", " << edge2.GetGlobalID();
        ASSERTL0(false, errstrm.str());
    }
 
    return returnval;
}
 
void SegGeom::v_GenGeomFactors()
{
    if (!m_setupState)
    {
        SegGeom::v_Setup();
    }
 
    if (m_geomFactorsState != ePtsFilled)
    {
        SpatialDomains::GeomType gType = eRegular;
        SegGeom::v_FillGeom();
 
        if (m_xmap->GetBasisNumModes(0) != 2)
        {
            gType = eDeformed;
        }
 
        m_geomFactors = MemoryManager<GeomFactors>::AllocateSharedPtr(
            gType, m_coordim, m_xmap, m_coeffs);
        m_geomFactorsState = ePtsFilled;
    }
}
 
void SegGeom::v_FillGeom()
{
    if (m_state != ePtsFilled)
    {
        int i;
 
        if (m_coordim > 0 && m_curve)
        {
            int npts = m_curve->m_points.size();
            LibUtilities::PointsKey pkey(npts + 1,
                                         LibUtilities::eGaussLobattoLegendre);
            Array<OneD, NekDouble> tmp(npts);
 
            if (m_verts[0]->dist(*(m_curve->m_points[0])) >
                NekConstants::kVertexTheSameDouble)
            {
                std::string err =
                    "Vertex 0 is separated from first point by more than ";
                std::stringstream strstrm;
                strstrm << NekConstants::kVertexTheSameDouble << " in edge "
                        << m_globalID;
                err += strstrm.str();
                NEKERROR(ErrorUtil::ewarning, err.c_str());
            }
 
            if (m_verts[1]->dist(*(m_curve->m_points[npts - 1])) >
                NekConstants::kVertexTheSameDouble)
            {
                std::string err =
                    "Vertex 1 is separated from last point by more than ";
                std::stringstream strstrm;
                strstrm << NekConstants::kVertexTheSameDouble << " in edge "
                        << m_globalID;
                err += strstrm.str();
                NEKERROR(ErrorUtil::ewarning, err.c_str());
            }
 
            LibUtilities::PointsKey fkey(npts, m_curve->m_ptype);
            DNekMatSharedPtr I0 =
                LibUtilities::PointsManager()[fkey]->GetI(pkey);
            NekVector<NekDouble> out(npts + 1);
 
            for (int i = 0; i < m_coordim; ++i)
            {
                // Load up coordinate values into tmp
                for (int j = 0; j < npts; ++j)
                {
                    tmp[j] = (m_curve->m_points[j]->GetPtr())[i];
                }
 
                // Interpolate to GLL points
                NekVector<NekDouble> in(npts, tmp, eWrapper);
                out = (*I0) * in;
 
                m_xmap->FwdTrans(out.GetPtr(), m_coeffs[i]);
            }
        }
 
        for (i = 0; i < m_coordim; ++i)
        {
            m_coeffs[i][0] = (*m_verts[0])[i];
            m_coeffs[i][1] = (*m_verts[1])[i];
        }
 
        m_state = ePtsFilled;
    }
}
 
void SegGeom::v_Reset(CurveMap &curvedEdges, CurveMap &curvedFaces)
{
    Geometry::v_Reset(curvedEdges, curvedFaces);
    CurveMap::iterator it = curvedEdges.find(m_globalID);
 
    if (it != curvedEdges.end())
    {
        m_curve = it->second;
    }
 
    SetUpXmap();
    SetUpCoeffs(m_xmap->GetNcoeffs());
}
 
void SegGeom::v_Setup()
{
    if (!m_setupState)
    {
        SetUpXmap();
        SetUpCoeffs(m_xmap->GetNcoeffs());
        m_setupState = true;
    }
}
 
PointGeomSharedPtr SegGeom::v_GetVertex(const int i) const
{
    PointGeomSharedPtr returnval;
 
    if (i >= 0 && i < kNverts)
    {
        returnval = m_verts[i];
    }
 
    return returnval;
}
 
int SegGeom::v_GetNumVerts() const
{
    return kNverts;
}
 
NekDouble SegGeom::v_FindDistance(const Array<OneD, const NekDouble> &xs,
                                  Array<OneD, NekDouble> &xiOut)
{
    if (m_geomFactors->GetGtype() == eRegular)
    {
        xiOut = Array<OneD, NekDouble>(1, 0.0);
 
        GetLocCoords(xs, xiOut);
        ClampLocCoords(xiOut);
 
        Array<OneD, NekDouble> gloCoord(m_coordim);
        NekDouble tmp = 0;
        for (int i = 0; i < m_coordim; ++i)
        {
            gloCoord[i] = GetCoord(i, xiOut);
            tmp += (xs[i] - gloCoord[i]) * (xs[i] - gloCoord[i]);
        }
 
        return sqrt(tmp);
    }
    // If deformed edge then the inverse mapping is non-linear so need to
    // numerically solve for the local coordinate
    else if (m_geomFactors->GetGtype() == eDeformed)
    {
        Array<OneD, NekDouble> xi(1, 0.0);
 
        // Armijo constants:
        // https://en.wikipedia.org/wiki/Backtracking_line_search
        const NekDouble c1 = 1e-4, c2 = 0.9;
 
        int dim = GetCoordim();
        int nq  = m_xmap->GetTotPoints();
 
        Array<OneD, Array<OneD, NekDouble>> x(dim), xder(dim), xder2(dim);
        // Get x,y,z phys values from coefficients
        for (int i = 0; i < dim; ++i)
        {
            x[i]     = Array<OneD, NekDouble>(nq);
            xder[i]  = Array<OneD, NekDouble>(nq);
            xder2[i] = Array<OneD, NekDouble>(nq);
 
            m_xmap->BwdTrans(m_coeffs[i], x[i]);
        }
 
        NekDouble fx_prev = std::numeric_limits<NekDouble>::max();
 
        // Minimisation loop (Quasi-newton method)
        for (int i = 0; i < NekConstants::kNewtonIterations; ++i)
        {
            // Compute the objective function, f(x_k) and its derivatives
            Array<OneD, NekDouble> xc(dim);
            Array<OneD, std::array<NekDouble, 3>> xc_der(dim);
            Array<OneD, std::array<NekDouble, 6>> xc_der2(dim);
            NekDouble fx = 0, fxp = 0, fxp2 = 0, xcDiff = 0;
            for (int j = 0; j < dim; ++j)
            {
                xc[j] = m_xmap->PhysEvaluate(xi, x[j], xc_der[j], xc_der2[j]);
 
                xcDiff = xc[j] - xs[j];
                // Objective function is the distance to the search point
                fx += xcDiff * xcDiff;
                fxp += xc_der[j][0] * xcDiff;
                fxp2 += xc_der2[j][0] * xcDiff + xc_der[j][0] * xc_der[j][0];
            }
 
            fxp *= 2;
            fxp2 *= 2;
 
            // Check for convergence
            if (std::abs(fx - fx_prev) < 1e-12)
            {
                fx_prev = fx;
                break;
            }
            else
            {
                fx_prev = fx;
            }
 
            NekDouble gamma = 1.0;
            bool conv       = false;
 
            // Search direction: Newton's method
            NekDouble pk = -fxp / fxp2;
 
            // Perform backtracking line search
            while (gamma > 1e-10)
            {
                Array<OneD, NekDouble> xi_pk(1);
                xi_pk[0] = xi[0] + pk * gamma;
 
                if (xi_pk[0] < -1.0 || xi_pk[0] > 1.0)
                {
                    gamma /= 2.0;
                    continue;
                }
 
                Array<OneD, NekDouble> xc_pk(dim);
                Array<OneD, std::array<NekDouble, 3>> xc_der_pk(dim);
                NekDouble fx_pk = 0, fxp_pk = 0, xc_pkDiff = 0;
                for (int j = 0; j < dim; ++j)
                {
                    xc_pk[j] = m_xmap->PhysEvaluate(xi_pk, x[j], xc_der_pk[j]);
 
                    xc_pkDiff = xc_pk[j] - xs[j];
                    fx_pk += xc_pkDiff * xc_pkDiff;
                    fxp_pk += xc_der_pk[j][0] * xc_pkDiff;
                }
 
                fxp_pk *= 2;
 
                // Check Wolfe conditions using Armijo constants
                // https://en.wikipedia.org/wiki/Wolfe_conditions
                if ((fx_pk - (fx + c1 * gamma * pk * fxp)) <
                        std::numeric_limits<NekDouble>::epsilon() &&
                    (-pk * fxp_pk + c2 * pk * fxp) <
                        std::numeric_limits<NekDouble>::epsilon())
                {
                    conv = true;
                    break;
                }
 
                gamma /= 2.0;
            }
 
            if (!conv)
            {
                break;
            }
 
            xi[0] += gamma * pk;
        }
 
        xiOut = xi;
        return sqrt(fx_prev);
    }
    else
    {
        ASSERTL0(false, "Geometry type unknown")
    }
 
    return -1.0;
}
 
} // namespace SpatialDomains
} // namespace Nektar