Deform.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: Deform.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: Deformation of mesh from fields.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <GlobalMapping/Deform.h>
#include <LibUtilities/Foundations/Interp.h>
#include <LocalRegions/Expansion3D.h>
#include <MultiRegions/ExpList.h>
#include <StdRegions/StdNodalTriExp.h>
#include <StdRegions/StdQuadExp.h>
#include <StdRegions/StdSegExp.h>
 
namespace Nektar::GlobalMapping
{
 
/**
 * @brief Update geometry according to displacement that is in current
 * fields.
 *
 * @param graph   The MeshGraph of the current geometry.
 * @param fields  The fields containing the displacement.
 */
void UpdateGeometry(SpatialDomains::MeshGraphSharedPtr graph,
                    Array<OneD, MultiRegions::ExpListSharedPtr> &fields,
                    Array<OneD, Array<OneD, NekDouble>> &PhysVals, bool modal)
{
    // Clear existing curvature.
    SpatialDomains::CurveMap &curvedEdges = graph->GetCurvedEdges();
    SpatialDomains::CurveMap &curvedFaces = graph->GetCurvedFaces();
    curvedEdges.clear();
    curvedFaces.clear();
 
    int i, j, k, l, dim;
 
    // Sets to hold IDs of updated vertices to avoid duplicating effort.
    std::set<int> updatedVerts, updatedEdges, updatedFaces;
 
    dim = graph->GetSpaceDimension();
    Array<OneD, Array<OneD, NekDouble>> phys(dim);
    Array<OneD, Array<OneD, NekDouble>> coord(dim);
 
    for (i = 0; i < fields[0]->GetExpSize(); ++i)
    {
        LocalRegions::ExpansionSharedPtr exp = fields[0]->GetExp(i);
        int offset                           = fields[0]->GetPhys_Offset(i);
        int nquad                            = exp->GetTotPoints();
 
        // Extract displacement for this element, allocate storage for
        // elemental coordinates.
        for (j = 0; j < dim; ++j)
        {
            phys[j]  = Array<OneD, NekDouble>(nquad, PhysVals[j] + offset);
            coord[j] = Array<OneD, NekDouble>(nquad);
        }
 
        // In 2D loop over edges.
        if (dim == 2)
        {
            exp->GetCoords(coord[0], coord[1]);
 
            SpatialDomains::Geometry2DSharedPtr geom =
                std::dynamic_pointer_cast<SpatialDomains::Geometry2D>(
                    exp->GetGeom());
 
            for (j = 0; j < exp->GetGeom()->GetNumEdges(); ++j)
            {
                SpatialDomains::Geometry1DSharedPtr edge = geom->GetEdge(j);
 
                // This edge has already been processed.
                if (updatedEdges.find(edge->GetGlobalID()) !=
                    updatedEdges.end())
                {
                    continue;
                }
 
                // Extract edge displacement.
                int nEdgePts = exp->GetTraceNumPoints(j);
                Array<OneD, Array<OneD, NekDouble>> edgePhys(dim);
                Array<OneD, Array<OneD, NekDouble>> edgeCoord(dim);
 
                const LibUtilities::BasisKey B(
                    LibUtilities::eModified_A, nEdgePts,
                    LibUtilities::PointsKey(
                        nEdgePts, LibUtilities::eGaussLobattoLegendre));
                StdRegions::StdExpansion1DSharedPtr seg =
                    MemoryManager<StdRegions::StdSegExp>::AllocateSharedPtr(B);
 
                for (k = 0; k < dim; ++k)
                {
                    edgePhys[k]  = Array<OneD, NekDouble>(nEdgePts);
                    edgeCoord[k] = Array<OneD, NekDouble>(nEdgePts);
                    exp->GetTracePhysVals(j, seg, phys[k], edgePhys[k]);
                    exp->GetTracePhysVals(j, seg, coord[k], edgeCoord[k]);
                }
 
                // Update verts
                for (k = 0; k < 2; ++k)
                {
                    int id = edge->GetVid(k);
                    if (updatedVerts.find(id) != updatedVerts.end())
                    {
                        continue;
                    }
 
                    SpatialDomains::PointGeomSharedPtr pt = edge->GetVertex(k);
 
                    pt->UpdatePosition(
                        (*pt)(0) + edgePhys[0][k * (nEdgePts - 1)],
                        (*pt)(1) + edgePhys[1][k * (nEdgePts - 1)], (*pt)(2));
 
                    updatedVerts.insert(id);
                }
 
                // Update curve
                SpatialDomains::CurveSharedPtr curve =
                    MemoryManager<SpatialDomains::Curve>::AllocateSharedPtr(
                        edge->GetGlobalID(),
                        LibUtilities::eGaussLobattoLegendre);
 
                for (k = 0; k < nEdgePts; ++k)
                {
                    SpatialDomains::PointGeomSharedPtr vert =
                        MemoryManager<SpatialDomains::PointGeom>::
                            AllocateSharedPtr(dim, edge->GetGlobalID(),
                                              edgeCoord[0][k] + edgePhys[0][k],
                                              edgeCoord[1][k] + edgePhys[1][k],
                                              0.0);
 
                    curve->m_points.push_back(vert);
                }
 
                curvedEdges[edge->GetGlobalID()] = curve;
                updatedEdges.insert(edge->GetGlobalID());
            }
        }
        else if (dim == 3)
        {
            exp->GetCoords(coord[0], coord[1], coord[2]);
 
            SpatialDomains::Geometry3DSharedPtr geom =
                std::dynamic_pointer_cast<SpatialDomains::Geometry3D>(
                    exp->GetGeom());
 
            for (j = 0; j < exp->GetNtraces(); ++j)
            {
                SpatialDomains::Geometry2DSharedPtr face = geom->GetFace(j);
 
                LocalRegions::Expansion3DSharedPtr exp3d =
                    exp->as<LocalRegions::Expansion3D>();
 
                // This edge has already been processed.
                if (updatedFaces.find(face->GetGlobalID()) !=
                    updatedFaces.end())
                {
                    continue;
                }
 
                // Extract face displacement.
                LibUtilities::BasisKey B0 = exp->GetTraceBasisKey(j, 0);
                LibUtilities::BasisKey B1 = exp->GetTraceBasisKey(j, 1);
                int nq0                   = B0.GetNumPoints();
                int nq1                   = B1.GetNumPoints();
 
                ASSERTL1(B0.GetPointsType() ==
                                 LibUtilities::eGaussLobattoLegendre &&
                             B1.GetPointsType() ==
                                 LibUtilities::eGaussLobattoLegendre,
                         "Deformation requires GLL points in both "
                         "directions on a face.");
 
                Array<OneD, Array<OneD, NekDouble>> newPos(dim);
 
                StdRegions::StdExpansion2DSharedPtr faceexp;
                StdRegions::Orientation orient = exp->GetTraceOrient(j);
 
                if (face->GetShapeType() == LibUtilities::eTriangle)
                {
                    faceexp =
                        MemoryManager<StdRegions::StdTriExp>::AllocateSharedPtr(
                            B0, B1);
                }
                else
                {
                    faceexp = MemoryManager<
                        StdRegions::StdQuadExp>::AllocateSharedPtr(B0, B1);
                }
 
                for (k = 0; k < dim; ++k)
                {
                    Array<OneD, NekDouble> tmp(nq0 * nq1);
                    newPos[k] = Array<OneD, NekDouble>(nq0 * nq1);
                    exp3d->GetTracePhysVals(j, faceexp, phys[k], tmp, orient);
                    exp3d->GetTracePhysVals(j, faceexp, coord[k], newPos[k],
                                            orient);
                    Vmath::Vadd(nq0 * nq1, tmp, 1, newPos[k], 1, newPos[k], 1);
                }
 
                // Now interpolate face onto a more reasonable set of
                // points.
                int nq = std::max(nq0, nq1);
                if (!modal)
                {
                    nq--;
                }
 
                LibUtilities::PointsKey edgePts(
                    nq, LibUtilities::eGaussLobattoLegendre);
                LibUtilities::PointsKey triPts(nq, LibUtilities::eNodalTriElec);
 
                Array<OneD, Array<OneD, NekDouble>> intPos(dim);
 
                for (k = 0; k < dim; ++k)
                {
                    intPos[k] = Array<OneD, NekDouble>(nq * nq);
                    LibUtilities::Interp2D(faceexp->GetPointsKeys()[0],
                                           faceexp->GetPointsKeys()[1],
                                           newPos[k], edgePts, edgePts,
                                           intPos[k]);
                }
 
                int edgeOff[2][4][2] = {
                    {{0, 1}, {nq - 1, nq}, {nq * (nq - 1), -nq}, {-1, -1}},
                    {{0, 1},
                     {nq - 1, nq},
                     {nq * nq - 1, -1},
                     {nq * (nq - 1), -nq}}};
 
                for (k = 0; k < face->GetNumVerts(); ++k)
                {
                    // Update verts
                    int id = face->GetVid(k);
                    const int o =
                        face->GetShapeType() - LibUtilities::eTriangle;
 
                    if (updatedVerts.find(id) == updatedVerts.end())
                    {
                        SpatialDomains::PointGeomSharedPtr pt =
                            face->GetVertex(k);
                        pt->UpdatePosition(intPos[0][edgeOff[o][k][0]],
                                           intPos[1][edgeOff[o][k][0]],
                                           intPos[2][edgeOff[o][k][0]]);
                        updatedVerts.insert(id);
                    }
 
                    // Update edges
                    id = face->GetEid(k);
                    if (updatedEdges.find(id) == updatedEdges.end())
                    {
                        SpatialDomains::Geometry1DSharedPtr edge =
                            face->GetEdge(k);
                        SpatialDomains::CurveSharedPtr curve =
                            MemoryManager<SpatialDomains::Curve>::
                                AllocateSharedPtr(
                                    edge->GetGlobalID(),
                                    LibUtilities::eGaussLobattoLegendre);
 
                        const int offset = edgeOff[o][k][0];
                        const int pos    = edgeOff[o][k][1];
 
                        if (face->GetEorient(k) == StdRegions::eBackwards)
                        {
                            for (l = nq - 1; l >= 0; --l)
                            {
                                int m = offset + pos * l;
                                SpatialDomains::PointGeomSharedPtr vert =
                                    MemoryManager<SpatialDomains::PointGeom>::
                                        AllocateSharedPtr(
                                            dim, edge->GetGlobalID(),
                                            intPos[0][m], intPos[1][m],
                                            intPos[2][m]);
                                curve->m_points.push_back(vert);
                            }
                        }
                        else
                        {
                            for (l = 0; l < nq; ++l)
                            {
                                int m = offset + pos * l;
                                SpatialDomains::PointGeomSharedPtr vert =
                                    MemoryManager<SpatialDomains::PointGeom>::
                                        AllocateSharedPtr(
                                            dim, edge->GetGlobalID(),
                                            intPos[0][m], intPos[1][m],
                                            intPos[2][m]);
                                curve->m_points.push_back(vert);
                            }
                        }
 
                        curvedEdges[edge->GetGlobalID()] = curve;
                        updatedEdges.insert(edge->GetGlobalID());
                    }
                }
 
                // Update face-interior curvature
                LibUtilities::PointsType pType =
                    face->GetShapeType() == LibUtilities::eTriangle
                        ? LibUtilities::eNodalTriElec
                        : LibUtilities::eGaussLobattoLegendre;
 
                SpatialDomains::CurveSharedPtr curve =
                    MemoryManager<SpatialDomains::Curve>::AllocateSharedPtr(
                        face->GetGlobalID(), pType);
 
                if (face->GetShapeType() == LibUtilities::eTriangle)
                {
                    // This code is probably pretty crappy. Have to go from
                    // GLL-GLL points -> GLL-Gauss-Radau -> nodal triangle
                    // points.
                    const LibUtilities::BasisKey B0(
                        LibUtilities::eOrtho_A, nq,
                        LibUtilities::PointsKey(
                            nq, LibUtilities::eGaussLobattoLegendre));
                    const LibUtilities::BasisKey B1(
                        LibUtilities::eOrtho_B, nq,
                        LibUtilities::PointsKey(
                            nq, LibUtilities::eGaussRadauMAlpha1Beta0));
                    StdRegions::StdNodalTriExp nodalTri(B0, B1, pType);
                    StdRegions::StdTriExp tri(B0, B1);
 
                    for (k = 0; k < dim; ++k)
                    {
                        Array<OneD, NekDouble> nodal(nq * nq);
 
                        LibUtilities::Interp2D(
                            faceexp->GetBasis(0)->GetBasisKey(),
                            faceexp->GetBasis(1)->GetBasisKey(), newPos[k], B0,
                            B1, nodal);
 
                        Array<OneD, NekDouble> tmp1(nq * (nq + 1) / 2);
                        Array<OneD, NekDouble> tmp2(nq * (nq + 1) / 2);
 
                        tri.FwdTrans(nodal, tmp1);
                        nodalTri.ModalToNodal(tmp1, tmp2);
                        newPos[k] = tmp2;
                    }
 
                    for (l = 0; l < nq * (nq + 1) / 2; ++l)
                    {
                        SpatialDomains::PointGeomSharedPtr vert =
                            MemoryManager<SpatialDomains::PointGeom>::
                                AllocateSharedPtr(dim, face->GetGlobalID(),
                                                  newPos[0][l], newPos[1][l],
                                                  newPos[2][l]);
                        curve->m_points.push_back(vert);
                    }
                }
                else
                {
                    for (l = 0; l < nq * nq; ++l)
                    {
                        SpatialDomains::PointGeomSharedPtr vert =
                            MemoryManager<SpatialDomains::PointGeom>::
                                AllocateSharedPtr(dim, face->GetGlobalID(),
                                                  intPos[0][l], intPos[1][l],
                                                  intPos[2][l]);
                        curve->m_points.push_back(vert);
                    }
                }
 
                curvedFaces[face->GetGlobalID()] = curve;
                updatedFaces.insert(face->GetGlobalID());
            }
        }
    }
 
    // Reset geometry information
    for (i = 0; i < fields.size(); ++i)
    {
        fields[i]->Reset();
    }
}
} // namespace Nektar::GlobalMapping