ProcessBL.cpp

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////////////////////////////////////////////////////////////////////////////////
//
//  File: ProcessBL.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: Refine prismatic or quadrilateral boundary layer elements.
//
////////////////////////////////////////////////////////////////////////////////

#include <string>

#include <LibUtilities/BasicUtils/ParseUtils.h>
#include <LibUtilities/BasicUtils/SharedArray.hpp>
#include <LibUtilities/Foundations/BLPoints.h>
#include <LibUtilities/Foundations/ManagerAccess.h>
#include <LibUtilities/Interpreter/Interpreter.h>
#include <LocalRegions/HexExp.h>
#include <LocalRegions/PrismExp.h>
#include <LocalRegions/QuadExp.h>

#include <NekMeshUtils/MeshElements/Element.h>
#include "ProcessBL.h"

using namespace std;
using namespace Nektar::NekMeshUtils;

namespace Nektar
{
namespace Utilities
{
ModuleKey ProcessBL::className = GetModuleFactory().RegisterCreatorFunction(
    ModuleKey(eProcessModule, "bl"),
    ProcessBL::create,
    "Refines a prismatic or quadrilateral boundary layer.");

int **helper2d(int lda, int arr[][2])
{
    int **ret = new int *[lda];
    for (int i = 0; i < lda; ++i)
    {
        ret[i]    = new int[2];
        ret[i][0] = arr[i][0];
        ret[i][1] = arr[i][1];
    }
    return ret;
}

int **helper2d(int lda, int arr[][4])
{
    int **ret = new int *[lda];
    for (int i = 0; i < lda; ++i)
    {
        ret[i]    = new int[4];
        ret[i][0] = arr[i][0];
        ret[i][1] = arr[i][1];
        ret[i][2] = arr[i][2];
        ret[i][3] = arr[i][3];
    }
    return ret;
}

struct SplitMapHelper
{
    int size;
    int layerOff;
    int *edge;
    int *offset;
    int *inc;
    int **conn;
    int bfacesSize;
    int *bfaces;
};

struct SplitEdgeHelper
{
    int size;
    int *edge;
    int **edgeVert;
    int *offset;
    int *inc;
};

ProcessBL::ProcessBL(MeshSharedPtr m) : ProcessModule(m)
{
    // BL mesh configuration.
    m_config["layers"] =
        ConfigOption(false, "2", "Number of layers to refine.");
    m_config["nq"] =
        ConfigOption(false, "5", "Number of points in high order elements.");
    m_config["surf"] =
        ConfigOption(false, "", "Tag identifying surface connected to prism.");
    m_config["r"] =
        ConfigOption(false, "2.0", "Ratio to use in geometry progression.");
}

ProcessBL::~ProcessBL()
{
}

void ProcessBL::Process()
{
    if (m_mesh->m_verbose)
    {
        cout << "ProcessBL: Refining boundary layer..." << endl;
    }
    int dim = m_mesh->m_expDim;
    switch (dim)
    {
        case 2:
        {
            BoundaryLayer2D();
        }
        break;

        case 3:
        {
            BoundaryLayer3D();
        }
        break;

        default:
            ASSERTL0(0,"Dimension not supported");
        break;
    }

    // Re-process mesh to eliminate duplicate vertices and edges.
    ProcessVertices();
    ProcessEdges();
    ProcessFaces();
    ProcessElements();
    ProcessComposites();
}

void ProcessBL::BoundaryLayer2D()
{
    int nodeId  = m_mesh->m_vertexSet.size();
    int nl      = m_config["layers"].as<int>();
    int nq      = m_config["nq"].    as<int>();

    // determine if geometric ratio is string or a constant.
    LibUtilities::Interpreter rEval;
    NekDouble r             =  1;
    int       rExprId       = -1;
    bool      ratioIsString = false;

    if (m_config["r"].isType<NekDouble>())
    {
        r = m_config["r"].as<NekDouble>();
    }
    else
    {
        std::string rstr = m_config["r"].as<string>();
        rExprId = rEval.DefineFunction("x y z", rstr);
        ratioIsString = true;
    }

    // Default PointsType.
    LibUtilities::PointsType pt = LibUtilities::eGaussLobattoLegendre;

    // Map which takes element ID to edge on surface. This enables
    // splitting to occur in either y-direction of the prism.
    map<int, int> splitEls;

    // edgeMap associates geometry edge IDs to the (nl+1) vertices which
    // are generated along that edge when a prism is split, and is used
    // to avoid generation of duplicate vertices. It is stored as an
    // unordered map for speed.
    std::unordered_map<int, vector<NodeSharedPtr> > edgeMap;

    string surf = m_config["surf"].as<string>();
    if (surf.size() > 0)
    {
        vector<unsigned int> surfs;
        ParseUtils::GenerateSeqVector(surf, surfs);
        sort(surfs.begin(), surfs.end());

        // If surface is defined, process list of elements to find those
        // that are connected to it.
        for (int i = 0; i < m_mesh->m_element[m_mesh->m_expDim].size(); ++i)
        {
            ElementSharedPtr el = m_mesh->m_element[m_mesh->m_expDim][i];
            int nSurf = el->GetEdgeCount();

            for (int j = 0; j < nSurf; ++j)
            {
                int bl = el->GetBoundaryLink(j);
                if (bl == -1)
                {
                    continue;
                }

                ElementSharedPtr bEl  = m_mesh->m_element[m_mesh->m_expDim-1][bl];
                vector<int>      tags = bEl->GetTagList();
                vector<int>      inter;

                sort(tags.begin(), tags.end());
                set_intersection(surfs.begin(), surfs.end(),
                                 tags .begin(), tags .end(),
                                 back_inserter(inter));
                ASSERTL0(inter.size() <= 1,
                         "Intersection of surfaces wrong");

                if (inter.size() == 1)
                {
                    if (el->GetConf().m_e != LibUtilities::eQuadrilateral)
                    {
                        cerr << "WARNING: Found non-quad element "
                             << "to split in surface " << surf
                             << "; ignoring" << endl;
                        continue;
                    }

                    if (splitEls.count(el->GetId()) > 0)
                    {
                        cerr << "WARNING: quad already found; "
                             << "ignoring" << endl;
                        continue;
                    }

                    splitEls[el->GetId()] = j;
                }
            }
        }
    }
    else
    {
        ASSERTL0(false, "Surface must be specified.");
    }

    if (splitEls.size() == 0)
    {
        cerr << "WARNING: No elements detected to split." << endl;
        return;
    }

    // Erase all elements from the element list. Elements will be
    // re-added as they are split.
    vector<ElementSharedPtr> el = m_mesh->m_element[m_mesh->m_expDim];
    m_mesh->m_element[m_mesh->m_expDim].clear();

    // Iterate over list of elements of expansion dimension.
    for (int i = 0; i < el.size(); ++i)
    {


        if (splitEls.count(el[i]->GetId()) == 0)
        {
            m_mesh->m_element[m_mesh->m_expDim].push_back(el[i]);
            continue;
        }

        // Find other boundary faces if any
        std::map<int, int> bLink;
        for (int j = 0; j < 4; j++)
        {
            int bl = el[i]->GetBoundaryLink(j);
            if ( (bl != -1) && ( j != splitEls[el[i]->GetId()]) )
            {
                bLink[j] = bl;
            }
        }

        // Get elemental geometry object.
        SpatialDomains::QuadGeomSharedPtr geom =
            std::dynamic_pointer_cast<SpatialDomains::QuadGeom>(
                el[i]->GetGeom(m_mesh->m_spaceDim));

        // Determine whether to use reverse points.
        // (if edges 1 or 2 are on the surface)
        LibUtilities::PointsType t = ( (splitEls[el[i]->GetId()]+1) %4) < 2 ?
            LibUtilities::eBoundaryLayerPoints :
            LibUtilities::eBoundaryLayerPointsRev;


        if(ratioIsString) // determine value of r base on geom
        {
            NekDouble x,y,z;
            NekDouble x1,y1,z1;
            int nverts = geom->GetNumVerts();

            x = y = z = 0.0;

            for(int i = 0; i < nverts; ++i)
            {
                geom->GetVertex(i)->GetCoords(x1,y1,z1);
                x += x1; y += y1; z += z1;
            }
            x /= (NekDouble) nverts;
            y /= (NekDouble) nverts;
            z /= (NekDouble) nverts;
            r = rEval.Evaluate(rExprId,x,y,z,0.0);
        }

        // Create basis.
        LibUtilities::BasisKey B0(
            LibUtilities::eModified_A, nq,
            LibUtilities::PointsKey(nq,pt));
        LibUtilities::BasisKey B1(
            LibUtilities::eModified_A, 2,
            LibUtilities::PointsKey(nl+1, t, r));

        // Create local region.
        LocalRegions::QuadExpSharedPtr q;
        if (splitEls[el[i]->GetId()] % 2)
        {
            q = MemoryManager<LocalRegions::QuadExp>::AllocateSharedPtr(
                B1,B0,geom);
        }
        else
        {
            q = MemoryManager<LocalRegions::QuadExp>::AllocateSharedPtr(
                B0,B1,geom);
        }

        // Grab co-ordinates.
        Array<OneD, NekDouble> x(nq*(nl+1), 0.0);
        Array<OneD, NekDouble> y(nq*(nl+1), 0.0);
        Array<OneD, NekDouble> z(nq*(nl+1), 0.0);
        q->GetCoords(x,y,z);

        vector<vector<NodeSharedPtr> > edgeNodes(2);

        // Loop over edges to be split.
        for (int j = 0; j < 2; ++j)
        {
            int locEdge = (splitEls[el[i]->GetId()]+1+2*j)%4;
            int edgeId  = el[i]->GetEdge(locEdge)->m_id;

            // Determine whether we have already generated vertices
            // along this edge.
            auto eIt = edgeMap.find(edgeId);

            if (eIt == edgeMap.end())
            {
                // If not then resize storage to hold new points.
                edgeNodes[j].resize(nl+1);

                // Re-use existing vertices at endpoints of edge to
                // avoid duplicating the existing vertices.
                edgeNodes[j][0]  = el[i]->GetVertex(locEdge);
                edgeNodes[j][nl] = el[i]->GetVertex((locEdge+1)%4);

                 // Variable geometric ratio
                if(ratioIsString)
                {
                    NekDouble x0,y0;
                    NekDouble x1,y1;
                    NekDouble xm,ym,zm=0.0;

                    // -> Find edge end and mid points
                    x0 = edgeNodes[j][0]->m_x;
                    y0 = edgeNodes[j][0]->m_y;

                    x1 = edgeNodes[j][nl]->m_x;
                    y1 = edgeNodes[j][nl]->m_y;

                    xm = 0.5*(x0+x1);
                    ym = 0.5*(y0+y1);

                    // evaluate r factor based on mid point value
                    NekDouble rnew;
                    rnew = rEval.Evaluate(rExprId,xm,ym,zm,0.0);

                    // Get basis with new r;
                    t =  (j==0) ? LibUtilities::eBoundaryLayerPoints :
                                 LibUtilities::eBoundaryLayerPointsRev;
                    LibUtilities::PointsKey Pkey(nl+1, t, rnew);
                    LibUtilities::PointsSharedPtr newP
                        = LibUtilities::PointsManager()[Pkey];

                    const Array<OneD, const NekDouble> z = newP->GetZ();

                    // Create new interior nodes based on this new blend
                    for (int k = 1; k < nl; ++k)
                    {
                        xm = 0.5*(1+z[k])*(x1-x0) + x0;
                        ym = 0.5*(1+z[k])*(y1-y0) + y0;
                        zm = 0.0;
                        edgeNodes[j][k] = NodeSharedPtr(
                                new Node(nodeId++, xm,ym,zm));
                    }
                }
                else
                {
                    // Create new interior nodes.
                    int pos = 0;
                    for (int k = 1; k < nl; ++k)
                    {
                        switch (locEdge)
                        {
                            case 0:
                                pos = k;
                                break;
                            case 1:
                                pos = nq -1 + k*nq;
                                break;
                            case 2:
                                pos = nq*(nl+1) -1 - k;
                                break;
                            case 3:
                                pos = nq*nl - k*nq;
                                break;
                            default:
                                NEKERROR(ErrorUtil::efatal,
                                         "Quad edge should be < 4.");
                            break;
                        }
                        edgeNodes[j][k] = NodeSharedPtr(
                            new Node(nodeId++, x[pos], y[pos], z[pos]));
                    }
                }

                // Store these edges in edgeMap.
                edgeMap[edgeId] = edgeNodes[j];
            }
            else
            {
                // Check orientation
                if (eIt->second[0] == el[i]->GetVertex(locEdge))
                {
                    // Same orientation: copy nodes
                    edgeNodes[j] = eIt->second;
                }
                else
                {
                    // Reversed orientation: copy in reversed order
                    edgeNodes[j].resize(nl+1);
                    for (int k = 0; k < nl+1; ++k)
                    {
                        edgeNodes[j][k] = eIt->second[nl-k];
                    }
                }

            }
        }

        // Create element layers.
        for (int j = 0; j < nl; ++j)
        {
            // Get corner vertices.
            vector<NodeSharedPtr> nodeList(4);
            switch (splitEls[el[i]->GetId()])
            {
                case 0:
                {
                    nodeList[0] = edgeNodes[1][nl-j  ];
                    nodeList[1] = edgeNodes[0][j  ];
                    nodeList[2] = edgeNodes[0][j+1];
                    nodeList[3] = edgeNodes[1][nl-j-1];
                    break;
                }
                case 1:
                {
                    nodeList[0] = edgeNodes[1][j];
                    nodeList[1] = edgeNodes[1][j+1];
                    nodeList[2] = edgeNodes[0][nl-j-1];
                    nodeList[3] = edgeNodes[0][nl-j];
                    break;
                }
                case 2:
                {
                    nodeList[0] = edgeNodes[0][nl-j  ];
                    nodeList[1] = edgeNodes[1][j  ];
                    nodeList[2] = edgeNodes[1][j+1];
                    nodeList[3] = edgeNodes[0][nl-j-1];
                    break;
                }
                case 3:
                {
                    nodeList[0] = edgeNodes[0][j];
                    nodeList[1] = edgeNodes[0][j+1];
                    nodeList[2] = edgeNodes[1][nl-j-1];
                    nodeList[3] = edgeNodes[1][nl-j];
                    break;
                }
            }
            // Create the element.
            ElmtConfig conf(LibUtilities::eQuadrilateral, 1, true, false, true);
            ElementSharedPtr elmt = GetElementFactory().
                CreateInstance(
              LibUtilities::eQuadrilateral,conf,nodeList,el[i]->GetTagList());

            // Add high order nodes to split edges.
            for (int l = 0; l < 2; ++l)
            {
                int locEdge = (splitEls[el[i]->GetId()]+2*l)%4;
                EdgeSharedPtr HOedge = elmt->GetEdge(
                    locEdge);
                int pos = 0;
                for (int k = 1; k < nq-1; ++k)
                {
                    switch (locEdge)
                    {
                        case 0:
                            pos = j*nq+ k;
                            break;
                        case 1:
                            pos = j+1 + k*(nl+1);
                            break;
                        case 2:
                            pos = (j+1)*nq + (nq-1) - k;
                            break;
                        case 3:
                            pos = (nl+1)*(nq-1) + j - k*(nl+1);
                            break;
                        default:
                            NEKERROR(ErrorUtil::efatal,
                                     "Quad edge should be < 4.");
                            break;
                    }
                    HOedge->m_edgeNodes.push_back(
                        NodeSharedPtr(
                            new Node(nodeId++,x[pos],y[pos],0.0)));
                }
                HOedge->m_curveType = pt;
            }

            // Change the elements on the boundary
            // to match the layers
            for (auto &it : bLink)
            {
                int eid = it.first;
                int bl  = it.second;

                if (j == 0)
                {
                    // For first layer reuse existing 2D element.
                    ElementSharedPtr e = m_mesh->m_element[m_mesh->m_expDim-1][bl];
                    for (int k = 0; k < 2; ++k)
                    {
                        e->SetVertex(
                            k, nodeList[(eid+k)%4]);
                    }
                }
                else
                {
                    // For all other layers create new element.
                    vector<NodeSharedPtr> qNodeList(2);
                    for (int k = 0; k < 2; ++k)
                    {
                        qNodeList[k] = nodeList[(eid+k)%4];
                    }
                    vector<int> tagBE;
                    tagBE = m_mesh->m_element[m_mesh->m_expDim-1][bl]->GetTagList();
                    ElmtConfig bconf(LibUtilities::eSegment,1,true,true,false);
                    ElementSharedPtr boundaryElmt = GetElementFactory().
                        CreateInstance(LibUtilities::eSegment,bconf,
                                       qNodeList,tagBE);
                    m_mesh->m_element[m_mesh->m_expDim-1].push_back(boundaryElmt);
                }
            }

            m_mesh->m_element[m_mesh->m_expDim].push_back(elmt);
        }
    }
}

void ProcessBL::BoundaryLayer3D()
{
    // A set containing all element types which are valid.
    set<LibUtilities::ShapeType> validElTypes;
    validElTypes.insert(LibUtilities::ePrism);
    validElTypes.insert(LibUtilities::eHexahedron);

    int nodeId = m_mesh->m_vertexSet.size();
    int nl     = m_config["layers"].as<int>();
    int nq     = m_config["nq"].as<int>();

    // determine if geometric ratio is string or a constant.
    LibUtilities::Interpreter rEval;
    NekDouble r        = 1;
    int rExprId        = -1;
    bool ratioIsString = false;

    if (m_config["r"].isType<NekDouble>())
    {
        r = m_config["r"].as<NekDouble>();
    }
    else
    {
        std::string rstr = m_config["r"].as<string>();
        rExprId          = rEval.DefineFunction("x y z", rstr);
        ratioIsString    = true;
    }

    // Prismatic node -> face map.
    int prismFaceNodes[5][4] = {
        {0, 1, 2, 3}, {0, 1, 4, -1}, {1, 2, 5, 4}, {3, 2, 5, -1}, {0, 3, 5, 4}};
    int hexFaceNodes[6][4] = {{0, 1, 2, 3},
                              {0, 1, 5, 4},
                              {1, 2, 6, 5},
                              {3, 2, 6, 7},
                              {0, 3, 7, 4},
                              {4, 5, 6, 7}};
    map<LibUtilities::ShapeType, int **> faceNodeMap;
    faceNodeMap[LibUtilities::ePrism]      = helper2d(5, prismFaceNodes);
    faceNodeMap[LibUtilities::eHexahedron] = helper2d(6, hexFaceNodes);

    // Default PointsType.
    LibUtilities::PointsType pt = LibUtilities::eGaussLobattoLegendre;

    // Map which takes element ID to face on surface. This enables
    // splitting to occur in either y-direction of the prism.
    std::unordered_map<int, int> splitEls;

    // Set up maps which takes an edge (in nektar++ ordering) and return
    // their offset and stride in the 3d array of collapsed quadrature
    // points. Note that this map includes only the edges that are on
    // the triangular faces as the edges in the normal direction are
    // linear.
    map<LibUtilities::ShapeType, map<int, SplitMapHelper> > splitMap;
    int po = nq * (nl + 1);

    SplitMapHelper splitPrism;
    int splitMapEdgePrism[6]    = {0, 2, 4, 5, 6, 7};
    int splitMapOffsetPrism[6]  = {0, nq, 0, nq - 1, nq + nq - 1, nq};
    int splitMapIncPrism[6]     = {1, 1, po, po, po, po};
    int splitMapBFacesPrism[3]  = {0, 2, 4};
    int splitMapConnPrism[6][2] = {
        {0, 0}, {1, 0}, {1, 1}, {0, 1}, {2, 0}, {2, 1}};
    splitPrism.size                   = 6;
    splitPrism.layerOff               = nq;
    splitPrism.edge                   = splitMapEdgePrism;
    splitPrism.offset                 = splitMapOffsetPrism;
    splitPrism.inc                    = splitMapIncPrism;
    splitPrism.conn                   = helper2d(6, splitMapConnPrism);
    splitPrism.bfacesSize             = 3;
    splitPrism.bfaces                 = splitMapBFacesPrism;
    splitMap[LibUtilities::ePrism][1] = splitPrism;
    splitMap[LibUtilities::ePrism][3] = splitPrism;

    int ho = nq * (nq - 1);
    int tl = nq * nq;
    SplitMapHelper splitHex0;
    int splitMapEdgeHex0[8]   = {0, 1, 2, 3, 8, 9, 10, 11};
    int splitMapOffsetHex0[8] = {
        0, nq - 1, tl - 1, ho, tl, tl + nq - 1, 2 * tl - 1, tl + ho};
    int splitMapIncHex0[8]     = {1, nq, -1, -nq, 1, nq, -1, -nq};
    int splitMapBFacesHex0[4]  = {1, 2, 3, 4};
    int splitMapConnHex0[8][2] = {
        {0, 0}, {1, 0}, {2, 0}, {3, 0}, {0, 1}, {1, 1}, {2, 1}, {3, 1}};
    splitHex0.size                         = 8;
    splitHex0.layerOff                     = nq * nq;
    splitHex0.edge                         = splitMapEdgeHex0;
    splitHex0.offset                       = splitMapOffsetHex0;
    splitHex0.inc                          = splitMapIncHex0;
    splitHex0.conn                         = helper2d(8, splitMapConnHex0);
    splitHex0.bfacesSize                   = 4;
    splitHex0.bfaces                       = splitMapBFacesHex0;
    splitMap[LibUtilities::eHexahedron][0] = splitHex0;
    splitMap[LibUtilities::eHexahedron][5] = splitHex0;

    // splitEdge enumerates the edges in the standard prism along which
    // new nodes should be generated. These edges are the three between
    // the two triangular faces.
    //
    // edgeVertMap specifies the vertices which comprise those edges in
    // splitEdge; for example splitEdge[0] = 3 which connects vertices 0
    // and 3.
    //
    // edgeOffset holds the offset of each of edges 3, 1 and 8
    // respectively inside the collapsed coordinate system.
    map<LibUtilities::ShapeType, map<int, SplitEdgeHelper> > splitEdge;

    int splitPrismEdges[3]       = {3, 1, 8};
    int splitPrismEdgeVert[3][2] = {{0, 3}, {1, 2}, {4, 5}};
    int splitPrismOffset[3]      = {0, nq - 1, nq * (nl + 1) * (nq - 1)};
    int splitPrismInc[3]         = {nq, nq, nq};
    SplitEdgeHelper splitPrismEdge;
    splitPrismEdge.size                = 3;
    splitPrismEdge.edge                = splitPrismEdges;
    splitPrismEdge.edgeVert            = helper2d(3, splitPrismEdgeVert);
    splitPrismEdge.offset              = splitPrismOffset;
    splitPrismEdge.inc                 = splitPrismInc;
    splitEdge[LibUtilities::ePrism][1] = splitPrismEdge;
    splitEdge[LibUtilities::ePrism][3] = splitPrismEdge;

    int splitHex0Edges[4]       = {4, 5, 6, 7};
    int splitHex0EdgeVert[4][2] = {{0, 4}, {1, 5}, {2, 6}, {3, 7}};
    int splitHex0Offset[4]      = {0, nq - 1, nq * nq - 1, nq * (nq - 1)};
    int splitHex0Inc[4]         = {nq * nq, nq * nq, nq * nq, nq * nq};
    SplitEdgeHelper splitHex0Edge;
    splitHex0Edge.size                      = 4;
    splitHex0Edge.edge                      = splitHex0Edges;
    splitHex0Edge.edgeVert                  = helper2d(4, splitHex0EdgeVert);
    splitHex0Edge.offset                    = splitHex0Offset;
    splitHex0Edge.inc                       = splitHex0Inc;
    splitEdge[LibUtilities::eHexahedron][0] = splitHex0Edge;
    splitEdge[LibUtilities::eHexahedron][5] = splitHex0Edge;

    map<LibUtilities::ShapeType, map<int, bool> > revPoints;
    revPoints[LibUtilities::ePrism][1] = true;
    revPoints[LibUtilities::ePrism][3] = false;

    revPoints[LibUtilities::eHexahedron][0] = true;
    revPoints[LibUtilities::eHexahedron][5] = false;

    // edgeMap associates geometry edge IDs to the (nl+1) vertices which
    // are generated along that edge when a prism is split, and is used
    // to avoid generation of duplicate vertices. It is stored as an
    // unordered map for speed.
    std::unordered_map<int, vector<NodeSharedPtr> > edgeMap;

    string surf = m_config["surf"].as<string>();
    if (surf.size() > 0)
    {
        vector<unsigned int> surfs;
        ParseUtils::GenerateVector(surf, surfs);
        sort(surfs.begin(), surfs.end());

        // If surface is defined, process list of elements to find those
        // that are connected to it.
        for (int i = 0; i < m_mesh->m_element[m_mesh->m_expDim].size(); ++i)
        {
            ElementSharedPtr el = m_mesh->m_element[m_mesh->m_expDim][i];
            int nSurf           = el->GetFaceCount();

            for (int j = 0; j < nSurf; ++j)
            {
                int bl = el->GetBoundaryLink(j);
                if (bl == -1)
                {
                    continue;
                }

                ElementSharedPtr bEl =
                    m_mesh->m_element[m_mesh->m_expDim - 1][bl];
                vector<int> tags = bEl->GetTagList();
                vector<int> inter;

                sort(tags.begin(), tags.end());
                set_intersection(surfs.begin(),
                                 surfs.end(),
                                 tags.begin(),
                                 tags.end(),
                                 back_inserter(inter));
                ASSERTL0(inter.size() <= 1, "Intersection of surfaces wrong");

                if (inter.size() == 1)
                {
                    if (el->GetConf().m_e == LibUtilities::ePrism)
                    {
                        if (j % 2 == 0)
                        {
                            cerr << "WARNING: Found quadrilateral face " << j
                                 << " on surface " << surf
                                 << " connected to prism; ignoring." << endl;
                            continue;
                        }

                        if (splitEls.count(el->GetId()) > 0)
                        {
                            cerr << "WARNING: prism already found; "
                                 << "ignoring" << endl;
                        }

                        splitEls[el->GetId()] = j;
                    }
                    else if (validElTypes.count(el->GetConf().m_e) == 0)
                    {
                        cerr << "WARNING: Unsupported element type "
                             << "found in surface " << j << "; "
                             << "ignoring" << endl;
                        continue;
                    }
                }
            }
        }
    }
    else
    {
        // Otherwise, add all prismatic elements and assume face 1 of
        // the prism lies on the surface.
        for (int i = 0; i < m_mesh->m_element[m_mesh->m_expDim].size(); ++i)
        {
            ElementSharedPtr el = m_mesh->m_element[m_mesh->m_expDim][i];

            if (el->GetConf().m_e == LibUtilities::ePrism)
            {
                splitEls[el->GetId()] = 1;
            }
            else if (validElTypes.count(el->GetConf().m_e) > 0)
            {
                splitEls[el->GetId()] = 0;
            }
            else
            {
                continue;
            }
        }
    }

    if (splitEls.size() == 0)
    {
        cerr << "WARNING: No elements detected to split." << endl;
        return;
    }

    // Erase all elements from the element list. Elements will be
    // re-added as they are split.
    vector<ElementSharedPtr> el = m_mesh->m_element[m_mesh->m_expDim];
    m_mesh->m_element[m_mesh->m_expDim].clear();

    map<int, SpatialDomains::Geometry3DSharedPtr> geomMap;
    for (int i = 0; i < el.size(); ++i)
    {
        const int elId = el[i]->GetId();
        if (splitEls.find(elId) == splitEls.end())
        {
            continue;
        }

        // Get elemental geometry object and put into map.
        geomMap[elId] = std::dynamic_pointer_cast<SpatialDomains::Geometry3D>(
            el[i]->GetGeom(m_mesh->m_spaceDim));
    }

    // Iterate over list of elements of expansion dimension.
    for (int i = 0; i < el.size(); ++i)
    {
        const int elId = el[i]->GetId();
        auto sIt       = splitEls.find(elId);

        if (sIt == splitEls.end())
        {
            m_mesh->m_element[m_mesh->m_expDim].push_back(el[i]);
            continue;
        }

        SpatialDomains::Geometry3DSharedPtr geom = geomMap[elId];

        const int faceNum              = sIt->second;
        LibUtilities::ShapeType elType = el[i]->GetConf().m_e;

        SplitMapHelper &sMap   = splitMap[elType][faceNum];
        SplitEdgeHelper &sEdge = splitEdge[elType][faceNum];

        // Find quadrilateral boundary faces if any
        std::map<int, int> bLink;
        for (int j = 0; j < sMap.bfacesSize; ++j)
        {
            int bl = el[i]->GetBoundaryLink(sMap.bfaces[j]);
            if (bl != -1)
            {
                bLink[sMap.bfaces[j]] = bl;
            }
        }

        // Determine whether to use reverse points.
        LibUtilities::PointsType t =
            revPoints[elType][faceNum] ? LibUtilities::eBoundaryLayerPoints
                                       : LibUtilities::eBoundaryLayerPointsRev;

        // Determine value of r based on geometry.
        if (ratioIsString)
        {
            NekDouble x, y, z;
            NekDouble x1, y1, z1;
            int nverts = geom->GetNumVerts();

            x = y = z = 0.0;

            for (int i = 0; i < nverts; ++i)
            {
                geom->GetVertex(i)->GetCoords(x1, y1, z1);
                x += x1;
                y += y1;
                z += z1;
            }
            x /= (NekDouble)nverts;
            y /= (NekDouble)nverts;
            z /= (NekDouble)nverts;
            r = rEval.Evaluate(rExprId, x, y, z, 0.0);
        }

        LocalRegions::ExpansionSharedPtr q;

        if (elType == LibUtilities::ePrism)
        {
            // Create basis.
            LibUtilities::BasisKey B0(
                LibUtilities::eModified_A, nq, LibUtilities::PointsKey(nq, pt));
            LibUtilities::BasisKey B1(LibUtilities::eModified_A,
                                      2,
                                      LibUtilities::PointsKey(nl + 1, t, r));
            LibUtilities::BasisKey B2(
                LibUtilities::eModified_B, nq, LibUtilities::PointsKey(nq, pt));

            // Create local region.
            SpatialDomains::PrismGeomSharedPtr g =
                std::dynamic_pointer_cast<SpatialDomains::PrismGeom>(geom);
            q = MemoryManager<LocalRegions::PrismExp>::AllocateSharedPtr(
                B0, B1, B2, g);
        }
        else if (elType == LibUtilities::eHexahedron)
        {
            // Create basis.
            LibUtilities::BasisKey B0(
                LibUtilities::eModified_A, nq, LibUtilities::PointsKey(nq, pt));
            LibUtilities::BasisKey B1(LibUtilities::eModified_A,
                                      2,
                                      LibUtilities::PointsKey(nl + 1, t, r));

            // Create local region.
            SpatialDomains::HexGeomSharedPtr g =
                std::dynamic_pointer_cast<SpatialDomains::HexGeom>(geom);
            q = MemoryManager<LocalRegions::HexExp>::AllocateSharedPtr(
                B0, B0, B1, g);
        }

        // Grab co-ordinates.
        Array<OneD, NekDouble> x(nq * nq * (nl + 1));
        Array<OneD, NekDouble> y(nq * nq * (nl + 1));
        Array<OneD, NekDouble> z(nq * nq * (nl + 1));
        q->GetCoords(x, y, z);

        int nSplitEdge = sEdge.size;
        vector<vector<NodeSharedPtr> > edgeNodes(nSplitEdge);

        // Loop over edges to be split.
        for (int j = 0; j < nSplitEdge; ++j)
        {
            int locEdge = sEdge.edge[j];
            int edgeId  = el[i]->GetEdge(locEdge)->m_id;

            // Determine whether we have already generated vertices
            // along this edge.
            auto eIt = edgeMap.find(edgeId);

            if (eIt == edgeMap.end())
            {
                // If not then resize storage to hold new points.
                edgeNodes[j].resize(nl + 1);

                // Re-use existing vertices at endpoints of edge to
                // avoid duplicating the existing vertices.
                edgeNodes[j][0]  = el[i]->GetVertex(sEdge.edgeVert[j][0]);
                edgeNodes[j][nl] = el[i]->GetVertex(sEdge.edgeVert[j][1]);

                // Variable geometric ratio
                if (ratioIsString)
                {
                    NekDouble x0, y0, z0;
                    NekDouble x1, y1, z1;
                    NekDouble xm, ym, zm;

                    // -> Find edge end and mid points
                    x0 = x[sEdge.offset[j]];
                    y0 = y[sEdge.offset[j]];
                    z0 = z[sEdge.offset[j]];

                    x1 = x[sEdge.offset[j] + nl * nq];
                    y1 = y[sEdge.offset[j] + nl * nq];
                    z1 = z[sEdge.offset[j] + nl * nq];

                    xm = 0.5 * (x0 + x1);
                    ym = 0.5 * (y0 + y1);
                    zm = 0.5 * (z0 + z1);

                    // evaluate r factor based on mid point value
                    NekDouble rnew;
                    rnew = rEval.Evaluate(rExprId, xm, ym, zm, 0.0);

                    // Get basis with new r;
                    LibUtilities::PointsKey Pkey(nl + 1, t, rnew);
                    LibUtilities::PointsSharedPtr newP =
                        LibUtilities::PointsManager()[Pkey];

                    const Array<OneD, const NekDouble> z = newP->GetZ();

                    // Create new interior nodes based on this new blend
                    for (int k = 1; k < nl; ++k)
                    {
                        xm = 0.5 * (1 + z[k]) * (x1 - x0) + x0;
                        ym = 0.5 * (1 + z[k]) * (y1 - y0) + y0;
                        zm = 0.5 * (1 + z[k]) * (z1 - z0) + z0;
                        edgeNodes[j][k] =
                            NodeSharedPtr(new Node(nodeId++, xm, ym, zm));
                    }
                }
                else
                {
                    // Create new interior nodes.
                    for (int k = 1; k < nl; ++k)
                    {
                        int pos         = sEdge.offset[j] + k * sEdge.inc[j];
                        edgeNodes[j][k] = NodeSharedPtr(
                            new Node(nodeId++, x[pos], y[pos], z[pos]));
                    }
                }

                // Store these edges in edgeMap.
                edgeMap[edgeId] = edgeNodes[j];
            }
            else
            {
                edgeNodes[j] = eIt->second;
            }
        }

        // Create element layers.
        for (int j = 0; j < nl; ++j)
        {
            // Offset of this layer within the collapsed coordinate
            // system.
            int offset = j * sMap.layerOff;

            // Get corner vertices.
            vector<NodeSharedPtr> nodeList(sMap.size);
            for (int k = 0; k < sMap.size; ++k)
            {
                nodeList[k] = edgeNodes[sMap.conn[k][0]][j + sMap.conn[k][1]];
            }

            // Create the element.
            ElmtConfig conf(elType, 1, true, true, false);
            ElementSharedPtr elmt = GetElementFactory().CreateInstance(
                elType, conf, nodeList, el[i]->GetTagList());

            // Add high order nodes to split prismatic edges.
            for (int l = 0; l < sMap.size; ++l)
            {
                EdgeSharedPtr HOedge = elmt->GetEdge(sMap.edge[l]);
                for (int k = 1; k < nq - 1; ++k)
                {
                    int pos = offset + sMap.offset[l] + k * sMap.inc[l];
                    HOedge->m_edgeNodes.push_back(NodeSharedPtr(
                        new Node(nodeId++, x[pos], y[pos], z[pos])));
                }
                HOedge->m_curveType = pt;
            }

            // Change the surface elements to match the layers of
            // elements on the boundary of the domain.
            for (auto &it : bLink)
            {
                int fid = it.first;
                int bl  = it.second;

                vector<NodeSharedPtr> qNodeList(4);
                for (int k = 0; k < 4; ++k)
                {
                    qNodeList[k] = nodeList[faceNodeMap[elType][fid][k]];
                }
                vector<int> tagBE;
                tagBE =
                    m_mesh->m_element[m_mesh->m_expDim - 1][bl]->GetTagList();
                ElmtConfig bconf(
                    LibUtilities::eQuadrilateral, 1, true, true, false);
                ElementSharedPtr boundaryElmt =
                    GetElementFactory().CreateInstance(
                        LibUtilities::eQuadrilateral, bconf, qNodeList, tagBE);

                // Overwrite first layer boundary element with new
                // boundary element, otherwise push this back to end of
                // the boundary list
                if (j == 0)
                {
                    m_mesh->m_element[m_mesh->m_expDim - 1][bl] = boundaryElmt;
                }
                else
                {
                    m_mesh->m_element[m_mesh->m_expDim - 1].push_back(
                        boundaryElmt);
                }
            }

            m_mesh->m_element[m_mesh->m_expDim].push_back(elmt);
        }
    }
}
}
}