source: palm/trunk/SOURCE/init_pegrid.f90 @ 1041

 SUBROUTINE init_pegrid

!--------------------------------------------------------------------------------!
! This file is part of PALM.
!
! PALM 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 3 of the License, or (at your option) any later version.
!
! PALM 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
! PALM. If not, see <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2012  Leibniz University Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! -----------------
! a 2d-topology is used by default for all machines
!
! Former revisions:
! -----------------
! $Id: init_pegrid.f90 1041 2012-11-06 02:36:29Z raasch $
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 1003 2012-09-14 14:35:53Z raasch
! subdomains must have identical size (grid matching = "match" removed)
!
! 1001 2012-09-13 14:08:46Z raasch
! all actions concerning upstream-spline-method removed
!
! 978 2012-08-09 08:28:32Z fricke
! dirichlet/neumann and neumann/dirichlet added
! nxlu and nysv are also calculated for inflow boundary
!
! 809 2012-01-30 13:32:58Z maronga
! Bugfix: replaced .AND. and .NOT. with && and ! in the preprocessor directives
!
! 807 2012-01-25 11:53:51Z maronga
! New cpp directive "__check" implemented which is used by check_namelist_files
!
! 780 2011-11-10 07:16:47Z raasch
! Bugfix for rev 778: Misplaced error message moved to the rigth place
!
! 778 2011-11-07 14:18:25Z fricke
! Calculation of subdomain_size now considers the number of ghost points.
! Further coarsening on PE0 is now possible for multigrid solver if the 
! collected field has more grid points than the subdomain of an PE.
!
! 759 2011-09-15 13:58:31Z raasch
! calculation of number of io_blocks and the io_group to which the respective
! PE belongs
!
! 755 2011-08-29 09:55:16Z witha
! 2d-decomposition is default for lcflow (ForWind cluster in Oldenburg)
!
! 722 2011-04-11 06:21:09Z raasch
! Bugfix: bc_lr/ns_cyc/dirrad/raddir replaced by bc_lr/ns, because variables
!         are not yet set here; grid_level set to 0
!
! 709 2011-03-30 09:31:40Z raasch
! formatting adjustments
!
! 707 2011-03-29 11:39:40Z raasch
! bc_lr/ns replaced by bc_lr/ns_cyc/dirrad/raddir
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! Moved determination of target_id's from init_coupling
! Determination of parameters needed for coupling (coupling_topology, ngp_a, 
! ngp_o) with different grid/processor-topology in ocean and atmosphere
! Adaption of ngp_xy, ngp_y to a dynamic number of ghost points.
! The maximum_grid_level changed from 1 to 0. 0 is the normal grid, 1 to 
! maximum_grid_level the grids for multigrid, in which 0 and 1 are normal grids.
! This distinction is due to reasons of data exchange and performance for the 
! normal grid and grids in poismg.
! The definition of MPI-Vectors adapted to a dynamic numer of ghost points.
! New MPI-Vectors for data exchange between left and right boundaries added. 
! This is due to reasons of performance (10% faster).
!
! 646 2010-12-15 13:03:52Z raasch
! lctit is now using a 2d decomposition by default
!
! 622 2010-12-10 08:08:13Z raasch
! optional barriers included in order to speed up collective operations
!
! 438 2010-02-01 04:32:43Z raasch
! 2d-decomposition is default for Cray-XT machines
!
! 274 2009-03-26 15:11:21Z heinze
! Output of messages replaced by message handling routine.
!
! 206 2008-10-13 14:59:11Z raasch
! Implementation of a MPI-1 coupling: added __parallel within the __mpi2 part
! 2d-decomposition is default on SGI-ICE systems
!
! 197 2008-09-16 15:29:03Z raasch
! multigrid levels are limited by subdomains if mg_switch_to_pe0_level = -1,
! nz is used instead nnz for calculating mg-levels
! Collect on PE0 horizontal index bounds from all other PEs,
! broadcast the id of the inflow PE (using the respective communicator)
!
! 114 2007-10-10 00:03:15Z raasch
! Allocation of wall flag arrays for multigrid solver
!
! 108 2007-08-24 15:10:38Z letzel
! Intercommunicator (comm_inter) and derived data type (type_xy) for
! coupled model runs created, assign coupling_mode_remote,
! indices nxlu and nysv are calculated (needed for non-cyclic boundary
! conditions)
!
! 82 2007-04-16 15:40:52Z raasch
! Cpp-directive lcmuk changed to intel_openmp_bug, setting of host on lcmuk by
! cpp-directive removed
!
! 75 2007-03-22 09:54:05Z raasch
! uxrp, vynp eliminated,
! dirichlet/neumann changed to dirichlet/radiation, etc.,
! poisfft_init is only called if fft-solver is switched on
!
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.28  2006/04/26 13:23:32  raasch
! lcmuk does not understand the !$ comment so a cpp-directive is required
!
! 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 grid_variables
    USE indices
    USE pegrid
    USE poisfft_mod
    USE poisfft_hybrid_mod
    USE statistics
    USE transpose_indices



    IMPLICIT NONE

    INTEGER ::  i, id_inflow_l, id_recycling_l, 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

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

    INTEGER, DIMENSION(2) :: pdims_remote

    LOGICAL ::  found

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

    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
          WRITE( message_string, * ) 'number of PEs of the prescribed ',      & 
                 'topology (', npex*npey,') does not match & the number of ', & 
                 'PEs available to the job (', numprocs, ')'
          CALL message( 'init_pegrid', 'PA0221', 1, 2, 0, 6, 0 )
       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
       message_string = 'if the processor topology is prescribed by the, ' //  &
                   ' user& both values of "npex" and "npey" must be given ' // &
                   'in the &NAMELIST-parameter file'
       CALL message( 'init_pegrid', 'PA0222', 1, 2, 0, 6, 0 )

    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
       message_string = 'psolver = "poisfft_hybrid" can only be' // &
                        '& used in case of a 1d-decomposition along x'
       CALL message( 'init_pegrid', 'PA0223', 1, 2, 0, 6, 0 )
    ENDIF

!
!-- For communication speedup, set barriers in front of collective
!-- communications by default on SGI-type systems
    IF ( host(3:5) == 'sgi' )  collective_wait = .TRUE.

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


#if ! defined( __check)
!
!-- 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 )

#endif

!
!-- Calculate array bounds along x-direction for every PE.
    ALLOCATE( nxlf(0:pdims(1)-1), nxrf(0:pdims(1)-1), nynf(0:pdims(2)-1), &
              nysf(0:pdims(2)-1) )

    IF ( MOD( nx+1 , pdims(1) ) /= 0 )  THEN
       WRITE( message_string, * ) 'x-direction: gridpoint number (',nx+1,') ',&
                               'is not an& integral divisor of the number ',  &
                               'processors (', pdims(1),')'
       CALL message( 'init_pegrid', 'PA0225', 1, 2, 0, 6, 0 )
    ELSE
       nnx  = ( nx + 1 ) / pdims(1)
       IF ( nnx*pdims(1) - ( nx + 1) > nnx )  THEN
          WRITE( message_string, * ) 'x-direction: nx does not match the',    & 
                       'requirements given by the number of PEs &used',       &
                       '& please use nx = ', nx - ( pdims(1) - ( nnx*pdims(1) &
                                   - ( nx + 1 ) ) ), ' instead of nx =', nx
          CALL message( 'init_pegrid', 'PA0226', 1, 2, 0, 6, 0 )
       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
    ENDDO

!
!-- Calculate array bounds in y-direction for every PE.
    IF ( MOD( ny+1 , pdims(2) ) /= 0 )  THEN
       WRITE( message_string, * ) 'y-direction: gridpoint number (',ny+1,') ', &
                           'is not an& integral divisor of the number of',     &
                           'processors (', pdims(2),')'
       CALL message( 'init_pegrid', 'PA0227', 1, 2, 0, 6, 0 )
    ELSE
       nny  = ( ny + 1 ) / pdims(2)
       IF ( nny*pdims(2) - ( ny + 1) > nny )  THEN
          WRITE( message_string, * ) 'y-direction: ny does not match the',    &
                       'requirements given by the number of PEs &used ',      &
                       '& please use ny = ', ny - ( pdims(2) - ( nnx*pdims(2) &
                                     - ( ny + 1 ) ) ), ' instead of ny =', ny
          CALL message( 'init_pegrid', 'PA0228', 1, 2, 0, 6, 0 )
       ENDIF
    ENDIF    

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

!
!-- Local array bounds of the respective PEs
    nxl = nxlf(pcoord(1))
    nxr = nxrf(pcoord(1))
    nys = nysf(pcoord(2))
    nyn = nynf(pcoord(2))
    nzb = 0
    nzt = nz
    nnz = nz

!
!-- Set switches to define if the PE is situated at the border of the virtual
!-- processor grid
    IF ( nxl == 0 )   left_border_pe  = .TRUE.
    IF ( nxr == nx )  right_border_pe = .TRUE.
    IF ( nys == 0 )   south_border_pe = .TRUE.
    IF ( nyn == ny )  north_border_pe = .TRUE.

!
!-- 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
    IF ( pdims(2) /= 1 )  THEN

       nys_x = nys
       nyn_x = nyn
       nny_x = nny
       IF ( MOD( nz , pdims(1) ) /= 0 )  THEN
          WRITE( message_string, * ) 'transposition z --> x:',                &
                       '&nz=',nz,' is not an integral divisior of pdims(1)=', &
                                                                   pdims(1)
          CALL message( 'init_pegrid', 'PA0230', 1, 2, 0, 6, 0 )
       ENDIF
       nnz_x = nz / pdims(1)
       nzb_x = 1 + myidx * nnz_x
       nzt_x = ( myidx + 1 ) * nnz_x
       sendrecvcount_zx = nnx * nny * nnz_x

    ELSE
!
!---   Setting of dummy values because otherwise variables are undefined in
!---   the next step  x --> y
!---   WARNING: This case has still to be clarified!!!!!!!!!!!!
       nnz_x = 1
       nzb_x = 1
       nzt_x = 1
       nny_x = nny

    ENDIF

!
!-- 2. transposition  x --> y
    nnz_y = nnz_x
    nzb_y = nzb_x
    nzt_y = nzt_x
    IF ( MOD( nx+1 , pdims(2) ) /= 0 )  THEN
       WRITE( message_string, * ) 'transposition x --> y:',                &
                         '&nx+1=',nx+1,' is not an integral divisor of ',&
                         'pdims(2)=',pdims(2)
       CALL message( 'init_pegrid', 'PA0231', 1, 2, 0, 6, 0 )
    ENDIF
    nnx_y = (nx+1) / pdims(2)
    nxl_y = myidy * nnx_y
    nxr_y = ( myidy + 1 ) * nnx_y - 1
    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 )  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_z = nxr_y
       IF ( MOD( ny+1 , pdims(1) ) /= 0 )  THEN
          WRITE( message_string, * ) 'transposition y --> z:',            &
                            '& ny+1=',ny+1,' is not an integral divisor of ',&
                            'pdims(1)=',pdims(1)
          CALL message( 'init_pegrid', 'PA0232', 1, 2, 0, 6, 0 )
       ENDIF
       nny_z = (ny+1) / pdims(1)
       nys_z = myidx * nny_z
       nyn_z = ( myidx + 1 ) * nny_z - 1
       sendrecvcount_yz = nnx_y * nny_z * nnz_y

    ELSE
!
!--    x --> y. This condition must be fulfilled for a 1D-decomposition along x
       IF ( MOD( ny+1 , pdims(1) ) /= 0 )  THEN
          WRITE( message_string, * ) 'transposition x --> y:',               &
                            '& ny+1=',ny+1,' is not an integral divisor of ',&
                            'pdims(1)=',pdims(1)
          CALL message( 'init_pegrid', 'PA0233', 1, 2, 0, 6, 0 )
       ENDIF

    ENDIF

!
!-- Indices for direct transpositions z --> y (used for calculating spectra)
    IF ( dt_dosp /= 9999999.9 )  THEN
       IF ( MOD( nz, pdims(2) ) /= 0 )  THEN
          WRITE( message_string, * ) 'direct transposition z --> y (needed ', &
                    'for spectra):& nz=',nz,' is not an integral divisor of ',&
                    'pdims(2)=',pdims(2)
          CALL message( 'init_pegrid', 'PA0234', 1, 2, 0, 6, 0 )
       ELSE
          nxl_yd = nxl
          nxr_yd = nxr
          nzb_yd = 1 + myidy * ( nz / pdims(2) )
          nzt_yd = ( myidy + 1 ) * ( nz / pdims(2) )
          sendrecvcount_zyd = nnx * nny * ( nz / 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_x = ( myid + 1 ) * nny_x - 1
       nzb_x = 1
       nzt_x = nz
       sendrecvcount_xy = nnx * nny_x * nz
    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_y = ( myid + 1 ) * nnx_y - 1
       nzb_y = 1
       nzt_y = nz
       sendrecvcount_xy = nnx_y * nny * nz
    ENDIF

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


#if ! defined( __check)
!
!-- Collect index bounds from other PEs (to be written to restart file later)
    ALLOCATE( hor_index_bounds(4,0:numprocs-1) )

    IF ( myid == 0 )  THEN

       hor_index_bounds(1,0) = nxl
       hor_index_bounds(2,0) = nxr
       hor_index_bounds(3,0) = nys
       hor_index_bounds(4,0) = nyn

!
!--    Receive data from all other PEs
       DO  i = 1, numprocs-1
          CALL MPI_RECV( ibuf, 4, MPI_INTEGER, i, MPI_ANY_TAG, comm2d, status, &
                         ierr )
          hor_index_bounds(:,i) = ibuf(1:4)
       ENDDO

    ELSE
!
!--    Send index bounds to PE0
       ibuf(1) = nxl
       ibuf(2) = nxr
       ibuf(3) = nys
       ibuf(4) = nyn
       CALL MPI_SEND( ibuf, 4, MPI_INTEGER, 0, myid, comm2d, ierr )

    ENDIF

#endif

#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))

!
!--    Receive 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

#if defined( __parallel ) && ! defined( __check)
#if defined( __mpi2 )
!
!-- In case of coupled runs, get the port name on PE0 of the atmosphere model
!-- and pass it to PE0 of the ocean model
    IF ( myid == 0 )  THEN

       IF ( coupling_mode == 'atmosphere_to_ocean' )  THEN

          CALL MPI_OPEN_PORT( MPI_INFO_NULL, port_name, ierr )

          CALL MPI_PUBLISH_NAME( 'palm_coupler', MPI_INFO_NULL, port_name, &
                                 ierr )

!
!--       Write a flag file for the ocean model and the other atmosphere
!--       processes.
!--       There seems to be a bug in MPICH2 which causes hanging processes
!--       in case that execution of LOOKUP_NAME is continued too early
!--       (i.e. before the port has been created)
          OPEN( 90, FILE='COUPLING_PORT_OPENED', FORM='FORMATTED' )
          WRITE ( 90, '(''TRUE'')' )
          CLOSE ( 90 )

       ELSEIF ( coupling_mode == 'ocean_to_atmosphere' )  THEN

!
!--       Continue only if the atmosphere model has created the port.
!--       There seems to be a bug in MPICH2 which causes hanging processes
!--       in case that execution of LOOKUP_NAME is continued too early
!--       (i.e. before the port has been created)
          INQUIRE( FILE='COUPLING_PORT_OPENED', EXIST=found )
          DO WHILE ( .NOT. found )
             INQUIRE( FILE='COUPLING_PORT_OPENED', EXIST=found )
          ENDDO

          CALL MPI_LOOKUP_NAME( 'palm_coupler', MPI_INFO_NULL, port_name, ierr )

       ENDIF

    ENDIF

!
!-- In case of coupled runs, establish the connection between the atmosphere
!-- and the ocean model and define the intercommunicator (comm_inter)
    CALL MPI_BARRIER( comm2d, ierr )
    IF ( coupling_mode == 'atmosphere_to_ocean' )  THEN

       CALL MPI_COMM_ACCEPT( port_name, MPI_INFO_NULL, 0, MPI_COMM_WORLD, &
                             comm_inter, ierr )
       coupling_mode_remote = 'ocean_to_atmosphere'

    ELSEIF ( coupling_mode == 'ocean_to_atmosphere' )  THEN

       CALL MPI_COMM_CONNECT( port_name, MPI_INFO_NULL, 0, MPI_COMM_WORLD, &
                              comm_inter, ierr )
       coupling_mode_remote = 'atmosphere_to_ocean'

    ENDIF
#endif

! 
!-- Determine the number of ghost point layers
    IF ( scalar_advec == 'ws-scheme' .OR. momentum_advec == 'ws-scheme' )  THEN
       nbgp = 3
    ELSE
       nbgp = 1
    ENDIF 

!
!-- Create a new MPI derived datatype for the exchange of surface (xy) data,
!-- which is needed for coupled atmosphere-ocean runs.
!-- First, calculate number of grid points of an xy-plane.
    ngp_xy  = ( nxr - nxl + 1 + 2 * nbgp ) * ( nyn - nys + 1 + 2 * nbgp )
    CALL MPI_TYPE_VECTOR( ngp_xy, 1, nzt-nzb+2, MPI_REAL, type_xy, ierr )
    CALL MPI_TYPE_COMMIT( type_xy, ierr )

    IF ( TRIM( coupling_mode ) /= 'uncoupled' )  THEN
   
!
!--    Pass the number of grid points of the atmosphere model to
!--    the ocean model and vice versa
       IF ( coupling_mode == 'atmosphere_to_ocean' )  THEN

          nx_a = nx
          ny_a = ny

          IF ( myid == 0 )  THEN

             CALL MPI_SEND( nx_a, 1, MPI_INTEGER, numprocs, 1, comm_inter,  &
                            ierr )
             CALL MPI_SEND( ny_a, 1, MPI_INTEGER, numprocs, 2, comm_inter,  &
                            ierr )
             CALL MPI_SEND( pdims, 2, MPI_INTEGER, numprocs, 3, comm_inter, &
                            ierr )
             CALL MPI_RECV( nx_o, 1, MPI_INTEGER, numprocs, 4, comm_inter,  &
                            status, ierr )
             CALL MPI_RECV( ny_o, 1, MPI_INTEGER, numprocs, 5, comm_inter,  &
                            status, ierr )
             CALL MPI_RECV( pdims_remote, 2, MPI_INTEGER, numprocs, 6,      &
                            comm_inter, status, ierr )
          ENDIF

          CALL MPI_BCAST( nx_o, 1, MPI_INTEGER, 0, comm2d, ierr )
          CALL MPI_BCAST( ny_o, 1, MPI_INTEGER, 0, comm2d, ierr ) 
          CALL MPI_BCAST( pdims_remote, 2, MPI_INTEGER, 0, comm2d, ierr )
       
       ELSEIF ( coupling_mode == 'ocean_to_atmosphere' )  THEN

          nx_o = nx
          ny_o = ny 

          IF ( myid == 0 ) THEN

             CALL MPI_RECV( nx_a, 1, MPI_INTEGER, 0, 1, comm_inter, status, &
                            ierr )
             CALL MPI_RECV( ny_a, 1, MPI_INTEGER, 0, 2, comm_inter, status, &
                            ierr )
             CALL MPI_RECV( pdims_remote, 2, MPI_INTEGER, 0, 3, comm_inter, &
                            status, ierr )
             CALL MPI_SEND( nx_o, 1, MPI_INTEGER, 0, 4, comm_inter, ierr )
             CALL MPI_SEND( ny_o, 1, MPI_INTEGER, 0, 5, comm_inter, ierr )
             CALL MPI_SEND( pdims, 2, MPI_INTEGER, 0, 6, comm_inter, ierr )
          ENDIF

          CALL MPI_BCAST( nx_a, 1, MPI_INTEGER, 0, comm2d, ierr)
          CALL MPI_BCAST( ny_a, 1, MPI_INTEGER, 0, comm2d, ierr) 
          CALL MPI_BCAST( pdims_remote, 2, MPI_INTEGER, 0, comm2d, ierr) 

       ENDIF
  
       ngp_a = ( nx_a+1 + 2 * nbgp ) * ( ny_a+1 + 2 * nbgp )
       ngp_o = ( nx_o+1 + 2 * nbgp ) * ( ny_o+1 + 2 * nbgp )

!
!--    Determine if the horizontal grid and the number of PEs in ocean and
!--    atmosphere is same or not
       IF ( nx_o == nx_a  .AND.  ny_o == ny_a  .AND.  &
            pdims(1) == pdims_remote(1) .AND. pdims(2) == pdims_remote(2) ) &
       THEN
          coupling_topology = 0
       ELSE
          coupling_topology = 1
       ENDIF 

!
!--    Determine the target PEs for the exchange between ocean and
!--    atmosphere (comm2d)
       IF ( coupling_topology == 0 )  THEN
!
!--       In case of identical topologies, every atmosphere PE has exactly one
!--       ocean PE counterpart and vice versa
          IF ( TRIM( coupling_mode ) == 'atmosphere_to_ocean' ) THEN
             target_id = myid + numprocs
          ELSE
             target_id = myid 
          ENDIF

       ELSE
!
!--       In case of nonequivalent topology in ocean and atmosphere only for
!--       PE0 in ocean and PE0 in atmosphere a target_id is needed, since
!--       data echxchange between ocean and atmosphere will be done only
!--       between these PEs.    
          IF ( myid == 0 )  THEN

             IF ( TRIM( coupling_mode ) == 'atmosphere_to_ocean' )  THEN
                target_id = numprocs 
             ELSE
                target_id = 0
             ENDIF

          ENDIF

       ENDIF

    ENDIF


#endif

#else

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

    ALLOCATE( hor_index_bounds(4,0:0) )
    hor_index_bounds(1,0) = nxl
    hor_index_bounds(2,0) = nxr
    hor_index_bounds(3,0) = nys
    hor_index_bounds(4,0) = nyn

!
!-- 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
    nzb_x = nzb + 1
    nzt_x = nzt

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

    nxl_z = nxl
    nxr_z = nxr
    nys_z = nys
    nyn_z = 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 = nz    ! do not use nnz because it might be > nz due to transposition
                 ! requirements
       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 identically processed on all PEs.
       IF ( numprocs > 1  .AND.  mg_switch_to_pe0_level /= -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
                message_string = 'mg_switch_to_pe0_level ' // &
                                 'out of range and reset to default (=0)'
                CALL message( 'init_pegrid', 'PA0235', 0, 1, 0, 6, 0 )
                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 ) && ! defined( __check )
!
!--          Save the grid size of the subdomain at the switch level, because
!--          it is needed in poismg.
             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
             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. Therefore the subdomain size of an PE is calculated and 
!--          the size of the gathered grid. These values are used in  
!--          routines pres and poismg
             subdomain_size = ( nxr - nxl + 2 * nbgp + 1 ) * &
                              ( nyn - nys + 2 * nbgp + 1 ) * ( nzt - nzb + 2 )
             gathered_size  = ( nxr_l - nxl_l + 3 ) * ( nyn_l - nys_l + 3 ) * &
                              ( nzt_l - nzb + 2 )

#elif ! defined ( __parallel )
             message_string = 'multigrid gather/scatter impossible ' // &
                          'in non parallel mode'
             CALL message( 'init_pegrid', 'PA0237', 1, 2, 0, 6, 0 )
#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

!
!--    Temporary problem: Currently calculation of maxerror iin routine poismg crashes
!--    if grid data are collected on PE0 already on the finest grid level.
!--    To be solved later.
       IF ( maximum_grid_level == mg_switch_to_pe0_level )  THEN
          message_string = 'grid coarsening on subdomain level cannot be performed'
          CALL message( 'poismg', 'PA0236', 1, 2, 0, 6, 0 )
       ENDIF

    ELSE

       maximum_grid_level = 0

    ENDIF

!
!-- Default level 0 tells exchange_horiz that all ghost planes have to be
!-- exchanged. grid_level is adjusted in poismg, where only one ghost plane
!-- is required.
    grid_level = 0

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

!
!-- Define new MPI derived datatypes for the exchange of ghost points in
!-- x- and y-direction for 2D-arrays (line)
    CALL MPI_TYPE_VECTOR( nxr-nxl+1+2*nbgp, nbgp, ngp_y, MPI_REAL, type_x, &
                          ierr )
    CALL MPI_TYPE_COMMIT( type_x, ierr )
    CALL MPI_TYPE_VECTOR( nxr-nxl+1+2*nbgp, nbgp, ngp_y, MPI_INTEGER, &
                          type_x_int, ierr )
    CALL MPI_TYPE_COMMIT( type_x_int, ierr )

    CALL MPI_TYPE_VECTOR( nbgp, ngp_y, ngp_y, MPI_REAL, type_y, ierr )
    CALL MPI_TYPE_COMMIT( type_y, ierr )
    CALL MPI_TYPE_VECTOR( nbgp, ngp_y, ngp_y, MPI_INTEGER, type_y_int, ierr )
    CALL MPI_TYPE_COMMIT( type_y_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(0:maximum_grid_level), type_xz(0:maximum_grid_level),&
               type_yz(0:maximum_grid_level) )

    nxl_l = nxl; nxr_l = nxr; nys_l = nys; nyn_l = nyn; nzb_l = nzb; nzt_l = nzt

!
!-- Discern between the model grid, which needs nbgp ghost points and
!-- grid levels for the multigrid scheme. In the latter case only one
!-- ghost point is necessary.
!-- First definition of MPI-datatypes for exchange of ghost layers on normal 
!-- grid. The following loop is needed for data exchange in poismg.f90.
!
!-- Determine number of grid points of yz-layer for exchange
    ngp_yz(0) = (nzt - nzb + 2) * (nyn - nys + 1 + 2 * nbgp)

!
!-- Define an MPI-datatype for the exchange of left/right boundaries.
!-- Although data are contiguous in physical memory (which does not
!-- necessarily require an MPI-derived datatype), the data exchange between
!-- left and right PE's using the MPI-derived type is 10% faster than without.
    CALL MPI_TYPE_VECTOR( nxr-nxl+1+2*nbgp, nbgp*(nzt-nzb+2), ngp_yz(0), &
                          MPI_REAL, type_xz(0), ierr )
    CALL MPI_TYPE_COMMIT( type_xz(0), ierr )

    CALL MPI_TYPE_VECTOR( nbgp, ngp_yz(0), ngp_yz(0), MPI_REAL, type_yz(0), &
                          ierr ) 
    CALL MPI_TYPE_COMMIT( type_yz(0), ierr )

!
!-- Definition of MPI-datatypes for multigrid method (coarser level grids)
    IF ( psolver == 'multigrid' )  THEN
!    
!--    Definition of MPI-datatyoe as above, but only 1 ghost level is used
       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 )

          CALL MPI_TYPE_VECTOR( 1, ngp_yz(i), ngp_yz(i), MPI_REAL, type_yz(i), &
                                ierr )
          CALL MPI_TYPE_COMMIT( type_yz(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
#endif

#if defined( __parallel ) && ! defined ( __check )
!
!-- Setting of flags for inflow/outflow conditions in case of non-cyclic
!-- horizontal boundary conditions.
    IF ( pleft == MPI_PROC_NULL )  THEN
       IF ( bc_lr == 'dirichlet/radiation' .OR. bc_lr == 'dirichlet/neumann' )  THEN
          inflow_l  = .TRUE.
       ELSEIF ( bc_lr == 'radiation/dirichlet' .OR. bc_lr == 'neumann/dirichlet' )  THEN
          outflow_l = .TRUE.
       ENDIF
    ENDIF

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

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

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

!
!-- Broadcast the id of the inflow PE
    IF ( inflow_l )  THEN
       id_inflow_l = myidx
    ELSE
       id_inflow_l = 0
    ENDIF
    IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
    CALL MPI_ALLREDUCE( id_inflow_l, id_inflow, 1, MPI_INTEGER, MPI_SUM, &
                        comm1dx, ierr )

!
!-- Broadcast the id of the recycling plane
!-- WARNING: needs to be adjusted in case of inflows other than from left side!
    IF ( ( recycling_width / dx ) >= nxl  .AND. &
         ( recycling_width / dx ) <= nxr )  THEN
       id_recycling_l = myidx
    ELSE
       id_recycling_l = 0
    ENDIF
    IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
    CALL MPI_ALLREDUCE( id_recycling_l, id_recycling, 1, MPI_INTEGER, MPI_SUM, &
                        comm1dx, ierr )

#elif ! defined ( __parallel )
    IF ( bc_lr == 'dirichlet/radiation' .OR. bc_lr == 'dirichlet/neumann' )  THEN
       inflow_l  = .TRUE.
       outflow_r = .TRUE.
    ELSEIF ( bc_lr == 'radiation/dirichlet' .OR. bc_lr == 'neumann/dirichlet' )  THEN
       outflow_l = .TRUE.
       inflow_r  = .TRUE.
    ENDIF

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

!
!-- At the inflow or outflow, u or v, respectively, have to be calculated for
!-- one more grid point.
    IF ( inflow_l .OR. outflow_l )  THEN
       nxlu = nxl + 1
    ELSE
       nxlu = nxl
    ENDIF
    IF ( inflow_s .OR. outflow_s )  THEN
       nysv = nys + 1
    ELSE
       nysv = nys
    ENDIF

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

!
!-- Allocate wall flag arrays used in the multigrid solver
    IF ( psolver == 'multigrid' )  THEN

       DO  i = maximum_grid_level, 1, -1

           SELECT CASE ( i )

              CASE ( 1 )
                 ALLOCATE( wall_flags_1(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 2 )
                 ALLOCATE( wall_flags_2(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 3 )
                 ALLOCATE( wall_flags_3(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 4 )
                 ALLOCATE( wall_flags_4(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 5 )
                 ALLOCATE( wall_flags_5(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 6 )
                 ALLOCATE( wall_flags_6(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 7 )
                 ALLOCATE( wall_flags_7(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 8 )
                 ALLOCATE( wall_flags_8(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 9 )
                 ALLOCATE( wall_flags_9(nzb:nzt_mg(i)+1,         &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE ( 10 )
                 ALLOCATE( wall_flags_10(nzb:nzt_mg(i)+1,        &
                                        nys_mg(i)-1:nyn_mg(i)+1, &
                                        nxl_mg(i)-1:nxr_mg(i)+1) )

              CASE DEFAULT
                 message_string = 'more than 10 multigrid levels'
                 CALL message( 'init_pegrid', 'PA0238', 1, 2, 0, 6, 0 )

          END SELECT

       ENDDO

    ENDIF

!
!-- Calculate the number of groups into which parallel I/O is split.
!-- The default for files which are opened by all PEs (or where each
!-- PE opens his own independent file) is, that all PEs are doing input/output
!-- in parallel at the same time. This might cause performance or even more
!-- severe problems depending on the configuration of the underlying file
!-- system.
!-- First, set the default:
    IF ( maximum_parallel_io_streams == -1  .OR. &
         maximum_parallel_io_streams > numprocs )  THEN
       maximum_parallel_io_streams = numprocs
    ENDIF

!
!-- Now calculate the number of io_blocks and the io_group to which the
!-- respective PE belongs. I/O of the groups is done in serial, but in parallel
!-- for all PEs belonging to the same group. A preliminary setting with myid
!-- based on MPI_COMM_WORLD has been done in parin.
    io_blocks = numprocs / maximum_parallel_io_streams
    io_group  = MOD( myid+1, io_blocks )
    

 END SUBROUTINE init_pegrid