/*============================================================================
 * Main structure associated to a mesh
 *============================================================================*/

/*
  This file is part of Code_Saturne, a general-purpose CFD tool.

  Copyright (C) 1998-2015 EDF S.A.

  This program is free software; you can redistribute it and/or modify it under
  the terms of the GNU General Public License as published by the Free Software
  Foundation; either version 2 of the License, or (at your option) any later
  version.

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

  You should have received a copy of the GNU General Public License along with
  this program; if not, write to the Free Software Foundation, Inc., 51 Franklin
  Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/

/*----------------------------------------------------------------------------*/

#include "cs_defs.h"

/*----------------------------------------------------------------------------
 * Standard C library headers
 *----------------------------------------------------------------------------*/

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <math.h>
#include <assert.h>

/*----------------------------------------------------------------------------
 *  Local headers
 *----------------------------------------------------------------------------*/

#include "bft_mem.h"
#include "bft_printf.h"

#include "fvm_io_num.h"
#include "fvm_periodicity.h"
#include "fvm_selector.h"

#include "cs_base.h"
#include "cs_halo.h"
#include "cs_halo_perio.h"
#include "cs_interface.h"
#include "cs_log.h"
#include "cs_mesh_halo.h"
#include "cs_numbering.h"
#include "cs_order.h"
#include "cs_mesh_quantities.h"
#include "cs_ext_neighborhood.h"
#include "cs_timer.h"

/*----------------------------------------------------------------------------
 *  Header for the current file
 *----------------------------------------------------------------------------*/

#include "cs_mesh.h"

/*----------------------------------------------------------------------------*/

BEGIN_C_DECLS

/*! \cond DOXYGEN_SHOULD_SKIP_THIS */

/*=============================================================================
 * Local Macro Definitions
 *============================================================================*/

#define CS_MESH_N_SUBS  5

/*============================================================================
 * Local structure definitions
 *============================================================================*/

/*=============================================================================
 * Local Macro definitions
 *============================================================================*/

/*============================================================================
 * Static global variables
 *============================================================================*/

cs_mesh_t  *cs_glob_mesh = NULL;  /* Pointer on the main mesh */

/*============================================================================
 * Private function definitions
 *============================================================================*/

/*----------------------------------------------------------------------------
 * Update cell family array in case of parallelism.
 *
 * This function aims at copying main values from cells in halo (id between 1
 * and n_cells) to ghost cells on distant ranks (id between n_cells + 1 to
 * n_cells_with_halo).
 *
 * parameters:
 *   mesh  <->  pointer to mesh structure
 *----------------------------------------------------------------------------*/

static void
_sync_cell_fam(cs_mesh_t   *const mesh)
{
  cs_halo_t  *halo = mesh->halo;

  if (halo == NULL)
    return;

  if (mesh->verbosity > 0)
    bft_printf(_("Synchronizing cell families\n"));

  cs_halo_sync_num(halo, CS_HALO_EXTENDED, mesh->cell_family);
}

/*----------------------------------------------------------------------------
 * Compute the minimum and the maximum of a vector (locally).
 *
 * parameters:
 *   n_vals    <-- local number of elements
 *   var       <-- pointer to vector
 *   min       --> minimum
 *   max       --> maximum
 *----------------------------------------------------------------------------*/

static void
_compute_local_minmax(cs_lnum_t        n_vals,
                      const cs_lnum_t  var[],
                      cs_lnum_t       *min,
                      cs_lnum_t       *max)
{
  cs_lnum_t  i;
  cs_lnum_t  _min = var[0], _max = var[0];

  for (i = 1; i < n_vals; i++) {
    _min = CS_MIN(_min, var[i]);
    _max = CS_MAX(_max, var[i]);
  }

  if (min != NULL)  *min = _min;
  if (max != NULL)  *max = _max;
}

/*----------------------------------------------------------------------------
 * Display the distribution of values of a integer vector.
 *
 * parameters:
 *   n_vals    <-- local number of elements
 *   var       <-- pointer to vector
 *----------------------------------------------------------------------------*/

static void
_display_histograms(cs_lnum_t        n_vals,
                    const cs_lnum_t  var[])
{
  cs_lnum_t  i, j, k, val_max, val_min;
  double step;

  cs_lnum_t count[CS_MESH_N_SUBS];
  cs_lnum_t n_steps = CS_MESH_N_SUBS;

  /* Compute local min and max */

  if (n_vals == 0) {
    bft_printf(_("    no value\n"));
    return;
  }

  val_max = var[0];
  val_min = var[0];
  _compute_local_minmax(n_vals, var, &val_min, &val_max);

  bft_printf(_("    minimum value =         %10d\n"), (int)val_min);
  bft_printf(_("    maximum value =         %10d\n\n"), (int)val_max);

  /* Define axis subdivisions */

  for (j = 0; j < n_steps; j++)
    count[j] = 0;

  if (val_max - val_min > 0) {

    if (val_max-val_min < n_steps)
      n_steps = CS_MAX(1, floor(val_max-val_min));

    step = (double)(val_max - val_min) / n_steps;

    /* Loop on values */

    for (i = 0; i < n_vals; i++) {

      /* Associated subdivision */

      for (j = 0, k = 1; k < n_steps; j++, k++) {
        if (var[i] < val_min + k*step)
          break;
      }
      count[j] += 1;

    }

    for (i = 0, j = 1; i < n_steps - 1; i++, j++)
      bft_printf("    %3d : [ %10d ; %10d [ = %10d\n",
                 i+1,
                 (int)(val_min + i*step),
                 (int)(val_min + j*step),
                 (int)(count[i]));

    bft_printf("    %3d : [ %10d ; %10d ] = %10d\n",
               n_steps,
               (int)(val_min + (n_steps - 1)*step),
               (int)val_max,
               (int)(count[n_steps - 1]));

  }

  else { /* if (val_max == val_min) */
    bft_printf("    %3d : [ %10d ; %10d ] = %10d\n",
               1, (int)(val_min), (int)val_max, (int)n_vals);
  }

}

/*----------------------------------------------------------------------------
 * Write a summary about halo features in listing
 *
 * parameters:
 *   mesh                   <-- pointer to cs_mesh_t structure
 *   interface_time         <-- time elapsed in interface build
 *   halo_time              <-- time elapsed in halo build
 *   ext_neighborhood_time  <-- time elapsed in extended neighborhood
 *                              connectivity building
 *----------------------------------------------------------------------------*/

static void
_print_halo_info(const cs_mesh_t  *mesh,
                 double            interface_time,
                 double            halo_time,
                 double            ext_neighborhood_time)
{
  /* Summary of the computional times */

  cs_log_printf(CS_LOG_PERFORMANCE,
                _("\nHalo creation times summary\n\n"));

  if (mesh->n_domains > 1 || mesh->n_init_perio > 0)
    cs_log_printf(CS_LOG_PERFORMANCE,
                  _("  Interface creation:                        %.3g s\n"),
                  interface_time);

  if (mesh->halo_type == CS_HALO_EXTENDED)
    cs_log_printf(CS_LOG_PERFORMANCE,
                  _("  Extended connectivity creation:            %.3g s\n"),
                  ext_neighborhood_time);

  cs_log_printf(CS_LOG_PERFORMANCE,
                _("  Halo creation:                             %.3g s\n\n"),
                halo_time);

  cs_log_printf(CS_LOG_PERFORMANCE,
                _("  Total time for halo creation:              %.3g s\n\n"),
                halo_time + interface_time + ext_neighborhood_time);

  cs_log_separator(CS_LOG_PERFORMANCE);
  cs_log_printf_flush(CS_LOG_PERFORMANCE);
}

/*----------------------------------------------------------------------------
 * Write a summary about cell neighbor features in listing
 *
 * parameters:
 *   mesh                   <-- pointer to cs_mesh_t structure
 *----------------------------------------------------------------------------*/

static void
_print_cell_neighbor_info(const cs_mesh_t  *mesh)
{
  cs_lnum_t i, j, k;
  float step;

  int n_steps = CS_MESH_N_SUBS;
  int n_min_neighbors = 0;
  int n_max_neighbors = 0;

  cs_gnum_t count[CS_MESH_N_SUBS];

  int  *n_cell_neighbors = NULL;

  /* Summary of the number of cell neighbors */

  BFT_MALLOC(n_cell_neighbors, mesh->n_cells_with_ghosts, int);

  for (i = 0; i < mesh->n_cells_with_ghosts; i++)
    n_cell_neighbors[i] = 0;

  for (i = 0; i < mesh->n_i_faces; i++) {
    cs_lnum_t c_id_0 = mesh->i_face_cells[i][0];
    cs_lnum_t c_id_1 = mesh->i_face_cells[i][1];
    n_cell_neighbors[c_id_0] += 1;
    n_cell_neighbors[c_id_1] += 1;
  }

  if (mesh->n_cells > 0)
    n_min_neighbors = n_cell_neighbors[0];

  for (i = 0; i < mesh->n_cells; i++) {
    if (n_cell_neighbors[i] < n_min_neighbors)
      n_min_neighbors = n_cell_neighbors[i];
    else if (n_cell_neighbors[i] > n_max_neighbors)
      n_max_neighbors = n_cell_neighbors[i];
  }

#if defined(HAVE_MPI)

  if (cs_glob_n_ranks > 1) {

    int n_g_min, n_g_max;

    MPI_Allreduce(&n_min_neighbors, &n_g_min, 1, MPI_INT, MPI_MIN,
                  cs_glob_mpi_comm);
    MPI_Allreduce(&n_max_neighbors, &n_g_max, 1, MPI_INT, MPI_MAX,
                  cs_glob_mpi_comm);

    n_min_neighbors = n_g_min;
    n_max_neighbors = n_g_max;
  }

#endif /* defined(HAVE_MPI) */

  bft_printf(_("\n Histogram of the number of interior faces per cell:\n\n"));

  bft_printf(_("    minimum value =         %10d\n"), n_min_neighbors);
  bft_printf(_("    maximum value =         %10d\n\n"), n_max_neighbors);

  /* Define axis subdivisions */

  for (i = 0; i < CS_MESH_N_SUBS; i++)
    count[i] = 0;

  if (n_max_neighbors - n_min_neighbors > 0) {

    if (n_max_neighbors - n_min_neighbors < n_steps)
      n_steps = n_max_neighbors - n_min_neighbors;

    step = (float)(n_max_neighbors - n_min_neighbors) / n_steps;

    /* Loop on values */

    for (i = 0; i < mesh->n_cells; i++) {

      /* Associated subdivision */
      for (j = 0, k = 1; k < n_steps; j++, k++) {
        if (n_cell_neighbors[i] < n_min_neighbors + k*step)
          break;
      }
      count[j] += 1;
    }

#if defined(HAVE_MPI)

    if (cs_glob_n_ranks > 1) {

      cs_gnum_t g_count[CS_MESH_N_SUBS];

      MPI_Allreduce(count, g_count, n_steps, CS_MPI_GNUM, MPI_SUM,
                    cs_glob_mpi_comm);

      for (i = 0; i < n_steps; i++)
        count[i] = g_count[i];
    }

#endif

    for (i = 0, j = 1; i < n_steps - 1; i++, j++)
      bft_printf("    %3d : [ %10d ; %10d [ = %10llu\n",
                 i+1,
                 (int)(n_min_neighbors + i*step),
                 (int)(n_min_neighbors + j*step),
                 (unsigned long long)(count[i]));

    bft_printf("    %3d : [ %10d ; %10d ] = %10llu\n",
               n_steps,
               (int)(n_min_neighbors + (n_steps - 1)*step),
               n_max_neighbors,
               (unsigned long long)(count[n_steps - 1]));
  }

  else { /* if (n_min_neighbors == n_max_neighbors) */
    bft_printf("    %3d : [ %10d ; %10d ] = %10llu\n",
               1, n_min_neighbors, n_max_neighbors,
               (unsigned long long)mesh->n_g_cells);

  }

  bft_printf("\n ----------------------------------------------------------\n");

  /* Cleanup */

  BFT_FREE(n_cell_neighbors);
}

/*----------------------------------------------------------------------------
 * Compare periodic couples in global numbering form (qsort function).
 *
 * parameters:
 *   x <-> pointer to first couple
 *   y <-> pointer to second couple
 *
 * returns:
 *   lexicographical
 *----------------------------------------------------------------------------*/

static int _compare_couples(const void *x, const void *y)
{
  int retval = 1;

  const cs_gnum_t *c0 = x;
  const cs_gnum_t *c1 = y;

  if (c0[0] < c1[0])
    retval = -1;

  else if (c0[0] == c1[0]) {
    if (c0[1] < c1[1])
      retval = -1;
    else if (c0[1] == c1[1])
      retval = 0;
  }

  return retval;
}

/*----------------------------------------------------------------------------
 * Define parameters for building an vertices interface set structure on
 * a given mesh.
 *
 * parameters:
 *   mesh              <-- pointer to mesh structure
 *   face_ifs          <-- pointer to face interface structure describing
 *                         periodic face couples
 *   p_n_perio_couples --> pointer to the number of periodic couples
 *   p_perio_couples   --> pointer to the periodic couple list
 *----------------------------------------------------------------------------*/

static void
_define_perio_vtx_couples(const cs_mesh_t      *mesh,
                          cs_interface_set_t   *face_ifs,
                          cs_lnum_t            *p_n_perio_couples[],
                          cs_gnum_t           **p_perio_couples[])
{
  cs_lnum_t *n_perio_couples = NULL;
  cs_gnum_t **perio_couples = NULL;

  int i, j;
  cs_lnum_t k, l;
  cs_lnum_t itf_start;

  int perio_count = 0;
  cs_lnum_t *send_index = NULL;
  cs_lnum_t *recv_index = NULL;
  cs_gnum_t *send_num = NULL, *recv_num = NULL;
  int  *tr_id = NULL;

  const int n_perio = mesh->n_init_perio;
  const int n_interfaces = cs_interface_set_size(face_ifs);
  const cs_lnum_t n_ifs_faces = cs_interface_set_n_elts(face_ifs);
  const cs_gnum_t *vtx_gnum = mesh->global_vtx_num;

  /* List direct and reverse transforms */

  BFT_MALLOC(n_perio_couples, n_perio, cs_lnum_t);
  BFT_MALLOC(perio_couples, n_perio, cs_gnum_t *);

  for (i = 0; i < n_perio; i++) {
    n_perio_couples[i] = 0;
    perio_couples[i] = NULL;
  }

  BFT_MALLOC(tr_id, n_perio*2, int);

  for (i = 0; i < n_perio*2; i++) {
    int rev_id = fvm_periodicity_get_reverse_id(mesh->periodicity, i);
    if (i < rev_id) {
      int parent_ids[2];
      fvm_periodicity_get_parent_ids(mesh->periodicity, i, parent_ids);
      if (parent_ids[0] < 0 && parent_ids[1] < 0) {
        tr_id[perio_count*2] = i + 1;
        tr_id[perio_count*2 + 1] = rev_id + 1;
        perio_count++;
      }
    }
  }
  assert(perio_count == n_perio);

  /* Count maximum vertex couples and build exchange index;
     count only couples in direct periodicity direction, as the number
     of faces in positive and reverse direction should match */

  BFT_MALLOC(send_index, n_ifs_faces + 1, cs_lnum_t);
  BFT_MALLOC(recv_index, n_ifs_faces + 1, cs_lnum_t);

  for (k = 0; k < n_ifs_faces + 1; k++) {
    send_index[k] = 0;
    recv_index[k] = 0;
  }

  for (i = 0, itf_start = 0; i < n_interfaces; i++) {

    const cs_interface_t *face_if = cs_interface_set_get(face_ifs, i);
    const cs_lnum_t *tr_index = cs_interface_get_tr_index(face_if);
    const cs_lnum_t *loc_id = cs_interface_get_elt_ids(face_if);

    for (j = 0; j < n_perio; j++) {

      const cs_lnum_t tr_start = tr_index[tr_id[j*2]];
      const cs_lnum_t tr_end = tr_index[tr_id[j*2] + 1];
      const cs_lnum_t rev_start = tr_index[tr_id[j*2+1]];
      const cs_lnum_t rev_end = tr_index[tr_id[j*2+1] + 1];

      for (k = rev_start; k < rev_end; k++) {
        cs_lnum_t l_id = loc_id[k];
        send_index[itf_start + k + 1]
          = (mesh->i_face_vtx_idx[l_id+1] - mesh->i_face_vtx_idx[l_id]);
      }
      for (k = tr_start; k < tr_end; k++) {
        cs_lnum_t l_id = loc_id[k];
        cs_lnum_t n_vtx = (  mesh->i_face_vtx_idx[l_id+1]
                           - mesh->i_face_vtx_idx[l_id]);
        recv_index[itf_start + k + 1] = n_vtx;
        n_perio_couples[j] += n_vtx;
      }
    }

    itf_start += cs_interface_size(face_if);

  }

  /* Transform count to index */

  for (k = 0; k < n_ifs_faces; k++) {
    send_index[k+1] += send_index[k];
    recv_index[k+1] += recv_index[k];
  }

  BFT_MALLOC(send_num, send_index[n_ifs_faces], cs_gnum_t);
  BFT_MALLOC(recv_num, recv_index[n_ifs_faces], cs_gnum_t);

  /* Prepare send buffer (send reverse transformation values) */

  for (i = 0, j = 0, l = 0; i < n_interfaces; i++) {

    const cs_interface_t *face_if = cs_interface_set_get(face_ifs, i);
    const cs_lnum_t *tr_index = cs_interface_get_tr_index(face_if);
    const cs_lnum_t *loc_id = cs_interface_get_elt_ids(face_if);

    for (j = 0; j < n_perio; j++) {

      const cs_lnum_t start_id = tr_index[tr_id[j*2+1]];
      const cs_lnum_t end_id = tr_index[tr_id[j*2+1] + 1];

      if (vtx_gnum != NULL) {

        for (k = start_id; k < end_id; k++) {
          cs_lnum_t v_id;
          cs_lnum_t f_id = loc_id[k];
          for (v_id = mesh->i_face_vtx_idx[f_id];
               v_id < mesh->i_face_vtx_idx[f_id + 1];
               v_id++)
            send_num[l++] = vtx_gnum[mesh->i_face_vtx_lst[v_id]];
        }

      }
      else {

        for (k = start_id; k < end_id; k++) {
          cs_lnum_t v_id;
          cs_lnum_t f_id = loc_id[k];
          for (v_id = mesh->i_face_vtx_idx[f_id];
               v_id < mesh->i_face_vtx_idx[f_id + 1];
               v_id++)
            send_num[l++] = mesh->i_face_vtx_lst[v_id] + 1;
        }

      }
    }
  }

  /* Exchange global vertex numbers */

  cs_interface_set_copy_indexed(face_ifs,
                                CS_GNUM_TYPE,
                                false, /* src_on_parent */
                                send_index,
                                recv_index,
                                send_num,
                                recv_num);

  BFT_FREE(send_num);
  BFT_FREE(recv_index);
  BFT_FREE(send_index);

  for (i = 0; i < n_perio; i++)
    BFT_MALLOC(perio_couples[i], n_perio_couples[i]*2, cs_gnum_t);

  /* Reset couples count */

  for (i = 0; i < n_perio; i++)
    n_perio_couples[i] = 0;

  /* Now fill couples */

  for (i = 0, j = 0, l = 0; i < n_interfaces; i++) {

    const cs_interface_t *face_if = cs_interface_set_get(face_ifs, i);
    const cs_lnum_t *tr_index = cs_interface_get_tr_index(face_if);
    const cs_lnum_t *loc_ids = cs_interface_get_elt_ids(face_if);

    for (j = 0; j < n_perio; j++) {

      cs_lnum_t nc = n_perio_couples[j]*2;
      const cs_lnum_t start_id = tr_index[tr_id[j*2]];
      const cs_lnum_t end_id = tr_index[tr_id[j*2] + 1];

      if (vtx_gnum != NULL) {

        for (k = start_id; k < end_id; k++) {
          cs_lnum_t v_id;
          cs_lnum_t f_id = loc_ids[k];
          for (v_id = mesh->i_face_vtx_idx[f_id];
               v_id < mesh->i_face_vtx_idx[f_id + 1];
               v_id++) {
            perio_couples[j][nc++] = vtx_gnum[mesh->i_face_vtx_lst[v_id]];
            perio_couples[j][nc++] = recv_num[l++];
          }
        }

      }
      else {

        for (k = start_id; k < end_id; k++) {
          cs_lnum_t v_id;
          cs_lnum_t f_id = loc_ids[k];
          for (v_id = mesh->i_face_vtx_idx[f_id];
               v_id < mesh->i_face_vtx_idx[f_id + 1];
               v_id++) {
            perio_couples[j][nc++] = mesh->i_face_vtx_lst[v_id] + 1;
            perio_couples[j][nc++] = recv_num[l++];
          }
        }
      }

      n_perio_couples[j] = nc/2;
    }
  }

  BFT_FREE(recv_num);
  BFT_FREE(tr_id);

  /* Finally, remove duplicate couples */

  for (i = 0; i < mesh->n_init_perio; i++) {

    if (n_perio_couples[i] > 1) {

      cs_lnum_t nc = n_perio_couples[i];
      cs_gnum_t *pc = perio_couples[i];

      qsort(pc, nc, sizeof(cs_gnum_t) * 2, &_compare_couples);

      for (k = 1, l = 0; k < nc; k++) {
        if ((pc[k*2] != pc[l*2]) && (pc[k*2+1] != pc[l*2+1])) {
          l += 1;
          pc[l*2] = pc[k*2];
          pc[l*2+1] = pc[k*2+1];
        }
      }
      n_perio_couples[i] = l+1;

      BFT_REALLOC(perio_couples[i], n_perio_couples[i]*2, cs_gnum_t);
    }
  }

  /* Set return values */

  *p_n_perio_couples = n_perio_couples;
  *p_perio_couples = perio_couples;
}

/*----------------------------------------------------------------------------
 * Assign a periodicity number and optionnaly a rank id to halo elements.
 *
 * parameters:
 *   mesh           <-- pointer to mesh structure
 *   halo_perio_num --> periodicity number associated with each halo cell,
 *                      signed for direct/reverse transform.
 *                      (size: mesh->n_ghost_cells)
 *   halo_rank_id   --> halo local rank id associated with each halo cell,
 *                      or NULL (size: mesh->n_ghost_cells)
 *
 * returns:
 *   the number of base periodicities defined
 *----------------------------------------------------------------------------*/

static int
_get_halo_perio_num(const cs_mesh_t  *mesh,
                    int               halo_perio_num[],
                    int               halo_rank_id[])
{
  int i, rank_id;
  cs_lnum_t j;

  int n_perio = 0;

  int *tr_id = NULL;

  const cs_halo_t  *halo = mesh->halo;
  const fvm_periodicity_t  *periodicity = mesh->periodicity;

  /* Initialization */

  assert(halo != NULL);
  assert(periodicity != NULL);

  /* List direct and non-combined transforms */

  BFT_MALLOC(tr_id, halo->n_transforms, int);
  for (i = 0; i < halo->n_transforms; i++)
    tr_id[i] = -1;

  n_perio = 0;

  for (i = 0; i < halo->n_transforms; i++) {
    int rev_id = fvm_periodicity_get_reverse_id(periodicity, i);
    if (i < rev_id) {
      int parent_ids[2];
      fvm_periodicity_get_parent_ids(periodicity, i, parent_ids);
      if (parent_ids[0] < 0 && parent_ids[1] < 0) {
        tr_id[n_perio*2] = i;
        tr_id[n_perio*2+1] = rev_id;
        n_perio++;
      }
    }
  }
  assert(n_perio == mesh->n_init_perio);

  BFT_REALLOC(tr_id, n_perio*2, int);
  assert(n_perio == mesh->n_init_perio);

  /* Initialize halo values */

  for (j = 0; j < mesh->n_ghost_cells; j++)
    halo_perio_num[j] = 0;

  if (halo_rank_id != NULL) {
    for (j = 0; j < mesh->n_ghost_cells; j++)
      halo_rank_id[j] = -1;
  }

  /* For each periodic face couple, we have 2 global ghost cells: one for
     the direct periodicity, one for the reverse. To match couples only
     once, we ignore the reverse periodicity, leaving exactly 1 ghost cell
     per couple (which may belong to multiple periodic faces). */

  /* Mark ghost cells with their periodicity number */

  for (i = 0; i < n_perio; i++) {

    cs_lnum_t shift, start, end;

    /* Direct periodicity */

    shift = 4 * halo->n_c_domains * tr_id[i*2];

    for (rank_id = 0; rank_id < halo->n_c_domains; rank_id++) {

      start = halo->perio_lst[shift + 4*rank_id];
      end = start + halo->perio_lst[shift + 4*rank_id + 1];

      for (j = start; j < end; j++)
        halo_perio_num[j] = i + 1;

      if (halo_rank_id != NULL) {
        for (j = start; j < end; j++)
          halo_rank_id[j] = rank_id;
      }
    }

    /* Reverse periodicity */

    shift = 4 * halo->n_c_domains * tr_id[i*2 + 1];

    for (rank_id = 0; rank_id < halo->n_c_domains; rank_id++) {

      start = halo->perio_lst[shift + 4*rank_id];
      end = start + halo->perio_lst[shift + 4*rank_id + 1];

      for (j = start; j < end; j++)
        halo_perio_num[j] = -(i + 1);

      if (halo_rank_id != NULL) {
        for (j = start; j < end; j++)
          halo_rank_id[j] = rank_id;
      }
    }
  }

  BFT_FREE(tr_id);

  return n_perio;
}

/*----------------------------------------------------------------------------
 * Build a cell -> face search structure for local cells with a periodic
 * face in the direct peridicity direction.
 *
 * The caller is responsible for freeing the arrays allocated and returned
 * by this function once they are no longer needed.
 *
 * parameters:
 *   mesh           <-- pointer to mesh structure
 *   halo_perio_num <-- periodicity number of ghost cells
 *   cell_face_idx  --> index (0 to n-1) of face ids for a given cell
 *   cell_face      --> face ids (0 to n-1) for a given cell
 *----------------------------------------------------------------------------*/

static void
_build_cell_face_perio_match(const cs_mesh_t    *mesh,
                             const int          *halo_perio_num,
                             cs_lnum_t         **cell_face_idx,
                             cs_lnum_t         **cell_face)
{
  cs_lnum_t i;

  cs_lnum_t *_cell_face_count, *_cell_face_idx, *_cell_face;

  /* Build cell -> face indexed search array containing only faces
     adjacent to the halo. */

  BFT_MALLOC(_cell_face_count, mesh->n_cells_with_ghosts, cs_lnum_t);
  BFT_MALLOC(_cell_face_idx, mesh->n_cells_with_ghosts + 1, cs_lnum_t);

  for (i = 0; i < mesh->n_cells_with_ghosts; i++)
    _cell_face_count[i] = 0;

  for (i = 0; i < mesh->n_i_faces; i++) {
    const cs_lnum_t c_id0 = mesh->i_face_cells[i][0];
    const cs_lnum_t c_id1 = mesh->i_face_cells[i][1];
    if (c_id0 < mesh->n_cells && c_id1 >= mesh->n_cells) {
      if (halo_perio_num[c_id1 - mesh->n_cells] < 0)
        _cell_face_count[c_id0] += 1;
    }
    else if (c_id1 < mesh->n_cells && c_id0 >= mesh->n_cells) {
      if (halo_perio_num[c_id0 - mesh->n_cells] < 0)
      _cell_face_count[c_id1] += 1;
    }
  }

  _cell_face_idx[0] = 0;
  for (i = 0; i < mesh->n_cells_with_ghosts; i++) {
    _cell_face_idx[i+1] = _cell_face_idx[i] + _cell_face_count[i];
    _cell_face_count[i] = 0;
  }

  BFT_MALLOC(_cell_face, _cell_face_idx[mesh->n_cells_with_ghosts], cs_lnum_t);

  for (i = 0; i < mesh->n_i_faces; i++) {
    const cs_lnum_t c_id0 = mesh->i_face_cells[i][0];
    const cs_lnum_t c_id1 = mesh->i_face_cells[i][1];
    if (c_id0 < mesh->n_cells && c_id1 >= mesh->n_cells) {
      if (halo_perio_num[c_id1 - mesh->n_cells] < 0) {
        _cell_face[_cell_face_idx[c_id0] + _cell_face_count[c_id0]] = i;
        _cell_face_count[c_id0] += 1;
      }
    }
    else if (c_id1 < mesh->n_cells && c_id0 >= mesh->n_cells) {
      if (halo_perio_num[c_id0 - mesh->n_cells] < 0) {
        _cell_face[_cell_face_idx[c_id1] + _cell_face_count[c_id1]] = i;
        _cell_face_count[c_id1] += 1;
      }
    }
  }

  BFT_FREE(_cell_face_count);

  *cell_face_idx = _cell_face_idx;
  *cell_face = _cell_face;
}

#if defined(HAVE_MPI)

/*----------------------------------------------------------------------------
 * Get global lists of periodic faces.
 *
 * The caller is responsible for freeing the arrays allocated and returned
 * by this function once they are no longer needed.
 *
 * parameters:
 *   mesh                 <-- pointer to mesh structure
 *   n_perio_face_couples --> local number of periodic couples per
 *                            periodicity (size: mesh->n_init_perio)
 *   perio_face_couples   --> arrays of global periodic couple face numbers,
 *                            for each periodicity
 *----------------------------------------------------------------------------*/

static void
_get_perio_faces_g(const cs_mesh_t    *mesh,
                   cs_lnum_t         **n_perio_face_couples,
                   cs_gnum_t        ***perio_face_couples)
{
  int         i, rank_id, perio_num;
  cs_lnum_t   j, k, l;
  cs_lnum_t   dest_c_id, src_c_id;

  cs_lnum_t   recv_size = 0;
  cs_lnum_t  *loc_cell_num = NULL;
  cs_lnum_t  *recv_count = NULL, *recv_idx = NULL;
  cs_lnum_t  *send_count = NULL, *send_idx = NULL;
  cs_lnum_t  *cell_face_idx, *cell_face;
  cs_gnum_t  *recv_vals = NULL, *send_vals = NULL;

  int  *halo_perio_num = NULL;
  int  *halo_rank_id = NULL;

  cs_lnum_t   *_n_perio_face_couples = NULL;
  cs_gnum_t  **_perio_face_couples = NULL;

  int           request_count = 0;
  MPI_Request  *halo_request = NULL;
  MPI_Status   *halo_status = NULL;

  const cs_halo_t  *halo = mesh->halo;
  const fvm_periodicity_t  *periodicity = mesh->periodicity;

  /* Initialization */

  BFT_MALLOC(_n_perio_face_couples, mesh->n_init_perio, cs_lnum_t);
  BFT_MALLOC(_perio_face_couples, mesh->n_init_perio, cs_gnum_t *);

  for (i = 0; i < mesh->n_init_perio; i++) {
    _n_perio_face_couples[i] = 0;
    _perio_face_couples[i] = NULL;
  }

  assert(halo != NULL);
  assert(periodicity != NULL);

  /* Mark ghost cells with their periodicity number and halo rank id */

  BFT_MALLOC(halo_perio_num, mesh->n_ghost_cells, int);
  BFT_MALLOC(halo_rank_id, mesh->n_ghost_cells, int);

  _get_halo_perio_num(mesh, halo_perio_num, halo_rank_id);

  /* Exchange local cell numbers, so that cell-face reverse matching
     is made easier later */

  BFT_MALLOC(loc_cell_num, mesh->n_cells_with_ghosts, cs_lnum_t);
  for (j = 0; j < mesh->n_cells; j++)
    loc_cell_num[j] = j+1;
  for (j = mesh->n_cells; j < mesh->n_cells_with_ghosts; j++)
    loc_cell_num[j] = 0;

  cs_halo_sync_num(halo, CS_HALO_STANDARD, loc_cell_num);

  /* Now compute send and receive counts and build indexes */

  BFT_MALLOC(send_count, halo->n_c_domains, cs_lnum_t);
  BFT_MALLOC(recv_count, halo->n_c_domains, cs_lnum_t);
  BFT_MALLOC(send_idx, halo->n_c_domains + 1, cs_lnum_t);
  BFT_MALLOC(recv_idx, halo->n_c_domains + 1, cs_lnum_t);

  for (i = 0; i < halo->n_c_domains; i++) {
    send_count[i] = 0;
    recv_count[i] = 0;
  }

  for (j = 0; j < mesh->n_i_faces; j++) {
    const cs_lnum_t h_id0 = mesh->i_face_cells[j][0] - mesh->n_cells;
    const cs_lnum_t h_id1 = mesh->i_face_cells[j][1] - mesh->n_cells;
    if (h_id0 >= 0) {
      perio_num = halo_perio_num[h_id0];
      if (perio_num > 0)
        send_count[halo_rank_id[h_id0]] += 1;
      else if (perio_num < 0)
        recv_count[halo_rank_id[h_id0]] += 1;
    }
    else if (h_id1 >= 0) {
      perio_num = halo_perio_num[h_id1];
      if (perio_num > 0)
        send_count[halo_rank_id[h_id1]] += 1;
      else if (perio_num < 0)
        recv_count[halo_rank_id[h_id1] ]+= 1;
    }
  }

  send_idx[0] = 0;
  recv_idx[0] = 0;
  for (i = 0; i < halo->n_c_domains; i++) {
    send_idx[i+1] = send_idx[i] + send_count[i];
    recv_idx[i+1] = recv_idx[i] + recv_count[i];
    send_count[i] = 0;
  }

  /* Assemble the tuples to send; a tuple contains:
     destination cell id (cell matched by direct periodicity),
     source cell (cell matched by reverse periodicity),
     periodicity number,
     global face number (2nd face in a couple). */

  BFT_MALLOC(send_vals, send_idx[halo->n_c_domains]*4, cs_gnum_t);

  for (j = 0; j < mesh->n_i_faces; j++) {

    const cs_lnum_t c_id0 = mesh->i_face_cells[j][0];
    const cs_lnum_t c_id1 = mesh->i_face_cells[j][1];

    dest_c_id = -1;
    if (c_id0 >= mesh->n_cells) {
      perio_num = halo_perio_num[c_id0  - mesh->n_cells];
      if (perio_num > 0) {
        dest_c_id = c_id1;
        src_c_id = c_id0;
        rank_id = halo_rank_id[c_id0  - mesh->n_cells];
      }
    }
    else if (c_id1 >= mesh->n_cells) {
      perio_num = halo_perio_num[c_id1 - mesh->n_cells];
      if (perio_num > 0) {
        dest_c_id = c_id0;
        src_c_id = c_id1;
        rank_id = halo_rank_id[c_id1  - mesh->n_cells];
      }
    }
    if (dest_c_id != -1) {
      k = send_idx[rank_id] + send_count[rank_id];
      send_vals[k*4] = loc_cell_num[dest_c_id];
      send_vals[k*4+1] = loc_cell_num[src_c_id];
      send_vals[k*4+2] = perio_num;
      send_vals[k*4+3] = mesh->global_i_face_num[j];
      send_count[rank_id] += 1;
    }
  }

  BFT_FREE(halo_rank_id);

  /* Now exchange face matching data */

  BFT_MALLOC(halo_request, halo->n_c_domains*2, MPI_Request);
  BFT_MALLOC(halo_status, halo->n_c_domains*2, MPI_Status);

  BFT_MALLOC(recv_vals, recv_idx[halo->n_c_domains]*4, cs_gnum_t);

  /* Receive data from distant ranks */

  for (rank_id = 0; rank_id < halo->n_c_domains; rank_id++) {
    if (recv_count[rank_id] > 0)
      MPI_Irecv(recv_vals + (recv_idx[rank_id]*4),
                recv_count[rank_id]*4,
                CS_MPI_GNUM,
                halo->c_domain_rank[rank_id],
                halo->c_domain_rank[rank_id],
                cs_glob_mpi_comm,
                &(halo_request[request_count++]));
  }

  /* Send data to distant ranks */

  for (rank_id = 0; rank_id < halo->n_c_domains; rank_id++) {
    if (send_count[rank_id] > 0)
      MPI_Isend(send_vals + (send_idx[rank_id]*4),
                send_count[rank_id]*4,
                CS_MPI_GNUM,
                halo->c_domain_rank[rank_id],
                cs_glob_rank_id,
                cs_glob_mpi_comm,
                &(halo_request[request_count++]));
  }

  /* Wait for all exchanges */

  MPI_Waitall(request_count, halo_request, halo_status);

  BFT_FREE(halo_request);
  BFT_FREE(halo_status);

  BFT_FREE(send_vals);
  BFT_FREE(send_count);
  BFT_FREE(send_idx);

  recv_size = recv_idx[halo->n_c_domains];

  BFT_FREE(recv_count);
  BFT_FREE(recv_idx);

  /* Count periodic face couples */

  for (j = 0; j < recv_size; j++) {
    perio_num = recv_vals[j*4+2];
    assert(perio_num > 0);
    _n_perio_face_couples[perio_num - 1] += 1;
  }

  /* Allocate periodic couple lists */

  for (i = 0; i < mesh->n_init_perio; i++) {
    BFT_MALLOC(_perio_face_couples[i],
               _n_perio_face_couples[i]*2,
               cs_gnum_t);
    _n_perio_face_couples[i] = 0;
  }

  /* Build cell -> face indexed search array containing only faces
     adjacent to the halo. */

  _build_cell_face_perio_match(mesh,
                               halo_perio_num,
                               &cell_face_idx,
                               &cell_face);

  /* Now match faces; faces already matched are marked so as not to be
     re-matched, in case faces have been split and multiple faces thus share
     the same cells (in which case we assume that subfaces are locally ordered
     identically). */

  for (j = 0; j <  recv_size; j++) {

    cs_lnum_t dest_c_num = recv_vals[j*4];
    cs_lnum_t src_c_num = recv_vals[j*4+1];
    int perio_id = recv_vals[j*4+2] - 1;
    cs_gnum_t perio_face_gnum = recv_vals[j*4+3];

    for (k = cell_face_idx[src_c_num-1]; k < cell_face_idx[src_c_num]; k++) {

      l = cell_face[k]; /* Face _id */

      if (l > -1) {
        cs_lnum_t loc_c_num, dist_c_id;
        if (mesh->i_face_cells[l][0] < mesh->i_face_cells[l][1]) {
          loc_c_num = mesh->i_face_cells[l][0] + 1;
          dist_c_id = mesh->i_face_cells[l][1];
        }
        else {
          loc_c_num = mesh->i_face_cells[l][1] + 1;
          dist_c_id = mesh->i_face_cells[l][0];
        }
        assert(loc_c_num <= mesh->n_cells && dist_c_id >= mesh->n_cells);

        /* If we have a match, update periodic couples */

        if (   src_c_num == loc_c_num
            && dest_c_num == loc_cell_num[dist_c_id]
            && halo_perio_num[dist_c_id-mesh->n_cells] == - (perio_id + 1)) {
          cs_lnum_t couple_id = _n_perio_face_couples[perio_id];
          cell_face[k] = -1; /* Mark as used */
          _perio_face_couples[perio_id][couple_id*2]
            = mesh->global_i_face_num[l];
          _perio_face_couples[perio_id][couple_id*2 + 1] = perio_face_gnum;
          _n_perio_face_couples[perio_id] += 1;
        }
      }
    }
  }

  BFT_FREE(halo_perio_num);

  BFT_FREE(cell_face_idx);
  BFT_FREE(cell_face);
  BFT_FREE(recv_vals);
  BFT_FREE(loc_cell_num);

  /* Set return values */

  *n_perio_face_couples = _n_perio_face_couples;
  *perio_face_couples = _perio_face_couples;
}

#endif /* defined(HAVE_MPI) */

/*----------------------------------------------------------------------------
 * Get global lists of periodic faces.
 *
 * This version is used for serial mode.
 *
 * The caller is responsible for freeing the arrays allocated and returned
 * by this function once they are no longer needed.
 *
 * parameters:
 *   mesh                 <-- pointer to mesh structure
 *   n_perio_face_couples --> global number of periodic couples per
 *                            periodicity (size: mesh->n_init_perio)
 *   perio_face_couples   --> arrays of global periodic couple face numbers,
 *                            for each periodicity
 *----------------------------------------------------------------------------*/

static void
_get_perio_faces_l(const cs_mesh_t    *mesh,
                   cs_lnum_t         **n_perio_face_couples,
                   cs_gnum_t        ***perio_face_couples)
{
  int        i, perio_num;
  cs_lnum_t  j, k, l;
  cs_lnum_t  dest_c_id, src_c_id;

  cs_lnum_t *loc_cell_num = NULL;
  cs_lnum_t *cell_face_idx, *cell_face;

  int *halo_perio_num = NULL;

  cs_lnum_t   *_n_perio_face_couples = NULL;
  cs_gnum_t  **_perio_face_couples = NULL;

  const cs_halo_t  *halo = mesh->halo;

  /* Initialization */

  BFT_MALLOC(_n_perio_face_couples, mesh->n_init_perio, cs_lnum_t);
  BFT_MALLOC(_perio_face_couples, mesh->n_init_perio, cs_gnum_t *);

  for (i = 0; i < mesh->n_init_perio; i++) {
    _n_perio_face_couples[i] = 0;
    _perio_face_couples[i] = NULL;
  }

  assert(halo != NULL);
  assert(halo->n_c_domains == 1);

  /* Mark ghost cells with their periodicity number */

  BFT_MALLOC(halo_perio_num, mesh->n_ghost_cells, int);

  _get_halo_perio_num(mesh, halo_perio_num, NULL);

  /* Exchange local cell numbers, so that cell-face reverse matching
     is made easier later */

  BFT_MALLOC(loc_cell_num, mesh->n_cells_with_ghosts, cs_lnum_t);
  for (j = 0; j < mesh->n_cells; j++)
    loc_cell_num[j] = j+1;
  for (j = mesh->n_cells; j < mesh->n_cells_with_ghosts; j++)
    loc_cell_num[j] = 0;

  cs_halo_sync_num(halo, CS_HALO_STANDARD, loc_cell_num);

  /* Now compute number of periodic couples */

  for (j = 0; j < mesh->n_i_faces; j++) {
    const cs_lnum_t h_id0 = mesh->i_face_cells[j][0] - mesh->n_cells;
    const cs_lnum_t h_id1 = mesh->i_face_cells[j][1] - mesh->n_cells;
    if (h_id0 >= 0) {
      if (halo_perio_num[h_id0] > 0)
        _n_perio_face_couples[halo_perio_num[h_id0] - 1] += 1;
    }
    else if (h_id1 >= 0) {
      if (halo_perio_num[h_id1] > 0)
        _n_perio_face_couples[halo_perio_num[h_id1] - 1] += 1;
    }
  }

  /* Allocate periodic couple lists */

  for (i = 0; i < mesh->n_init_perio; i++) {
    BFT_MALLOC(_perio_face_couples[i],
               _n_perio_face_couples[i]*2,
               cs_gnum_t);
    _n_perio_face_couples[i] = 0;
  }

  /* Build cell -> face indexed search array containing only faces
     adjacent to the halo. */

  _build_cell_face_perio_match(mesh,
                               halo_perio_num,
                               &cell_face_idx,
                               &cell_face);

  /* Now match faces; faces already matched are marked so as not to be
     re-matched, in case faces have been split and multiple faces thus share
     the same cells (in which case we assume that subfaces are locally ordered
     identically). */

  for (j = 0; j < mesh->n_i_faces; j++) {

    const cs_lnum_t c_id0 = mesh->i_face_cells[j][0];
    const cs_lnum_t c_id1 = mesh->i_face_cells[j][1];

    dest_c_id = -1;
    if (c_id0 >= mesh->n_cells) {
      perio_num = halo_perio_num[c_id0 - mesh->n_cells];
      if (perio_num > 0) {
        dest_c_id = c_id1;
        src_c_id = c_id0;
      }
    }
    else if (c_id1 >= mesh->n_cells) {
      perio_num = halo_perio_num[c_id1 - mesh->n_cells];
      if (perio_num > 0) {
        dest_c_id = c_id0;
        src_c_id = c_id1;
      }
    }
    if (dest_c_id != -1) {

      cs_lnum_t dest_c_num = loc_cell_num[dest_c_id];
      cs_lnum_t src_c_num = loc_cell_num[src_c_id];

      for (k = cell_face_idx[src_c_num-1]; k < cell_face_idx[src_c_num]; k++) {

        l = cell_face[k]; /* Face _id */

        if (l > -1) {
          cs_lnum_t loc_c_num, dist_c_id;
          if (mesh->i_face_cells[l][0] < mesh->i_face_cells[l][1]) {
            loc_c_num = mesh->i_face_cells[l][0] + 1;
            dist_c_id = mesh->i_face_cells[l][1];
          }
          else {
            loc_c_num = mesh->i_face_cells[l][1] + 1;
            dist_c_id = mesh->i_face_cells[l][0];
          }
          assert(loc_c_num <= mesh->n_cells && dist_c_id >= mesh->n_cells);

          /* If we have a match, update periodic couples */

          if (   src_c_num == loc_c_num
              && dest_c_num == loc_cell_num[dist_c_id]
              && halo_perio_num[dist_c_id-mesh->n_cells] == -perio_num) {
            int perio_id = perio_num - 1;
            cs_lnum_t couple_id = _n_perio_face_couples[perio_id];
            cell_face[k] = -1; /* Mark as used */
            _perio_face_couples[perio_id][couple_id*2] = l+1;
            _perio_face_couples[perio_id][couple_id*2 + 1] = j+1;
            _n_perio_face_couples[perio_id] += 1;
          }
        }
      }
    }
  }

  if (mesh->global_i_face_num != NULL) {
    for (i = 0; i < mesh->n_init_perio; i++) {
      for (j = 0; j < _n_perio_face_couples[i]*2; j++)
        _perio_face_couples[i][j]
          = mesh->global_i_face_num[_perio_face_couples[i][j] - 1];
    }
  }

  BFT_FREE(halo_perio_num);

  BFT_FREE(cell_face_idx);
  BFT_FREE(cell_face);
  BFT_FREE(loc_cell_num);

  /* Set return values */

  *n_perio_face_couples = _n_perio_face_couples;
  *perio_face_couples = _perio_face_couples;
}

/*----------------------------------------------------------------------------
 * Discard free (unreferenced) vertices from a mesh.
 *
 * parameters:
 *   mesh    <-> pointer to mesh structure
 *----------------------------------------------------------------------------*/

static void
_discard_free_vertices(cs_mesh_t  *mesh)
{
  cs_lnum_t  i;
  cs_lnum_t  n_vertices = 0;
  cs_lnum_t *new_vertex_id = NULL;

  /* Mark vertices */

  BFT_MALLOC(new_vertex_id, mesh->n_vertices, cs_lnum_t);

  for (i = 0; i < mesh->n_vertices; i++)
    new_vertex_id[i] = -1;

  for (i = 0; i < mesh->i_face_vtx_connect_size; i++)
    new_vertex_id[mesh->i_face_vtx_lst[i]] = 0;

  for (i = 0; i < mesh->b_face_vtx_connect_size; i++)
    new_vertex_id[mesh->b_face_vtx_lst[i]] = 0;

  /* Transform marker to mapping */

  for (i = 0; i < mesh->n_vertices; i++) {
    if (new_vertex_id[i] != -1)
      new_vertex_id[i] = n_vertices++;
  }

  /* Update local mesh structure if necessary */

  if (n_vertices < mesh->n_vertices) {

    /* Update face connectivity */

    for (i = 0; i < mesh->i_face_vtx_connect_size; i++)
      mesh->i_face_vtx_lst[i] = new_vertex_id[mesh->i_face_vtx_lst[i]];

    for (i = 0; i < mesh->b_face_vtx_connect_size; i++)
      mesh->b_face_vtx_lst[i] = new_vertex_id[mesh->b_face_vtx_lst[i]];

    /* Update vertex connectivity and global numbering */

    for (i = 0; i < mesh->n_vertices; i++) {
      int l;
      const cs_lnum_t j = new_vertex_id[i];
      if (j != -1) {
        for (l = 0; l < 3; l++)
          mesh->vtx_coord[j*3 + l] = mesh->vtx_coord[i*3 + l];
        if (mesh->global_vtx_num != NULL)
          mesh->global_vtx_num[j] = mesh->global_vtx_num[i];
      }
    }

    /* Update extended connectivity */

    if (mesh->gcell_vtx_lst != NULL) {
      const cs_lnum_t n = mesh->gcell_vtx_idx[mesh->n_ghost_cells];
      for (i = 0; i < n; i++)
        mesh->gcell_vtx_lst[i] = new_vertex_id[mesh->gcell_vtx_lst[i]];
    }

    /* Update mesh structure */

    mesh->n_vertices = n_vertices;

    BFT_REALLOC(mesh->vtx_coord, n_vertices*3, cs_real_t);

    if (mesh->global_vtx_num != NULL)
      BFT_REALLOC(mesh->global_vtx_num, n_vertices, cs_gnum_t);
  }

  if (mesh->vtx_interfaces != NULL)
    cs_interface_set_renumber(mesh->vtx_interfaces, new_vertex_id);

  BFT_FREE(new_vertex_id);

  /* Build an I/O numbering to compact the global numbering */

  if (cs_glob_n_ranks > 1) {

    fvm_io_num_t *tmp_num = fvm_io_num_create(NULL,
                                              mesh->global_vtx_num,
                                              mesh->n_vertices,
                                              0);

    if (mesh->n_vertices > 0)
      memcpy(mesh->global_vtx_num,
             fvm_io_num_get_global_num(tmp_num),
             mesh->n_vertices*sizeof(cs_gnum_t));

    mesh->n_g_vertices = fvm_io_num_get_global_count(tmp_num);

    assert(fvm_io_num_get_local_count(tmp_num) == (cs_lnum_t)mesh->n_vertices);

    tmp_num = fvm_io_num_destroy(tmp_num);

  }
  else { /* if (cs_glob_ranks == 1) */

    assert(mesh->global_vtx_num == NULL);
    mesh->n_g_vertices = mesh->n_vertices;

  }
}

/*----------------------------------------------------------------------------
 * Prepare local processor count for mesh stats.
 *
 * parameters:
 *   mesh          <-- pointer to mesh structure
 *   n_group_elts  --> number of cells, interior faces, boundary faces,
 *                     and isolated faces belonging to each group
 *                     (size: mesh->n_groups * 4, interleaved)
 *   n_perio_faces --> number of faces belonging to each group
 *                     (size: mesh->n_init_perio)
 *----------------------------------------------------------------------------*/

static void
_prepare_mesh_group_stats(const cs_mesh_t  *mesh,
                          cs_gnum_t         n_group_elts[],
                          cs_gnum_t         n_perio_faces[])
{
  cs_lnum_t i, j;

  int *i_face_flag = NULL;
  cs_lnum_t *f_count = NULL;

  /* In case of parallel and/or periodic faces, build a flag so as to count
     purely parallel faces only once, but periodic faces twice.
     The flag is defined to the periodicity number for periodic faces,
     0 for regular or purely parallel faces with an "outside" ghost cell,
     -1 for purely parallel faces with an "inside" ghost cell. */

  if (mesh->halo != NULL) {

    BFT_MALLOC(i_face_flag, mesh->n_i_faces, int);

    if (mesh->n_init_perio > 0) {
      cs_mesh_get_face_perio_num(mesh, i_face_flag);
      for (i = 0; i < mesh->n_i_faces; i++)
        if (i_face_flag[i] < 0)
          i_face_flag[i] = - i_face_flag[i];
    }
    else {
      for (i = 0; i < mesh->n_i_faces; i++)
        i_face_flag[i] = 0;
    }

    for (i = 0; i < mesh->n_i_faces; i++) {
      cs_lnum_t c_num_0 = mesh->i_face_cells[i][0] + 1;
      if (i_face_flag[i] == 0 && c_num_0 > mesh->n_cells)
        i_face_flag[i] = -1;
    }

  }

  /* Set counts to zero */

  BFT_MALLOC(f_count, mesh->n_families*4, cs_lnum_t);
  for (i = 0; i < mesh->n_families*4; i++)
    f_count[i] = 0;

  for (i = 0; i < mesh->n_init_perio; i++)
    n_perio_faces[i] = 0;

  /* Cell counters */

  for (i = 0; i < mesh->n_cells; i++)
    f_count[(mesh->cell_family[i] - 1) * 4] += 1;

  /* Interior face counters */

  if (i_face_flag != NULL) {
    for (i = 0; i < mesh->n_i_faces; i++) {
      const int flag = i_face_flag[i];
      if (flag > 0)
        n_perio_faces[flag - 1] += 1;
      if (flag > -1)
        f_count[(mesh->i_face_family[i] - 1) * 4 + 1] += 1;
    }
    BFT_FREE(i_face_flag);
  }
  else {
    for (i = 0; i < mesh->n_i_faces; i++)
      f_count[(mesh->i_face_family[i] - 1) * 4 + 1] += 1;
  }

  /* Boundary face counters */

  if (mesh->n_b_faces > 0) {
    for (i = 0; i < mesh->n_b_faces; i++) {
      int col = (mesh->b_face_cells[i] > -1) ? 2 : 3;
      f_count[(mesh->b_face_family[i] - 1) * 4 + col] += 1;
    }
  }

  /* Now transfer count from group classes to groups */

  for (i = 0; i < mesh->n_groups*4; i++)
    n_group_elts[i] = 0;

  for (i = 0; i < mesh->n_families; i++) {
    for (j = 0; j < mesh->n_max_family_items; j++) {
      int group_id = -1 - mesh->family_item[mesh->n_families*j + i];
      if (group_id >= 0) {
        int k;
        for (k = 0; k < 4; k++)
          n_group_elts[group_id*4 + k] += f_count[i*4 + k];
      }
    }
  }

  BFT_FREE(f_count);
}

/*----------------------------------------------------------------------------
 * Print mesh group statistics.
 *
 * parameters:
 *   mesh <-- pointer to mesh structure
 *----------------------------------------------------------------------------*/

static void
_print_mesh_group_stats(const cs_mesh_t  *mesh)
{
  int i;
  size_t count_size = mesh->n_groups*4 + mesh->n_init_perio;
  cs_gnum_t *count = NULL, *n_elt_groups = NULL, *n_perio_faces = NULL;

  if (count_size == 0)
    return;

  BFT_MALLOC(count, count_size, cs_gnum_t);

  n_elt_groups = count;
  n_perio_faces = count + mesh->n_groups*4;

  _prepare_mesh_group_stats(mesh, n_elt_groups, n_perio_faces);

#if defined(HAVE_MPI)
  if (cs_glob_n_ranks > 1) {
    cs_gnum_t *_count = NULL;
    BFT_MALLOC(_count, count_size, cs_gnum_t);
    MPI_Allreduce(count, _count, count_size, CS_MPI_GNUM, MPI_SUM,
                  cs_glob_mpi_comm);
    memcpy(count, _count, sizeof(cs_gnum_t)*count_size);
    BFT_FREE(_count);
  }
#endif

  /* Print perodic faces information */

  if (mesh->n_init_perio > 0) {


    bft_printf(_("\n Periodic faces (which are also interior faces):\n"));

    for (i = 0; i < mesh->n_init_perio; i++)
      bft_printf(_("     Periodicity %2d:          %llu face couples\n"),
                 i+1, (unsigned long long)(n_perio_faces[i]/2));

  }

  /* Print group information */

  if (mesh->n_groups > 0) {

    bft_printf(_("\n Groups:\n"));

    for (i = 0; i < mesh->n_groups; i++) {
      bft_printf("    \"%s\"\n", mesh->group_lst + (mesh->group_idx[i] - 1));
      if (n_elt_groups[i*4] > 0)
        bft_printf(_("       cells:          %12llu\n"),
                   (unsigned long long)(n_elt_groups[i*4]));
      if (n_elt_groups[i*4 + 1] > 0)
        bft_printf(_("       interior faces: %12llu\n"),
                   (unsigned long long)(n_elt_groups[i*4 + 1]));
      if (n_elt_groups[i*4 + 2] > 0)
        bft_printf(_("       boundary faces: %12llu\n"),
                   (unsigned long long)(n_elt_groups[i*4 + 2]));
      if (n_elt_groups[i*4 + 3] > 0)
        bft_printf(_("       isolated faces: %12llu\n"),
                   (unsigned long long)(n_elt_groups[i*4 + 2]));
    }

  }

  BFT_FREE(count);

  if (mesh->n_init_perio > 0 || mesh->n_groups > 0)
    bft_printf("\n");
}

/*----------------------------------------------------------------------------
 * Write a summary about mesh features in log file
 *
 * parameters:
 *   mesh                   <-- pointer to cs_mesh_t structure
 *----------------------------------------------------------------------------*/

static void
_print_mesh_info(cs_mesh_t  *mesh)
{
  cs_halo_t  *halo = mesh->halo;

  cs_lnum_t  *rank_buffer = NULL;

  /* Summary of cell and ghost cell distribution */

  if (mesh->n_domains > 1) {

    BFT_MALLOC(rank_buffer, mesh->n_domains, cs_lnum_t);

#if defined(HAVE_MPI)
    MPI_Allgather(&(mesh->n_cells), 1, CS_MPI_INT,
                  rank_buffer     , 1, CS_MPI_INT, cs_glob_mpi_comm);
#endif

    bft_printf(_("\n Histogram of the number of cells per rank:\n\n"));

    _display_histograms(mesh->n_domains, rank_buffer);

  } /* End if n_domains > 1 */

  else
    bft_printf
      (_(" Number of cells:                                      %d\n"),
       mesh->n_cells);


  bft_printf("\n ----------------------------------------------------------\n");

  if (mesh->n_domains > 1) {

#if defined(HAVE_MPI)
    MPI_Allgather(&(mesh->n_cells_with_ghosts), 1, CS_MPI_INT,
                  rank_buffer, 1, CS_MPI_INT, cs_glob_mpi_comm);
#endif

    bft_printf(_("\n Histogram of the number of standard + halo cells "
                 "per rank:\n\n"));

    _display_histograms(mesh->n_domains, rank_buffer);

  } /* End if n_domains > 1 */

  else
    bft_printf
      (_(" Number of cells + halo cells:                         %d\n\n"),
       mesh->n_cells_with_ghosts);


  bft_printf("\n ----------------------------------------------------------\n");

  if (halo != NULL) {

    cs_lnum_t  n_std_ghost_cells = halo->n_elts[CS_HALO_STANDARD];

    if (mesh->n_domains > 1) {

      cs_lnum_t  n_gcells = mesh->n_ghost_cells;

#if defined(HAVE_MPI)
      MPI_Allgather(&n_gcells  , 1, CS_MPI_INT,
                    rank_buffer, 1, CS_MPI_INT, cs_glob_mpi_comm);
#endif

      bft_printf
        (_("\n Histogram of the number of ghost cells per rank:\n\n"));

      _display_histograms(mesh->n_domains, rank_buffer);

      if (mesh->halo_type == CS_HALO_EXTENDED) {

#if defined(HAVE_MPI)
        MPI_Allgather(&n_std_ghost_cells, 1, CS_MPI_INT,
                      rank_buffer, 1, CS_MPI_INT, cs_glob_mpi_comm);
#endif

        bft_printf
          (_("\n"
             " Histogram of the number of ghost cells\n"
             " in the standard neighborhood per rank:\n\n"));

        _display_histograms(mesh->n_domains, rank_buffer);
      }

    } /* If n_ranks > 1 */

    else {
      bft_printf(_("\n Number of ghost cells:                          %10d\n"),
                 mesh->n_ghost_cells);
      if (mesh->halo_type == CS_HALO_EXTENDED)
        bft_printf(_("   in the standard neighborhood:              %10d\n"),
                   n_std_ghost_cells);
    }

    bft_printf("\n"
               " ----------------------------------------------------------\n");

  } /* End if halo != NULL */

  /* Summary of faces distribution */

  if (mesh->n_domains > 1) {

#if defined(HAVE_MPI)
    MPI_Allgather(&(mesh->n_i_faces), 1, CS_MPI_INT,
                  rank_buffer, 1, CS_MPI_INT, cs_glob_mpi_comm);
#endif

    bft_printf
      (_("\n Histogram of the number of interior faces per rank:\n\n"));

    _display_histograms(mesh->n_domains, rank_buffer);

  } /* End if n_domains > 1 */

  else
    bft_printf
      (_(" Number of interior faces:                             %d\n"),
       mesh->n_i_faces);

  bft_printf("\n ----------------------------------------------------------\n");

  if (mesh->n_domains > 1) {

#if defined(HAVE_MPI)
    MPI_Allgather(&(mesh->n_b_faces), 1, CS_MPI_INT,
                  rank_buffer, 1, CS_MPI_INT, cs_glob_mpi_comm);
#endif

    bft_printf
      (_("\n Histogram of the number of boundary faces per rank:\n\n"));

    _display_histograms(mesh->n_domains, rank_buffer);

  } /* End if n_domains > 1 */

  else
    bft_printf
      (_(" Number of boundary faces:                             %d\n"),
       mesh->n_b_faces);

  bft_printf("\n ----------------------------------------------------------\n");

  /* Add cell neighbor info */

  _print_cell_neighbor_info(mesh);

#if defined(HAVE_MPI)

  /* Summary of the number of neighbors */

  if (mesh->n_domains > 1) {

    cs_lnum_t  n_c_domains = halo->n_c_domains;

    MPI_Allgather(&n_c_domains, 1, CS_MPI_INT,
                  rank_buffer , 1, CS_MPI_INT, cs_glob_mpi_comm);

    bft_printf(_("\n Histogram of the number of neighboring domains "
                 "per rank:\n\n"));

    _display_histograms(mesh->n_domains, rank_buffer);

    bft_printf("\n"
               " ----------------------------------------------------------\n");

  } /* If n_domains > 1 */

#endif

  /* Cleanup */

  if (mesh->n_domains > 1)
    BFT_FREE(rank_buffer);

  bft_printf_flush();
}

/*! (DOXYGEN_SHOULD_SKIP_THIS) \endcond */

/*============================================================================
 *  Public function definitions for Fortran API
 *============================================================================*/

/*----------------------------------------------------------------------------
 * Update a scalar array in case of parallelism and/or periodicity.
 *
 * Fortran interface:
 *
 * subroutine synsca(var)
 * *****************
 *
 * var   : <-> : scalar array
 *----------------------------------------------------------------------------*/

void CS_PROCF(synsca, SYNSCA)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_scal(var);
}

/*----------------------------------------------------------------------------
 * Update a scalar array in case of parallelism and/or periodicity,
 * using an extended halo.
 *
 * Fortran interface:
 *
 * subroutine synsce(var)
 * *****************
 *
 * var   : <-> : scalar array
 *----------------------------------------------------------------------------*/

void CS_PROCF(synsce, SYNSCE)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_scal_ext(var);
}

/*----------------------------------------------------------------------------
 * Update a scalar array in case of parallelism and/or periodicity,
 * ignoring periodicity of rotation
 *
 * Fortran interface:
 *
 * subroutine syncmp(var)
 * *****************
 *
 * var   : <-> : scalar array
 *----------------------------------------------------------------------------*/

void CS_PROCF(syncmp, SYNCMP)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_component(var);
}

/*----------------------------------------------------------------------------
 * Update a vector array in case of parallelism and/or periodicity.
 *
 * Fortran interface:
 *
 * subroutine synvec(var)
 * *****************
 *
 * var1   : <-> : vector component 1 array
 * var2   : <-> : vector component 2 array
 * var3   : <-> : vector component 3 array
 *----------------------------------------------------------------------------*/

void CS_PROCF(synvec, SYNVEC)
(
 cs_real_t  var1[],
 cs_real_t  var2[],
 cs_real_t  var3[]
)
{
  cs_mesh_sync_var_vect_ni(var1, var2, var3);
}

/*----------------------------------------------------------------------------
 * Update a vector array in case of parallelism and/or periodicity.
 *
 * Fortran interface:
 *
 * subroutine synvin(var)
 * *****************
 *
 * var   : <-> : interleaved vector (of dimension 3)
 *----------------------------------------------------------------------------*/

void CS_PROCF(synvin, SYNVIN)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_vect(var);
}

/*----------------------------------------------------------------------------
 * Update a vector array in case of parallelism and/or periodicity,
 * using an extended halo.
 *
 * Fortran interface:
 *
 * subroutine synvin(var)
 * *****************
 *
 * var   : <-> : interleaved vector (of dimension 3)
 *----------------------------------------------------------------------------*/

void CS_PROCF(synvie, SYNVIE)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_vect_ext(var);
}

/*----------------------------------------------------------------------------
 * Update a vector array in case of parallelism and/or periodicity,
 * ignoring periodicity of rotation.
 *
 * Fortran interface:
 *
 * subroutine synvnr(var)
 * *****************
 *
 * var   : <-> : interleaved vector (of dimension 3)
 *----------------------------------------------------------------------------*/

void
CS_PROCF (synvnr, SYNVNR)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_vect_no_rotation(var);
}

/*----------------------------------------------------------------------------
 * Update a diagonal tensor array in case of parallelism and/or periodicity.
 *
 * Fortran interface:
 *
 * subroutine syndia(var)
 * *****************
 *
 * var11   : <-> : diagonal tensor component 11 array
 * var22   : <-> : diagonal tensor component 22 array
 * var33   : <-> : diagonal tensor component 33 array
 *----------------------------------------------------------------------------*/

void CS_PROCF(syndia, SYNDIA)
(
 cs_real_t  var11[],
 cs_real_t  var22[],
 cs_real_t  var33[]
)
{
  cs_mesh_sync_var_diag_ni(var11, var22, var33);
}

/*----------------------------------------------------------------------------
 * Update a tensor array in case of parallelism and/or periodicity.
 *
 * Fortran interface:
 *
 * subroutine synten(var)
 * *****************
 *
 * var11   : <-> : tensor component 11 array
 * var12   : <-> : tensor component 12 array
 * var13   : <-> : tensor component 13 array
 * var21   : <-> : tensor component 21 array
 * var22   : <-> : tensor component 22 array
 * var23   : <-> : tensor component 23 array
 * var31   : <-> : tensor component 31 array
 * var32   : <-> : tensor component 32 array
 * var33   : <-> : tensor component 33 array
 *----------------------------------------------------------------------------*/

void CS_PROCF(synten, SYNTEN)
(
 cs_real_t  var11[],
 cs_real_t  var12[],
 cs_real_t  var13[],
 cs_real_t  var21[],
 cs_real_t  var22[],
 cs_real_t  var23[],
 cs_real_t  var31[],
 cs_real_t  var32[],
 cs_real_t  var33[]
)
{
  cs_mesh_sync_var_tens_ni(var11, var12, var13,
                           var21, var22, var23,
                           var31, var32, var33);
}

/*----------------------------------------------------------------------------
 * Update a tensor array in case of parallelism and/or periodicity.
 *
 * Fortran interface:
 *
 * subroutine syntin(var)
 * *****************
 *
 * var   : <-> : interleaved tensor (of dimension 3x3)
 *----------------------------------------------------------------------------*/

void CS_PROCF(syntin, SYNTIN)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_tens(var);
}

/*----------------------------------------------------------------------------
 * Update a symmetric tensor array in case of parallelism and/or periodicity.
 *
 * Fortran interface:
 *
 * subroutine syntis(var)
 * *****************
 *
 * var   : <-> : interleaved symmetric tensor (of dimension 6)
 *----------------------------------------------------------------------------*/

void CS_PROCF(syntis, SYNTIS)
(
 cs_real_t  var[]
)
{
  cs_mesh_sync_var_sym_tens(var);
}

/*=============================================================================
 * Public function definitions
 *============================================================================*/

/*----------------------------------------------------------------------------
 * Create an empty mesh structure
 *
 * returns:
 *   pointer to created mesh structure
 *----------------------------------------------------------------------------*/

cs_mesh_t *
cs_mesh_create(void)
{
  cs_mesh_t  *mesh = NULL;

  BFT_MALLOC (mesh, 1, cs_mesh_t);

  /* General features */

  mesh->dim = 3;
  mesh->domain_num = cs_glob_rank_id + 1;
  mesh->n_domains = 0;

  /* Local dimensions */

  mesh->n_cells = 0;
  mesh->n_i_faces = 0;
  mesh->n_b_faces = 0;
  mesh->n_vertices = 0;
  mesh->i_face_vtx_connect_size = 0;
  mesh->b_face_vtx_connect_size = 0;

  /* Global dimensions */

  mesh->n_g_cells = 0;
  mesh->n_g_i_faces = 0;
  mesh->n_g_b_faces = 0;
  mesh->n_g_vertices = 0;

  /* Local structures */

  mesh->vtx_coord = NULL;
  mesh->i_face_cells = NULL;
  mesh->b_face_cells = NULL;
  mesh->i_face_vtx_idx = NULL;
  mesh->b_face_vtx_idx = NULL;
  mesh->i_face_vtx_lst = NULL;
  mesh->b_face_vtx_lst = NULL;

  /* Global numbering */

  mesh->global_cell_num = NULL;
  mesh->global_i_face_num = NULL;
  mesh->global_b_face_num = NULL;
  mesh->global_vtx_num = NULL;

  /* Periodic features */

  mesh->n_init_perio = 0;
  mesh->n_transforms = 0;
  mesh->have_rotation_perio = 0;
  mesh->periodicity = NULL;

  /* Halo features */

  mesh->vtx_interfaces = NULL;
  mesh->halo_type = CS_HALO_N_TYPES;
  mesh->n_ghost_cells = 0;
  mesh->n_cells_with_ghosts = 0;
  mesh->halo = NULL;

  /* Extended connectivity and neighborhood */

  mesh->n_b_cells = 0;
  mesh->b_cells = NULL;

  mesh->cell_cells_idx = NULL;
  mesh->cell_cells_lst = NULL;
  mesh->gcell_vtx_idx = NULL;
  mesh->gcell_vtx_lst = NULL;

  /* Numbering info */

  mesh->cell_numbering = NULL;
  mesh->i_face_numbering = NULL;
  mesh->b_face_numbering = NULL;

  /* Group and family features */

  mesh->n_groups = 0;
  mesh->group_idx = NULL;
  mesh->group_lst = NULL;

  mesh->n_max_family_items = 0;
  mesh->n_families = 0;

  mesh->family_item = NULL;
  mesh->cell_family = NULL;
  mesh->i_face_family = NULL;
  mesh->b_face_family = NULL;

  /* Selector features */

  mesh->class_defs = NULL;

  mesh->select_cells = NULL;
  mesh->select_i_faces = NULL;
  mesh->select_b_faces = NULL;

  /* Status flags */

  mesh->n_g_free_faces = 0;
  mesh->verbosity = 1;
  mesh->modified = 0;

  return (mesh);
}

/*----------------------------------------------------------------------------
 * Destroy a mesh structure.
 *
 * mesh       <->  pointer to a mesh structure
 *
 * returns:
 *   NULL pointer
 *----------------------------------------------------------------------------*/

cs_mesh_t *
cs_mesh_destroy(cs_mesh_t  *mesh)
{
  BFT_FREE(mesh->vtx_coord);
  BFT_FREE(mesh->i_face_cells);
  BFT_FREE(mesh->b_face_cells);
  BFT_FREE(mesh->i_face_vtx_idx);
  BFT_FREE(mesh->b_face_vtx_idx);
  BFT_FREE(mesh->i_face_vtx_lst);
  BFT_FREE(mesh->b_face_vtx_lst);

  BFT_FREE(mesh->global_cell_num);
  BFT_FREE(mesh->global_i_face_num);
  BFT_FREE(mesh->global_b_face_num);
  BFT_FREE(mesh->global_vtx_num);

  BFT_FREE(mesh->group_idx);
  BFT_FREE(mesh->group_lst);

  BFT_FREE(mesh->family_item);
  BFT_FREE(mesh->cell_family);
  BFT_FREE(mesh->i_face_family);
  BFT_FREE(mesh->b_face_family);

  /* Free periodic structures */

  if (mesh->n_init_perio > 0)
    mesh->periodicity = fvm_periodicity_destroy(mesh->periodicity);

  cs_mesh_free_rebuildable(mesh, true);

  BFT_FREE(mesh);

  return mesh;
}

/*----------------------------------------------------------------------------
 * Remove arrays and structures that may be rebuilt.
 *
 * mesh       <-> pointer to a mesh structure
 * free_halos <-- if true, free halos and parallel/periodic interface
 *                structures
 *----------------------------------------------------------------------------*/

void
cs_mesh_free_rebuildable(cs_mesh_t  *mesh,
                         bool        free_halos)
{
  /* Free structures that may be rebuilt */

  if (mesh->b_cells != NULL)
    BFT_FREE(mesh->b_cells);

  if (mesh->cell_cells_idx != NULL) {
    BFT_FREE(mesh->cell_cells_idx);
    BFT_FREE(mesh->cell_cells_lst);
  }

  if (mesh->gcell_vtx_idx != NULL) {
    BFT_FREE(mesh->gcell_vtx_idx);
    BFT_FREE(mesh->gcell_vtx_lst);
  }

  /* Free halo and interface structures */

  if (free_halos) {

    if (mesh == cs_glob_mesh)
      cs_halo_free_buffer();

    if (mesh->vtx_interfaces != NULL)
      cs_interface_set_destroy(&(mesh->vtx_interfaces));
    mesh->halo = cs_halo_destroy(mesh->halo);

  }

  /* Free numbering info */

  if (mesh->cell_numbering != NULL)
    cs_numbering_destroy(&(mesh->cell_numbering));
  if (mesh->i_face_numbering != NULL)
    cs_numbering_destroy(&(mesh->i_face_numbering));
  if (mesh->b_face_numbering != NULL)
    cs_numbering_destroy(&(mesh->b_face_numbering));

  /* Free selection structures */

  if (mesh->select_cells != NULL)
    mesh->select_cells = fvm_selector_destroy(mesh->select_cells);
  if (mesh->select_i_faces != NULL)
    mesh->select_i_faces = fvm_selector_destroy(mesh->select_i_faces);
  if (mesh->select_b_faces != NULL)
    mesh->select_b_faces = fvm_selector_destroy(mesh->select_b_faces);

  /* Destroy group class set after selectors, who reference it */

  if (mesh->class_defs != NULL)
    mesh->class_defs
      = fvm_group_class_set_destroy(mesh->class_defs);
}

/*----------------------------------------------------------------------------
 * Discard free (isolated) faces from a mesh.
 *
 * This should always be done before using the mesh for computation.
 *
 * parameters:
 *   mesh    <-> pointer to mesh structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_discard_free_faces(cs_mesh_t  *mesh)
{
  cs_lnum_t  i;
  cs_gnum_t  n_g_b_faces_old = 0, n_g_vertices_old = 0;
  cs_lnum_t  j = 0, k = 0, l = 0;

  if (mesh->n_g_free_faces == 0)
    return;

  n_g_b_faces_old = mesh->n_g_b_faces;
  n_g_vertices_old = mesh->n_g_vertices;

  for (i = 0; i < mesh->n_b_faces; i++) {

    if (mesh->b_face_cells[i] > -1) {

      mesh->b_face_cells[j] = mesh->b_face_cells[i];
      mesh->b_face_family[j] = mesh->b_face_family[i];

      mesh->b_face_vtx_idx[j] = l;
      for (k = mesh->b_face_vtx_idx[i]; k < mesh->b_face_vtx_idx[i+1]; k++)
        mesh->b_face_vtx_lst[l++] = mesh->b_face_vtx_lst[k];

      if (mesh->global_b_face_num != NULL)
        mesh->global_b_face_num[j] = mesh->global_b_face_num[i];

      j += 1;
    }

  }

  mesh->b_face_vtx_idx[j] = l;
  mesh->b_face_vtx_connect_size = l;

  /* Resize arrays if necessary */

  if (j < i) {

    BFT_REALLOC(mesh->b_face_cells, j, cs_lnum_t);
    BFT_REALLOC(mesh->b_face_family, j, int);
    BFT_REALLOC(mesh->b_face_vtx_idx, j+1, cs_lnum_t);
    BFT_REALLOC(mesh->b_face_vtx_lst, k, cs_lnum_t);
    if (mesh->global_b_face_num != NULL) {
      BFT_REALLOC(mesh->global_b_face_num, j, cs_gnum_t);
    }

    mesh->n_b_faces = j;
  }

  /* Build an I/O numbering on boundary faces to compact the global numbering */

  if (cs_glob_n_ranks > 1) {

    fvm_io_num_t *tmp_num = fvm_io_num_create(NULL,
                                              mesh->global_b_face_num,
                                              mesh->n_b_faces,
                                              0);

    if (mesh->n_b_faces > 0)
      memcpy(mesh->global_b_face_num,
             fvm_io_num_get_global_num(tmp_num),
             mesh->n_b_faces*sizeof(cs_gnum_t));

    mesh->n_g_b_faces = fvm_io_num_get_global_count(tmp_num);

    assert(fvm_io_num_get_local_count(tmp_num) == (cs_lnum_t)mesh->n_b_faces);

    tmp_num = fvm_io_num_destroy(tmp_num);

  }
  else { /* if (cs_glob_ranks == 1) */

    assert(mesh->global_b_face_num == NULL);
    mesh->n_g_b_faces = mesh->n_b_faces;

  }

  /* Now also clean-up unreferenced vertices */

  _discard_free_vertices(mesh);

  bft_printf(_("\n"
               " Removed %llu isolated faces\n"
               "     Number of initial vertices:  %llu\n"
               "     Number of vertices:          %llu\n\n"),
             (unsigned long long)(n_g_b_faces_old - mesh->n_g_b_faces),
             (unsigned long long)(n_g_vertices_old),
             (unsigned long long)(mesh->n_g_vertices));

  mesh->n_g_free_faces = 0;
}

/*----------------------------------------------------------------------------
 * Compute global face connectivity size.
 *
 * Faces on simple parallel boundaries are counted only once, but periodic
 * faces are counted twice.
 *
 * parameters:
 *   mesh                   <-- pointer to a cs_mesh_t structure
 *   g_i_face_vertices_size --> global interior face connectivity size, or NULL
 *   g_b_face_vertices_size --> global boundary face connectivity size, or NULL
 *----------------------------------------------------------------------------*/

void
cs_mesh_g_face_vertices_sizes(const cs_mesh_t  *mesh,
                              cs_gnum_t        *g_i_face_vertices_size,
                              cs_gnum_t        *g_b_face_vertices_size)
{
  cs_gnum_t  _g_face_vertices_size[2] = {0, 0};

#if defined(HAVE_MPI)

  if (cs_glob_n_ranks > 1) {

    cs_lnum_t i;
    cs_gnum_t _l_face_vertices_size[2] = {0, 0};

    /* Without periodicity, count faces bordering halo once */

    if (mesh->n_init_perio == 0) {
      for (i = 0; i < mesh->n_i_faces; i++) {
        if (mesh->i_face_cells[i][0] < mesh->n_cells)
          _l_face_vertices_size[0] += (  mesh->i_face_vtx_idx[i+1]
                                       - mesh->i_face_vtx_idx[i]);
      }
    }

    /* With periodicity, count faces bordering halo once for purely parallel
       halo */

    else {

      cs_lnum_t  rank_id, t_id, shift;
      cs_lnum_t  start = 0, end = 0;
      int *perio_flag = NULL;

      const cs_halo_t *halo = mesh->halo;
      const cs_lnum_t  n_transforms = halo->n_transforms;

      BFT_MALLOC(perio_flag, mesh->n_ghost_cells, int);
      for (i = 0; i < mesh->n_ghost_cells; i++)
        perio_flag[i] = 0;

      for (t_id = 0; t_id < n_transforms; t_id++) {
        shift = 4 * halo->n_c_domains * t_id;
        for (rank_id = 0; rank_id < halo->n_c_domains; rank_id++) {
          start = halo->perio_lst[shift + 4*rank_id];
          end = start + halo->perio_lst[shift + 4*rank_id + 1];
          for (i = start; i < end; i++)
            perio_flag[i] = 1;
        }
      }

      for (i = 0; i < mesh->n_i_faces; i++) {
        int count_face = 1;
        if (mesh->i_face_cells[i][0] >= mesh->n_cells) {
          if (perio_flag[mesh->i_face_cells[i][0] - mesh->n_cells] == 0)
            count_face = 0;
        }
        if (count_face)
          _l_face_vertices_size[0] += (  mesh->i_face_vtx_idx[i+1]
                                       - mesh->i_face_vtx_idx[i]);
      }

      BFT_FREE(perio_flag);
    }

    _l_face_vertices_size[1] = mesh->b_face_vtx_connect_size;

    MPI_Allreduce(&_l_face_vertices_size, &_g_face_vertices_size, 2,
                  CS_MPI_GNUM, MPI_SUM, cs_glob_mpi_comm);
  }

#endif /* defined(HAVE_MPI) */

  if (cs_glob_n_ranks == 1) {
    _g_face_vertices_size[0] = mesh->i_face_vtx_connect_size;
    _g_face_vertices_size[1] = mesh->b_face_vtx_connect_size;
  }

  if (g_i_face_vertices_size != NULL)
    *g_i_face_vertices_size = _g_face_vertices_size[0];
  if (g_b_face_vertices_size != NULL)
    *g_b_face_vertices_size = _g_face_vertices_size[1];
}

/*----------------------------------------------------------------------------
 * Compute or update mesh structure members that depend on other members,
 * but whose results may be reused, such as global number of elements
 * (cells, vertices, internal and border faces) and sync cell family.
 *
 * parameters:
 *   mesh  <->  pointer to a cs_mesh_t structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_update_auxiliary(cs_mesh_t  *mesh)
{
  cs_lnum_t  i;

#if defined(HAVE_MPI)

  if (cs_glob_n_ranks > 1) {

    cs_gnum_t  n_g_elts[4], max_elt_num[4];

    if (mesh->verbosity > 0)
      bft_printf(_("\n Global definition of the number of elements "
                   "(cells, vertices, faces...)\n"));

    /* Global dimensions of the mesh */

    max_elt_num[0] = mesh->n_cells;
    MPI_Allreduce(max_elt_num, n_g_elts, 1, CS_MPI_GNUM, MPI_SUM,
                  cs_glob_mpi_comm);

    max_elt_num[1] = 0;
    for (i = 0; i < mesh->n_i_faces; i++) {
      if (mesh->global_i_face_num[i] > max_elt_num[1])
        max_elt_num[1] = mesh->global_i_face_num[i];
    }

    max_elt_num[2] = 0;
    for (i = 0; i < mesh->n_b_faces; i++) {
      if (mesh->global_b_face_num[i] > max_elt_num[2])
        max_elt_num[2] = mesh->global_b_face_num[i];
    }

    max_elt_num[3] = 0;
    for (i = 0; i < mesh->n_vertices; i++) {
      if (mesh->global_vtx_num[i] > max_elt_num[3])
        max_elt_num[3] = mesh->global_vtx_num[i];
    }

    MPI_Allreduce(max_elt_num + 1, n_g_elts + 1, 3, CS_MPI_GNUM, MPI_MAX,
                  cs_glob_mpi_comm);

    mesh->n_g_cells = n_g_elts[0];
    mesh->n_g_i_faces = n_g_elts[1];
    mesh->n_g_b_faces = n_g_elts[2];
    mesh->n_g_vertices = n_g_elts[3];

  }

#endif

  /* Sync cell family array (also in case of periodicity) */

  _sync_cell_fam(mesh);

  /* Number of boundary cells */

  {
    cs_lnum_t n_b_cells = 0;
    _Bool *flag = NULL;

    BFT_MALLOC(flag, mesh->n_cells, _Bool);

    for (i = 0; i < mesh->n_cells; i++)
      flag[i] = false;

    for (i = 0; i < mesh->n_b_faces; i++) {
      if (mesh->b_face_cells[i] > -1)
        flag[mesh->b_face_cells[i]] = true;
    }

    for (i = 0, n_b_cells = 0; i < mesh->n_cells; i++) {
      if (flag[i] == true)
        n_b_cells++;
    }

    mesh->n_b_cells = n_b_cells;
    BFT_REALLOC(mesh->b_cells, mesh->n_b_cells, cs_lnum_t);

    for (i = 0, n_b_cells = 0; i < mesh->n_cells; i++) {
      if (flag[i] == true)
        mesh->b_cells[n_b_cells++] = i;
    }

    BFT_FREE(flag);
  }
}

/*----------------------------------------------------------------------------
 * Creation and initialization of halo structures.
 *
 * Treatment of parallel and/or periodic halos for standard and extended
 * ghost cells according to halo type requested by global options.
 *
 * parameters:
 *   mesh       <->  pointer to mesh structure
 *   mb         <->  pointer to mesh builder (in case of periodicity)
 *   halo_type  <->  type of halo (standard or extended)
 *----------------------------------------------------------------------------*/

void
cs_mesh_init_halo(cs_mesh_t          *mesh,
                  cs_mesh_builder_t  *mb,
                  cs_halo_type_t      halo_type)
{
  cs_lnum_t  i;
  double  t1, t2;
  double  halo_time = 0, interface_time = 0, ext_neighborhood_time = 0;

  int  *perio_num = NULL;
  cs_lnum_t  *gcell_vtx_idx = NULL, *gcell_vtx_lst = NULL;
  cs_lnum_t  *n_periodic_couples = NULL;
  cs_gnum_t  *g_i_face_num = NULL;
  cs_gnum_t  *g_vertex_num = NULL;
  cs_gnum_t  **periodic_couples = NULL;

  cs_interface_set_t  *face_interfaces = NULL;

  const cs_lnum_t  n_i_faces = mesh->n_i_faces;
  const cs_lnum_t  n_vertices = mesh->n_vertices;

  /* Build halo */

  mesh->halo_type = halo_type;

  if (mesh->n_domains > 1 || mesh->n_init_perio > 0) {

    t1 = cs_timer_wtime();

    if (mesh->verbosity > 0)
      bft_printf("\n"
                 " ----------------------------------------------------------"
                 "\n");

    if (mesh->periodicity != NULL) {
      if (fvm_periodicity_get_n_levels(mesh->periodicity) == 1) {
        if (mesh->verbosity > 0)
          bft_printf(_(" Composing periodicities\n"));
        fvm_periodicity_combine(mesh->periodicity, 0);
      }
    }

    if (mesh->verbosity > 0) {
      if (halo_type ==  CS_HALO_EXTENDED)
        bft_printf(_("\n Halo construction with extended neighborhood\n"
                     " ============================================\n\n"));

      else
        bft_printf(_("\n Halo construction with standard neighborhood\n"
                     " ============================================\n\n"));
    }

    /* Build periodic numbering */

    if (mesh->n_init_perio > 0) {
      BFT_MALLOC(perio_num, mesh->n_init_perio, int);
      for (i = 0; i < mesh->n_init_perio; i++)
        perio_num[i] = i+1;
    }

    if (mesh->verbosity > 0)
      bft_printf(_(" Face interfaces creation\n"));

    /* Build purely parallel cs_interface_set structure */

    g_i_face_num = mesh->global_i_face_num;
    g_vertex_num = mesh->global_vtx_num;

    if (g_i_face_num == NULL) {
      BFT_MALLOC(g_i_face_num, n_i_faces, cs_gnum_t);
      for (i = 0; i < n_i_faces; i++)
        g_i_face_num[i] = (cs_gnum_t)i+1;
    }

    if (mb != NULL) {
      face_interfaces = cs_interface_set_create(n_i_faces,
                                                NULL,
                                                g_i_face_num,
                                                mesh->periodicity,
                                                mesh->n_init_perio,
                                                perio_num,
                                                mb->n_per_face_couples,
                      (const cs_gnum_t *const *)(mb->per_face_couples));
      for (i = 0; i < mb->n_perio; i++)
        BFT_FREE(mb->per_face_couples[i]);
      BFT_FREE(mb->per_face_couples);
      BFT_FREE(mb->n_per_face_couples);
      mb->n_perio = 0;
    }
    else
      face_interfaces = cs_interface_set_create(n_i_faces,
                                                NULL,
                                                g_i_face_num,
                                                mesh->periodicity,
                                                0,
                                                NULL,
                                                NULL,
                                                NULL);

    if (mesh->global_i_face_num != g_i_face_num)
      BFT_FREE(g_i_face_num);

    if (g_vertex_num == NULL) {
      BFT_MALLOC(g_vertex_num, n_vertices, cs_gnum_t);
      for (i = 0; i < n_vertices; i++)
        g_vertex_num[i] = (cs_gnum_t)i+1;
    }

    if (mesh->n_init_perio > 0) {

      mesh->n_transforms = fvm_periodicity_get_n_transforms(mesh->periodicity);

      bft_printf(_(" Definition of periodic vertices\n"));

      _define_perio_vtx_couples(mesh,
                                face_interfaces,
                                &n_periodic_couples,
                                &periodic_couples);

#if 0 /* For debugging purposes */
      for (i = 0; i < mesh->n_init_perio; i++) {
        cs_lnum_t  j;
        bft_printf("\n\n  Periodicity number: %d\n", perio_num[i]);
        bft_printf("  Number of couples : %d\n", n_periodic_couples[i]);
        for (j = 0; j < n_periodic_couples[i]; j++)
          bft_printf("%12d --> %12d\n",
                     periodic_couples[i][2*j], periodic_couples[i][2*j + 1]);
      }
      fvm_periodicity_dump(mesh->periodicity);
#endif

    }

    if (mesh->verbosity > 0)
      bft_printf(_(" Vertex interfaces creation\n"));

    mesh->vtx_interfaces = cs_interface_set_create(n_vertices,
                                                   NULL,
                                                   g_vertex_num,
                                                   mesh->periodicity,
                                                   mesh->n_init_perio,
                                                   perio_num,
                                                   n_periodic_couples,
                         (const cs_gnum_t *const *)periodic_couples);

    if (mesh->global_vtx_num != g_vertex_num)
      BFT_FREE(g_vertex_num);

    BFT_FREE(perio_num);
    BFT_FREE(n_periodic_couples);

    for (i = 0; i < mesh->n_init_perio; i++)
      BFT_FREE(periodic_couples[i]);
    BFT_FREE(periodic_couples);

#if 0 /* For debugging purposes */
    bft_printf("Dump final vertices interface:\n");
    cs_interface_set_add_match_ids(mesh->vtx_interfaces);
    cs_interface_set_dump(mesh->vtx_interfaces);
    cs_interface_set_free_match_ids(mesh->vtx_interfaces);
#endif

    t2 = cs_timer_wtime();
    interface_time = t2-t1;

    t1 = cs_timer_wtime();

    /* Creation of the cs_halo_t structure. */

    if (mesh->verbosity > 0) {
      bft_printf(_(" Halo creation\n"));
      bft_printf_flush();
    }

    mesh->halo = cs_halo_create(mesh->vtx_interfaces);

    if (mesh->verbosity > 0) {
      bft_printf(_(" Halo definition\n"));
      bft_printf_flush();
    }

    cs_mesh_halo_define(mesh,
                        face_interfaces,
                        mesh->vtx_interfaces,
                        &gcell_vtx_idx,
                        &gcell_vtx_lst);

    cs_interface_set_destroy(&face_interfaces);

    t2 = cs_timer_wtime();
    halo_time = t2-t1;

  } /* end if (mesh->n_domains > 1 || mesh->n_init_perio > 0) */

  /* Define a cell -> cells connectivity for the extended neighborhood
     if necessary */

  if (halo_type ==  CS_HALO_EXTENDED) {

    t1 = cs_timer_wtime();
    if (mesh->verbosity > 0) {
      bft_printf(_(" Extended neighborhood structures definition\n"));
      bft_printf_flush();
    }

    mesh->gcell_vtx_idx = gcell_vtx_idx;
    mesh->gcell_vtx_lst = gcell_vtx_lst;

    cs_ext_neighborhood_define(mesh);

    bft_printf_flush();
    t2 = cs_timer_wtime();
    ext_neighborhood_time = t2-t1;

  }
  else {
    BFT_FREE(gcell_vtx_idx);
    BFT_FREE(gcell_vtx_lst);
  }

  /* Output for listing */

  if (mesh->verbosity > 0) {

    if (mesh->halo_type != CS_HALO_N_TYPES)
      _print_halo_info(mesh,
                       interface_time,
                       halo_time,
                       ext_neighborhood_time);

    else if (halo_type ==  CS_HALO_EXTENDED) {
      cs_log_printf(CS_LOG_PERFORMANCE,
                    _("\nExtended connectivity creation (%.3g s)\n"),
                    ext_neighborhood_time);
      cs_log_printf(CS_LOG_PERFORMANCE, "\n");
      cs_log_separator(CS_LOG_PERFORMANCE);
    }

    _print_mesh_info(mesh);

  }
}

/*----------------------------------------------------------------------------
 * Get the global number of ghost cells.
 *
 * parameters:
 *   mesh  <--  pointer to a mesh structure
 *
 * returns:
 *   global number of ghost cells
 *---------------------------------------------------------------------------*/

cs_gnum_t
cs_mesh_n_g_ghost_cells(cs_mesh_t  *mesh)
{
  cs_gnum_t  n_g_ghost_cells = mesh->n_ghost_cells;

#if defined(HAVE_MPI)
  if (cs_glob_n_ranks > 1) {
    cs_gnum_t  _n_g_ghost_cells = n_g_ghost_cells;
    MPI_Allreduce(&_n_g_ghost_cells, &n_g_ghost_cells, 1, CS_MPI_GNUM,
                  MPI_SUM, cs_glob_mpi_comm);
  }
#endif

  return n_g_ghost_cells;
}

/*----------------------------------------------------------------------------
 * Order family numbers and remove duplicates
 *
 * parameters
 *   mesh <-> pointer to mesh structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_clean_families(cs_mesh_t  *mesh)
{
  size_t i, j, gc_id, gc_id_prev;
  int max_val = 0;
  size_t gc_count = 0;
  size_t n_gc = mesh->n_families;
  size_t n_gc_vals = mesh->n_max_family_items;
  size_t size_tot = n_gc * n_gc_vals;
  cs_gnum_t *interlaced = NULL;
  int *order = NULL, *renum = NULL;

  if (mesh->n_families < 2)
    return;

  /* Build and order interlaced copy with only positive values */

  BFT_MALLOC(interlaced, size_tot, cs_gnum_t);

  for (i = 0; i < size_tot; i++) {
    int val = mesh->family_item[i];
    if (val > max_val)
      max_val = val;
  }

  for (i = 0; i < n_gc; i++) {
    for (j = 0; j < n_gc_vals; j++) {
      int val = mesh->family_item[j*n_gc + i];
      if (val < 0)
        val = -val + max_val;
      interlaced[i*n_gc_vals + j] = val;
    }
  }

  order = cs_order_gnum_s(NULL, interlaced, n_gc_vals, n_gc);

  /* Prepare removal of duplicates and renumbering */

  BFT_MALLOC(renum, n_gc, int);

  gc_id = order[0];
  gc_id_prev = gc_id;
  gc_count = 1;
  renum[gc_id] = 0;

  for (i = 1; i < n_gc; i++) {
    char is_same = '\1';
    gc_id = order[i];
    for (j = 0; j < n_gc_vals; j++) {
      if (   interlaced[gc_id_prev*n_gc_vals + j]
          != interlaced[gc_id*n_gc_vals + j])
        is_same = '\0';
    }
    if (is_same != '\1') {
      gc_id_prev = gc_id;
      gc_count += 1;
    }
    renum[gc_id] = gc_count - 1;
  }

  /* Update definitions */

  mesh->n_families = gc_count;
  BFT_REALLOC(mesh->family_item, gc_count*n_gc_vals, cs_lnum_t);

  for (i = 0; i < n_gc; i++) {
    gc_id = renum[i];
    for (j = 0; j < n_gc_vals; j++)
      mesh->family_item[j*gc_count + gc_id] = interlaced[i*n_gc_vals + j];
  }

  size_tot = gc_count * n_gc_vals;
  for (i = 0; i < size_tot; i++) {
    int val = mesh->family_item[i];
    if (val > max_val)
      val = -(val - max_val);
    mesh->family_item[i] = val;
  }

  BFT_FREE(interlaced);
  BFT_FREE(order);

  /* Update references */

  if (mesh->cell_family != NULL) {
    for (i = 0; i < (size_t)(mesh->n_cells); i++) {
      int val = mesh->cell_family[i];
      if (val != 0)
        mesh->cell_family[i] = renum[val -1] + 1;
    }
  }

  if (mesh->i_face_family != NULL) {
    for (i = 0; i < (size_t)(mesh->n_i_faces); i++) {
      int val = mesh->i_face_family[i];
      if (val != 0)
        mesh->i_face_family[i] = renum[val - 1] + 1;
    }
  }

  if (mesh->b_face_family != NULL) {
    for (i = 0; i < (size_t)(mesh->n_b_faces); i++) {
      int val = mesh->b_face_family[i];
      if (val != 0)
        mesh->b_face_family[i] = renum[val - 1] + 1;
    }
  }

  BFT_FREE(renum);
}

/*----------------------------------------------------------------------------
 * Create group classes based on a mesh's family definitions.
 *
 * parameters:
 *   mesh <-- pointer to mesh structure
 *
 * returns:
 *   pointer to group classes structure based on mesh's family definitions
 *----------------------------------------------------------------------------*/

fvm_group_class_set_t *
cs_mesh_create_group_classes(cs_mesh_t  *mesh)
{
  int  i, j;
  int  grp_nbr, grp_num, grp_idx;

  char **group = NULL;

  fvm_group_class_set_t *class_defs = fvm_group_class_set_create();

  /* Construction of the fvm_group_class structure */

  BFT_MALLOC(group, mesh->n_max_family_items, char*);

  for (i = 0; i < mesh->n_families; i++) {

    grp_nbr  = 0;

    for (j = 0; j <  mesh->n_max_family_items; j++) {

      if (mesh->family_item[j * mesh->n_families + i] < 0) {
        /* Fortran formulation */
        grp_num = -mesh->family_item[j*mesh->n_families + i] -1;
        grp_idx = mesh->group_idx[grp_num];
        group[grp_nbr++] = mesh->group_lst + grp_idx -1;
      }

    }

    fvm_group_class_set_add(class_defs,
                            grp_nbr,
                            (const char **)group);

  } /* End of loop on families */

  BFT_FREE(group);

  return class_defs;
}

/*----------------------------------------------------------------------------
 * Define group classes for a mesh based on its family definitions.
 *
 * parameters:
 *   mesh <-> pointer to mesh structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_init_group_classes(cs_mesh_t  *mesh)
{
  if (mesh->class_defs != NULL)
    mesh->class_defs = fvm_group_class_set_destroy(mesh->class_defs);

  mesh->class_defs = cs_mesh_create_group_classes(mesh);
}

/*----------------------------------------------------------------------------
 * Assign selectors to global mesh.
 *
 * Should be called once the mesh is fully built.
 *----------------------------------------------------------------------------*/

void
cs_mesh_init_selectors(void)
{
  if (cs_glob_mesh->class_defs == NULL)
    cs_mesh_init_group_classes(cs_glob_mesh);

  /* Construction of the selectors */

  cs_glob_mesh->select_cells
    = fvm_selector_create(cs_glob_mesh->dim,
                          cs_glob_mesh->n_cells,
                          cs_glob_mesh->class_defs,
                          cs_glob_mesh->cell_family,
                          1,
                          cs_glob_mesh_quantities->cell_cen,
                          NULL);

  cs_glob_mesh->select_b_faces
    = fvm_selector_create(cs_glob_mesh->dim,
                          cs_glob_mesh->n_b_faces,
                          cs_glob_mesh->class_defs,
                          cs_glob_mesh->b_face_family,
                          1,
                          cs_glob_mesh_quantities->b_face_cog,
                          cs_glob_mesh_quantities->b_face_normal);

  cs_glob_mesh->select_i_faces
    = fvm_selector_create(cs_glob_mesh->dim,
                          cs_glob_mesh->n_i_faces,
                          cs_glob_mesh->class_defs,
                          cs_glob_mesh->i_face_family,
                          1,
                          cs_glob_mesh_quantities->i_face_cog,
                          cs_glob_mesh_quantities->i_face_normal);

}

/*----------------------------------------------------------------------------
 * Update a scalar array in case of parallelism and/or periodicity.
 *
 * Note: this function is only present so that a C equivalent to the
 *       Fortran wrappers is available. In C code, directly using the
 *       cs_halo_sync_var() is preferred.
 *
 * parameters:
 *   var  <->  scalar array
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_scal(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo != NULL)
    cs_halo_sync_var(halo, CS_HALO_STANDARD, var);
}

/*----------------------------------------------------------------------------
 * Update a scalar array in case of parallelism and/or periodicity,
 * using an extended halo.
 *
 * Note: this function is only present so that a C equivalent to the
 *       Fortran wrappers is available. In C code, directly using the
 *       cs_halo_sync_var() is preferred.
 *
 * parameters:
 *   var  <->  scalar array
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_scal_ext(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo != NULL)
    cs_halo_sync_var(halo, CS_HALO_EXTENDED, var);
}

/*----------------------------------------------------------------------------
 * Update a component of a vector for parallelism and/or periodicity,
 * ignoring periodicity of rotation.
 *
 * Note: this function is only present so that a C equivalent to the
 *       Fortran wrappers is available. In C code, directly using the
 *       cs_halo_sync_var() is preferred.
 *
 * parameters:
 *   var  <->  scalar array
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_component(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo != NULL)
    cs_halo_sync_component(halo,
                           CS_HALO_STANDARD,
                           CS_HALO_ROTATION_IGNORE,
                           var);
}

/*----------------------------------------------------------------------------
 * Update a vector array in case of parallelism and/or periodicity.
 *
 * parameters:
 *   var1  <->  vector component 1 array
 *   var2  <->  vector component 2 array
 *   var3  <->  vector component 3 array
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_vect_ni(cs_real_t  *var1,
                         cs_real_t  *var2,
                         cs_real_t  *var3)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_var(halo, CS_HALO_STANDARD, var1);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var2);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var3);

  if (cs_glob_mesh->n_init_perio > 0)
    cs_halo_perio_sync_var_vect_ni(halo,
                                   CS_HALO_STANDARD,
                                   var1, var2, var3);
}

/*----------------------------------------------------------------------------
 * Update a vector array in case of parallelism and/or periodicity.
 *
 * parameters:
 *   var  <->  interleaved vector (of dimension 3)
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_vect(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_var_strided(halo, CS_HALO_STANDARD, var, 3);

  if (cs_glob_mesh->n_init_perio > 0)
    cs_halo_perio_sync_var_vect(halo,
                                CS_HALO_STANDARD,
                                var,
                                3);
}

/*----------------------------------------------------------------------------
 * Update a vector array in case of parallelism and/or periodicity,
 * using an extended halo.
 *
 * parameters:
 *   var  <->  interleaved vector (of dimension 3)
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_vect_ext(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_var_strided(halo, CS_HALO_EXTENDED, var, 3);

  if (cs_glob_mesh->n_init_perio > 0)
    cs_halo_perio_sync_var_vect(halo,
                                CS_HALO_EXTENDED,
                                var,
                                3);
}

/*----------------------------------------------------------------------------
 * Update a components of a vector for parallelism and/or periodicity,
 * ignoring periodicity of rotation.
 *
 *   var                  <-> gradient components (interleaved)
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_vect_no_rotation(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_components_strided(halo,
                                  CS_HALO_STANDARD,
                                  CS_HALO_ROTATION_IGNORE,
                                  var,
                                  3);
}

/*----------------------------------------------------------------------------
 * Update a diagonal tensor array in case of parallelism and/or periodicity.
 *
 * parameters:
 *   var11  <->  diagonal tensor component 11 array
 *   var22  <->  diagonal tensor component 22 array
 *   var33  <->  diagonal tensor component 33 array
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_diag_ni(cs_real_t  *var11,
                         cs_real_t  *var22,
                         cs_real_t  *var33)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_var(halo, CS_HALO_STANDARD, var11);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var22);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var33);

  if (cs_glob_mesh->n_init_perio > 0)
    cs_halo_perio_sync_var_diag_ni(halo,
                                   CS_HALO_STANDARD,
                                   var11, var22, var33);
}

/*----------------------------------------------------------------------------
 * Update a tensor array in case of parallelism and/or periodicity.
 *
 * parameters:
 *   var11  <->  tensor component 11 array
 *   var12  <->  tensor component 12 array
 *   var13  <->  tensor component 13 array
 *   var21  <->  tensor component 21 array
 *   var22  <->  tensor component 22 array
 *   var23  <->  tensor component 23 array
 *   var31  <->  tensor component 31 array
 *   var32  <->  tensor component 32 array
 *   var33  <->  tensor component 33 array
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_tens_ni(cs_real_t  *var11,
                         cs_real_t  *var12,
                         cs_real_t  *var13,
                         cs_real_t  *var21,
                         cs_real_t  *var22,
                         cs_real_t  *var23,
                         cs_real_t  *var31,
                         cs_real_t  *var32,
                         cs_real_t  *var33)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_var(halo, CS_HALO_STANDARD, var11);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var12);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var13);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var21);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var22);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var23);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var31);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var32);
  cs_halo_sync_var(halo, CS_HALO_STANDARD, var33);

  if (cs_glob_mesh->n_init_perio > 0)
    cs_halo_perio_sync_var_tens_ni(halo,
                                   CS_HALO_STANDARD,
                                   var11, var12, var13,
                                   var21, var22, var33,
                                   var31, var32, var33);
}

/*----------------------------------------------------------------------------
 * Update a tensor array in case of parallelism and/or periodicity.
 *
 * parameters:
 *   var  <->  interleaved tensor (of dimension 3x3)
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_tens(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_var_strided(halo, CS_HALO_STANDARD, var, 9);

  if (cs_glob_mesh->n_init_perio > 0)
    cs_halo_perio_sync_var_tens(halo,
                                CS_HALO_STANDARD,
                                var);
}

/*----------------------------------------------------------------------------
 * Update a symmetric tensor array in case of parallelism and/or periodicity.
 *
 * parameters:
 *   var  <->  symmetric interleaved tensor (of dimension 6)
 *----------------------------------------------------------------------------*/

void
cs_mesh_sync_var_sym_tens(cs_real_t  *var)
{
  const cs_halo_t  *halo = cs_glob_mesh->halo;

  if (halo == NULL) return;

  cs_halo_sync_var_strided(halo, CS_HALO_STANDARD, var, 6);

  if (cs_glob_mesh->n_init_perio > 0)
    cs_halo_perio_sync_var_sym_tens(halo,
                                    CS_HALO_STANDARD,
                                    var);
}

/*----------------------------------------------------------------------------
 * Get global lists of periodic face couples.
 *
 * In parallel, each face couple may appear on only one rank.
 *
 * The caller is responsible for freeing the arrays allocated and returned
 * by this function once they are no onger needed.
 *
 * parameters:
 *   mesh                 <-- pointer to mesh structure
 *   n_perio_face_couples --> global number of periodic couples per
 *                            periodicity (size: mesh->n_init_perio)
 *   perio_face_couples   --> arrays of global periodic couple face numbers,
 *                            for each periodicity
 *----------------------------------------------------------------------------*/

void
cs_mesh_get_perio_faces(const cs_mesh_t    *mesh,
                        cs_lnum_t         **n_perio_face_couples,
                        cs_gnum_t        ***perio_face_couples)
{
  assert (mesh != NULL);

  if (mesh->n_init_perio == 0)
    return;

#if defined(HAVE_MPI)

  if (cs_glob_n_ranks > 1)
    _get_perio_faces_g(mesh,
                       n_perio_face_couples,
                       perio_face_couples);

#endif /* defined(HAVE_MPI) */

  if (cs_glob_n_ranks == 1)
    _get_perio_faces_l(mesh,
                       n_perio_face_couples,
                       perio_face_couples);

  /* Ensure couples are sorted (not normally necessary, but safe) */

  if (n_perio_face_couples != NULL) {
    int i;
    for (i = 0; i < mesh->n_init_perio; i++) {
      if ((*n_perio_face_couples)[i] > 1)
        qsort((*perio_face_couples)[i],
              (*n_perio_face_couples)[i],
              sizeof(cs_gnum_t) * 2,
              &_compare_couples);
    }
  }
}

/*----------------------------------------------------------------------------
 * Build global cell numbering array extended to ghost cell values.
 *
 * If the blank_perio flag is nonzero, periodic ghost cell numbers
 * are set to zero instead of the value of the matching cell.
 *
 * The caller is responsible for freeing the returned array when it
 * is no longer useful.
 *
 * parameters:
 *   mesh        <-- pointer to mesh structure
 *   blank_perio <-- flag to zeroe periodic cell values
 *----------------------------------------------------------------------------*/

cs_gnum_t *
cs_mesh_get_cell_gnum(const cs_mesh_t  *mesh,
                      int               blank_perio)
{
  cs_lnum_t i;
  cs_gnum_t *cell_gnum = NULL;

  assert (mesh != NULL);

  /* Allocate array */

  BFT_MALLOC(cell_gnum, mesh->n_cells_with_ghosts, cs_gnum_t);

  /* Build global cell numbering including parallel halos */

  for (i = 0; i < mesh->n_cells; i++)
    cell_gnum[i] = mesh->global_cell_num[i];
  for (i = mesh->n_cells; i < mesh->n_cells_with_ghosts; i++)
    cell_gnum[i] = 0;

  if (mesh->halo != NULL) {

    cs_halo_sync_untyped(mesh->halo,
                         CS_HALO_EXTENDED,
                         sizeof(cs_gnum_t),
                         cell_gnum);

    if (blank_perio) {

      const cs_halo_t *halo = mesh->halo;

      cs_lnum_t  rank_id, t_id, shift;
      cs_lnum_t  start = 0, end = 0;

      const cs_lnum_t  n_transforms = halo->n_transforms;
      const cs_lnum_t  n_elts = halo->n_local_elts;

      for (t_id = 0; t_id < n_transforms; t_id++) {

        shift = 4 * halo->n_c_domains * t_id;

        for (rank_id = 0; rank_id < halo->n_c_domains; rank_id++) {

          start = halo->perio_lst[shift + 4*rank_id];
          end = start + halo->perio_lst[shift + 4*rank_id + 1];
          for (i = start; i < end; i++)
            cell_gnum[n_elts+i] = 0;

          start = halo->perio_lst[shift + 4*rank_id + 2];
          end = start + halo->perio_lst[shift + 4*rank_id + 3];
          for (i = start; i < end; i++)
            cell_gnum[n_elts+i] = 0;

        } /* End of loop on ranks */

      } /* End of loop on transformation */

    } /* End for blank_perio */

  }

  /* Return global cell number */

  return cell_gnum;
}

/*----------------------------------------------------------------------------
 * Mark interior faces with the number of their associated periodic
 * transform id.
 *
 * parameters:
 *   mesh      <-- pointer to mesh structure
 *   perio_num --> periodicity number associated with each face, signed for
 *                 direct/reverse transform, 0 for non-periodic faces
 *                 (size: mesh->n_i_faces)
 *----------------------------------------------------------------------------*/

void
cs_mesh_get_face_perio_num(const cs_mesh_t  *mesh,
                           int               perio_num[])
{
  cs_lnum_t i;

  for (i = 0; i < mesh->n_i_faces; i++)
    perio_num[i] = 0;

  if (mesh->n_init_perio > 0) {

    int *halo_perio_num = NULL;

    /* Mark ghost cells with their periodicity number */

    BFT_MALLOC(halo_perio_num, mesh->n_ghost_cells, int);

    _get_halo_perio_num(mesh, halo_perio_num, NULL);

    for (i = 0; i < mesh->n_i_faces; i++) {
      const cs_lnum_t h_id0 = mesh->i_face_cells[i][0] - mesh->n_cells;
      const cs_lnum_t h_id1 = mesh->i_face_cells[i][1] - mesh->n_cells;
      if (h_id0 >= 0) {
        if (halo_perio_num[h_id0] != 0)
          perio_num[i] = halo_perio_num[h_id0];
      }
      else if (h_id1 >= 0) {
        if (halo_perio_num[h_id1] != 0)
          perio_num[i] = halo_perio_num[h_id1];
      }
    }

    BFT_FREE(halo_perio_num);
  }
}

/*----------------------------------------------------------------------------
 * Print information on a mesh structure.
 *
 * parameters:
 *   mesh  <--  pointer to mesh structure.
 *   name  <--  associated name.
 *----------------------------------------------------------------------------*/

void
cs_mesh_print_info(const cs_mesh_t  *mesh,
                   const char       *name)
{
  if (mesh->n_g_vertices > 0) {

    cs_lnum_t  i, vtx_id;
    cs_lnum_t  dim = mesh->dim;
    cs_real_t  min_xyz[3] = { 1.e127,  1.e127,  1.e127};
    cs_real_t  max_xyz[3] = {-1.e127, -1.e127, -1.e127};

    for (vtx_id = 0 ; vtx_id < mesh->n_vertices ; vtx_id++) {

      for (i = 0 ; i < dim ; i++) {

        if (mesh->vtx_coord[vtx_id*dim + i] < min_xyz[i])
          min_xyz[i] = mesh->vtx_coord[vtx_id*dim + i];

        if (mesh->vtx_coord[vtx_id*dim + i] > max_xyz[i])
          max_xyz[i] = mesh->vtx_coord[vtx_id*dim + i];

      }

    } /* End of loop on vertices */

#if defined(HAVE_MPI)

    if (cs_glob_n_ranks > 1) {
      cs_real_t  g_min_xyz[3];
      cs_real_t  g_max_xyz[3];
      MPI_Allreduce(min_xyz, g_min_xyz, dim, CS_MPI_REAL, MPI_MIN,
                    cs_glob_mpi_comm);
      MPI_Allreduce(max_xyz, g_max_xyz, dim, CS_MPI_REAL, MPI_MAX,
                    cs_glob_mpi_comm);
      for (i = 0 ; i < dim ; i++) {
        min_xyz[i] = g_min_xyz[i];
        max_xyz[i] = g_max_xyz[i];
      }
    }

#endif

    bft_printf(_("\n"
                 " Mesh coordinates:               minimum    and maximum\n"
                 "                       X : %14.7e %14.7e\n"
                 "                       Y : %14.7e %14.7e\n"
                 "                       Z : %14.7e %14.7e\n"),
               min_xyz[0], max_xyz[0], min_xyz[1], max_xyz[1],
               min_xyz[2], max_xyz[2]);

  }

  bft_printf(_(" %s\n"
               "     Number of cells:          %llu\n"
               "     Number of interior faces: %llu\n"
               "     Number of boundary faces: %llu\n"
               "     Number of vertices:       %llu\n"),
             name,
             (unsigned long long)(mesh->n_g_cells),
             (unsigned long long)(mesh->n_g_i_faces),
             (unsigned long long)(mesh->n_g_b_faces - mesh->n_g_free_faces),
             (unsigned long long)(mesh->n_g_vertices));

  if (mesh->n_g_free_faces > 0)
    bft_printf(_("\n"
                 "     Number of isolated faces: %llu\n"),
               (unsigned long long)(mesh->n_g_free_faces));

  _print_mesh_group_stats(mesh);
}

/*----------------------------------------------------------------------------
 * Print statistics about mesh selectors usage to log.
 *
 * parameters:
 *   mesh <-- pointer to a mesh structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_selector_stats(cs_mesh_t  *mesh)
{
  int n_calls[3] = {0, 0, 0};
  double wtimes[3] = {0., 0., 0.};

  if (mesh->select_cells != NULL)
    fvm_selector_get_stats(mesh->select_cells, n_calls, wtimes);
  if (mesh->select_i_faces != NULL)
    fvm_selector_get_stats(mesh->select_i_faces, n_calls + 1, wtimes + 1);
  if (mesh->select_b_faces != NULL)
    fvm_selector_get_stats(mesh->select_b_faces, n_calls + 2, wtimes + 2);

#if defined(HAVE_MPI)
  if (cs_glob_n_ranks > 1) {
    int i;
    double wtimes_glob[3];
    MPI_Allreduce(wtimes, wtimes_glob, 3, MPI_DOUBLE, MPI_MAX,
                  cs_glob_mpi_comm);
    for (i = 0; i < 3; i++)
      wtimes[i] = wtimes_glob[i];
  }
#endif

  cs_log_printf(CS_LOG_PERFORMANCE,
                _("\n"
                  "Mesh entity selections by criteria statistics:\n\n"
                  "  entity type     evaluations          time\n"
                  "  -----------------------------------------\n"
                  "  cells            %10d  %12.5f\n"
                  "  interior faces   %10d  %12.5f\n"
                  "  boundary faces   %10d  %12.5f\n"),
                n_calls[0], wtimes[0],
                n_calls[1], wtimes[1],
                n_calls[2], wtimes[2]);

  cs_log_printf(CS_LOG_PERFORMANCE, "\n");
  cs_log_separator(CS_LOG_PERFORMANCE);
}

/*----------------------------------------------------------------------------
 * Dump of a mesh structure.
 *
 * parameters:
 *   mesh  <--  pointer to mesh structure.
 *----------------------------------------------------------------------------*/

void
cs_mesh_dump(const cs_mesh_t  *mesh)
{
  cs_lnum_t  i, j;

  bft_printf("\n\nDUMP OF THE MESH STRUCTURE: %p\n\n", (const void *)mesh);

  bft_printf("space dim :        %d\n"
             "n_domains :        %d\n"
             "domain_num:        %d\n",
             mesh->dim, mesh->n_domains, mesh->domain_num);

  bft_printf("\nLocal dimensions:\n"
             "n_cells:                  %d\n"
             "n_cells_with_ghosts:      %d\n"
             "n_vertices:               %d\n"
             "n_i_faces:                %d\n"
             "n_b_faces:                %d\n",
             mesh->n_cells, mesh->n_cells_with_ghosts,
             mesh->n_vertices,
             mesh->n_i_faces, mesh->n_b_faces);

  bft_printf("\nGlobal dimensions:\n"
             "n_g_cells:                %llu\n"
             "n_g_vertices:             %llu\n"
             "n_g_i_faces:              %llu\n"
             "n_g_b_faces:              %llu\n",
             (unsigned long long)mesh->n_g_cells,
             (unsigned long long)mesh->n_g_vertices,
             (unsigned long long)mesh->n_g_i_faces,
             (unsigned long long)mesh->n_g_b_faces);

  bft_printf("\n\n        --------"
             "        Vertices"
             "        --------\n\n");

  bft_printf("\nVertex coordinates:\n");
  for (i = 0; i < mesh->n_vertices; i++)
    bft_printf("   <%3d >  %10.3f        %10.3f        %10.3f\n",
               i, mesh->vtx_coord[3*i], mesh->vtx_coord[3*i+1],
               mesh->vtx_coord[3*i+2]);

  if (mesh->n_domains > 1) {
    bft_printf("\nGlobal vertex numbering:\n");
    for (i = 0; i < mesh->n_vertices; i++)
      bft_printf("   <%7d >  %10llu\n",
                 i, (unsigned long long)(mesh->global_vtx_num[i]));
  }

  bft_printf("\n\n        ---------------------------"
             "        Internal faces connectivity"
             "        ---------------------------\n\n");

  bft_printf("\nInternal faces -> Cells connectivity:\n");
  for (i = 0; i < mesh->n_i_faces; i++)
    bft_printf("   < %7d >  %7d  <---->  %7d\n", i,
               mesh->i_face_cells[i][0], mesh->i_face_cells[i][1]);

  bft_printf("\nInternal faces -> vertices connectivity:\n");
  for (i = 0; i < mesh->n_i_faces; i++) {
    bft_printf("    < %7d >", i);
    for (j = mesh->i_face_vtx_idx[i]; j < mesh->i_face_vtx_idx[i+1]; j++)
      bft_printf("  %7d ",mesh->i_face_vtx_lst[j]);
    bft_printf("\n");
  }

  if (mesh->global_i_face_num != NULL) {

    bft_printf("\nInternal faces global numbering:\n");
    for (i = 0; i < mesh->n_i_faces; i++)
      bft_printf("   < %7d >  %12llu",
                 i, (unsigned long long)(mesh->global_i_face_num[i]));
    bft_printf("\n");

  }

  bft_printf("\n\n        -------------------------"
             "        Border faces connectivity"
             "        -------------------------\n\n");

  bft_printf("\nBorder faces -> Cells connectivity:\n");
  for (i = 0; i < mesh->n_b_faces; i++)
    bft_printf("   < %7d >  %7d\n", i, mesh->b_face_cells[i]);

  bft_printf("\nBorder faces -> vertices connectivity:\n");
  for (i = 0; i < mesh->n_b_faces; i++) {
    bft_printf("   < %7d >", i);
    for (j = mesh->b_face_vtx_idx[i]; j < mesh->b_face_vtx_idx[i+1]; j++)
      bft_printf("  %7d ",mesh->b_face_vtx_lst[j]);
    bft_printf("\n");
  }

  bft_printf("\n\n        -------------------------"
             "        Cells"
             "        -------------------------\n\n");

  if (mesh->global_cell_num != NULL) {

    bft_printf("\nCell global numbering:\n");
    for (i = 0; i < mesh->n_cells; i++)
      bft_printf("   < %7d >  %12llu", i,
                 (unsigned long long)(mesh->global_cell_num[i]));
    bft_printf("\n");

  }

  bft_printf("\nNumber of families: %3d\n",mesh->n_families);
  bft_printf("Family of each cell:\n");
  for (i = 0; i < mesh->n_cells_with_ghosts; i++)
    bft_printf("   < %3d >  %5d\n", i, mesh->cell_family[i]);

  if (mesh->halo != NULL) {

    cs_halo_t  *halo = mesh->halo;

    bft_printf("\nHalo information: %p\n", (const void *)halo);

    bft_printf("n_c_domains:              %d\n", halo->n_c_domains);
    bft_printf("n_ghost_cells:            %d\n", mesh->n_ghost_cells);
    bft_printf("n_std_ghost_cells:        %d\n",
               halo->n_elts[CS_HALO_STANDARD]);
    bft_printf("n_ext_ghost_cells:        %d\n",
               halo->n_elts[CS_HALO_EXTENDED] - halo->n_elts[CS_HALO_STANDARD]);

    for (i = 0; i < halo->n_c_domains; i++) {

      bft_printf("\n\nRank id:        %d\n"
                 "Halo index start:        %d        end:        %d\n"
                 "Send index start:        %d        end:        %d\n"
                 "Send cell ids:\n",
                 halo->c_domain_rank[i],
                 halo->index[2*i], halo->index[2*i+2],
                 halo->send_index[2*i], halo->send_index[2*i+2]);
      for (j = halo->send_index[2*i]; j < halo->send_index[2*i+2]; j++)
        bft_printf("  %10d : %10d\n", j, halo->send_list[j]);

    } /* End of loop on the frontiers of halo */

    if (mesh->n_init_perio > 0 && halo->perio_lst != NULL) {

      const cs_lnum_t  n_c_domains = halo->n_c_domains;
      const cs_lnum_t  n_transforms = mesh->n_transforms;

      bft_printf("\n\nHalo's data in case of periodicity:\n");
      bft_printf("n_transforms:                %d\n",mesh->n_transforms);

      bft_printf("\nData in the standard halo\n");
      for (i = 0; i < n_transforms; i++)
        for (j = 0; j < n_c_domains; j++)
          bft_printf("< rank:%3d >< transform:%2d > start_idx: %5d"
                     "        n_elts: %5d\n",
                     halo->c_domain_rank[j], i,
                     halo->perio_lst[4*n_c_domains*i + 4*j],
                     halo->perio_lst[4*n_c_domains*i + 4*j+1]);

      bft_printf("\nData in the extended halo\n");
      for (i = 0; i < n_transforms; i++)
        for (j = 0; j < n_c_domains; j++)
          bft_printf("< rank:%3d >< transform:%2d >        "
                     "start_idx:  %5d, n_elts:  %5d\n",
                     halo->c_domain_rank[j], i,
                     halo->perio_lst[4*n_c_domains*i + 4*j+2],
                     halo->perio_lst[4*n_c_domains*i + 4*j+3]);

    } /* End if n_perio > 0 */

  } /* End if mesh->halo != NULL */

  if (mesh->cell_cells_idx != NULL) {

    bft_printf("\n\nCell -> cells connectivity for extended neighborhood\n\n");
    for (i = 0; i < mesh->n_cells; i++) {
      bft_printf("< cell id:%3d>         ", i);
      for (j = mesh->cell_cells_idx[i]; j < mesh->cell_cells_idx[i+1]; j++)
        bft_printf("%d        ", mesh->cell_cells_lst[j]);
      bft_printf("\n");
    }

  }

  if (mesh->gcell_vtx_idx != NULL) {

    bft_printf("\n\nGhost cell -> vertices connectivity "
               "for extended neighborhood\n\n");
    for (i = 0; i < mesh->n_ghost_cells; i++) {
      bft_printf("< gcell id:%3d>        ", i + mesh->n_cells);
      for (j = mesh->gcell_vtx_idx[i]; j < mesh->gcell_vtx_idx[i+1]; j++)
        bft_printf("%d        ", mesh->gcell_vtx_lst[j]);
      bft_printf("\n");
    }

  }

  /* Dump numbering info */

  cs_numbering_dump(mesh->cell_numbering);
  cs_numbering_dump(mesh->i_face_numbering);
  cs_numbering_dump(mesh->b_face_numbering);

  /* Modification flag */

  bft_printf("\nModification flag:\n");
  bft_printf("modified:         %d\n",mesh->modified);

  bft_printf("\n\nEND OF DUMP OF MESH STRUCTURE\n\n");
  bft_printf_flush();
}

/*----------------------------------------------------------------------------*/

END_C_DECLS
