/*============================================================================
 * Management of mesh quantities
 *============================================================================*/

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

  Copyright (C) 1998-2013 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 <math.h>
#include <float.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>

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

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

#include "cs_base.h"
#include "cs_halo_perio.h"
#include "cs_mesh.h"
#include "cs_mesh_connect.h"
#include "cs_parall.h"

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

#include "cs_mesh_quantities.h"

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

BEGIN_C_DECLS

/*============================================================================
 * Local type definitions
 *============================================================================*/

typedef double  _vtx_coords_t[3];

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

enum {X, Y, Z};

#define _CS_CROSS_PRODUCT(prod_vect, vect1, vect2)  \
  (prod_vect[X] = vect1[Y] * vect2[Z] - vect2[Y] * vect1[Z], \
   prod_vect[Y] = vect2[X] * vect1[Z] - vect1[X] * vect2[Z], \
   prod_vect[Z] = vect1[X] * vect2[Y] - vect2[X] * vect1[Y])

#define _CS_DOT_PRODUCT(vect1, vect2) \
  (vect1[X] * vect2[X] + vect1[Y] * vect2[Y] + vect1[Z] * vect2[Z])

#define _CS_MODULE(vect) \
  sqrt(vect[X] * vect[X] + vect[Y] * vect[Y] + vect[Z] * vect[Z])

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

/* Pointer to cs_mesh_quantities_t structure for the main mesh */

cs_mesh_quantities_t  *cs_glob_mesh_quantities = NULL;

/* Choice of the algorithm for computing gravity centres of the cells */

static int cs_glob_mesh_quantities_cell_cen = 0;

/* Choice of the option for computing cocg (iterative or Least square method)
   or not */

static bool _compute_cocg_s_it = false;
static bool _compute_cocg_s_lsq = false;
static bool _compute_cocg_it = false;
static bool _compute_cocg_lsq = false;

/* Number of computation updates */

static int _n_computations = 0;

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

/*----------------------------------------------------------------------------
 * Compute 3x3 matrix cocg for the scalar gradient iterative algorithm
 *
 * parameters:
 *   m    <--  mesh
 *   fvq  <->  mesh quantities
 *----------------------------------------------------------------------------*/

static void
_compute_cell_cocg_s_it(const cs_mesh_t      *m,
                        cs_mesh_quantities_t *fvq)
{
  const int n_cells = m->n_cells;
  const int n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;

  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict dofij
    = (const cs_real_3_t *restrict)fvq->dofij;

  cs_real_33_t   *restrict cocgb = fvq->cocgb_s_it;
  cs_real_33_t   *restrict cocg = fvq->cocg_s_it;

  cs_lnum_t  cell_id, face_id, ii, jj, ll, mm;
  int        g_id, t_id;
  cs_real_t  a11, a12, a13, a21, a22, a23, a31, a32, a33;
  cs_real_t  cocg11, cocg12, cocg13, cocg21, cocg22, cocg23;
  cs_real_t  cocg31, cocg32, cocg33;
  cs_real_t  det_inv;
  cs_real_4_t  fctb;

  if (cocg == NULL) {
    BFT_MALLOC(cocgb, m->n_b_cells, cs_real_33_t);
    BFT_MALLOC(cocg, n_cells_ext, cs_real_33_t);
    fvq->cocgb_s_it = cocgb;
    fvq->cocg_s_it = cocg;
  }

  /* Compute cocg */

# pragma omp parallel for
  for (cell_id = 0; cell_id < n_cells_ext; cell_id++) {
    cocg[cell_id][0][0] = cell_vol[cell_id];
    cocg[cell_id][0][1] = 0.0;
    cocg[cell_id][0][2] = 0.0;
    cocg[cell_id][1][0] = 0.0;
    cocg[cell_id][1][1] = cell_vol[cell_id];
    cocg[cell_id][1][2] = 0.0;
    cocg[cell_id][2][0] = 0.0;
    cocg[cell_id][2][1] = 0.0;
    cocg[cell_id][2][2] = cell_vol[cell_id];
  }

  /* Contribution from interior faces */

  for (g_id = 0; g_id < n_i_groups; g_id++) {

#   pragma omp parallel for private(face_id, ii, jj, ll, fctb)
    for (t_id = 0; t_id < n_i_threads; t_id++) {

      for (face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
           face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
           face_id++) {

        ii = i_face_cells[face_id][0] - 1;
        jj = i_face_cells[face_id][1] - 1;

        for (ll = 0; ll < 3; ll++) {
          fctb[0] = -dofij[face_id][0] * 0.5 * i_face_normal[face_id][ll];
          fctb[1] = -dofij[face_id][1] * 0.5 * i_face_normal[face_id][ll];
          fctb[2] = -dofij[face_id][2] * 0.5 * i_face_normal[face_id][ll];
          cocg[ii][ll][0] += fctb[0];
          cocg[ii][ll][1] += fctb[1];
          cocg[ii][ll][2] += fctb[2];
          cocg[jj][ll][0] -= fctb[0];
          cocg[jj][ll][1] -= fctb[1];
          cocg[jj][ll][2] -= fctb[2];
        }

      } /* loop on faces */

    } /* loop on threads */

  } /* loop on thread groups */

  /* Save partial cocg at interior faces of boundary cells */

# pragma omp parallel for private(cell_id, ll, mm)
  for (ii = 0; ii < m->n_b_cells; ii++) {
    cell_id = m->b_cells[ii] - 1;
    for (ll = 0; ll < 3; ll++) {
      for (mm = 0; mm < 3; mm++)
        cocgb[ii][ll][mm] = cocg[cell_id][ll][mm];
    }
  }

  /* Invert for all cells. */
  /*-----------------------*/

  /* The cocg term for interior cells only changes if the mesh does */

# pragma omp parallel for private(cocg11, cocg12, cocg13, cocg21, cocg22, \
                                  cocg23, cocg31, cocg32, cocg33, a11, a12, \
                                  a13, a21, a22, a23, a31, a32, a33, det_inv)
  for (cell_id = 0; cell_id < n_cells; cell_id++) {

    cocg11 = cocg[cell_id][0][0];
    cocg12 = cocg[cell_id][0][1];
    cocg13 = cocg[cell_id][0][2];
    cocg21 = cocg[cell_id][1][0];
    cocg22 = cocg[cell_id][1][1];
    cocg23 = cocg[cell_id][1][2];
    cocg31 = cocg[cell_id][2][0];
    cocg32 = cocg[cell_id][2][1];
    cocg33 = cocg[cell_id][2][2];

    a11 = cocg22*cocg33 - cocg32*cocg23;
    a12 = cocg32*cocg13 - cocg12*cocg33;
    a13 = cocg12*cocg23 - cocg22*cocg13;
    a21 = cocg31*cocg23 - cocg21*cocg33;
    a22 = cocg11*cocg33 - cocg31*cocg13;
    a23 = cocg21*cocg13 - cocg11*cocg23;
    a31 = cocg21*cocg32 - cocg31*cocg22;
    a32 = cocg31*cocg12 - cocg11*cocg32;
    a33 = cocg11*cocg22 - cocg21*cocg12;

    det_inv = 1. / (cocg11*a11 + cocg21*a12 + cocg31*a13);

    cocg[cell_id][0][0] = a11 * det_inv;
    cocg[cell_id][0][1] = a12 * det_inv;
    cocg[cell_id][0][2] = a13 * det_inv;
    cocg[cell_id][1][0] = a21 * det_inv;
    cocg[cell_id][1][1] = a22 * det_inv;
    cocg[cell_id][1][2] = a23 * det_inv;
    cocg[cell_id][2][0] = a31 * det_inv;
    cocg[cell_id][2][1] = a32 * det_inv;
    cocg[cell_id][2][2] = a33 * det_inv;

  }

}

/*----------------------------------------------------------------------------
 * Compute 3x3 matrix cocg for the scalar gradient least squares algorithm
 *
 * parameters:
 *   m    <--  mesh
 *   fvq  <->  mesh quantities
 *----------------------------------------------------------------------------*/

static void
_compute_cell_cocg_s_lsq(const cs_mesh_t      *m,
                         cs_mesh_quantities_t *fvq)
{
  const int n_cells = m->n_cells;
  const int n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_lnum_t *restrict cell_cells_idx
    = (const cs_lnum_t *restrict)m->cell_cells_idx;
  const cs_lnum_t *restrict cell_cells_lst
    = (const cs_lnum_t *restrict)m->cell_cells_lst;

  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_t *restrict b_face_surf
    = (const cs_real_t *restrict)fvq->b_face_surf;

  cs_real_33_t   *restrict cocgb = fvq->cocgb_s_lsq;
  cs_real_33_t   *restrict cocg = fvq->cocg_s_lsq;

  cs_lnum_t  cell_id, cidx, face_id, ii, jj, ll, mm;
  int        g_id, t_id;
  cs_real_t  a11, a12, a13, a22, a23, a33;
  cs_real_t  cocg11, cocg12, cocg13, cocg22, cocg23, cocg33;
  cs_real_t  det_inv, uddij2, udbfs;
  cs_real_3_t  dc, dddij;

  if (cocg == NULL) {
    BFT_MALLOC(cocgb, m->n_b_cells, cs_real_33_t);
    BFT_MALLOC(cocg, n_cells_ext, cs_real_33_t);
    fvq->cocgb_s_lsq = cocgb;
    fvq->cocg_s_lsq = cocg;
  }

  /* Initialization */

# pragma omp parallel for private(ll, mm)
  for (cell_id = 0; cell_id < n_cells_ext; cell_id++) {
    for (ll = 0; ll < 3; ll++) {
      for (mm = 0; mm < 3; mm++)
        cocg[cell_id][ll][mm] = 0.0;
    }
  }

  /* Contribution from interior faces */

  for (g_id = 0; g_id < n_i_groups; g_id++) {

#   pragma omp parallel for private(face_id, ii, jj, ll, mm, uddij2, dc)
    for (t_id = 0; t_id < n_i_threads; t_id++) {

      for (face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
           face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
           face_id++) {

        ii = i_face_cells[face_id][0] - 1;
        jj = i_face_cells[face_id][1] - 1;

        for (ll = 0; ll < 3; ll++)
          dc[ll] = cell_cen[jj][ll] - cell_cen[ii][ll];
        uddij2 = 1. / (dc[0]*dc[0] + dc[1]*dc[1] + dc[2]*dc[2]);

        for (ll = 0; ll < 3; ll++) {
          for (mm = 0; mm < 3; mm++)
            cocg[ii][ll][mm] += dc[ll] * dc[mm] * uddij2;
        }
        for (ll = 0; ll < 3; ll++) {
          for (mm = 0; mm < 3; mm++)
            cocg[jj][ll][mm] += dc[ll] * dc[mm] * uddij2;
        }

      } /* loop on faces */

    } /* loop on threads */

  } /* loop on thread groups */

  /* Contribution from extended neighborhood */

  if (m->halo_type == CS_HALO_EXTENDED) {

#   pragma omp parallel for private(cidx, jj, ll, mm, uddij2, dc)
    for (ii = 0; ii < n_cells; ii++) {
      for (cidx = cell_cells_idx[ii]; cidx < cell_cells_idx[ii+1]; cidx++) {

        jj = cell_cells_lst[cidx - 1] - 1;

        for (ll = 0; ll < 3; ll++)
          dc[ll] = cell_cen[jj][ll] - cell_cen[ii][ll];
        uddij2 = 1. / (dc[0]*dc[0] + dc[1]*dc[1] + dc[2]*dc[2]);

        for (ll = 0; ll < 3; ll++) {
          for (mm = 0; mm < 3; mm++)
            cocg[ii][ll][mm] += dc[ll] * dc[mm] * uddij2;
        }

      }
    }

  } /* End for extended neighborhood */

  /* Save partial cocg at interior faces of boundary cells */

# pragma omp parallel for private(cell_id, ll, mm)
  for (ii = 0; ii < m->n_b_cells; ii++) {
    cell_id = m->b_cells[ii] - 1;
    for (ll = 0; ll < 3; ll++) {
      for (mm = 0; mm < 3; mm++)
        cocgb[ii][ll][mm] = cocg[cell_id][ll][mm];
    }
  }

  /* Contribution from boundary faces, assuming symmetry everywhere
     so as to avoid obtaining a non-invertible matrix in 2D cases. */

  for (g_id = 0; g_id < n_b_groups; g_id++) {

#   pragma omp parallel for private(face_id, ii, ll, mm, udbfs, dddij)
    for (t_id = 0; t_id < n_b_threads; t_id++) {

      for (face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
           face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
           face_id++) {

        ii = b_face_cells[face_id] - 1;

        udbfs = 1 / b_face_surf[face_id];

        for (ll = 0; ll < 3; ll++)
          dddij[ll] =   udbfs * b_face_normal[face_id][ll];

        for (ll = 0; ll < 3; ll++) {
          for (mm = 0; mm < 3; mm++)
            cocg[ii][ll][mm] += dddij[ll]*dddij[mm];
        }

      } /* loop on faces */

    } /* loop on threads */

  } /* loop on thread groups */

  /* Invert for all cells. */
  /*-----------------------*/

  /* The cocg term for interior cells only changes if the mesh does */

# pragma omp parallel for private(cocg11, cocg12, cocg13, cocg22, \
                                  cocg23, cocg33, a11, a12,       \
                                  a13, a22, a23, a33, det_inv)
  for (cell_id = 0; cell_id < n_cells; cell_id++) {

    cocg11 = cocg[cell_id][0][0];
    cocg12 = cocg[cell_id][0][1];
    cocg13 = cocg[cell_id][0][2];
    cocg22 = cocg[cell_id][1][1];
    cocg23 = cocg[cell_id][1][2];
    cocg33 = cocg[cell_id][2][2];

    a11 = cocg22*cocg33 - cocg23*cocg23;
    a12 = cocg23*cocg13 - cocg12*cocg33;
    a13 = cocg12*cocg23 - cocg22*cocg13;
    a22 = cocg11*cocg33 - cocg13*cocg13;
    a23 = cocg12*cocg13 - cocg11*cocg23;
    a33 = cocg11*cocg22 - cocg12*cocg12;

    det_inv = 1. / (cocg11*a11 + cocg12*a12 + cocg13*a13);

    cocg[cell_id][0][0] = a11 * det_inv;
    cocg[cell_id][0][1] = a12 * det_inv;
    cocg[cell_id][0][2] = a13 * det_inv;
    cocg[cell_id][1][0] = a12 * det_inv;
    cocg[cell_id][1][1] = a22 * det_inv;
    cocg[cell_id][1][2] = a23 * det_inv;
    cocg[cell_id][2][0] = a13 * det_inv;
    cocg[cell_id][2][1] = a23 * det_inv;
    cocg[cell_id][2][2] = a33 * det_inv;

  }
}

/*----------------------------------------------------------------------------
 * Compute 3x3 matrix cocg for the iterative algorithm
 *
 * parameters:
 *   m               <--  mesh
 *   fvq             <->  mesh quantities
 *----------------------------------------------------------------------------*/

static void
_compute_cell_cocg_it(const cs_mesh_t      *m,
                      cs_mesh_quantities_t *fvq)
{
  /* Local variables */

  const int n_cells = m->n_cells;
  const int n_cells_with_ghosts = m->n_cells_with_ghosts;
  const int n_i_faces = m->n_i_faces;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;

  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict dofij
    = (const cs_real_3_t *restrict)fvq->dofij;
  cs_real_33_t *restrict cocg
    = fvq->cocg_it;

  cs_lnum_t  cell_id, face_id, i, j, cell_id1, cell_id2;
  cs_real_t  pfac, vecfac, ddet;
  cs_real_t  dvol1, dvol2;

  cs_real_t  cocg11, cocg12, cocg13, cocg21, cocg22, cocg23;
  cs_real_t  cocg31, cocg32, cocg33;
  cs_real_t  a11, a12, a13, a21, a22, a23, a31, a32, a33;

  /* compute the dimensionless matrix COCG for each cell*/

  for (cell_id = 0; cell_id < n_cells_with_ghosts; cell_id++) {
    dvol1 = cell_vol[cell_id];
    cocg[cell_id][0][0]= 1.0;
    cocg[cell_id][0][1]= 0.0;
    cocg[cell_id][0][2]= 0.0;
    cocg[cell_id][1][0]= 0.0;
    cocg[cell_id][1][1]= 1.0;
    cocg[cell_id][1][2]= 0.0;
    cocg[cell_id][2][0]= 0.0;
    cocg[cell_id][2][1]= 0.0;
    cocg[cell_id][2][2]= 1.0;
  }

  /* Interior face treatment */

  for (face_id = 0; face_id < n_i_faces; face_id++) {
    cell_id1 = i_face_cells[face_id][0] - 1;
    cell_id2 = i_face_cells[face_id][1] - 1;

    dvol1 = 1./cell_vol[cell_id1];
    dvol2 = 1./cell_vol[cell_id2];

    for (i = 0; i < 3; i++) {

      pfac = -0.5*dofij[face_id][i];

      for (j = 0; j < 3; j++) {
        vecfac = pfac*i_face_normal[face_id][j];
        cocg[cell_id1][i][j] += vecfac * dvol1;
        cocg[cell_id2][i][j] -= vecfac * dvol2;
      }
    }
  }

  /* 3x3 Matrix inversion*/

  for (cell_id = 0; cell_id < n_cells; cell_id++) {

    cocg11 = cocg[cell_id][0][0];
    cocg12 = cocg[cell_id][0][1];
    cocg13 = cocg[cell_id][0][2];
    cocg21 = cocg[cell_id][1][0];
    cocg22 = cocg[cell_id][1][1];
    cocg23 = cocg[cell_id][1][2];
    cocg31 = cocg[cell_id][2][0];
    cocg32 = cocg[cell_id][2][1];
    cocg33 = cocg[cell_id][2][2];

    a11=cocg22*cocg33-cocg32*cocg23;
    a12=cocg32*cocg13-cocg12*cocg33;
    a13=cocg12*cocg23-cocg22*cocg13;
    a21=cocg31*cocg23-cocg21*cocg33;
    a22=cocg11*cocg33-cocg31*cocg13;
    a23=cocg21*cocg13-cocg11*cocg23;
    a31=cocg21*cocg32-cocg31*cocg22;
    a32=cocg31*cocg12-cocg11*cocg32;
    a33=cocg11*cocg22-cocg21*cocg12;

    ddet = 1.0/(cocg11*a11 +cocg21*a12+cocg31*a13);

    cocg[cell_id][0][0] = a11*ddet;
    cocg[cell_id][0][1] = a12*ddet;
    cocg[cell_id][0][2] = a13*ddet;
    cocg[cell_id][1][0] = a21*ddet;
    cocg[cell_id][1][1] = a22*ddet;
    cocg[cell_id][1][2] = a23*ddet;
    cocg[cell_id][2][0] = a31*ddet;
    cocg[cell_id][2][1] = a32*ddet;
    cocg[cell_id][2][2] = a33*ddet;

  }

}

/*----------------------------------------------------------------------------
 * Compute 3x3 matrix cocg for the least square iterative gradient
 *
 * parameters:
 *   m               <--  mesh
 *   fvq             <->  mesh quantities
 *----------------------------------------------------------------------------*/

static void
_compute_cell_cocg_lsq(const cs_mesh_t      *m,
                       cs_mesh_quantities_t *fvq)
{
  /* Local variables */

  const int n_cells = m->n_cells;
  const int n_cells_ext = m->n_cells_with_ghosts;

  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_lnum_t *restrict cell_cells_idx
    = (const cs_lnum_t *restrict)m->cell_cells_idx;
  const cs_lnum_t *restrict cell_cells_lst
    = (const cs_lnum_t *restrict)m->cell_cells_lst;

  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict b_face_cog
    = (const cs_real_3_t *restrict)fvq->b_face_cog;
  cs_real_33_t *restrict cocg = fvq->cocg_lsq;

  cs_lnum_t  cell_id, cidx, face_id, cell_id1, cell_id2, i, j;
  int        g_id, t_id;
  cs_real_t  a11, a12, a13, a22, a23, a33;
  cs_real_t  cocg11, cocg12, cocg13, cocg22, cocg23, cocg33;
  cs_real_t  pfac, det_inv;
  cs_real_t  ddc;
  cs_real_3_t  dc;

  /* Compute cocg */

  /* Initialization */

# pragma omp parallel for private(i, j)
  for (cell_id = 0; cell_id < n_cells_ext; cell_id++)
    for (i = 0; i < 3; i++)
      for (j = 0; j < 3; j++)
        cocg[cell_id][i][j] = 0.0;

  /* Contribution from interior faces */
  /*----------------------------------*/

  for (g_id = 0; g_id < n_i_groups; g_id++) {

#   pragma omp parallel for private(face_id, cell_id1, cell_id2,\
                                    i, j, ddc, dc, pfac)
    for (t_id = 0; t_id < n_i_threads; t_id++) {

      for (face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
           face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
           face_id++) {

        cell_id1 = i_face_cells[face_id][0] - 1;
        cell_id2 = i_face_cells[face_id][1] - 1;

        for (i = 0; i < 3; i++)
          dc[i] = cell_cen[cell_id2][i] - cell_cen[cell_id1][i];

        ddc = 1./(dc[0]*dc[0] + dc[1]*dc[1] + dc[2]*dc[2]);

        for (i = 0; i < 3; i++) {
          for (j = 0; j < 3; j++) {
            pfac = dc[i]*dc[j]*ddc;
            cocg[cell_id1][i][j] += pfac;
            cocg[cell_id2][i][j] += pfac;
          }
        }

      } /* loop on faces */

    } /* loop on threads */

  } /* loop on thread groups */

  /* Contribution from extended neighborhood */
  /*-----------------------------------------*/

  if (m->halo_type == CS_HALO_EXTENDED) {

#   pragma omp parallel for private(cidx, cell_id2, ddc, dc, i, j)
    for (cell_id1 = 0; cell_id1 < n_cells; cell_id1++) {
      for (cidx = cell_cells_idx[cell_id1];
           cidx < cell_cells_idx[cell_id1+1];
           cidx++) {

        cell_id2 = cell_cells_lst[cidx - 1] - 1;

        for (i = 0; i < 3; i++)
          dc[i] = cell_cen[cell_id2][i] - cell_cen[cell_id1][i];

        ddc = 1./(dc[0]*dc[0] + dc[1]*dc[1] + dc[2]*dc[2]);

        for (i = 0; i < 3; i++)
          for (j = 0; j < 3; j++)
            cocg[cell_id1][i][j] += dc[i]*dc[j]*ddc;

      }
    }

  } /* End for extended neighborhood */

  /* Contribution from boundary faces */
  /*----------------------------------*/

  for (g_id = 0; g_id < n_b_groups; g_id++) {

#   pragma omp parallel for private(face_id, cell_id1, i, j, ddc, dc)
    for (t_id = 0; t_id < n_b_threads; t_id++) {

      for (face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
           face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
           face_id++) {

        cell_id1 = b_face_cells[face_id] - 1;

        for (i = 0; i < 3; i++)
          dc[i] = b_face_cog[face_id][i] - cell_cen[cell_id1][i];

        ddc = 1./(dc[0]*dc[0] + dc[1]*dc[1] + dc[2]*dc[2]);

        for (i = 0; i < 3; i++)
          for (j = 0; j < 3; j++)
            cocg[cell_id1][i][j] += dc[i]*dc[j]*ddc;

      } /* loop on faces */

    } /* loop on threads */

  } /* loop on thread groups */

  /* Invert for all cells. */
  /*-----------------------*/

  /* The cocg term for interior cells only changes if the mesh does */

# pragma omp parallel for private(cocg11, cocg12, cocg13, cocg22, \
                                  cocg23, cocg33, a11, a12, \
                                  a13, a22, a23, a33, det_inv)
  for (cell_id = 0; cell_id < n_cells; cell_id++) {

    cocg11 = cocg[cell_id][0][0];
    cocg12 = cocg[cell_id][0][1];
    cocg13 = cocg[cell_id][0][2];
    cocg22 = cocg[cell_id][1][1];
    cocg23 = cocg[cell_id][1][2];
    cocg33 = cocg[cell_id][2][2];

    a11 = cocg22*cocg33 - cocg23*cocg23;
    a12 = cocg23*cocg13 - cocg12*cocg33;
    a13 = cocg12*cocg23 - cocg22*cocg13;
    a22 = cocg11*cocg33 - cocg13*cocg13;
    a23 = cocg12*cocg13 - cocg11*cocg23;
    a33 = cocg11*cocg22 - cocg12*cocg12;

    det_inv = 1./(cocg11*a11 + cocg12*a12 + cocg13*a13);

    cocg[cell_id][0][0] = a11 * det_inv;
    cocg[cell_id][0][1] = a12 * det_inv;
    cocg[cell_id][0][2] = a13 * det_inv;
    cocg[cell_id][1][0] = a12 * det_inv;
    cocg[cell_id][1][1] = a22 * det_inv;
    cocg[cell_id][1][2] = a23 * det_inv;
    cocg[cell_id][2][0] = a13 * det_inv;
    cocg[cell_id][2][1] = a23 * det_inv;
    cocg[cell_id][2][2] = a33 * det_inv;

  }
}

/*----------------------------------------------------------------------------
 * Compute quantities associated to faces (border or internal)
 *
 * parameters:
 *   dim             <--  dimension
 *   n_faces         <--  number of faces
 *   vtx_coord       <--  vertex coordinates
 *   face_vtx_idx    <--  "face -> vertices" connectivity index
 *   face_vtx_lst    <--  "face -> vertices" connectivity list
 *   face_normal     -->  surface normal of the face
 *
 *
 *                          Pi+1
 *              *---------*                   B  : barycentre of the polygon
 *             / .       . \
 *            /   .     .   \                 Pi : vertices of the polygon
 *           /     .   .     \
 *          /       . .  Ti   \               Ti : triangle
 *         *.........B.........* Pi
 *     Pn-1 \       . .       /
 *           \     .   .     /
 *            \   .     .   /
 *             \ .   T0  . /
 *              *---------*
 *            P0
 *----------------------------------------------------------------------------*/

static void
_compute_face_normal(cs_lnum_t         dim,
                     cs_lnum_t         n_faces,
                     const cs_real_t   vtx_coord[],
                     const cs_lnum_t   face_vtx_idx[],
                     const cs_lnum_t   face_vtx_lst[],
                     cs_real_t         face_normal[])
{
  cs_lnum_t  i, face_id, tri_id, vtx_id, start_id, end_id, shift;
  cs_lnum_t  n_face_vertices, n_max_face_vertices;
  _vtx_coords_t  this_face_normal, this_face_barycentre;
  _vtx_coords_t  vect1, vect2;

  _vtx_coords_t  *face_vtx_coord = NULL;
  _vtx_coords_t  *triangle_normal = NULL;

  /* Return if there is not enough data (some SolCom meshes) */

  if (face_vtx_idx == NULL || face_vtx_lst == NULL)
    return;

  /* Checking */

  if (dim != 3)
    bft_error(__FILE__, __LINE__,0,
              _("Face geometric quantities computation is only\n"
                "implemented in 3D."));

  assert(face_normal != NULL || n_faces == 0);

  /* Counting and allocation */

  n_max_face_vertices = 0;

  for (face_id = 0; face_id < n_faces; face_id++) {
    n_face_vertices = face_vtx_idx[face_id + 1] - face_vtx_idx[face_id];
    if (n_max_face_vertices <= n_face_vertices)
      n_max_face_vertices = n_face_vertices;
  }

  BFT_MALLOC(face_vtx_coord, n_max_face_vertices + 1, _vtx_coords_t);
  BFT_MALLOC(triangle_normal, n_max_face_vertices, _vtx_coords_t);

  /* Loop on each face */

  for (face_id = 0; face_id < n_faces; face_id++) {

    /* Initialization */

    n_face_vertices = 0;

    start_id = face_vtx_idx[face_id] - 1;
    end_id = face_vtx_idx[face_id + 1] - 1;

    for (i = 0; i < 3; i++)
      this_face_normal[i] = 0.0;

    /* Define the polygon (P) according to the vertices (Pi) of the face */

    for (vtx_id = start_id; vtx_id < end_id; vtx_id++) {

      shift = 3 * (face_vtx_lst[vtx_id] - 1);
      for (i = 0; i < 3; i++)
        face_vtx_coord[n_face_vertices][i] = vtx_coord[shift + i];
      n_face_vertices++;

    }

    for (i = 0; i < 3; i++)
      face_vtx_coord[n_face_vertices][i] = face_vtx_coord[0][i];

    /* Compute the barycentre of the face */

    for (i = 0; i < 3; i++) {

      this_face_barycentre[i] = 0.0;
      for (vtx_id = 0; vtx_id < n_face_vertices; vtx_id++)
        this_face_barycentre[i] += face_vtx_coord[vtx_id][i];
      this_face_barycentre[i] /= n_face_vertices;

    }

    /* Loop on the triangles of the face (defined by an edge of the face
       and its barycentre) */

    for (tri_id = 0 ; tri_id < n_face_vertices ; tri_id++) {

      /*----------------------------------------------------------------------*/
      /* Computation of the normal of each triangle Ti :                      */
      /*                                                                      */
      /*  ->            -->   -->                                             */
      /*  N(Ti) = 1/2 ( BPi X BPi+1 )                                         */
      /*----------------------------------------------------------------------*/

      for (i = 0; i < 3; i++) {
        vect1[i] = face_vtx_coord[tri_id    ][i] - this_face_barycentre[i];
        vect2[i] = face_vtx_coord[tri_id + 1][i] - this_face_barycentre[i];
      }

      _CS_CROSS_PRODUCT(triangle_normal[tri_id], vect1, vect2);

      for (i = 0; i < 3; i++)
        triangle_normal[tri_id][i] *= 0.5;

      /*----------------------------------------------------------------------*/
      /* Computation of the normal of the polygon                             */
      /*  => vectorial sum of normals of each triangle                        */
      /*                                                                      */
      /*  ->      n-1   ->                                                    */
      /*  N(P) =  Sum ( N(Ti) )                                               */
      /*          i=0                                                         */
      /*----------------------------------------------------------------------*/

      for (i = 0; i < 3; i++)
        this_face_normal[i] += triangle_normal[tri_id][i];

    } /* End of loop on triangles of the face */

    /* Store result in appropriate structure */

    for (i = 0; i < 3; i++)
      face_normal[face_id * 3 + i] = this_face_normal[i];

  } /* End of loop on faces */

  BFT_FREE(triangle_normal);
  BFT_FREE(face_vtx_coord);

}

/*----------------------------------------------------------------------------
 * Compute quantities associated to faces (border or internal)
 *
 * parameters:
 *   dim             <--  dimension
 *   n_faces         <--  number of faces
 *   vtx_coord       <--  vertex coordinates
 *   face_vtx_idx    <--  "face -> vertices" connectivity index
 *   face_vtx_lst    <--  "face -> vertices" connectivity list
 *   face_cog        -->  coordinates of the centre of gravity of the faces
 *   face_norm       -->  face surface normals
 *   face_surf       -->  face surfaces (optional), or NULL
 *
 *                          Pi+1
 *              *---------*                   B  : barycentre of the polygon
 *             / .       . \
 *            /   .     .   \                 Pi : vertices of the polygon
 *           /     .   .     \
 *          /       . .  Ti   \               Ti : triangle
 *         *.........B.........* Pi
 *     Pn-1 \       . .       /
 *           \     .   .     /
 *            \   .     .   /
 *             \ .   T0  . /
 *              *---------*
 *            P0
 *----------------------------------------------------------------------------*/

static void
_compute_face_quantities(const cs_lnum_t   dim,
                         const cs_lnum_t   n_faces,
                         const cs_real_t   vtx_coord[],
                         const cs_lnum_t   face_vtx_idx[],
                         const cs_lnum_t   face_vtx_lst[],
                         cs_real_t         face_cog[],
                         cs_real_t         face_norm[],
                         cs_real_t         face_surf[])
{
  cs_lnum_t  i, fac_id, tri_id;
  cs_lnum_t  vtx_id, lower_vtx_id, upper_vtx_id;
  cs_lnum_t  n_face_vertices, n_max_face_vertices;
  cs_lnum_t  lower_coord_id;
  cs_real_t  face_surface, tri_surface;
  cs_real_t  face_vol_part, tri_vol_part, rectif_cog;
  _vtx_coords_t  face_barycentre, face_normal;
  _vtx_coords_t  face_centre, tri_centre;
  _vtx_coords_t  vect1, vect2;

  _vtx_coords_t  *face_vtx_coord = NULL;
  _vtx_coords_t  *triangle_norm = NULL;

  /* Return if there is not enough data (some SolCom meshes) */

  if (face_vtx_idx == NULL || face_vtx_lst == NULL)
    return;

  /* Checking */

  if (dim != 3)
    bft_error(__FILE__, __LINE__,0,
              _("Face geometric quantities computation is only\n"
                "implemented in 3D."));

  assert(face_cog != NULL || n_faces == 0);
  assert(face_norm != NULL || n_faces == 0);

  /* Counting and allocation */

  n_max_face_vertices = 0;

  for (fac_id = 0; fac_id < n_faces; fac_id++) {
    n_face_vertices = face_vtx_idx[fac_id + 1] - face_vtx_idx[fac_id];
    if (n_max_face_vertices <= n_face_vertices)
      n_max_face_vertices = n_face_vertices;
  }

  BFT_MALLOC(face_vtx_coord, n_max_face_vertices + 1, _vtx_coords_t);
  BFT_MALLOC(triangle_norm, n_max_face_vertices, _vtx_coords_t);

  /*=========================================================================*/
  /* Loop on faces                                                           */
  /*=========================================================================*/

  for (fac_id = 0; fac_id < n_faces; fac_id++) {

    tri_vol_part = 0.;
    face_surface = 0.0;

    /* Define the polygon (P) according to the vertices (Pi) of the face */

    lower_vtx_id = face_vtx_idx[fac_id] - 1;
    upper_vtx_id = face_vtx_idx[fac_id + 1] - 1;

    n_face_vertices = 0;

    for (vtx_id = lower_vtx_id; vtx_id < upper_vtx_id; vtx_id++) {

      lower_coord_id = 3 * (face_vtx_lst[vtx_id] - 1);

      for (i = X; i < 3; i++)
        face_vtx_coord[n_face_vertices][i] = vtx_coord[lower_coord_id + i];

      n_face_vertices++;

    }

    for (i = X; i < 3; i++)
      face_vtx_coord[n_face_vertices][i] = face_vtx_coord[0][i];

    /*------------------------------------------------------------------------
     * Compute barycentre (B) coordinates for the polygon (P)
     *
     *  -->    1   n-1  -->
     *  OB  =  -  Somme OPi
     *         n   i=0
     *------------------------------------------------------------------------*/

    for (i = X; i < 3; i++) {

      face_barycentre[i] = 0.0;

      for (vtx_id = 0; vtx_id < n_face_vertices; vtx_id++)
        face_barycentre[i] += face_vtx_coord[vtx_id][i];

      face_barycentre[i] /= n_face_vertices;

    }

    for (i = X; i < 3; i++) {
      face_normal[i] = 0.0;
      face_centre[i] = 0.0;
    }

    /* First loop on triangles of the face (computation of surface normals)   */
    /*========================================================================*/

    for (tri_id = 0 ; tri_id < n_face_vertices ; tri_id++) {

      /*----------------------------------------------------------------------
       * Computation of the normal of the triangle Ti :
       *
       *  ->            -->   -->
       *  N(Ti) = 1/2 ( BPi X BPi+1 )
       *----------------------------------------------------------------------*/

      for (i = X; i < 3; i++) {
        vect1[i] = face_vtx_coord[tri_id    ][i] - face_barycentre[i];
        vect2[i] = face_vtx_coord[tri_id + 1][i] - face_barycentre[i];
      }

      _CS_CROSS_PRODUCT(triangle_norm[tri_id], vect1, vect2);

      for (i = X; i < 3; i++)
        triangle_norm[tri_id][i] *= 0.5;

      /*----------------------------------------------------------------------
       * Computation of the normal of the polygon
       *  => vector sum of normals of triangles
       *
       *  ->      n-1   ->
       *  N(P) =  Sum ( N(Ti) )
       *          i=0
       *----------------------------------------------------------------------*/

      for (i = X; i < 3; i++)
        face_normal[i] += triangle_norm[tri_id][i];

    } /* End of loop on triangles of the face */

    /* Second loop on triangles of the face (for the barycentre)        */
    /*==================================================================*/

    for (tri_id = 0; tri_id < n_face_vertices; tri_id++) {

      /*----------------------------------------------------------------------
       * Compation of the gravity centre G(Ti) of each triangle (Ti)
       *
       *  -->            -->  -->   -->
       *  OG(Ti) = 1/3 ( OB + OPi + OPi+1 )
       *
       * And their part in the volume of Ti
       *
       *  -->    ->
       *  OG(Ti).N(Ti)
       *----------------------------------------------------------------------*/

      for (i = X; i < 3; i++) {

        tri_centre[i] = face_barycentre[i]
                      + face_vtx_coord[tri_id    ][i]
                      + face_vtx_coord[tri_id + 1][i];

        tri_centre[i] /= 3.0;

        tri_vol_part += (tri_centre[i] * triangle_norm[tri_id][i]);

      }

      /*----------------------------------------------------------------------
       * Computation of the area of Ti (norm of the surface normal)
       *
       *               ->
       *  Surf(Ti) = | N(Ti) |
       *----------------------------------------------------------------------*/

      tri_surface = _CS_MODULE(triangle_norm[tri_id]);

      if (_CS_DOT_PRODUCT(triangle_norm[tri_id], face_normal) < 0.0)
        tri_surface *= -1.0;

      face_surface += tri_surface;

      /*----------------------------------------------------------------------
       *   n-1
       *   Sum  Surf(Ti) G(Ti)
       *   i=0
       *----------------------------------------------------------------------*/

      for (i = X; i < 3; i++)
        face_centre[i] += tri_surface * tri_centre[i];

    } /* End of second loop  on triangles of the face */

    /*------------------------------------------------------------------------
     * Compute the centre of gravity G(P) of the polygon P :
     *
     *           n-1
     *           Sum  Surf(Ti) G(Ti)
     *           i=0
     *  G(P) = -----------------------
     *           n-1
     *           Sum  Surf(Ti)
     *           i=0
     *
     * Computation of the part of volume of the polygon (before rectification)
     *
     *  -->    ->
     *  OG(P).N(P)
     *------------------------------------------------------------------------*/

    face_vol_part = 0.0;

    for (i = X; i < 3; i++) {
      face_centre[i] = face_centre[i] / face_surface;
      face_vol_part += (face_centre[i] * face_normal[i]);
    }

    rectif_cog = (tri_vol_part - face_vol_part) / (face_surface * face_surface);

    for (i = X; i < 3; i++)
      face_centre[i] += rectif_cog * face_normal[i];

    /* Store result in appropriate structure */

    for (i = X; i < 3; i++) {
      face_cog[fac_id * 3 + i] = face_centre[i];
      face_norm[fac_id * 3 + i] = face_normal[i];
    }

  } /* End of loop on faces */

  BFT_FREE(triangle_norm);
  BFT_FREE(face_vtx_coord);

  if (face_norm == NULL || face_surf == NULL)
    return;

  if (dim != 3)
    bft_error(__FILE__, __LINE__,0,
              _("Face surface computation is only\n"
                "implemented in 3D."));

  /* Compute optional face surfaces */
  /*--------------------------------*/

  if (face_surf != NULL) {

    for (fac_id = 0; fac_id < n_faces; fac_id++) {
      double nx = face_norm[fac_id*3];
      double ny = face_norm[fac_id*3+1];
      double nz = face_norm[fac_id*3+2];
      face_surf[fac_id] = sqrt(nx*nx + ny*ny + nz*nz);
    }
  }
}

/*----------------------------------------------------------------------------*
 * Compute centre of gravity of cells C from their vertices S(i) where
 * i=0, n-1
 *
 * -->      1    n-1   -->
 * OB(C) = ---   Sum   OSi
 *          n    i=0
 *
 * parameters:
 *   mesh          <--  pointer to mesh structure
 *   cell_cen      -->  centre of gravity of cells
 *----------------------------------------------------------------------------*/

static void
_compute_cell_cen_vertex(const cs_mesh_t  *mesh,
                         cs_real_t         cell_cen[])
{
  cs_lnum_t  i, j, k, cell_id, fac_id, vtx_id;
  cs_lnum_t  face_num, vtx_counter;

  cs_lnum_t  *vtx_tag = NULL;
  cs_lnum_t  *_face_vtx_idx = NULL, *_face_vtx_lst = NULL;
  cs_lnum_t  *cell_faces_idx = NULL, *cell_faces_lst = NULL;

  /* Return if there is not enough data (Solcom case except radiative module) */

  if (mesh->i_face_vtx_lst == NULL && mesh->b_face_vtx_lst == NULL)
    return;

  /* Checking */

  if (mesh->dim != 3)
    bft_error(__FILE__, __LINE__,0,
              _("Cell centre computation is only implemented in 3D."));

  assert(cell_cen != NULL);

  /* Allocation and initialization */

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

  for (vtx_id = 0 ; vtx_id < mesh->n_vertices ; vtx_id++)
    vtx_tag[vtx_id] = -1;

  /* Initialization */

  for (i = 0; i < 3*mesh->n_cells_with_ghosts; i++)
    cell_cen[i] = 0.0;

  /* Extract "cell -> faces" connectivity */

  cs_mesh_connect_get_cell_faces(mesh,
                                 mesh->n_cells,
                                 NULL,
                                 &cell_faces_idx,
                                 &cell_faces_lst);

  /* Loop on cells */
  /* ------------- */

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

    vtx_counter = 0;

    /* Loop on faces of the cell */

    for (j = cell_faces_idx[cell_id]; j < cell_faces_idx[cell_id + 1]; j++) {

      face_num = cell_faces_lst[j - 1];

      /* Internal or border face */

      if (face_num > mesh->n_b_faces) {
        fac_id = face_num - mesh->n_b_faces - 1;
        _face_vtx_idx = mesh->i_face_vtx_idx;
        _face_vtx_lst = mesh->i_face_vtx_lst;
      }
      else {
        fac_id = face_num - 1;
        _face_vtx_idx = mesh->b_face_vtx_idx;
        _face_vtx_lst = mesh->b_face_vtx_lst;
      }

      /* Loop on vertices of the face */

      for (k = _face_vtx_idx[fac_id]-1; k < _face_vtx_idx[fac_id + 1]-1; k++) {

        vtx_id = _face_vtx_lst[k] - 1;

        if (vtx_tag[vtx_id] < cell_id) {
          for (i = 0 ; i < 3 ; i++)
            cell_cen[cell_id*3 + i] += mesh->vtx_coord[vtx_id*3 + i];
          vtx_counter += 1;
          vtx_tag[vtx_id] = cell_id;
        }

      }

    } /* End of loop on faces of the cell */

    for (i = 0; i < 3; i++)
      cell_cen[cell_id*3 + i] /= (double)vtx_counter;

  } /* End of loop on cells */

  /* Free memory */

  BFT_FREE(vtx_tag);
  BFT_FREE(cell_faces_idx);
  BFT_FREE(cell_faces_lst);

}

/*----------------------------------------------------------------------------*
 * Compute centre of gravity of cells C from their faces F(i) where i=0, n-1
 *
 *           n-1
 *           Sum  Surf(Fi) G(Fi)
 *           i=0
 *  G(C) = -----------------------
 *           n-1
 *           Sum  Surf(Fi)
 *           i=0
 *
 * parameters:
 *   mesh           <--  pointer to mesh structure
 *   i_face_norm    <--  surface normal of internal faces
 *   i_face_cog     <--  centre of gravity of internal faces
 *   b_face_norm    <--  surface normal of border faces
 *   b_face_cog     <--  centre of gravity of border faces
 *   cell_cen       -->  centre of gravity of cells
 *----------------------------------------------------------------------------*/

static void
_compute_cell_cen_face(const cs_mesh_t  *mesh,
                       const cs_real_t   i_face_norm[],
                       const cs_real_t   i_face_cog[],
                       const cs_real_t   b_face_norm[],
                       const cs_real_t   b_face_cog[],
                       cs_real_t         cell_cen[])
{
  cs_lnum_t  i, j, fac_id, cell_id, cell_id1, cell_id2;
  cs_real_t  area;
  cs_real_t  _norm[3];

  cs_real_t  *cell_area = NULL;

  /* Mesh connectivity */

  const  cs_lnum_t  dim = mesh->dim;
  const  cs_lnum_t  n_i_faces = mesh->n_i_faces;
  const  cs_lnum_t  n_b_faces = mesh->n_b_faces;
  const  cs_lnum_t  n_cells = mesh->n_cells;
  const  cs_lnum_t  n_cells_with_ghosts = mesh->n_cells_with_ghosts;
  const  cs_lnum_t  *i_face_cells = mesh->i_face_cells;
  const  cs_lnum_t  *b_face_cells = mesh->b_face_cells;

  /* Return if ther is not enough data (Solcom case except rediative module
     or Pre-processor 1.2.d without option "-n") */

  if (mesh->i_face_vtx_lst == NULL && mesh->b_face_vtx_lst == NULL)
    return;

  /* Checking */

  if (dim != 3)
    bft_error(__FILE__, __LINE__,0,
              _("Cell centre computation is only implemented in 3D."));

  assert(cell_cen != NULL);

  /* Initialization */

  BFT_MALLOC(cell_area, n_cells_with_ghosts, cs_real_t);

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

    cell_area[j] = 0.;

    for (i = 0; i < dim; i++)
      cell_cen[dim*j + i] = 0. ;

  }

  /* ---------------------- */
  /* Loop on internal faces */
  /* ---------------------- */

  for (fac_id = 0; fac_id < n_i_faces; fac_id++) {

    /* ----------------------------------------------------------
     * For each cell sharing the internal face, we update
     * cell_cen and cell_area
     * ---------------------------------------------------------- */

    cell_id1 = i_face_cells[2*fac_id    ] - 1;
    cell_id2 = i_face_cells[2*fac_id + 1] - 1;

    /* Computation of the area of the face */

    for (i = 0; i < dim; i++)
      _norm[i] = i_face_norm[dim*fac_id + i];

    area = _CS_MODULE(_norm);

    cell_area[cell_id1] += area;
    cell_area[cell_id2] += area;

    /* Computation of the numerator */

    for (i = 0; i < dim; i++) {
      cell_cen[dim*cell_id1 + i] += i_face_cog[dim*fac_id + i]*area;
      cell_cen[dim*cell_id2 + i] += i_face_cog[dim*fac_id + i]*area;
    }

  } /* End of loop on internal faces */

  /* -------------------- */
  /* Loop on border faces */
  /* -------------------- */

  for (fac_id = 0; fac_id < n_b_faces; fac_id++) {

    /* -------------------------------------------------------------
     * For each cell sharing a border face, we update the numerator
     * of cell_cen and cell_area
     * ------------------------------------------------------------- */

    cell_id1 = b_face_cells[fac_id] - 1;

    /* Computation of the area of the face */

    for (i = 0; i < dim; i++)
      _norm[i] = b_face_norm[dim*fac_id + i];

    area = _CS_MODULE(_norm);
    cell_area[cell_id1] += area;

    /* Computation of the numerator */

    for (i = 0; i < dim; i++)
      cell_cen[dim*cell_id1 + i] += b_face_cog[dim*fac_id + i]*area;

  } /* End of loop on border faces */

  /* ------------------------------------------------------------------
   * Loop on cells to finalize the computation of centre of gravity
   * ------------------------------------------------------------------*/

  for (cell_id = 0; cell_id < n_cells; cell_id++) {

    for (i = 0; i < dim; i++)
      cell_cen[cell_id*dim + i] /= cell_area[cell_id];

  } /* End of loop on cells */

  /* Free memory */

  BFT_FREE(cell_area);

}

/*----------------------------------------------------------------------------
 * Compute the volume of cells C from their n faces F(i) and their center of
 * gravity G(Fi) where i=0, n-1
 *
 *         1    n-1
 *  G(C) = - .  Sum  Surf(Fi) G(Fi)
 *         3    i=0
 *
 * parameters:
 *   mesh           <--  pointer to mesh structure
 *   i_face_norm    <--  surface normal of internal faces
 *   i_face_cog     <--  centre of gravity of internal faces
 *   b_face_norm    <--  surface normal of border faces
 *   b_face_cog     <--  centre of gravity of border faces
 *   cell_vol       -->  cells volume
 *   min_vol        -->  minimum control volume
 *   max_vol        -->  maximum control volume
 *   tot_vol        -->  total   control volume
 *----------------------------------------------------------------------------*/

static void
_compute_cell_volume(const cs_mesh_t  *mesh,
                     const cs_real_t   i_face_norm[],
                     const cs_real_t   i_face_cog[],
                     const cs_real_t   b_face_norm[],
                     const cs_real_t   b_face_cog[],
                     cs_real_t         cell_vol[],
                     cs_real_t         *min_vol,
                     cs_real_t         *max_vol,
                     cs_real_t         *tot_vol)
{
  cs_lnum_t  id1, id2, i, fac_id, cell_id;

  cs_real_t  flux = 0;

  const cs_real_t  a_third = 1.0/3.0;
  const cs_lnum_t  dim = mesh->dim;

  /* Initialization */

  for (cell_id = 0; cell_id < mesh->n_cells_with_ghosts; cell_id++)
    cell_vol[cell_id] = 0;

  *min_vol =  1.e12;
  *max_vol = -1.e12;
  *tot_vol = 0.;

  /* Loop on internal faces */

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

    id1 = mesh->i_face_cells[2*fac_id] - 1;
    id2 = mesh->i_face_cells[2*fac_id + 1] - 1;

    flux = 0;
    for (i = 0; i < dim; i++)
      flux += i_face_norm[dim*fac_id + i] * i_face_cog[dim*fac_id + i];

    cell_vol[id1] += flux;
    cell_vol[id2] -= flux;

  }

  /* Loop on border faces */

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

    id1 = mesh->b_face_cells[fac_id] - 1;

    flux = 0;
    for (i = 0; i < dim; i++)
      flux += b_face_norm[dim*fac_id + i] * b_face_cog[dim*fac_id + i];

    cell_vol[id1] += flux;

  }

  /* Computation of the volume */

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

    cell_vol[cell_id] *= a_third;

    *min_vol = CS_MIN(*min_vol, cell_vol[cell_id]);
    *max_vol = CS_MAX(*max_vol, cell_vol[cell_id]);
    *tot_vol = *tot_vol + cell_vol[cell_id];

  }
}

/*----------------------------------------------------------------------------
 * Compute some distances relative to faces and associated weighting.
 *
 * parameters:
 *   dim            <--  dimension
 *   n_i_faces      <--  number of interior faces
 *   n_b_faces      <--  number of border  faces
 *   i_face_cells   <--  interior "faces -> cells" connectivity
 *   b_face_cells   <--  border "faces -> cells" connectivity
 *   i_face_norm    <--  surface normal of interior faces
 *   b_face_norm    <--  surface normal of border faces
 *   i_face_cog     <--  centre of gravity of interior faces
 *   b_face_cog     <--  centre of gravity of border faces
 *   i_face_surf    <--  interior faces surface
 *   b_face_surf    <--  border faces surface
 *   cell_cen       <--  cell center
 *   i_dist         -->  distance IJ.Nij for interior faces
 *   b_dist         -->  likewise for border faces
 *   weight         -->  weighting factor (Aij=pond Ai+(1-pond)Aj)
 *----------------------------------------------------------------------------*/

static void
_compute_face_distances(const cs_lnum_t  dim,
                        const cs_lnum_t  n_i_faces,
                        const cs_lnum_t  n_b_faces,
                        const cs_lnum_t  i_face_cells[],
                        const cs_lnum_t  b_face_cells[],
                        const cs_real_t  i_face_normal[],
                        const cs_real_t  b_face_normal[],
                        const cs_real_t  i_face_cog[],
                        const cs_real_t  b_face_cog[],
                        const cs_real_t  i_face_surf[],
                        const cs_real_t  b_face_surf[],
                        const cs_real_t  cell_cen[],
                        cs_real_t        i_dist[],
                        cs_real_t        b_dist[],
                        cs_real_t        weight[])
{
  cs_lnum_t face_id;
  cs_lnum_t cell_id, cell_id1, cell_id2;

  cs_real_t surfn, surfx, surfy, surfz;
  cs_real_t xvn, yvn, zvn, xvv, yvv, zvv;
  cs_real_t dist2f;

  cs_gnum_t w_count = 0;

  /* Interior faces */

  for (face_id = 0; face_id < n_i_faces; face_id++) {

    surfx = i_face_normal[face_id*dim];
    surfy = i_face_normal[face_id*dim + 1];
    surfz = i_face_normal[face_id*dim + 2];

    surfn = i_face_surf[face_id];

    cell_id1 = i_face_cells[2*face_id] - 1;
    cell_id2 = i_face_cells[2*face_id + 1] - 1;

    /* Distance between the face centre of gravity
       and the neighbor cell centre */
    xvn = cell_cen[cell_id2*dim]     - i_face_cog[face_id*dim];
    yvn = cell_cen[cell_id2*dim + 1] - i_face_cog[face_id*dim + 1];
    zvn = cell_cen[cell_id2*dim + 2] - i_face_cog[face_id*dim + 2];

    /* Distance between the neighbor cell centres */
    xvv = cell_cen[cell_id2*dim]     - cell_cen[cell_id1*dim];
    yvv = cell_cen[cell_id2*dim + 1] - cell_cen[cell_id1*dim + 1];
    zvv = cell_cen[cell_id2*dim + 2] - cell_cen[cell_id1*dim + 2];

    /* dot-product with the normal */
    i_dist[face_id] = (xvv*surfx + yvv*surfy + zvv*surfz) / surfn;

    if (CS_ABS(i_dist[face_id]) > 1e-12) {
      /* dot-product with the normal */
      dist2f = (xvn*surfx + yvn*surfy + zvn*surfz) / surfn;
      weight[face_id] = dist2f / i_dist[face_id];
    }
    else {
      w_count++;
      weight[face_id] = 0.5;
    }

  }

  cs_parall_counter(&w_count, 1);

  if (w_count > 0)
    bft_printf(_("\n"
                 "%llu faces have a null distance between centers.\n"
                 "For these faces, the weight is set to 0.5.\n"),
               (unsigned long long)w_count);

  /* Border faces */

  for (face_id = 0; face_id < n_b_faces; face_id++) {

    surfx = b_face_normal[face_id*dim];
    surfy = b_face_normal[face_id*dim + 1];
    surfz = b_face_normal[face_id*dim + 2];

    surfn = b_face_surf[face_id];

    cell_id = b_face_cells[face_id] - 1;

    /* Distance between the face centre of gravity
       and the neighbor cell centre */
    xvn = b_face_cog[face_id*dim]     - cell_cen[cell_id*dim];
    yvn = b_face_cog[face_id*dim + 1] - cell_cen[cell_id*dim + 1];
    zvn = b_face_cog[face_id*dim + 2] - cell_cen[cell_id*dim + 2];

    b_dist[face_id] = (xvn*surfx + yvn*surfy + zvn*surfz) / surfn;

  }
}

/*----------------------------------------------------------------------------
 * Compute some vectors to handle non-orthogonalities.
 *
 * Let a face and I, J the centers of neighboring cells
 *   (only I is defined for a border face)
 *
 * The face is oriented from I to J, with Nij its normal.
 *   (border faces are oriented towards the exterior)
 * The norm of Nij is 1.
 * The face surface is Sij.
 *
 * I' and J' are defined as the orthogonal projection of I and J on the line
 * orthogonal to the face passing through the center of gravity F of the face.
 *   (only I' is defined for a border face)
 *
 * We compute here the vector I'J' for interior faces (dijpf)
 *                 the vector II'  for border faces   (diipb)
 *                 the vector OF   for interior faces (dofij)
 *
 * We also have the following formulae
 *   II' = IG - (IG.Nij)Nij
 *   JJ' = JG - (JG.Nij)Nij
 *
 * parameters:
 *   dim            <--  dimension
 *   n_i_faces      <--  number of interior faces
 *   n_b_faces      <--  number of border  faces
 *   i_face_cells   <--  interior "faces -> cells" connectivity
 *   b_face_cells   <--  border "faces -> cells" connectivity
 *   i_face_norm    <--  surface normal of interior faces
 *   b_face_norm    <--  surface normal of border faces
 *   i_face_cog     <--  centre of gravity of interior faces
 *   b_face_cog     <--  centre of gravity of border faces
 *   i_face_surf    <--  interior faces surface
 *   b_face_surf    <--  border faces surface
 *   cell_cen       <--  cell center
 *   weight         <--  weighting factor (Aij=pond Ai+(1-pond)Aj)
 *   dijpf          -->  vector i'j' for interior faces
 *   diipb          -->  vector ii'  for border faces
 *   dofij          -->  vector OF   for interior faces
 *----------------------------------------------------------------------------*/

static void
_compute_face_vectors(const cs_lnum_t  dim,
                      const cs_lnum_t  n_i_faces,
                      const cs_lnum_t  n_b_faces,
                      const cs_lnum_t  i_face_cells[],
                      const cs_lnum_t  b_face_cells[],
                      const cs_real_t  i_face_normal[],
                      const cs_real_t  b_face_normal[],
                      const cs_real_t  i_face_cog[],
                      const cs_real_t  b_face_cog[],
                      const cs_real_t  i_face_surf[],
                      const cs_real_t  b_face_surf[],
                      const cs_real_t  cell_cen[],
                      const cs_real_t  weight[],
                      cs_real_t        dijpf[],
                      cs_real_t        diipb[],
                      cs_real_t        dofij[])
{
  cs_lnum_t face_id;
  cs_lnum_t cell_id, cell_id1, cell_id2;

  cs_real_t dipjp, psi, pond;
  cs_real_t surfnx, surfny, surfnz;
  cs_real_t vecigx, vecigy, vecigz, vecijx, vecijy, vecijz;

  /* Interior faces */

  for (face_id = 0; face_id < n_i_faces; face_id++) {

    cell_id1 = i_face_cells[2*face_id] - 1;
    cell_id2 = i_face_cells[2*face_id  + 1] - 1;

    /* Normalized normal */
    surfnx = i_face_normal[face_id*dim]     / i_face_surf[face_id];
    surfny = i_face_normal[face_id*dim + 1] / i_face_surf[face_id];
    surfnz = i_face_normal[face_id*dim + 2] / i_face_surf[face_id];

    /* ---> IJ */
    vecijx = cell_cen[cell_id2*dim]     - cell_cen[cell_id1*dim];
    vecijy = cell_cen[cell_id2*dim + 1] - cell_cen[cell_id1*dim + 1];
    vecijz = cell_cen[cell_id2*dim + 2] - cell_cen[cell_id1*dim + 2];

    /* ---> DIJPP = IJ.NIJ */
    dipjp = vecijx*surfnx + vecijy*surfny + vecijz*surfnz;

    /* ---> DIJPF = (IJ.NIJ).NIJ */
    dijpf[face_id*dim]     = dipjp*surfnx;
    dijpf[face_id*dim + 1] = dipjp*surfny;
    dijpf[face_id*dim + 2] = dipjp*surfnz;

    pond = weight[face_id];

    /* ---> DOFIJ = OF */
    dofij[face_id*dim]     = i_face_cog[face_id*dim]
      - (        pond *cell_cen[cell_id1*dim]
         + (1. - pond)*cell_cen[cell_id2*dim]);

    dofij[face_id*dim + 1] = i_face_cog[face_id*dim + 1]
      - (        pond *cell_cen[cell_id1*dim + 1]
         + (1. - pond)*cell_cen[cell_id2*dim + 1]);

    dofij[face_id*dim + 2] = i_face_cog[face_id*dim + 2]
      - (        pond *cell_cen[cell_id1*dim + 2]
         + (1. - pond)*cell_cen[cell_id2*dim + 2]);
  }

  /* Border faces */

  for (face_id = 0; face_id < n_b_faces; face_id++) {

    cell_id = b_face_cells[face_id] - 1;

    /* Normalized normal */
    surfnx = b_face_normal[face_id*dim]     / b_face_surf[face_id];
    surfny = b_face_normal[face_id*dim + 1] / b_face_surf[face_id];
    surfnz = b_face_normal[face_id*dim + 2] / b_face_surf[face_id];

    /* ---> IG */
    vecigx = b_face_cog[face_id*dim]     - cell_cen[cell_id*dim];
    vecigy = b_face_cog[face_id*dim + 1] - cell_cen[cell_id*dim + 1];
    vecigz = b_face_cog[face_id*dim + 2] - cell_cen[cell_id*dim + 2];

    /* ---> PSI = IG.NIJ */
    psi = vecigx*surfnx + vecigy*surfny + vecigz*surfnz;

    /* ---> DIIPB = IG - (IG.NIJ)NIJ */
    diipb[face_id*dim]     = vecigx - psi*surfnx;
    diipb[face_id*dim + 1] = vecigy - psi*surfny;
    diipb[face_id*dim + 2] = vecigz - psi*surfnz;

  }
}

/*----------------------------------------------------------------------------
 * Compute some vectors to handle non-orthogonalities.
 *
 * Let a face and I, J the centers of neighboring cells
 *   (only I is defined for a border face)
 *
 * The face is oriented from I to J, with Nij its normal.
 *   (border faces are oriented towards the exterior)
 * The norm of Nij is 1.
 * The face surface is Sij.
 *
 * I' and J' are defined as the orthogonal projection of I and J on the line
 * orthogonal to the face passing through the center of gravity F of the face.
 *   (only I' is defined for a border face)
 *
 * We compute here the vector II' for interior faces (diipf)
 *                 the vector JJ' for interior faces (djjpf)
 *
 * We also have the following formulae
 *   II' = IG - (IG.Nij)Nij
 *   JJ' = JG - (JG.Nij)Nij
 *
 * parameters:
 *   dim            <--  dimension
 *   n_i_faces      <--  number of interior faces
 *   i_face_cells   <--  interior "faces -> cells" connectivity
 *   i_face_norm    <--  surface normal of interior faces
 *   i_face_cog     <--  centre of gravity of interior faces
 *   i_face_surf    <--  interior faces surface
 *   cell_cen       <--  cell center
 *   diipf          -->  vector ii' for interior faces
 *   djjpf          -->  vector jj' for interior faces
 *----------------------------------------------------------------------------*/

static void
_compute_face_sup_vectors(const cs_lnum_t  dim,
                          const cs_lnum_t  n_i_faces,
                          const cs_lnum_t  i_face_cells[],
                          const cs_real_t  i_face_normal[],
                          const cs_real_t  i_face_cog[],
                          const cs_real_t  i_face_surf[],
                          const cs_real_t  cell_cen[],
                          cs_real_t        diipf[],
                          cs_real_t        djjpf[])
{
  cs_lnum_t face_id;
  cs_lnum_t cell_id1, cell_id2;

  cs_real_t diipp, djjpp;
  cs_real_t surfnx, surfny, surfnz;
  cs_real_t vecigx, vecigy, vecigz, vecjgx, vecjgy, vecjgz;

  /* Interior faces */

  for (face_id = 0; face_id < n_i_faces; face_id++) {

    cell_id1 = i_face_cells[2*face_id] - 1;
    cell_id2 = i_face_cells[2*face_id  + 1] - 1;

    /* Normalized normal */
    surfnx = i_face_normal[face_id*dim]     / i_face_surf[face_id];
    surfny = i_face_normal[face_id*dim + 1] / i_face_surf[face_id];
    surfnz = i_face_normal[face_id*dim + 2] / i_face_surf[face_id];

    /* ---> IG and JG */
    vecigx = i_face_cog[face_id*dim]     - cell_cen[cell_id1*dim];
    vecigy = i_face_cog[face_id*dim + 1] - cell_cen[cell_id1*dim + 1];
    vecigz = i_face_cog[face_id*dim + 2] - cell_cen[cell_id1*dim + 2];

    vecjgx = i_face_cog[face_id*dim]     - cell_cen[cell_id2*dim];
    vecjgy = i_face_cog[face_id*dim + 1] - cell_cen[cell_id2*dim + 1];
    vecjgz = i_face_cog[face_id*dim + 2] - cell_cen[cell_id2*dim + 2];

    /* ---> DIIPP = IG.Nij */
    diipp = vecigx*surfnx + vecigy*surfny + vecigz*surfnz;

    /* ---> DJJPP = JG.Nij */
    djjpp = vecjgx*surfnx + vecjgy*surfny + vecjgz*surfnz;

    /* ---> DIIPF = IG - (IG.Nij)Nij */
    diipf[face_id*dim]     = vecigx - diipp*surfnx;
    diipf[face_id*dim + 1] = vecigy - diipp*surfny;
    diipf[face_id*dim + 2] = vecigz - diipp*surfnz;

    /* ---> DJJPF = JG - (JG.Nij)Nij */
    djjpf[face_id*dim]     = vecjgx - djjpp*surfnx;
    djjpf[face_id*dim + 1] = vecjgy - djjpp*surfny;
    djjpf[face_id*dim + 2] = vecjgz - djjpp*surfnz;

  }
}

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

/*----------------------------------------------------------------------------
 * Query or modification of the option for computing cell centers.
 *
 * This function returns 1 or 2 according to the selected algorithm.
 *
 * Fortran interface :
 *
 * SUBROUTINE ALGCEN (IOPT)
 * *****************
 *
 * INTEGER          IOPT        : <-> : Choice of the algorithm
 *                                      < 0 : query
 *                                        0 : computation based
 *                                            on faces (default choice)
 *                                        1 : computation based
 *                                            on vertices
 *----------------------------------------------------------------------------*/

void
CS_PROCF (algcen, ALGCEN) (cs_int_t  *const iopt)
{
  int  iopt_ret = cs_mesh_quantities_cell_cen_choice((int)(*iopt));

  *iopt = iopt_ret;
}

/*----------------------------------------------------------------------------
 * Set behavior for computing the cocg matrixes for the iterative algo
 * and for the Least square method for scalar and vector gradients.
 *
 * Fortran interface :
 *
 * subroutine comcoc (imrgra)
 * *****************
 *
 * integer          imrgra        : <-- : gradient reconstruction option
 *----------------------------------------------------------------------------*/

void
CS_PROCF (comcoc, COMCOC) (const cs_int_t  *const imrgra)
{
  cs_mesh_quantities_set_cocg_options(*imrgra);
}

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

/*----------------------------------------------------------------------------
 * Query or modification of the option for computing cell centers.
 *
 *  < 0 : query
 *    0 : computation based on faces (default choice)
 *    1 : computation based on vertices
 *
 * algo_choice  <--  choice of algorithm to compute cell centers.
 *
 * returns:
 *  1 or 2 according to the selected algorithm.
 *----------------------------------------------------------------------------*/

int
cs_mesh_quantities_cell_cen_choice(const int algo_choice)
{
  if (algo_choice > 1)
    bft_error
      (__FILE__, __LINE__,0,
       _("The algorithm selection indicator for the cell center of gravity computation\n"
         "can take the following values:\n"
         "  0: computation based on the face centres and surfaces\n"
         "  1: computation based on the vertices\n"
         "and not %d."), cs_glob_mesh_quantities_cell_cen);

  else if (algo_choice >= 0)
    cs_glob_mesh_quantities_cell_cen = algo_choice;

  return cs_glob_mesh_quantities_cell_cen;
}

/*----------------------------------------------------------------------------
 * Compute cocg for iterative gradient reconstruction for scalars.
 *
 * parameters:
 *   gradient_option <-- gradient option (Fortran IMRGRA)
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_set_cocg_options(int  gradient_option)
{
  int _gradient_option = CS_ABS(gradient_option);

  assert(_gradient_option <= 6);

  switch (_gradient_option) {
  case 0:
    _compute_cocg_s_it = true;
    break;
  case 1:
  case 2:
  case 3:
    _compute_cocg_s_lsq = true;
    break;
  case 4:
  case 5:
  case 6:
    _compute_cocg_s_it = true;
    _compute_cocg_s_lsq = true;
    break;
  default:
    break;
  }

  if (gradient_option > 0)
    _compute_cocg_s_it = true;

  _compute_cocg_it = _compute_cocg_s_it;
  _compute_cocg_lsq = _compute_cocg_s_lsq;
}

/*----------------------------------------------------------------------------
 * Create a mesh quantities structure.
 *
 * returns:
 *   pointer to created cs_mesh_quantities_t structure
 *----------------------------------------------------------------------------*/

cs_mesh_quantities_t  *
cs_mesh_quantities_create(void)
{
  cs_mesh_quantities_t  *mesh_quantities = NULL;

  BFT_MALLOC(mesh_quantities, 1, cs_mesh_quantities_t);

  mesh_quantities->cell_cen = NULL;
  mesh_quantities->cell_vol = NULL;
  mesh_quantities->i_face_normal = NULL;
  mesh_quantities->b_face_normal = NULL;
  mesh_quantities->i_face_cog = NULL;
  mesh_quantities->b_face_cog = NULL;
  mesh_quantities->i_face_surf = NULL;
  mesh_quantities->b_face_surf = NULL;
  mesh_quantities->i_dist = NULL;
  mesh_quantities->b_dist = NULL;
  mesh_quantities->weight = NULL;
  mesh_quantities->dijpf = NULL;
  mesh_quantities->diipb = NULL;
  mesh_quantities->dofij = NULL;
  mesh_quantities->diipf = NULL;
  mesh_quantities->djjpf = NULL;
  mesh_quantities->cocgb_s_it = NULL;
  mesh_quantities->cocg_s_it = NULL;
  mesh_quantities->cocgb_s_lsq = NULL;
  mesh_quantities->cocg_s_lsq = NULL;
  mesh_quantities->cocg_it = NULL;
  mesh_quantities->cocg_lsq = NULL;
  mesh_quantities->b_sym_flag = NULL;
  mesh_quantities->bad_cell_flag = NULL;

  return (mesh_quantities);
}

/*----------------------------------------------------------------------------
 * Destroy a mesh quantities structure
 *
 * mesh_quantities <-- pointer to a cs_mesh_quantities_t structure
 *
 * returns:
 *   NULL
 *----------------------------------------------------------------------------*/

cs_mesh_quantities_t *
cs_mesh_quantities_destroy(cs_mesh_quantities_t  *mesh_quantities)
{

  BFT_FREE(mesh_quantities->cell_cen);
  BFT_FREE(mesh_quantities->cell_vol);
  BFT_FREE(mesh_quantities->i_face_normal);
  BFT_FREE(mesh_quantities->b_face_normal);
  BFT_FREE(mesh_quantities->i_face_cog);
  BFT_FREE(mesh_quantities->b_face_cog);
  BFT_FREE(mesh_quantities->i_face_surf);
  BFT_FREE(mesh_quantities->b_face_surf);
  BFT_FREE(mesh_quantities->i_dist);
  BFT_FREE(mesh_quantities->b_dist);
  BFT_FREE(mesh_quantities->weight);
  BFT_FREE(mesh_quantities->dijpf);
  BFT_FREE(mesh_quantities->diipb);
  BFT_FREE(mesh_quantities->dofij);
  BFT_FREE(mesh_quantities->diipf);
  BFT_FREE(mesh_quantities->djjpf);
  BFT_FREE(mesh_quantities->cocgb_s_it);
  BFT_FREE(mesh_quantities->cocg_s_it);
  BFT_FREE(mesh_quantities->cocgb_s_lsq);
  BFT_FREE(mesh_quantities->cocg_s_lsq);
  BFT_FREE(mesh_quantities->cocg_it);
  BFT_FREE(mesh_quantities->cocg_lsq);
  BFT_FREE(mesh_quantities->b_sym_flag);
  BFT_FREE(mesh_quantities->bad_cell_flag);

  BFT_FREE(mesh_quantities);

  return (mesh_quantities);
}

/*----------------------------------------------------------------------------
 * Compute mesh quantities
 *
 * parameters:
 *   mesh            <-- pointer to a cs_mesh_t structure
 *   mesh_quantities <-> pointer to a cs_mesh_quantities_t structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_compute(const cs_mesh_t       *mesh,
                           cs_mesh_quantities_t  *mesh_quantities)
{
  cs_lnum_t  dim = mesh->dim;
  cs_lnum_t  n_i_faces = mesh->n_i_faces;
  cs_lnum_t  n_b_faces = mesh->n_b_faces;
  cs_lnum_t  n_cells_with_ghosts = mesh->n_cells_with_ghosts;

  /* Update the number of passes */

  _n_computations++;

  /* If this is not an update, allocate members of the structure */

  if (mesh_quantities->i_face_normal == NULL)
    BFT_MALLOC(mesh_quantities->i_face_normal, n_i_faces*dim, cs_real_t);

  if (mesh_quantities->i_face_cog == NULL)
    BFT_MALLOC(mesh_quantities->i_face_cog, n_i_faces*dim, cs_real_t);

  if (mesh_quantities->b_face_normal == NULL)
    BFT_MALLOC(mesh_quantities->b_face_normal, n_b_faces*dim, cs_real_t);

  if (mesh_quantities->b_face_cog == NULL)
    BFT_MALLOC(mesh_quantities->b_face_cog, n_b_faces*dim, cs_real_t);

  if (mesh_quantities->cell_cen == NULL)
    BFT_MALLOC(mesh_quantities->cell_cen, n_cells_with_ghosts*dim, cs_real_t);

  if (mesh_quantities->cell_vol == NULL)
    BFT_MALLOC(mesh_quantities->cell_vol, n_cells_with_ghosts, cs_real_t);

  if (mesh_quantities->i_face_surf == NULL)
    BFT_MALLOC(mesh_quantities->i_face_surf, n_i_faces, cs_real_t);

  if (mesh_quantities->b_face_surf == NULL)
    BFT_MALLOC(mesh_quantities->b_face_surf, n_b_faces, cs_real_t);

  if (mesh_quantities->i_dist == NULL)
    BFT_MALLOC(mesh_quantities->i_dist, n_i_faces, cs_real_t);

  if (mesh_quantities->b_dist == NULL)
    BFT_MALLOC(mesh_quantities->b_dist, n_b_faces, cs_real_t);

  if (mesh_quantities->weight == NULL)
    BFT_MALLOC(mesh_quantities->weight, n_i_faces, cs_real_t);

  if (mesh_quantities->dijpf == NULL)
    BFT_MALLOC(mesh_quantities->dijpf, n_i_faces*dim, cs_real_t);

  if (mesh_quantities->diipb == NULL)
    BFT_MALLOC(mesh_quantities->diipb, n_b_faces*dim, cs_real_t);

  if (mesh_quantities->dofij == NULL)
    BFT_MALLOC(mesh_quantities->dofij, n_i_faces*dim, cs_real_t);

  /* Compute 3x3 cocg dimensionless matrix */

  if (_compute_cocg_it == 1) {
    if (mesh_quantities->cocg_it == NULL)
      BFT_MALLOC(mesh_quantities->cocg_it, n_cells_with_ghosts, cs_real_33_t);
  }

  if (_compute_cocg_lsq == 1) {
    if (mesh_quantities->cocg_lsq == NULL)
      BFT_MALLOC(mesh_quantities->cocg_lsq, n_cells_with_ghosts, cs_real_33_t);
  }

  if (mesh_quantities->b_sym_flag == NULL)
    BFT_MALLOC(mesh_quantities->b_sym_flag, n_b_faces, cs_int_t);

  /* Compute centres of gravity, normals, and surfaces of interior faces */

  _compute_face_quantities(dim,
                           n_i_faces,
                           mesh->vtx_coord,
                           mesh->i_face_vtx_idx,
                           mesh->i_face_vtx_lst,
                           mesh_quantities->i_face_cog,
                           mesh_quantities->i_face_normal,
                           mesh_quantities->i_face_surf);

  /* Compute centres of gravity, normals, and surfaces of boundary faces */

  _compute_face_quantities(dim,
                           n_b_faces,
                           mesh->vtx_coord,
                           mesh->b_face_vtx_idx,
                           mesh->b_face_vtx_lst,
                           mesh_quantities->b_face_cog,
                           mesh_quantities->b_face_normal,
                           mesh_quantities->b_face_surf);

  /* Compute cell centers from face barycentres or vertices */

  switch (cs_glob_mesh_quantities_cell_cen) {

  case 0:
    _compute_cell_cen_face(mesh,
                           mesh_quantities->i_face_normal,
                           mesh_quantities->i_face_cog,
                           mesh_quantities->b_face_normal,
                           mesh_quantities->b_face_cog,
                           mesh_quantities->cell_cen);
    break;

  case 1:
    _compute_cell_cen_vertex(mesh,
                             mesh_quantities->cell_cen);
    break;

  default:
    assert(0);

  }

  /* Compute the volume of cells */

  _compute_cell_volume(mesh,
                       mesh_quantities->i_face_normal,
                       mesh_quantities->i_face_cog,
                       mesh_quantities->b_face_normal,
                       mesh_quantities->b_face_cog,
                       mesh_quantities->cell_vol,
                       &(mesh_quantities->min_vol),
                       &(mesh_quantities->max_vol),
                       &(mesh_quantities->tot_vol));

  /* Synchronize geometric quantities */

  if (mesh->halo != NULL) {

    cs_halo_sync_var_strided(mesh->halo, CS_HALO_EXTENDED,
                             mesh_quantities->cell_cen, 3);
    if (mesh->n_init_perio > 0)
      cs_halo_perio_sync_coords(mesh->halo, CS_HALO_EXTENDED,
                                mesh_quantities->cell_cen);

    cs_halo_sync_var(mesh->halo, CS_HALO_EXTENDED, mesh_quantities->cell_vol);

#if defined(HAVE_MPI)
    if (cs_glob_n_ranks > 1) {

      cs_real_t  _min_vol, _max_vol, _tot_vol;

      MPI_Allreduce(&(mesh_quantities->min_vol), &_min_vol, 1, CS_MPI_REAL,
                    MPI_MIN, cs_glob_mpi_comm);

      MPI_Allreduce(&(mesh_quantities->max_vol), &_max_vol, 1, CS_MPI_REAL,
                    MPI_MAX, cs_glob_mpi_comm);

      MPI_Allreduce(&(mesh_quantities->tot_vol), &_tot_vol, 1, CS_MPI_REAL,
                    MPI_SUM, cs_glob_mpi_comm);

      mesh_quantities->min_vol = _min_vol;
      mesh_quantities->max_vol = _max_vol;
      mesh_quantities->tot_vol = _tot_vol;

    }
#endif

  }

  /* Compute some distances relative to faces and associated weighting */

  _compute_face_distances(dim,
                          mesh->n_i_faces,
                          mesh->n_b_faces,
                          mesh->i_face_cells,
                          mesh->b_face_cells,
                          mesh_quantities->i_face_normal,
                          mesh_quantities->b_face_normal,
                          mesh_quantities->i_face_cog,
                          mesh_quantities->b_face_cog,
                          mesh_quantities->i_face_surf,
                          mesh_quantities->b_face_surf,
                          mesh_quantities->cell_cen,
                          mesh_quantities->i_dist,
                          mesh_quantities->b_dist,
                          mesh_quantities->weight);

  /* Compute some vectors relative to faces to handle non-orthogonalities */

  _compute_face_vectors(dim,
                        mesh->n_i_faces,
                        mesh->n_b_faces,
                        mesh->i_face_cells,
                        mesh->b_face_cells,
                        mesh_quantities->i_face_normal,
                        mesh_quantities->b_face_normal,
                        mesh_quantities->i_face_cog,
                        mesh_quantities->b_face_cog,
                        mesh_quantities->i_face_surf,
                        mesh_quantities->b_face_surf,
                        mesh_quantities->cell_cen,
                        mesh_quantities->weight,
                        mesh_quantities->dijpf,
                        mesh_quantities->diipb,
                        mesh_quantities->dofij);

  /* Compute 3x3 cocg matrixes */

  if (_compute_cocg_s_it == 1)
    _compute_cell_cocg_s_it(mesh, mesh_quantities);

  if (_compute_cocg_s_lsq == 1)
    _compute_cell_cocg_s_lsq(mesh, mesh_quantities);

  if (_compute_cocg_it == 1)
    _compute_cell_cocg_it(mesh, mesh_quantities);

  if (_compute_cocg_lsq == 1)
    _compute_cell_cocg_lsq(mesh, mesh_quantities);

  /* Print some information on the control volumes, and check min volume */

  if (_n_computations == 1)
    bft_printf(_(" --- Information on the volumes\n"
                 "       Minimum control volume      = %14.7e\n"
                 "       Maximum control volume      = %14.7e\n"
                 "       Total volume for the domain = %14.7e\n"),
               mesh_quantities->min_vol, mesh_quantities->max_vol,
               mesh_quantities->tot_vol);
  else
    if (mesh_quantities->min_vol <= 0.) {
      bft_printf(_(" --- Information on the volumes\n"
                   "       Minimum control volume      = %14.7e\n"
                   "       Maximum control volume      = %14.7e\n"
                   "       Total volume for the domain = %14.7e\n"),
                 mesh_quantities->min_vol, mesh_quantities->max_vol,
                 mesh_quantities->tot_vol);
      bft_printf(_("\nAbort due to the detection of a negative control "
                   "volume.\n"));
    }
}

/*----------------------------------------------------------------------------
 * Compute mesh quantities -> vectors II' and JJ'
 *
 * parameters:
 *   mesh            <-- pointer to a cs_mesh_t structure
 *   mesh_quantities <-> pointer to a cs_mesh_quantities_t structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_sup_vectors(const cs_mesh_t       *mesh,
                               cs_mesh_quantities_t  *mesh_quantities)
{
  cs_lnum_t  dim = mesh->dim;
  cs_lnum_t  n_i_faces = mesh->n_i_faces;

  if (mesh_quantities->diipf == NULL)
    BFT_MALLOC(mesh_quantities->diipf, n_i_faces*dim, cs_real_t);

  if (mesh_quantities->djjpf == NULL)
    BFT_MALLOC(mesh_quantities->djjpf, n_i_faces*dim, cs_real_t);

  _compute_face_sup_vectors(dim,
                            mesh->n_i_faces,
                            mesh->i_face_cells,
                            mesh_quantities->i_face_normal,
                            mesh_quantities->i_face_cog,
                            mesh_quantities->i_face_surf,
                            mesh_quantities->cell_cen,
                            mesh_quantities->diipf,
                            mesh_quantities->djjpf);
}

/*----------------------------------------------------------------------------
 * Compute internal and border face normal.
 *
 * parameters:
 *   mesh            <-- pointer to a cs_mesh_t structure
 *   p_i_face_normal <-> pointer to the internal face normal array
 *   p_b_face_normal <-> pointer to the border face normal array
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_face_normal(const cs_mesh_t   *mesh,
                               cs_real_t         *p_i_face_normal[],
                               cs_real_t         *p_b_face_normal[])
{
  cs_real_t  *i_face_normal = NULL, *b_face_normal = NULL;

  const cs_lnum_t  n_b_faces = mesh->n_b_faces;
  const cs_lnum_t  n_i_faces = mesh->n_i_faces;
  const cs_lnum_t  dim = mesh->dim;

  /* Internal face treatment */

  BFT_MALLOC(i_face_normal, n_i_faces * dim, cs_real_t);

  _compute_face_normal(dim,
                       mesh->n_i_faces,
                       mesh->vtx_coord,
                       mesh->i_face_vtx_idx,
                       mesh->i_face_vtx_lst,
                       i_face_normal);

  *p_i_face_normal = i_face_normal;

  /* Border face treatment */

  BFT_MALLOC(b_face_normal, n_b_faces * dim, cs_real_t);

  _compute_face_normal(dim,
                       mesh->n_b_faces,
                       mesh->vtx_coord,
                       mesh->b_face_vtx_idx,
                       mesh->b_face_vtx_lst,
                       b_face_normal);

  *p_b_face_normal = b_face_normal;

}

/*----------------------------------------------------------------------------
 * Compute interior face centers and normals.
 *
 * The corresponding arrays are allocated by this function, and it is the
 * caller's responsibility to free them when they are no longer needed.
 *
 * parameters:
 *   mesh            <-- pointer to a cs_mesh_t structure
 *   p_i_face_cog    <-> pointer to the interior face center array
 *   p_i_face_normal <-> pointer to the interior face normal array
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_i_faces(const cs_mesh_t   *mesh,
                           cs_real_t         *p_i_face_cog[],
                           cs_real_t         *p_i_face_normal[])
{
  cs_real_t  *i_face_cog = NULL, *i_face_normal = NULL;

  BFT_MALLOC(i_face_cog, mesh->n_i_faces * mesh->dim, cs_real_t);
  BFT_MALLOC(i_face_normal, mesh->n_i_faces * mesh->dim, cs_real_t);

  _compute_face_quantities(mesh->dim,
                           mesh->n_i_faces,
                           mesh->vtx_coord,
                           mesh->i_face_vtx_idx,
                           mesh->i_face_vtx_lst,
                           i_face_cog,
                           i_face_normal,
                           NULL);

  *p_i_face_cog = i_face_cog;
  *p_i_face_normal = i_face_normal;
}

/*----------------------------------------------------------------------------
 * Compute border face centers and normals.
 *
 * The corresponding arrays are allocated by this function, and it is the
 * caller's responsibility to free them when they are no longer needed.
 *
 * parameters:
 *   mesh            <-- pointer to a cs_mesh_t structure
 *   p_b_face_cog    <-> pointer to the border face center array
 *   p_b_face_normal <-> pointer to the border face normal array
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_b_faces(const cs_mesh_t   *mesh,
                           cs_real_t         *p_b_face_cog[],
                           cs_real_t         *p_b_face_normal[])
{
  cs_real_t  *b_face_cog = NULL, *b_face_normal = NULL;

  BFT_MALLOC(b_face_cog, mesh->n_b_faces * mesh->dim, cs_real_t);
  BFT_MALLOC(b_face_normal, mesh->n_b_faces * mesh->dim, cs_real_t);

  _compute_face_quantities(mesh->dim,
                           mesh->n_b_faces,
                           mesh->vtx_coord,
                           mesh->b_face_vtx_idx,
                           mesh->b_face_vtx_lst,
                           b_face_cog,
                           b_face_normal,
                           NULL);

  *p_b_face_cog = b_face_cog;
  *p_b_face_normal = b_face_normal;
}

/*----------------------------------------------------------------------------
 * Check that no negative volumes are present, and exit on error otherwise.
 *
 * parameters:
 *   mesh            <-- pointer to mesh structure
 *   mesh_quantities <-- pointer to mesh quantities structure
 *   allow_error     <-- 1 if errors are allowed, 0 otherwise
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_check_vol(const cs_mesh_t             *mesh,
                             const cs_mesh_quantities_t  *mesh_quantities,
                             int                          allow_error)
{
  cs_lnum_t  cell_id;

  cs_gnum_t  error_count = 0;

  for (cell_id = 0; cell_id < mesh->n_cells; cell_id++) {
    if (mesh_quantities->cell_vol[cell_id] < 0.0)
      error_count += 1;
  }

#if defined(HAVE_MPI)
  if (cs_glob_n_ranks > 1) {
    cs_gnum_t tot_error_count = 0;
    MPI_Allreduce(&error_count, &tot_error_count, 1, CS_MPI_GNUM, MPI_SUM,
                  cs_glob_mpi_comm);
    error_count = tot_error_count;
  }
#endif

  /* Exit with error */

  if (error_count > 0) {
    const char fmt[]
      = N_("  %llu cells have a Negative volume.\n"
           " Run mesh quality check for post-processing output.\n"
           " In case of mesh joining, this may be due to overly "
           " agressive joining parameters.");

    if (allow_error) {
      cs_base_warn(__FILE__, __LINE__);
      bft_printf(_(fmt), (unsigned long long)error_count);
      bft_printf("\n\n");
    }
    else
      bft_error(__FILE__, __LINE__, 0,
                _(fmt), (unsigned long long)error_count);
  }
}

/*----------------------------------------------------------------------------
 * Update mesh quantities relative to extended ghost cells when the
 * neighborhood is reduced.
 *
 * parameters:
 *   mesh            <-- pointer to a cs_mesh_t structure
 *   mesh_quantities <-> pointer to a cs_mesh_quantities_t structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_reduce_extended(const cs_mesh_t       *mesh,
                                   cs_mesh_quantities_t  *mesh_quantities)
{
  if (_compute_cocg_lsq == 1)
    _compute_cell_cocg_lsq(mesh, mesh_quantities);
  if (_compute_cocg_s_lsq == 1)
    _compute_cell_cocg_s_lsq(mesh, mesh_quantities);
}

/*----------------------------------------------------------------------------
 * Return the number of times mesh quantities have been computed.
 *
 * returns:
 *   number of times mesh quantities have been computed
 *----------------------------------------------------------------------------*/

int
cs_mesh_quantities_compute_count(void)
{
  return _n_computations;
}

/*----------------------------------------------------------------------------
 * Dump a cs_mesh_quantities_t structure
 *
 * parameters:
 *   mesh            <-- pointer to a cs_mesh_t structure
 *   mesh_quantities <-- pointer to a cs_mesh_quantities_t structure
 *----------------------------------------------------------------------------*/

void
cs_mesh_quantities_dump(const cs_mesh_t             *mesh,
                        const cs_mesh_quantities_t  *mesh_quantities)
{
  cs_lnum_t  i;

  const cs_lnum_t  n_cells = mesh->n_cells_with_ghosts;
  const cs_lnum_t  n_i_faces = mesh->n_i_faces;
  const cs_lnum_t  n_b_faces = mesh->n_b_faces;

  const cs_real_t  *cell_cen = mesh_quantities->cell_cen;
  const cs_real_t  *cell_vol = mesh_quantities->cell_vol;
  const cs_real_t  *i_fac_norm = mesh_quantities->i_face_normal;
  const cs_real_t  *b_fac_norm = mesh_quantities->b_face_normal;
  const cs_real_t  *i_fac_cog = mesh_quantities->i_face_cog;
  const cs_real_t  *b_fac_cog = mesh_quantities->b_face_cog;
  const cs_real_t  *i_fac_surf = mesh_quantities->i_face_surf;
  const cs_real_t  *b_fac_surf = mesh_quantities->b_face_surf;

  bft_printf("\n\nDUMP OF A MESH QUANTITIES STRUCTURE: %p\n\n",
             (const void *)mesh_quantities);

  if (mesh_quantities == NULL)
    return;

  /* Cell data */

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

  bft_printf("Cell center coordinates:\n");
  for (i = 0; i < n_cells; i++)
    bft_printf("    < %d >    %.3f    %.3f    %.3f\n", i+1,
               cell_cen[3*i], cell_cen[3*i+1], cell_cen[3*i+2]);

  bft_printf("\nCell volume:\n");
  for (i = 0; i < n_cells; i++)
    bft_printf("    < %d >    %.3f\n", i+1, cell_vol[i]);

  /* Internal faces data */

  bft_printf("\n\n"
             "    ------------------------"
             "    Interior face quantities"
             "    ------------------------\n\n");

  bft_printf("\nInterior face normals\n");
  for (i = 0; i < n_i_faces; i++)
    bft_printf("    < %d >    %.3f    %.3f    %.3f\n", i+1,
               i_fac_norm[3*i], i_fac_norm[3*i+1], i_fac_norm[3*i+2]);

  bft_printf("\nInterior face centers\n");
  for (i = 0; i < n_i_faces; i++)
    bft_printf("    < %d >    %.3f    %.3f    %.3f\n", i+1,
               i_fac_cog[3*i], i_fac_cog[3*i+1], i_fac_cog[3*i+2]);

  bft_printf("\nInterior face surfaces\n");
  for (i = 0; i < n_i_faces; i++)
    bft_printf("    < %d >    %.3f\n", i+1, i_fac_surf[i]);

  /* Border faces data */

  bft_printf("\n\n"
             "    ------------------------"
             "    Boundary face quantities"
             "    ------------------------\n\n");

  bft_printf("\nBoundary face normals\n");
  for (i = 0; i < n_b_faces; i++)
    bft_printf("    < %d >    %.3f    %.3f    %.3f\n", i+1,
               b_fac_norm[3*i], b_fac_norm[3*i+1], b_fac_norm[3*i+2]);

  bft_printf("\nBoundary faces centers\n");
  for (i = 0; i < n_b_faces; i++)
    bft_printf("    < %d >    %.3f    %.3f    %.3f\n", i+1,
               b_fac_cog[3*i], b_fac_cog[3*i+1], b_fac_cog[3*i+2]);

  bft_printf("\nBoundary face surfaces\n");
  for (i = 0; i < n_b_faces; i++)
    bft_printf("    < %d >    %.3f\n", i+1, b_fac_surf[i]);

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

}

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

#if 0 /* Test if face orientation is OK */

  cs_lnum_t  i, fac_id, cell_id;
  cs_real_t  cogfac[3];
  cs_real_t  cogcel[3];
  cs_real_t  normal[3];
  cs_real_t  pscal;

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

    cell_id = mesh->b_face_cells[fac_id] - 1;
    pscal = 0;

    for (i = 0 ; i < 3 ; i++) {
      cogcel[i]  = cs_glob_mesh_quantities->cell_cen[cell_id*3 + i];
      cogfac[i]  = cs_glob_mesh_quantities->b_face_cog[fac_id*3 + i];
      normal[i] = cs_glob_mesh_quantities->b_face_normal[fac_id*3 + i];
      pscal += normal[i] * (cogfac[i] - cogcel[i]);
    }

    if (pscal < 0.0)
      printf("num_fac_brd = %d, num_cel = %d, pscal = %f\n",
             fac_id + 1, cell_id + 1, pscal);
  }

#endif


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

/* Delete local macro definitions */

#undef _CS_CROSS_PRODUCT
#undef _CS_DOT_PRODUCT
#undef _CS_MODULE

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

END_C_DECLS
