source: palm/trunk/SOURCE/init_pegrid.f90 @ 1

 SUBROUTINE init_pegrid

!------------------------------------------------------------------------------!
! Actual revisions:
! -----------------
! 
!
! Former revisions:
! -----------------
! $Log: init_pegrid.f90,v $
! Revision 1.28  2006/04/26 13:23:32  raasch
! lcmuk does not understand the !$ comment so a cpp-directive is required
!
! Revision 1.27  2006/04/26 12:50:32  raasch
! Get the number of OpenMP threads
!
! Revision 1.26  2006/02/23 12:34:57  raasch
! Calculation of nanz_sums, nanz_2dh and nanz_3d moved to init_3d_model,
! anz_y.. renamed ngp_y.., + MPI type type_x_int
!
! Revision 1.25  2005/10/20 15:37:36  raasch
! error removed: the last PE in a row is not allowed to have more grid points
! than the other PES (only less)
!
! Revision 1.24  2005/03/26 20:35:06  raasch
! Extensions for non-cyclic boundary conditions
! MIN function must be used instead of MAX for deciding if a switch to PE0 is
! useful (multigrid-method), maximuma_grid_level_l is defined in case that a
! pre-defined value for mg_switch_to_pe0_level is given (caused errors on NEC)
!
! Revision 1.23  2004/04/30 12:27:13  raasch
! Setting 1d-decomposition as default on decalpha, indices for direct
! transpositions z --> y and y --> x added, +module poisfft_mod,
! data types for mpi_alltoallv removed (not neeeded any more),
! poisfft_hybrid is no longer enforced in case of a 1d-decomposition along x,
! an enlarged grid which will fit all transposition demands is calculated,
! impulse_advec renamed momentum_advec
!
! Revision 1.22  2003/10/29 08:56:20  raasch
! Number of possible grid levels for the mulitgrid-method are calculated
! based on the total domain grid
!
! Revision 1.21  2003/08/01 08:40:03  raasch
! Error removed: for a 1D-decomposition along x, the number PEs must also
! be an integral divisor of the number of gridpoints along y
!
! Revision 1.20  2003/05/09 14:27:26  raasch
! Setting 1d-decomposition as default on linux clusters
!
! Revision 1.19  2003/04/16 13:00:11  raasch
! Call of fft_1dd_init, +module fft_for_1d_decomp
!
! Revision 1.18  2003/03/16 09:39:57  raasch
! Two underscores (_) are placed in front of all define-strings
!
! Revision 1.17  2003/03/12 16:32:47  raasch
! A 1d-decomposition along x is the default on NEC hosts
!
! Revision 1.16  2002/12/19 15:40:39  raasch
! In case of 1d-decomposition along x only a part of the integral divisor
! conditions is checked, on IBM hosts a 1d-decomposition along x is the
! default, a switch from Poisson-FFT-solver to the hybrid-solver is made
! in case of 1d-decomposition along x, the hybrid-solver does not force a
! 1d-decomposition any more, STOP replaced by call of local_stop
!
! Revision 1.15  2002/06/11 13:10:58  raasch
! Usage of the Poisson-hybrid-solver forces a 1d-decomposition,
! initialization of hybrid-solver
!
! Revision 1.14  2001/08/21  09:49:45  09:49:45  raasch (Siegfried Raasch)
! MPI_COMM_WORLD replaced by comm_palm
! 
! Revision 1.13  2001/07/20 13:07:26  raasch
! In case of using multigrid method, grid levels and additional MPI derived data
! types are calculated. anz_yz and type_xz are now arrays.
!
! Revision 1.12  2001/03/30 07:32:01  raasch
! Calculations of nw and nw1 removed,
! Translation of remaining German identifiers (variables, subroutines, etc.)
!
! Revision 1.11  2001/01/22 08:33:48  raasch
! Module test_variables removed
!
! Revision 1.9  2000/12/28 13:16:37  raasch
! definition of mpi_particle_type moved to subroutine init_particles
!
! Revision 1.8  2000/04/27 06:54:03  raasch
! Processor topology can now be prescribed by the user using npex and npey,
! all comments translated into English
!
! Revision 1.7  1999/11/25 16:23:36  raasch
! MPI-Datentyp fuer Partikeltransfer vereinbart
!
! Revision 1.6  1998/07/16 06:50:23  raasch
! cpp-Direktiven fuer t3ej2 und t3ej5 erweitert
!
! Revision 1.5  1998/07/06 12:17:06  raasch
! + USE test_variables
!
! Revision 1.4  1998/03/18 20:13:42  raasch
! myid_char auf 5 Zeichen erweitert
!
! Revision 1.3  1998/01/23 10:02:08  raasch
! Gitterpunktzahlen und Datentyp fuer 2D-Randaustausch
! anz_yz_p, type_xz_p in anz_yz und type_xz umbenannt
!
! Revision 1.2  1997/08/11 06:18:28  raasch
! Gitterpunktanzahl von globalen Feldern werden berechnet
!
! Revision 1.1  1997/07/24 11:15:09  raasch
! Initial revision
!
!
! Description:
! ------------
! Determination of the virtual processor topology (if not prescribed by the
! user)and computation of the grid point number and array bounds of the local
! domains.
!------------------------------------------------------------------------------!

    USE control_parameters
    USE fft_xy
    USE indices
    USE pegrid
    USE poisfft_mod
    USE poisfft_hybrid_mod
    USE statistics
    USE transpose_indices


    IMPLICIT NONE

    INTEGER ::  gathered_size, i, ind(5), j, k, maximum_grid_level_l,     &
                mg_switch_to_pe0_level_l, mg_levels_x, mg_levels_y,       &
                mg_levels_z, nnx_y, nnx_z, nny_x, nny_z, nnz_x, nnz_y,    &
                numproc_sqr, nx_total, nxl_l, nxr_l, nyn_l, nys_l, nzb_l, &
                nzt_l, omp_get_num_threads, subdomain_size

    INTEGER, DIMENSION(:), ALLOCATABLE ::  ind_all, nxlf, nxrf, nynf, nysf

    LOGICAL ::  found

!
!-- Get the number of OpenMP threads
    !$OMP PARALLEL
#if defined( __lcmuk )
    threads_per_task = omp_get_num_threads()
#else
!$  threads_per_task = omp_get_num_threads()
#endif
    !$OMP END PARALLEL


#if defined( __parallel )
!
!-- Determine the processor topology or check it, if prescribed by the user
    IF ( npex == -1  .AND.  npey == -1 )  THEN

!
!--    Automatic determination of the topology
!--    The default on SMP- and cluster-hosts is a 1d-decomposition along x
#if defined( __lcmuk )
       host = 'lcmuk'
#endif
       IF ( host(1:3) == 'ibm'  .OR.  host(1:3) == 'nec'  .OR. &
            host(1:2) == 'lc'   .OR.  host(1:3) == 'dec' )  THEN

          pdims(1) = numprocs
          pdims(2) = 1

       ELSE

          numproc_sqr = SQRT( REAL( numprocs ) )
          pdims(1)    = MAX( numproc_sqr , 1 )
          DO  WHILE ( MOD( numprocs , pdims(1) ) /= 0 )
             pdims(1) = pdims(1) - 1
          ENDDO
          pdims(2) = numprocs / pdims(1)

       ENDIF

    ELSEIF ( npex /= -1  .AND.  npey /= -1 )  THEN

!
!--    Prescribed by user. Number of processors on the prescribed topology
!--    must be equal to the number of PEs available to the job
       IF ( ( npex * npey ) /= numprocs )  THEN
          PRINT*, '+++ init_pegrid:'
          PRINT*, '    number of PEs of the prescribed topology (', npex*npey, &
                      ') does not match the number of PEs available to the ',  &
                      'job (', numprocs, ')'
          CALL local_stop
       ENDIF
       pdims(1) = npex
       pdims(2) = npey

    ELSE
!
!--    If the processor topology is prescribed by the user, the number of
!--    PEs must be given in both directions
       PRINT*, '+++ init_pegrid:'
       PRINT*, '    if the processor topology is prescribed by the user, ',   &
                    'both values of "npex" and "npey" must be given in the ', &
                    'NAMELIST-parameter file'
       CALL local_stop

    ENDIF

!
!-- The hybrid solver can only be used in case of a 1d-decomposition along x
    IF ( pdims(2) /= 1  .AND.  psolver == 'poisfft_hybrid' )  THEN
       IF ( myid == 0 )  THEN
          PRINT*, '*** init_pegrid: psolver = "poisfft_hybrid" can only be'
          PRINT*, '                 used in case of a 1d-decomposition along x'
       ENDIF
    ENDIF

!
!-- If necessary, set horizontal boundary conditions to non-cyclic
    IF ( bc_lr /= 'cyclic' )  cyclic(1) = .FALSE.
    IF ( bc_ns /= 'cyclic' )  cyclic(2) = .FALSE.

!
!-- Create the virtual processor grid
    CALL MPI_CART_CREATE( comm_palm, ndim, pdims, cyclic, reorder, &
                          comm2d, ierr )
    CALL MPI_COMM_RANK( comm2d, myid, ierr )
    WRITE (myid_char,'(''_'',I4.4)')  myid

    CALL MPI_CART_COORDS( comm2d, myid, ndim, pcoord, ierr )
    CALL MPI_CART_SHIFT( comm2d, 0, 1, pleft, pright, ierr )
    CALL MPI_CART_SHIFT( comm2d, 1, 1, psouth, pnorth, ierr )

!
!-- Determine sub-topologies for transpositions
!-- Transposition from z to x:
    remain_dims(1) = .TRUE.
    remain_dims(2) = .FALSE.
    CALL MPI_CART_SUB( comm2d, remain_dims, comm1dx, ierr )
    CALL MPI_COMM_RANK( comm1dx, myidx, ierr )
!
!-- Transposition from x to y
    remain_dims(1) = .FALSE.
    remain_dims(2) = .TRUE.
    CALL MPI_CART_SUB( comm2d, remain_dims, comm1dy, ierr )
    CALL MPI_COMM_RANK( comm1dy, myidy, ierr )


!
!-- Find a grid (used for array d) which will match the transposition demands
    IF ( grid_matching == 'strict' )  THEN

       nxa = nx;  nya = ny;  nza = nz

    ELSE

       found = .FALSE.
   xn: DO  nxa = nx, 2*nx
!
!--       Meet conditions for nx
          IF ( MOD( nxa+1, pdims(1) ) /= 0 .OR. &
               MOD( nxa+1, pdims(2) ) /= 0 )  CYCLE xn

      yn: DO  nya = ny, 2*ny
!
!--          Meet conditions for ny
             IF ( MOD( nya+1, pdims(2) ) /= 0 .OR. &
                  MOD( nya+1, pdims(1) ) /= 0 )  CYCLE yn


         zn: DO  nza = nz, 2*nz
!
!--             Meet conditions for nz
                IF ( ( MOD( nza, pdims(1) ) /= 0  .AND.  pdims(1) /= 1  .AND. &
                       pdims(2) /= 1 )  .OR.                                  &
                     ( MOD( nza, pdims(2) ) /= 0  .AND.  dt_dosp /= 9999999.9 &
                     ) )  THEN
                   CYCLE zn
                ELSE
                   found = .TRUE.
                   EXIT xn
                ENDIF

             ENDDO zn

          ENDDO yn

       ENDDO xn

       IF ( .NOT. found )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ init_pegrid: no matching grid for transpositions found'
          ENDIF
          CALL local_stop
       ENDIF

    ENDIF

!
!-- Calculate array bounds in x-direction for every PE.
!-- The last PE along x may get less grid points than the others
    ALLOCATE( nxlf(0:pdims(1)-1), nxrf(0:pdims(1)-1), nynf(0:pdims(2)-1), &
              nysf(0:pdims(2)-1), nnx_pe(0:pdims(1)-1), nny_pe(0:pdims(2)-1) )

    IF ( MOD( nxa+1 , pdims(1) ) /= 0 )  THEN
       IF ( myid == 0 )  THEN
          PRINT*,'+++ x-direction:  gridpoint number (',nx+1,') is not an'
          PRINT*,'                  integral divisor of the number of proces', &
                                   &'sors (', pdims(1),')'
       ENDIF
       CALL local_stop
    ELSE
       nnx  = ( nxa + 1 ) / pdims(1)
       IF ( nnx*pdims(1) - ( nx + 1) > nnx )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ x-direction: nx does not match the requirements ', &
                         'given by the number of PEs'
             PRINT*,'                 used'
             PRINT*,'    please use nx = ', nx - ( pdims(1) - ( nnx*pdims(1) &
                         - ( nx + 1 ) ) ), ' instead of nx =', nx
          ENDIF
          CALL local_stop
       ENDIF
    ENDIF    

!
!-- Left and right array bounds, number of gridpoints
    DO  i = 0, pdims(1)-1
       nxlf(i)   = i * nnx
       nxrf(i)   = ( i + 1 ) * nnx - 1
       nnx_pe(i) = MIN( nx, nxrf(i) ) - nxlf(i) + 1
    ENDDO

!
!-- Calculate array bounds in y-direction for every PE.
    IF ( MOD( nya+1 , pdims(2) ) /= 0 )  THEN
       IF ( myid == 0 )  THEN
          PRINT*,'+++ y-direction:  gridpoint number (',ny+1,') is not an'
          PRINT*,'                  integral divisor of the number of proces', &
                                   &'sors (', pdims(2),')'
       ENDIF
       CALL local_stop
    ELSE
       nny  = ( nya + 1 ) / pdims(2)
       IF ( nny*pdims(2) - ( ny + 1) > nny )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ x-direction: nx does not match the requirements ', &
                         'given by the number of PEs'
             PRINT*,'                 used'
             PRINT*,'    please use nx = ', nx - ( pdims(1) - ( nnx*pdims(1) &
                         - ( nx + 1 ) ) ), ' instead of nx =', nx
          ENDIF
          CALL local_stop
       ENDIF
    ENDIF    

!
!-- South and north array bounds
    DO  j = 0, pdims(2)-1
       nysf(j)   = j * nny
       nynf(j)   = ( j + 1 ) * nny - 1
       nny_pe(j) = MIN( ny, nynf(j) ) - nysf(j) + 1
    ENDDO

!
!-- Local array bounds of the respective PEs
    nxl  = nxlf(pcoord(1))
    nxra = nxrf(pcoord(1))
    nxr  = MIN( nx, nxra )
    nys  = nysf(pcoord(2))
    nyna = nynf(pcoord(2))
    nyn  = MIN( ny, nyna )
    nzb  = 0
    nzta = nza
    nzt  = MIN( nz, nzta )
    nnz  = nza

!
!-- Calculate array bounds and gridpoint numbers for the transposed arrays
!-- (needed in the pressure solver)
!-- For the transposed arrays, cyclic boundaries as well as top and bottom
!-- boundaries are omitted, because they are obstructive to the transposition

!
!-- 1. transposition  z --> x
!-- This transposition is not neccessary in case of a 1d-decomposition along x,
!-- except that the uptream-spline method is switched on
    IF ( pdims(2) /= 1  .OR.  momentum_advec == 'ups-scheme'  .OR. &
         scalar_advec == 'ups-scheme' )  THEN

       IF ( pdims(2) == 1  .AND. ( momentum_advec == 'ups-scheme'  .OR. &
            scalar_advec == 'ups-scheme' ) )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ WARNING: init_pegrid: 1d-decomposition along x ', &
                                &'chosen but nz restrictions may occur'
             PRINT*,'             since ups-scheme is activated'
          ENDIF
       ENDIF
       nys_x  = nys
       nyn_xa = nyna
       nyn_x  = nyn
       nny_x  = nny
       IF ( MOD( nza , pdims(1) ) /= 0 )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ transposition z --> x:'
             PRINT*,'    nz=',nz,' is not an integral divisior of pdims(1)=', &
                    &pdims(1)
          ENDIF
          CALL local_stop
       ENDIF
       nnz_x  = nza / pdims(1)
       nzb_x  = 1 + myidx * nnz_x
       nzt_xa = ( myidx + 1 ) * nnz_x
       nzt_x  = MIN( nzt, nzt_xa )

       sendrecvcount_zx = nnx * nny * nnz_x

    ENDIF

!
!-- 2. transposition  x --> y
    nnz_y  = nnz_x
    nzb_y  = nzb_x
    nzt_ya = nzt_xa
    nzt_y  = nzt_x
    IF ( MOD( nxa+1 , pdims(2) ) /= 0 )  THEN
       IF ( myid == 0 )  THEN
          PRINT*,'+++ transposition x --> y:'
          PRINT*,'    nx+1=',nx+1,' is not an integral divisor of ',&
                 &'pdims(2)=',pdims(2)
       ENDIF
       CALL local_stop
    ENDIF
    nnx_y = (nxa+1) / pdims(2)
    nxl_y = myidy * nnx_y
    nxr_ya = ( myidy + 1 ) * nnx_y - 1
    nxr_y  = MIN( nx, nxr_ya )

    sendrecvcount_xy = nnx_y * nny_x * nnz_y

!
!-- 3. transposition  y --> z  (ELSE:  x --> y  in case of 1D-decomposition
!-- along x)
    IF ( pdims(2) /= 1  .OR.  momentum_advec == 'ups-scheme'  .OR. &
         scalar_advec == 'ups-scheme' )  THEN
!
!--    y --> z
!--    This transposition is not neccessary in case of a 1d-decomposition
!--    along x, except that the uptream-spline method is switched on
       nnx_z  = nnx_y
       nxl_z  = nxl_y
       nxr_za = nxr_ya
       nxr_z  = nxr_y
       IF ( MOD( nya+1 , pdims(1) ) /= 0 )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ Transposition y --> z:'
             PRINT*,'    ny+1=',ny+1,' is not an integral divisor of ',&
                    &'pdims(1)=',pdims(1)
          ENDIF
          CALL local_stop
       ENDIF
       nny_z  = (nya+1) / pdims(1)
       nys_z  = myidx * nny_z
       nyn_za = ( myidx + 1 ) * nny_z - 1
       nyn_z  = MIN( ny, nyn_za )

       sendrecvcount_yz = nnx_y * nny_z * nnz_y

    ELSE
!
!--    x --> y. This condition must be fulfilled for a 1D-decomposition along x
       IF ( MOD( nya+1 , pdims(1) ) /= 0 )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ Transposition x --> y:'
             PRINT*,'    ny+1=',ny+1,' is not an integral divisor of ',&
                    &'pdims(1)=',pdims(1)
          ENDIF
          CALL local_stop
       ENDIF

    ENDIF

!
!-- Indices for direct transpositions z --> y (used for calculating spectra)
    IF ( dt_dosp /= 9999999.9 )  THEN
       IF ( MOD( nza, pdims(2) ) /= 0 )  THEN
          IF ( myid == 0 )  THEN
             PRINT*,'+++ Direct transposition z --> y (needed for spectra):'
             PRINT*,'    nz=',nz,' is not an integral divisor of ',&
                    &'pdims(2)=',pdims(2)
          ENDIF
          CALL local_stop
       ELSE
          nxl_yd  = nxl
          nxr_yda = nxra
          nxr_yd  = nxr
          nzb_yd  = 1 + myidy * ( nza / pdims(2) )
          nzt_yda = ( myidy + 1 ) * ( nza / pdims(2) )
          nzt_yd  = MIN( nzt, nzt_yda )

          sendrecvcount_zyd = nnx * nny * ( nza / pdims(2) )
       ENDIF
    ENDIF

!
!-- Indices for direct transpositions y --> x (they are only possible in case
!-- of a 1d-decomposition along x)
    IF ( pdims(2) == 1 )  THEN
       nny_x  = nny / pdims(1)
       nys_x  = myid * nny_x
       nyn_xa = ( myid + 1 ) * nny_x - 1
       nyn_x  = MIN( ny, nyn_xa )
       nzb_x  = 1
       nzt_xa = nza
       nzt_x  = nz
       sendrecvcount_xy = nnx * nny_x * nza
    ENDIF

!
!-- Indices for direct transpositions x --> y (they are only possible in case
!-- of a 1d-decomposition along y)
    IF ( pdims(1) == 1 )  THEN
       nnx_y  = nnx / pdims(2)
       nxl_y  = myid * nnx_y
       nxr_ya = ( myid + 1 ) * nnx_y - 1
       nxr_y  = MIN( nx, nxr_ya )
       nzb_y  = 1
       nzt_ya = nza
       nzt_y  = nz
       sendrecvcount_xy = nnx_y * nny * nza
    ENDIF

!
!-- Arrays for storing the array bounds are needed any more
    DEALLOCATE( nxlf , nxrf , nynf , nysf )

#if defined( __print )
!
!-- Control output
    IF ( myid == 0 )  THEN
       PRINT*, '*** processor topology ***'
       PRINT*, ' '
       PRINT*, 'myid   pcoord    left right  south north  idx idy   nxl: nxr',&
               &'   nys: nyn'
       PRINT*, '------------------------------------------------------------',&
               &'-----------'
       WRITE (*,1000)  0, pcoord(1), pcoord(2), pleft, pright, psouth, pnorth, &
                       myidx, myidy, nxl, nxr, nys, nyn
1000   FORMAT (I4,2X,'(',I3,',',I3,')',3X,I4,2X,I4,3X,I4,2X,I4,2X,I3,1X,I3, &
               2(2X,I4,':',I4))

!
!--    Recieve data from the other PEs
       DO  i = 1,numprocs-1
          CALL MPI_RECV( ibuf, 12, MPI_INTEGER, i, MPI_ANY_TAG, comm2d, status, &
                         ierr )
          WRITE (*,1000)  i, ( ibuf(j) , j = 1,12 )
       ENDDO
    ELSE

!
!--    Send data to PE0
       ibuf(1) = pcoord(1); ibuf(2) = pcoord(2); ibuf(3) = pleft
       ibuf(4) = pright; ibuf(5) = psouth; ibuf(6) = pnorth; ibuf(7) = myidx
       ibuf(8) = myidy; ibuf(9) = nxl; ibuf(10) = nxr; ibuf(11) = nys
       ibuf(12) = nyn
       CALL MPI_SEND( ibuf, 12, MPI_INTEGER, 0, myid, comm2d, ierr )       
    ENDIF
#endif

#else

!
!-- Array bounds when running on a single PE (respectively a non-parallel
!-- machine)
    nxl  = 0
    nxr  = nx
    nxra = nx
    nnx  = nxr - nxl + 1
    nys  = 0
    nyn  = ny
    nyna = ny
    nny  = nyn - nys + 1
    nzb  = 0
    nzt  = nz
    nzta = nz
    nnz  = nz

!
!-- For non-cyclic boundaries extend array u (v) by one gridpoint
    IF ( bc_lr /= 'cyclic' )  uxrp = 1
    IF ( bc_ns /= 'cyclic' )  vynp = 1

!
!-- Array bounds for the pressure solver (in the parallel code, these bounds
!-- are the ones for the transposed arrays)
    nys_x  = nys
    nyn_x  = nyn
    nyn_xa = nyn
    nzb_x  = nzb + 1
    nzt_x  = nzt
    nzt_xa = nzt

    nxl_y  = nxl
    nxr_y  = nxr
    nxr_ya = nxr
    nzb_y  = nzb + 1
    nzt_y  = nzt
    nzt_ya = nzt

    nxl_z  = nxl
    nxr_z  = nxr
    nxr_za = nxr
    nys_z  = nys
    nyn_z  = nyn
    nyn_za = nyn

#endif

!
!-- Calculate number of grid levels necessary for the multigrid poisson solver
!-- as well as the gridpoint indices on each level
    IF ( psolver == 'multigrid' )  THEN

!
!--    First calculate number of possible grid levels for the subdomains
       mg_levels_x = 1
       mg_levels_y = 1
       mg_levels_z = 1

       i = nnx
       DO WHILE ( MOD( i, 2 ) == 0  .AND.  i /= 2 )
          i = i / 2
          mg_levels_x = mg_levels_x + 1
       ENDDO

       j = nny
       DO WHILE ( MOD( j, 2 ) == 0  .AND.  j /= 2 )
          j = j / 2
          mg_levels_y = mg_levels_y + 1
       ENDDO

       k = nnz
       DO WHILE ( MOD( k, 2 ) == 0  .AND.  k /= 2 )
          k = k / 2
          mg_levels_z = mg_levels_z + 1
       ENDDO

       maximum_grid_level = MIN( mg_levels_x, mg_levels_y, mg_levels_z )

!
!--    Find out, if the total domain allows more levels. These additional
!--    levels are processed on PE0 only.
       IF ( numprocs > 1 )  THEN
          IF ( mg_levels_z > MIN( mg_levels_x, mg_levels_y ) )  THEN
             mg_switch_to_pe0_level_l = maximum_grid_level

             mg_levels_x = 1
             mg_levels_y = 1

             i = nx+1
             DO WHILE ( MOD( i, 2 ) == 0  .AND.  i /= 2 )
                i = i / 2
                mg_levels_x = mg_levels_x + 1
             ENDDO

             j = ny+1
             DO WHILE ( MOD( j, 2 ) == 0  .AND.  j /= 2 )
                j = j / 2
                mg_levels_y = mg_levels_y + 1
             ENDDO

             maximum_grid_level_l = MIN( mg_levels_x, mg_levels_y, mg_levels_z )

             IF ( maximum_grid_level_l > mg_switch_to_pe0_level_l )  THEN
                mg_switch_to_pe0_level_l = maximum_grid_level_l - &
                                           mg_switch_to_pe0_level_l + 1
             ELSE
                mg_switch_to_pe0_level_l = 0
             ENDIF
          ELSE
             mg_switch_to_pe0_level_l = 0
             maximum_grid_level_l = maximum_grid_level
          ENDIF

!
!--       Use switch level calculated above only if it is not pre-defined
!--       by user
          IF ( mg_switch_to_pe0_level == 0 )  THEN

             IF ( mg_switch_to_pe0_level_l /= 0 )  THEN
                mg_switch_to_pe0_level = mg_switch_to_pe0_level_l
                maximum_grid_level     = maximum_grid_level_l
             ENDIF

          ELSE
!
!--          Check pre-defined value and reset to default, if neccessary
             IF ( mg_switch_to_pe0_level < mg_switch_to_pe0_level_l  .OR.  &
                  mg_switch_to_pe0_level >= maximum_grid_level_l )  THEN
                IF ( myid == 0 )  THEN
                   PRINT*, '+++ WARNING init_pegrid: mg_switch_to_pe0_level ', &
                               'out of range and reset to default (=0)'
                ENDIF
                mg_switch_to_pe0_level = 0
             ELSE
!
!--             Use the largest number of possible levels anyway and recalculate
!--             the switch level to this largest number of possible values
                maximum_grid_level = maximum_grid_level_l

             ENDIF
          ENDIF

       ENDIF

       ALLOCATE( grid_level_count(maximum_grid_level),                   &
                 nxl_mg(maximum_grid_level), nxr_mg(maximum_grid_level), &
                 nyn_mg(maximum_grid_level), nys_mg(maximum_grid_level), &
                 nzt_mg(maximum_grid_level) )

       grid_level_count = 0
       nxl_l = nxl; nxr_l = nxr; nys_l = nys; nyn_l = nyn; nzt_l = nzt

       DO  i = maximum_grid_level, 1 , -1

          IF ( i == mg_switch_to_pe0_level )  THEN
#if defined( __parallel )
!
!--          Save the grid size of the subdomain at the switch level, because
!--          it is needed in poismg.
!--          Array bounds of the local subdomain grids are gathered on PE0
             ind(1) = nxl_l; ind(2) = nxr_l
             ind(3) = nys_l; ind(4) = nyn_l
             ind(5) = nzt_l
             ALLOCATE( ind_all(5*numprocs), mg_loc_ind(5,0:numprocs-1) )
             CALL MPI_ALLGATHER( ind, 5, MPI_INTEGER, ind_all, 5, &
                                 MPI_INTEGER, comm2d, ierr )
             DO  j = 0, numprocs-1
                DO  k = 1, 5
                   mg_loc_ind(k,j) = ind_all(k+j*5)
                ENDDO
             ENDDO
             DEALLOCATE( ind_all )
!
!--          Calculate the grid size of the total domain gathered on PE0
             nxr_l = ( nxr_l-nxl_l+1 ) * pdims(1) - 1
             nxl_l = 0
             nyn_l = ( nyn_l-nys_l+1 ) * pdims(2) - 1
             nys_l = 0
!
!--          The size of this gathered array must not be larger than the
!--          array tend, which is used in the multigrid scheme as a temporary
!--          array
             subdomain_size = ( nxr - nxl + 3 )     * ( nyn - nys + 3 )     * &
                              ( nzt - nzb + 2 )
             gathered_size  = ( nxr_l - nxl_l + 3 ) * ( nyn_l - nys_l + 3 ) * &
                              ( nzt_l - nzb + 2 )

             IF ( gathered_size > subdomain_size )  THEN
                IF ( myid == 0 )  THEN
                   PRINT*, '+++ init_pegrid: not enough memory for storing ', &
                               'gathered multigrid data on PE0'
                ENDIF
                CALL local_stop
             ENDIF
#else
             PRINT*, '+++ init_pegrid: multigrid gather/scatter impossible ', &
                          'in non parallel mode'
             CALL local_stop
#endif
          ENDIF

          nxl_mg(i) = nxl_l
          nxr_mg(i) = nxr_l
          nys_mg(i) = nys_l
          nyn_mg(i) = nyn_l
          nzt_mg(i) = nzt_l

          nxl_l = nxl_l / 2 
          nxr_l = nxr_l / 2
          nys_l = nys_l / 2 
          nyn_l = nyn_l / 2 
          nzt_l = nzt_l / 2 
       ENDDO

    ELSE

       maximum_grid_level = 1

    ENDIF

    grid_level = maximum_grid_level

#if defined( __parallel )
!
!-- Gridpoint number for the exchange of ghost points (y-line for 2D-arrays)
    ngp_y  = nyn - nys + 1

!
!-- Define a new MPI derived datatype for the exchange of ghost points in
!-- y-direction for 2D-arrays (line)
    CALL MPI_TYPE_VECTOR( nxr-nxl+3, 1, ngp_y+2, MPI_REAL, type_x, ierr )
    CALL MPI_TYPE_COMMIT( type_x, ierr )
    CALL MPI_TYPE_VECTOR( nxr-nxl+3, 1, ngp_y+2, MPI_INTEGER, type_x_int, ierr )
    CALL MPI_TYPE_COMMIT( type_x_int, ierr )

!
!-- Calculate gridpoint numbers for the exchange of ghost points along x
!-- (yz-plane for 3D-arrays) and define MPI derived data type(s) for the
!-- exchange of ghost points in y-direction (xz-plane).
!-- Do these calculations for the model grid and (if necessary) also
!-- for the coarser grid levels used in the multigrid method
    ALLOCATE ( ngp_yz(maximum_grid_level), type_xz(maximum_grid_level) )

    nxl_l = nxl; nxr_l = nxr; nys_l = nys; nyn_l = nyn; nzb_l = nzb; nzt_l = nzt
         
    DO i = maximum_grid_level, 1 , -1
       ngp_yz(i) = (nzt_l - nzb_l + 2) * (nyn_l - nys_l + 3)

       CALL MPI_TYPE_VECTOR( nxr_l-nxl_l+3, nzt_l-nzb_l+2, ngp_yz(i), &
                             MPI_REAL, type_xz(i), ierr )
       CALL MPI_TYPE_COMMIT( type_xz(i), ierr )

       nxl_l = nxl_l / 2 
       nxr_l = nxr_l / 2
       nys_l = nys_l / 2 
       nyn_l = nyn_l / 2 
       nzt_l = nzt_l / 2 
    ENDDO
#endif

#if defined( __parallel )
!
!-- Setting of flags for inflow/outflow conditions in case of non-cyclic
!-- horizontal boundary conditions. Set variables for extending array u (v)
!-- by one gridpoint on the left/rightmost (northest/southest) processor
    IF ( pleft == MPI_PROC_NULL )  THEN
       IF ( bc_lr == 'dirichlet/neumann' )  THEN
          inflow_l  = .TRUE.
       ELSEIF ( bc_lr == 'neumann/dirichlet' )  THEN
          outflow_l = .TRUE.
       ENDIF
    ENDIF

    IF ( pright == MPI_PROC_NULL )  THEN
       IF ( bc_lr == 'dirichlet/neumann' )  THEN
          outflow_r = .TRUE.
       ELSEIF ( bc_lr == 'neumann/dirichlet' )  THEN
          inflow_r  = .TRUE.
       ENDIF
       uxrp      = 1
    ENDIF

    IF ( psouth == MPI_PROC_NULL )  THEN
       IF ( bc_ns == 'dirichlet/neumann' )  THEN
          outflow_s = .TRUE.
       ELSEIF ( bc_ns == 'neumann/dirichlet' )  THEN
          inflow_s  = .TRUE.
       ENDIF
    ENDIF

    IF ( pnorth == MPI_PROC_NULL )  THEN
       IF ( bc_ns == 'dirichlet/neumann' )  THEN
          inflow_n  = .TRUE.
       ELSEIF ( bc_ns == 'neumann/dirichlet' )  THEN
          outflow_n = .TRUE.
       ENDIF
       vynp      = 1
    ENDIF

!
!-- Additional MPI derived data type for the exchange of ghost points along x
!-- needed in case of non-cyclic boundary conditions along y on the northmost
!-- processors (for the exchange of the enlarged v array)
    IF ( bc_ns /= 'cyclic'  .AND.  pnorth == MPI_PROC_NULL )  THEN
       ngp_yz_p = ( nzt - nzb + 2 ) * ( nyn + vynp - nys + 3 )
       CALL MPI_TYPE_VECTOR( nxr-nxl+3, nzt-nzb+2, ngp_yz_p, &
                             MPI_REAL, type_xz_p, ierr )
       CALL MPI_TYPE_COMMIT( type_xz_p, ierr )
    ENDIF
#else
    IF ( bc_lr == 'dirichlet/neumann' )  THEN
       inflow_l  = .TRUE.
       outflow_r = .TRUE.
       uxrp      = 1
    ELSEIF ( bc_lr == 'neumann/dirichlet' )  THEN
       outflow_l = .TRUE.
       inflow_r  = .TRUE.
    ENDIF

    IF ( bc_ns == 'dirichlet/neumann' )  THEN
       inflow_n  = .TRUE.
       outflow_s = .TRUE.
    ELSEIF ( bc_ns == 'neumann/dirichlet' )  THEN
       outflow_n = .TRUE.
       inflow_s  = .TRUE.
       vynp      = 1
    ENDIF
#endif

    IF ( psolver == 'poisfft_hybrid' )  THEN
       CALL poisfft_hybrid_ini
    ELSE
       CALL poisfft_init
    ENDIF

 END SUBROUTINE init_pegrid