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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

Line
1	MODULE poisfft_mod
2
3	!------------------------------------------------------------------------------!
4	! Actual revisions:
5	! -----------------
6	!
7	!
8	! Former revisions:
9	! -----------------
10	! $Id: poisfft.f90 392 2009-09-24 10:39:14Z raasch $
11	!
12	! 377 2009-09-04 11:09:00Z raasch
13	! __lcmuk changed to __lc to avoid problems with Intel compiler on sgi-ice
14	!
15	! 164 2008-05-15 08:46:15Z raasch
16	! Arguments removed from transpose routines
17	!
18	! 128 2007-10-26 13:11:14Z raasch
19	! Bugfix: wavenumber calculation for even nx in routines maketri
20	!
21	! 85 2007-05-11 09:35:14Z raasch
22	! Bugfix: work_fft*_vec removed from some PRIVATE-declarations
23	!
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	!
28	! RCS Log replace by Id keyword, revision history cleaned up
29	!
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' )
160	CALL transpose_zx( ar, work, ar )
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' )
170	CALL transpose_xy( ar, work, ar )
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' )
180	CALL transpose_yz( ar, work, ar )
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' )
193	CALL transpose_zy( ar, work, ar )
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' )
203	CALL transpose_yx( ar, work, ar )
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' )
213	CALL transpose_xz( ar, work, ar )
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
354	IF ( i >= 0 .AND. i <= nnxh ) THEN
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
407	USE control_parameters
408
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
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
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
650	!$OMP PARALLEL PRIVATE ( i, j, k )
651	!$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	!$OMP END PARALLEL
713
714	ENDIF
715	CALL cpu_log( log_point_s(7), 'fft_y', 'pause' )
716
717	!
718	!-- Transpose array
719	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' )
720	CALL MPI_ALLTOALL( work(nxl,1,0), sendrecvcount_xy, MPI_REAL, &
721	f_out(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, &
722	comm1dx, ierr )
723	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' )
724
725	END SUBROUTINE ffty_tr_yx
726
727
728	SUBROUTINE tr_xy_ffty( f_in, work, f_out )
729
730	!------------------------------------------------------------------------------!
731	! Transposition x --> y with a subsequent backward Fourier transformation for
732	! a 1d-decomposition along x
733	!------------------------------------------------------------------------------!
734
735	USE control_parameters
736	USE cpulog
737	USE indices
738	USE interfaces
739	USE pegrid
740	USE transpose_indices
741
742	IMPLICIT NONE
743
744	INTEGER :: i, iend, iouter, ir, j, k
745	INTEGER, PARAMETER :: stridex = 4
746
747	REAL, DIMENSION(0:ny,stridex) :: work_ffty
748	#if defined( __nec )
749	REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec
750	#endif
751	REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: f_in
752	REAL, DIMENSION(1:nza,0:nya,nxl:nxra) :: f_out
753	REAL, DIMENSION(nxl:nxra,1:nza,0:nya) :: work
754
755	!
756	!-- Transpose array
757	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' )
758	CALL MPI_ALLTOALL( f_in(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, &
759	work(nxl,1,0), sendrecvcount_xy, MPI_REAL, &
760	comm1dx, ierr )
761	CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' )
762
763	!
764	!-- Resort the data in a way that y becomes the first index and carry out the
765	!-- backward fft along y.
766	CALL cpu_log( log_point_s(7), 'fft_y', 'continue' )
767
768	IF ( host(1:3) == 'nec' ) THEN
769	#if defined( __nec )
770	!
771	!-- Code optimized for vector processors
772	!$OMP PARALLEL PRIVATE ( i, j, k )
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
1012	!$OMP PARALLEL PRIVATE ( i, j, k )
1013	!$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
1123	!$OMP PARALLEL PRIVATE ( i, j, k )
1124	!$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()
1354	! CALL local_flush( 120+tn )
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()
1363	! CALL local_flush( 120+tn )
1364
1365	IF ( j <= nnyh ) THEN
1366	#if defined( __lc )
1367	CALL maketri_1dd( j, tri )
1368	#else
1369	CALL maketri_1dd( j )
1370	#endif
1371	ELSE
1372	#if defined( __lc )
1373	CALL maketri_1dd( ny+1-j, tri )
1374	#else
1375	CALL maketri_1dd( ny+1-j )
1376	#endif
1377	ENDIF
1378	#if defined( __lc )
1379	CALL split_1dd( tri )
1380	#else
1381	CALL split_1dd
1382	#endif
1383	CALL substi_1dd( ar, tri )
1384
1385	CONTAINS
1386
1387	#if defined( __lc )
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
1406	#if defined( __lc )
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
1419	IF ( i >= 0 .AND. i <= nnxh ) THEN
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
1453	#if defined( __lc )
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
1467	#if defined( __lc )
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
1495	INTEGER :: i, k
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
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
1536	END SUBROUTINE substi_1dd
1537
1538	END SUBROUTINE tridia_1dd
1539
1540	#endif
1541
1542	END MODULE poisfft_mod

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