ParallelHelper.cpp

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#include "ParallelHelper.hpp"

#include <mpi.h>

#include <cstdio>
#include <cassert>
#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <ctime>

#include "MsqVertex.hpp"
#include "MsqError.hpp"

#define VERTEX_HEADER              1
#define VERTEX_BLOCK               1000
#define GHOST_NODE_INFO            2000
#define GHOST_NODE_VERTICES_WANTED 2001
#define GHOST_NODE_VERTEX_GIDS     2002
#define GHOST_NODE_VERTEX_UPDATES  2003

#define ARRPTR( x ) arrptr( x, true )

namespace MBMesquite
{

void parallel_barrier()
{
    int is_init = 0;
    int err     = MPI_Initialized( &is_init );
    if( MPI_SUCCESS != err ) return;
    if( is_init ) MPI_Barrier( MPI_COMM_WORLD );
}

int get_parallel_rank()
{
    int rank    = 0;
    int is_init = 0;
    int err     = MPI_Initialized( &is_init );
    if( MPI_SUCCESS != err ) return 0;
    if( is_init ) MPI_Comm_rank( MPI_COMM_WORLD, &rank );
    return rank;
}

int get_parallel_size()
{
    int nprocs  = 0;
    int is_init = 0;
    int err     = MPI_Initialized( &is_init );
    if( MPI_SUCCESS != err ) return 0;
    if( is_init ) MPI_Comm_size( MPI_COMM_WORLD, &nprocs );
    return nprocs;
}

double reduce_parallel_max( double value )
{
    int is_init = 0;
    int err     = MPI_Initialized( &is_init );
    if( MPI_SUCCESS != err ) return value;
    if( !is_init ) return value;

    double d_max[1];
    double d_max_recv[1];
    d_max[0] = value;
    int rval = MPI_Allreduce( d_max, d_max_recv, 1, MPI_DOUBLE, MPI_MAX, MPI_COMM_WORLD );
    if( MPI_SUCCESS != rval ) return value;

    return d_max_recv[0];
}

static const char* mpi_err_string( int error_code )
{
    static char buffer[128];
    int len = sizeof( buffer );
    int e   = MPI_Error_string( error_code, buffer, &len );
    if( MPI_SUCCESS != e ) len = 0;

    if( len >= (int)sizeof( buffer ) ) len = sizeof( buffer ) - 1;
    buffer[len] = '\0';
    return buffer;
}

#define CHECK_MPI( RVAL, ERR )                                                                          \
    do                                                                                                  \
    {                                                                                                   \
        if( MPI_SUCCESS != ( RVAL ) )                                                                   \
        {                                                                                               \
            MSQ_SETERR( err )                                                                           \
            ( MsqError::UNKNOWN_ERROR, "MPI Error %d: %s", (int)( RVAL ), mpi_err_string( ( RVAL ) ) ); \
            return;                                                                                     \
        }                                                                                               \
    } while( false )

#define CHECK_MPI_RZERO( RVAL, ERR )                                                                    \
    do                                                                                                  \
    {                                                                                                   \
        if( MPI_SUCCESS != ( RVAL ) )                                                                   \
        {                                                                                               \
            MSQ_SETERR( err )                                                                           \
            ( MsqError::UNKNOWN_ERROR, "MPI Error %d: %s", (int)( RVAL ), mpi_err_string( ( RVAL ) ) ); \
            return 0;                                                                                   \
        }                                                                                               \
    } while( false )

static bool vertex_map_insert( VertexIdMap& map, size_t glob_id, int proc_id, int value )
{
    VertexIdMapKey vid;
    vid.glob_id = glob_id;
    vid.proc_id = proc_id;
    return map.insert( VertexIdMap::value_type( vid, value ) ).second;
}

static int vertex_map_find( const VertexIdMap& map, size_t glob_id, int proc_id )
{
    VertexIdMapKey vid;
    vid.glob_id                             = glob_id;
    vid.proc_id                             = proc_id;
    VertexIdMap::const_iterator map_element = map.find( vid );
    if( map_element == map.end() )
    {
        return 0;
    }
    else
    {
        return map_element->second;
    }
}

static void my_quicksort( int* a, size_t* b, MBMesquite::Mesh::VertexHandle* c, int i, int j )
{
    int in_i = i;
    int in_j = j;
    int wa;
    size_t wb;
    MBMesquite::Mesh::VertexHandle w1;
    int key = a[( i + j ) / 2];
    do
    {
        while( a[i] < key )
            i++;
        while( a[j] > key )
            j--;
        if( i < j )
        {
            wa   = a[i];
            a[i] = a[j];
            a[j] = wa;
            wb   = b[i];
            b[i] = b[j];
            b[j] = wb;
            w1   = c[i];
            c[i] = c[j];
            c[j] = w1;
        }
    } while( ++i <= --j );
    if( i == j + 3 )
    {
        i--;
        j++;
    }
    if( j > in_i ) my_quicksort( a, b, c, in_i, j );
    if( i < in_j ) my_quicksort( a, b, c, i, in_j );
}

static int hash6432shift( unsigned long long key )
{
    key = ( ~key ) + ( key << 18 );  // key = (key << 18) - key - 1;
    key = key ^ ( key >> 31 );
    key = key * 21;  // key = (key + (key << 2)) + (key << 4);
    key = key ^ ( key >> 11 );
    key = key + ( key << 6 );
    key = key ^ ( key >> 22 );
    return (int)key;
}

static unsigned long long hash64shift( unsigned long long key )
{
    key = ( ~key ) + ( key << 21 );  // key = (key << 21) - key - 1;
    key = key ^ ( key >> 24 );
    key = ( key + ( key << 3 ) ) + ( key << 8 );  // key * 265
    key = key ^ ( key >> 14 );
    key = ( key + ( key << 2 ) ) + ( key << 4 );  // key * 21
    key = key ^ ( key >> 28 );
    key = key + ( key << 31 );
    return key;
}

static double generate_random_number( int generate_random_numbers, int proc_id, size_t glob_id )
{
    int gid;

    if( sizeof( size_t ) == sizeof( unsigned long long ) )
    {
        gid = hash6432shift( (unsigned long long)glob_id );
    }
    else
    {
        gid = (int)glob_id;
    }

    if( generate_random_numbers == 1 )
    {
        // count number of on bits
        int on            = 0;
        unsigned int mist = (unsigned int)gid;
        while( mist )
        {
            if( mist & 1 ) on++;
            mist = mist >> 1;
        }
        unsigned short xsubi[3];
        if( on & 1 )
            mist = (unsigned int)gid;
        else
            mist = (unsigned int)( -gid );
        if( on & 2 )
        {
            xsubi[0] = (unsigned short)( 65535 & mist );
            xsubi[1] = (unsigned short)( 65535 & ( mist >> 16 ) );
        }
        else
        {
            xsubi[1] = (unsigned short)( 65535 & mist );
            xsubi[0] = (unsigned short)( 65535 & ( mist >> 16 ) );
        }
        xsubi[2] = proc_id;

#if( defined WIN32 || defined WIN64 )
        time_t seed = ( gid + xsubi[1] ) / ( ( time( NULL ) % 10 ) + 1 );
        srand( (int)seed );
        return rand() / ( RAND_MAX + 1.0 );
#else
        return erand48( xsubi );
#endif
    }
    else if( generate_random_numbers == 2 )
    {
        // count number of on bits
        int on            = 0;
        unsigned int mist = (unsigned int)gid;
        while( mist )
        {
            if( mist & 1 ) on++;
            mist = mist >> 1;
        }
        unsigned short xsubi[3];
        if( on & 1 )
            mist = (unsigned int)gid;
        else
            mist = (unsigned int)( -gid );
        if( on & 2 )
        {
            xsubi[0] = (unsigned short)( 65535 & mist );
            xsubi[1] = (unsigned short)( 65535 & ( mist >> 16 ) );
        }
        else
        {
            xsubi[1] = (unsigned short)( 65535 & mist );
            xsubi[0] = (unsigned short)( 65535 & ( mist >> 16 ) );
        }
        xsubi[2] = proc_id ^ xsubi[1];

#if( defined WIN32 || defined WIN64 )
        time_t seed = ( gid + xsubi[1] ) / ( ( time( NULL ) % 10 ) + 1 );
        srand( (int)seed );
        return rand() / ( RAND_MAX + 1.0 );
#else
        return erand48( xsubi );
#endif
    }
    else if( generate_random_numbers == 3 )
    {
        unsigned long long key = (unsigned long long)gid;
        key                    = key << 32;
        key                    = key | proc_id;
        return (double)hash64shift( key );
    }
    else if( generate_random_numbers == 4 )
    {
        unsigned long long key = (unsigned long long)gid;
        key                    = key << 32;
        key                    = key | proc_id;
        key                    = hash64shift( key );
        unsigned short xsubi[3];
        xsubi[0] = (unsigned short)( key >> 48 );
        xsubi[1] = (unsigned short)( key >> 32 );
        xsubi[2] = (unsigned short)( key >> 16 );

#if( defined WIN32 || defined WIN64 )
        time_t seed = ( gid + xsubi[1] ) / ( ( time( NULL ) % 10 ) + 1 );
        srand( (int)seed );
        return rand() / ( RAND_MAX + 1.0 );
#else
        return erand48( xsubi );
#endif
    }
    else
    {
        return -1;
    }
}

ParallelHelperImpl::ParallelHelperImpl()
{
    mesh = 0;
    set_communicator( MPI_COMM_WORLD );
    communication_model = TrulyNonBlockingAvoidAllReduce;

    MPI_Comm_rank( (MPI_Comm)communicator, &rank );
    MPI_Comm_size( (MPI_Comm)communicator, &nprocs );

    // variable defaults for VertexMover::loop_over_mesh()
    generate_random_numbers = 2;

    // memory chunks referenced for VertexMover::loop_over_mesh()
    vertices.clear();
    vtx_in_partition_boundary.clear();
    part_vertices.clear();
    unghost_vertices.clear();
    part_proc_owner.clear();
    part_gid.clear();
    part_smoothed_flag.clear();
    part_rand_number.clear();
    exportVtxGIDs.clear();
    exportVtxLIDs.clear();
    exportProc.clear();
    in_independent_set.clear();
    vid_map.clear();
    neighbourProcSend.clear();
    neighbourProcRecv.clear();
    neighbourProcSendRemain.clear();
    neighbourProcRecvRemain.clear();
    vtx_off_proc_list.clear();
    neighbourProc.clear();
}

ParallelHelperImpl::~ParallelHelperImpl() {}

void ParallelHelperImpl::set_parallel_mesh( ParallelMesh* pmesh )
{
    this->mesh = pmesh;
}

void ParallelHelperImpl::set_communicator( size_t comm )
{
    communicator = comm;
    MPI_Comm_rank( (MPI_Comm)communicator, &rank );
    MPI_Comm_size( (MPI_Comm)communicator, &nprocs );
}

void ParallelHelperImpl::set_communication_model( int model, MsqError& )
{
    communication_model = model;
}

void ParallelHelperImpl::set_generate_random_numbers( int grn, MsqError& )
{
    this->generate_random_numbers = grn;
}

void ParallelHelperImpl::smoothing_init( MsqError& err )
{

    int i, j, k, rval;
    size_t l;

    if( !mesh )
    {
        MSQ_SETERR( err )( MsqError::INVALID_STATE );
        return;
    }
    if( nprocs == 1 ) return;

    /* get the vertices */
    mesh->get_all_vertices( vertices, err );MSQ_ERRRTN( err );
    num_vertex = vertices.size();

    /* allocate the data arrays we'll use for smoothing */
    std::vector< size_t > gid( num_vertex );
    std::vector< int > proc_owner( num_vertex );
    std::vector< unsigned char > app_fixed( num_vertex );

    /* get the data from the mesquite mesh */
    mesh->vertices_get_global_id( ARRPTR( vertices ), ARRPTR( gid ), num_vertex, err );MSQ_ERRRTN( err );
    mesh->vertices_get_byte( ARRPTR( vertices ), ARRPTR( app_fixed ), num_vertex, err );MSQ_ERRRTN( err );
    mesh->vertices_get_processor_id( ARRPTR( vertices ), ARRPTR( proc_owner ), num_vertex, err );MSQ_ERRRTN( err );
    if( false )
    {
        int ncull = 0;
        for( i = 0; i < num_vertex; ++i )
        {
            if( app_fixed[i] & MsqVertex::MSQ_CULLED )
            {
                ++ncull;
            }
        }
        std::cout << "P[" << rank << "] smoothing_init ncull= " << ncull << " num_vertex= " << num_vertex << std::endl;
    }

    /* only interested in fixed flag from vertex byte? Clear others. */
    // srkenno AT sandia.gov 1/19/12: bug fix: changed from |= which makes all vertices fixed
    for( i = 0; i < num_vertex; ++i )
        app_fixed[i] &= MsqVertex::MSQ_HARD_FIXED;

    /* create temporary Tag for the local IDs */
    std::vector< int > lid( num_vertex );
    for( i = 0; i < num_vertex; i++ )
        lid[i] = i;
    const char LOCAL_ID_NAME[] = "LOCAL_ID";
    TagHandle lid_tag          = mesh->tag_create( LOCAL_ID_NAME, Mesh::INT, 1, NULL, err );MSQ_ERRRTN( err );
    mesh->tag_set_vertex_data( lid_tag, num_vertex, ARRPTR( vertices ), ARRPTR( lid ), err );MSQ_ERRRTN( err );

    if( false ) printf( "[%d] set local tags on %d vertices\n", rank, num_vertex );

    /* get the elements */
    std::vector< MBMesquite::Mesh::ElementHandle > elements;
    mesh->get_all_elements( elements, err );MSQ_ERRRTN( err );
    int num_elems = elements.size();

    /****************************************************************
    PARTITION BOUNDARY VERTEX DETERMINATION
    ***********************************************************************/

    /* initialize the vertex partition boundary array */
    vtx_in_partition_boundary.clear();
    vtx_in_partition_boundary.resize( num_vertex, 0 );
    int incident_vtx, vtx_off_proc, vtx_on_proc;

    /* get the array that contains the adjacent vertices for each mesh element */
    std::vector< MBMesquite::Mesh::VertexHandle > adj_vertices;
    std::vector< size_t > vtx_offsets;
    mesh->elements_get_attached_vertices( ARRPTR( elements ), num_elems, adj_vertices, vtx_offsets, err );
    std::vector< int > adj_vertices_lid( adj_vertices.size() );
    mesh->tag_get_vertex_data( lid_tag, adj_vertices.size(), ARRPTR( adj_vertices ), ARRPTR( adj_vertices_lid ), err );

    if( false ) printf( "[%d] gotten adjacent elements for %d elements\n", rank, num_elems );

    /* determine which vertices are smoothed as part of the boundary (and which are unused ghost
     * vertices) */
    num_vtx_partition_boundary_local  = 0;
    num_vtx_partition_boundary_remote = 0;
    for( i = 0; i < num_elems; i++ )
    {
        /* count how many vertices of the current element are on/off a different processor */
        vtx_off_proc = 0;
        vtx_on_proc  = 0;
        for( j = vtx_offsets[i]; j < (int)( vtx_offsets[i + 1] ); j++ )
        {
            incident_vtx = adj_vertices_lid[j];
            /* obviously the vertex only counts if it is not app_fixed */
            if( !app_fixed[incident_vtx] )
            {
                if( proc_owner[incident_vtx] != rank )
                {
                    vtx_off_proc++;
                }
                else
                {
                    vtx_on_proc++;
                }
            }
        }

        /* if vertices are on different processors mark all local vertices as boundary1 and all
         * remote vertices as boundary2 */
        if( vtx_off_proc > 0 && vtx_on_proc > 0 )
        {
            /* collect stats */
            //  smooth_stats.num_part_bndy_elem++;
            /* mark the vertices */
            for( j = vtx_offsets[i]; j < (int)( vtx_offsets[i + 1] ); j++ )
            {
                incident_vtx = adj_vertices_lid[j];
                /* obviously the vertex does not need to be marked if it was already marked or if it
                 * is app_fixed*/
                if( vtx_in_partition_boundary[incident_vtx] <= 0 && app_fixed[incident_vtx] == 0 )
                {
                    /* mark and count the vertex */
                    if( proc_owner[incident_vtx] != rank )
                    {
                        vtx_in_partition_boundary[incident_vtx] = 2;
                        num_vtx_partition_boundary_remote++;
                    }
                    else
                    {
                        vtx_in_partition_boundary[incident_vtx] = 1;
                        num_vtx_partition_boundary_local++;
                    }
                }
            }
        }
        else if( vtx_off_proc > 0 )
        {
            /* mark the vertices as boundary-1 (aka unused ghost) if the element has only
             * off-processor vertices */
            for( j = vtx_offsets[i]; j < (int)( vtx_offsets[i + 1] ); j++ )
            {
                incident_vtx = adj_vertices_lid[j];
                /* obviously the vertex is not marked if it was already marked or if it is
                 * app_fixed*/
                if( vtx_in_partition_boundary[incident_vtx] == 0 && app_fixed[incident_vtx] == 0 )
                {
                    vtx_in_partition_boundary[incident_vtx] = -1;
                }
            }
        }
    }

    if( false )
    {
        printf( "[%d]i%d local %d remote %d ", rank, iteration, num_vtx_partition_boundary_local,
                num_vtx_partition_boundary_remote );
        printf( "[%d]i%d pb1 ", rank, iteration );
        for( i = 0; i < num_vertex; i++ )
            if( vtx_in_partition_boundary[i] == 1 ) printf( "%d,%lu ", i, gid[i] );
        printf( "\n" );
        printf( "[%d]i%d pb2 ", rank, iteration );
        for( i = 0; i < num_vertex; i++ )
            if( vtx_in_partition_boundary[i] == 2 ) printf( "%d,%lu ", i, gid[i] );
        printf( "\n" );
        fflush( NULL );
    }

    num_vtx_partition_boundary = num_vtx_partition_boundary_local + num_vtx_partition_boundary_remote;

    /********************************************************************
   COLLECT THE PARTITION BOUNDARY VERTICES AND THE UNUSED GHOST VERTICES
    ********************************************************************/

    /* create the vectors to store the partition boundary vertex data */
    part_vertices.resize( num_vtx_partition_boundary );
    part_proc_owner.resize( num_vtx_partition_boundary );
    part_gid.resize( num_vtx_partition_boundary );
    part_smoothed_flag.resize( num_vtx_partition_boundary );
    part_rand_number.resize( num_vtx_partition_boundary );

    /* create the partition boundary map and its inverse */
    std::vector< int > vtx_partition_boundary_map_inverse( num_vertex );

    j = 0;
    /* first we map the partition boundary vertices that we will smooth on this processor */
    for( i = 0; i < num_vertex; i++ )
    {
        if( vtx_in_partition_boundary[i] == 1 )
        {
            part_vertices[j]   = vertices[i];
            part_proc_owner[j] = rank;
            assert( proc_owner[i] == rank );
            part_gid[j]                           = gid[i];
            vtx_partition_boundary_map_inverse[i] = j;
            j++;
        }
    }

    vid_map.clear();

    /* then we map the ghost vertices that will be smoothed on other processors */
    for( i = 0; i < num_vertex; i++ )
    {
        if( vtx_in_partition_boundary[i] == 2 )
        {
            part_vertices[j]   = vertices[i];
            part_proc_owner[j] = proc_owner[i];
            assert( proc_owner[i] != rank );
            part_gid[j]                           = gid[i];
            vtx_partition_boundary_map_inverse[i] = j;
            /* only insert those vertices in the map that are smoothed on other processors */
            vertex_map_insert( vid_map, part_gid[j], part_proc_owner[j], j );
            // printf("[%d] inserting vertex with gid %u and pid %d \n", rank, part_gid[j],
            // part_proc_owner[j]);
            j++;
        }
    }

    /* create our own 'very pseudo random' numbers */
    for( i = 0; i < num_vtx_partition_boundary; i++ )
        part_rand_number[i] = generate_random_number( generate_random_numbers, part_proc_owner[i], part_gid[i] );

    /* count the number of unused ghost vertices */
    unghost_num_vtx = 0;
    for( i = 0; i < num_vertex; i++ )
    {
        if( vtx_in_partition_boundary[i] == -1 )
        {
            unghost_num_vtx++;
        }
    }
    // printf("[%d] found %d unused ghost vertices (local %d remote %d)\n",rank, unghost_num_vtx,
    // num_vtx_partition_boundary_local,num_vtx_partition_boundary_remote);

    /* create the vectors to store the unused ghost vertices */
    unghost_vertices.resize( unghost_num_vtx );
    std::vector< int > unghost_proc_owner( unghost_num_vtx );
    std::vector< size_t > unghost_gid( unghost_num_vtx );

    /* store the unused ghost vertices that are copies of vertices from other processors and will
     * need to be received */
    j = 0;
    for( i = 0; i < num_vertex; i++ )
    {
        if( vtx_in_partition_boundary[i] == -1 )
        {
            unghost_vertices[j]   = vertices[i];
            unghost_proc_owner[j] = proc_owner[i];
            assert( proc_owner[i] != rank );
            unghost_gid[j] = gid[i];
            // printf(" %d", unghost_gid[j]);
            j++;
        }
    }

    /* no longer needed */
    // delete [] gid; gid = 0;
    // delete [] proc_owner; proc_owner = 0;

    unghost_num_procs = 0;
    unghost_procs.clear();
    unghost_procs_offset.clear();
    unghost_procs_num_vtx.clear();
    if( unghost_num_vtx )
    {
        /* sort the unused ghost vertices by processor */
        my_quicksort( ARRPTR( unghost_proc_owner ), ARRPTR( unghost_gid ), &( unghost_vertices[0] ), 0,
                      unghost_num_vtx - 1 );

        /* count the number of processors we have unused ghost data from that we want to get updated
         */
        unghost_num_procs = 1;
        for( i = 1; i < unghost_num_vtx; i++ )
        {
            if( unghost_proc_owner[i - 1] != unghost_proc_owner[i] ) unghost_num_procs++;
        }

        /* get the ids of those processors and the number of vertices we want from each */
        unghost_procs.resize( unghost_num_procs );
        unghost_procs_offset.resize( unghost_num_procs + 1 );
        unghost_procs_num_vtx.resize( unghost_num_procs );
        unghost_procs[0]        = unghost_proc_owner[0];
        unghost_procs_offset[0] = 0;
        for( i = 1, j = 1; i < unghost_num_vtx; i++ )
        {
            if( unghost_proc_owner[i - 1] != unghost_proc_owner[i] )
            {
                unghost_procs[j]             = unghost_proc_owner[i];
                unghost_procs_offset[j]      = i;
                unghost_procs_num_vtx[j - 1] = unghost_procs_offset[j] - unghost_procs_offset[j - 1];
                assert( unghost_procs_num_vtx[j - 1] > 0 );
                j++;
            }
        }
        unghost_procs_offset[j]      = i;
        unghost_procs_num_vtx[j - 1] = unghost_procs_offset[j] - unghost_procs_offset[j - 1];
        assert( unghost_procs_num_vtx[j - 1] > 0 );
        assert( j == unghost_num_procs );

        // delete [] unghost_proc_owner; unghost_proc_owner = 0;

        // printf("[%d] have ugns from %d processor(s) (%d,%d,%d)\n", rank, unghost_num_procs,
        // unghost_procs[0], (unghost_num_procs>1) ? unghost_procs[1] : -1, (unghost_num_procs>2) ?
        // unghost_procs[1] : -1);
    }

    /* this will eventually store to how many processors each processor needs to send unused ghost
     * data to */
    std::vector< int > num_sends_of_unghost;

    /* gather the information about how many processors need ghost data */
    if( rank == 0 )
    {
        /* this will eventually store to how many processors each processor needs to send unused
         * ghost data to */
        num_sends_of_unghost.resize( nprocs );
    }
    /* temporary used for the initial gather in which each proc tells the root from how many procs
     * it wants unused ghost data updates */
    rval = MPI_Gather( &unghost_num_procs, 1, MPI_INT, ARRPTR( num_sends_of_unghost ), 1, MPI_INT, 0,
                       (MPI_Comm)communicator );
    CHECK_MPI( rval, err );

    /* now each processor tells the root node from which processors they want unused ghost nodes
     * information */
    if( rank == 0 )
    {
        int procs_num = 0;
        int procs_max = 0;
        /* first count how many processors will send unused ghost node info and find the maximum
         * they will send */
        for( i = 1; i < nprocs; i++ )
        {
            if( num_sends_of_unghost[i] )
            {
                procs_num++;
                if( num_sends_of_unghost[i] > procs_max ) procs_max = num_sends_of_unghost[i];
            }
        }
        /* clean the temporary used array */
        for( i = 0; i < nprocs; i++ )
            num_sends_of_unghost[i] = 0;
        /* process rank 0's unused ghost nodes procs first */
        for( j = 0; j < unghost_num_procs; j++ )
        {
            num_sends_of_unghost[unghost_procs[j]]++;
        }
        /* now we process messages from all other processors that want unused ghost node information
         */
        int* unghost_procs_array = new int[procs_max];
        for( i = 0; i < procs_num; i++ )
        {
            MPI_Status status;
            rval = MPI_Recv( unghost_procs_array, procs_max, MPI_INT, MPI_ANY_SOURCE, GHOST_NODE_INFO,
                             (MPI_Comm)communicator, &status );
            CHECK_MPI( rval, err );
            int count;
            MPI_Get_count( &status, MPI_INT, &count );
            for( j = 0; j < count; j++ )
            {
                num_sends_of_unghost[unghost_procs_array[j]]++;
            }
        }
        delete[] unghost_procs_array;
    }
    else
    {
        if( unghost_num_vtx )
        {
            rval = MPI_Send( ARRPTR( unghost_procs ), unghost_num_procs, MPI_INT, 0, GHOST_NODE_INFO,
                             (MPI_Comm)communicator );
            CHECK_MPI( rval, err );
        }
    }

    /* now the root node knows for each processor on how many other processors they have ghost nodes
     * (which need updating) */
    /* the scatter distributes this information to each processor */
    rval = MPI_Scatter( ARRPTR( num_sends_of_unghost ), 1, MPI_INT, &update_num_procs, 1, MPI_INT, 0,
                        (MPI_Comm)communicator );
    CHECK_MPI( rval, err );

    // if (rank == 0) delete [] num_sends_of_unghost;

    // printf("[%d] i have unused ghost nodes from %d procs and i need to send updates to %d
    // procs\n", rank, unghost_num_procs, update_num_procs);

    /* now the processors can negotiate amongst themselves: */

    /* first tell each processor the number of unused ghost nodes we want from them */
    std::vector< MPI_Request > requests_unghost( unghost_num_procs );
    for( j = 0; j < unghost_num_procs; j++ )
    {
        rval = MPI_Isend( &( unghost_procs_num_vtx[j] ), 1, MPI_INT, unghost_procs[j], GHOST_NODE_VERTICES_WANTED,
                          (MPI_Comm)communicator, &( requests_unghost[j] ) );
        CHECK_MPI( rval, err );
    }

    /* then listen to as many processors as there are that want updates from us */
    std::vector< MPI_Request > requests_updates( update_num_procs );
    update_procs_num_vtx.resize( update_num_procs );
    for( j = 0; j < update_num_procs; j++ )
    {
        rval = MPI_Irecv( &( update_procs_num_vtx[j] ), 1, MPI_INT, MPI_ANY_SOURCE, GHOST_NODE_VERTICES_WANTED,
                          (MPI_Comm)communicator, &( requests_updates[j] ) );
        CHECK_MPI( rval, err );
    }

    /* wait until we have heard from all processors how many ghost nodes updates they want from us
     */
    std::vector< MPI_Status > status_update( update_num_procs );
    update_procs.resize( update_num_procs );
    rval = MPI_Waitall( update_num_procs, ARRPTR( requests_updates ), ARRPTR( status_update ) );
    CHECK_MPI( rval, err );
    for( j = 0; j < update_num_procs; j++ )
    {
        update_procs[j] = status_update[j].MPI_SOURCE;
        // printf("[%d] i have to send %d vertices to processor %d\n", rank,
        // update_procs_num_vtx[j], update_procs[j]);
    }

    /* count the total number of vertices that we need to update elsewhere */
    update_procs_offset.resize( update_num_procs + 1 );
    update_num_vtx         = 0;
    update_procs_offset[0] = 0;
    for( j = 0; j < update_num_procs; j++ )
    {
        update_num_vtx += update_procs_num_vtx[j];
        update_procs_offset[j + 1] = update_num_vtx;
    }

    /* create enough space to receive all the vertex indices */
    update_gid.resize( update_num_vtx );

    /* tell each processor which vertices we want from them */
    for( j = 0; j < unghost_num_procs; j++ )
    {
        rval = MPI_Isend( &( unghost_gid[unghost_procs_offset[j]] ), unghost_procs_num_vtx[j],
                          sizeof( size_t ) == 4 ? MPI_INT : MPI_DOUBLE, unghost_procs[j], GHOST_NODE_VERTEX_GIDS,
                          (MPI_Comm)communicator, &( requests_unghost[j] ) );
        CHECK_MPI( rval, err );
    }

    /* receive from each processor the info which vertices they want from us */
    for( j = 0; j < update_num_procs; j++ )
    {
        rval = MPI_Irecv( &( update_gid[update_procs_offset[j]] ), update_procs_num_vtx[j],
                          sizeof( size_t ) == 4 ? MPI_INT : MPI_DOUBLE, update_procs[j], GHOST_NODE_VERTEX_GIDS,
                          (MPI_Comm)communicator, &( requests_updates[j] ) );
        CHECK_MPI( rval, err );
    }

    /* wait until we have heard from all processors which vertices they want from us */
    rval = MPI_Waitall( update_num_procs, ARRPTR( requests_updates ), ARRPTR( status_update ) );
    CHECK_MPI( rval, err );

    /* wait until we have sent to all processors which vertices we want from them */
    std::vector< MPI_Status > status_unghost( unghost_num_procs );
    rval = MPI_Waitall( unghost_num_procs, ARRPTR( requests_unghost ), ARRPTR( status_unghost ) );
    CHECK_MPI( rval, err );

    /*
    for (j = 0; j < update_num_procs; j++)
    {
      printf("[%d] will send to proc %d:", rank, update_procs[j]);
      for (i = update_procs_offset[j]; i < update_procs_offset[j+1]; i++) printf(" %d",
    update_gid[i]); printf("\n");
    }
    */

    /***********************************************************************
   COMPUTE THE SET OF NEIGHBORS THAT OUR VERTICES HAVE ON OTHER PROCESSORS
                 COMPUTE THE SET OF NEIGHBORS PROCESSORS
    ***********************************************************************/

    if( num_vtx_partition_boundary_local == 0 )
    {
        /* this processor does not partake in the boundary smoothing */
        neighbourProc.clear();
        mesh->tag_delete( lid_tag, err );
        vtx_partition_boundary_map_inverse.clear();
        return;
    }

    /* init the neighbour processor list */
    neighbourProc.clear();

    /* init the neighbour lists */

    vtx_off_proc_list.clear();
    vtx_off_proc_list.resize( num_vtx_partition_boundary_local );

    /* get the adjacency arrays that we need */
    std::vector< MBMesquite::Mesh::ElementHandle > adj_elements;
    std::vector< MBMesquite::Mesh::VertexHandle > adj_adj_vertices;
    std::vector< size_t > elem_offsets;
    std::vector< size_t > adj_vtx_offsets;
    mesh->vertices_get_attached_elements( ARRPTR( part_vertices ), num_vtx_partition_boundary_local, adj_elements,
                                          elem_offsets, err );
    mesh->elements_get_attached_vertices( ARRPTR( adj_elements ), adj_elements.size(), adj_adj_vertices,
                                          adj_vtx_offsets, err );
    // delete adj_elements; adj_elements = 0;
    std::vector< int > adj_adj_vertices_lid( adj_adj_vertices.size() );
    mesh->tag_get_vertex_data( lid_tag, adj_adj_vertices.size(), ARRPTR( adj_adj_vertices ),
                               ARRPTR( adj_adj_vertices_lid ), err );
    // delete adj_adj_vertices; adj_adj_vertices = 0;
    mesh->tag_delete( lid_tag, err );

    for( i = 0; i < num_vtx_partition_boundary_local; i++ )
    {
        /* loop over the elements surrounding that vertex */
        for( j = elem_offsets[i]; j < (int)( elem_offsets[i + 1] ); j++ )
        {
            /* loop over the neighbors of the considered vertex (i.e. the vertices of these element)
             */
            for( k = adj_vtx_offsets[j]; k < (int)( adj_vtx_offsets[j + 1] ); k++ )
            {
                /* get the next neighbour */
                incident_vtx = adj_adj_vertices_lid[k];
                /* if this neighbour is a vertex that is smoothed on a different processor */
                if( vtx_in_partition_boundary[incident_vtx] == 2 )
                {
                    /* then map it into our domain */
                    incident_vtx = vtx_partition_boundary_map_inverse[incident_vtx];
                    /* is this vertex already in our neighbour list ? */
                    if( std::find( vtx_off_proc_list[i].begin(), vtx_off_proc_list[i].end(), incident_vtx ) ==
                        vtx_off_proc_list[i].end() )
                    {
                        /* if the vertex is not in the list yet ... add it */
                        vtx_off_proc_list[i].push_back( incident_vtx );
                        /* is the processor of this vertex already in the processor list */
                        incident_vtx = part_proc_owner[incident_vtx];
                        /* check by scanning the list for this processor */
                        if( std::find( neighbourProc.begin(), neighbourProc.end(), incident_vtx ) ==
                            neighbourProc.end() )
                        {
                            /* the processor is not in the list yet ... add it */
                            neighbourProc.push_back( incident_vtx );
                        }
                    }
                }
            }
        }
    }

    /* sort the list of neighbour processors */

    std::sort( neighbourProc.begin(), neighbourProc.end() );

    /***********************************************************************
      COMPUTE HOW MANY VERTICES WE NEED TO SEND/RECV FROM EACH PROCESSOR
    ***********************************************************************/
    neighbourProcSend.clear();
    neighbourProcRecv.clear();
    neighbourProcSendRemain.clear();
    neighbourProcRecvRemain.clear();

    if( communication_model & 1 )  // AVOID_ALL_REDUCE
    {
        total_num_vertices_to_smooth = num_vtx_partition_boundary_local;
        total_num_vertices_to_recv   = num_vtx_partition_boundary_remote;
        neighbourProcSend.resize( neighbourProc.size(), 0 );
        neighbourProcRecv.resize( neighbourProc.size(), 0 );

        /* for each vertex we smooth find the processors we need to send it too */
        for( i = 0; i < num_vtx_partition_boundary_local; i++ )
        {
            /* loop over its adjacent off-processor vertices */
            for( j = 0; j < (long)vtx_off_proc_list[i].size(); j++ )
            {
                /* get the processor id of these vertices */
                incident_vtx = part_proc_owner[vtx_off_proc_list[i][j]];
                /* check if we got this processor id before */
                for( k = 0; k < j; k++ )
                {
                    if( incident_vtx == part_proc_owner[vtx_off_proc_list[i][k]] )
                    {
                        /* if we have has this procesor id already we do not need to count it again
                         */
                        incident_vtx = -1;
                        break;
                    }
                }
                /* if this was a new processor id */
                if( incident_vtx != -1 )
                {
                    /* find the processor in the list and increment its counter */
                    for( l = 0; l < neighbourProc.size(); l++ )
                    {
                        if( neighbourProc[l] == incident_vtx )
                        {
                            neighbourProcSend[l]++;
                            break;
                        }
                    }
                }
            }
        }
        for( i = num_vtx_partition_boundary_local; i < num_vtx_partition_boundary; i++ )
        {
            incident_vtx = part_proc_owner[i];
            for( l = 0; l < neighbourProc.size(); l++ )
            {
                if( neighbourProc[l] == incident_vtx )
                {
                    neighbourProcRecv[l]++;
                    break;
                }
            }
        }
        neighbourProcSendRemain.resize( neighbourProc.size() );
        neighbourProcRecvRemain.resize( neighbourProc.size() );
    }

    exportVtxGIDs.resize( num_vtx_partition_boundary );
    exportVtxLIDs.resize( num_vtx_partition_boundary );
    exportProc.resize( num_vtx_partition_boundary );
    in_independent_set.resize( num_vtx_partition_boundary_local );
}

void ParallelHelperImpl::compute_first_independent_set( std::vector< Mesh::VertexHandle >& fixed_vertices )
{
    if( nprocs == 1 ) return;

    int i;

    // to avoid all reduce we need to know how many vertices we send & receive
    if( communication_model & 1 )  // AVOID_ALL_REDUCE
    {
        for( i = 0; i < (long)neighbourProc.size(); i++ )
        {
            neighbourProcSendRemain[i] = neighbourProcSend[i];
            neighbourProcRecvRemain[i] = neighbourProcRecv[i];
        }
    }

    // this is iteration zero of the bounday smooting process
    iteration = 0;

    // mark all boundary partition vertices as not smoothed
    for( i = 0; i < num_vtx_partition_boundary; i++ )
    {
        part_smoothed_flag[i] = 0;
    }

    // populates the in_independent_set and the vertex export arrays
    compute_independent_set();

    // counts how many vertices are already smoothed
    num_already_smoothed_vertices = 0;

    fixed_vertices.clear();

    /* mark which local boundary partition vertices are already smoothed (i.e. they are in the 1st
     * independent set) */
    for( i = 0; i < num_vtx_partition_boundary_local; i++ )
    {
        if( in_independent_set[i] )
        {
            part_smoothed_flag[i] = 1;
            num_already_smoothed_vertices++;
        }
        else
        {
            fixed_vertices.push_back( part_vertices[i] );  // fix vertices *not* in the independent set
        }
    }

    if( false )
    {
        printf( "[%d]i%d after first we smoothed %d of %d\n", rank, iteration, num_already_smoothed_vertices,
                num_vtx_partition_boundary_local );
        fflush( NULL );
    }

    // fix the ghost vertices that are smoothed on another processor
    for( i = num_vtx_partition_boundary_local; i < num_vtx_partition_boundary; i++ )
    {
        fixed_vertices.push_back( part_vertices[i] );
    }

    // fix the ghost vertices that are unused
    for( i = 0; i < (int)( unghost_vertices.size() ); i++ )
    {
        fixed_vertices.push_back( unghost_vertices[i] );
    }
}

void ParallelHelperImpl::communicate_first_independent_set( MsqError& err )
{
    if( nprocs == 1 ) return;

    switch( communication_model )
    {
        case TrulyNonBlocking:
            num_already_recv_vertices = comm_smoothed_vtx_tnb( err );
            break;
        case TrulyNonBlockingAvoidAllReduce:
            num_already_recv_vertices = comm_smoothed_vtx_tnb_no_all( err );
            break;
        case NonBlocking:
            num_already_recv_vertices = comm_smoothed_vtx_nb( err );
            break;
        case NonBlockingAvoidAllReduce:
            num_already_recv_vertices = comm_smoothed_vtx_nb_no_all( err );
            break;
        case Blocking:
            num_already_recv_vertices = comm_smoothed_vtx_b( err );
            break;
        case BlockingAvoidAllReduce:
            num_already_recv_vertices = comm_smoothed_vtx_b_no_all( err );
            break;
    }
    global_work_remains = ( neighbourProc.size() ? 1 : 0 );MSQ_CHKERR( err );
}

bool ParallelHelperImpl::compute_next_independent_set()
{
    if( nprocs == 1 ) return false;

    if( global_work_remains && ( iteration < 20 ) )
    {
        iteration++;
        if( false ) printf( "[%d] work remains %d after %d iterations\n", rank, global_work_remains, iteration );
        compute_independent_set();
        next_vtx_partition_boundary = 0;
        return true;
    }
    else
    {
        if( global_work_remains )
        {
            printf( "WARNING: global work remains %d after %d iterations\n", global_work_remains, iteration );
        }
        return false;
    }
}

bool ParallelHelperImpl::get_next_partition_boundary_vertex( MBMesquite::Mesh::VertexHandle& vertex_handle )
{
    while( next_vtx_partition_boundary < num_vtx_partition_boundary_local )
    {
        if( in_independent_set[next_vtx_partition_boundary] )
        {
            vertex_handle = part_vertices[next_vtx_partition_boundary];
            num_already_smoothed_vertices++;
            assert( part_smoothed_flag[next_vtx_partition_boundary] == 0 );
            part_smoothed_flag[next_vtx_partition_boundary] = 1;
            next_vtx_partition_boundary++;
            return true;
        }
        next_vtx_partition_boundary++;
    }
    if( false )
    {
        printf( "[%d]i%d after next we smoothed %d of %d\n", rank, iteration, num_already_smoothed_vertices,
                num_vtx_partition_boundary_local );
        fflush( NULL );
    }
    return false;
}

void ParallelHelperImpl::communicate_next_independent_set( MsqError& err )
{
    switch( communication_model )
    {
        case TrulyNonBlocking:
            num_already_recv_vertices += comm_smoothed_vtx_tnb( err );
            break;
        case TrulyNonBlockingAvoidAllReduce:
            num_already_recv_vertices += comm_smoothed_vtx_tnb_no_all( err );
            break;
        case NonBlocking:
            num_already_recv_vertices += comm_smoothed_vtx_nb( err );
            break;
        case NonBlockingAvoidAllReduce:
            num_already_recv_vertices += comm_smoothed_vtx_nb_no_all( err );
            break;
        case Blocking:
            num_already_recv_vertices += comm_smoothed_vtx_b( err );
            break;
        case BlockingAvoidAllReduce:
            num_already_recv_vertices += comm_smoothed_vtx_b_no_all( err );
            break;
    }

    if( communication_model & 1 )  // AVOID_ALL_REDUCE
    {
        global_work_remains = ( total_num_vertices_to_smooth - num_already_smoothed_vertices ) +
                              ( total_num_vertices_to_recv - num_already_recv_vertices );
        if( false )
        {
            printf( "[%d]i%d %d - %d + %d  - %d = %d \n", rank, iteration, total_num_vertices_to_smooth,
                    num_already_smoothed_vertices, total_num_vertices_to_recv, num_already_recv_vertices,
                    global_work_remains );
            fflush( NULL );
        }
    }
    else
    {
        int i, work_remains = 0;
        for( i = 0; i < num_vtx_partition_boundary_local; i++ )
        {
            if( part_smoothed_flag[i] == 0 )
            {
                work_remains++;
            }
        }
        int rval = MPI_Allreduce( &work_remains, &global_work_remains, 1, MPI_INT, MPI_SUM, (MPI_Comm)communicator );
        CHECK_MPI( rval, err );
    }
}

void ParallelHelperImpl::smoothing_close( MsqError& err )
{
    int i, j, rval;

    if( nprocs == 1 ) return;

    //  printf("[%d] used %d iterations\n", rank, iteration);

    // communicate unused ghost nodes

    std::vector< double > update_updates;
    std::vector< MPI_Request > update_requests;

    if( update_num_procs )
    {
        /* get the tags so we can find the requested vertices */
        std::vector< size_t > gid( num_vertex );
        mesh->vertices_get_global_id( ARRPTR( vertices ), ARRPTR( gid ), num_vertex, err );MSQ_ERRRTN( err );
        std::vector< unsigned char > app_fixed( num_vertex );
        mesh->vertices_get_byte( ARRPTR( vertices ), ARRPTR( app_fixed ), num_vertex, err );MSQ_ERRRTN( err );
        std::vector< int > proc_owner( num_vertex );
        mesh->vertices_get_processor_id( ARRPTR( vertices ), ARRPTR( proc_owner ), num_vertex, err );MSQ_ERRRTN( err );

        if( false )
        {
            int ncull = 0;
            for( i = 0; i < num_vertex; ++i )
            {
                if( app_fixed[i] & MsqVertex::MSQ_CULLED )
                {
                    ++ncull;
                }
            }
            std::cout << "P[" << rank << "] ncull= " << ncull << " num_vertex= " << num_vertex << std::endl;
        }

        /* only interested in fixed flag from vertex byte? Clear others. */
        // srkenno AT sandia.gov 1/19/12: bug fix: changed from |= which makes all vertices fixed
        for( i = 0; i < num_vertex; ++i )
            app_fixed[i] &= MsqVertex::MSQ_HARD_FIXED;

        /* insert all our unfixed vertices into a map so we can find the requested vertices
         * efficiently */
        VertexIdMap temp_vid_map;
        for( j = 0; j < num_vertex; j++ )
        {
            if( proc_owner[j] == rank && app_fixed[j] == false )
            {
                vertex_map_insert( temp_vid_map, gid[j], rank, j );
            }
        }

        /* deallocate the tags */
        // delete [] gid; gid = 0;
        // delete [] app_fixed; app_fixed = 0;
        // delete [] proc_owner; proc_owner = 0;

        /* find the requested updates and collect them into an array */
        MBMesquite::MsqVertex coordinates;
        update_updates.resize( update_num_vtx * 3 );
        for( i = 0; i < update_num_vtx; i++ )
        {
            j = vertex_map_find( temp_vid_map, update_gid[i], rank );
            mesh->vertices_get_coordinates( &( vertices[j] ), &coordinates, 1, err );MSQ_ERRRTN( err );
            update_updates[3 * i + 0] = coordinates[0];
            update_updates[3 * i + 1] = coordinates[1];
            update_updates[3 * i + 2] = coordinates[2];
            //      printf("[%d] send gid %d with %g %g %g\n", rank, update_gid[i], coordinates[0],
            //      coordinates[1], coordinates[2]);
        }

        /* deallocate the map and the gid array */
        // delete temp_vid_map; temp_vid_map = 0;
        // delete [] update_gid; update_gid = 0;

        update_requests.resize( update_num_procs );
        /* send each processor the unused ghost node updates that they requested */
        for( j = 0; j < update_num_procs; j++ )
        {
            rval = MPI_Isend( &( update_updates[update_procs_offset[j] * 3] ), update_procs_num_vtx[j] * 3, MPI_DOUBLE,
                              update_procs[j], GHOST_NODE_VERTEX_UPDATES, (MPI_Comm)communicator,
                              &( update_requests[j] ) );
            //      printf("[%d] sending %d of %d from %d with offset %d \n", rank,
            //      update_procs_num_vtx[j], update_num_vtx, update_procs[j],
            //      update_procs_offset[j]);
            CHECK_MPI( rval, err );
        }

        /* deallocate more arrays that we no longer need */
        // delete [] update_procs_offset; update_procs_offset = 0;
        // delete [] update_procs_num_vtx; update_procs_num_vtx = 0;
        // delete [] update_procs; update_procs = 0;
    }

    if( unghost_num_procs )
    {
        std::vector< MPI_Request > unghost_requests( unghost_num_procs );
        /* receive from each processor the unused ghost nodes updates i want from them */
        std::vector< double > unghost_updates( unghost_num_vtx * 3 );
        for( j = 0; j < unghost_num_procs; j++ )
        {
            rval = MPI_Irecv( &( unghost_updates[unghost_procs_offset[j] * 3] ), unghost_procs_num_vtx[j] * 3,
                              MPI_DOUBLE, unghost_procs[j], GHOST_NODE_VERTEX_UPDATES, (MPI_Comm)communicator,
                              &( unghost_requests[j] ) );
            //      printf("[%d] receiving %d of %d from %d with offset %d \n", rank,
            //      unghost_procs_num_vtx[j], unghost_num_vtx, unghost_procs[j],
            //      unghost_procs_offset[j]);
            CHECK_MPI( rval, err );
        }

        /* deallocate more arrays that we no longer need */
        // delete [] unghost_procs_offset; unghost_procs_offset = 0;
        // delete [] unghost_procs_num_vtx; unghost_procs_num_vtx = 0;
        // delete [] unghost_procs; unghost_procs = 0;

        std::vector< MPI_Status > status( unghost_num_procs );
        rval = MPI_Waitall( unghost_num_procs, ARRPTR( unghost_requests ), ARRPTR( status ) );
        CHECK_MPI( rval, err );

        /* apply the received updates for the unused ghost vertices */
        for( i = 0; i < unghost_num_vtx; i++ )
        {
            MBMesquite::Vector3D coordinates;
            coordinates[0] = unghost_updates[3 * i + 0];
            coordinates[1] = unghost_updates[3 * i + 1];
            coordinates[2] = unghost_updates[3 * i + 2];
            //      printf("[%d] recv %g %g %g\n", rank, coordinates[0], coordinates[1],
            //      coordinates[2]);
            mesh->vertex_set_coordinates( unghost_vertices[i], coordinates, err );MSQ_ERRRTN( err );
        }

        /* deallocate more arrays that we no longer need */
        // delete unghost_vertices; unghost_vertices = 0;
        // delete [] unghost_updates; unghost_updates = 0;
        // delete [] unghost_requests; unghost_requests = 0;
    }

    // if (update_num_procs)
    //{
    //  delete [] update_updates; update_updates = 0;
    //  delete [] update_requests; update_requests = 0;
    //}

    // if (vertices) delete vertices; vertices = 0;
    // if (vtx_in_partition_boundary) delete [] vtx_in_partition_boundary; vtx_in_partition_boundary
    // = 0; if (part_vertices) delete part_vertices; part_vertices = 0; if (unghost_vertices) delete
    // unghost_vertices; unghost_vertices = 0; if (part_proc_owner) delete [] part_proc_owner;
    // part_proc_owner = 0; if (part_gid) delete [] part_gid; part_gid = 0; if (part_smoothed_flag)
    // delete [] part_smoothed_flag; part_smoothed_flag = 0; if (part_rand_number) delete []
    // part_rand_number; part_rand_number = 0; if (exportVtxGIDs) delete [] exportVtxGIDs;
    // exportVtxGIDs = 0; if (exportVtxLIDs) delete [] exportVtxLIDs; exportVtxLIDs = 0; if
    // (exportProc) delete [] exportProc; exportProc = 0; if (in_independent_set) delete []
    // in_independent_set; in_independent_set = 0; if (vid_map) delete vid_map; vid_map = 0; if
    // (neighbourProcSend) delete [] neighbourProcSend; neighbourProcSend = 0; if (neighbourProcRecv)
    // delete [] neighbourProcRecv; neighbourProcRecv = 0; if (neighbourProcSendRemain) delete []
    // neighbourProcSendRemain; neighbourProcSendRemain = 0; if (neighbourProcRecvRemain) delete []
    // neighbourProcRecvRemain; neighbourProcRecvRemain = 0; if (vtx_off_proc_list_size) delete []
    // vtx_off_proc_list_size; vtx_off_proc_list_size = 0; if (vtx_off_proc_list) {
    //  for (i = 0; i < num_vtx_partition_boundary_local; i++) free(vtx_off_proc_list[i]);
    //  delete [] vtx_off_proc_list; vtx_off_proc_list = 0;
    //}
    // if (neighbourProc) free(neighbourProc); neighbourProc = 0;
}

typedef struct VertexPack
{
    double x;
    double y;
    double z;
    union
    {
        double mist;
        size_t glob_id;
    };
} VertexPack;

int ParallelHelperImpl::comm_smoothed_vtx_tnb( MsqError& err )
{
    int i, j, k, rval;

    // printf("[%d]i%d truly non blocking\n",rank, iteration);fflush(NULL);

    /* compute how many vertices we send to each processor */

    std::vector< int > numVtxPerProcSend( neighbourProc.size(), 0 );
    std::vector< int > numVtxPerProcRecv( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                /* increment count */
                numVtxPerProcSend[j]++;
                /* end loop */
                break;
            }
        }
        /* did loop end without finding the processor */
        if( j == (long)neighbourProc.size() )
        {
            printf( "[%d]i%d WARNING: did not find exportProc[%d] = %d in list of %lu processors.\n", rank, iteration,
                    i, exportProc[i], (unsigned long)neighbourProc.size() );
        }
    }

    /* tell each processor how many vertices they can expect from us */
    /* also ask each processor how many vertices we can expect from them */

    int num_neighbourProcSend = 0;
    int num_neighbourProcRecv = 0;
    std::vector< MPI_Request > requests_send( neighbourProc.size() );
    std::vector< MPI_Request > requests_recv( neighbourProc.size() );
    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        /* send the vertex count to this processor */
        if( 0 )
        {
            printf( "[%d]i%d Announce send %d vertices from proc %d\n", rank, iteration, numVtxPerProcSend[j],
                    neighbourProc[j] );
            fflush( NULL );
        }
        rval = MPI_Isend( &( numVtxPerProcSend[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                          (MPI_Comm)communicator, &( requests_send[j] ) );
        CHECK_MPI_RZERO( rval, err );
        num_neighbourProcSend++;

        /* recv the vertex count for this processor */
        if( 0 )
        {
            printf( "[%d]i%d Listen  recv %d vertices from proc %d\n", rank, iteration, numVtxPerProcRecv[j],
                    neighbourProc[j] );
            fflush( NULL );
        }
        rval = MPI_Irecv( &( numVtxPerProcRecv[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                          (MPI_Comm)communicator, &( requests_recv[j] ) );
        CHECK_MPI_RZERO( rval, err );
        num_neighbourProcRecv++;
    }

    /* set up memory for the outgoing vertex data blocks */

    std::vector< VertexPack > vertex_pack_export( num_exportVtx + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_export( neighbourProc.size() );
    if( neighbourProc.size() ) packed_vertices_export[0] = ARRPTR( vertex_pack_export );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices_export[i] = packed_vertices_export[i - 1] + numVtxPerProcSend[i - 1];
    }

    /* place vertex data going to the same processor into consecutive memory space */

    std::vector< int > numVtxPerProcSendPACKED( neighbourProc.size() );
    for( i = 0; i < (long)neighbourProc.size(); i++ )
    {
        numVtxPerProcSendPACKED[i] = 0;
    }
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                VertexPack* packing_vertex = packed_vertices_export[j] + numVtxPerProcSendPACKED[j];
                numVtxPerProcSendPACKED[j]++;
                MBMesquite::MsqVertex coordinates;
                mesh->vertices_get_coordinates( &part_vertices[exportVtxLIDs[i]], &coordinates, 1, err );
                MSQ_ERRZERO( err );
                packing_vertex->x       = coordinates[0];
                packing_vertex->y       = coordinates[1];
                packing_vertex->z       = coordinates[2];
                packing_vertex->glob_id = exportVtxGIDs[i];
            }
        }
    }

    /* wait until we have heard from all processors how many vertices we will receive from them */

    std::vector< MPI_Status > status( neighbourProc.size() );

    if( num_neighbourProcRecv )
    {
        rval = MPI_Waitall( neighbourProc.size(), ARRPTR( requests_recv ), ARRPTR( status ) );
        CHECK_MPI_RZERO( rval, err );
    }

    /* how many vertices will we receive */

    int numVtxImport = 0;
    for( i = 0; i < (long)neighbourProc.size(); i++ )
    {
        numVtxImport += numVtxPerProcRecv[i];
    }

    /* set up memory for the incoming vertex data blocks */

    std::vector< VertexPack > vertex_pack_import( numVtxImport + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_import( neighbourProc.size() );
    if( neighbourProc.size() ) packed_vertices_import[0] = ARRPTR( vertex_pack_import );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices_import[i] = packed_vertices_import[i - 1] + numVtxPerProcRecv[i - 1];
    }

    /* post receives for all processors that have something for us */
    /* post sends for all processors that we have something for */

    num_neighbourProcRecv = 0;

    for( i = 0; i < (long)neighbourProc.size(); i++ )
    {
        if( numVtxPerProcRecv[i] )
        {
            if( 0 )
            {
                printf( "[%d]i%d Will recv %d vertices from proc %d\n", rank, iteration, numVtxPerProcRecv[i],
                        neighbourProc[i] );
                fflush( NULL );
            }
            rval = MPI_Irecv( packed_vertices_import[i], 4 * numVtxPerProcRecv[i], MPI_DOUBLE, neighbourProc[i],
                              VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( requests_recv[i] ) );
            CHECK_MPI_RZERO( rval, err );
            num_neighbourProcRecv++;
        }
        else
        {
            requests_recv[i] = MPI_REQUEST_NULL;
        }
        if( numVtxPerProcSend[i] )
        {
            if( 0 )
            {
                printf( "[%d]i%d Will send %d vertices to proc %d\n", rank, iteration, numVtxPerProcSend[i],
                        neighbourProc[i] );
                fflush( NULL );
            }
            rval = MPI_Isend( packed_vertices_export[i], 4 * numVtxPerProcSend[i], MPI_DOUBLE, neighbourProc[i],
                              VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( requests_send[i] ) );
            CHECK_MPI_RZERO( rval, err );
        }
        else
        {
            requests_send[i] = MPI_REQUEST_NULL;
        }
    }

    /* wait for some receive to arrive */

    int local_id;
    while( num_neighbourProcRecv )
    {
        rval = MPI_Waitany( neighbourProc.size(), ARRPTR( requests_recv ), &k, ARRPTR( status ) );
        CHECK_MPI_RZERO( rval, err );
        /* unpack all vertices */
        for( i = 0; i < numVtxPerProcRecv[k]; i++ )
        {
            local_id = vertex_map_find( vid_map, packed_vertices_import[k][i].glob_id, neighbourProc[k] );
            if( local_id )
            {
                MBMesquite::Vector3D coordinates;
                coordinates.set( packed_vertices_import[k][i].x, packed_vertices_import[k][i].y,
                                 packed_vertices_import[k][i].z );
                mesh->vertex_set_coordinates( part_vertices[local_id], coordinates, err );
                MSQ_ERRZERO( err );
                assert( part_smoothed_flag[local_id] == 0 );
                part_smoothed_flag[local_id] = 1;
            }
            else
            {
                printf( "[%d]i%d vertex with gid %lu and pid %d not in map\n", rank, iteration,
                        packed_vertices_import[k][i].glob_id, neighbourProc[k] );
            }
        }
        num_neighbourProcRecv--;
    }

    /* all receives have completed. it is save to release the memory */
    // free(vertex_pack_import);

    /* wait until the sends have completed */

    if( num_neighbourProcSend )
    {
        rval = MPI_Waitall( neighbourProc.size(), ARRPTR( requests_send ), ARRPTR( status ) );
        CHECK_MPI_RZERO( rval, err );
    }

    /* all sends have completed. it is save to release the memory */
    // free(vertex_pack_export);

    return numVtxImport;
}

int ParallelHelperImpl::comm_smoothed_vtx_tnb_no_all( MsqError& err )
{
    int i, j, k, rval;

    // printf("[%d]i%d truly non blocking avoid reduce all\n", rank, iteration); fflush(NULL);

    /* compute how many vertices we send to each processor */

    std::vector< int > numVtxPerProcSend( neighbourProc.size(), 0 );
    std::vector< int > numVtxPerProcRecv( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                /* increment count */
                numVtxPerProcSend[j]++;
                /* end loop */
                break;
            }
        }
        /* did loop end without finding the processor */
        if( j == (long)neighbourProc.size() )
        {
            printf( "[%d]i%d WARNING: did not find exportProc[%d] = %d in list of %lu processors.\n", rank, iteration,
                    i, exportProc[i], (unsigned long)neighbourProc.size() );
        }
    }

    /* tell each processor how many vertices they can expect from us */
    /* also ask each processor how many vertices we can expect from them */

    int num_neighbourProcSend = 0;
    int num_neighbourProcRecv = 0;
    std::vector< MPI_Request > requests_send( neighbourProc.size() );
    std::vector< MPI_Request > requests_recv( neighbourProc.size() );
    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        if( neighbourProcSendRemain[j] )
        {
            /* send the vertex count to this processor */
            if( 0 )
            {
                printf( "[%d]i%d Announce send %d vertices to proc %d\n", rank, iteration, numVtxPerProcSend[j],
                        neighbourProc[j] );
                fflush( NULL );
            }
            rval = MPI_Isend( &( numVtxPerProcSend[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                              (MPI_Comm)communicator, &( requests_send[j] ) );
            CHECK_MPI_RZERO( rval, err );
            num_neighbourProcSend++;
        }
        else
        {
            requests_send[j] = MPI_REQUEST_NULL;
        }
        if( neighbourProcRecvRemain[j] )
        {
            /* recv the vertex count for this processor */
            if( 0 )
            {
                printf( "[%d]i%d Listen recv xx vertices from proc %d\n", rank, iteration, neighbourProc[j] );
                fflush( NULL );
            }
            rval = MPI_Irecv( &( numVtxPerProcRecv[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                              (MPI_Comm)communicator, &( requests_recv[j] ) );
            CHECK_MPI_RZERO( rval, err );
            num_neighbourProcRecv++;
        }
        else
        {
            requests_recv[j] = MPI_REQUEST_NULL;
        }
    }

    /* set up memory for the outgoing vertex data blocks */

    std::vector< VertexPack > vertex_pack_export( num_exportVtx + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_export( neighbourProc.size() );
    if( neighbourProc.size() ) packed_vertices_export[0] = ARRPTR( vertex_pack_export );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices_export[i] = packed_vertices_export[i - 1] + numVtxPerProcSend[i - 1];
    }

    /* place vertex data going to the same processor into consecutive memory space */

    std::vector< int > numVtxPerProcSendPACKED( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                VertexPack* packing_vertex = packed_vertices_export[j] + numVtxPerProcSendPACKED[j];
                numVtxPerProcSendPACKED[j]++;
                MBMesquite::MsqVertex coordinates;
                mesh->vertices_get_coordinates( &part_vertices[exportVtxLIDs[i]], &coordinates, 1, err );
                MSQ_ERRZERO( err );
                packing_vertex->x       = coordinates[0];
                packing_vertex->y       = coordinates[1];
                packing_vertex->z       = coordinates[2];
                packing_vertex->glob_id = exportVtxGIDs[i];
                if( 0 )
                    printf( "[%d]i%d vertex %lu packed %g %g %g\n", rank, iteration, (unsigned long)exportVtxGIDs[i],
                            packing_vertex->x, packing_vertex->y, packing_vertex->z );
            }
        }
    }

    /* wait until we have heard from all processors how many vertices we will receive from them */

    std::vector< MPI_Status > status( neighbourProc.size() );

    if( num_neighbourProcRecv )
    {
        rval = MPI_Waitall( neighbourProc.size(), ARRPTR( requests_recv ), ARRPTR( status ) );
        CHECK_MPI_RZERO( rval, err );
    }

    /* how many vertices will we receive */

    int numVtxImport = 0;
    for( i = 0; i < (long)neighbourProc.size(); i++ )
    {
        numVtxImport += numVtxPerProcRecv[i];
        neighbourProcRecvRemain[i] -= numVtxPerProcRecv[i];
        neighbourProcSendRemain[i] -= numVtxPerProcSend[i];
    }

    /* set up memory for the incoming vertex data blocks */

    std::vector< VertexPack > vertex_pack_import( numVtxImport + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_import( neighbourProc.size() );
    if( neighbourProc.size() ) packed_vertices_import[0] = ARRPTR( vertex_pack_import );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices_import[i] = packed_vertices_import[i - 1] + numVtxPerProcRecv[i - 1];
    }

    /* post receives for all processors that have something for us */
    /* post sends for all processors that we have something for */

    num_neighbourProcRecv = 0;

    for( i = 0; i < (long)neighbourProc.size(); i++ )
    {
        if( 0 )
        {
            printf( "[%d]i%d Will recv %d vertices from proc %d\n", rank, iteration, numVtxPerProcRecv[i],
                    neighbourProc[i] );
            fflush( NULL );
        }
        if( numVtxPerProcRecv[i] )
        {
            rval = MPI_Irecv( packed_vertices_import[i], 4 * numVtxPerProcRecv[i], MPI_DOUBLE, neighbourProc[i],
                              VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( requests_recv[i] ) );
            CHECK_MPI_RZERO( rval, err );
            num_neighbourProcRecv++;
        }
        else
        {
            requests_recv[i] = MPI_REQUEST_NULL;
        }
        if( 0 )
        {
            printf( "[%d]i%d Will send %d vertices to proc %d\n", rank, iteration, numVtxPerProcSend[i],
                    neighbourProc[i] );
            fflush( NULL );
        }
        if( numVtxPerProcSend[i] )
        {
            rval = MPI_Isend( packed_vertices_export[i], 4 * numVtxPerProcSend[i], MPI_DOUBLE, neighbourProc[i],
                              VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( requests_send[i] ) );
            CHECK_MPI_RZERO( rval, err );
        }
        else
        {
            requests_send[i] = MPI_REQUEST_NULL;
        }
    }

    /* wait for some receive to arrive */

    int local_id;
    while( num_neighbourProcRecv )
    {
        rval = MPI_Waitany( neighbourProc.size(), ARRPTR( requests_recv ), &k, ARRPTR( status ) );
        CHECK_MPI_RZERO( rval, err );
        /* unpack all vertices */
        for( i = 0; i < numVtxPerProcRecv[k]; i++ )
        {
            local_id = vertex_map_find( vid_map, packed_vertices_import[k][i].glob_id, neighbourProc[k] );
            if( local_id )
            {
                MBMesquite::Vector3D coordinates;
                coordinates.set( packed_vertices_import[k][i].x, packed_vertices_import[k][i].y,
                                 packed_vertices_import[k][i].z );
                if( 0 )
                    printf( "[%d]i%d vertex %d becomes %g %g %g\n", rank, iteration, local_id,
                            packed_vertices_import[k][i].x, packed_vertices_import[k][i].y,
                            packed_vertices_import[k][i].z );
                mesh->vertex_set_coordinates( part_vertices[local_id], coordinates, err );
                MSQ_ERRZERO( err );
                assert( part_smoothed_flag[local_id] == 0 );
                part_smoothed_flag[local_id] = 1;
            }
            else
            {
                printf( "[%d]i%d vertex with gid %lu and pid %d not in map\n", rank, iteration,
                        packed_vertices_import[k][i].glob_id, neighbourProc[k] );
            }
        }
        num_neighbourProcRecv--;
    }

    /* all receives have completed. it is save to release the memory */
    // free(vertex_pack_import);

    /* wait until the sends have completed */

    if( num_neighbourProcSend )
    {
        rval = MPI_Waitall( neighbourProc.size(), ARRPTR( requests_send ), ARRPTR( status ) );
        CHECK_MPI_RZERO( rval, err );
    }

    /* all sends have completed. it is save to release the memory */
    // free(vertex_pack_export);

    return numVtxImport;
}

int ParallelHelperImpl::comm_smoothed_vtx_nb( MsqError& err )
{
    int i, j, k, rval;

    // printf("[%d] %d %d non blocking\n",rank, iteration, pass);fflush(NULL);

    /* how many vertices will we receive */

    std::vector< int > numVtxPerProcSend( neighbourProc.size() );
    for( i = 0; i < (long)neighbourProc.size(); i++ )
    {
        numVtxPerProcSend[i] = 0;
    }
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                /* increment count */
                numVtxPerProcSend[j]++;
                /* end loop */
                break;
            }
        }
        /* assert loop did not end without finding processor */
        assert( j != (long)neighbourProc.size() );
    }

    /* tell each processor how many vertices to expect */

    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        rval = MPI_Send( &( numVtxPerProcSend[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                         (MPI_Comm)communicator );
        CHECK_MPI_RZERO( rval, err );
        //    printf("[%d]i%d Announcing %d vertices to proc
        //    %d\n",rank,iteration,numVtxPerProcSend[j],neighbourProc[j]); fflush(NULL);
    }

    /* place vertex data going to the same processor into consecutive memory space */
    std::vector< VertexPack > vertex_pack_export( num_exportVtx + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_export( neighbourProc.size() );
    if( neighbourProc.size() ) packed_vertices_export[0] = ARRPTR( vertex_pack_export );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices_export[i] = packed_vertices_export[i - 1] + numVtxPerProcSend[i - 1];
    }

    std::vector< int > numVtxPerProcSendPACKED( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                VertexPack* packing_vertex = packed_vertices_export[j] + numVtxPerProcSendPACKED[j];
                numVtxPerProcSendPACKED[j]++;
                MBMesquite::MsqVertex coordinates;
                mesh->vertices_get_coordinates( &part_vertices[exportVtxLIDs[i]], &coordinates, 1, err );
                MSQ_ERRZERO( err );
                packing_vertex->x       = coordinates[0];
                packing_vertex->y       = coordinates[1];
                packing_vertex->z       = coordinates[2];
                packing_vertex->glob_id = exportVtxGIDs[i];
            }
        }
    }
    // delete [] numVtxPerProcSendPACKED;

    /* now ask each processor how many vertices to expect */

    int num;
    int proc;
    int numVtxImport          = 0;
    int num_neighbourProcRecv = 0;
    std::vector< int > numVtxPerProcRecv( neighbourProc.size() );
    MPI_Status status;
    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        numVtxPerProcRecv[j] = 0;
    }

    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        /* get the vertex count for some processor */
        rval = MPI_Recv( &num,                      /* message buffer */
                         1,                         /* one data item */
                         MPI_INT,                   /* of type int */
                         MPI_ANY_SOURCE,            /* receive from any sender */
                         VERTEX_HEADER + iteration, /* receive only VERTEX HEADERs from this iteration */
                         (MPI_Comm)communicator,    /* default communicator */
                         &status );                 /* info about the received message */
        CHECK_MPI_RZERO( rval, err );
        proc = status.MPI_SOURCE;
        /* will we import vertices from this processor */

        //    printf("[%d]i%d Heard we will receive %d vertices from proc
        //    %d\n",rank,iteration,num,proc); fflush(NULL);

        if( num )
        {
            /* increase number of processors we will receive from */
            num_neighbourProcRecv++;
            /* add number of vertices we will receive to the import total */
            numVtxImport += num;
        }
        /* find this processor in the list */
        for( i = 0; i < (long)neighbourProc.size(); i++ )
        {
            if( neighbourProc[i] == proc )
            {
                numVtxPerProcRecv[i] = num;
                break;
            }
        }
        /* assert loop did not end without finding processor */
        assert( i != (long)neighbourProc.size() );
        if( 0 ) printf( "[%d]i%d Will receive %d vertices from proc %d\n", rank, iteration, num, proc );
        fflush( NULL );
    }

    /* create list of processors we receive from */
    std::vector< int > neighbourProcRecv( num_neighbourProcRecv );
    std::vector< int > numVtxPerProcRecvRecv( num_neighbourProcRecv );
    for( i = 0, k = 0; i < (long)neighbourProc.size(); i++ )
    {
        if( 0 )
            printf( "[%d]i%d Will receive %d vertices from proc %d\n", rank, iteration, numVtxPerProcRecv[i],
                    neighbourProc[i] );
        fflush( NULL );
        if( numVtxPerProcRecv[i] )
        {
            neighbourProcRecv[k]     = neighbourProc[i];
            numVtxPerProcRecvRecv[k] = numVtxPerProcRecv[i];
            k++;
        }
    }

    /* set up memory for the incoming vertex data blocks */
    std::vector< VertexPack > vertex_pack_import( numVtxImport + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_import( num_neighbourProcRecv );
    if( neighbourProc.size() ) packed_vertices_import[0] = ARRPTR( vertex_pack_import );
    for( i = 1; i < num_neighbourProcRecv; i++ )
    {
        packed_vertices_import[i] = packed_vertices_import[i - 1] + numVtxPerProcRecvRecv[i - 1];
    }

    /* receive from all processors that have something for us */
    std::vector< MPI_Request > request( num_neighbourProcRecv );
    for( j = 0; j < num_neighbourProcRecv; j++ )
    {
        rval = MPI_Irecv( packed_vertices_import[j], 4 * numVtxPerProcRecvRecv[j], MPI_DOUBLE, neighbourProcRecv[j],
                          VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( request[j] ) );
        CHECK_MPI_RZERO( rval, err );
        if( false )
        {
            printf( "[%d]i%d Scheduling receipt of %d vertices to proc %d\n", rank, iteration, numVtxPerProcRecvRecv[j],
                    neighbourProcRecv[j] );
            fflush( NULL );
        }
    }

    /* now send the data blocks */

    std::vector< MPI_Request > requests_send( neighbourProc.size() );
    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        if( numVtxPerProcSend[j] )
        {
            rval = MPI_Isend( packed_vertices_export[j], 4 * numVtxPerProcSend[j], MPI_DOUBLE, neighbourProc[j],
                              VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( requests_send[j] ) );
            CHECK_MPI_RZERO( rval, err );
            if( 0 )
            {
                printf( "[%d]i%d Scheduling send of %d vertices to proc %d\n", rank, iteration, numVtxPerProcSend[j],
                        neighbourProc[j] );
                fflush( NULL );
            }
        }
        else
        {
            requests_send[j] = MPI_REQUEST_NULL;
        }
    }

    /* process messages as they arrive */

    int local_id;
    for( j = 0; j < num_neighbourProcRecv; j++ )
    {
        rval = MPI_Waitany( num_neighbourProcRecv, ARRPTR( request ), &k, &status );
        CHECK_MPI_RZERO( rval, err );

        /* unpack messages */
        proc = status.MPI_SOURCE;
        int count;
        MPI_Get_count( &status, MPI_INT, &count );
        if( 0 )
            printf( "[%d]i%d Received %d (%d) vertices from proc %d (%d)\n", rank, iteration, numVtxPerProcRecvRecv[k],
                    count, neighbourProcRecv[k], proc );
        fflush( NULL );
        for( i = 0; i < numVtxPerProcRecvRecv[k]; i++ )
        {
            local_id = vertex_map_find( vid_map, packed_vertices_import[k][i].glob_id, neighbourProcRecv[k] );
            if( local_id )
            {
                MBMesquite::Vector3D coordinates;
                coordinates.set( packed_vertices_import[k][i].x, packed_vertices_import[k][i].y,
                                 packed_vertices_import[k][i].z );
                mesh->vertex_set_coordinates( part_vertices[local_id], coordinates, err );
                MSQ_ERRZERO( err );
                assert( part_smoothed_flag[local_id] == 0 );
                part_smoothed_flag[local_id] = 1;
                if( 0 )
                    printf( "[%d]i%d updating vertex with global_id %d to %g %g %g \n", rank, iteration,
                            (int)( packed_vertices_import[k][i].glob_id ), packed_vertices_import[k][i].x,
                            packed_vertices_import[k][i].y, packed_vertices_import[k][i].z );
            }
            else
            {
                printf( "[%d]i%d vertex with gid %lu and pid %d not in map\n", rank, iteration,
                        packed_vertices_import[k][i].glob_id, neighbourProcRecv[k] );
            }
        }
    }

    /* all receives have completed. it is save to release the memory */
    // free(vertex_pack_import);
    /* wait until the sends have completed */
    std::vector< MPI_Status > stati( neighbourProc.size() );
    rval = MPI_Waitall( neighbourProc.size(), ARRPTR( requests_send ), ARRPTR( stati ) );
    CHECK_MPI_RZERO( rval, err );
    /* all sends have completed. it is save to release the memory */
    // free(vertex_pack_export);

    return numVtxImport;
}

int ParallelHelperImpl::comm_smoothed_vtx_nb_no_all( MsqError& err )
{
    int i, j, k, rval;

    // printf("[%d] %d %d non blocking avoid reduce all\n",rank, iteration, pass);fflush(NULL);

    /* how many vertices will we receive */

    std::vector< int > numVtxPerProcSend( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                /* increment count */
                numVtxPerProcSend[j]++;
                /* end loop */
                break;
            }
        }
        /* assert loop did not end without finding processor */
        assert( j != (long)neighbourProc.size() );
    }

    /* tell each processor how many vertices to expect */

    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        if( neighbourProcSendRemain[j] )
        {
            assert( neighbourProcSendRemain[j] >= numVtxPerProcSend[j] );
            neighbourProcSendRemain[j] -= numVtxPerProcSend[j];
            rval = MPI_Send( &( numVtxPerProcSend[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                             (MPI_Comm)communicator );
            CHECK_MPI_RZERO( rval, err );
            //    printf("[%d]i%d Announcing %d vertices to proc
            //    %d\n",rank,iteration,numVtxPerProcSend[j],neighbourProc[j]); fflush(NULL);
        }
        else
        {
            assert( numVtxPerProcSend[j] == 0 );
        }
    }

    /* place vertex data going to the same processor into consecutive memory space */
    std::vector< VertexPack > vertex_pack_export( num_exportVtx + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_export( neighbourProc.size() );
    if( neighbourProc.size() ) packed_vertices_export[0] = ARRPTR( vertex_pack_export );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices_export[i] = packed_vertices_export[i - 1] + numVtxPerProcSend[i - 1];
    }

    std::vector< int > numVtxPerProcSendPACKED( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                VertexPack* packing_vertex = packed_vertices_export[j] + numVtxPerProcSendPACKED[j];
                numVtxPerProcSendPACKED[j]++;
                MBMesquite::MsqVertex coordinates;
                mesh->vertices_get_coordinates( &part_vertices[exportVtxLIDs[i]], &coordinates, 1, err );
                MSQ_ERRZERO( err );
                packing_vertex->x       = coordinates[0];
                packing_vertex->y       = coordinates[1];
                packing_vertex->z       = coordinates[2];
                packing_vertex->glob_id = exportVtxGIDs[i];
            }
        }
    }
    // delete [] numVtxPerProcSendPACKED;

    /* now ask each processor how many vertices to expect */

    int num;
    int proc;
    int numVtxImport          = 0;
    int num_neighbourProcRecv = 0;
    std::vector< int > numVtxPerProcRecv( neighbourProc.size(), 0 );
    MPI_Status status;

    int num_neighbourProcRecvRemain = 0;
    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        if( neighbourProcRecvRemain[j] )
        {
            num_neighbourProcRecvRemain++;
        }
    }
    for( j = 0; j < num_neighbourProcRecvRemain; j++ )
    {
        /* get the vertex count for some processor */
        rval = MPI_Recv( &num,                      /* message buffer */
                         1,                         /* one data item */
                         MPI_INT,                   /* of type int */
                         MPI_ANY_SOURCE,            /* receive from any sender */
                         VERTEX_HEADER + iteration, /* receive only VERTEX HEADERs from this iteration */
                         (MPI_Comm)communicator,    /* default communicator */
                         &status );                 /* info about the received message */
        CHECK_MPI_RZERO( rval, err );
        proc = status.MPI_SOURCE;
        /* will we import vertices from this processor */

        //    printf("[%d]i%d Heard we will receive %d vertices from proc
        //    %d\n",rank,iteration,num,proc); fflush(NULL);

        if( num )
        {
            /* increase number of processors we will receive from */
            num_neighbourProcRecv++;
            /* add number of vertices we will receive to the import total */
            numVtxImport += num;
        }
        /* find this processor in the list */
        for( i = 0; i < (long)neighbourProc.size(); i++ )
        {
            if( neighbourProc[i] == proc )
            {
                numVtxPerProcRecv[i] = num;
                assert( neighbourProcRecvRemain[i] >= num );
                neighbourProcRecvRemain[i] -= num;
                break;
            }
        }
        /* assert loop did not end without finding processor */
        assert( i != (long)neighbourProc.size() );
        if( false ) printf( "[%d]i%d Will receive %d vertices from proc %d\n", rank, iteration, num, proc );
        fflush( NULL );
    }

    /* create list of processors we receive from */
    std::vector< int > neighbourProcRecv( num_neighbourProcRecv );
    std::vector< int > numVtxPerProcRecvRecv( num_neighbourProcRecv );
    for( i = 0, k = 0; i < (long)neighbourProc.size(); i++ )
    {
        if( 0 )
            printf( "[%d]i%d Will receive %d vertices from proc %d\n", rank, iteration, numVtxPerProcRecv[i],
                    neighbourProc[i] );
        fflush( NULL );
        if( numVtxPerProcRecv[i] )
        {
            neighbourProcRecv[k]     = neighbourProc[i];
            numVtxPerProcRecvRecv[k] = numVtxPerProcRecv[i];
            k++;
        }
    }

    /* set up memory for the incoming vertex data blocks */
    std::vector< VertexPack > vertex_pack_import( numVtxImport + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices_import( num_neighbourProcRecv );
    if( neighbourProc.size() ) packed_vertices_import[0] = ARRPTR( vertex_pack_import );
    for( i = 1; i < num_neighbourProcRecv; i++ )
    {
        packed_vertices_import[i] = packed_vertices_import[i - 1] + numVtxPerProcRecvRecv[i - 1];
    }

    /* receive from all processors that have something for us */
    std::vector< MPI_Request > request( num_neighbourProcRecv );
    for( j = 0; j < num_neighbourProcRecv; j++ )
    {
        rval = MPI_Irecv( packed_vertices_import[j], 4 * numVtxPerProcRecvRecv[j], MPI_DOUBLE, neighbourProcRecv[j],
                          VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( request[j] ) );
        CHECK_MPI_RZERO( rval, err );
        if( false )
        {
            printf( "[%d]i%d Scheduling receipt of %d vertices to proc %d\n", rank, iteration, numVtxPerProcRecvRecv[j],
                    neighbourProcRecv[j] );
            fflush( NULL );
        }
    }

    /* now send the data blocks */

    std::vector< MPI_Request > requests_send( neighbourProc.size() );
    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        if( numVtxPerProcSend[j] )
        {
            rval = MPI_Isend( packed_vertices_export[j], 4 * numVtxPerProcSend[j], MPI_DOUBLE, neighbourProc[j],
                              VERTEX_BLOCK + iteration, (MPI_Comm)communicator, &( requests_send[j] ) );
            CHECK_MPI_RZERO( rval, err );
            if( 0 )
            {
                printf( "[%d]i%d Scheduling send of %d vertices to proc %d\n", rank, iteration, numVtxPerProcSend[j],
                        neighbourProc[j] );
                fflush( NULL );
            }
        }
        else
        {
            requests_send[j] = MPI_REQUEST_NULL;
        }
    }

    /* process messages as they arrive */

    int local_id;
    for( j = 0; j < num_neighbourProcRecv; j++ )
    {
        rval = MPI_Waitany( num_neighbourProcRecv, ARRPTR( request ), &k, &status );
        CHECK_MPI_RZERO( rval, err );

        /* unpack messages */
        proc = status.MPI_SOURCE;
        int count;
        MPI_Get_count( &status, MPI_INT, &count );
        if( 0 )
            printf( "[%d]i%d Received %d (%d) vertices from proc %d (%d)\n", rank, iteration, numVtxPerProcRecvRecv[k],
                    count, neighbourProcRecv[k], proc );
        fflush( NULL );
        for( i = 0; i < numVtxPerProcRecvRecv[k]; i++ )
        {
            local_id = vertex_map_find( vid_map, packed_vertices_import[k][i].glob_id, neighbourProcRecv[k] );
            if( local_id )
            {
                MBMesquite::Vector3D coordinates;
                coordinates.set( packed_vertices_import[k][i].x, packed_vertices_import[k][i].y,
                                 packed_vertices_import[k][i].z );
                mesh->vertex_set_coordinates( part_vertices[local_id], coordinates, err );
                MSQ_ERRZERO( err );
                assert( part_smoothed_flag[local_id] == 0 );
                part_smoothed_flag[local_id] = 1;
                if( 0 )
                    printf( "[%d]i%d updating vertex with global_id %d to %g %g %g \n", rank, iteration,
                            (int)( packed_vertices_import[k][i].glob_id ), packed_vertices_import[k][i].x,
                            packed_vertices_import[k][i].y, packed_vertices_import[k][i].z );
            }
            else
            {
                printf( "[%d]i%d vertex with gid %lu and pid %d not in map\n", rank, iteration,
                        packed_vertices_import[k][i].glob_id, neighbourProcRecv[k] );
            }
        }
    }

    /* all receives have completed. it is save to release the memory */
    // free(vertex_pack_import);
    /* wait until the sends have completed */
    std::vector< MPI_Status > stati( neighbourProc.size() );
    rval = MPI_Waitall( neighbourProc.size(), ARRPTR( requests_send ), ARRPTR( stati ) );
    CHECK_MPI_RZERO( rval, err );
    /* all sends have completed. it is save to release the memory */
    // free(vertex_pack_export);

    return numVtxImport;
}

int ParallelHelperImpl::comm_smoothed_vtx_b( MsqError& err )
{
    int i, j, rval;

    // printf("[%d] %d %d blocking\n",rank, iteration, pass);fflush(NULL);

    /* how many vertices per processor */

    std::vector< int > numVtxPerProc( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                /* increment count */
                numVtxPerProc[j]++;
                /* end loop */
                break;
            }
            /* assert loop did not end without finding the processor */
            assert( j != (long)neighbourProc.size() );
        }
    }

    /* place vertices going to the same processor into consecutive memory space */

    std::vector< VertexPack > vertex_pack( num_exportVtx + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices( neighbourProc.size() );
    VertexPack* packing_vertex;
    packed_vertices[0] = ARRPTR( vertex_pack );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices[i] = packed_vertices[i - 1] + numVtxPerProc[i - 1];
    }

    std::vector< int > numVtxPackedPerProc( neighbourProc.size(), 0 );

    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                packing_vertex = packed_vertices[j] + numVtxPackedPerProc[j];
                numVtxPackedPerProc[j]++;
                MBMesquite::MsqVertex coordinates;
                mesh->vertices_get_coordinates( &part_vertices[exportVtxLIDs[i]], &coordinates, 1, err );
                MSQ_ERRZERO( err );
                packing_vertex->x       = coordinates[0];
                packing_vertex->y       = coordinates[1];
                packing_vertex->z       = coordinates[2];
                packing_vertex->glob_id = exportVtxGIDs[i];
            }
        }
    }

    // delete [] numVtxPackedPerProc;

    /* send each block so the corresponding processor preceeded by the number of vertices */

    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {

        //    printf("[%d]i%dp%d Announcing %d vertices to proc
        //    %d\n",rank,iteration,pass,numVtxPerProc[j],neighbourProc[j]); fflush(NULL);

        rval = MPI_Send( &( numVtxPerProc[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                         (MPI_Comm)communicator );
        CHECK_MPI_RZERO( rval, err );
        // printf("[%d]i%dp%d Sending %d vertices to proc
        // %d\n",rank,iteration,pass,numVtxPerProc[j],neighbourProc[j]); fflush(NULL);

        /* is there any vertex data to be sent */

        if( numVtxPerProc[j] )
        {
            rval = MPI_Send( packed_vertices[j], 4 * numVtxPerProc[j], MPI_DOUBLE, neighbourProc[j],
                             VERTEX_BLOCK + iteration, (MPI_Comm)communicator );
            CHECK_MPI_RZERO( rval, err );
            // printf("[%d]i%dp%d Sent %d vertices to proc
            // %d\n",rank,iteration,pass,numVtxPerProc[j],neighbourProc[j]); fflush(NULL);
        }
    }

    int num;
    int proc;
    // int tag;
    int count;
    int numVtxImport = 0;
    MPI_Status status;
    int local_id;

    //  printf("[%d]i%dp%d Waiting to receive vertices from %d processors ...
    //  \n",rank,iteration,pass,neighbourProc.size()); fflush(NULL);

    /* receiving blocks from other processors */

    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        rval = MPI_Recv( &num,                      /* message buffer */
                         1,                         /* one data item */
                         MPI_INT,                   /* of type int */
                         MPI_ANY_SOURCE,            /* receive from any sender */
                         VERTEX_HEADER + iteration, /* receive only VERTEX HEADERs */
                         (MPI_Comm)communicator,    /* default communicator */
                         &status );                 /* info about the received message */
        CHECK_MPI_RZERO( rval, err );
        proc = status.MPI_SOURCE;
        // tag = status.MPI_TAG;
        MPI_Get_count( &status, MPI_INT, &count );

        //    printf("[%d]i%dp%d Receiving %d vertices from proc
        //    %d/%d/%d\n",rank,iteration,pass,num,proc,tag,count); fflush(NULL);

        /* is there any vertex data to be received */

        if( num )
        {

            numVtxImport += num;

            /* do we have enough space allocated */

            if( num_exportVtx + 10 < num )
            {
                // if (vertex_pack) free(vertex_pack);
                num_exportVtx = num;
                vertex_pack.resize( num_exportVtx + 10 );
                // vertex_pack = (VertexPack*)malloc(sizeof(VertexPack)*(num_exportVtx+10));
            }

            rval = MPI_Recv( ARRPTR( vertex_pack ),    /* message buffer */
                             4 * num,                  /* num data's item with 4 doubles each */
                             MPI_DOUBLE,               /* of type double */
                             proc,                     /* receive from this procesor only */
                             VERTEX_BLOCK + iteration, /* receive only VERTEX BLOCKs */
                             (MPI_Comm)communicator,   /* default communicator */
                             &status );                /* info about the received message */
            CHECK_MPI_RZERO( rval, err );

            proc = status.MPI_SOURCE;
            // tag = status.MPI_TAG;
            MPI_Get_count( &status, MPI_DOUBLE, &count );

            if( count != 4 * num )
                printf( "[%d]i%d WARNING: expected %d vertices = %d bytes from proc %d but only "
                        "got %d bytes\n",
                        rank, iteration, num, num * 4, proc, count );
            fflush( NULL );

            //      printf("[%d]i%d Received %d vertices from proc
            //      %d/%d/%d\n",rank,iteration,num,proc,tag,count); fflush(NULL);

            /* update the received vertices in our boundary mesh */
            for( i = 0; i < num; i++ )
            {
                /*  printf("[%d]i%d updating vertex %d with global_id
                 * %d\n",rank,iteration,i,(int)(vertex_pack[i].glob_id)); fflush(NULL); */
                local_id = vertex_map_find( vid_map, (int)( vertex_pack[i].glob_id ), proc );
                if( local_id )
                {
                    MBMesquite::Vector3D coordinates;
                    coordinates.set( vertex_pack[i].x, vertex_pack[i].y, vertex_pack[i].z );
                    mesh->vertex_set_coordinates( part_vertices[local_id], coordinates, err );
                    MSQ_ERRZERO( err );
                    assert( part_smoothed_flag[local_id] == 0 );
                    part_smoothed_flag[local_id] = 1;
                    if( 0 )
                        printf( "[%d]i%d updating vertex with global_id %d to %g %g %g \n", rank, iteration,
                                (int)( vertex_pack[i].glob_id ), vertex_pack[i].x, vertex_pack[i].y, vertex_pack[i].z );
                }
                else
                {
                    printf( "[%d]i%d vertex with gid %lu and pid %d not in map\n", rank, iteration,
                            vertex_pack[i].glob_id, proc );
                }
            }
        }
    }
    // if (vertex_pack) free(vertex_pack);

    return numVtxImport;
}

int ParallelHelperImpl::comm_smoothed_vtx_b_no_all( MsqError& err )
{
    int i, j, rval;

    // printf("[%d] %d %d blocking avoid reduce all\n",rank, iteration, pass);fflush(NULL);

    /* how many vertices per processor */

    std::vector< int > numVtxPerProc( neighbourProc.size(), 0 );
    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                /* increment count */
                numVtxPerProc[j]++;
                /* end loop */
                break;
            }
            /* assert loop did not end without finding the processor */
            assert( j != (long)neighbourProc.size() );
        }
    }

    /* place vertices going to the same processor into consecutive memory space */

    std::vector< VertexPack > vertex_pack( num_exportVtx + 10 ); /* add 10 to have enough memory */
    std::vector< VertexPack* > packed_vertices( neighbourProc.size() );
    VertexPack* packing_vertex;
    packed_vertices[0] = ARRPTR( vertex_pack );
    for( i = 1; i < (long)neighbourProc.size(); i++ )
    {
        packed_vertices[i] = packed_vertices[i - 1] + numVtxPerProc[i - 1];
    }

    std::vector< int > numVtxPackedPerProc( neighbourProc.size(), 0 );

    for( i = 0; i < num_exportVtx; i++ )
    {
        for( j = 0; j < (long)neighbourProc.size(); j++ )
        {
            if( exportProc[i] == neighbourProc[j] )
            {
                packing_vertex = packed_vertices[j] + numVtxPackedPerProc[j];
                numVtxPackedPerProc[j]++;
                MBMesquite::MsqVertex coordinates;
                mesh->vertices_get_coordinates( &part_vertices[exportVtxLIDs[i]], &coordinates, 1, err );
                MSQ_ERRZERO( err );
                packing_vertex->x       = coordinates[0];
                packing_vertex->y       = coordinates[1];
                packing_vertex->z       = coordinates[2];
                packing_vertex->glob_id = exportVtxGIDs[i];
            }
        }
    }

    // delete [] numVtxPackedPerProc;

    /* send each block so the corresponding processor preceeded by the number of vertices */

    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {

        if( neighbourProcSendRemain[j] )
        {
            assert( neighbourProcSendRemain[j] >= numVtxPerProc[j] );
            neighbourProcSendRemain[j] -= numVtxPerProc[j];

            // printf("[%d]i%dp%d Announcing %d vertices to proc
            // %d\n",rank,iteration,pass,numVtxPerProc[j],neighbourProc[j]); fflush(NULL);

            rval = MPI_Send( &( numVtxPerProc[j] ), 1, MPI_INT, neighbourProc[j], VERTEX_HEADER + iteration,
                             (MPI_Comm)communicator );
            CHECK_MPI_RZERO( rval, err );

            // printf("[%d]i%dp%d Sending %d vertices to proc
            // %d\n",rank,iteration,pass,numVtxPerProc[j],neighbourProc[j]); fflush(NULL);

            /* is there any vertex data to be sent */

            if( numVtxPerProc[j] )
            {
                rval = MPI_Send( packed_vertices[j], 4 * numVtxPerProc[j], MPI_DOUBLE, neighbourProc[j],
                                 VERTEX_BLOCK + iteration, (MPI_Comm)communicator );
                CHECK_MPI_RZERO( rval, err );

                // printf("[%d]i%dp%d Sent %d vertices to proc
                // %d\n",rank,iteration,pass,numVtxPerProc[j],neighbourProc[j]); fflush(NULL);
            }
        }
        else
        {
            // printf("[%d]i%dp%d no longer sending to %d\n",rank,iteration,neighbourProc[j]);
            // fflush(NULL);
        }
    }

    int num;
    int proc;
    // int tag;
    int count;
    int numVtxImport = 0;
    MPI_Status status;
    int local_id;

    //  printf("[%d]i%dp%d Waiting to receive vertices from %d processors ...
    //  \n",rank,iteration,pass,neighbourProc.size()); fflush(NULL);

    /* receiving blocks in any order from other processors */

    int num_neighbourProcRecvRemain = 0;
    for( j = 0; j < (long)neighbourProc.size(); j++ )
    {
        if( neighbourProcRecvRemain[j] )
        {
            num_neighbourProcRecvRemain++;
        }
    }
    for( j = 0; j < num_neighbourProcRecvRemain; j++ )
    {
        rval = MPI_Recv( &num,                      /* message buffer */
                         1,                         /* one data item */
                         MPI_INT,                   /* of type int */
                         MPI_ANY_SOURCE,            /* receive from any sender */
                         VERTEX_HEADER + iteration, /* receive only VERTEX HEADERs */
                         (MPI_Comm)communicator,    /* default communicator */
                         &status );                 /* info about the received message */
        CHECK_MPI_RZERO( rval, err );
        proc = status.MPI_SOURCE;
        // tag = status.MPI_TAG;
        MPI_Get_count( &status, MPI_INT, &count );

        // printf("[%d]i%dp%d Receiving %d vertices from proc
        // %d/%d/%d\n",rank,iteration,pass,num,proc,tag,count); fflush(NULL);

        /* is there any vertex data to be received */

        if( num )
        {

            numVtxImport += num;

            /* do we have enough space allocated */

            if( num_exportVtx + 10 < num )
            {
                // if (vertex_pack) free(vertex_pack);
                num_exportVtx = num;
                // vertex_pack = (VertexPack*)malloc(sizeof(VertexPack)*(num_exportVtx+10));
                vertex_pack.resize( num_exportVtx + 10 );
            }

            rval = MPI_Recv( ARRPTR( vertex_pack ),    /* message buffer */
                             4 * num,                  /* num data's item with 4 doubles each */
                             MPI_DOUBLE,               /* of type double */
                             proc,                     /* receive from this procesor only */
                             VERTEX_BLOCK + iteration, /* receive only VERTEX BLOCKs */
                             (MPI_Comm)communicator,   /* default communicator */
                             &status );                /* info about the received message */
            CHECK_MPI_RZERO( rval, err );

            proc = status.MPI_SOURCE;
            // tag = status.MPI_TAG;
            MPI_Get_count( &status, MPI_DOUBLE, &count );

            if( count != 4 * num )
                printf( "[%d]i%d WARNING: expected %d vertices = %d bytes from proc %d but only "
                        "got %d bytes\n",
                        rank, iteration, num, num * 4, proc, count );
            fflush( NULL );

            // printf("[%d]i%d Received %d vertices from proc
            // %d/%d/%d\n",rank,iteration,num,proc,tag,count); fflush(NULL);

            /* update the received vertices in our boundary mesh */
            for( i = 0; i < num; i++ )
            {
                /*  printf("[%d]i%d updating vertex %d with global_id
                 * %d\n",rank,iteration,i,(int)(vertex_pack[i].glob_id)); fflush(NULL); */
                local_id = vertex_map_find( vid_map, (int)( vertex_pack[i].glob_id ), proc );
                if( local_id )
                {
                    MBMesquite::Vector3D coordinates;
                    coordinates.set( vertex_pack[i].x, vertex_pack[i].y, vertex_pack[i].z );
                    mesh->vertex_set_coordinates( part_vertices[local_id], coordinates, err );
                    MSQ_ERRZERO( err );
                    assert( part_smoothed_flag[local_id] == 0 );
                    part_smoothed_flag[local_id] = 1;
                    if( 0 && rank == 1 )
                        printf( "[%d]i%d updating vertex with global_id %d to %g %g %g \n", rank, iteration,
                                (int)( vertex_pack[i].glob_id ), vertex_pack[i].x, vertex_pack[i].y, vertex_pack[i].z );
                }
                else
                {
                    printf( "[%d]i%d vertex with gid %lu and pid %d not in map\n", rank, iteration,
                            vertex_pack[i].glob_id, proc );
                }
            }
        }
        for( i = 0; i < (long)neighbourProc.size(); i++ )
        {
            if( proc == neighbourProc[i] )
            {
                assert( neighbourProcRecvRemain[i] >= num );
                neighbourProcRecvRemain[i] -= num;
                break;
            }
        }
    }
    // if (vertex_pack) free(vertex_pack);

    return numVtxImport;
}

/***********************************************************************
COMPUTING THE INDEPENDENT SET AND EXPORT INFORMATION
***********************************************************************/
/* the only thing that can prevent a vertex from being in the independent
   set is that is has an neighbouring vertex on a different processor that
   has not been smoothed yet and that has a larger random number */

void ParallelHelperImpl::compute_independent_set()
{
    int i, j, k, l;
    int incident_vtx;
    bool done;

    for( i = 0; i < num_vtx_partition_boundary_local; i++ )
        in_independent_set[i] = false;

    bool found_more = true;
    int found_iter  = 0;

    num_exportVtx = 0;

    while( found_more )
    {
        found_iter++;
        found_more = false;
        for( i = 0; i < num_vtx_partition_boundary_local; i++ )
        {
            /* if this vertex could become part of the independent set */
            if( part_smoothed_flag[i] == 0 && in_independent_set[i] == false )
            {
                /* assume it's in the independent set */
                done = false;
                /* then loop over the neighbors it has on other processors */
                for( j = 0; !done && j < (long)vtx_off_proc_list[i].size(); j++ )
                {
                    incident_vtx = vtx_off_proc_list[i][j];
                    /* if this neighbour has not yet been smoothed and is not covered and ... */
                    if( part_smoothed_flag[incident_vtx] == 0 )
                    {
                        /* ... has a higher rand_number than me */
                        if( part_rand_number[i] < part_rand_number[incident_vtx] )
                        {
                            /* then I am not in the independent set */
                            done = true;
                            break;
                        }
                        /* ... or has the same rand_number than me but a higher processor id */
                        else if( ( part_rand_number[i] == part_rand_number[incident_vtx] ) &&
                                 ( rank < part_proc_owner[incident_vtx] ) )
                        {
                            /* then I am not in the independent set */
                            done = true;
                            break;
                        }
                    }
                }
                /* if the vertex is in the independent set, add it to the export list */
                if( !done )
                {
                    found_more = true;
                    //  if (found_iter > 1) printf("[%d]i%d found another one %d in iteration
                    //%d\n",rank,iteration,i, found_iter);
                    in_independent_set[i] = true;
                    /* mark vertices with lower random numbers as covered */
                    for( j = 0; j < (long)vtx_off_proc_list[i].size(); j++ )
                    {
                        incident_vtx = vtx_off_proc_list[i][j];
                        /* if this neighbour has not yet been smoothed or covered mark it as covered
                         */
                        if( part_smoothed_flag[incident_vtx] == 0 )
                        {
                            part_smoothed_flag[incident_vtx] = 2;
                        }
                    }
                    k = num_exportVtx;
                    /* then loop over the neighbors it has on other processors */
                    for( j = 0; j < (long)vtx_off_proc_list[i].size(); j++ )
                    {
                        incident_vtx = vtx_off_proc_list[i][j];
                        /* check to see if this processor already on the list */
                        done = false;
                        for( l = k; l < num_exportVtx && !done; l++ )
                        {
                            if( exportProc[l] == part_proc_owner[incident_vtx] )
                            {
                                done = true;
                            }
                        }
                        /* if it's not on the list add it */
                        if( !done )
                        {
                            exportVtxLIDs[num_exportVtx] = i;
                            exportVtxGIDs[num_exportVtx] = part_gid[i];
                            exportProc[num_exportVtx]    = part_proc_owner[incident_vtx];
                            num_exportVtx++;
                        }
                    }
                }
            }
        }
    }

    if( false )
    {
        int in_set = 0;
        for( i = 0; i < num_vtx_partition_boundary_local; i++ )
            if( in_independent_set[i] ) in_set++;
        ;
        printf( "[%d]i%d independent set has %d of %d vertices sent out %d times\n", rank, iteration, in_set,
                num_vtx_partition_boundary_local, num_exportVtx );
        fflush( NULL );
    }

    /* unmark the vertices that have been marked as covered */
    for( i = num_vtx_partition_boundary_local; i < num_vtx_partition_boundary; i++ )
        if( part_smoothed_flag[i] == 2 ) part_smoothed_flag[i] = 0;
}

int ParallelHelperImpl::get_rank() const
{
    return rank;
}

int ParallelHelperImpl::get_nprocs() const
{
    return nprocs;
}

bool ParallelHelperImpl::is_our_element( MBMesquite::Mesh::ElementHandle element_handle, MsqError& err ) const
{
    int i;
    std::vector< Mesh::VertexHandle > pvertices;
    std::vector< size_t > junk;
    mesh->elements_get_attached_vertices( &element_handle, 1, pvertices, junk, err );
    MSQ_ERRZERO( err );
    int num_verts = pvertices.size();
    std::vector< int > proc_ids( num_verts );
    mesh->vertices_get_processor_id( ARRPTR( pvertices ), ARRPTR( proc_ids ), num_verts, err );
    MSQ_ERRZERO( err );
    int max_proc_id = proc_ids[0];
    for( i = 1; i < num_verts; i++ )
        if( max_proc_id < proc_ids[i] ) max_proc_id = proc_ids[i];
    return ( max_proc_id == rank );
}

bool ParallelHelperImpl::is_our_vertex( MBMesquite::Mesh::VertexHandle vertex_handle, MsqError& err ) const
{
    int proc_id;
    mesh->vertices_get_processor_id( &vertex_handle, &proc_id, 1, err );
    return !MSQ_CHKERR( err ) && ( proc_id == rank );
}

void ParallelHelperImpl::communicate_min_max_to_all( double* minimum, double* maximum, MsqError& err ) const
{
    double d_min[2];
    double d_min_recv[2];
    d_min[0] = -( *maximum );
    d_min[1] = *minimum;
    int rval = MPI_Allreduce( d_min, d_min_recv, 2, MPI_DOUBLE, MPI_MIN, (MPI_Comm)communicator );
    CHECK_MPI( rval, err );
    *maximum = -d_min_recv[0];
    *minimum = d_min_recv[1];
}

void ParallelHelperImpl::communicate_min_max_to_zero( double* minimum, double* maximum, MsqError& err ) const
{
    double d_min[2];
    double d_min_recv[2];
    d_min[0] = -( *maximum );
    d_min[1] = *minimum;
    int rval = MPI_Reduce( d_min, d_min_recv, 2, MPI_DOUBLE, MPI_MIN, 0, (MPI_Comm)communicator );
    CHECK_MPI( rval, err );
    if( rank == 0 )
    {
        *maximum = -d_min_recv[0];
        *minimum = d_min_recv[1];
    }
}

void ParallelHelperImpl::communicate_sums_to_zero( size_t* freeElementCount,
                                                   int* invertedElementCount,
                                                   size_t* elementCount,
                                                   int* invertedSampleCount,
                                                   size_t* sampleCount,
                                                   long unsigned int* count,
                                                   long unsigned int* invalid,
                                                   double* sum,
                                                   double* sqrSum,
                                                   MsqError& err ) const
{
    double d_sum[9];
    double d_sum_recv[9];

    d_sum[0] = (double)( *freeElementCount );
    d_sum[1] = (double)( *invertedElementCount );
    d_sum[2] = (double)( *elementCount );
    d_sum[3] = (double)( *invertedSampleCount );
    d_sum[4] = (double)( *sampleCount );
    d_sum[5] = (double)( *count );
    d_sum[6] = (double)( *invalid );
    d_sum[7] = *sum;
    d_sum[8] = *sqrSum;

    int rval = MPI_Reduce( d_sum, d_sum_recv, 9, MPI_DOUBLE, MPI_SUM, 0, (MPI_Comm)communicator );
    CHECK_MPI( rval, err );

    if( rank == 0 )
    {
        *freeElementCount     = (size_t)d_sum_recv[0];
        *invertedElementCount = (int)d_sum_recv[1];
        *elementCount         = (size_t)d_sum_recv[2];
        *invertedSampleCount  = (int)d_sum_recv[3];
        *sampleCount          = (size_t)d_sum_recv[4];
        *count                = (long unsigned int)d_sum_recv[5];
        *invalid              = (long unsigned int)d_sum_recv[6];
        *sum                  = d_sum_recv[7];
        *sqrSum               = d_sum_recv[8];
    }
}

void ParallelHelperImpl::communicate_power_sum_to_zero( double* pMean, MsqError& err ) const
{
    double result;
    int rval = MPI_Reduce( pMean, &result, 1, MPI_DOUBLE, MPI_SUM, 0, (MPI_Comm)communicator );
    CHECK_MPI( rval, err );
    if( rank == 0 ) *pMean = result;
}

void ParallelHelperImpl::communicate_histogram_to_zero( std::vector< int >& histogram, MsqError& err ) const
{
    std::vector< int > histogram_recv( histogram.size() );
    int rval = MPI_Reduce( &( histogram[0] ), &( histogram_recv[0] ), histogram.size(), MPI_INT, MPI_SUM, 0,
                           (MPI_Comm)communicator );
    CHECK_MPI( rval, err );
    if( rank == 0 )
    {
        histogram.swap( histogram_recv );
    }
}

/// if any proc has a true input @param value, return true to all
void ParallelHelperImpl::communicate_any_true( bool& value, MsqError& err ) const
{
    int byte_out = value, byte_in;
    int rval     = MPI_Allreduce( &byte_out, &byte_in, 1, MPI_INT, MPI_MAX, (MPI_Comm)communicator );
    CHECK_MPI( rval, err );
    value = ( byte_in != 0 );
}

/// srkenno AT sandia.gov 1/19/12: bug fix: changed from MPI_MAX to MIN - this makes the name of the
/// function correct, if all proc's values are true, it returns true.  @see communicate_any_true
/// above

/// return true in @param value if all procs have value=true, else if any have it false, return
/// false
void ParallelHelperImpl::communicate_all_true( bool& value, MsqError& err ) const
{
    int byte_out = value, byte_in;
    int rval     = MPI_Allreduce( &byte_out, &byte_in, 1, MPI_INT, MPI_MIN, (MPI_Comm)communicator );
    CHECK_MPI( rval, err );
    value = ( byte_in != 0 );
}

}  // namespace MBMesquite