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poisfft.f90 @ 449

Last change on this file since 449 was 392, checked in by raasch, 15 years ago

New:
---

Adapted for machine lck
(mrun, mbuild, subjob)

bc_lr/bc_ns in most subroutines replaced by LOGICAL variables bc_lr_cyc,
bc_ns_cyc for speed optimization
(check_parameters, diffusion_u, diffusion_v, diffusion_w, modules)

Additional timestep criterion in case of simulations with plant canopy (timestep)

Check for illegal entries in section_xy|xz|yz that exceed nz+1|ny+1|nx+1
(check_parameters)

Clipping of dvrp output implemented. Default colourtable for particles
implemented, particle attributes (color, dvrp_size) can be set with new
parameters particle_color, particle_dvrpsize, color_interval,
dvrpsize_interval (init_dvrp, data_output_dvrp, modules, user_data_output_dvrp).
Slicer attributes (dvrp) are set with new routine set_slicer_attributes_dvrp
and are controlled with existing parameters slicer_range_limits.
(set_slicer_attributes_dvrp)

Ocean atmosphere coupling allows to use independent precursor runs in order
to account for different spin-up times. The time when coupling has to be
started is given by new inipar parameter coupling_start_time. The precursor
ocean run has to be started using new mrun option "-y" in order to add
appendix "_O" to all output files.
(check_for_restart, check_parameters, data_output_2d, data_output_3d,
data_output_profiles, data_output_ptseries, data_output_spectra,
data_output_tseries, header, init_coupling, modules, mrun,
parin, read_var_list, surface_coupler, time_integration, write_var_list)

Polygon reduction for topography and ground plate isosurface. Reduction level
for buildings can be chosen with parameter cluster_size. (init_dvrp)

External pressure gradient (check_parameters, header, init_3d_model, modules,
parin, prognostic_equations, read_var_list, write_var_list)

New topography case 'single_street_canyon' (header, init_grid, modules, parin,
read_var_list, user_check_parameters, user_header, user_init_grid, write_var_list)

Option to predefine a target bulk velocity for conserve_volume_flow
(check_parameters, header, init_3d_model, modules, parin, read_var_list,
write_var_list)

Option for user defined 2D data output in xy cross sections at z=nzb+1
(data_output_2d, user_data_output_2d)

xy cross section output of surface heatfluxes (latent, sensible)
(average_3d_data, check_parameters, data_output_2d, modules, read_3d_binary,
sum_up_3d_data, write_3d_binary)

average_3d_data, check_for_restart, check_parameters, data_output_2d, data_output_3d, data_output_dvrp, data_output_profiles, data_output_ptseries, data_output_spectra, data_output_tseries, init_coupling, init_dvrp, init_grid, init_3d_model, header, mbuild, modules, mrun, package_parin, parin, prognostic_equations, read_3d_binary, read_var_list, subjob, surface_coupler, timestep, time_integration, user_check_parameters, user_data_output_2d, user_data_output_dvrp, user_header, user_init_grid, write_3d_binary, write_var_list

New: set_particle_attributes, set_slicer_attributes_dvrp

Changed:

lcmuk changed to lc to avoid problems with Intel compiler on sgi-ice
(poisfft)

For extended NetCDF files, the updated title attribute includes an update of
time_average_text where appropriate. (netcdf)

In case of restart runs without extension, initial profiles are not written
to NetCDF-file anymore. (data_output_profiles, modules, read_var_list, write_var_list)

Small change in formatting of the message handling routine concering the output in the
job protocoll. (message)

initializing_actions='read_data_for_recycling' renamed to 'cyclic_fill', now
independent of turbulent_inflow (check_parameters, header, init_3d_model)

2 NetCDF error numbers changed. (data_output_3d)

A Link to the website appendix_a.html is printed for further information
about the possible errors. (message)

Temperature gradient criterion for estimating the boundary layer height
replaced by the gradient criterion of Sullivan et al. (1998). (flow_statistics)

NetCDF unit attribute in timeseries output in case of statistic regions added
(netcdf)

Output of NetCDF messages with aid of message handling routine.
(check_open, close_file, data_output_2d, data_output_3d,
data_output_profiles, data_output_ptseries, data_output_spectra,
data_output_tseries, netcdf, output_particles_netcdf)

Output of messages replaced by message handling routine.
(advec_particles, advec_s_bc, buoyancy, calc_spectra, check_for_restart,
check_open, coriolis, cpu_log, data_output_2d, data_output_3d, data_output_dvrp,
data_output_profiles, data_output_spectra, fft_xy, flow_statistics, header,
init_1d_model, init_3d_model, init_dvrp, init_grid, init_particles, init_pegrid,
netcdf, parin, plant_canopy_model, poisfft_hybrid, poismg, read_3d_binary,
read_var_list, surface_coupler, temperton_fft, timestep, user_actions,
user_data_output_dvrp, user_dvrp_coltab, user_init_grid, user_init_plant_canopy,
user_parin, user_read_restart_data, user_spectra )

Maximum number of tails is calculated from maximum number of particles and
skip_particles_for_tail (init_particles)

Value of vertical_particle_advection may differ for each particle group
(advec_particles, header, modules)

First constant in array den also defined as type double. (eqn_state_seawater)

Parameter dvrp_psize moved from particles_par to dvrp_graphics_par. (package_parin)

topography_grid_convention moved from userpar to inipar (check_parameters,
header, parin, read_var_list, user_check_parameters, user_header,
user_init_grid, user_parin, write_var_list)

Default value of grid_matching changed to strict.

Adjustments for runs on lcxt4 (necessary due to an software update on CRAY) and
for coupled runs on ibmy (mrun, subjob)

advec_particles, advec_s_bc, buoyancy, calc_spectra, check_for_restart, check_open, check_parameters, close_file, coriolis, cpu_log, data_output_2d, data_output_3d, data_output_dvrp, data_output_profiles, data_output_ptseries, data_output_spectra, data_output_tseries, eqn_state_seawater, fft_xy, flow_statistics, header, init_1d_model, init_3d_model, init_dvrp, init_grid, init_particles, init_pegrid, message, mrun, netcdf, output_particles_netcdf, package_parin, parin, plant_canopy_model, poisfft, poisfft_hybrid, poismg, read_3d_binary, read_var_list, sort_particles, subjob, user_check_parameters, user_header, user_init_grid, user_parin, surface_coupler, temperton_fft, timestep, user_actions, user_data_output_dvrp, user_dvrp_coltab, user_init_grid, user_init_plant_canopy, user_parin, user_read_restart_data, user_spectra, write_var_list

Errors:

Bugfix: Initial hydrostatic pressure profile in case of ocean runs is now
calculated in 5 iteration steps. (init_ocean)

Bugfix: wrong sign in buoyancy production of ocean part in case of not using
the reference density (only in 3D routine production_e) (production_e)

Bugfix: output of averaged 2d/3d quantities requires that an avaraging
interval has been set, respective error message is included (check_parameters)

Bugfix: Output on unit 14 only if requested by write_binary.
(user_last_actions)

Bugfix to avoid zero division by km_neutral (production_e)

Bugfix for extended NetCDF files: In order to avoid 'data mode' errors if
updated attributes are larger than their original size, NF90_PUT_ATT is called
in 'define mode' enclosed by NF90_REDEF and NF90_ENDDEF calls. This implies a
possible performance loss; an alternative strategy would be to ensure equal
attribute size in a job chain. (netcdf)

Bugfix: correction of initial volume flow for non-flat topography (init_3d_model)
Bugfix: zero initialization of arrays within buildings for 'cyclic_fill' (init_3d_model)

Bugfix: to_be_resorted => s_av for time-averaged scalars (data_output_2d, data_output_3d)

Bugfix: error in formatting the output (message)

Bugfix: avoid that ngp_2dh_s_inner becomes zero (init_3_model)

Typographical error: unit of wpt in dots_unit (modules)

Bugfix: error in check, if particles moved further than one subdomain length.
This check must not be applied for newly released particles. (advec_particles)

Bugfix: several tail counters are initialized, particle_tail_coordinates is
only written to file if its third index is > 0, arrays for tails are allocated
with a minimum size of 10 tails if there is no tail initially (init_particles,
advec_particles)

Bugfix: pressure included for profile output (check_parameters)

Bugfix: Type of count and count_rate changed to default INTEGER on NEC machines
(cpu_log)

Bugfix: output if particle time series only if particle advection is switched
on. (time_integration)

Bugfix: qsws was calculated in case of constant heatflux = .FALSE. (prandtl_fluxes)

Bugfix: averaging along z is not allowed for 2d quantities (e.g. u* and z0) (data_output_2d)

Typographical errors (netcdf)

If the inversion height calculated by the prerun is zero, inflow_damping_height
must be explicitly specified (init_3d_model)

Small bugfix concerning 3d 64bit netcdf output format (header)

Bugfix: dt_fixed removed from the restart file, because otherwise, no change
from a fixed to a variable timestep would be possible in restart runs.
(read_var_list, write_var_list)

Bugfix: initial setting of time_coupling in coupled restart runs (time_integration)

advec_particles, check_parameters, cpu_log, data_output_2d, data_output_3d, header, init_3d_model, init_particles, init_ocean, modules, netcdf, prandtl_fluxes, production_e, read_var_list, time_integration, user_last_actions, write_var_list

Property svn:keywords set to Id

File size: 44.6 KB

Rev	Line
[1]	1	MODULE poisfft_mod
	2
	3	!------------------------------------------------------------------------------!
	4	! Actual revisions:
	5	! -----------------
[392]	6	!
[1]	7	!
	8	! Former revisions:
	9	! -----------------
[3]	10	! $Id: poisfft.f90 392 2009-09-24 10:39:14Z raasch $
[77]	11	!
[392]	12	! 377 2009-09-04 11:09:00Z raasch
	13	! __lcmuk changed to __lc to avoid problems with Intel compiler on sgi-ice
	14	!
[198]	15	! 164 2008-05-15 08:46:15Z raasch
	16	! Arguments removed from transpose routines
	17	!
[139]	18	! 128 2007-10-26 13:11:14Z raasch
	19	! Bugfix: wavenumber calculation for even nx in routines maketri
	20	!
[90]	21	! 85 2007-05-11 09:35:14Z raasch
	22	! Bugfix: work_fft*_vec removed from some PRIVATE-declarations
	23	!
[77]	24	! 76 2007-03-29 00:58:32Z raasch
	25	! Tridiagonal coefficients adjusted for Neumann boundary conditions both at
	26	! the bottom and the top.
	27	!
[3]	28	! RCS Log replace by Id keyword, revision history cleaned up
	29	!
[1]	30	! Revision 1.24 2006/08/04 15:00:24 raasch
	31	! Default setting of the thread number tn in case of not using OpenMP
	32	!
	33	! Revision 1.23 2006/02/23 12:48:38 raasch
	34	! Additional compiler directive in routine tridia_1dd for preventing loop
	35	! exchange on NEC-SX6
	36	!
	37	! Revision 1.20 2004/04/30 12:38:09 raasch
	38	! Parts of former poisfft_hybrid moved to this subroutine,
	39	! former subroutine changed to a module, renaming of FFT-subroutines and
	40	! -module, FFTs completely substituted by calls of fft_x and fft_y,
	41	! NAG fft used in the non-parallel case completely removed, l in maketri
	42	! is now a 1d-array, variables passed by modules instead of using parameter
	43	! lists, enlarged transposition arrays introduced
	44	!
	45	! Revision 1.1 1997/07/24 11:24:14 raasch
	46	! Initial revision
	47	!
	48	!
	49	! Description:
	50	! ------------
	51	! See below.
	52	!------------------------------------------------------------------------------!
	53
	54	!--------------------------------------------------------------------------!
	55	! poisfft !
	56	! !
	57	! Original version: Stephan Siano (pois3d) !
	58	! !
	59	! Institute of Meteorology and Climatology, University of Hannover !
	60	! Germany !
	61	! !
	62	! Version as of July 23,1996 !
	63	! !
	64	! !
	65	! Version for parallel computers: Siegfried Raasch !
	66	! !
	67	! Version as of July 03,1997 !
	68	! !
	69	! Solves the Poisson equation with a 2D spectral method !
	70	! d^2 p / dx^2 + d^2 p / dy^2 + d^2 p / dz^2 = s !
	71	! !
	72	! Input: !
	73	! real ar contains in the (nnx,nny,nnz) elements, !
	74	! starting from the element (1,nys,nxl), the !
	75	! values for s !
	76	! real work Temporary array !
	77	! !
	78	! Output: !
	79	! real ar contains the solution for p !
	80	!--------------------------------------------------------------------------!
	81
	82	USE fft_xy
	83	USE indices
	84	USE transpose_indices
	85
	86	IMPLICIT NONE
	87
	88	PRIVATE
	89	PUBLIC poisfft, poisfft_init
	90
	91	INTERFACE poisfft
	92	MODULE PROCEDURE poisfft
	93	END INTERFACE poisfft
	94
	95	INTERFACE poisfft_init
	96	MODULE PROCEDURE poisfft_init
	97	END INTERFACE poisfft_init
	98
	99	CONTAINS
	100
	101	SUBROUTINE poisfft_init
	102
	103	CALL fft_init
	104
	105	END SUBROUTINE poisfft_init
	106
	107
	108	SUBROUTINE poisfft( ar, work )
	109
	110	USE cpulog
	111	USE interfaces
	112	USE pegrid
	113
	114	IMPLICIT NONE
	115
	116	REAL, DIMENSION(1:nza,nys:nyna,nxl:nxra) :: ar, work
	117
	118
	119	CALL cpu_log( log_point_s(3), 'poisfft', 'start' )
	120
	121	!
	122	!-- Two-dimensional Fourier Transformation in x- and y-direction.
	123	#if defined( __parallel )
	124	IF ( pdims(2) == 1 ) THEN
	125
	126	!
	127	!-- 1d-domain-decomposition along x:
	128	!-- FFT along y and transposition y --> x
	129	CALL ffty_tr_yx( ar, work, ar )
	130
	131	!
	132	!-- FFT along x, solving the tridiagonal system and backward FFT
	133	CALL fftx_tri_fftx( ar )
	134
	135	!
	136	!-- Transposition x --> y and backward FFT along y
	137	CALL tr_xy_ffty( ar, work, ar )
	138
	139	ELSEIF ( pdims(1) == 1 ) THEN
	140
	141	!
	142	!-- 1d-domain-decomposition along y:
	143	!-- FFT along x and transposition x --> y
	144	CALL fftx_tr_xy( ar, work, ar )
	145
	146	!
	147	!-- FFT along y, solving the tridiagonal system and backward FFT
	148	CALL ffty_tri_ffty( ar )
	149
	150	!
	151	!-- Transposition y --> x and backward FFT along x
	152	CALL tr_yx_fftx( ar, work, ar )
	153
	154	ELSE
	155
	156	!
	157	!-- 2d-domain-decomposition
	158	!-- Transposition z --> x
	159	CALL cpu_log( log_point_s(5), 'transpo forward', 'start' )
[164]	160	CALL transpose_zx( ar, work, ar )
[1]	161	CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' )
	162
	163	CALL cpu_log( log_point_s(4), 'fft_x', 'start' )
	164	CALL fftxp( ar, 'forward' )
	165	CALL cpu_log( log_point_s(4), 'fft_x', 'pause' )
	166
	167	!
	168	!-- Transposition x --> y
	169	CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' )
[164]	170	CALL transpose_xy( ar, work, ar )
[1]	171	CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' )
	172
	173	CALL cpu_log( log_point_s(7), 'fft_y', 'start' )
	174	CALL fftyp( ar, 'forward' )
	175	CALL cpu_log( log_point_s(7), 'fft_y', 'pause' )
	176
	177	!
	178	!-- Transposition y --> z
	179	CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' )
[164]	180	CALL transpose_yz( ar, work, ar )
[1]	181	CALL cpu_log( log_point_s(5), 'transpo forward', 'stop' )
	182
	183	!
	184	!-- Solve the Poisson equation in z-direction in cartesian space.
	185	CALL cpu_log( log_point_s(6), 'tridia', 'start' )
	186	CALL tridia( ar )
	187	CALL cpu_log( log_point_s(6), 'tridia', 'stop' )
	188
	189	!
	190	!-- Inverse Fourier Transformation
	191	!-- Transposition z --> y
	192	CALL cpu_log( log_point_s(8), 'transpo invers', 'start' )
[164]	193	CALL transpose_zy( ar, work, ar )
[1]	194	CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' )
	195
	196	CALL cpu_log( log_point_s(7), 'fft_y', 'continue' )
	197	CALL fftyp( ar, 'backward' )
	198	CALL cpu_log( log_point_s(7), 'fft_y', 'stop' )
	199
	200	!
	201	!-- Transposition y --> x
	202	CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' )
[164]	203	CALL transpose_yx( ar, work, ar )
[1]	204	CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' )
	205
	206	CALL cpu_log( log_point_s(4), 'fft_x', 'continue' )
	207	CALL fftxp( ar, 'backward' )
	208	CALL cpu_log( log_point_s(4), 'fft_x', 'stop' )
	209
	210	!
	211	!-- Transposition x --> z
	212	CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' )
[164]	213	CALL transpose_xz( ar, work, ar )
[1]	214	CALL cpu_log( log_point_s(8), 'transpo invers', 'stop' )
	215
	216	ENDIF
	217
	218	#else
	219
	220	!
	221	!-- Two-dimensional Fourier Transformation along x- and y-direction.
	222	CALL cpu_log( log_point_s(4), 'fft_x', 'start' )
	223	CALL fftx( ar, 'forward' )
	224	CALL cpu_log( log_point_s(4), 'fft_x', 'pause' )
	225	CALL cpu_log( log_point_s(7), 'fft_y', 'start' )
	226	CALL ffty( ar, 'forward' )
	227	CALL cpu_log( log_point_s(7), 'fft_y', 'pause' )
	228
	229	!
	230	!-- Solve the Poisson equation in z-direction in cartesian space.
	231	CALL cpu_log( log_point_s(6), 'tridia', 'start' )
	232	CALL tridia( ar )
	233	CALL cpu_log( log_point_s(6), 'tridia', 'stop' )
	234
	235	!
	236	!-- Inverse Fourier Transformation.
	237	CALL cpu_log( log_point_s(7), 'fft_y', 'continue' )
	238	CALL ffty( ar, 'backward' )
	239	CALL cpu_log( log_point_s(7), 'fft_y', 'stop' )
	240	CALL cpu_log( log_point_s(4), 'fft_x', 'continue' )
	241	CALL fftx( ar, 'backward' )
	242	CALL cpu_log( log_point_s(4), 'fft_x', 'stop' )
	243
	244	#endif
	245
	246	CALL cpu_log( log_point_s(3), 'poisfft', 'stop' )
	247
	248	END SUBROUTINE poisfft
	249
	250
	251
	252	SUBROUTINE tridia( ar )
	253
	254	!------------------------------------------------------------------------------!
	255	! solves the linear system of equations:
	256	!
	257	! -(4 pi^2(i^2/(dx^2nnx^2)+j^2/(dy^2nny^2))+
	258	! 1/(dzu(k)dzw(k))+1/(dzu(k-1)dzw(k)))*p(i,j,k)+
	259	! 1/(dzu(k)dzw(k))p(i,j,k+1)+1/(dzu(k-1)dzw(k))p(i,j,k-1)=d(i,j,k)
	260	!
	261	! by using the Thomas algorithm
	262	!------------------------------------------------------------------------------!
	263
	264	USE arrays_3d
	265
	266	IMPLICIT NONE
	267
	268	INTEGER :: i, j, k, nnyh
	269
	270	REAL, DIMENSION(nxl_z:nxr_z,0:nz-1) :: ar1
	271	REAL, DIMENSION(5,nxl_z:nxr_z,0:nz-1) :: tri
	272
	273	#if defined( __parallel )
	274	REAL :: ar(nxl_z:nxr_za,nys_z:nyn_za,1:nza)
	275	#else
	276	REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z)
	277	#endif
	278
	279
	280	nnyh = (ny+1) / 2
	281
	282	!
	283	!-- Define constant elements of the tridiagonal matrix.
	284	DO k = 0, nz-1
	285	DO i = nxl_z, nxr_z
	286	tri(2,i,k) = ddzu(k+1) * ddzw(k+1)
	287	tri(3,i,k) = ddzu(k+2) * ddzw(k+1)
	288	ENDDO
	289	ENDDO
	290
	291	#if defined( __parallel )
	292	!
	293	!-- Repeat for all y-levels.
	294	DO j = nys_z, nyn_z
	295	IF ( j <= nnyh ) THEN
	296	CALL maketri( tri, j )
	297	ELSE
	298	CALL maketri( tri, ny+1-j )
	299	ENDIF
	300	CALL split( tri )
	301	CALL substi( ar, ar1, tri, j )
	302	ENDDO
	303	#else
	304	!
	305	!-- First y-level.
	306	CALL maketri( tri, nys_z )
	307	CALL split( tri )
	308	CALL substi( ar, ar1, tri, 0 )
	309
	310	!
	311	!-- Further y-levels.
	312	DO j = 1, nnyh - 1
	313	CALL maketri( tri, j )
	314	CALL split( tri )
	315	CALL substi( ar, ar1, tri, j )
	316	CALL substi( ar, ar1, tri, ny+1-j )
	317	ENDDO
	318	CALL maketri( tri, nnyh )
	319	CALL split( tri )
	320	CALL substi( ar, ar1, tri, nnyh+nys )
	321	#endif
	322
	323	CONTAINS
	324
	325	SUBROUTINE maketri( tri, j )
	326
	327	!------------------------------------------------------------------------------!
	328	! Computes the i- and j-dependent component of the matrix
	329	!------------------------------------------------------------------------------!
	330
	331	USE arrays_3d
	332	USE constants
	333	USE control_parameters
	334	USE grid_variables
	335
	336	IMPLICIT NONE
	337
	338	INTEGER :: i, j, k, nnxh
	339	REAL :: a, c
	340	REAL :: ll(nxl_z:nxr_z)
	341	REAL :: tri(5,nxl_z:nxr_z,0:nz-1)
	342
	343
	344	nnxh = ( nx + 1 ) / 2
	345
	346	!
	347	!-- Provide the tridiagonal matrix for solution of the Poisson equation in
	348	!-- Fourier space. The coefficients are computed following the method of
	349	!-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan
	350	!-- Siano's original version by discretizing the Poisson equation,
	351	!-- before it is Fourier-transformed
	352	#if defined( __parallel )
	353	DO i = nxl_z, nxr_z
[128]	354	IF ( i >= 0 .AND. i <= nnxh ) THEN
[1]	355	ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / &
	356	FLOAT( nx+1 ) ) ) / ( dx * dx ) + &
	357	2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / &
	358	FLOAT( ny+1 ) ) ) / ( dy * dy )
	359	ELSE
	360	ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / &
	361	FLOAT( nx+1 ) ) ) / ( dx * dx ) + &
	362	2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / &
	363	FLOAT( ny+1 ) ) ) / ( dy * dy )
	364	ENDIF
	365	DO k = 0,nz-1
	366	a = -1.0 * ddzu(k+2) * ddzw(k+1)
	367	c = -1.0 * ddzu(k+1) * ddzw(k+1)
	368	tri(1,i,k) = a + c - ll(i)
	369	ENDDO
	370	ENDDO
	371	#else
	372	DO i = 0, nnxh
	373	ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / FLOAT( nx+1 ) ) ) / &
	374	( dx * dx ) + &
	375	2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / FLOAT( ny+1 ) ) ) / &
	376	( dy * dy )
	377	DO k = 0, nz-1
	378	a = -1.0 * ddzu(k+2) * ddzw(k+1)
	379	c = -1.0 * ddzu(k+1) * ddzw(k+1)
	380	tri(1,i,k) = a + c - ll(i)
	381	IF ( i >= 1 .and. i < nnxh ) THEN
	382	tri(1,nx+1-i,k) = tri(1,i,k)
	383	ENDIF
	384	ENDDO
	385	ENDDO
	386	#endif
	387	IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN
	388	DO i = nxl_z, nxr_z
	389	tri(1,i,0) = tri(1,i,0) + tri(2,i,0)
	390	ENDDO
	391	ENDIF
	392	IF ( ibc_p_t == 1 ) THEN
	393	DO i = nxl_z, nxr_z
	394	tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1)
	395	ENDDO
	396	ENDIF
	397
	398	END SUBROUTINE maketri
	399
	400
	401	SUBROUTINE substi( ar, ar1, tri, j )
	402
	403	!------------------------------------------------------------------------------!
	404	! Substitution (Forward and Backward) (Thomas algorithm)
	405	!------------------------------------------------------------------------------!
	406
[76]	407	USE control_parameters
	408
[1]	409	IMPLICIT NONE
	410
	411	INTEGER :: i, j, k
	412	REAL :: ar1(nxl_z:nxr_z,0:nz-1)
	413	REAL :: tri(5,nxl_z:nxr_z,0:nz-1)
	414	#if defined( __parallel )
	415	REAL :: ar(nxl_z:nxr_za,nys_z:nyn_za,1:nza)
	416	#else
	417	REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z)
	418	#endif
	419
	420	!
	421	!-- Forward substitution.
	422	DO i = nxl_z, nxr_z
	423	#if defined( __parallel )
	424	ar1(i,0) = ar(i,j,1)
	425	#else
	426	ar1(i,0) = ar(1,j,i)
	427	#endif
	428	ENDDO
	429	DO k = 1, nz - 1
	430	DO i = nxl_z, nxr_z
	431	#if defined( __parallel )
	432	ar1(i,k) = ar(i,j,k+1) - tri(5,i,k) * ar1(i,k-1)
	433	#else
	434	ar1(i,k) = ar(k+1,j,i) - tri(5,i,k) * ar1(i,k-1)
	435	#endif
	436	ENDDO
	437	ENDDO
	438
	439	!
	440	!-- Backward substitution.
	441	DO i = nxl_z, nxr_z
	442	#if defined( __parallel )
	443	ar(i,j,nz) = ar1(i,nz-1) / tri(4,i,nz-1)
	444	#else
	445	ar(nz,j,i) = ar1(i,nz-1) / tri(4,i,nz-1)
	446	#endif
	447	ENDDO
	448	DO k = nz-2, 0, -1
	449	DO i = nxl_z, nxr_z
	450	#if defined( __parallel )
	451	ar(i,j,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,j,k+2) ) &
	452	/ tri(4,i,k)
	453	#else
	454	ar(k+1,j,i) = ( ar1(i,k) - tri(3,i,k) * ar(k+2,j,i) ) &
	455	/ tri(4,i,k)
	456	#endif
	457	ENDDO
	458	ENDDO
	459
[76]	460	!
	461	!-- Indices i=0, j=0 correspond to horizontally averaged pressure.
	462	!-- The respective values of ar should be zero at all k-levels if
	463	!-- acceleration of horizontally averaged vertical velocity is zero.
	464	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN
	465	IF ( j == 0 .AND. nxl_z == 0 ) THEN
	466	#if defined( __parallel )
	467	DO k = 1, nz
	468	ar(nxl_z,j,k) = 0.0
	469	ENDDO
	470	#else
	471	DO k = 1, nz
	472	ar(k,j,nxl_z) = 0.0
	473	ENDDO
	474	#endif
	475	ENDIF
	476	ENDIF
	477
[1]	478	END SUBROUTINE substi
	479
	480
	481	SUBROUTINE split( tri )
	482
	483	!------------------------------------------------------------------------------!
	484	! Splitting of the tridiagonal matrix (Thomas algorithm)
	485	!------------------------------------------------------------------------------!
	486
	487	IMPLICIT NONE
	488
	489	INTEGER :: i, k
	490	REAL :: tri(5,nxl_z:nxr_z,0:nz-1)
	491
	492	!
	493	!-- Splitting.
	494	DO i = nxl_z, nxr_z
	495	tri(4,i,0) = tri(1,i,0)
	496	ENDDO
	497	DO k = 1, nz-1
	498	DO i = nxl_z, nxr_z
	499	tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1)
	500	tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k)
	501	ENDDO
	502	ENDDO
	503
	504	END SUBROUTINE split
	505
	506	END SUBROUTINE tridia
	507
	508
	509	#if defined( __parallel )
	510	SUBROUTINE fftxp( ar, direction )
	511
	512	!------------------------------------------------------------------------------!
	513	! Fourier-transformation along x-direction Parallelized version
	514	!------------------------------------------------------------------------------!
	515
	516	IMPLICIT NONE
	517
	518	CHARACTER (LEN=*) :: direction
	519	INTEGER :: j, k
	520	REAL :: ar(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa)
	521
	522	!
	523	!-- Performing the fft with one of the methods implemented
	524	DO k = nzb_x, nzt_x
	525	DO j = nys_x, nyn_x
	526	CALL fft_x( ar(0:nx,j,k), direction )
	527	ENDDO
	528	ENDDO
	529
	530	END SUBROUTINE fftxp
	531
	532	#else
	533	SUBROUTINE fftx( ar, direction )
	534
	535	!------------------------------------------------------------------------------!
	536	! Fourier-transformation along x-direction Non parallel version
	537	!------------------------------------------------------------------------------!
	538
	539	IMPLICIT NONE
	540
	541	CHARACTER (LEN=*) :: direction
	542	INTEGER :: i, j, k
	543	REAL :: ar(1:nz,0:ny,0:nx)
	544
	545	!
	546	!-- Performing the fft with one of the methods implemented
	547	DO k = 1, nz
	548	DO j = 0, ny
	549	CALL fft_x( ar(k,j,0:nx), direction )
	550	ENDDO
	551	ENDDO
	552
	553	END SUBROUTINE fftx
	554	#endif
	555
	556
	557	#if defined( __parallel )
	558	SUBROUTINE fftyp( ar, direction )
	559
	560	!------------------------------------------------------------------------------!
	561	! Fourier-transformation along y-direction Parallelized version
	562	!------------------------------------------------------------------------------!
	563
	564	IMPLICIT NONE
	565
	566	CHARACTER (LEN=*) :: direction
	567	INTEGER :: i, k
	568	REAL :: ar(0:nya,nxl_y:nxr_ya,nzb_y:nzt_ya)
	569
	570	!
	571	!-- Performing the fft with one of the methods implemented
	572	DO k = nzb_y, nzt_y
	573	DO i = nxl_y, nxr_y
	574	CALL fft_y( ar(0:ny,i,k), direction )
	575	ENDDO
	576	ENDDO
	577
	578	END SUBROUTINE fftyp
	579
	580	#else
	581	SUBROUTINE ffty( ar, direction )
	582
	583	!------------------------------------------------------------------------------!
	584	! Fourier-transformation along y-direction Non parallel version
	585	!------------------------------------------------------------------------------!
	586
	587	IMPLICIT NONE
	588
	589	CHARACTER (LEN=*) :: direction
	590	INTEGER :: i, k
	591	REAL :: ar(1:nz,0:ny,0:nx)
	592
	593	!
	594	!-- Performing the fft with one of the methods implemented
	595	DO k = 1, nz
	596	DO i = 0, nx
	597	CALL fft_y( ar(k,0:ny,i), direction )
	598	ENDDO
	599	ENDDO
	600
	601	END SUBROUTINE ffty
	602	#endif
	603
	604	#if defined( __parallel )
	605	SUBROUTINE ffty_tr_yx( f_in, work, f_out )
	606
	607	!------------------------------------------------------------------------------!
	608	! Fourier-transformation along y with subsequent transposition y --> x for
	609	! a 1d-decomposition along x
	610	!
	611	! ATTENTION: The performance of this routine is much faster on the NEC-SX6,
	612	! if the first index of work_ffty_vec is odd. Otherwise
	613	! memory bank conflicts may occur (especially if the index is a
	614	! multiple of 128). That's why work_ffty_vec is dimensioned as
	615	! 0:ny+1.
	616	! Of course, this will not work if users are using an odd number
	617	! of gridpoints along y.
	618	!------------------------------------------------------------------------------!
	619
	620	USE control_parameters
	621	USE cpulog
	622	USE indices
	623	USE interfaces
	624	USE pegrid
	625	USE transpose_indices
	626
	627	IMPLICIT NONE
	628
	629	INTEGER :: i, iend, iouter, ir, j, k
	630	INTEGER, PARAMETER :: stridex = 4
	631
	632	REAL, DIMENSION(0:ny,stridex) :: work_ffty
	633	#if defined( __nec )
	634	REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec
	635	#endif
	636	REAL, DIMENSION(1:nza,0:nya,nxl:nxra) :: f_in
	637	REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: f_out
	638	REAL, DIMENSION(nxl:nxra,1:nza,0:nya) :: work
	639
	640	!
	641	!-- Carry out the FFT along y, where all data are present due to the
	642	!-- 1d-decomposition along x. Resort the data in a way that x becomes
	643	!-- the first index.
	644	CALL cpu_log( log_point_s(7), 'fft_y', 'start' )
	645
	646	IF ( host(1:3) == 'nec' ) THEN
	647	#if defined( __nec )
	648	!
	649	!-- Code optimized for vector processors
[85]	650	!$OMP PARALLEL PRIVATE ( i, j, k )
[1]	651	!$OMP DO
	652	DO i = nxl, nxr
	653
	654	DO j = 0, ny
	655	DO k = 1, nz
	656	work_ffty_vec(j,k,i) = f_in(k,j,i)
	657	ENDDO
	658	ENDDO
	659
	660	CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'forward' )
	661
	662	ENDDO
	663
	664	!$OMP DO
	665	DO k = 1, nz
	666	DO j = 0, ny
	667	DO i = nxl, nxr
	668	work(i,k,j) = work_ffty_vec(j,k,i)
	669	ENDDO
	670	ENDDO
	671	ENDDO
	672	!$OMP END PARALLEL
	673	#endif
	674
	675	ELSE
	676
	677	!
	678	!-- Cache optimized code.
	679	!-- The i-(x-)direction is split into a strided outer loop and an inner
	680	!-- loop for better cache performance
	681	!$OMP PARALLEL PRIVATE (i,iend,iouter,ir,j,k,work_ffty)
	682	!$OMP DO
	683	DO iouter = nxl, nxr, stridex
	684
	685	iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop
	686
	687	DO k = 1, nz
	688
	689	DO i = iouter, iend
	690
	691	ir = i-iouter+1 ! counter within a stride
	692	DO j = 0, ny
	693	work_ffty(j,ir) = f_in(k,j,i)
	694	ENDDO
	695	!
	696	!-- FFT along y
	697	CALL fft_y( work_ffty(:,ir), 'forward' )
	698
	699	ENDDO
	700
	701	!
	702	!-- Resort
	703	DO j = 0, ny
	704	DO i = iouter, iend
	705	work(i,k,j) = work_ffty(j,i-iouter+1)
	706	ENDDO
	707	ENDDO
	708
	709	ENDDO
	710
	711	ENDDO
	712	!$OMP END PARALLEL
	713
	714	ENDIF
	715	CALL cpu_log( log_point_s(7), 'fft_y', 'pause' )
	716
	717	!
	718	!-- Transpose array
	719	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' )
	720	CALL MPI_ALLTOALL( work(nxl,1,0), sendrecvcount_xy, MPI_REAL, &
	721	f_out(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, &
	722	comm1dx, ierr )
	723	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' )
	724
	725	END SUBROUTINE ffty_tr_yx
	726
	727
	728	SUBROUTINE tr_xy_ffty( f_in, work, f_out )
	729
	730	!------------------------------------------------------------------------------!
	731	! Transposition x --> y with a subsequent backward Fourier transformation for
	732	! a 1d-decomposition along x
	733	!------------------------------------------------------------------------------!
	734
	735	USE control_parameters
	736	USE cpulog
	737	USE indices
	738	USE interfaces
	739	USE pegrid
	740	USE transpose_indices
	741
	742	IMPLICIT NONE
	743
	744	INTEGER :: i, iend, iouter, ir, j, k
	745	INTEGER, PARAMETER :: stridex = 4
	746
	747	REAL, DIMENSION(0:ny,stridex) :: work_ffty
	748	#if defined( __nec )
	749	REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec
	750	#endif
	751	REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: f_in
	752	REAL, DIMENSION(1:nza,0:nya,nxl:nxra) :: f_out
	753	REAL, DIMENSION(nxl:nxra,1:nza,0:nya) :: work
	754
	755	!
	756	!-- Transpose array
	757	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' )
	758	CALL MPI_ALLTOALL( f_in(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, &
	759	work(nxl,1,0), sendrecvcount_xy, MPI_REAL, &
	760	comm1dx, ierr )
	761	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' )
	762
	763	!
	764	!-- Resort the data in a way that y becomes the first index and carry out the
	765	!-- backward fft along y.
	766	CALL cpu_log( log_point_s(7), 'fft_y', 'continue' )
	767
	768	IF ( host(1:3) == 'nec' ) THEN
	769	#if defined( __nec )
	770	!
	771	!-- Code optimized for vector processors
[85]	772	!$OMP PARALLEL PRIVATE ( i, j, k )
[1]	773	!$OMP DO
	774	DO k = 1, nz
	775	DO j = 0, ny
	776	DO i = nxl, nxr
	777	work_ffty_vec(j,k,i) = work(i,k,j)
	778	ENDDO
	779	ENDDO
	780	ENDDO
	781
	782	!$OMP DO
	783	DO i = nxl, nxr
	784
	785	CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'backward' )
	786
	787	DO j = 0, ny
	788	DO k = 1, nz
	789	f_out(k,j,i) = work_ffty_vec(j,k,i)
	790	ENDDO
	791	ENDDO
	792
	793	ENDDO
	794	!$OMP END PARALLEL
	795	#endif
	796
	797	ELSE
	798
	799	!
	800	!-- Cache optimized code.
	801	!-- The i-(x-)direction is split into a strided outer loop and an inner
	802	!-- loop for better cache performance
	803	!$OMP PARALLEL PRIVATE ( i, iend, iouter, ir, j, k, work_ffty )
	804	!$OMP DO
	805	DO iouter = nxl, nxr, stridex
	806
	807	iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop
	808
	809	DO k = 1, nz
	810	!
	811	!-- Resort
	812	DO j = 0, ny
	813	DO i = iouter, iend
	814	work_ffty(j,i-iouter+1) = work(i,k,j)
	815	ENDDO
	816	ENDDO
	817
	818	DO i = iouter, iend
	819
	820	!
	821	!-- FFT along y
	822	ir = i-iouter+1 ! counter within a stride
	823	CALL fft_y( work_ffty(:,ir), 'backward' )
	824
	825	DO j = 0, ny
	826	f_out(k,j,i) = work_ffty(j,ir)
	827	ENDDO
	828	ENDDO
	829
	830	ENDDO
	831
	832	ENDDO
	833	!$OMP END PARALLEL
	834
	835	ENDIF
	836
	837	CALL cpu_log( log_point_s(7), 'fft_y', 'stop' )
	838
	839	END SUBROUTINE tr_xy_ffty
	840
	841
	842	SUBROUTINE fftx_tri_fftx( ar )
	843
	844	!------------------------------------------------------------------------------!
	845	! FFT along x, solution of the tridiagonal system and backward FFT for
	846	! a 1d-decomposition along x
	847	!
	848	! WARNING: this subroutine may still not work for hybrid parallelization
	849	! with OpenMP (for possible necessary changes see the original
	850	! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002)
	851	!------------------------------------------------------------------------------!
	852
	853	USE control_parameters
	854	USE cpulog
	855	USE grid_variables
	856	USE indices
	857	USE interfaces
	858	USE pegrid
	859	USE transpose_indices
	860
	861	IMPLICIT NONE
	862
	863	character(len=3) :: myth_char
	864
	865	INTEGER :: i, j, k, m, n, omp_get_thread_num, tn
	866
	867	REAL, DIMENSION(0:nx) :: work_fftx
	868	REAL, DIMENSION(0:nx,1:nz) :: work_trix
	869	REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: ar
	870	REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri
	871
	872
	873	CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'start' )
	874
	875	ALLOCATE( tri(5,0:nx,0:nz-1,0:threads_per_task-1) )
	876
	877	tn = 0 ! Default thread number in case of one thread
	878	!$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_fftx, work_trix )
	879	DO j = nys_x, nyn_x
	880
	881	!$ tn = omp_get_thread_num()
	882
	883	IF ( host(1:3) == 'nec' ) THEN
	884	!
	885	!-- Code optimized for vector processors
	886	DO k = 1, nz
	887
	888	m = 0
	889	DO n = 1, pdims(1)
	890	DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!!
	891	work_trix(m,k) = ar(i,k,j,n)
	892	m = m + 1
	893	ENDDO
	894	ENDDO
	895
	896	ENDDO
	897
	898	CALL fft_x_m( work_trix, 'forward' )
	899
	900	ELSE
	901	!
	902	!-- Cache optimized code
	903	DO k = 1, nz
	904
	905	m = 0
	906	DO n = 1, pdims(1)
	907	DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!!
	908	work_fftx(m) = ar(i,k,j,n)
	909	m = m + 1
	910	ENDDO
	911	ENDDO
	912
	913	CALL fft_x( work_fftx, 'forward' )
	914
	915	DO i = 0, nx
	916	work_trix(i,k) = work_fftx(i)
	917	ENDDO
	918
	919	ENDDO
	920
	921	ENDIF
	922
	923	!
	924	!-- Solve the linear equation system
	925	CALL tridia_1dd( ddx2, ddy2, nx, ny, j, work_trix, tri(:,:,:,tn) )
	926
	927	IF ( host(1:3) == 'nec' ) THEN
	928	!
	929	!-- Code optimized for vector processors
	930	CALL fft_x_m( work_trix, 'backward' )
	931
	932	DO k = 1, nz
	933
	934	m = 0
	935	DO n = 1, pdims(1)
	936	DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!!
	937	ar(i,k,j,n) = work_trix(m,k)
	938	m = m + 1
	939	ENDDO
	940	ENDDO
	941
	942	ENDDO
	943
	944	ELSE
	945	!
	946	!-- Cache optimized code
	947	DO k = 1, nz
	948
	949	DO i = 0, nx
	950	work_fftx(i) = work_trix(i,k)
	951	ENDDO
	952
	953	CALL fft_x( work_fftx, 'backward' )
	954
	955	m = 0
	956	DO n = 1, pdims(1)
	957	DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!!
	958	ar(i,k,j,n) = work_fftx(m)
	959	m = m + 1
	960	ENDDO
	961	ENDDO
	962
	963	ENDDO
	964
	965	ENDIF
	966
	967	ENDDO
	968
	969	DEALLOCATE( tri )
	970
	971	CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'stop' )
	972
	973	END SUBROUTINE fftx_tri_fftx
	974
	975
	976	SUBROUTINE fftx_tr_xy( f_in, work, f_out )
	977
	978	!------------------------------------------------------------------------------!
	979	! Fourier-transformation along x with subsequent transposition x --> y for
	980	! a 1d-decomposition along y
	981	!
	982	! ATTENTION: The NEC-branch of this routine may significantly profit from
	983	! further optimizations. So far, performance is much worse than
	984	! for routine ffty_tr_yx (more than three times slower).
	985	!------------------------------------------------------------------------------!
	986
	987	USE control_parameters
	988	USE cpulog
	989	USE indices
	990	USE interfaces
	991	USE pegrid
	992	USE transpose_indices
	993
	994	IMPLICIT NONE
	995
	996	INTEGER :: i, j, k
	997
	998	REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx
	999	REAL, DIMENSION(1:nza,nys:nyna,0:nxa) :: f_in
	1000	REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: f_out
	1001	REAL, DIMENSION(nys:nyna,1:nza,0:nxa) :: work
	1002
	1003	!
	1004	!-- Carry out the FFT along x, where all data are present due to the
	1005	!-- 1d-decomposition along y. Resort the data in a way that y becomes
	1006	!-- the first index.
	1007	CALL cpu_log( log_point_s(4), 'fft_x', 'start' )
	1008
	1009	IF ( host(1:3) == 'nec' ) THEN
	1010	!
	1011	!-- Code for vector processors
[85]	1012	!$OMP PARALLEL PRIVATE ( i, j, k )
[1]	1013	!$OMP DO
	1014	DO i = 0, nx
	1015
	1016	DO j = nys, nyn
	1017	DO k = 1, nz
	1018	work_fftx(i,k,j) = f_in(k,j,i)
	1019	ENDDO
	1020	ENDDO
	1021
	1022	ENDDO
	1023
	1024	!$OMP DO
	1025	DO j = nys, nyn
	1026
	1027	CALL fft_x_m( work_fftx(:,:,j), 'forward' )
	1028
	1029	DO k = 1, nz
	1030	DO i = 0, nx
	1031	work(j,k,i) = work_fftx(i,k,j)
	1032	ENDDO
	1033	ENDDO
	1034
	1035	ENDDO
	1036	!$OMP END PARALLEL
	1037
	1038	ELSE
	1039
	1040	!
	1041	!-- Cache optimized code (there might be still a potential for better
	1042	!-- optimization).
	1043	!$OMP PARALLEL PRIVATE (i,j,k,work_fftx)
	1044	!$OMP DO
	1045	DO i = 0, nx
	1046
	1047	DO j = nys, nyn
	1048	DO k = 1, nz
	1049	work_fftx(i,k,j) = f_in(k,j,i)
	1050	ENDDO
	1051	ENDDO
	1052
	1053	ENDDO
	1054
	1055	!$OMP DO
	1056	DO j = nys, nyn
	1057	DO k = 1, nz
	1058
	1059	CALL fft_x( work_fftx(0:nx,k,j), 'forward' )
	1060
	1061	DO i = 0, nx
	1062	work(j,k,i) = work_fftx(i,k,j)
	1063	ENDDO
	1064	ENDDO
	1065
	1066	ENDDO
	1067	!$OMP END PARALLEL
	1068
	1069	ENDIF
	1070	CALL cpu_log( log_point_s(4), 'fft_x', 'pause' )
	1071
	1072	!
	1073	!-- Transpose array
	1074	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' )
	1075	CALL MPI_ALLTOALL( work(nys,1,0), sendrecvcount_xy, MPI_REAL, &
	1076	f_out(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, &
	1077	comm1dy, ierr )
	1078	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' )
	1079
	1080	END SUBROUTINE fftx_tr_xy
	1081
	1082
	1083	SUBROUTINE tr_yx_fftx( f_in, work, f_out )
	1084
	1085	!------------------------------------------------------------------------------!
	1086	! Transposition y --> x with a subsequent backward Fourier transformation for
	1087	! a 1d-decomposition along x
	1088	!------------------------------------------------------------------------------!
	1089
	1090	USE control_parameters
	1091	USE cpulog
	1092	USE indices
	1093	USE interfaces
	1094	USE pegrid
	1095	USE transpose_indices
	1096
	1097	IMPLICIT NONE
	1098
	1099	INTEGER :: i, j, k
	1100
	1101	REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx
	1102	REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: f_in
	1103	REAL, DIMENSION(1:nza,nys:nyna,0:nxa) :: f_out
	1104	REAL, DIMENSION(nys:nyna,1:nza,0:nxa) :: work
	1105
	1106	!
	1107	!-- Transpose array
	1108	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' )
	1109	CALL MPI_ALLTOALL( f_in(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, &
	1110	work(nys,1,0), sendrecvcount_xy, MPI_REAL, &
	1111	comm1dy, ierr )
	1112	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' )
	1113
	1114	!
	1115	!-- Carry out the FFT along x, where all data are present due to the
	1116	!-- 1d-decomposition along y. Resort the data in a way that y becomes
	1117	!-- the first index.
	1118	CALL cpu_log( log_point_s(4), 'fft_x', 'continue' )
	1119
	1120	IF ( host(1:3) == 'nec' ) THEN
	1121	!
	1122	!-- Code optimized for vector processors
[85]	1123	!$OMP PARALLEL PRIVATE ( i, j, k )
[1]	1124	!$OMP DO
	1125	DO j = nys, nyn
	1126
	1127	DO k = 1, nz
	1128	DO i = 0, nx
	1129	work_fftx(i,k,j) = work(j,k,i)
	1130	ENDDO
	1131	ENDDO
	1132
	1133	CALL fft_x_m( work_fftx(:,:,j), 'backward' )
	1134
	1135	ENDDO
	1136
	1137	!$OMP DO
	1138	DO i = 0, nx
	1139	DO j = nys, nyn
	1140	DO k = 1, nz
	1141	f_out(k,j,i) = work_fftx(i,k,j)
	1142	ENDDO
	1143	ENDDO
	1144	ENDDO
	1145	!$OMP END PARALLEL
	1146
	1147	ELSE
	1148
	1149	!
	1150	!-- Cache optimized code (there might be still a potential for better
	1151	!-- optimization).
	1152	!$OMP PARALLEL PRIVATE (i,j,k,work_fftx)
	1153	!$OMP DO
	1154	DO j = nys, nyn
	1155	DO k = 1, nz
	1156
	1157	DO i = 0, nx
	1158	work_fftx(i,k,j) = work(j,k,i)
	1159	ENDDO
	1160
	1161	CALL fft_x( work_fftx(0:nx,k,j), 'backward' )
	1162
	1163	ENDDO
	1164	ENDDO
	1165
	1166	!$OMP DO
	1167	DO i = 0, nx
	1168	DO j = nys, nyn
	1169	DO k = 1, nz
	1170	f_out(k,j,i) = work_fftx(i,k,j)
	1171	ENDDO
	1172	ENDDO
	1173	ENDDO
	1174	!$OMP END PARALLEL
	1175
	1176	ENDIF
	1177	CALL cpu_log( log_point_s(4), 'fft_x', 'stop' )
	1178
	1179	END SUBROUTINE tr_yx_fftx
	1180
	1181
	1182	SUBROUTINE ffty_tri_ffty( ar )
	1183
	1184	!------------------------------------------------------------------------------!
	1185	! FFT along y, solution of the tridiagonal system and backward FFT for
	1186	! a 1d-decomposition along y
	1187	!
	1188	! WARNING: this subroutine may still not work for hybrid parallelization
	1189	! with OpenMP (for possible necessary changes see the original
	1190	! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002)
	1191	!------------------------------------------------------------------------------!
	1192
	1193	USE control_parameters
	1194	USE cpulog
	1195	USE grid_variables
	1196	USE indices
	1197	USE interfaces
	1198	USE pegrid
	1199	USE transpose_indices
	1200
	1201	IMPLICIT NONE
	1202
	1203	INTEGER :: i, j, k, m, n, omp_get_thread_num, tn
	1204
	1205	REAL, DIMENSION(0:ny) :: work_ffty
	1206	REAL, DIMENSION(0:ny,1:nz) :: work_triy
	1207	REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: ar
	1208	REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri
	1209
	1210
	1211	CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'start' )
	1212
	1213	ALLOCATE( tri(5,0:ny,0:nz-1,0:threads_per_task-1) )
	1214
	1215	tn = 0 ! Default thread number in case of one thread
	1216	!$OMP PARALLEL PRIVATE ( i, j, k, m, n, tn, work_ffty, work_triy )
	1217	!$OMP DO
	1218	DO i = nxl_y, nxr_y
	1219
	1220	!$ tn = omp_get_thread_num()
	1221
	1222	IF ( host(1:3) == 'nec' ) THEN
	1223	!
	1224	!-- Code optimized for vector processors
	1225	DO k = 1, nz
	1226
	1227	m = 0
	1228	DO n = 1, pdims(2)
	1229	DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!!
	1230	work_triy(m,k) = ar(j,k,i,n)
	1231	m = m + 1
	1232	ENDDO
	1233	ENDDO
	1234
	1235	ENDDO
	1236
	1237	CALL fft_y_m( work_triy, ny, 'forward' )
	1238
	1239	ELSE
	1240	!
	1241	!-- Cache optimized code
	1242	DO k = 1, nz
	1243
	1244	m = 0
	1245	DO n = 1, pdims(2)
	1246	DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!!
	1247	work_ffty(m) = ar(j,k,i,n)
	1248	m = m + 1
	1249	ENDDO
	1250	ENDDO
	1251
	1252	CALL fft_y( work_ffty, 'forward' )
	1253
	1254	DO j = 0, ny
	1255	work_triy(j,k) = work_ffty(j)
	1256	ENDDO
	1257
	1258	ENDDO
	1259
	1260	ENDIF
	1261
	1262	!
	1263	!-- Solve the linear equation system
	1264	CALL tridia_1dd( ddy2, ddx2, ny, nx, i, work_triy, tri(:,:,:,tn) )
	1265
	1266	IF ( host(1:3) == 'nec' ) THEN
	1267	!
	1268	!-- Code optimized for vector processors
	1269	CALL fft_y_m( work_triy, ny, 'backward' )
	1270
	1271	DO k = 1, nz
	1272
	1273	m = 0
	1274	DO n = 1, pdims(2)
	1275	DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!!
	1276	ar(j,k,i,n) = work_triy(m,k)
	1277	m = m + 1
	1278	ENDDO
	1279	ENDDO
	1280
	1281	ENDDO
	1282
	1283	ELSE
	1284	!
	1285	!-- Cache optimized code
	1286	DO k = 1, nz
	1287
	1288	DO j = 0, ny
	1289	work_ffty(j) = work_triy(j,k)
	1290	ENDDO
	1291
	1292	CALL fft_y( work_ffty, 'backward' )
	1293
	1294	m = 0
	1295	DO n = 1, pdims(2)
	1296	DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!!
	1297	ar(j,k,i,n) = work_ffty(m)
	1298	m = m + 1
	1299	ENDDO
	1300	ENDDO
	1301
	1302	ENDDO
	1303
	1304	ENDIF
	1305
	1306	ENDDO
	1307	!$OMP END PARALLEL
	1308
	1309	DEALLOCATE( tri )
	1310
	1311	CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'stop' )
	1312
	1313	END SUBROUTINE ffty_tri_ffty
	1314
	1315
	1316	SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri )
	1317
	1318	!------------------------------------------------------------------------------!
	1319	! Solves the linear system of equations for a 1d-decomposition along x (see
	1320	! tridia)
	1321	!
	1322	! Attention: when using the intel compiler, array tri must be passed as an
	1323	! argument to the contained subroutines. Otherwise addres faults
	1324	! will occur.
	1325	! On NEC, tri should not be passed (except for routine substi_1dd)
	1326	! because this causes very bad performance.
	1327	!------------------------------------------------------------------------------!
	1328
	1329	USE arrays_3d
	1330	USE control_parameters
	1331
	1332	USE pegrid
	1333
	1334	IMPLICIT NONE
	1335
	1336	INTEGER :: i, j, k, nnyh, nx, ny, omp_get_thread_num, tn
	1337
	1338	REAL :: ddx2, ddy2
	1339
	1340	REAL, DIMENSION(0:nx,1:nz) :: ar
	1341	REAL, DIMENSION(0:nx,0:nz-1) :: ar1
	1342	REAL, DIMENSION(5,0:nx,0:nz-1) :: tri
	1343
	1344
	1345	nnyh = ( ny + 1 ) / 2
	1346
	1347	!
	1348	!-- Define constant elements of the tridiagonal matrix.
	1349	!-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2,
	1350	!-- the exchanged loops create bank conflicts. The following directive
	1351	!-- prohibits loop exchange and the loops perform much better.
	1352	! tn = omp_get_thread_num()
	1353	! WRITE( 120+tn, * ) '+++ id=',myid,' nx=',nx,' thread=', omp_get_thread_num()
[82]	1354	! CALL local_flush( 120+tn )
[1]	1355	!CDIR NOLOOPCHG
	1356	DO k = 0, nz-1
	1357	DO i = 0,nx
	1358	tri(2,i,k) = ddzu(k+1) * ddzw(k+1)
	1359	tri(3,i,k) = ddzu(k+2) * ddzw(k+1)
	1360	ENDDO
	1361	ENDDO
	1362	! WRITE( 120+tn, * ) '+++ id=',myid,' end of first tridia loop thread=', omp_get_thread_num()
[82]	1363	! CALL local_flush( 120+tn )
[1]	1364
	1365	IF ( j <= nnyh ) THEN
[377]	1366	#if defined( __lc )
[1]	1367	CALL maketri_1dd( j, tri )
	1368	#else
	1369	CALL maketri_1dd( j )
	1370	#endif
	1371	ELSE
[377]	1372	#if defined( __lc )
[1]	1373	CALL maketri_1dd( ny+1-j, tri )
	1374	#else
	1375	CALL maketri_1dd( ny+1-j )
	1376	#endif
	1377	ENDIF
[377]	1378	#if defined( __lc )
[1]	1379	CALL split_1dd( tri )
	1380	#else
	1381	CALL split_1dd
	1382	#endif
	1383	CALL substi_1dd( ar, tri )
	1384
	1385	CONTAINS
	1386
[377]	1387	#if defined( __lc )
[1]	1388	SUBROUTINE maketri_1dd( j, tri )
	1389	#else
	1390	SUBROUTINE maketri_1dd( j )
	1391	#endif
	1392
	1393	!------------------------------------------------------------------------------!
	1394	! computes the i- and j-dependent component of the matrix
	1395	!------------------------------------------------------------------------------!
	1396
	1397	USE constants
	1398
	1399	IMPLICIT NONE
	1400
	1401	INTEGER :: i, j, k, nnxh
	1402	REAL :: a, c
	1403
	1404	REAL, DIMENSION(0:nx) :: l
	1405
[377]	1406	#if defined( __lc )
[1]	1407	REAL, DIMENSION(5,0:nx,0:nz-1) :: tri
	1408	#endif
	1409
	1410
	1411	nnxh = ( nx + 1 ) / 2
	1412	!
	1413	!-- Provide the tridiagonal matrix for solution of the Poisson equation in
	1414	!-- Fourier space. The coefficients are computed following the method of
	1415	!-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan
	1416	!-- Siano's original version by discretizing the Poisson equation,
	1417	!-- before it is Fourier-transformed
	1418	DO i = 0, nx
[128]	1419	IF ( i >= 0 .AND. i <= nnxh ) THEN
[1]	1420	l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / &
	1421	FLOAT( nx+1 ) ) ) * ddx2 + &
	1422	2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / &
	1423	FLOAT( ny+1 ) ) ) * ddy2
	1424	ELSE
	1425	l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / &
	1426	FLOAT( nx+1 ) ) ) * ddx2 + &
	1427	2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / &
	1428	FLOAT( ny+1 ) ) ) * ddy2
	1429	ENDIF
	1430	ENDDO
	1431
	1432	DO k = 0, nz-1
	1433	DO i = 0, nx
	1434	a = -1.0 * ddzu(k+2) * ddzw(k+1)
	1435	c = -1.0 * ddzu(k+1) * ddzw(k+1)
	1436	tri(1,i,k) = a + c - l(i)
	1437	ENDDO
	1438	ENDDO
	1439	IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN
	1440	DO i = 0, nx
	1441	tri(1,i,0) = tri(1,i,0) + tri(2,i,0)
	1442	ENDDO
	1443	ENDIF
	1444	IF ( ibc_p_t == 1 ) THEN
	1445	DO i = 0, nx
	1446	tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1)
	1447	ENDDO
	1448	ENDIF
	1449
	1450	END SUBROUTINE maketri_1dd
	1451
	1452
[377]	1453	#if defined( __lc )
[1]	1454	SUBROUTINE split_1dd( tri )
	1455	#else
	1456	SUBROUTINE split_1dd
	1457	#endif
	1458
	1459	!------------------------------------------------------------------------------!
	1460	! Splitting of the tridiagonal matrix (Thomas algorithm)
	1461	!------------------------------------------------------------------------------!
	1462
	1463	IMPLICIT NONE
	1464
	1465	INTEGER :: i, k
	1466
[377]	1467	#if defined( __lc )
[1]	1468	REAL, DIMENSION(5,0:nx,0:nz-1) :: tri
	1469	#endif
	1470
	1471
	1472	!
	1473	!-- Splitting
	1474	DO i = 0, nx
	1475	tri(4,i,0) = tri(1,i,0)
	1476	ENDDO
	1477	DO k = 1, nz-1
	1478	DO i = 0, nx
	1479	tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1)
	1480	tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k)
	1481	ENDDO
	1482	ENDDO
	1483
	1484	END SUBROUTINE split_1dd
	1485
	1486
	1487	SUBROUTINE substi_1dd( ar, tri )
	1488
	1489	!------------------------------------------------------------------------------!
	1490	! Substitution (Forward and Backward) (Thomas algorithm)
	1491	!------------------------------------------------------------------------------!
	1492
	1493	IMPLICIT NONE
	1494
[76]	1495	INTEGER :: i, k
[1]	1496
	1497	REAL, DIMENSION(0:nx,nz) :: ar
	1498	REAL, DIMENSION(0:nx,0:nz-1) :: ar1
	1499	REAL, DIMENSION(5,0:nx,0:nz-1) :: tri
	1500
	1501	!
	1502	!-- Forward substitution
	1503	DO i = 0, nx
	1504	ar1(i,0) = ar(i,1)
	1505	ENDDO
	1506	DO k = 1, nz-1
	1507	DO i = 0, nx
	1508	ar1(i,k) = ar(i,k+1) - tri(5,i,k) * ar1(i,k-1)
	1509	ENDDO
	1510	ENDDO
	1511
	1512	!
	1513	!-- Backward substitution
	1514	DO i = 0, nx
	1515	ar(i,nz) = ar1(i,nz-1) / tri(4,i,nz-1)
	1516	ENDDO
	1517	DO k = nz-2, 0, -1
	1518	DO i = 0, nx
	1519	ar(i,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,k+2) ) &
	1520	/ tri(4,i,k)
	1521	ENDDO
	1522	ENDDO
	1523
[76]	1524	!
	1525	!-- Indices i=0, j=0 correspond to horizontally averaged pressure.
	1526	!-- The respective values of ar should be zero at all k-levels if
	1527	!-- acceleration of horizontally averaged vertical velocity is zero.
	1528	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN
	1529	IF ( j == 0 ) THEN
	1530	DO k = 1, nz
	1531	ar(0,k) = 0.0
	1532	ENDDO
	1533	ENDIF
	1534	ENDIF
	1535
[1]	1536	END SUBROUTINE substi_1dd
	1537
	1538	END SUBROUTINE tridia_1dd
	1539
	1540	#endif
	1541
	1542	END MODULE poisfft_mod

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