source: XIOS/trunk/extern/remap/src/mapper.cpp @ 1114

#include "mpi.hpp"
#include <map>
#include "cputime.hpp"       /* time */
#include "meshutil.hpp"
#include "polyg.hpp"
#include "circle.hpp"
#include "intersect.hpp"
#include "intersection_ym.hpp"
#include "errhandle.hpp"
#include "mpi_routing.hpp"
#include "gridRemap.hpp"

#include "mapper.hpp"

namespace sphereRemap {

/* A subdivition of an array into N sub-arays
   can be represented by the length of the N arrays
   or by the offsets when each of the N arrays starts.
   This function convertes from the former to the latter. */
void cptOffsetsFromLengths(const int *lengths, int *offsets, int sz)
{
        offsets[0] = 0;
        for (int i = 1; i < sz; i++)
                offsets[i] = offsets[i-1] + lengths[i-1];
}


void Mapper::setSourceMesh(const double* boundsLon, const double* boundsLat, int nVertex, int nbCells, const double* pole, const long int* globalId)
{
  srcGrid.pole = Coord(pole[0], pole[1], pole[2]);

        int mpiRank, mpiSize;
        MPI_Comm_rank(communicator, &mpiRank);
        MPI_Comm_size(communicator, &mpiSize);

        sourceElements.reserve(nbCells);
        sourceMesh.reserve(nbCells);
  sourceGlobalId.resize(nbCells) ;

  if (globalId==NULL)
  {
    long int offset ;
    long int nb=nbCells ;
    MPI_Scan(&nb,&offset,1,MPI_LONG,MPI_SUM,communicator) ;
    offset=offset-nb ;
    for(int i=0;i<nbCells;i++) sourceGlobalId[i]=offset+i ;
  }
  else sourceGlobalId.assign(globalId,globalId+nbCells);

        for (int i = 0; i < nbCells; i++)
        {
                int offs = i*nVertex;
                Elt elt(boundsLon + offs, boundsLat + offs, nVertex);
                elt.src_id.rank = mpiRank;
                elt.src_id.ind = i;
    elt.src_id.globalId = sourceGlobalId[i];
                sourceElements.push_back(elt);
                sourceMesh.push_back(Node(elt.x, cptRadius(elt), &sourceElements.back()));
                cptEltGeom(sourceElements[i], Coord(pole[0], pole[1], pole[2]));
        }

}

void Mapper::setTargetMesh(const double* boundsLon, const double* boundsLat, int nVertex, int nbCells, const double* pole, const long int* globalId)
{
  tgtGrid.pole = Coord(pole[0], pole[1], pole[2]);

        int mpiRank, mpiSize;
        MPI_Comm_rank(communicator, &mpiRank);
        MPI_Comm_size(communicator, &mpiSize);

        targetElements.reserve(nbCells);
        targetMesh.reserve(nbCells);

  targetGlobalId.resize(nbCells) ;
  if (globalId==NULL)
  {
    long int offset ;
    long int nb=nbCells ;
    MPI_Scan(&nb,&offset,1,MPI_LONG,MPI_SUM,communicator) ;
    offset=offset-nb ;
    for(int i=0;i<nbCells;i++) targetGlobalId[i]=offset+i ;
  }
  else targetGlobalId.assign(globalId,globalId+nbCells);

        for (int i = 0; i < nbCells; i++)
        {
                int offs = i*nVertex;
                Elt elt(boundsLon + offs, boundsLat + offs, nVertex);
                targetElements.push_back(elt);
                targetMesh.push_back(Node(elt.x, cptRadius(elt), &sourceElements.back()));
                cptEltGeom(targetElements[i], Coord(pole[0], pole[1], pole[2]));
        }


}

void Mapper::setSourceValue(const double* val)
{
  int size=sourceElements.size() ;
  for(int i=0;i<size;++i) sourceElements[i].val=val[i] ;
}

void Mapper::getTargetValue(double* val)
{
  int size=targetElements.size() ;
  for(int i=0;i<size;++i) val[i]=targetElements[i].val ;
}

vector<double> Mapper::computeWeights(int interpOrder, bool renormalize, bool quantity)
{
        vector<double> timings;
        int mpiSize, mpiRank;
        MPI_Comm_size(communicator, &mpiSize);
        MPI_Comm_rank(communicator, &mpiRank);

  this->buildSSTree(sourceMesh, targetMesh);

        if (mpiRank == 0 && verbose) cout << "Computing intersections ..." << endl;
        double tic = cputime();
        computeIntersection(&targetElements[0], targetElements.size());
        timings.push_back(cputime() - tic);

        tic = cputime();
        if (interpOrder == 2) {
                if (mpiRank == 0 && verbose) cout << "Computing grads ..." << endl;
                buildMeshTopology();
                computeGrads();
        }
        timings.push_back(cputime() - tic);

        /* Prepare computation of weights */
        /* compute number of intersections which for the first order case
           corresponds to the number of edges in the remap matrix */
        int nIntersections = 0;
        for (int j = 0; j < targetElements.size(); j++)
        {
                Elt &elt = targetElements[j];
                for (list<Polyg*>::iterator it = elt.is.begin(); it != elt.is.end(); it++)
                        nIntersections++;
        }
        /* overallocate for NMAX neighbours for each elements */
        remapMatrix = new double[nIntersections*NMAX];
        srcAddress = new int[nIntersections*NMAX];
        srcRank = new int[nIntersections*NMAX];
        dstAddress = new int[nIntersections*NMAX];
  sourceWeightId =new long[nIntersections*NMAX];
  targetWeightId =new long[nIntersections*NMAX];


        if (mpiRank == 0 && verbose) cout << "Remapping..." << endl;
        tic = cputime();
        nWeights = remap(&targetElements[0], targetElements.size(), interpOrder, renormalize, quantity);
        timings.push_back(cputime() - tic);

  for (int i = 0; i < targetElements.size(); i++) targetElements[i].delete_intersections();

        return timings;
}

/**
   @param elements are cells of the target grid that are distributed over CPUs
          indepentently of the distribution of the SS-tree.
   @param nbElements is the size of the elements array.
   @param order is the order of interpolaton (must be 1 or 2).
*/
int Mapper::remap(Elt *elements, int nbElements, int order, bool renormalize, bool quantity)
{
        int mpiSize, mpiRank;
        MPI_Comm_size(communicator, &mpiSize);
        MPI_Comm_rank(communicator, &mpiRank);

        /* create list of intersections (super mesh elements) for each rank */
        multimap<int, Polyg *> *elementList = new multimap<int, Polyg *>[mpiSize];
        for (int j = 0; j < nbElements; j++)
        {
                Elt& e = elements[j];
                for (list<Polyg *>::iterator it = e.is.begin(); it != e.is.end(); it++)
                        elementList[(*it)->id.rank].insert(pair<int, Polyg *>((*it)->id.ind, *it));
        }

        int *nbSendElement = new int[mpiSize];
        int **sendElement = new int*[mpiSize]; /* indices of elements required from other rank */
        double **recvValue = new double*[mpiSize];
        double **recvArea = new double*[mpiSize];
        Coord **recvGrad = new Coord*[mpiSize];
        GloId **recvNeighIds = new GloId*[mpiSize]; /* ids of the of the source neighbours which also contribute through gradient */
        for (int rank = 0; rank < mpiSize; rank++)
        {
                /* get size for allocation */
                int last = -1; /* compares unequal to any index */
                int index = -1; /* increased to starting index 0 in first iteration */
                for (multimap<int, Polyg *>::iterator it = elementList[rank].begin(); it != elementList[rank].end(); ++it)
                {
                        if (last != it->first)
                                index++;
                        (it->second)->id.ind = index;
                        last = it->first;
                }
                nbSendElement[rank] = index + 1;

                /* if size is non-zero allocate and collect indices of elements on other ranks that we intersect */
                if (nbSendElement[rank] > 0)
                {
                        sendElement[rank] = new int[nbSendElement[rank]];
                        recvValue[rank]   = new double[nbSendElement[rank]];
                        recvArea[rank]    = new double[nbSendElement[rank]];
                        if (order == 2)
                        {
                                recvNeighIds[rank] = new GloId[nbSendElement[rank]*(NMAX+1)];
                                recvGrad[rank]    = new Coord[nbSendElement[rank]*(NMAX+1)];
                        }
                        else
                                recvNeighIds[rank] = new GloId[nbSendElement[rank]];

                        last = -1;
                        index = -1;
                        for (multimap<int, Polyg *>::iterator it = elementList[rank].begin(); it != elementList[rank].end(); ++it)
                        {
                                if (last != it->first)
                                        index++;
                                sendElement[rank][index] = it->first;
                                last = it->first;
                        }
                }
        }

        /* communicate sizes of source elements to be sent (index lists and later values and gradients) */
        int *nbRecvElement = new int[mpiSize];
        MPI_Alltoall(nbSendElement, 1, MPI_INT, nbRecvElement, 1, MPI_INT, communicator);

        /* communicate indices of source elements on other ranks whoes value and gradient we need (since intersection) */
        int nbSendRequest = 0;
        int nbRecvRequest = 0;
        int **recvElement = new int*[mpiSize];
        double **sendValue = new double*[mpiSize];
        double **sendArea = new double*[mpiSize];
        Coord **sendGrad = new Coord*[mpiSize];
        GloId **sendNeighIds = new GloId*[mpiSize];
        MPI_Request *sendRequest = new MPI_Request[3*mpiSize];
        MPI_Request *recvRequest = new MPI_Request[3*mpiSize];
        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendElement[rank] > 0)
                {
                        MPI_Issend(sendElement[rank], nbSendElement[rank], MPI_INT, rank, 0, communicator, &sendRequest[nbSendRequest]);
                        nbSendRequest++;
                }

                if (nbRecvElement[rank] > 0)
                {
                        recvElement[rank] = new int[nbRecvElement[rank]];
                        sendValue[rank]   = new double[nbRecvElement[rank]];
                        sendArea[rank]   = new double[nbRecvElement[rank]];
                        if (order == 2)
                        {
                                sendNeighIds[rank] = new GloId[nbRecvElement[rank]*(NMAX+1)];
                                sendGrad[rank]    = new Coord[nbRecvElement[rank]*(NMAX+1)];
                        }
                        else
                        {
                                sendNeighIds[rank] = new GloId[nbRecvElement[rank]];
                        }
                        MPI_Irecv(recvElement[rank], nbRecvElement[rank], MPI_INT, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                        nbRecvRequest++;
                }
        }
        MPI_Status *status = new MPI_Status[3*mpiSize];
        MPI_Waitall(nbRecvRequest, recvRequest, status);
        MPI_Waitall(nbSendRequest, sendRequest, status);

        /* for all indices that have been received from requesting ranks: pack values and gradients, then send */
        nbSendRequest = 0;
        nbRecvRequest = 0;
        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbRecvElement[rank] > 0)
                {
                        int jj = 0; // jj == j if no weight writing
                        for (int j = 0; j < nbRecvElement[rank]; j++)
                        {
                                sendValue[rank][j] = sstree.localElements[recvElement[rank][j]].val;
                                sendArea[rank][j] = sstree.localElements[recvElement[rank][j]].area;
                                if (order == 2)
                                {
                                        sendGrad[rank][jj] = sstree.localElements[recvElement[rank][j]].grad;
//          cout<<"grad  "<<jj<<"  "<<recvElement[rank][j]<<"  "<<sendGrad[rank][jj]<<" "<<sstree.localElements[recvElement[rank][j]].grad<<endl ;
                                        sendNeighIds[rank][jj] = sstree.localElements[recvElement[rank][j]].src_id;
                                        jj++;
                                        for (int i = 0; i < NMAX; i++)
                                        {
                                                sendGrad[rank][jj] = sstree.localElements[recvElement[rank][j]].gradNeigh[i];
//            cout<<"grad  "<<jj<<"  "<<sendGrad[rank][jj]<<" "<<sstree.localElements[recvElement[rank][j]].grad<<endl ;
            sendNeighIds[rank][jj] = sstree.localElements[recvElement[rank][j]].neighId[i];
                                                jj++;
                                        }
                                }
                                else
                                        sendNeighIds[rank][j] = sstree.localElements[recvElement[rank][j]].src_id;
                        }
                        MPI_Issend(sendValue[rank],  nbRecvElement[rank], MPI_DOUBLE, rank, 0, communicator, &sendRequest[nbSendRequest]);
                        nbSendRequest++;
                        MPI_Issend(sendArea[rank],  nbRecvElement[rank], MPI_DOUBLE, rank, 0, communicator, &sendRequest[nbSendRequest]);
                        nbSendRequest++;
                        if (order == 2)
                        {
                                MPI_Issend(sendGrad[rank], 3*nbRecvElement[rank]*(NMAX+1),
                                                                MPI_DOUBLE, rank, 0, communicator, &sendRequest[nbSendRequest]);
                                nbSendRequest++;
                                MPI_Issend(sendNeighIds[rank], 4*nbRecvElement[rank]*(NMAX+1), MPI_INT, rank, 0, communicator, &sendRequest[nbSendRequest]);
//ym  --> attention taille GloId
                                nbSendRequest++;
                        }
                        else
                        {
                                MPI_Issend(sendNeighIds[rank], 4*nbRecvElement[rank], MPI_INT, rank, 0, communicator, &sendRequest[nbSendRequest]);
//ym  --> attention taille GloId
                                nbSendRequest++;
                        }
                }
                if (nbSendElement[rank] > 0)
                {
                        MPI_Irecv(recvValue[rank],  nbSendElement[rank], MPI_DOUBLE, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                        nbRecvRequest++;
                        MPI_Irecv(recvArea[rank],  nbSendElement[rank], MPI_DOUBLE, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                        nbRecvRequest++;
                        if (order == 2)
                        {
                                MPI_Irecv(recvGrad[rank], 3*nbSendElement[rank]*(NMAX+1),
                                                MPI_DOUBLE, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                                nbRecvRequest++;
                                MPI_Irecv(recvNeighIds[rank], 4*nbSendElement[rank]*(NMAX+1), MPI_INT, rank, 0, communicator, &recvRequest[nbRecvRequest]);
//ym  --> attention taille GloId
                                nbRecvRequest++;
                        }
                        else
                        {
                                MPI_Irecv(recvNeighIds[rank], 4*nbSendElement[rank], MPI_INT, rank, 0, communicator, &recvRequest[nbRecvRequest]);
//ym  --> attention taille GloId
                                nbRecvRequest++;
                        }
                }
        }
        MPI_Waitall(nbRecvRequest, recvRequest, status);
        MPI_Waitall(nbSendRequest, sendRequest, status);

        /* now that all values and gradients are available use them to computed interpolated values on target
           and also to compute weights */
        int i = 0;
        for (int j = 0; j < nbElements; j++)
        {
                Elt& e = elements[j];

                /* since for the 2nd order case source grid elements can contribute to a destination grid element over several "paths"
                   (step1: gradient is computed using neighbours on same grid, step2: intersection uses several elements on other grid)
                   accumulate them so that there is only one final weight between two elements */
                map<GloId,double> wgt_map;

                /* for destination element `e` loop over all intersetions/the corresponding source elements */
                for (list<Polyg *>::iterator it = e.is.begin(); it != e.is.end(); it++)
                {
                        /* it is the intersection element, so it->x and it->area are barycentre and area of intersection element (super mesh)
                        but it->id is id of the source element that it intersects */
                        int n1 = (*it)->id.ind;
                        int rank = (*it)->id.rank;
                        double fk = recvValue[rank][n1];
                        double srcArea = recvArea[rank][n1];
                        double w = (*it)->area;
      if (quantity) w/=srcArea ;

                        /* first order: src value times weight (weight = supermesh area), later divide by target area */
                        int kk = (order == 2) ? n1 * (NMAX + 1) : n1;
                        GloId neighID = recvNeighIds[rank][kk];
                        wgt_map[neighID] += w;

                        if (order == 2)
                        {
                                for (int k = 0; k < NMAX+1; k++)
                                {
                                        int kk = n1 * (NMAX + 1) + k;
                                        GloId neighID = recvNeighIds[rank][kk];
                                        if (neighID.ind != -1)  wgt_map[neighID] += w * scalarprod(recvGrad[rank][kk], (*it)->x);
                                }

                        }
                }

    double renorm=0;
    if (renormalize) 
      for (map<GloId,double>::iterator it = wgt_map.begin(); it != wgt_map.end(); it++) renorm+=it->second / e.area;
    else renorm=1. ;

    for (map<GloId,double>::iterator it = wgt_map.begin(); it != wgt_map.end(); it++)
                {
      if (quantity)  this->remapMatrix[i] = (it->second ) / renorm;
                        else this->remapMatrix[i] = (it->second / e.area) / renorm;
                        this->srcAddress[i] = it->first.ind;
                        this->srcRank[i] = it->first.rank;
                        this->dstAddress[i] = j;
      this->sourceWeightId[i]= it->first.globalId ;
      this->targetWeightId[i]= targetGlobalId[j] ;
                        i++;
                }
        }

        /* free all memory allocated in this function */
        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendElement[rank] > 0)
                {
                        delete[] sendElement[rank];
                        delete[] recvValue[rank];
                        delete[] recvArea[rank];
                        if (order == 2)
                        {
                                delete[] recvGrad[rank];
                        }
                        delete[] recvNeighIds[rank];
                }
                if (nbRecvElement[rank] > 0)
                {
                        delete[] recvElement[rank];
                        delete[] sendValue[rank];
                        delete[] sendArea[rank];
                        if (order == 2)
                                delete[] sendGrad[rank];
                        delete[] sendNeighIds[rank];
                }
        }
        delete[] status;
        delete[] sendRequest;
        delete[] recvRequest;
        delete[] elementList;
        delete[] nbSendElement;
        delete[] nbRecvElement;
        delete[] sendElement;
        delete[] recvElement;
        delete[] sendValue;
        delete[] recvValue;
        delete[] sendGrad;
        delete[] recvGrad;
        delete[] sendNeighIds;
        delete[] recvNeighIds;
        return i;
}

void Mapper::computeGrads()
{
        /* array of pointers to collect local elements and elements received from other cpu */
        vector<Elt*> globalElements(sstree.nbLocalElements + nbNeighbourElements);
        int index = 0;
        for (int i = 0; i < sstree.nbLocalElements; i++, index++)
                globalElements[index] = &(sstree.localElements[i]);
        for (int i = 0; i < nbNeighbourElements; i++, index++)
                globalElements[index] = &neighbourElements[i];

        update_baryc(sstree.localElements, sstree.nbLocalElements);
        computeGradients(&globalElements[0], sstree.nbLocalElements);
}

/** for each element of the source grid, finds all the neighbouring elements that share an edge
    (filling array neighbourElements). This is used later to compute gradients */
void Mapper::buildMeshTopology()
{
        int mpiSize, mpiRank;
        MPI_Comm_size(communicator, &mpiSize);
        MPI_Comm_rank(communicator, &mpiRank);

        vector<Node> *routingList = new vector<Node>[mpiSize];
        vector<vector<int> > routes(sstree.localTree.leafs.size());

        sstree.routeIntersections(routes, sstree.localTree.leafs);

        for (int i = 0; i < routes.size(); ++i)
                for (int k = 0; k < routes[i].size(); ++k)
                        routingList[routes[i][k]].push_back(sstree.localTree.leafs[i]);
        routingList[mpiRank].clear();


        CMPIRouting mpiRoute(communicator);
        mpiRoute.init(routes);
        int nRecv = mpiRoute.getTotalSourceElement();
// cout << mpiRank << " NRECV " << nRecv << "(" << routes.size() << ")"<< endl;

        int *nbSendNode = new int[mpiSize];
        int *nbRecvNode = new int[mpiSize];
        int *sendMessageSize = new int[mpiSize];
        int *recvMessageSize = new int[mpiSize];

        for (int rank = 0; rank < mpiSize; rank++)
        {
                nbSendNode[rank] = routingList[rank].size();
                sendMessageSize[rank] = 0;
                for (size_t j = 0; j < routingList[rank].size(); j++)
                {
                        Elt *elt = (Elt *) (routingList[rank][j].data);
                        sendMessageSize[rank] += packedPolygonSize(*elt);
                }
        }

        MPI_Alltoall(nbSendNode, 1, MPI_INT, nbRecvNode, 1, MPI_INT, communicator);
        MPI_Alltoall(sendMessageSize, 1, MPI_INT, recvMessageSize, 1, MPI_INT, communicator);

        char **sendBuffer = new char*[mpiSize];
        char **recvBuffer = new char*[mpiSize];
        int *pos = new int[mpiSize];

        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendNode[rank] > 0) sendBuffer[rank] = new char[sendMessageSize[rank]];
                if (nbRecvNode[rank] > 0) recvBuffer[rank] = new char[recvMessageSize[rank]];
        }

        for (int rank = 0; rank < mpiSize; rank++)
        {
                pos[rank] = 0;
                for (size_t j = 0; j < routingList[rank].size(); j++)
                {
                        Elt *elt = (Elt *) (routingList[rank][j].data);
                        packPolygon(*elt, sendBuffer[rank], pos[rank]);
                }
        }
        delete [] routingList;


        int nbSendRequest = 0;
        int nbRecvRequest = 0;
        MPI_Request *sendRequest = new MPI_Request[mpiSize];
        MPI_Request *recvRequest = new MPI_Request[mpiSize];
        MPI_Status  *status      = new MPI_Status[mpiSize];

        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendNode[rank] > 0)
                {
                        MPI_Issend(sendBuffer[rank], sendMessageSize[rank], MPI_CHAR, rank, 0, communicator, &sendRequest[nbSendRequest]);
                        nbSendRequest++;
                }
                if (nbRecvNode[rank] > 0)
                {
                        MPI_Irecv(recvBuffer[rank], recvMessageSize[rank], MPI_CHAR, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                        nbRecvRequest++;
                }
        }

        MPI_Waitall(nbRecvRequest, recvRequest, status);
        MPI_Waitall(nbSendRequest, sendRequest, status);

        for (int rank = 0; rank < mpiSize; rank++)
                if (nbSendNode[rank] > 0) delete [] sendBuffer[rank];
        delete [] sendBuffer;

        char **sendBuffer2 = new char*[mpiSize];
        char **recvBuffer2 = new char*[mpiSize];

        for (int rank = 0; rank < mpiSize; rank++)
        {
                nbSendNode[rank] = 0;
                sendMessageSize[rank] = 0;

                if (nbRecvNode[rank] > 0)
                {
                        set<NodePtr> neighbourList;
                        pos[rank] = 0;
                        for (int j = 0; j < nbRecvNode[rank]; j++)
                        {
                                Elt elt;
                                unpackPolygon(elt, recvBuffer[rank], pos[rank]);
                                Node node(elt.x, cptRadius(elt), &elt);
                                findNeighbour(sstree.localTree.root, &node, neighbourList);
                        }
                        nbSendNode[rank] = neighbourList.size();
                        for (set<NodePtr>::iterator it = neighbourList.begin(); it != neighbourList.end(); it++)
                        {
                                Elt *elt = (Elt *) ((*it)->data);
                                sendMessageSize[rank] += packedPolygonSize(*elt);
                        }

                        sendBuffer2[rank] = new char[sendMessageSize[rank]];
                        pos[rank] = 0;

                        for (set<NodePtr>::iterator it = neighbourList.begin(); it != neighbourList.end(); it++)
                        {
                                Elt *elt = (Elt *) ((*it)->data);
                                packPolygon(*elt, sendBuffer2[rank], pos[rank]);
                        }
                }
        }
        for (int rank = 0; rank < mpiSize; rank++)
                if (nbRecvNode[rank] > 0) delete [] recvBuffer[rank];
        delete [] recvBuffer;


        MPI_Barrier(communicator);
        MPI_Alltoall(nbSendNode, 1, MPI_INT, nbRecvNode, 1, MPI_INT, communicator);
        MPI_Alltoall(sendMessageSize, 1, MPI_INT, recvMessageSize, 1, MPI_INT, communicator);

        for (int rank = 0; rank < mpiSize; rank++)
                if (nbRecvNode[rank] > 0) recvBuffer2[rank] = new char[recvMessageSize[rank]];

        nbSendRequest = 0;
        nbRecvRequest = 0;

        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendNode[rank] > 0)
                {
                        MPI_Issend(sendBuffer2[rank], sendMessageSize[rank], MPI_CHAR, rank, 0, communicator, &sendRequest[nbSendRequest]);
                        nbSendRequest++;
                }
                if (nbRecvNode[rank] > 0)
                {
                        MPI_Irecv(recvBuffer2[rank], recvMessageSize[rank], MPI_CHAR, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                        nbRecvRequest++;
                }
        }

        MPI_Waitall(nbRecvRequest, recvRequest, status);
        MPI_Waitall(nbSendRequest, sendRequest, status);

        int nbNeighbourNodes = 0;
        for (int rank = 0; rank < mpiSize; rank++)
                nbNeighbourNodes += nbRecvNode[rank];

        neighbourElements = new Elt[nbNeighbourNodes];
        nbNeighbourElements = nbNeighbourNodes;

        int index = 0;
        for (int rank = 0; rank < mpiSize; rank++)
        {
                pos[rank] = 0;
                for (int j = 0; j < nbRecvNode[rank]; j++)
                {
                        unpackPolygon(neighbourElements[index], recvBuffer2[rank], pos[rank]);
                        neighbourElements[index].id.ind = sstree.localTree.leafs.size() + index;
                        index++;
                }
        }
        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbRecvNode[rank] > 0) delete [] recvBuffer2[rank];
                if (nbSendNode[rank] > 0) delete [] sendBuffer2[rank];
        }
        delete [] recvBuffer2;
        delete [] sendBuffer2;
        delete [] sendMessageSize;
        delete [] recvMessageSize;
        delete [] nbSendNode;
        delete [] nbRecvNode;
        delete [] sendRequest;
        delete [] recvRequest;
        delete [] status;
        delete [] pos;

        /* re-compute on received elements to avoid having to send this information */
        neighbourNodes.resize(nbNeighbourNodes);
        setCirclesAndLinks(neighbourElements, neighbourNodes);
        cptAllEltsGeom(neighbourElements, nbNeighbourNodes, srcGrid.pole);

        /* the local SS tree must include nodes from other cpus if they are potential
           intersector of a local node */
        sstree.localTree.insertNodes(neighbourNodes);

        /* for every local element,
           use the SS-tree to find all elements (including neighbourElements)
           who are potential neighbours because their circles intersect,
           then check all canditates for common edges to build up connectivity information
        */
        for (int j = 0; j < sstree.localTree.leafs.size(); j++)
        {
                Node& node = sstree.localTree.leafs[j];

                /* find all leafs whoes circles that intersect node's circle and save into node->intersectors */
                node.search(sstree.localTree.root);

                Elt *elt = (Elt *)(node.data);

                for (int i = 0; i < elt->n; i++) elt->neighbour[i] = NOT_FOUND;

                /* for element `elt` loop through all nodes in the SS-tree
                   whoes circles intersect with the circle around `elt` (the SS intersectors)
                   and check if they are neighbours in the sense that the two elements share an edge.
                   If they do, save this information for elt */
                for (list<NodePtr>::iterator it = (node.intersectors).begin(); it != (node.intersectors).end(); ++it)
                {
                        Elt *elt2 = (Elt *)((*it)->data);
                        set_neighbour(*elt, *elt2);
                }

/*
                for (int i = 0; i < elt->n; i++)
                {
                        if (elt->neighbour[i] == NOT_FOUND)
                                error_exit("neighbour not found");
                }
*/
        }
}

/** @param elements are the target grid elements */
void Mapper::computeIntersection(Elt *elements, int nbElements)
{
        int mpiSize, mpiRank;
        MPI_Comm_size(communicator, &mpiSize);
        MPI_Comm_rank(communicator, &mpiRank);

        MPI_Barrier(communicator);

        vector<Node> *routingList = new vector<Node>[mpiSize];

        vector<Node> routeNodes;  routeNodes.reserve(nbElements);
        for (int j = 0; j < nbElements; j++)
        {
                elements[j].id.ind = j;
                elements[j].id.rank = mpiRank;
                routeNodes.push_back(Node(elements[j].x, cptRadius(elements[j]), &elements[j]));
        }

        vector<vector<int> > routes(routeNodes.size());
        sstree.routeIntersections(routes, routeNodes);
        for (int i = 0; i < routes.size(); ++i)
                for (int k = 0; k < routes[i].size(); ++k)
                        routingList[routes[i][k]].push_back(routeNodes[i]);

        if (verbose >= 2)
        {
                cout << " --> rank  " << mpiRank << " nbElements " << nbElements << " : ";
                for (int rank = 0; rank < mpiSize; rank++)
                        cout << routingList[rank].size() << "   ";
                cout << endl;
        }
        MPI_Barrier(communicator);

        int *nbSendNode = new int[mpiSize];
        int *nbRecvNode = new int[mpiSize];
        int *sentMessageSize = new int[mpiSize];
        int *recvMessageSize = new int[mpiSize];

        for (int rank = 0; rank < mpiSize; rank++)
        {
                nbSendNode[rank] = routingList[rank].size();
                sentMessageSize[rank] = 0;
                for (size_t j = 0; j < routingList[rank].size(); j++)
                {
                        Elt *elt = (Elt *) (routingList[rank][j].data);
                        sentMessageSize[rank] += packedPolygonSize(*elt);
                }
        }

        MPI_Alltoall(nbSendNode, 1, MPI_INT, nbRecvNode, 1, MPI_INT, communicator);
        MPI_Alltoall(sentMessageSize, 1, MPI_INT, recvMessageSize, 1, MPI_INT, communicator);

        int total = 0;

        for (int rank = 0; rank < mpiSize; rank++)
        {
                total = total + nbRecvNode[rank];
        }

        if (verbose >= 2) cout << "---> rank " << mpiRank << " : compute intersection : total received nodes  " << total << endl;
        char **sendBuffer = new char*[mpiSize];
        char **recvBuffer = new char*[mpiSize];
        int *pos = new int[mpiSize];

        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendNode[rank] > 0) sendBuffer[rank] = new char[sentMessageSize[rank]];
                if (nbRecvNode[rank] > 0) recvBuffer[rank] = new char[recvMessageSize[rank]];
        }

        for (int rank = 0; rank < mpiSize; rank++)
        {
                pos[rank] = 0;
                for (size_t j = 0; j < routingList[rank].size(); j++)
                {
                        Elt* elt = (Elt *) (routingList[rank][j].data);
                        packPolygon(*elt, sendBuffer[rank], pos[rank]);
                }
        }
        delete [] routingList;

        int nbSendRequest = 0;
        int nbRecvRequest = 0;
        MPI_Request *sendRequest = new MPI_Request[mpiSize];
        MPI_Request *recvRequest = new MPI_Request[mpiSize];
        MPI_Status   *status = new MPI_Status[mpiSize];

        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendNode[rank] > 0)
                {
                        MPI_Issend(sendBuffer[rank], sentMessageSize[rank], MPI_CHAR, rank, 0, communicator, &sendRequest[nbSendRequest]);
                        nbSendRequest++;
                }
                if (nbRecvNode[rank] > 0)
                {
                        MPI_Irecv(recvBuffer[rank], recvMessageSize[rank], MPI_CHAR, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                        nbRecvRequest++;
                }
        }

        MPI_Waitall(nbRecvRequest, recvRequest, status);
        MPI_Waitall(nbSendRequest, sendRequest, status);
        char **sendBuffer2 = new char*[mpiSize];
        char **recvBuffer2 = new char*[mpiSize];

        double tic = cputime();
        for (int rank = 0; rank < mpiSize; rank++)
        {
                sentMessageSize[rank] = 0;

                if (nbRecvNode[rank] > 0)
                {
                        Elt *recvElt = new Elt[nbRecvNode[rank]];
                        pos[rank] = 0;
                        for (int j = 0; j < nbRecvNode[rank]; j++)
                        {
                                unpackPolygon(recvElt[j], recvBuffer[rank], pos[rank]);
                                cptEltGeom(recvElt[j], tgtGrid.pole);
                                Node recvNode(recvElt[j].x, cptRadius(recvElt[j]), &recvElt[j]);
                                recvNode.search(sstree.localTree.root);
                                /* for a node holding an element of the target, loop throught candidates for intersecting source */
                                for (list<NodePtr>::iterator it = (recvNode.intersectors).begin(); it != (recvNode.intersectors).end(); ++it)
                                {
                                        Elt *elt2 = (Elt *) ((*it)->data);
                                        /* recvElt is target, elt2 is source */
//                                      intersect(&recvElt[j], elt2);
                                        intersect_ym(&recvElt[j], elt2);
                                }

                                if (recvElt[j].is.size() > 0) sentMessageSize[rank] += packIntersectionSize(recvElt[j]);

                                // here recvNode goes out of scope
                        }

                        if (sentMessageSize[rank] > 0)
                        {
                                sentMessageSize[rank] += sizeof(int);
                                sendBuffer2[rank] = new char[sentMessageSize[rank]];
                                *((int *) sendBuffer2[rank]) = 0;
                                pos[rank] = sizeof(int);
                                for (int j = 0; j < nbRecvNode[rank]; j++)
                                {
                                        packIntersection(recvElt[j], sendBuffer2[rank], pos[rank]);
                                        //FIXME should be deleted: recvElt[j].delete_intersections(); // intersection areas have been packed to buffer and won't be used any more
                                }
                        }
                        delete [] recvElt;

                }
        }
        delete [] pos;

        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbSendNode[rank] > 0) delete [] sendBuffer[rank];
                if (nbRecvNode[rank] > 0) delete [] recvBuffer[rank];
                nbSendNode[rank] = 0;
        }

        if (verbose >= 2) cout << "Rank " << mpiRank << "  Compute (internal) intersection " << cputime() - tic << " s" << endl;
        MPI_Alltoall(sentMessageSize, 1, MPI_INT, recvMessageSize, 1, MPI_INT, communicator);

        for (int rank = 0; rank < mpiSize; rank++)
                if (recvMessageSize[rank] > 0)
                        recvBuffer2[rank] = new char[recvMessageSize[rank]];

        nbSendRequest = 0;
        nbRecvRequest = 0;

        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (sentMessageSize[rank] > 0)
                {
                        MPI_Issend(sendBuffer2[rank], sentMessageSize[rank], MPI_CHAR, rank, 0, communicator, &sendRequest[nbSendRequest]);
                        nbSendRequest++;
                }
                if (recvMessageSize[rank] > 0)
                {
                        MPI_Irecv(recvBuffer2[rank], recvMessageSize[rank], MPI_CHAR, rank, 0, communicator, &recvRequest[nbRecvRequest]);
                        nbRecvRequest++;
                }
        }

        MPI_Waitall(nbRecvRequest, recvRequest, status);
        MPI_Waitall(nbSendRequest, sendRequest, status);

        delete [] sendRequest;
        delete [] recvRequest;
        delete [] status;
        for (int rank = 0; rank < mpiSize; rank++)
        {
                if (nbRecvNode[rank] > 0)
                {
                        if (sentMessageSize[rank] > 0)
                                delete [] sendBuffer2[rank];
                }

                if (recvMessageSize[rank] > 0)
                {
                        unpackIntersection(elements, recvBuffer2[rank]);
                        delete [] recvBuffer2[rank];
                }
        }
        delete [] sendBuffer2;
        delete [] recvBuffer2;
        delete [] sendBuffer;
        delete [] recvBuffer;

        delete [] nbSendNode;
        delete [] nbRecvNode;
        delete [] sentMessageSize;
        delete [] recvMessageSize;
}

Mapper::~Mapper()
{
        delete [] remapMatrix;
        delete [] srcAddress;
        delete [] srcRank;
        delete [] dstAddress;
        if (neighbourElements) delete [] neighbourElements;
}

}