SundanceBasicSimplicialMesh.cpp

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/* @HEADER@ */
// ************************************************************************
// 
//                              Sundance
//                 Copyright (2005) Sandia Corporation
// 
// Copyright (year first published) Sandia Corporation.  Under the terms 
// of Contract DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government 
// retains certain rights in this software.
// 
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//  
// This library 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
// Lesser General Public License for more details.
//                                                                                 
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA                                                                                
// Questions? Contact Kevin Long (krlong@sandia.gov), 
// Sandia National Laboratories, Livermore, California, USA
// 
// ************************************************************************
/* @HEADER@ */

#include "SundanceBasicSimplicialMesh.hpp"
#include "SundanceMeshType.hpp"
#include "SundanceCellJacobianBatch.hpp"
#include "SundanceMaximalCofacetBatch.hpp"
#include "SundanceMeshSource.hpp"
#include "SundanceDebug.hpp"
#include "SundanceOut.hpp"
#include "PlayaMPIContainerComm.hpp"
#include "Teuchos_Time.hpp"
#include "Teuchos_TimeMonitor.hpp"
#include "SundanceObjectWithVerbosity.hpp"
#include "SundanceCollectiveExceptionCheck.hpp"

#include <algorithm>
#include <unistd.h>

using namespace Sundance;
using namespace Teuchos;
using Playa::MPIComm;
using Playa::MPIContainerComm;

using std::endl;


#ifdef BSM_LOW_LEVEL_TIMER

static Time& getAddElementTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("BSM addElement"); 
  return *rtn;
}

static Time& getFacetRegistrationTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("BSM element facet registration"); 
  return *rtn;
}


static Time& getAddVertexTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("BSM addVertex"); 
  return *rtn;
}


static Time& getAddEdgeTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("BSM addEdge"); 
  return *rtn;
}

static Time& getAddFaceTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("BSM addFace"); 
  return *rtn;
}

static Time& getLookupLIDTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("BSM lookup LID"); 
  return *rtn;
}

#endif

static Time& batchedFacetGrabTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("batched facet grabbing"); 
  return *rtn;
}

void sort(const Array<int>& in, Array<int>& rtn)
{
  rtn.resize(in.size());
  const int* pIn = &(in[0]);
  int* pRtn = &(rtn[0]);
  for (int i=0; i<in.size(); i++) pRtn[i] = pIn[i];
  
  for (int j=1; j<in.size(); j++)
  {
    int key = pRtn[j];
    int i=j-1;
    while (i>=0 && pRtn[i]>key)
    {
      pRtn[i+1]=pRtn[i];
      i--;
    }
    pRtn[i+1]=key;
  }
  //std::sort(rtn.begin(), rtn.end());
}


static Time& getJacobianTimer() 
{
  static RCP<Time> rtn 
    = TimeMonitor::getNewTimer("cell Jacobian grabbing"); 
  return *rtn;
}


//#define SKIP_FACES

BasicSimplicialMesh::BasicSimplicialMesh(int dim, const MPIComm& comm, 
  const MeshEntityOrder& order)
  : IncrementallyCreatableMesh(dim, comm, order),
    numCells_(dim+1),
    points_(),
    edgeVerts_(2),
    faceVertLIDs_(dim),
    faceVertGIDs_(dim),
    faceEdges_(dim),
    faceEdgeSigns_(dim),
    elemVerts_(dim+1),
    elemEdges_(),
    elemEdgeSigns_(),
    elemFaces_(dim+1),
    elemFaceRotations_(dim+1),
    vertexSetToFaceIndexMap_(),
    edgeFaces_(),
    edgeCofacets_(),
    faceCofacets_(),
    vertEdges_(),
    vertFaces_(),
    vertCofacets_(),
    vertEdgePartners_(),
    LIDToGIDMap_(dim+1),
    GIDToLIDMap_(dim+1),
    labels_(dim+1),
    ownerProcID_(dim+1),
    faceVertGIDBase_(1),
    hasEdgeGIDs_(false),
    hasFaceGIDs_(false),
    neighbors_(),
    neighborsAreSynchronized_(false)
{
  estimateNumVertices(1000);
  estimateNumElements(1000);

  /* Set up the pointer giving a view of the face vertex array.
   * Resize to 1 so that phony dereference will work, then resize to zero to make the
   * new array logically empty */
  faceVertGIDs_.resize(1);
  faceVertGIDBase_[0] = &(faceVertGIDs_.value(0,0));
  faceVertGIDs_.resize(0);

  /* size the element edge lists as appropriate to the mesh's dimension */
  if (spatialDim()==2) 
  {
    elemEdges_.setTupleSize(3);
    elemEdgeSigns_.setTupleSize(3);
  }
  if (spatialDim()==3) 
  {
    elemEdges_.setTupleSize(6);
    elemEdgeSigns_.setTupleSize(6);
  }

  neighbors_.put(comm.getRank());
}


void BasicSimplicialMesh::getJacobians(int cellDim, const Array<int>& cellLID,
  CellJacobianBatch& jBatch) const
{
  TimeMonitor timer(getJacobianTimer());

  int flops = 0 ;
  int nCells = cellLID.size();

  TEUCHOS_TEST_FOR_EXCEPTION(cellDim < 0 || cellDim > spatialDim(), std::logic_error,
    "cellDim=" << cellDim 
    << " is not in expected range [0, " << spatialDim()
    << "]");

  jBatch.resize(cellLID.size(), spatialDim(), cellDim);

  if (cellDim < spatialDim())
  {
    switch(cellDim)
    {
      case 1:
        flops += 3*nCells;
        break;
      case 2:
        // 4 flops for two pt subtractions, 10 for a cross product
        flops += (4 + 10)*nCells;
        break;
      default:
        break;
    }

    for (int i=0; i<nCells; i++)
    {
      int lid = cellLID[i];
      double* detJ = jBatch.detJ(i);
      switch(cellDim)
      {
        case 0:
          *detJ = 1.0;
          break;
        case 1:
        {
          int a = edgeVerts_.value(lid, 0);
          int b = edgeVerts_.value(lid, 1);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          Point dx = pb-pa;
          *detJ = sqrt(dx*dx);
        }
        break;
        case 2:
        {
          int a = faceVertLIDs_.value(lid, 0);
          int b = faceVertLIDs_.value(lid, 1);
          int c = faceVertLIDs_.value(lid, 2);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          const Point& pc = points_[c];
          Point directedArea = cross(pc-pa, pb-pa);
          *detJ = sqrt(directedArea*directedArea);
        }
        break;
        default:
          TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error, "impossible switch value "
            "cellDim=" << cellDim 
            << " in BasicSimplicialMesh::getJacobians()");
      }
    }
  }
  else
  {
    Array<double> J(cellDim*cellDim);
  
    flops += cellDim*cellDim*nCells;

    for (int i=0; i<cellLID.size(); i++)
    {
      int lid = cellLID[i];
      double* J = jBatch.jVals(i);
      switch(cellDim)
      {
        case 0:
          J[0] = 1.0;
          break;
        case 1:
        {
          int a = elemVerts_.value(lid, 0);
          int b = elemVerts_.value(lid, 1);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          J[0] = fabs(pa[0]-pb[0]);
        }
        break;
        case 2:
        {
          int a = elemVerts_.value(lid, 0);
          int b = elemVerts_.value(lid, 1);
          int c = elemVerts_.value(lid, 2);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          const Point& pc = points_[c];
          J[0] = pb[0] - pa[0];
          J[1] = pc[0] - pa[0];
          J[2] = pb[1] - pa[1];
          J[3] = pc[1] - pa[1];
            
        }
        break;
        case 3:
        {
          int a = elemVerts_.value(lid, 0);
          int b = elemVerts_.value(lid, 1);
          int c = elemVerts_.value(lid, 2);
          int d = elemVerts_.value(lid, 3);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          const Point& pc = points_[c];
          const Point& pd = points_[d];
          J[0] = pb[0] - pa[0];
          J[1] = pc[0] - pa[0];
          J[2] = pd[0] - pa[0];
          J[3] = pb[1] - pa[1];
          J[4] = pc[1] - pa[1];
          J[5] = pd[1] - pa[1];
          J[6] = pb[2] - pa[2];
          J[7] = pc[2] - pa[2];
          J[8] = pd[2] - pa[2];
        }
        break;
        default:
          TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error, "impossible switch value "
            "cellDim=" << cellDim 
            << " in BasicSimplicialMesh::getJacobians()");
      }
    }
  }
  CellJacobianBatch::addFlops(flops);
}



void BasicSimplicialMesh::getCellDiameters(int cellDim, const Array<int>& cellLID,
  Array<double>& cellDiameters) const
{
  TEUCHOS_TEST_FOR_EXCEPTION(cellDim < 0 || cellDim > spatialDim(), std::logic_error,
    "cellDim=" << cellDim 
    << " is not in expected range [0, " << spatialDim()
    << "]");

  cellDiameters.resize(cellLID.size());

  if (cellDim < spatialDim())
  {
    for (int i=0; i<cellLID.size(); i++)
    {
      int lid = cellLID[i];
      switch(cellDim)
      {
        case 0:
          cellDiameters[i] = 1.0;
          break;
        case 1:
        {
          int a = edgeVerts_.value(lid, 0);
          int b = edgeVerts_.value(lid, 1);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          Point dx = pb-pa;
          cellDiameters[i] = sqrt(dx*dx);
        }
        break;
        case 2:
        {
          int a = faceVertLIDs_.value(lid, 0);
          int b = faceVertLIDs_.value(lid, 1);
          int c = faceVertLIDs_.value(lid, 2);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          const Point& pc = points_[c];
          Point directedArea = cross(pc-pa, pb-pa);
          cellDiameters[i] = sqrt(directedArea*directedArea);
        }
        break;
        default:
          TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error, "impossible switch value "
            "cellDim=" << cellDim 
            << " in BasicSimplicialMesh::getCellDiameters()");
      }
    }
  }
  else
  {
    for (int i=0; i<cellLID.size(); i++)
    {
      int lid = cellLID[i];
      switch(cellDim)
      {
        case 0:
          cellDiameters[i] = 1.0;
          break;
        case 1:
        {
          int a = elemVerts_.value(lid, 0);
          int b = elemVerts_.value(lid, 1);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          cellDiameters[i] = fabs(pa[0]-pb[0]);
        }
        break;
        case 2:
        {
          int a = elemVerts_.value(lid, 0);
          int b = elemVerts_.value(lid, 1);
          int c = elemVerts_.value(lid, 2);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          const Point& pc = points_[c];
          cellDiameters[i] 
            = (pa.distance(pb) + pb.distance(pc) + pa.distance(pc))/3.0;
        }
        break;
        case 3:
        {
          int a = elemVerts_.value(lid, 0);
          int b = elemVerts_.value(lid, 1);
          int c = elemVerts_.value(lid, 2);
          int d = elemVerts_.value(lid, 3);
          const Point& pa = points_[a];
          const Point& pb = points_[b];
          const Point& pc = points_[c];
          const Point& pd = points_[d];
                
          cellDiameters[i] 
            = (pa.distance(pb) + pa.distance(pc) + pa.distance(pd)
              + pb.distance(pc) + pb.distance(pd)
              + pc.distance(pd))/6.0;
        }
        break;
        default:
          TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error, "impossible switch value "
            "cellDim=" << cellDim 
            << " in BasicSimplicialMesh::getCellDiameters()");
      }
    }
  }
}


void BasicSimplicialMesh::pushForward(int cellDim, const Array<int>& cellLID,
  const Array<Point>& refQuadPts,
  Array<Point>& physQuadPts) const
{
  TEUCHOS_TEST_FOR_EXCEPTION(cellDim < 0 || cellDim > spatialDim(), std::logic_error,
    "cellDim=" << cellDim 
    << " is not in expected range [0, " << spatialDim()
    << "]");
  int flops = 0;
  int nQuad = refQuadPts.size();
  int nCells = cellLID.size();
  Array<double> J(cellDim*cellDim);

  if (physQuadPts.size() > 0) physQuadPts.resize(0);
  physQuadPts.reserve(cellLID.size() * refQuadPts.size());

  switch(cellDim)
  {
    case 1:
      flops += nCells * (1 + 2*nQuad);
      break;
    case 2:
      if (spatialDim()==2)
      {
        flops += nCells*(4 + 8*nQuad);
      }
      else
      {
        flops += 18*nCells*nQuad;
      }
      break;
    case 3:
      flops += 27*nCells*nQuad;
      break;
    default:
      break;
  }


  for (int i=0; i<cellLID.size(); i++)
  {
    int lid = cellLID[i];
    switch(cellDim)
    {
      case 0:
        physQuadPts.append(points_[lid]);
        break;
      case 1:
      {
        int a, b;
        if (spatialDim()==1)
        {
          a = elemVerts_.value(lid, 0);
          b = elemVerts_.value(lid, 1);
        }
        else
        {
          a = edgeVerts_.value(lid, 0);
          b = edgeVerts_.value(lid, 1);
        }
        const Point& pa = points_[a];
        const Point& pb = points_[b];
        Point dx = pb-pa;
        for (int q=0; q<nQuad; q++)
        {
          physQuadPts.append(pa + refQuadPts[q][0]*dx);
        }
      }
      break;
      case 2:
      {
        int a,b,c;
        if (spatialDim()==2)
        {
          a = elemVerts_.value(lid, 0);
          b = elemVerts_.value(lid, 1);
          c = elemVerts_.value(lid, 2);
        }
        else
        {
          a = faceVertLIDs_.value(lid, 0);
          b = faceVertLIDs_.value(lid, 1);
          c = faceVertLIDs_.value(lid, 2);
        }
        const Point& pa = points_[a];
        const Point& pb = points_[b];
        const Point& pc = points_[c];

        if (spatialDim()==2)
        {
          J[0] = pb[0] - pa[0];
          J[1] = pc[0] - pa[0];
          J[2] = pb[1] - pa[1];
          J[3] = pc[1] - pa[1];
          for (int q=0; q<nQuad; q++)
          {
            physQuadPts.append(pa 
              + Point(J[0]*refQuadPts[q][0] +J[1]*refQuadPts[q][1],
                J[2]*refQuadPts[q][0] +J[3]*refQuadPts[q][1]) );
          }
        }
        else
        {
          for (int q=0; q<nQuad; q++)
          {
            physQuadPts.append(pa 
              + (pb-pa)*refQuadPts[q][0] 
              + (pc-pa)*refQuadPts[q][1]);
          }
        }
            
      }
      break;
      case 3:
      {
        int a = elemVerts_.value(lid, 0);
        int b = elemVerts_.value(lid, 1);
        int c = elemVerts_.value(lid, 2);
        int d = elemVerts_.value(lid, 3);
        const Point& pa = points_[a];
        const Point& pb = points_[b];
        const Point& pc = points_[c];
        const Point& pd = points_[d];
        J[0] = pb[0] - pa[0];
        J[1] = pc[0] - pa[0];
        J[2] = pd[0] - pa[0];
        J[3] = pb[1] - pa[1];
        J[4] = pc[1] - pa[1];
        J[5] = pd[1] - pa[1];
        J[6] = pb[2] - pa[2];
        J[7] = pc[2] - pa[2];
        J[8] = pd[2] - pa[2];
            
        for (int q=0; q<nQuad; q++)
        {
          physQuadPts.append(pa 
            + Point(J[0]*refQuadPts[q][0] 
              + J[1]*refQuadPts[q][1]
              + J[2]*refQuadPts[q][2],
              J[3]*refQuadPts[q][0] 
              + J[4]*refQuadPts[q][1]
              + J[5]*refQuadPts[q][2],
              J[6]*refQuadPts[q][0] 
              + J[7]*refQuadPts[q][1]
              + J[8]*refQuadPts[q][2]));

        }
            
      }
      break;
      default:
        TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error, "impossible switch value "
          "in BasicSimplicialMesh::getJacobians()");
    }
  }

  CellJacobianBatch::addFlops(flops);
}

void BasicSimplicialMesh::estimateNumVertices(int nPts)
{
  points_.reserve(nPts);
  vertCofacets_.reserve(nPts);
  vertEdges_.reserve(nPts);
  vertEdgePartners_.reserve(nPts);

  ownerProcID_[0].reserve(nPts);
  LIDToGIDMap_[0].reserve(nPts);
  GIDToLIDMap_[0] = Hashtable<int,int>(nPts, 0.6);
  labels_[0].reserve(nPts);
}

void BasicSimplicialMesh::estimateNumElements(int nElems)
{
  int nEdges = 0;
  int nFaces = 0;

  if (spatialDim()==3) 
  {
    nFaces = 5*nElems;
    nEdges = 5*nElems;
    labels_[2].reserve(nFaces);
  }
  else if (spatialDim()==2)
  {
    nEdges = 3*nElems;
  }
  
  labels_[1].reserve(nEdges);
  vertexSetToFaceIndexMap_ = Hashtable<VertexView, int>(nFaces);

  edgeVerts_.reserve(nEdges);
  faceVertLIDs_.reserve(nFaces);
  faceVertGIDs_.reserve(nFaces);
  faceEdges_.reserve(nFaces);
  elemVerts_.reserve(nElems);
  elemEdges_.reserve(nElems);
  elemEdgeSigns_.reserve(nElems);
  elemFaces_.reserve(nElems);
  edgeCofacets_.reserve(nEdges);
  faceCofacets_.reserve(nFaces);

  ownerProcID_[spatialDim()].reserve(nElems);
  LIDToGIDMap_[spatialDim()].reserve(nElems);
  GIDToLIDMap_[spatialDim()] = Hashtable<int,int>(nElems, 0.6);
  labels_[spatialDim()].reserve(nElems);

  /* resize to 1 so that phony dereference will work, then resize to zero to make the
   * new array logically empty */
  faceVertGIDs_.resize(1);
  faceVertGIDBase_[0] = &(faceVertGIDs_.value(0,0));
  faceVertGIDs_.resize(0);
}



int BasicSimplicialMesh::numCells(int cellDim) const
{
  return numCells_[cellDim];
}

int BasicSimplicialMesh::ownerProcID(int cellDim, int cellLID) const
{
  return ownerProcID_[cellDim][cellLID];
}

int BasicSimplicialMesh::numFacets(int cellDim, int cellLID, 
  int facetDim) const
{
  if (cellDim==1)
  {
    return 2;
  }
  else if (cellDim==2)
  {
    return 3;
  }
  else 
  {
    if (facetDim==0) return 4;
    if (facetDim==1) return 6;
    return 4;
  }
}

void BasicSimplicialMesh::getFacetLIDs(int cellDim, 
  const Array<int>& cellLID,
  int facetDim,
  Array<int>& facetLID,
  Array<int>& facetSign) const 
{
  TimeMonitor timer(batchedFacetGrabTimer());

  int nf = numFacets(cellDim, cellLID[0], facetDim);
  facetLID.resize(cellLID.size() * nf);
  if (facetDim > 0) facetSign.resize(cellLID.size() * nf);

  
  if (facetDim==0)
  {
    if (cellDim == spatialDim())
    {
      int ptr=0;
      for (int c=0; c<cellLID.size(); c++)
      {
        const int* fPtr = &(elemVerts_.value(cellLID[c], 0));
        for (int f=0; f<nf; f++, ptr++)
        {
          facetLID[ptr] = fPtr[f];
        }
      }
    }
    else if (cellDim==1) 
    {
      int ptr=0;
      for (int c=0; c<cellLID.size(); c++)
      {
        const int* fPtr = &(edgeVerts_.value(cellLID[c], 0));
        for (int f=0; f<nf; f++, ptr++)
        {
          facetLID[ptr] = fPtr[f];
        }
      }
    }
    else if (cellDim==2) 
    {
      int ptr=0;
      for (int c=0; c<cellLID.size(); c++)
      {
        const int* fPtr = &(faceVertLIDs_.value(cellLID[c], 0));
        for (int f=0; f<nf; f++, ptr++)
        {
          facetLID[ptr] = fPtr[f];
        }
      }
    }
  }
  else if (facetDim==1)
  {
    int ptr=0;
    if (cellDim == spatialDim())
    {
      for (int c=0; c<cellLID.size(); c++)
      {
        const int* fPtr = &(elemEdges_.value(cellLID[c], 0));
//        const int* fsPtr = &(elemEdgeSigns_.value(cellLID[c], 0));
        for (int f=0; f<nf; f++, ptr++)
        {
          facetLID[ptr] = fPtr[f];
          facetSign[ptr] = 1;//fsPtr[f];
        }
      }
    }
    else
    {
      for (int c=0; c<cellLID.size(); c++)
      {
        const int* fPtr = &(faceEdges_.value(cellLID[c], 0));
        //    const int* fsPtr = &(faceEdgeSigns_.value(cellLID[c], 0));
        for (int f=0; f<nf; f++, ptr++)
        {
          facetLID[ptr] = fPtr[f];
          //  facetSign[ptr] = fsPtr[f];
        }
      }
    }
  }
  else
  {
    int ptr=0;
    for (int c=0; c<cellLID.size(); c++)
    {
      const int* fPtr = &(elemFaces_.value(cellLID[c], 0));
//      const int* fsPtr = &(elemFaceRotations_.value(cellLID[c], 0));
      for (int f=0; f<nf; f++, ptr++)
      {
        facetLID[ptr] = fPtr[f];
        facetSign[ptr] = 1;//fsPtr[f];
      }
    }
  }
}

int BasicSimplicialMesh::facetLID(int cellDim, int cellLID,
  int facetDim, int facetIndex, int& facetSign) const 
{

  if (facetDim==0)
  {
    if (cellDim == spatialDim())
    {
      return elemVerts_.value(cellLID, facetIndex);
    }
    else if (cellDim==1) return edgeVerts_.value(cellLID, facetIndex);
    else if (cellDim==2) return faceVertLIDs_.value(cellLID, facetIndex);
  }
  if (facetDim==1)
  {
    if (cellDim==spatialDim())
    {
      facetSign = 1;//elemEdgeSigns_.value(cellLID, facetIndex);
      return elemEdges_.value(cellLID, facetIndex);
    }
    else
    {
      //facetSign = faceEdgeSigns_.value(cellLID, facetIndex);
      return faceEdges_.value(cellLID, facetIndex);
    }
  }
  else
  {
    facetSign = 1;//elemFaceRotations_.value(cellLID, facetIndex);
    return elemFaces_.value(cellLID, facetIndex);
  }
}


int BasicSimplicialMesh::numMaxCofacets(int cellDim, int cellLID) const 
{

  if (cellDim==0)
  {
    return vertCofacets_[cellLID].length();
  }
  if (cellDim==1)
  {
    return edgeCofacets_[cellLID].length();
  }
  if (cellDim==2)
  {
    return faceCofacets_[cellLID].length();
  }
  return -1; // -Wall
}



int BasicSimplicialMesh::maxCofacetLID(int cellDim, int cellLID,
  int cofacetIndex,
  int& facetIndex) const
{
  int rtn = -1;
  if (cellDim==0)
  {
    rtn = vertCofacets_[cellLID][cofacetIndex];
  }
  else if (cellDim==1)
  {
    rtn = edgeCofacets_[cellLID][cofacetIndex];
  }
  else if (cellDim==2)
  {
    rtn = faceCofacets_[cellLID][cofacetIndex];
  }
  else
  {
    TEUCHOS_TEST_FOR_EXCEPTION(true, std::runtime_error, 
      "invalid cell dimension " << cellDim
      << " in request for cofacet");
  }

//  Out::os() << "facet LID=" << cellLID << " cofacetIndex=" << cofacetIndex
//            << " recovered cofacet=" << rtn << endl;
  int dummy;
  for (int f=0; f<numFacets(spatialDim(), rtn, cellDim); f++)
  {
//    Tabs tab;
    int c = facetLID(spatialDim(), rtn, cellDim, f, dummy);
//    Out::os() << "f=" << f << " facet LID=" << c << endl;
    if (cellLID==c)
    {
      facetIndex = f;
      return rtn;
    }
  }
  TEUCHOS_TEST_FOR_EXCEPTION(true, std::runtime_error, "reverse pointer to facet not found"
    " in request for cofacet");
  return -1; // -Wall
}


void BasicSimplicialMesh::getMaxCofacetLIDs(
  const Array<int>& cellLIDs,
  MaximalCofacetBatch& cofacets) const
{
  TEUCHOS_TEST_FOR_EXCEPT(cellLIDs.size()==0);
  int d = spatialDim() - 1;
  int nc = numMaxCofacets(d, cellLIDs[0]);  

  cofacets.reset(cellLIDs.size(), nc);

  for (int i=0; i<cellLIDs.size(); i++) 
  {
    int f1;
    int cofacet1 = maxCofacetLID(d, cellLIDs[i], 0, f1);
    if (nc==1) cofacets.addSingleCofacet(i, cofacet1, f1);
    else
    {
      int f2;
      int cofacet2 = maxCofacetLID(d, cellLIDs[i], 1, f2);
      cofacets.addTwoCofacets(i, cofacet1, f1, cofacet2, f2);
    }
  }
}

void BasicSimplicialMesh::getCofacets(int cellDim, int cellLID,
  int cofacetDim, Array<int>& cofacetLIDs) const 
{
  //  TimeMonitor timer(cofacetGrabTimer());
  TEUCHOS_TEST_FOR_EXCEPTION(cofacetDim > spatialDim() || cofacetDim < 0, std::runtime_error,
    "invalid cofacet dimension=" << cofacetDim);
  TEUCHOS_TEST_FOR_EXCEPTION( cofacetDim <= cellDim, std::runtime_error,
    "invalid cofacet dimension=" << cofacetDim
    << " for cell dim=" << cellDim);
  if (cofacetDim==spatialDim())
  {
    cofacetLIDs.resize(numMaxCofacets(cellDim, cellLID));
    int dum=0;
    for (int f=0; f<cofacetLIDs.size(); f++)
    {
      cofacetLIDs[f] = maxCofacetLID(cellDim, cellLID, f, dum);
    }
  }
  else
  {
    if (cellDim==0)
    {
      if (cofacetDim==1) cofacetLIDs = vertEdges_[cellLID];
      else if (cofacetDim==2) cofacetLIDs = vertFaces_[cellLID];
      else TEUCHOS_TEST_FOR_EXCEPT(true);
    }
    else if (cellDim==1)
    { 
      if (cofacetDim==2) cofacetLIDs = edgeFaces_[cellLID];
      else TEUCHOS_TEST_FOR_EXCEPT(true);
    }
    else if (cellDim==2)
    {
      /* this should never happen, because the only possibility is a maximal cofacet,
       * which would have been handled above */
      TEUCHOS_TEST_FOR_EXCEPT(true);
    }
    else
    {
      TEUCHOS_TEST_FOR_EXCEPT(true);
    }
  }
}

int BasicSimplicialMesh::mapGIDToLID(int cellDim, int globalIndex) const
{
  return GIDToLIDMap_[cellDim].get(globalIndex);
}

bool BasicSimplicialMesh::hasGID(int cellDim, int globalIndex) const
{
  return GIDToLIDMap_[cellDim].containsKey(globalIndex);
}

int BasicSimplicialMesh::mapLIDToGID(int cellDim, int localIndex) const
{
  return LIDToGIDMap_[cellDim][localIndex];
}

CellType BasicSimplicialMesh::cellType(int cellDim) const
{

  switch(cellDim)
  {
    case 0:
      return PointCell;
    case 1:
      return LineCell;
    case 2:
      return TriangleCell;
    case 3:
      return TetCell;
    default:
      return NullCell; // -Wall
  }
}

int BasicSimplicialMesh::label(int cellDim, 
  int cellLID) const
{
  return labels_[cellDim][cellLID];
}

void BasicSimplicialMesh::getLabels(int cellDim, const Array<int>& cellLID, 
  Array<int>& labels) const
{
  labels.resize(cellLID.size());
  const Array<int>& ld = labels_[cellDim];
  for (int i=0; i<cellLID.size(); i++)
  {
    labels[i] = ld[cellLID[i]];
  }
}


Set<int> BasicSimplicialMesh::getAllLabelsForDimension(int cellDim) const
{
  Set<int> rtn;

  const Array<int>& ld = labels_[cellDim];
  for (int i=0; i<ld.size(); i++)
  {
    rtn.put(ld[i]);
  }
  
  return rtn;
}

void BasicSimplicialMesh::getLIDsForLabel(int cellDim, int label, Array<int>& cellLIDs) const
{
  cellLIDs.resize(0);
  const Array<int>& ld = labels_[cellDim];
  for (int i=0; i<ld.size(); i++)
  {
    if (ld[i] == label) cellLIDs.append(i);
  }
}




int BasicSimplicialMesh::addVertex(int globalIndex, const Point& x,
  int ownerProcID, int label)
{
#ifdef BSM_LOW_LEVEL_TIMER
  TimeMonitor timer(getAddVertexTimer());
#endif
  int lid = points_.length();
  points_.append(x);

  SUNDANCE_OUT(this->verb() > 1,
    "BSM added point " << x << " lid = " << lid);

  numCells_[0]++;

  LIDToGIDMap_[0].append(globalIndex);
  GIDToLIDMap_[0].put(globalIndex, lid);

  if (comm().getRank() != ownerProcID) neighbors_.put(ownerProcID);
  ownerProcID_[0].append(ownerProcID);
  labels_[0].append(label);

  vertCofacets_.resize(points_.length());
  vertEdges_.resize(points_.length());
  if (spatialDim() > 2) vertFaces_.resize(points_.length());
  vertEdgePartners_.resize(points_.length());
  
  return lid;
}

int BasicSimplicialMesh::addElement(int globalIndex, 
  const Array<int>& vertGID,
  int ownerProcID, int label)
{
#ifdef BSM_LOW_LEVEL_TIMER
  TimeMonitor timer(getAddElementTimer());
#endif
  SUNDANCE_VERB_HIGH("p=" << comm().getRank() << "adding element " << globalIndex 
    << " with vertices:" << vertGID);

  static Array<int> sortedVertGID;
  sort(vertGID, sortedVertGID);

  /* 
   * do basic administrative steps for the new element: 
   * set LID, label, and procID; update element count. 
   */
  int lid = elemVerts_.length();
  elemEdgeSigns_.resize(lid+1);

  numCells_[spatialDim()]++;

  LIDToGIDMap_[spatialDim()].append(globalIndex);
  GIDToLIDMap_[spatialDim()].put(globalIndex, lid);
  labels_[spatialDim()].append(label);
  ownerProcID_[spatialDim()].append(ownerProcID);
  if (comm().getRank() != ownerProcID) neighbors_.put(ownerProcID);

  /* these little arrays will get used repeatedly, so make them static
   * to save a few cycles. */
  static Array<int> edges;
  static Array<int> faces;
  static Array<int> faceRotations;
  static Array<int> vertLID;

  /* find the vertex LIDs given the input GIDs */
  {
#ifdef BSM_LOW_LEVEL_TIMER
    TimeMonitor timer(getLookupLIDTimer());
#endif
    vertLID.resize(vertGID.size());
    for (int i=0; i<vertGID.size(); i++) 
    {
      vertLID[i] = GIDToLIDMap_[0].get(sortedVertGID[i]);
    }
  }
  
  /* 
   * Now comes the fun part: creating edges and faces for the 
   * new element, and registering it as a cofacet of its
   * lower-dimensional facets. 
   */
  

  if (spatialDim()==1)  
  {
    /* In 1D, there are neither edges nor faces. */
    edges.resize(0);
    faces.resize(0);
    /* register the new element as a cofacet of its vertices. */
    vertCofacets_[vertLID[0]].append(lid);
    vertCofacets_[vertLID[1]].append(lid);
  }
  if (spatialDim()==2)
  {
    /* In 2D, we need to define edges but not faces for the new element. */
    edges.resize(3);
    faces.resize(0);

    /* add the edges and define the relative orientations of the edges */
    edges[0] = addEdge(vertLID[1], vertLID[2], lid, globalIndex, 0);
    edges[1] = addEdge(vertLID[0], vertLID[2], lid, globalIndex, 1);
    edges[2] = addEdge(vertLID[0], vertLID[1], lid, globalIndex, 2);

    /* register the new element as a cofacet of its vertices. */
    vertCofacets_[vertLID[0]].append(lid);
    vertCofacets_[vertLID[1]].append(lid);
    vertCofacets_[vertLID[2]].append(lid);

  }
  else if (spatialDim()==3)
  {
    /* In 3D, we need to define edges and faces for the new element. */
    edges.resize(6);
    faces.resize(4);

    /* add the edges and define the relative orientations of the edges */
    edges[0] = addEdge(vertLID[2], vertLID[3], lid, globalIndex,  0);
    edges[1] = addEdge(vertLID[1], vertLID[3], lid, globalIndex,  1);
    edges[2] = addEdge(vertLID[1], vertLID[2], lid, globalIndex,  2);
    edges[3] = addEdge(vertLID[0], vertLID[3], lid, globalIndex,  3);
    edges[4] = addEdge(vertLID[0], vertLID[2], lid, globalIndex,  4);
    edges[5] = addEdge(vertLID[0], vertLID[1], lid, globalIndex,  5);

    /* register the new element as a cofacet of its vertices. */
    vertCofacets_[vertLID[0]].append(lid);
    vertCofacets_[vertLID[1]].append(lid);
    vertCofacets_[vertLID[2]].append(lid);
    vertCofacets_[vertLID[3]].append(lid);

    /* add the faces */
    static Array<int> tmpVertLID(3);
    static Array<int> tmpSortedVertGID(3);
    static Array<int> tmpEdges(4);
#define BSM_OPT_CODE
#ifndef BSM_OPT_CODE
    faces[0] = addFace(tuple(vertLID[1], vertLID[2], vertLID[3]), 
      tuple(sortedVertGID[1], sortedVertGID[2], sortedVertGID[3]), 
      tuple(edges[2], edges[0], edges[1]), lid, globalIndex);

    faces[1] = addFace(tuple(vertLID[0], vertLID[2], vertLID[3]), 
      tuple(sortedVertGID[0], sortedVertGID[2], sortedVertGID[3]), 
      tuple(edges[3], edges[4], edges[0]), lid, globalIndex);

    faces[2] = addFace(tuple(vertLID[0], vertLID[1], vertLID[3]), 
      tuple(sortedVertGID[0], sortedVertGID[1], sortedVertGID[3]), 
      tuple(edges[5], edges[1], edges[3]), lid, globalIndex);

    faces[3] = addFace(tuple(vertLID[0], vertLID[1], vertLID[2]), 
      tuple(sortedVertGID[0], sortedVertGID[1], sortedVertGID[2]), 
      tuple(edges[5], edges[2], edges[4]), lid, globalIndex);
#else
    tmpVertLID[0] = vertLID[1];
    tmpVertLID[1] = vertLID[2];
    tmpVertLID[2] = vertLID[3];
    tmpSortedVertGID[0] = sortedVertGID[1];
    tmpSortedVertGID[1] = sortedVertGID[2];
    tmpSortedVertGID[2] = sortedVertGID[3];
    tmpEdges[0] = edges[2];
    tmpEdges[1] = edges[0];
    tmpEdges[2] = edges[1];
    faces[0] = addFace(tmpVertLID, tmpSortedVertGID, 
                       tmpEdges, lid, globalIndex);

    tmpVertLID[0] = vertLID[0];
    tmpVertLID[1] = vertLID[2];
    tmpVertLID[2] = vertLID[3];
    tmpSortedVertGID[0] = sortedVertGID[0];
    tmpSortedVertGID[1] = sortedVertGID[2];
    tmpSortedVertGID[2] = sortedVertGID[3];
    tmpEdges[0] = edges[3];
    tmpEdges[1] = edges[4];
    tmpEdges[2] = edges[0];
    faces[1] = addFace(tmpVertLID, tmpSortedVertGID, 
                       tmpEdges, lid, globalIndex);

    tmpVertLID[0] = vertLID[0];
    tmpVertLID[1] = vertLID[1];
    tmpVertLID[2] = vertLID[3];
    tmpSortedVertGID[0] = sortedVertGID[0];
    tmpSortedVertGID[1] = sortedVertGID[1];
    tmpSortedVertGID[2] = sortedVertGID[3];
    tmpEdges[0] = edges[5];
    tmpEdges[1] = edges[1];
    tmpEdges[2] = edges[3];
    faces[2] = addFace(tmpVertLID, tmpSortedVertGID, 
                       tmpEdges, lid, globalIndex);

    tmpVertLID[0] = vertLID[0];
    tmpVertLID[1] = vertLID[1];
    tmpVertLID[2] = vertLID[2];
    tmpSortedVertGID[0] = sortedVertGID[0];
    tmpSortedVertGID[1] = sortedVertGID[1];
    tmpSortedVertGID[2] = sortedVertGID[2];
    tmpEdges[0] = edges[5];
    tmpEdges[1] = edges[2];
    tmpEdges[2] = edges[4];
    faces[3] = addFace(tmpVertLID, tmpSortedVertGID, 
                       tmpEdges, lid, globalIndex);

    
#endif
  }

  {
#ifdef BSM_LOW_LEVEL_TIMER
    TimeMonitor timer(getFacetRegistrationTimer());
#endif
    elemVerts_.append(vertLID);
    if (edges.length() > 0) elemEdges_.append(edges);
    
    if (faces.length() > 0) 
    {
      elemFaces_.append(faces);
      elemFaceRotations_.append(faceRotations);
    }
    
  }

  for (int i=0; i<edges.length(); i++) edgeCofacets_[edges[i]].append(lid);


  for (int i=0; i<faces.length(); i++) faceCofacets_[faces[i]].append(lid);

  return lid;
}

int BasicSimplicialMesh::addFace(
  const Array<int>& vertLID,
  const Array<int>& vertGID,
  const Array<int>& edgeLID,
  int elemLID,
  int elemGID)
{
#ifdef BSM_LOW_LEVEL_TIMER
  TimeMonitor timer(getAddFaceTimer());
#endif

  /* First we check whether the face already exists */
  int lid = lookupFace(vertGID);

  if (lid >= 0) /* if the face already exists, we're done */
  {
    return lid;
  }
  else /* we need to register the face */
  {
    /* get a LID for the new face */
    lid = faceVertLIDs_.length();
      
    /* record the new face's vertex sets (both GID and LID, ordered by GID)
     * and its edges (reordered to the the sorted-GID orientation) */
    faceVertGIDs_.append(&(vertGID[0]), 3);
    faceVertLIDs_.append(&(vertLID[0]), 3);
    faceEdges_.append(&(edgeLID[0]), 3);

    SUNDANCE_VERB_EXTREME("p=" << comm().getRank() << " adding face "
      << vertGID);


    /* If we own all vertices, we own the face. 
     * Otherwise, mark it for later assignment of ownership */
    int vert1Owner = ownerProcID_[0][vertLID[0]];
    int vert2Owner = ownerProcID_[0][vertLID[1]];
    int vert3Owner = ownerProcID_[0][vertLID[2]];
    int myRank = comm().getRank();
    if (vert1Owner==myRank && vert2Owner==myRank && vert3Owner==myRank) 
    {
      ownerProcID_[2].append(myRank);
    }
    else ownerProcID_[2].append(-1);

    /* the face doesn't yet have a label, so set it to zero */
    labels_[2].append(0);
      
    /* update the view pointer to stay in synch with the resized
     * face vertex GID array */
    faceVertGIDBase_[0] = &(faceVertGIDs_.value(0,0));
      
    /* create a vertex set view that points to the new face's 
     * vertex GIDs. The first argument gives a pointer to the base of the
     * vertex GID array. The view is offset from the base by the face's
     * LID, and is of length 3. */
    VertexView face(&(faceVertGIDBase_[0]), lid, 3);
      
    /* record this vertex set in the hashtable of 
     * existing face vertex sets */
    vertexSetToFaceIndexMap_.put(face, lid);
      
    /* create space for the new face's cofacets */
    faceCofacets_.resize(lid+1);
      
    /* update the cell count */
    numCells_[spatialDim()-1]++;

    /* Register the face as a cofacet of its edges */
    edgeFaces_[edgeLID[0]].append(lid);
    edgeFaces_[edgeLID[1]].append(lid);
    edgeFaces_[edgeLID[2]].append(lid);

    /* Register the face as a cofacet of its vertices */
    vertFaces_[vertLID[0]].append(lid);
    vertFaces_[vertLID[1]].append(lid);
    vertFaces_[vertLID[2]].append(lid);

    /* return the LID of the new face */
    return lid;
  }

}


int BasicSimplicialMesh::checkForExistingEdge(int vertLID1, int vertLID2)
{
  const Array<int>& edgePartners = vertEdgePartners_[vertLID1];
  for (int i=0; i<edgePartners.length(); i++)
  {
    if (edgePartners[i] == vertLID2)
    {
      return vertEdges_[vertLID1][i];
    }
  }
  return -1;
}

int BasicSimplicialMesh::lookupFace(const Array<int>& vertGID) 
{
  /* see if the face is already in existence by checking for the
   * presence of the same ordered set of vertices. */
  int* base = const_cast<int*>(&(vertGID[0]));
  int** basePtr = &base;
  VertexView inputFaceView(basePtr, 0, 3);

  if (vertexSetToFaceIndexMap_.containsKey(inputFaceView)) 
  {
    /* return the existing face's LID */
    return vertexSetToFaceIndexMap_.get(inputFaceView);
  }
  else 
  {
    /* return -1 as an indication that the face does not yet exist */
    return -1;
  }
}
                                        
int BasicSimplicialMesh::addEdge(int v1, int v2, 
  int elemLID, int elemGID,
  int myFacetNumber)
{
#ifdef BSM_LOW_LEVEL_TIMER
  TimeMonitor timer(getAddEdgeTimer());
#endif
  /* 
   * First we ask if this edge already exists in the mesh. If so,
   * we're done. 
   */
  int lid = checkForExistingEdge(v1, v2);

  if (lid >= 0) 
  {
    /* determine the sign of the existing edge */
    int g1 = LIDToGIDMap_[0][v1];
    int g2 = LIDToGIDMap_[0][v2];
    TEUCHOS_TEST_FOR_EXCEPT(g2 <= g1);

    /* return the LID of the pre-existing edge */
    return lid;
  }
  else
  {
    /* get the LID of the new edge */
    lid = edgeVerts_.length();

    edgeVerts_.append(tuple(v1,v2));

    /* if we own all vertices, we own the edge. Otherwise, mark it
     * for later assignment. */
    int vert1Owner = ownerProcID_[0][v1];
    int vert2Owner = ownerProcID_[0][v2];
    if (vert2Owner==comm().getRank() && vert1Owner==comm().getRank()) 
      ownerProcID_[1].append(vert1Owner);
    else ownerProcID_[1].append(-1);

    /* register the new edge with its vertices */
    vertEdges_[v1].append(lid);
    vertEdgePartners_[v1].append(v2);
    vertEdges_[v2].append(lid);
    vertEdgePartners_[v2].append(v1);
    /* create storage for the cofacets of the new edge */
    edgeCofacets_.resize(lid+1);
    if (spatialDim() > 2) edgeFaces_.resize(lid+1);
      
      
    /* the new edge is so far unlabeled, so set its label to zero */
    labels_[1].append(0);
      
    /* update the edge count */
    numCells_[1]++;
  }
  /* return the LID of the edge */
  return lid;
}


void BasicSimplicialMesh::synchronizeGIDNumbering(int dim, int localCount) 
{
  
  SUNDANCE_OUT(this->verb() > 2, 
    "sharing offsets for GID numbering for dim=" << dim);
  SUNDANCE_OUT(this->verb() > 2, 
    "I have " << localCount << " cells");
  Array<int> gidOffsets;
  int total;
  MPIContainerComm<int>::accumulate(localCount, gidOffsets, total, comm());
  int myOffset = gidOffsets[comm().getRank()];

  SUNDANCE_OUT(this->verb() > 2, 
    "back from MPI accumulate: offset for d=" << dim
    << " on p=" << comm().getRank() << " is " << myOffset);

  for (int i=0; i<numCells(dim); i++)
  {
    if (LIDToGIDMap_[dim][i] == -1) continue;
    LIDToGIDMap_[dim][i] += myOffset;
    GIDToLIDMap_[dim].put(LIDToGIDMap_[dim][i], i);
  }
  SUNDANCE_OUT(this->verb() > 2, 
    "done sharing offsets for GID numbering for dim=" << dim);
}


void BasicSimplicialMesh::assignIntermediateCellGIDs(int cellDim)
{
  int myRank = comm().getRank();
//  if (comm().getNProc() == 1) return;
  SUNDANCE_VERB_MEDIUM("p=" << myRank << " assigning " << cellDim 
    << "-cell owners");

  /* If we are debugging parallel code, we may want to stagger the output
   * from the different processors. This is done by looping over processors,
   * letting one do its work while the others are idle; a synchronization
   * point after each iteration forces this procedure to occur such
   * that the processors' output is staggered. 
   *
   * If we don't want staggering (as will usually be the case in production
   * runs) numWaits should be set to 1. 
   */  
  int numWaits = 1;
  if (staggerOutput())
  {
    SUNDANCE_VERB_LOW("p=" << myRank << " doing staggered output in "
      "assignIntermediateCellOwners()");
    numWaits = comm().getNProc();
  }
  

  /* list of vertex GIDs which serve to identify the cells whose
   * GIDs are needed */
  Array<Array<int> > outgoingRequests(comm().getNProc());
  Array<Array<int> > incomingRequests(comm().getNProc());

  /* lists of cells for which GIDs are needed from each processor */
  Array<Array<int> > outgoingRequestLIDs(comm().getNProc());

  /* lists of GIDs to be communicated. */
  Array<Array<int> > outgoingGIDs(comm().getNProc());
  Array<Array<int> > incomingGIDs(comm().getNProc());

  /* Define these so we're not constantly dereferencing the owners arrays */
  Array<int>& cellOwners = ownerProcID_[cellDim];

  /* run through the cells, assigning GID numbers to the locally owned ones
   * and compiling a list of the remotely owned ones. */
  int localCount = 0;
  ArrayOfTuples<int>* cellVerts;
  if (cellDim==2) cellVerts = &(faceVertLIDs_);
  else cellVerts = &(edgeVerts_);

  LIDToGIDMap_[cellDim].resize(numCells(cellDim));
  
  SUNDANCE_OUT(this->verb() > 2,  
    "starting loop over cells");


  /*
   * We assign edge owners as follows: 
   *
   * (1) Any edge whose vertices are owned by the same proc is owned
   * by that proc.  This can be done at the time of construction of
   * the edge.
   *
   * (2) For edges not resolved by step 1, we send a specification of
   * that edge to all processors neighboring this one. Each processor
   * then returns either its processor rank or -1 for each edge
   * specification it receives, according to whether or not both
   * vertex GIDs exist on that processor.
   *
   * (3) The ranks of all processors seeing each disputed edge having
   * been collected in step 2, the edge is assigned to the processor
   * with the largest rank.
   */
  
  try
  {
    resolveEdgeOwnership(cellDim);
  }
  catch(std::exception& e0)
  {
    SUNDANCE_TRACE_MSG(e0, "while resolving edge ownership");
  }

  
  for (int q=0; q<numWaits; q++)
  {
    if (numWaits > 1 && q != myRank) 
    {
      TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
        "off-proc error detected on proc=" << myRank
        << " while computing GID resolution requests");
      continue;
    }
    try
    {
      for (int i=0; i<numCells(cellDim); i++)
      {  
        SUNDANCE_OUT(this->verb() > 3, 
          "p=" << myRank 
          <<" cell " << i);
              
        /* If the cell is locally owned, give it a temporary
         * GID. This GID is temporary because it's one of a
         * sequence numbered from zero rather than the lowest
         * GID on this processor. We'll offset all of these GIDs
         * once we know how many cells this processor owns. */
        int owner = cellOwners[i];
        if (owner==myRank)
        {
          SUNDANCE_VERB_EXTREME("p=" << myRank 
            << " assigning GID=" << localCount
            << " to cell " 
            << cellToStr(cellDim, i));
          LIDToGIDMap_[cellDim][i] = localCount++;
        }
        else /* If the cell is remotely owned, we can't give it
              * a GID now. Give it a GID of -1 to mark it as
              * unresolved, and then add it to a list of cells for
              * which we'll need remote GIDs. To get a GID, we have
              * to look up this cell on another processor.  We can't
              * use the LID to identify the cell, since other procs
              * won't know our LID numbering. Thus we send the GIDs
              * of the cell's vertices, which are sufficient to
              * identify the cell on the other processor. */
        {
          LIDToGIDMap_[cellDim][i] = -1;
          SUNDANCE_OUT(this->verb() > 3, 
            "p=" << myRank << " adding cell LID=" << i 
            << " to req list");
          outgoingRequestLIDs[owner].append(i);
          for (int v=0; v<=cellDim; v++)
          {
            int ptLID = cellVerts->value(i, v);
            int ptGID = LIDToGIDMap_[0][ptLID];
            SUNDANCE_OUT(this->verb() > 3, 
              "p=" << myRank << " adding pt LID=" << ptLID
              << " GID=" << ptGID
              << " to req list");
            outgoingRequests[owner].append(ptGID);
          }
          SUNDANCE_VERB_EXTREME("p=" << myRank 
            << " deferring GID assignment for cell "
            << cellToStr(cellDim, i));
        }
      }
    }
    catch(std::exception& e0)
    {
      reportFailure(comm());
      SUNDANCE_TRACE_MSG(e0, "while computing GID resolution requests");
    }
    TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
      "off-proc error detected on proc=" << myRank
      << " while computing GID resolution requests");
  }

  /* Now that we know how many cells are locally owned, we can 
   * set up a global GID numbering */
  try
  {
    synchronizeGIDNumbering(cellDim, localCount);
  }
  catch(std::exception& e0)
  {
    reportFailure(comm());
    SUNDANCE_TRACE_MSG(e0, "while computing GID offsets");
  }
  TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
    "off-proc error detected on proc=" << myRank
    << " while computing GID offsets");
  
  /* We now share requests for cells for which remote GIDs are needed */
  for (int q=0; q<numWaits; q++)
  {
    if (numWaits > 1) comm().synchronize();
    if (numWaits > 1 && q!=myRank) continue;
    SUNDANCE_OUT(this->verb() > 3,
      "p=" << myRank << "sending requests: " 
      << outgoingRequests);
  }

  try
  {
    MPIContainerComm<int>::allToAll(outgoingRequests,
      incomingRequests,
      comm()); 
  }
  catch(std::exception& e0)
  {
    reportFailure(comm());
    SUNDANCE_TRACE_MSG(e0, "while distributing GID resolution requests");
  }
  TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
    "off-proc error detected on proc=" << myRank
    << " while distributing GID resolution requests");


  for (int q=0; q<numWaits; q++)
  {
    if (numWaits > 1) comm().synchronize();
    if (numWaits > 1 && q!=myRank) continue;
    SUNDANCE_OUT(this->verb() > 3,
      "p=" << myRank << "recv'd requests: " << incomingRequests);
  }


  for (int q=0; q<numWaits; q++)
  {
    if (numWaits>1 && q != myRank) 
    {
      TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
        "off-proc error detected on proc=" << myRank
        << " while computing edge/face GID responses");
      continue;
    }
    try
    {
      /* Answer the requests incoming to this processor */
      for (int p=0; p<comm().getNProc(); p++)
      {
        const Array<int>& requestsFromProc = incomingRequests[p];
              
        for (int c=0; c<requestsFromProc.size(); c+=(cellDim+1))
        {
          SUNDANCE_OUT(this->verb() > 3,
            "p=" << myRank << "processing request c=" 
            << c/(cellDim+1));
          /* The request for each cell is a tuple of vertex GIDs. 
           * Find the LID of the local cell that contains them */
          int cellLID;
          if (cellDim==1) 
          {
            int vertLID1 = mapGIDToLID(0, requestsFromProc[c]);
            int vertLID2 = mapGIDToLID(0, requestsFromProc[c+1]);
            SUNDANCE_VERB_HIGH("p=" << myRank 
              << " edge vertex GIDs are "
              <<  requestsFromProc[c+1]
              << ", " << requestsFromProc[c]);
            cellLID = checkForExistingEdge(vertLID1, vertLID2);
          }
          else
          {
                      
            SUNDANCE_VERB_HIGH("p=" << myRank 
              << " face vertex GIDs are "
              <<  requestsFromProc[c]
              << ", " << requestsFromProc[c+1]
              << ", " << requestsFromProc[c+2]);
            cellLID = lookupFace(tuple(requestsFromProc[c],
                requestsFromProc[c+1],
                requestsFromProc[c+2]));
          }
          SUNDANCE_VERB_HIGH("p=" << myRank << "cell LID is " 
            << cellLID);
                  
          TEUCHOS_TEST_FOR_EXCEPTION(cellLID < 0, std::runtime_error,
            "unable to find requested cell "
            << cellStr(cellDim+1, &(requestsFromProc[c])));
                  
          /* Finally, we get the cell's GID and append to the list 
           * of GIDs to send back as answers. */
          int cellGID = mapLIDToGID(cellDim, cellLID);
          TEUCHOS_TEST_FOR_EXCEPTION(cellGID < 0, std::runtime_error,
            "proc " << myRank 
            << " was asked by proc " << p
            << " to provide a GID for cell "
            << cellStr(cellDim+1, &(requestsFromProc[c]))
            << " with LID=" << cellLID
            << " but its GID is undefined");
                  
          outgoingGIDs[p].append(mapLIDToGID(cellDim, cellLID));
        }
      }
    }
    catch(std::exception& e0)
    {
      reportFailure(comm());
      SUNDANCE_TRACE_MSG(e0, "while computing edge/face GID responses");
    }
    TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
      "off-proc error detected "
      "on proc=" << myRank
      << " while computing edge/face GID responses");
  }


  /* We now share the GIDs for the requested cells */
  for (int q=0; q<numWaits; q++)
  {
    if (numWaits>1) comm().synchronize();
    if (numWaits>1 && q!=myRank) continue;
    SUNDANCE_OUT(this->verb() > 3,
      "p=" << myRank << "sending GIDs: " << outgoingGIDs);
  }

  
  try
  {
    MPIContainerComm<int>::allToAll(outgoingGIDs,
      incomingGIDs,
      comm());
  }
  catch(std::exception& e0)
  {
    reportFailure(comm());
    SUNDANCE_TRACE_MSG(e0, "while distributing edge/face GIDs");
  }
  TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
    "off-proc error detected on proc=" << myRank
    << " while distributing edge/face GIDs");
  



  for (int q=0; q<numWaits; q++)
  {
    if (numWaits > 1 && q != myRank) 
    {
      TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
        "off-proc error detected on proc=" << myRank
        << " while setting remote edge/face GIDs");
      continue;
    }
    try
    {
      SUNDANCE_OUT(this->verb() > 3,
        "p=" << myRank << "recv'ing GIDs: " << incomingGIDs);
          
      /* Now assign the cell GIDs we've recv'd from from the other procs */
      for (int p=0; p<comm().getNProc(); p++)
      {
        const Array<int>& gidsFromProc = incomingGIDs[p];
        for (int c=0; c<gidsFromProc.size(); c++)
        {
          int cellLID = outgoingRequestLIDs[p][c];
          int cellGID = incomingGIDs[p][c];
          SUNDANCE_OUT(this->verb() > 3,
            "p=" << myRank << 
            " assigning GID=" << cellGID << " to LID=" 
            << cellLID);
          LIDToGIDMap_[cellDim][cellLID] = cellGID;
          GIDToLIDMap_[cellDim].put(cellGID, cellLID);
        }
      }
          

      SUNDANCE_OUT(this->verb() > 2,  
        "p=" << myRank 
        << "done synchronizing cells of dimension " 
        << cellDim);
    }
    catch(std::exception& e0)
    {
      reportFailure(comm());
      SUNDANCE_TRACE_MSG(e0, " while setting remote edge/face GIDs");
    }
    TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
      "off-proc error detected on proc=" << myRank
      << " while setting remote edge/face GIDs");
  }
  if (cellDim==1) hasEdgeGIDs_ = true;
  else hasFaceGIDs_ = true;
}







void BasicSimplicialMesh::synchronizeNeighborLists()
{
  if (neighborsAreSynchronized_) return ;

  Array<Array<int> > outgoingNeighborFlags(comm().getNProc());
  Array<Array<int> > incomingNeighborFlags(comm().getNProc());

  int myRank = comm().getRank();

  for (int p=0; p<comm().getNProc(); p++)
  {
    if (neighbors_.contains(p)) outgoingNeighborFlags[p].append(myRank);
  }

  try
  {
    MPIContainerComm<int>::allToAll(outgoingNeighborFlags,
      incomingNeighborFlags,
      comm()); 
  }
  catch(std::exception& e0)
  {
    reportFailure(comm());
    SUNDANCE_TRACE_MSG(e0, "while distributing neighbor information");
  }
  TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
    "off-proc error detected on proc=" << myRank
    << " while distributing neighbor information");

  

  for (int p=0; p<comm().getNProc(); p++)
  {
    if (incomingNeighborFlags[p].size() > 0) neighbors_.put(p);
  }

  neighborsAreSynchronized_ = true;
}




void BasicSimplicialMesh::resolveEdgeOwnership(int cellDim) 
{
  int myRank = comm().getRank();
  SUNDANCE_VERB_LOW("p=" << myRank << " finding " 
    << cellDim << "-cell owners");


  /* If we are debugging parallel code, we may want to stagger the output
   * from the different processors. This is done by looping over processors,
   * letting one do its work while the others are idle; a synchronization
   * point after each iteration forces this procedure to occur such
   * that the processors' output is staggered. 
   *
   * If we don't want staggering (as will usually be the case in production
   * runs) numWaits should be set to 1. 
   */  
  int numWaits = 1;
  if (staggerOutput())
  {
    SUNDANCE_VERB_LOW("p=" << myRank << " doing staggered output in "
      "assignIntermediateCellOwners()");
    numWaits = comm().getNProc();
  }

  synchronizeNeighborLists();

  /* Define some helper variables to save us from lots of dereferencing */
  Array<int>& cellOwners = ownerProcID_[cellDim];
  ArrayOfTuples<int>* cellVerts;
  if (cellDim==2) cellVerts = &(faceVertLIDs_);
  else cellVerts = &(edgeVerts_);

  /* Dump neighbor set into an array to simplify looping */
  Array<int> neighbors = neighbors_.elements();
  SUNDANCE_VERB_LOW("p=" << myRank << " neighbors are " << neighbors);
  


  /*
   * In 3D it is not possible to assign all edge owners without communication. 
   * We assign edge owners as follows:
   * (1) Any edge whose vertices are owned by the same proc is owned by 
   *     that proc. This can be done at the time of construction of the edge. 
   * (2) For edges not resolved by step 1, we send a specification of that edge
   *     to all processors neighboring this one. Each processor then returns 
   *     either its processor rank or -1 for each edge specification it 
   *     receives, according to whether or not both vertex GIDs exist 
   *     on that processor. 
   * (3) The ranks of all processors seeing each disputed edge having been 
   *     collected in step 2, the edge is assigned to the processor 
   *     with the largest rank.
   */


      
  /* the index to LID map will let us remember the LIDs of edges
   * we've sent off for owner information */
  Array<int> reqIndexToEdgeLIDMap;

  /* compile lists of specifiers to be communicated to neighbors */
  Array<Array<int> > outgoingEdgeSpecifiers(comm().getNProc());
  Array<int> vertLID(cellDim+1);
  Array<int> vertGID(cellDim+1);

  for (int q=0; q<numWaits; q++)
  {
    if (numWaits > 1 && q != myRank) 
    {
      TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
        "off-proc error detected on proc=" << myRank
        << " while determining edges to be resolved");
      continue;
    }
    try
    {
      for (int i=0; i<numCells(cellDim); i++)
      {  
        int owner = cellOwners[i];
        /* if we don't know the owner of the edge, send
         * information about the edge to all neighbors so we can
         * come to a consensus on the ownership of the edge
         */
        if (owner==-1)
        {
          /* The specification of the edge is the set of 
           * vertices defining the edge. */
          for (int v=0; v<=cellDim; v++) 
          {
            vertLID[v] = cellVerts->value(i, v);
            vertGID[v] = LIDToGIDMap_[0][vertLID[v]];
          }
          /* make a request to all neighbors */
          for (int n=0; n<neighbors.size(); n++)
          {
            for (int v=0; v<=cellDim; v++)
            {
              outgoingEdgeSpecifiers[neighbors[n]].append(vertGID[v]);
            }
          }
          SUNDANCE_VERB_HIGH("p=" << myRank 
            << " is asking all neighbors to resolve edge "
            << cellToStr(cellDim, i));

          /* Remember the LIDs of the edges about whom we're requesting
           * information. */
          reqIndexToEdgeLIDMap.append(i);
        }
      }

      SUNDANCE_VERB_MEDIUM("p=" << myRank 
        << " initially unresolved edge LIDs are "
        << reqIndexToEdgeLIDMap);

      SUNDANCE_VERB_HIGH("p=" << myRank 
        << " sending outgoing edge specs:") ;
      for (int p=0; p<comm().getNProc(); p++)
      {
        SUNDANCE_VERB_HIGH(outgoingEdgeSpecifiers[p].size()/(cellDim+1) 
          << " edge reqs to proc "<< p) ;
      }
      SUNDANCE_VERB_HIGH("p=" << myRank << " outgoing edge specs are " 
        << outgoingEdgeSpecifiers);
    }
    catch(std::exception& e0)
    {
      reportFailure(comm());
      SUNDANCE_TRACE_MSG(e0, "while determining edges to be resolved");
    }
    TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
      "off-proc error detected on proc=" << myRank
      << " while determining edges to be resolved");
  }
  


  /* share the unresolved edges with my neighbors */
  Array<Array<int> > incomingEdgeSpecifiers(comm().getNProc());


  try
  {
    MPIContainerComm<int>::allToAll(outgoingEdgeSpecifiers,
      incomingEdgeSpecifiers,
      comm()); 
  }
  catch(std::exception& e0)
  {
    reportFailure(comm());
    SUNDANCE_TRACE_MSG(e0, "while distributing edge resolution reqs");
  }
  TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
    "off-proc error detected on proc=" << myRank
    << " while distributing edge resolution reqs");
    

  Array<Array<int> > outgoingEdgeContainers(comm().getNProc());    
  for (int q=0; q<numWaits; q++)
  {

    if (numWaits > 1 && q != myRank) 
    {
      TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
        "off-proc error detected on proc=" << myRank
        << " while resolving edge ownership results");
      continue;
    }
      
    try
    {
      SUNDANCE_VERB_HIGH("p=" << myRank << " incoming edge specs are " 
        << incomingEdgeSpecifiers);
      /* Now, put on my receiver hat. I have received from each
       * other processor  an array of vertex GID pairs, each of
       * which may or may not exist on this processor. I need to
       * send back to my neighbors an indicator of whether or not I
       * know about both vertices defining each edge.
       */
      for (int p=0; p<comm().getNProc(); p++)
      {
        const Array<int>& edgesFromProc = incomingEdgeSpecifiers[p];
              
        int numVerts = cellDim+1;
        for (int c=0; c<edgesFromProc.size(); c+=numVerts)
        {
          SUNDANCE_VERB_LOW("p=" << myRank << " doing c=" << c/numVerts
            << " of " << edgesFromProc.size()/numVerts
            << " reqs from proc=" << p);
          /* The request for each cell is a tuple of vertex
           * GIDs. Find out whether this processor knows about
           * all of them. If this processor contains knows
           * both vertices of the edge and the vertex pair
           * forms an edge, add my rank to the pool of
           * potential edge owners to be returned. Otherwise,
           * mark with -1. */

          int cellLID;
          SUNDANCE_VERB_LOW("p=" << myRank << " looking at "
            << cellStr(numVerts, &(edgesFromProc[c])));
          /* The response will be:
           * (*) -1 if the proc doesn't know the edge
           * (*) 0  if the proc knows the edge, but doesn't know who owns it
           * (*) 1  if the proc owns it
           */
          int response = 0;
          /* See if all verts are present on this proc. Respond with -1 of not. */
          for (int v=0; v<numVerts; v++)
          {
            vertGID[v] = edgesFromProc[c+v];
            if (!GIDToLIDMap_[0].containsKey(vertGID[v])) 
            {
              response = -1;
              break;
            }
            else
            {
              vertLID[v] = GIDToLIDMap_[0].get(vertGID[v]);
            }
          }
          if (response != -1)
          {
            /* Make sure the vertices are actually organized into an edge
             * on this processor */
            if (cellDim==1)
            {
              cellLID = checkForExistingEdge(vertLID[0], vertLID[1]);
            }
            else
            {
              cellLID = lookupFace(tuple(vertGID[0], vertGID[1], vertGID[2]));
            }
            /* Respond with -1 if the edge/face doesn't exist on this proc */
            if (cellLID==-1)
            {
              response = -1;
            }
          }

          if (response == -1)
          {
            SUNDANCE_VERB_HIGH("p=" << myRank << " is unaware of cell "
              << cellStr(numVerts, &(vertGID[0])));
          } 
          else
          {
            SUNDANCE_VERB_HIGH("p=" << myRank << " knows about cell "
              << cellStr(numVerts, &(vertGID[0])));
            if (ownerProcID_[cellDim][cellLID] != -1) response = 1;
          }
          /* add the response to the data stream to be returned */
          outgoingEdgeContainers[p].append(response);
          SUNDANCE_VERB_LOW("p=" << myRank << " did c=" << c/numVerts
            << " of " << edgesFromProc.size()/numVerts 
            << " reqs from proc=" << p);
        }
        SUNDANCE_VERB_LOW("p=" << myRank << " done all reqs from proc "
          << p);
          
      }
      SUNDANCE_VERB_LOW("p=" << myRank << " done processing edge reqs");
      SUNDANCE_VERB_HIGH("p=" << myRank 
        << " outgoing edge containers are " 
        << outgoingEdgeContainers);
    }
    catch(std::exception& e0)
    {
      reportFailure(comm());
      SUNDANCE_TRACE_MSG(e0, "while resolving edge ownership results");
    }
    TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
      "off-proc error detected on proc=" << myRank
      << " while resolving edge ownership results");
  }
  

  
  /* share the information about which edges I am aware of */
  
  Array<Array<int> > incomingEdgeContainers(comm().getNProc());
  try
  {
    MPIContainerComm<int>::allToAll(outgoingEdgeContainers,
      incomingEdgeContainers,
      comm()); 
  }
  catch(std::exception& e0)
  {
    reportFailure(comm());
    SUNDANCE_TRACE_MSG(e0, "while distributing edge resolution results");
  }
  TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
    "off-proc error detected on proc=" << myRank
    << " while distributing edge ownership results");

  



  /* Process the edge data incoming to this processor */
  for (int q=0; q<numWaits; q++)
  {
    if (numWaits > 1 && q != myRank)
    {
      TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
        "off-proc error detected on proc=" << myRank
        << " while finalizing edge ownership");
      continue;
    }

    try
    {
      SUNDANCE_VERB_HIGH("p=" << myRank 
        << " incoming edge containers are " 
        << incomingEdgeContainers);
      Set<int> resolved;
      for (int p=0; p<comm().getNProc(); p++)
      {
        const Array<int>& edgeContainers = incomingEdgeContainers[p];
              
        for (int c=0; c<edgeContainers.size(); c++)
        {
          int edgeLID = reqIndexToEdgeLIDMap[c];
          /* If the state of the edge is unknown, 
           * update the owner to the largest rank of all procs 
           * containing this edge */
          if (edgeContainers[c] == 0 && !resolved.contains(edgeLID)) 
          {
            /* because p is increasing in the loop, p is
             * equivalent to max(cellOwners[edgeLID], p) */
            cellOwners[edgeLID] = p;
          }
          /* If one of the processors reports it owns the edge, set
           * the owner and mark it as resolved so that it won't be modified 
           * further */
          else if (edgeContainers[c]==1)
          {
            cellOwners[edgeLID] = p;
            resolved.put(edgeLID);
          }
        }
      }
      /* Any remaining unresolved edges appear only on this processor, so 
       * I own them. */
      for (int c=0; c<reqIndexToEdgeLIDMap.size(); c++)
      {
        int edgeLID = reqIndexToEdgeLIDMap[c];
        if (cellOwners[edgeLID] < 0) cellOwners[edgeLID] = myRank;
        SUNDANCE_VERB_EXTREME("p=" << myRank 
          << " has decided cell "
          << cellToStr(cellDim, edgeLID) 
          << " is owned by proc=" 
          << cellOwners[edgeLID]);
      }
      SUNDANCE_VERB_LOW("p=" << myRank << " done finalizing ownership"); 
    }
    catch(std::exception& e0)
    {
      reportFailure(comm());
      SUNDANCE_TRACE_MSG(e0, "while finalizing edge ownership");
    }
    TEUCHOS_TEST_FOR_EXCEPTION(checkForFailures(comm()), std::runtime_error, 
      "off-proc error detected on proc=" << myRank
      << " while finalizing edge ownership");
  }
}

string BasicSimplicialMesh::cellStr(int dim, const int* verts) const
{
  std::string rtn="(";
  for (int i=0; i<dim; i++)
  {
    if (i!=0) rtn += ", ";
    rtn += Teuchos::toString(verts[i]);
  }
  rtn += ")";
  return rtn;
}

string BasicSimplicialMesh::cellToStr(int cellDim, int cellLID) const
{
  TeuchosOStringStream os;

  if (cellDim > 0)
  {
    const ArrayOfTuples<int>* cellVerts;
    if (cellDim==spatialDim()) 
    {
      cellVerts = &(elemVerts_);
    }
    else
    {
      if (cellDim==2) cellVerts = &(faceVertLIDs_);
      else cellVerts = &(edgeVerts_);
    }
    os << "(";
    for (int j=0; j<cellVerts->tupleSize(); j++)
    {
      if (j!=0) os << ", ";
      os << mapLIDToGID(0, cellVerts->value(cellLID,j));
    }
    os << ")" << std::endl;
  }
  else
  {
    os << LIDToGIDMap_[0][cellLID] << std::endl;
  }
  return os.str();
}

string BasicSimplicialMesh::printCells(int cellDim) const
{
  TeuchosOStringStream os;

  if (cellDim > 0)
  {
    const ArrayOfTuples<int>* cellVerts;
    if (cellDim==spatialDim()) 
    {
      cellVerts = &(elemVerts_);
    }
    else
    {
      if (cellDim==2) cellVerts = &(faceVertLIDs_);
      else cellVerts = &(edgeVerts_);
    }

    os << "printing cells for processor " << comm().getRank() << std::endl;
    for (int i=0; i<cellVerts->length(); i++)
    {
      os << i << " (";
      for (int j=0; j<cellVerts->tupleSize(); j++)
      {
        if (j!=0) os << ", ";
        os << mapLIDToGID(0, cellVerts->value(i,j));
      }
      os << ")" << std::endl;
    }
  }
  else
  {
    os << LIDToGIDMap_[0] << std::endl;
  }
  
  return os.str();
}

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