globalMeshData.C

/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | www.openfoam.com
     \\/     M anipulation  |
-------------------------------------------------------------------------------
    Copyright (C) 2011-2017 OpenFOAM Foundation
    Copyright (C) 2015-2019 OpenCFD Ltd.
-------------------------------------------------------------------------------
License
    This file is part of OpenFOAM.

    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.

    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.

\*---------------------------------------------------------------------------*/

#include "globalMeshData.H"
#include "Pstream.H"
#include "PstreamCombineReduceOps.H"
#include "processorPolyPatch.H"
#include "globalPoints.H"
#include "polyMesh.H"
#include "mapDistribute.H"
#include "labelIOList.H"
#include "mergePoints.H"
#include "globalIndexAndTransform.H"

// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //

namespace Foam
{
defineTypeNameAndDebug(globalMeshData, 0);

const scalar globalMeshData::matchTol_ = 1e-8;

template<>
class minEqOp<labelPair>
{
public:
    void operator()(labelPair& x, const labelPair& y) const
    {
        x[0] = min(x[0], y[0]);
        x[1] = min(x[1], y[1]);
    }
};
}


// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //

void Foam::globalMeshData::initProcAddr()
{
    processorPatchIndices_.setSize(mesh_.boundaryMesh().size());
    processorPatchIndices_ = -1;

    processorPatchNeighbours_.setSize(mesh_.boundaryMesh().size());
    processorPatchNeighbours_ = -1;

    // Construct processor patch indexing. processorPatchNeighbours_ only
    // set if running in parallel!
    processorPatches_.setSize(mesh_.boundaryMesh().size());

    label nNeighbours = 0;

    forAll(mesh_.boundaryMesh(), patchi)
    {
        if (isA<processorPolyPatch>(mesh_.boundaryMesh()[patchi]))
        {
            processorPatches_[nNeighbours] = patchi;
            processorPatchIndices_[patchi] = nNeighbours++;
        }
    }
    processorPatches_.setSize(nNeighbours);


    if (Pstream::parRun())
    {
        PstreamBuffers pBufs(Pstream::commsTypes::nonBlocking);

        // Send indices of my processor patches to my neighbours
        for (const label patchi : processorPatches_)
        {
            UOPstream toNeighbour
            (
                refCast<const processorPolyPatch>
                (
                    mesh_.boundaryMesh()[patchi]
                ).neighbProcNo(),
                pBufs
            );

            toNeighbour << processorPatchIndices_[patchi];
        }

        pBufs.finishedSends();

        for (const label patchi : processorPatches_)
        {
            UIPstream fromNeighbour
            (
                refCast<const processorPolyPatch>
                (
                    mesh_.boundaryMesh()[patchi]
                ).neighbProcNo(),
                pBufs
            );

            fromNeighbour >> processorPatchNeighbours_[patchi];
        }
    }
}


void Foam::globalMeshData::calcSharedPoints() const
{
    if
    (
        nGlobalPoints_ != -1
     || sharedPointLabelsPtr_.valid()
     || sharedPointAddrPtr_.valid()
    )
    {
        FatalErrorInFunction
            << "Shared point addressing already done" << abort(FatalError);
    }

    // Calculate all shared points (exclude points that are only
    // on two coupled patches). This does all the hard work.
    globalPoints parallelPoints(mesh_, false, true);

    // Count the number of master points
    label nMaster = 0;
    forAll(parallelPoints.pointPoints(), i)
    {
        const labelList& pPoints = parallelPoints.pointPoints()[i];
        const labelList& transPPoints =
            parallelPoints.transformedPointPoints()[i];

        if (pPoints.size()+transPPoints.size() > 0)
        {
            nMaster++;
        }
    }

    // Allocate global numbers
    globalIndex masterNumbering(nMaster);

    nGlobalPoints_ = masterNumbering.size();


    // Push master number to slaves
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    // 1. Fill master and slave slots
    nMaster = 0;
    labelList master(parallelPoints.map().constructSize(), -1);
    forAll(parallelPoints.pointPoints(), i)
    {
        const labelList& pPoints = parallelPoints.pointPoints()[i];
        const labelList& transPPoints =
            parallelPoints.transformedPointPoints()[i];

        if (pPoints.size()+transPPoints.size() > 0)
        {
            master[i] = masterNumbering.toGlobal(nMaster);
            forAll(pPoints, j)
            {
                master[pPoints[j]] = master[i];
            }
            forAll(transPPoints, j)
            {
                master[transPPoints[j]] = master[i];
            }
            nMaster++;
        }
    }


    // 2. Push slave slots back to local storage on originating processor
    // For all the four types of points:
    // - local master : already set
    // - local transformed slave point : the reverse transform at
    //   reverseDistribute will have copied it back to its originating local
    //   point
    // - remote untransformed slave point : sent back to originating processor
    // - remote transformed slave point : the reverse transform will
    //   copy it back into the remote slot which then gets sent back to
    //   originating processor

    parallelPoints.map().reverseDistribute
    (
        parallelPoints.map().constructSize(),
        master
    );


    // Collect all points that are a master or refer to a master.
    nMaster = 0;
    forAll(parallelPoints.pointPoints(), i)
    {
        if (master[i] != -1)
        {
            nMaster++;
        }
    }

    sharedPointLabelsPtr_.reset(new labelList(nMaster));
    labelList& sharedPointLabels = sharedPointLabelsPtr_();
    sharedPointAddrPtr_.reset(new labelList(nMaster));
    labelList& sharedPointAddr = sharedPointAddrPtr_();
    nMaster = 0;

    forAll(parallelPoints.pointPoints(), i)
    {
        if (master[i] != -1)
        {
            // I am master or slave
            sharedPointLabels[nMaster] = i;
            sharedPointAddr[nMaster] = master[i];
            nMaster++;
        }
    }

    if (debug)
    {
        Pout<< "globalMeshData : nGlobalPoints_:" << nGlobalPoints_ << nl
            << "globalMeshData : sharedPointLabels_:"
            << sharedPointLabelsPtr_().size() << nl
            << "globalMeshData : sharedPointAddr_:"
            << sharedPointAddrPtr_().size() << endl;
    }
}


void Foam::globalMeshData::countSharedEdges
(
    const EdgeMap<labelList>& procSharedEdges,
    EdgeMap<label>& globalShared,
    label& sharedEdgeI
)
{
    // Count occurrences of procSharedEdges in global shared edges table.
    forAllConstIters(procSharedEdges, iter)
    {
        const edge& e = iter.key();

        auto globalFnd = globalShared.find(e);

        if (globalFnd.found())
        {
            if (globalFnd() == -1)
            {
                // Second time occurrence of this edge.
                // Assign proper edge label.
                globalFnd() = sharedEdgeI++;
            }
        }
        else
        {
            // First time occurrence of this edge. Check how many we are adding.
            if (iter().size() == 1)
            {
                // Only one edge. Mark with special value.
                globalShared.insert(e, -1);
            }
            else
            {
                // Edge used more than once (even by local shared edges alone)
                // so allocate proper shared edge label.
                globalShared.insert(e, sharedEdgeI++);
            }
        }
    }
}


void Foam::globalMeshData::calcSharedEdges() const
{
    // Shared edges are shared between multiple processors. By their nature both
    // of their endpoints are shared points. (but not all edges using two shared
    // points are shared edges! There might e.g. be an edge between two
    // unrelated clusters of shared points)

    if
    (
        nGlobalEdges_ != -1
     || sharedEdgeLabelsPtr_.valid()
     || sharedEdgeAddrPtr_.valid()
    )
    {
        FatalErrorInFunction
            << "Shared edge addressing already done" << abort(FatalError);
    }


    const labelList& sharedPtAddr = sharedPointAddr();
    const labelList& sharedPtLabels = sharedPointLabels();

    // Since don't want to construct pointEdges for whole mesh create
    // Map for all shared points.
    Map<label> meshToShared(2*sharedPtLabels.size());
    forAll(sharedPtLabels, i)
    {
        meshToShared.insert(sharedPtLabels[i], i);
    }

    // Find edges using shared points. Store correspondence to local edge
    // numbering. Note that multiple local edges can have the same shared
    // points! (for cyclics or separated processor patches)
    EdgeMap<labelList> localShared(2*sharedPtAddr.size());

    const edgeList& edges = mesh_.edges();

    forAll(edges, edgeI)
    {
        const edge& e = edges[edgeI];

        const auto e0Fnd = meshToShared.cfind(e[0]);

        if (e0Fnd.found())
        {
            const auto e1Fnd = meshToShared.cfind(e[1]);

            if (e1Fnd.found())
            {
                // Found edge which uses shared points. Probably shared.

                // Construct the edge in shared points (or rather global indices
                // of the shared points)
                edge sharedEdge
                (
                    sharedPtAddr[e0Fnd()],
                    sharedPtAddr[e1Fnd()]
                );

                auto iter = localShared.find(sharedEdge);

                if (!iter.found())
                {
                    // First occurrence of this point combination. Store.
                    localShared.insert(sharedEdge, labelList(1, edgeI));
                }
                else
                {
                    // Add this edge to list of edge labels.
                    labelList& edgeLabels = iter();

                    const label sz = edgeLabels.size();
                    edgeLabels.setSize(sz+1);
                    edgeLabels[sz] = edgeI;
                }
            }
        }
    }


    // Now we have a table on every processors which gives its edges which use
    // shared points. Send this all to the master and have it allocate
    // global edge numbers for it. But only allocate a global edge number for
    // edge if it is used more than once!
    // Note that we are now sending the whole localShared to the master whereas
    // we only need the local count (i.e. the number of times a global edge is
    // used). But then this only gets done once so not too bothered about the
    // extra global communication.

    EdgeMap<label> globalShared(nGlobalPoints());

    if (Pstream::master())
    {
        label sharedEdgeI = 0;

        // Merge my shared edges into the global list
        if (debug)
        {
            Pout<< "globalMeshData::calcSharedEdges : Merging in from proc0 : "
                << localShared.size() << endl;
        }
        countSharedEdges(localShared, globalShared, sharedEdgeI);

        // Receive data from slaves and insert
        if (Pstream::parRun())
        {
            for
            (
                int slave=Pstream::firstSlave();
                slave<=Pstream::lastSlave();
                slave++
            )
            {
                // Receive the edges using shared points from the slave.
                IPstream fromSlave(Pstream::commsTypes::blocking, slave);
                EdgeMap<labelList> procSharedEdges(fromSlave);

                if (debug)
                {
                    Pout<< "globalMeshData::calcSharedEdges : "
                        << "Merging in from proc"
                        << Foam::name(slave) << " : " << procSharedEdges.size()
                        << endl;
                }
                countSharedEdges(procSharedEdges, globalShared, sharedEdgeI);
            }
        }

        // Now our globalShared should have some edges with -1 as edge label
        // These were only used once so are not proper shared edges.
        // Remove them.
        {
            EdgeMap<label> oldSharedEdges(globalShared);

            globalShared.clear();

            forAllConstIters(oldSharedEdges, iter)
            {
                if (iter() != -1)
                {
                    globalShared.insert(iter.key(), iter());
                }
            }
            if (debug)
            {
                Pout<< "globalMeshData::calcSharedEdges : Filtered "
                    << oldSharedEdges.size()
                    << " down to " << globalShared.size() << endl;
            }
        }


        // Send back to slaves.
        if (Pstream::parRun())
        {
            for
            (
                int slave=Pstream::firstSlave();
                slave<=Pstream::lastSlave();
                slave++
            )
            {
                // Receive the edges using shared points from the slave.
                OPstream toSlave(Pstream::commsTypes::blocking, slave);
                toSlave << globalShared;
            }
        }
    }
    else
    {
        // Send local edges to master
        {
            OPstream toMaster
            (
                Pstream::commsTypes::blocking,
                Pstream::masterNo()
            );
            toMaster << localShared;
        }
        // Receive merged edges from master.
        {
            IPstream fromMaster
            (
                Pstream::commsTypes::blocking,
                Pstream::masterNo()
            );
            fromMaster >> globalShared;
        }
    }

    // Now use the global shared edges list (globalShared) to classify my local
    // ones (localShared)

    nGlobalEdges_ = globalShared.size();

    DynamicList<label> dynSharedEdgeLabels(globalShared.size());
    DynamicList<label> dynSharedEdgeAddr(globalShared.size());

    forAllConstIters(localShared, iter)
    {
        const edge& e = iter.key();

        const auto edgeFnd = globalShared.cfind(e);

        if (edgeFnd.found())
        {
            // My local edge is indeed a shared one. Go through all local edge
            // labels with this point combination.
            const labelList& edgeLabels = iter();

            for (const label edgei : edgeLabels)
            {
                // Store label of local mesh edge
                dynSharedEdgeLabels.append(edgei);

                // Store label of shared edge
                dynSharedEdgeAddr.append(edgeFnd());
            }
        }
    }


    sharedEdgeLabelsPtr_.reset(new labelList());
    labelList& sharedEdgeLabels = sharedEdgeLabelsPtr_();
    sharedEdgeLabels.transfer(dynSharedEdgeLabels);

    sharedEdgeAddrPtr_.reset(new labelList());
    labelList& sharedEdgeAddr = sharedEdgeAddrPtr_();
    sharedEdgeAddr.transfer(dynSharedEdgeAddr);

    if (debug)
    {
        Pout<< "globalMeshData : nGlobalEdges_:" << nGlobalEdges_ << nl
            << "globalMeshData : sharedEdgeLabels:" << sharedEdgeLabels.size()
            << nl
            << "globalMeshData : sharedEdgeAddr:" << sharedEdgeAddr.size()
            << endl;
    }
}


void Foam::globalMeshData::calcGlobalPointSlaves() const
{
    if (debug)
    {
        Pout<< "globalMeshData::calcGlobalPointSlaves() :"
            << " calculating coupled master to slave point addressing."
            << endl;
    }

    // Calculate connected points for master points.
    globalPoints globalData(mesh_, coupledPatch(), true, true);

    globalPointSlavesPtr_.reset
    (
        new labelListList
        (
            std::move(globalData.pointPoints())
        )
    );
    globalPointTransformedSlavesPtr_.reset
    (
        new labelListList
        (
            std::move(globalData.transformedPointPoints())
        )
    );

    globalPointSlavesMapPtr_.reset
    (
        new mapDistribute
        (
            std::move(globalData.map())
        )
    );
}


void Foam::globalMeshData::calcPointConnectivity
(
    List<labelPairList>& allPointConnectivity
) const
{
    const globalIndexAndTransform& transforms = globalTransforms();
    const labelListList& slaves = globalPointSlaves();
    const labelListList& transformedSlaves = globalPointTransformedSlaves();


    // Create field with my local data
    labelPairList myData(globalPointSlavesMap().constructSize());
    forAll(slaves, pointi)
    {
        myData[pointi] = transforms.encode
        (
            Pstream::myProcNo(),
            pointi,
            transforms.nullTransformIndex()
        );
    }
    // Send to master
    globalPointSlavesMap().distribute(myData);


    // String of connected points with their transform
    allPointConnectivity.setSize(globalPointSlavesMap().constructSize());
    allPointConnectivity = labelPairList(0);

    // Pass1: do the master points since these also update local slaves
    //        (e.g. from local cyclics)
    forAll(slaves, pointi)
    {
        // Reconstruct string of connected points
        const labelList& pSlaves = slaves[pointi];
        const labelList& pTransformSlaves = transformedSlaves[pointi];

        if (pSlaves.size()+pTransformSlaves.size())
        {
            labelPairList& pConnectivity = allPointConnectivity[pointi];

            pConnectivity.setSize(1+pSlaves.size()+pTransformSlaves.size());
            label connI = 0;

            // Add myself
            pConnectivity[connI++] = myData[pointi];
            // Add untransformed points
            forAll(pSlaves, i)
            {
                pConnectivity[connI++] = myData[pSlaves[i]];
            }
            // Add transformed points.
            forAll(pTransformSlaves, i)
            {
                // Get transform from index
                label transformI = globalPointSlavesMap().whichTransform
                (
                    pTransformSlaves[i]
                );
                // Add transform to connectivity
                const labelPair& n = myData[pTransformSlaves[i]];
                label proci = transforms.processor(n);
                label index = transforms.index(n);
                pConnectivity[connI++] = transforms.encode
                (
                    proci,
                    index,
                    transformI
                );
            }

            // Put back in slots
            forAll(pSlaves, i)
            {
                allPointConnectivity[pSlaves[i]] = pConnectivity;
            }
            forAll(pTransformSlaves, i)
            {
                allPointConnectivity[pTransformSlaves[i]] = pConnectivity;
            }
        }
    }


    // Pass2: see if anything is still unset (should not be the case)
    forAll(slaves, pointi)
    {
        labelPairList& pConnectivity = allPointConnectivity[pointi];

        if (pConnectivity.size() == 0)
        {
            pConnectivity.setSize(1, myData[pointi]);
        }
    }


    globalPointSlavesMap().reverseDistribute
    (
        slaves.size(),
        allPointConnectivity
    );
}


void Foam::globalMeshData::calcGlobalPointEdges
(
    labelListList& globalPointEdges,
    List<labelPairList>& globalPointPoints
) const
{
    const edgeList& edges = coupledPatch().edges();
    const labelListList& pointEdges = coupledPatch().pointEdges();
    const globalIndex& globalEdgeNumbers = globalEdgeNumbering();
    const labelListList& slaves = globalPointSlaves();
    const labelListList& transformedSlaves = globalPointTransformedSlaves();
    const globalIndexAndTransform& transforms = globalTransforms();


    // Create local version
    globalPointEdges.setSize(globalPointSlavesMap().constructSize());
    globalPointPoints.setSize(globalPointSlavesMap().constructSize());
    forAll(pointEdges, pointi)
    {
        const labelList& pEdges = pointEdges[pointi];
        globalPointEdges[pointi] = globalEdgeNumbers.toGlobal(pEdges);

        labelPairList& globalPPoints = globalPointPoints[pointi];
        globalPPoints.setSize(pEdges.size());
        forAll(pEdges, i)
        {
            label otherPointi = edges[pEdges[i]].otherVertex(pointi);
            globalPPoints[i] = transforms.encode
            (
                Pstream::myProcNo(),
                otherPointi,
                transforms.nullTransformIndex()
            );
        }
    }

    // Pull slave data to master. Dummy transform.
    globalPointSlavesMap().distribute(globalPointEdges);
    globalPointSlavesMap().distribute(globalPointPoints);
    // Add all pointEdges
    forAll(slaves, pointi)
    {
        const labelList& pSlaves = slaves[pointi];
        const labelList& pTransformSlaves = transformedSlaves[pointi];

        label n = 0;
        forAll(pSlaves, i)
        {
            n += globalPointEdges[pSlaves[i]].size();
        }
        forAll(pTransformSlaves, i)
        {
            n += globalPointEdges[pTransformSlaves[i]].size();
        }

        // Add all the point edges of the slaves to those of the (master) point
        {
            labelList& globalPEdges = globalPointEdges[pointi];
            label sz = globalPEdges.size();
            globalPEdges.setSize(sz+n);
            forAll(pSlaves, i)
            {
                const labelList& otherData = globalPointEdges[pSlaves[i]];
                forAll(otherData, j)
                {
                    globalPEdges[sz++] = otherData[j];
                }
            }
            forAll(pTransformSlaves, i)
            {
                const labelList& otherData =
                    globalPointEdges[pTransformSlaves[i]];
                forAll(otherData, j)
                {
                    globalPEdges[sz++] = otherData[j];
                }
            }

            // Put back in slots
            forAll(pSlaves, i)
            {
                globalPointEdges[pSlaves[i]] = globalPEdges;
            }
            forAll(pTransformSlaves, i)
            {
                globalPointEdges[pTransformSlaves[i]] = globalPEdges;
            }
        }


        // Same for corresponding pointPoints
        {
            labelPairList& globalPPoints = globalPointPoints[pointi];
            label sz = globalPPoints.size();
            globalPPoints.setSize(sz + n);

            // Add untransformed points
            forAll(pSlaves, i)
            {
                const labelPairList& otherData = globalPointPoints[pSlaves[i]];
                forAll(otherData, j)
                {
                    globalPPoints[sz++] = otherData[j];
                }
            }
            // Add transformed points.
            forAll(pTransformSlaves, i)
            {
                // Get transform from index
                label transformI = globalPointSlavesMap().whichTransform
                (
                    pTransformSlaves[i]
                );

                const labelPairList& otherData =
                    globalPointPoints[pTransformSlaves[i]];
                forAll(otherData, j)
                {
                    // Add transform to connectivity
                    const labelPair& n = otherData[j];
                    label proci = transforms.processor(n);
                    label index = transforms.index(n);
                    globalPPoints[sz++] = transforms.encode
                    (
                        proci,
                        index,
                        transformI
                    );
                }
            }

            // Put back in slots
            forAll(pSlaves, i)
            {
                globalPointPoints[pSlaves[i]] = globalPPoints;
            }
            forAll(pTransformSlaves, i)
            {
                globalPointPoints[pTransformSlaves[i]] = globalPPoints;
            }
        }
    }
    // Push back
    globalPointSlavesMap().reverseDistribute
    (
        slaves.size(),
        globalPointEdges
    );
    // Push back
    globalPointSlavesMap().reverseDistribute
    (
        slaves.size(),
        globalPointPoints
    );
}


Foam::label Foam::globalMeshData::findTransform
(
    const labelPairList& info,
    const labelPair& remotePoint,
    const label localPoint
) const
{
    const globalIndexAndTransform& transforms = globalTransforms();

    const label remoteProci = transforms.processor(remotePoint);
    const label remoteIndex = transforms.index(remotePoint);

    label remoteTransformI = -1;
    label localTransformI = -1;
    forAll(info, i)
    {
        label proci = transforms.processor(info[i]);
        label pointi = transforms.index(info[i]);
        label transformI = transforms.transformIndex(info[i]);

        if (proci == Pstream::myProcNo() && pointi == localPoint)
        {
            localTransformI = transformI;
            //Pout<< "For local :" << localPoint
            //    << " found transform:" << localTransformI
            //    << endl;
        }
        if (proci == remoteProci && pointi == remoteIndex)
        {
            remoteTransformI = transformI;
            //Pout<< "For remote:" << remotePoint
            //    << " found transform:" << remoteTransformI
            //    << " at index:" << i
            //    << endl;
        }
    }

    if (remoteTransformI == -1 || localTransformI == -1)
    {
        FatalErrorInFunction
            << "Problem. Cannot find " << remotePoint
            << " or " << localPoint  << " "
            << coupledPatch().localPoints()[localPoint]
            << " in " << info
            << endl
            << "remoteTransformI:" << remoteTransformI << endl
            << "localTransformI:" << localTransformI
            << abort(FatalError);
    }

    return transforms.subtractTransformIndex
    (
        remoteTransformI,
        localTransformI
    );
}


void Foam::globalMeshData::calcGlobalEdgeSlaves() const
{
    if (debug)
    {
        Pout<< "globalMeshData::calcGlobalEdgeSlaves() :"
            << " calculating coupled master to slave edge addressing." << endl;
    }

    const edgeList& edges = coupledPatch().edges();
    const globalIndex& globalEdgeNumbers = globalEdgeNumbering();
    const globalIndexAndTransform& transforms = globalTransforms();


    // The whole problem with deducting edge-connectivity from
    // point-connectivity is that one of the endpoints might be
    // a local master but the other endpoint might not. So we first
    // need to make sure that all points know about connectivity and
    // the transformations.


    // 1. collect point connectivity - basically recreating globalPoints output.
    // All points will now have a string of coupled points. The transforms are
    // in respect to the master.
    List<labelPairList> allPointConnectivity;
    calcPointConnectivity(allPointConnectivity);


    // 2. Get all pointEdges and pointPoints
    // Coupled point to global coupled edges and corresponding endpoint.
    labelListList globalPointEdges;
    List<labelPairList> globalPointPoints;
    calcGlobalPointEdges(globalPointEdges, globalPointPoints);


    // 3. Now all points have
    //      - all the connected points with original transform
    //      - all the connected global edges

    // Now all we need to do is go through all the edges and check
    // both endpoints. If there is a edge between the two which is
    // produced by transforming both points in the same way it is a shared
    // edge.

    // Collect strings of connected edges.
    List<labelPairList> allEdgeConnectivity(edges.size());

    forAll(edges, edgeI)
    {
        const edge& e = edges[edgeI];
        const labelList& pEdges0 = globalPointEdges[e[0]];
        const labelPairList& pPoints0 = globalPointPoints[e[0]];
        const labelList& pEdges1 = globalPointEdges[e[1]];
        const labelPairList& pPoints1 = globalPointPoints[e[1]];

        // Most edges will be size 2
        DynamicList<labelPair> eEdges(2);
        // Append myself.
        eEdges.append
        (
            transforms.encode
            (
                Pstream::myProcNo(),
                edgeI,
                transforms.nullTransformIndex()
            )
        );

        forAll(pEdges0, i)
        {
            forAll(pEdges1, j)
            {
                if
                (
                    pEdges0[i] == pEdges1[j]
                 && pEdges0[i] != globalEdgeNumbers.toGlobal(edgeI)
                )
                {
                    // Found a shared edge. Now check if the endpoints
                    // go through the same transformation.
                    // Local: e[0]    remote:pPoints1[j]
                    // Local: e[1]    remote:pPoints0[i]


                    // Find difference in transforms to go from point on remote
                    // edge (pPoints1[j]) to this point.

                    label transform0 = findTransform
                    (
                        allPointConnectivity[e[0]],
                        pPoints1[j],
                        e[0]
                    );
                    label transform1 = findTransform
                    (
                        allPointConnectivity[e[1]],
                        pPoints0[i],
                        e[1]
                    );

                    if (transform0 == transform1)
                    {
                        label proci = globalEdgeNumbers.whichProcID(pEdges0[i]);
                        eEdges.append
                        (
                            transforms.encode
                            (
                                proci,
                                globalEdgeNumbers.toLocal(proci, pEdges0[i]),
                                transform0
                            )
                        );
                    }
                }
            }
        }