1 | MODULE poisfft_mod |
---|
2 | |
---|
3 | !------------------------------------------------------------------------------! |
---|
4 | ! Current revisions: |
---|
5 | ! ----------------- |
---|
6 | ! |
---|
7 | ! |
---|
8 | ! Former revisions: |
---|
9 | ! ----------------- |
---|
10 | ! $Id: poisfft.f90 763 2011-10-06 09:32:09Z suehring $ |
---|
11 | ! |
---|
12 | ! 761 2011-10-05 17:58:52Z suehring |
---|
13 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
---|
14 | ! pressure at the top of the model domain. |
---|
15 | ! |
---|
16 | ! 696 2011-03-18 07:03:49Z raasch |
---|
17 | ! work_fftx removed from PRIVATE clauses in fftx_tr_xy and tr_yx_fftx |
---|
18 | ! |
---|
19 | ! 683 2011-02-09 14:25:15Z raasch |
---|
20 | ! openMP parallelization for 2d-domain-decomposition |
---|
21 | ! |
---|
22 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
---|
23 | ! ddzu replaced by ddzu_pres due to changes in zu(0) |
---|
24 | ! |
---|
25 | ! 622 2010-12-10 08:08:13Z raasch |
---|
26 | ! optional barriers included in order to speed up collective operations |
---|
27 | ! |
---|
28 | ! 377 2009-09-04 11:09:00Z raasch |
---|
29 | ! __lcmuk changed to __lc to avoid problems with Intel compiler on sgi-ice |
---|
30 | ! |
---|
31 | ! 164 2008-05-15 08:46:15Z raasch |
---|
32 | ! Arguments removed from transpose routines |
---|
33 | ! |
---|
34 | ! 128 2007-10-26 13:11:14Z raasch |
---|
35 | ! Bugfix: wavenumber calculation for even nx in routines maketri |
---|
36 | ! |
---|
37 | ! 85 2007-05-11 09:35:14Z raasch |
---|
38 | ! Bugfix: work_fft*_vec removed from some PRIVATE-declarations |
---|
39 | ! |
---|
40 | ! 76 2007-03-29 00:58:32Z raasch |
---|
41 | ! Tridiagonal coefficients adjusted for Neumann boundary conditions both at |
---|
42 | ! the bottom and the top. |
---|
43 | ! |
---|
44 | ! RCS Log replace by Id keyword, revision history cleaned up |
---|
45 | ! |
---|
46 | ! Revision 1.24 2006/08/04 15:00:24 raasch |
---|
47 | ! Default setting of the thread number tn in case of not using OpenMP |
---|
48 | ! |
---|
49 | ! Revision 1.23 2006/02/23 12:48:38 raasch |
---|
50 | ! Additional compiler directive in routine tridia_1dd for preventing loop |
---|
51 | ! exchange on NEC-SX6 |
---|
52 | ! |
---|
53 | ! Revision 1.20 2004/04/30 12:38:09 raasch |
---|
54 | ! Parts of former poisfft_hybrid moved to this subroutine, |
---|
55 | ! former subroutine changed to a module, renaming of FFT-subroutines and |
---|
56 | ! -module, FFTs completely substituted by calls of fft_x and fft_y, |
---|
57 | ! NAG fft used in the non-parallel case completely removed, l in maketri |
---|
58 | ! is now a 1d-array, variables passed by modules instead of using parameter |
---|
59 | ! lists, enlarged transposition arrays introduced |
---|
60 | ! |
---|
61 | ! Revision 1.1 1997/07/24 11:24:14 raasch |
---|
62 | ! Initial revision |
---|
63 | ! |
---|
64 | ! |
---|
65 | ! Description: |
---|
66 | ! ------------ |
---|
67 | ! See below. |
---|
68 | !------------------------------------------------------------------------------! |
---|
69 | |
---|
70 | !--------------------------------------------------------------------------! |
---|
71 | ! poisfft ! |
---|
72 | ! ! |
---|
73 | ! Original version: Stephan Siano (pois3d) ! |
---|
74 | ! ! |
---|
75 | ! Institute of Meteorology and Climatology, University of Hannover ! |
---|
76 | ! Germany ! |
---|
77 | ! ! |
---|
78 | ! Version as of July 23,1996 ! |
---|
79 | ! ! |
---|
80 | ! ! |
---|
81 | ! Version for parallel computers: Siegfried Raasch ! |
---|
82 | ! ! |
---|
83 | ! Version as of July 03,1997 ! |
---|
84 | ! ! |
---|
85 | ! Solves the Poisson equation with a 2D spectral method ! |
---|
86 | ! d^2 p / dx^2 + d^2 p / dy^2 + d^2 p / dz^2 = s ! |
---|
87 | ! ! |
---|
88 | ! Input: ! |
---|
89 | ! real ar contains in the (nnx,nny,nnz) elements, ! |
---|
90 | ! starting from the element (1,nys,nxl), the ! |
---|
91 | ! values for s ! |
---|
92 | ! real work Temporary array ! |
---|
93 | ! ! |
---|
94 | ! Output: ! |
---|
95 | ! real ar contains the solution for p ! |
---|
96 | !--------------------------------------------------------------------------! |
---|
97 | |
---|
98 | USE fft_xy |
---|
99 | USE indices |
---|
100 | USE transpose_indices |
---|
101 | |
---|
102 | IMPLICIT NONE |
---|
103 | |
---|
104 | PRIVATE |
---|
105 | PUBLIC poisfft, poisfft_init |
---|
106 | |
---|
107 | INTERFACE poisfft |
---|
108 | MODULE PROCEDURE poisfft |
---|
109 | END INTERFACE poisfft |
---|
110 | |
---|
111 | INTERFACE poisfft_init |
---|
112 | MODULE PROCEDURE poisfft_init |
---|
113 | END INTERFACE poisfft_init |
---|
114 | |
---|
115 | CONTAINS |
---|
116 | |
---|
117 | SUBROUTINE poisfft_init |
---|
118 | |
---|
119 | CALL fft_init |
---|
120 | |
---|
121 | END SUBROUTINE poisfft_init |
---|
122 | |
---|
123 | |
---|
124 | SUBROUTINE poisfft( ar, work ) |
---|
125 | |
---|
126 | USE cpulog |
---|
127 | USE interfaces |
---|
128 | USE pegrid |
---|
129 | |
---|
130 | IMPLICIT NONE |
---|
131 | |
---|
132 | REAL, DIMENSION(1:nza,nys:nyna,nxl:nxra) :: ar, work |
---|
133 | |
---|
134 | |
---|
135 | CALL cpu_log( log_point_s(3), 'poisfft', 'start' ) |
---|
136 | |
---|
137 | ! |
---|
138 | !-- Two-dimensional Fourier Transformation in x- and y-direction. |
---|
139 | #if defined( __parallel ) |
---|
140 | IF ( pdims(2) == 1 ) THEN |
---|
141 | |
---|
142 | ! |
---|
143 | !-- 1d-domain-decomposition along x: |
---|
144 | !-- FFT along y and transposition y --> x |
---|
145 | CALL ffty_tr_yx( ar, work, ar ) |
---|
146 | |
---|
147 | ! |
---|
148 | !-- FFT along x, solving the tridiagonal system and backward FFT |
---|
149 | CALL fftx_tri_fftx( ar ) |
---|
150 | |
---|
151 | ! |
---|
152 | !-- Transposition x --> y and backward FFT along y |
---|
153 | CALL tr_xy_ffty( ar, work, ar ) |
---|
154 | |
---|
155 | ELSEIF ( pdims(1) == 1 ) THEN |
---|
156 | |
---|
157 | ! |
---|
158 | !-- 1d-domain-decomposition along y: |
---|
159 | !-- FFT along x and transposition x --> y |
---|
160 | CALL fftx_tr_xy( ar, work, ar ) |
---|
161 | |
---|
162 | ! |
---|
163 | !-- FFT along y, solving the tridiagonal system and backward FFT |
---|
164 | CALL ffty_tri_ffty( ar ) |
---|
165 | |
---|
166 | ! |
---|
167 | !-- Transposition y --> x and backward FFT along x |
---|
168 | CALL tr_yx_fftx( ar, work, ar ) |
---|
169 | |
---|
170 | ELSE |
---|
171 | |
---|
172 | ! |
---|
173 | !-- 2d-domain-decomposition |
---|
174 | !-- Transposition z --> x |
---|
175 | CALL cpu_log( log_point_s(5), 'transpo forward', 'start' ) |
---|
176 | CALL transpose_zx( ar, work, ar ) |
---|
177 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
---|
178 | |
---|
179 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
---|
180 | CALL fftxp( ar, 'forward' ) |
---|
181 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
---|
182 | |
---|
183 | ! |
---|
184 | !-- Transposition x --> y |
---|
185 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
---|
186 | CALL transpose_xy( ar, work, ar ) |
---|
187 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
---|
188 | |
---|
189 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
---|
190 | CALL fftyp( ar, 'forward' ) |
---|
191 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
---|
192 | |
---|
193 | ! |
---|
194 | !-- Transposition y --> z |
---|
195 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
---|
196 | CALL transpose_yz( ar, work, ar ) |
---|
197 | CALL cpu_log( log_point_s(5), 'transpo forward', 'stop' ) |
---|
198 | |
---|
199 | ! |
---|
200 | !-- Solve the Poisson equation in z-direction in cartesian space. |
---|
201 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
---|
202 | CALL tridia( ar ) |
---|
203 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
---|
204 | |
---|
205 | ! |
---|
206 | !-- Inverse Fourier Transformation |
---|
207 | !-- Transposition z --> y |
---|
208 | CALL cpu_log( log_point_s(8), 'transpo invers', 'start' ) |
---|
209 | CALL transpose_zy( ar, work, ar ) |
---|
210 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
---|
211 | |
---|
212 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
---|
213 | CALL fftyp( ar, 'backward' ) |
---|
214 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
---|
215 | |
---|
216 | ! |
---|
217 | !-- Transposition y --> x |
---|
218 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
---|
219 | CALL transpose_yx( ar, work, ar ) |
---|
220 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
---|
221 | |
---|
222 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
---|
223 | CALL fftxp( ar, 'backward' ) |
---|
224 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
---|
225 | |
---|
226 | ! |
---|
227 | !-- Transposition x --> z |
---|
228 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
---|
229 | CALL transpose_xz( ar, work, ar ) |
---|
230 | CALL cpu_log( log_point_s(8), 'transpo invers', 'stop' ) |
---|
231 | |
---|
232 | ENDIF |
---|
233 | |
---|
234 | #else |
---|
235 | |
---|
236 | ! |
---|
237 | !-- Two-dimensional Fourier Transformation along x- and y-direction. |
---|
238 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
---|
239 | CALL fftx( ar, 'forward' ) |
---|
240 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
---|
241 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
---|
242 | CALL ffty( ar, 'forward' ) |
---|
243 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
---|
244 | |
---|
245 | ! |
---|
246 | !-- Solve the Poisson equation in z-direction in cartesian space. |
---|
247 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
---|
248 | CALL tridia( ar ) |
---|
249 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
---|
250 | |
---|
251 | ! |
---|
252 | !-- Inverse Fourier Transformation. |
---|
253 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
---|
254 | CALL ffty( ar, 'backward' ) |
---|
255 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
---|
256 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
---|
257 | CALL fftx( ar, 'backward' ) |
---|
258 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
---|
259 | |
---|
260 | #endif |
---|
261 | |
---|
262 | CALL cpu_log( log_point_s(3), 'poisfft', 'stop' ) |
---|
263 | |
---|
264 | END SUBROUTINE poisfft |
---|
265 | |
---|
266 | |
---|
267 | |
---|
268 | SUBROUTINE tridia( ar ) |
---|
269 | |
---|
270 | !------------------------------------------------------------------------------! |
---|
271 | ! solves the linear system of equations: |
---|
272 | ! |
---|
273 | ! -(4 pi^2(i^2/(dx^2*nnx^2)+j^2/(dy^2*nny^2))+ |
---|
274 | ! 1/(dzu(k)*dzw(k))+1/(dzu(k-1)*dzw(k)))*p(i,j,k)+ |
---|
275 | ! 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) |
---|
276 | ! |
---|
277 | ! by using the Thomas algorithm |
---|
278 | !------------------------------------------------------------------------------! |
---|
279 | |
---|
280 | USE arrays_3d |
---|
281 | |
---|
282 | IMPLICIT NONE |
---|
283 | |
---|
284 | INTEGER :: i, j, k, nnyh |
---|
285 | |
---|
286 | REAL, DIMENSION(nxl_z:nxr_z,0:nz-1) :: ar1 |
---|
287 | REAL, DIMENSION(5,nxl_z:nxr_z,0:nz-1) :: tri |
---|
288 | |
---|
289 | #if defined( __parallel ) |
---|
290 | REAL :: ar(nxl_z:nxr_za,nys_z:nyn_za,1:nza) |
---|
291 | #else |
---|
292 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
---|
293 | #endif |
---|
294 | |
---|
295 | |
---|
296 | nnyh = (ny+1) / 2 |
---|
297 | |
---|
298 | ! |
---|
299 | !-- Define constant elements of the tridiagonal matrix. |
---|
300 | !$OMP PARALLEL PRIVATE ( k, i ) |
---|
301 | !$OMP DO |
---|
302 | DO k = 0, nz-1 |
---|
303 | DO i = nxl_z, nxr_z |
---|
304 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
---|
305 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
---|
306 | ENDDO |
---|
307 | ENDDO |
---|
308 | !$OMP END PARALLEL |
---|
309 | |
---|
310 | #if defined( __parallel ) |
---|
311 | ! |
---|
312 | !-- Repeat for all y-levels. |
---|
313 | !$OMP PARALLEL FIRSTPRIVATE( tri ) PRIVATE ( ar1, j ) |
---|
314 | !$OMP DO |
---|
315 | DO j = nys_z, nyn_z |
---|
316 | IF ( j <= nnyh ) THEN |
---|
317 | CALL maketri( tri, j ) |
---|
318 | ELSE |
---|
319 | CALL maketri( tri, ny+1-j ) |
---|
320 | ENDIF |
---|
321 | CALL split( tri ) |
---|
322 | CALL substi( ar, ar1, tri, j ) |
---|
323 | ENDDO |
---|
324 | !$OMP END PARALLEL |
---|
325 | #else |
---|
326 | ! |
---|
327 | !-- First y-level. |
---|
328 | CALL maketri( tri, nys_z ) |
---|
329 | CALL split( tri ) |
---|
330 | CALL substi( ar, ar1, tri, 0 ) |
---|
331 | |
---|
332 | ! |
---|
333 | !-- Further y-levels. |
---|
334 | DO j = 1, nnyh - 1 |
---|
335 | CALL maketri( tri, j ) |
---|
336 | CALL split( tri ) |
---|
337 | CALL substi( ar, ar1, tri, j ) |
---|
338 | CALL substi( ar, ar1, tri, ny+1-j ) |
---|
339 | ENDDO |
---|
340 | CALL maketri( tri, nnyh ) |
---|
341 | CALL split( tri ) |
---|
342 | CALL substi( ar, ar1, tri, nnyh+nys ) |
---|
343 | #endif |
---|
344 | |
---|
345 | CONTAINS |
---|
346 | |
---|
347 | SUBROUTINE maketri( tri, j ) |
---|
348 | |
---|
349 | !------------------------------------------------------------------------------! |
---|
350 | ! Computes the i- and j-dependent component of the matrix |
---|
351 | !------------------------------------------------------------------------------! |
---|
352 | |
---|
353 | USE arrays_3d |
---|
354 | USE constants |
---|
355 | USE control_parameters |
---|
356 | USE grid_variables |
---|
357 | |
---|
358 | IMPLICIT NONE |
---|
359 | |
---|
360 | INTEGER :: i, j, k, nnxh |
---|
361 | REAL :: a, c |
---|
362 | REAL :: ll(nxl_z:nxr_z) |
---|
363 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
364 | |
---|
365 | |
---|
366 | nnxh = ( nx + 1 ) / 2 |
---|
367 | |
---|
368 | ! |
---|
369 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
---|
370 | !-- Fourier space. The coefficients are computed following the method of |
---|
371 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
---|
372 | !-- Siano's original version by discretizing the Poisson equation, |
---|
373 | !-- before it is Fourier-transformed |
---|
374 | #if defined( __parallel ) |
---|
375 | DO i = nxl_z, nxr_z |
---|
376 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
---|
377 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
---|
378 | FLOAT( nx+1 ) ) ) / ( dx * dx ) + & |
---|
379 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
380 | FLOAT( ny+1 ) ) ) / ( dy * dy ) |
---|
381 | ELSE |
---|
382 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
383 | FLOAT( nx+1 ) ) ) / ( dx * dx ) + & |
---|
384 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
385 | FLOAT( ny+1 ) ) ) / ( dy * dy ) |
---|
386 | ENDIF |
---|
387 | DO k = 0,nz-1 |
---|
388 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
389 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
390 | tri(1,i,k) = a + c - ll(i) |
---|
391 | ENDDO |
---|
392 | ENDDO |
---|
393 | #else |
---|
394 | DO i = 0, nnxh |
---|
395 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / FLOAT( nx+1 ) ) ) / & |
---|
396 | ( dx * dx ) + & |
---|
397 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / FLOAT( ny+1 ) ) ) / & |
---|
398 | ( dy * dy ) |
---|
399 | DO k = 0, nz-1 |
---|
400 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
401 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
402 | tri(1,i,k) = a + c - ll(i) |
---|
403 | IF ( i >= 1 .and. i < nnxh ) THEN |
---|
404 | tri(1,nx+1-i,k) = tri(1,i,k) |
---|
405 | ENDIF |
---|
406 | ENDDO |
---|
407 | ENDDO |
---|
408 | #endif |
---|
409 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
410 | DO i = nxl_z, nxr_z |
---|
411 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
412 | ENDDO |
---|
413 | ENDIF |
---|
414 | IF ( ibc_p_t == 1 ) THEN |
---|
415 | DO i = nxl_z, nxr_z |
---|
416 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
417 | ENDDO |
---|
418 | ENDIF |
---|
419 | |
---|
420 | END SUBROUTINE maketri |
---|
421 | |
---|
422 | |
---|
423 | SUBROUTINE substi( ar, ar1, tri, j ) |
---|
424 | |
---|
425 | !------------------------------------------------------------------------------! |
---|
426 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
427 | !------------------------------------------------------------------------------! |
---|
428 | |
---|
429 | USE control_parameters |
---|
430 | |
---|
431 | IMPLICIT NONE |
---|
432 | |
---|
433 | INTEGER :: i, j, k |
---|
434 | REAL :: ar1(nxl_z:nxr_z,0:nz-1) |
---|
435 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
436 | #if defined( __parallel ) |
---|
437 | REAL :: ar(nxl_z:nxr_za,nys_z:nyn_za,1:nza) |
---|
438 | #else |
---|
439 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
---|
440 | #endif |
---|
441 | |
---|
442 | ! |
---|
443 | !-- Forward substitution. |
---|
444 | DO i = nxl_z, nxr_z |
---|
445 | #if defined( __parallel ) |
---|
446 | ar1(i,0) = ar(i,j,1) |
---|
447 | #else |
---|
448 | ar1(i,0) = ar(1,j,i) |
---|
449 | #endif |
---|
450 | ENDDO |
---|
451 | DO k = 1, nz - 1 |
---|
452 | DO i = nxl_z, nxr_z |
---|
453 | #if defined( __parallel ) |
---|
454 | ar1(i,k) = ar(i,j,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
455 | #else |
---|
456 | ar1(i,k) = ar(k+1,j,i) - tri(5,i,k) * ar1(i,k-1) |
---|
457 | #endif |
---|
458 | ENDDO |
---|
459 | ENDDO |
---|
460 | |
---|
461 | ! |
---|
462 | !-- Backward substitution. |
---|
463 | DO i = nxl_z, nxr_z |
---|
464 | #if defined( __parallel ) |
---|
465 | ar(i,j,nz) = ar1(i,nz-1) / tri(4,i,nz-1) |
---|
466 | #else |
---|
467 | ar(nz,j,i) = ar1(i,nz-1) / tri(4,i,nz-1) |
---|
468 | #endif |
---|
469 | ENDDO |
---|
470 | DO k = nz-2, 0, -1 |
---|
471 | DO i = nxl_z, nxr_z |
---|
472 | #if defined( __parallel ) |
---|
473 | ar(i,j,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,j,k+2) ) & |
---|
474 | / tri(4,i,k) |
---|
475 | #else |
---|
476 | ar(k+1,j,i) = ( ar1(i,k) - tri(3,i,k) * ar(k+2,j,i) ) & |
---|
477 | / tri(4,i,k) |
---|
478 | #endif |
---|
479 | ENDDO |
---|
480 | ENDDO |
---|
481 | |
---|
482 | ! |
---|
483 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
484 | !-- The respective values of ar should be zero at all k-levels if |
---|
485 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
486 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
487 | IF ( j == 0 .AND. nxl_z == 0 ) THEN |
---|
488 | #if defined( __parallel ) |
---|
489 | DO k = 1, nz |
---|
490 | ar(nxl_z,j,k) = 0.0 |
---|
491 | ENDDO |
---|
492 | #else |
---|
493 | DO k = 1, nz |
---|
494 | ar(k,j,nxl_z) = 0.0 |
---|
495 | ENDDO |
---|
496 | #endif |
---|
497 | ENDIF |
---|
498 | ENDIF |
---|
499 | |
---|
500 | END SUBROUTINE substi |
---|
501 | |
---|
502 | |
---|
503 | SUBROUTINE split( tri ) |
---|
504 | |
---|
505 | !------------------------------------------------------------------------------! |
---|
506 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
507 | !------------------------------------------------------------------------------! |
---|
508 | |
---|
509 | IMPLICIT NONE |
---|
510 | |
---|
511 | INTEGER :: i, k |
---|
512 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
513 | |
---|
514 | ! |
---|
515 | !-- Splitting. |
---|
516 | DO i = nxl_z, nxr_z |
---|
517 | tri(4,i,0) = tri(1,i,0) |
---|
518 | ENDDO |
---|
519 | DO k = 1, nz-1 |
---|
520 | DO i = nxl_z, nxr_z |
---|
521 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
522 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
523 | ENDDO |
---|
524 | ENDDO |
---|
525 | |
---|
526 | END SUBROUTINE split |
---|
527 | |
---|
528 | END SUBROUTINE tridia |
---|
529 | |
---|
530 | |
---|
531 | #if defined( __parallel ) |
---|
532 | SUBROUTINE fftxp( ar, direction ) |
---|
533 | |
---|
534 | !------------------------------------------------------------------------------! |
---|
535 | ! Fourier-transformation along x-direction Parallelized version |
---|
536 | !------------------------------------------------------------------------------! |
---|
537 | |
---|
538 | IMPLICIT NONE |
---|
539 | |
---|
540 | CHARACTER (LEN=*) :: direction |
---|
541 | INTEGER :: j, k |
---|
542 | REAL :: ar(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa) |
---|
543 | |
---|
544 | ! |
---|
545 | !-- Performing the fft with one of the methods implemented |
---|
546 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
547 | !$OMP DO |
---|
548 | DO k = nzb_x, nzt_x |
---|
549 | DO j = nys_x, nyn_x |
---|
550 | CALL fft_x( ar(0:nx,j,k), direction ) |
---|
551 | ENDDO |
---|
552 | ENDDO |
---|
553 | !$OMP END PARALLEL |
---|
554 | |
---|
555 | END SUBROUTINE fftxp |
---|
556 | |
---|
557 | #else |
---|
558 | SUBROUTINE fftx( ar, direction ) |
---|
559 | |
---|
560 | !------------------------------------------------------------------------------! |
---|
561 | ! Fourier-transformation along x-direction Non parallel version |
---|
562 | !------------------------------------------------------------------------------! |
---|
563 | |
---|
564 | IMPLICIT NONE |
---|
565 | |
---|
566 | CHARACTER (LEN=*) :: direction |
---|
567 | INTEGER :: i, j, k |
---|
568 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
569 | |
---|
570 | ! |
---|
571 | !-- Performing the fft with one of the methods implemented |
---|
572 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
573 | !$OMP DO |
---|
574 | DO k = 1, nz |
---|
575 | DO j = 0, ny |
---|
576 | CALL fft_x( ar(k,j,0:nx), direction ) |
---|
577 | ENDDO |
---|
578 | ENDDO |
---|
579 | !$OMP END PARALLEL |
---|
580 | |
---|
581 | END SUBROUTINE fftx |
---|
582 | #endif |
---|
583 | |
---|
584 | |
---|
585 | #if defined( __parallel ) |
---|
586 | SUBROUTINE fftyp( ar, direction ) |
---|
587 | |
---|
588 | !------------------------------------------------------------------------------! |
---|
589 | ! Fourier-transformation along y-direction Parallelized version |
---|
590 | !------------------------------------------------------------------------------! |
---|
591 | |
---|
592 | IMPLICIT NONE |
---|
593 | |
---|
594 | CHARACTER (LEN=*) :: direction |
---|
595 | INTEGER :: i, k |
---|
596 | REAL :: ar(0:nya,nxl_y:nxr_ya,nzb_y:nzt_ya) |
---|
597 | |
---|
598 | ! |
---|
599 | !-- Performing the fft with one of the methods implemented |
---|
600 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
601 | !$OMP DO |
---|
602 | DO k = nzb_y, nzt_y |
---|
603 | DO i = nxl_y, nxr_y |
---|
604 | CALL fft_y( ar(0:ny,i,k), direction ) |
---|
605 | ENDDO |
---|
606 | ENDDO |
---|
607 | !$OMP END PARALLEL |
---|
608 | |
---|
609 | END SUBROUTINE fftyp |
---|
610 | |
---|
611 | #else |
---|
612 | SUBROUTINE ffty( ar, direction ) |
---|
613 | |
---|
614 | !------------------------------------------------------------------------------! |
---|
615 | ! Fourier-transformation along y-direction Non parallel version |
---|
616 | !------------------------------------------------------------------------------! |
---|
617 | |
---|
618 | IMPLICIT NONE |
---|
619 | |
---|
620 | CHARACTER (LEN=*) :: direction |
---|
621 | INTEGER :: i, k |
---|
622 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
623 | |
---|
624 | ! |
---|
625 | !-- Performing the fft with one of the methods implemented |
---|
626 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
627 | !$OMP DO |
---|
628 | DO k = 1, nz |
---|
629 | DO i = 0, nx |
---|
630 | CALL fft_y( ar(k,0:ny,i), direction ) |
---|
631 | ENDDO |
---|
632 | ENDDO |
---|
633 | !$OMP END PARALLEL |
---|
634 | |
---|
635 | END SUBROUTINE ffty |
---|
636 | #endif |
---|
637 | |
---|
638 | #if defined( __parallel ) |
---|
639 | SUBROUTINE ffty_tr_yx( f_in, work, f_out ) |
---|
640 | |
---|
641 | !------------------------------------------------------------------------------! |
---|
642 | ! Fourier-transformation along y with subsequent transposition y --> x for |
---|
643 | ! a 1d-decomposition along x |
---|
644 | ! |
---|
645 | ! ATTENTION: The performance of this routine is much faster on the NEC-SX6, |
---|
646 | ! if the first index of work_ffty_vec is odd. Otherwise |
---|
647 | ! memory bank conflicts may occur (especially if the index is a |
---|
648 | ! multiple of 128). That's why work_ffty_vec is dimensioned as |
---|
649 | ! 0:ny+1. |
---|
650 | ! Of course, this will not work if users are using an odd number |
---|
651 | ! of gridpoints along y. |
---|
652 | !------------------------------------------------------------------------------! |
---|
653 | |
---|
654 | USE control_parameters |
---|
655 | USE cpulog |
---|
656 | USE indices |
---|
657 | USE interfaces |
---|
658 | USE pegrid |
---|
659 | USE transpose_indices |
---|
660 | |
---|
661 | IMPLICIT NONE |
---|
662 | |
---|
663 | INTEGER :: i, iend, iouter, ir, j, k |
---|
664 | INTEGER, PARAMETER :: stridex = 4 |
---|
665 | |
---|
666 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
667 | #if defined( __nec ) |
---|
668 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
669 | #endif |
---|
670 | REAL, DIMENSION(1:nza,0:nya,nxl:nxra) :: f_in |
---|
671 | REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: f_out |
---|
672 | REAL, DIMENSION(nxl:nxra,1:nza,0:nya) :: work |
---|
673 | |
---|
674 | ! |
---|
675 | !-- Carry out the FFT along y, where all data are present due to the |
---|
676 | !-- 1d-decomposition along x. Resort the data in a way that x becomes |
---|
677 | !-- the first index. |
---|
678 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
---|
679 | |
---|
680 | IF ( host(1:3) == 'nec' ) THEN |
---|
681 | #if defined( __nec ) |
---|
682 | ! |
---|
683 | !-- Code optimized for vector processors |
---|
684 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
685 | !$OMP DO |
---|
686 | DO i = nxl, nxr |
---|
687 | |
---|
688 | DO j = 0, ny |
---|
689 | DO k = 1, nz |
---|
690 | work_ffty_vec(j,k,i) = f_in(k,j,i) |
---|
691 | ENDDO |
---|
692 | ENDDO |
---|
693 | |
---|
694 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'forward' ) |
---|
695 | |
---|
696 | ENDDO |
---|
697 | |
---|
698 | !$OMP DO |
---|
699 | DO k = 1, nz |
---|
700 | DO j = 0, ny |
---|
701 | DO i = nxl, nxr |
---|
702 | work(i,k,j) = work_ffty_vec(j,k,i) |
---|
703 | ENDDO |
---|
704 | ENDDO |
---|
705 | ENDDO |
---|
706 | !$OMP END PARALLEL |
---|
707 | #endif |
---|
708 | |
---|
709 | ELSE |
---|
710 | |
---|
711 | ! |
---|
712 | !-- Cache optimized code. |
---|
713 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
714 | !-- loop for better cache performance |
---|
715 | !$OMP PARALLEL PRIVATE (i,iend,iouter,ir,j,k,work_ffty) |
---|
716 | !$OMP DO |
---|
717 | DO iouter = nxl, nxr, stridex |
---|
718 | |
---|
719 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
720 | |
---|
721 | DO k = 1, nz |
---|
722 | |
---|
723 | DO i = iouter, iend |
---|
724 | |
---|
725 | ir = i-iouter+1 ! counter within a stride |
---|
726 | DO j = 0, ny |
---|
727 | work_ffty(j,ir) = f_in(k,j,i) |
---|
728 | ENDDO |
---|
729 | ! |
---|
730 | !-- FFT along y |
---|
731 | CALL fft_y( work_ffty(:,ir), 'forward' ) |
---|
732 | |
---|
733 | ENDDO |
---|
734 | |
---|
735 | ! |
---|
736 | !-- Resort |
---|
737 | DO j = 0, ny |
---|
738 | DO i = iouter, iend |
---|
739 | work(i,k,j) = work_ffty(j,i-iouter+1) |
---|
740 | ENDDO |
---|
741 | ENDDO |
---|
742 | |
---|
743 | ENDDO |
---|
744 | |
---|
745 | ENDDO |
---|
746 | !$OMP END PARALLEL |
---|
747 | |
---|
748 | ENDIF |
---|
749 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
---|
750 | |
---|
751 | ! |
---|
752 | !-- Transpose array |
---|
753 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
754 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
755 | CALL MPI_ALLTOALL( work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
756 | f_out(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
757 | comm1dx, ierr ) |
---|
758 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
759 | |
---|
760 | END SUBROUTINE ffty_tr_yx |
---|
761 | |
---|
762 | |
---|
763 | SUBROUTINE tr_xy_ffty( f_in, work, f_out ) |
---|
764 | |
---|
765 | !------------------------------------------------------------------------------! |
---|
766 | ! Transposition x --> y with a subsequent backward Fourier transformation for |
---|
767 | ! a 1d-decomposition along x |
---|
768 | !------------------------------------------------------------------------------! |
---|
769 | |
---|
770 | USE control_parameters |
---|
771 | USE cpulog |
---|
772 | USE indices |
---|
773 | USE interfaces |
---|
774 | USE pegrid |
---|
775 | USE transpose_indices |
---|
776 | |
---|
777 | IMPLICIT NONE |
---|
778 | |
---|
779 | INTEGER :: i, iend, iouter, ir, j, k |
---|
780 | INTEGER, PARAMETER :: stridex = 4 |
---|
781 | |
---|
782 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
783 | #if defined( __nec ) |
---|
784 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
785 | #endif |
---|
786 | REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: f_in |
---|
787 | REAL, DIMENSION(1:nza,0:nya,nxl:nxra) :: f_out |
---|
788 | REAL, DIMENSION(nxl:nxra,1:nza,0:nya) :: work |
---|
789 | |
---|
790 | ! |
---|
791 | !-- Transpose array |
---|
792 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
793 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
794 | CALL MPI_ALLTOALL( f_in(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
795 | work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
796 | comm1dx, ierr ) |
---|
797 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
798 | |
---|
799 | ! |
---|
800 | !-- Resort the data in a way that y becomes the first index and carry out the |
---|
801 | !-- backward fft along y. |
---|
802 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
---|
803 | |
---|
804 | IF ( host(1:3) == 'nec' ) THEN |
---|
805 | #if defined( __nec ) |
---|
806 | ! |
---|
807 | !-- Code optimized for vector processors |
---|
808 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
809 | !$OMP DO |
---|
810 | DO k = 1, nz |
---|
811 | DO j = 0, ny |
---|
812 | DO i = nxl, nxr |
---|
813 | work_ffty_vec(j,k,i) = work(i,k,j) |
---|
814 | ENDDO |
---|
815 | ENDDO |
---|
816 | ENDDO |
---|
817 | |
---|
818 | !$OMP DO |
---|
819 | DO i = nxl, nxr |
---|
820 | |
---|
821 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'backward' ) |
---|
822 | |
---|
823 | DO j = 0, ny |
---|
824 | DO k = 1, nz |
---|
825 | f_out(k,j,i) = work_ffty_vec(j,k,i) |
---|
826 | ENDDO |
---|
827 | ENDDO |
---|
828 | |
---|
829 | ENDDO |
---|
830 | !$OMP END PARALLEL |
---|
831 | #endif |
---|
832 | |
---|
833 | ELSE |
---|
834 | |
---|
835 | ! |
---|
836 | !-- Cache optimized code. |
---|
837 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
838 | !-- loop for better cache performance |
---|
839 | !$OMP PARALLEL PRIVATE ( i, iend, iouter, ir, j, k, work_ffty ) |
---|
840 | !$OMP DO |
---|
841 | DO iouter = nxl, nxr, stridex |
---|
842 | |
---|
843 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
844 | |
---|
845 | DO k = 1, nz |
---|
846 | ! |
---|
847 | !-- Resort |
---|
848 | DO j = 0, ny |
---|
849 | DO i = iouter, iend |
---|
850 | work_ffty(j,i-iouter+1) = work(i,k,j) |
---|
851 | ENDDO |
---|
852 | ENDDO |
---|
853 | |
---|
854 | DO i = iouter, iend |
---|
855 | |
---|
856 | ! |
---|
857 | !-- FFT along y |
---|
858 | ir = i-iouter+1 ! counter within a stride |
---|
859 | CALL fft_y( work_ffty(:,ir), 'backward' ) |
---|
860 | |
---|
861 | DO j = 0, ny |
---|
862 | f_out(k,j,i) = work_ffty(j,ir) |
---|
863 | ENDDO |
---|
864 | ENDDO |
---|
865 | |
---|
866 | ENDDO |
---|
867 | |
---|
868 | ENDDO |
---|
869 | !$OMP END PARALLEL |
---|
870 | |
---|
871 | ENDIF |
---|
872 | |
---|
873 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
---|
874 | |
---|
875 | END SUBROUTINE tr_xy_ffty |
---|
876 | |
---|
877 | |
---|
878 | SUBROUTINE fftx_tri_fftx( ar ) |
---|
879 | |
---|
880 | !------------------------------------------------------------------------------! |
---|
881 | ! FFT along x, solution of the tridiagonal system and backward FFT for |
---|
882 | ! a 1d-decomposition along x |
---|
883 | ! |
---|
884 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
885 | ! with OpenMP (for possible necessary changes see the original |
---|
886 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
887 | !------------------------------------------------------------------------------! |
---|
888 | |
---|
889 | USE control_parameters |
---|
890 | USE cpulog |
---|
891 | USE grid_variables |
---|
892 | USE indices |
---|
893 | USE interfaces |
---|
894 | USE pegrid |
---|
895 | USE transpose_indices |
---|
896 | |
---|
897 | IMPLICIT NONE |
---|
898 | |
---|
899 | character(len=3) :: myth_char |
---|
900 | |
---|
901 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
902 | |
---|
903 | REAL, DIMENSION(0:nx) :: work_fftx |
---|
904 | REAL, DIMENSION(0:nx,1:nz) :: work_trix |
---|
905 | REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: ar |
---|
906 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
907 | |
---|
908 | |
---|
909 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'start' ) |
---|
910 | |
---|
911 | ALLOCATE( tri(5,0:nx,0:nz-1,0:threads_per_task-1) ) |
---|
912 | |
---|
913 | tn = 0 ! Default thread number in case of one thread |
---|
914 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_fftx, work_trix ) |
---|
915 | DO j = nys_x, nyn_x |
---|
916 | |
---|
917 | !$ tn = omp_get_thread_num() |
---|
918 | |
---|
919 | IF ( host(1:3) == 'nec' ) THEN |
---|
920 | ! |
---|
921 | !-- Code optimized for vector processors |
---|
922 | DO k = 1, nz |
---|
923 | |
---|
924 | m = 0 |
---|
925 | DO n = 1, pdims(1) |
---|
926 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
927 | work_trix(m,k) = ar(i,k,j,n) |
---|
928 | m = m + 1 |
---|
929 | ENDDO |
---|
930 | ENDDO |
---|
931 | |
---|
932 | ENDDO |
---|
933 | |
---|
934 | CALL fft_x_m( work_trix, 'forward' ) |
---|
935 | |
---|
936 | ELSE |
---|
937 | ! |
---|
938 | !-- Cache optimized code |
---|
939 | DO k = 1, nz |
---|
940 | |
---|
941 | m = 0 |
---|
942 | DO n = 1, pdims(1) |
---|
943 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
944 | work_fftx(m) = ar(i,k,j,n) |
---|
945 | m = m + 1 |
---|
946 | ENDDO |
---|
947 | ENDDO |
---|
948 | |
---|
949 | CALL fft_x( work_fftx, 'forward' ) |
---|
950 | |
---|
951 | DO i = 0, nx |
---|
952 | work_trix(i,k) = work_fftx(i) |
---|
953 | ENDDO |
---|
954 | |
---|
955 | ENDDO |
---|
956 | |
---|
957 | ENDIF |
---|
958 | |
---|
959 | ! |
---|
960 | !-- Solve the linear equation system |
---|
961 | CALL tridia_1dd( ddx2, ddy2, nx, ny, j, work_trix, tri(:,:,:,tn) ) |
---|
962 | |
---|
963 | IF ( host(1:3) == 'nec' ) THEN |
---|
964 | ! |
---|
965 | !-- Code optimized for vector processors |
---|
966 | CALL fft_x_m( work_trix, 'backward' ) |
---|
967 | |
---|
968 | DO k = 1, nz |
---|
969 | |
---|
970 | m = 0 |
---|
971 | DO n = 1, pdims(1) |
---|
972 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
973 | ar(i,k,j,n) = work_trix(m,k) |
---|
974 | m = m + 1 |
---|
975 | ENDDO |
---|
976 | ENDDO |
---|
977 | |
---|
978 | ENDDO |
---|
979 | |
---|
980 | ELSE |
---|
981 | ! |
---|
982 | !-- Cache optimized code |
---|
983 | DO k = 1, nz |
---|
984 | |
---|
985 | DO i = 0, nx |
---|
986 | work_fftx(i) = work_trix(i,k) |
---|
987 | ENDDO |
---|
988 | |
---|
989 | CALL fft_x( work_fftx, 'backward' ) |
---|
990 | |
---|
991 | m = 0 |
---|
992 | DO n = 1, pdims(1) |
---|
993 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
994 | ar(i,k,j,n) = work_fftx(m) |
---|
995 | m = m + 1 |
---|
996 | ENDDO |
---|
997 | ENDDO |
---|
998 | |
---|
999 | ENDDO |
---|
1000 | |
---|
1001 | ENDIF |
---|
1002 | |
---|
1003 | ENDDO |
---|
1004 | |
---|
1005 | DEALLOCATE( tri ) |
---|
1006 | |
---|
1007 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'stop' ) |
---|
1008 | |
---|
1009 | END SUBROUTINE fftx_tri_fftx |
---|
1010 | |
---|
1011 | |
---|
1012 | SUBROUTINE fftx_tr_xy( f_in, work, f_out ) |
---|
1013 | |
---|
1014 | !------------------------------------------------------------------------------! |
---|
1015 | ! Fourier-transformation along x with subsequent transposition x --> y for |
---|
1016 | ! a 1d-decomposition along y |
---|
1017 | ! |
---|
1018 | ! ATTENTION: The NEC-branch of this routine may significantly profit from |
---|
1019 | ! further optimizations. So far, performance is much worse than |
---|
1020 | ! for routine ffty_tr_yx (more than three times slower). |
---|
1021 | !------------------------------------------------------------------------------! |
---|
1022 | |
---|
1023 | USE control_parameters |
---|
1024 | USE cpulog |
---|
1025 | USE indices |
---|
1026 | USE interfaces |
---|
1027 | USE pegrid |
---|
1028 | USE transpose_indices |
---|
1029 | |
---|
1030 | IMPLICIT NONE |
---|
1031 | |
---|
1032 | INTEGER :: i, j, k |
---|
1033 | |
---|
1034 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
1035 | REAL, DIMENSION(1:nza,nys:nyna,0:nxa) :: f_in |
---|
1036 | REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: f_out |
---|
1037 | REAL, DIMENSION(nys:nyna,1:nza,0:nxa) :: work |
---|
1038 | |
---|
1039 | ! |
---|
1040 | !-- Carry out the FFT along x, where all data are present due to the |
---|
1041 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
1042 | !-- the first index. |
---|
1043 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
---|
1044 | |
---|
1045 | IF ( host(1:3) == 'nec' ) THEN |
---|
1046 | ! |
---|
1047 | !-- Code for vector processors |
---|
1048 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
1049 | !$OMP DO |
---|
1050 | DO i = 0, nx |
---|
1051 | |
---|
1052 | DO j = nys, nyn |
---|
1053 | DO k = 1, nz |
---|
1054 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
1055 | ENDDO |
---|
1056 | ENDDO |
---|
1057 | |
---|
1058 | ENDDO |
---|
1059 | |
---|
1060 | !$OMP DO |
---|
1061 | DO j = nys, nyn |
---|
1062 | |
---|
1063 | CALL fft_x_m( work_fftx(:,:,j), 'forward' ) |
---|
1064 | |
---|
1065 | DO k = 1, nz |
---|
1066 | DO i = 0, nx |
---|
1067 | work(j,k,i) = work_fftx(i,k,j) |
---|
1068 | ENDDO |
---|
1069 | ENDDO |
---|
1070 | |
---|
1071 | ENDDO |
---|
1072 | !$OMP END PARALLEL |
---|
1073 | |
---|
1074 | ELSE |
---|
1075 | |
---|
1076 | ! |
---|
1077 | !-- Cache optimized code (there might be still a potential for better |
---|
1078 | !-- optimization). |
---|
1079 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
1080 | !$OMP DO |
---|
1081 | DO i = 0, nx |
---|
1082 | |
---|
1083 | DO j = nys, nyn |
---|
1084 | DO k = 1, nz |
---|
1085 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
1086 | ENDDO |
---|
1087 | ENDDO |
---|
1088 | |
---|
1089 | ENDDO |
---|
1090 | |
---|
1091 | !$OMP DO |
---|
1092 | DO j = nys, nyn |
---|
1093 | DO k = 1, nz |
---|
1094 | |
---|
1095 | CALL fft_x( work_fftx(0:nx,k,j), 'forward' ) |
---|
1096 | |
---|
1097 | DO i = 0, nx |
---|
1098 | work(j,k,i) = work_fftx(i,k,j) |
---|
1099 | ENDDO |
---|
1100 | ENDDO |
---|
1101 | |
---|
1102 | ENDDO |
---|
1103 | !$OMP END PARALLEL |
---|
1104 | |
---|
1105 | ENDIF |
---|
1106 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
---|
1107 | |
---|
1108 | ! |
---|
1109 | !-- Transpose array |
---|
1110 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
1111 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
1112 | CALL MPI_ALLTOALL( work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
1113 | f_out(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
1114 | comm1dy, ierr ) |
---|
1115 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
1116 | |
---|
1117 | END SUBROUTINE fftx_tr_xy |
---|
1118 | |
---|
1119 | |
---|
1120 | SUBROUTINE tr_yx_fftx( f_in, work, f_out ) |
---|
1121 | |
---|
1122 | !------------------------------------------------------------------------------! |
---|
1123 | ! Transposition y --> x with a subsequent backward Fourier transformation for |
---|
1124 | ! a 1d-decomposition along x |
---|
1125 | !------------------------------------------------------------------------------! |
---|
1126 | |
---|
1127 | USE control_parameters |
---|
1128 | USE cpulog |
---|
1129 | USE indices |
---|
1130 | USE interfaces |
---|
1131 | USE pegrid |
---|
1132 | USE transpose_indices |
---|
1133 | |
---|
1134 | IMPLICIT NONE |
---|
1135 | |
---|
1136 | INTEGER :: i, j, k |
---|
1137 | |
---|
1138 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
1139 | REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: f_in |
---|
1140 | REAL, DIMENSION(1:nza,nys:nyna,0:nxa) :: f_out |
---|
1141 | REAL, DIMENSION(nys:nyna,1:nza,0:nxa) :: work |
---|
1142 | |
---|
1143 | ! |
---|
1144 | !-- Transpose array |
---|
1145 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
1146 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
1147 | CALL MPI_ALLTOALL( f_in(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
1148 | work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
1149 | comm1dy, ierr ) |
---|
1150 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
1151 | |
---|
1152 | ! |
---|
1153 | !-- Carry out the FFT along x, where all data are present due to the |
---|
1154 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
1155 | !-- the first index. |
---|
1156 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
---|
1157 | |
---|
1158 | IF ( host(1:3) == 'nec' ) THEN |
---|
1159 | ! |
---|
1160 | !-- Code optimized for vector processors |
---|
1161 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
1162 | !$OMP DO |
---|
1163 | DO j = nys, nyn |
---|
1164 | |
---|
1165 | DO k = 1, nz |
---|
1166 | DO i = 0, nx |
---|
1167 | work_fftx(i,k,j) = work(j,k,i) |
---|
1168 | ENDDO |
---|
1169 | ENDDO |
---|
1170 | |
---|
1171 | CALL fft_x_m( work_fftx(:,:,j), 'backward' ) |
---|
1172 | |
---|
1173 | ENDDO |
---|
1174 | |
---|
1175 | !$OMP DO |
---|
1176 | DO i = 0, nx |
---|
1177 | DO j = nys, nyn |
---|
1178 | DO k = 1, nz |
---|
1179 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
1180 | ENDDO |
---|
1181 | ENDDO |
---|
1182 | ENDDO |
---|
1183 | !$OMP END PARALLEL |
---|
1184 | |
---|
1185 | ELSE |
---|
1186 | |
---|
1187 | ! |
---|
1188 | !-- Cache optimized code (there might be still a potential for better |
---|
1189 | !-- optimization). |
---|
1190 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
1191 | !$OMP DO |
---|
1192 | DO j = nys, nyn |
---|
1193 | DO k = 1, nz |
---|
1194 | |
---|
1195 | DO i = 0, nx |
---|
1196 | work_fftx(i,k,j) = work(j,k,i) |
---|
1197 | ENDDO |
---|
1198 | |
---|
1199 | CALL fft_x( work_fftx(0:nx,k,j), 'backward' ) |
---|
1200 | |
---|
1201 | ENDDO |
---|
1202 | ENDDO |
---|
1203 | |
---|
1204 | !$OMP DO |
---|
1205 | DO i = 0, nx |
---|
1206 | DO j = nys, nyn |
---|
1207 | DO k = 1, nz |
---|
1208 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
1209 | ENDDO |
---|
1210 | ENDDO |
---|
1211 | ENDDO |
---|
1212 | !$OMP END PARALLEL |
---|
1213 | |
---|
1214 | ENDIF |
---|
1215 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
---|
1216 | |
---|
1217 | END SUBROUTINE tr_yx_fftx |
---|
1218 | |
---|
1219 | |
---|
1220 | SUBROUTINE ffty_tri_ffty( ar ) |
---|
1221 | |
---|
1222 | !------------------------------------------------------------------------------! |
---|
1223 | ! FFT along y, solution of the tridiagonal system and backward FFT for |
---|
1224 | ! a 1d-decomposition along y |
---|
1225 | ! |
---|
1226 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
1227 | ! with OpenMP (for possible necessary changes see the original |
---|
1228 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
1229 | !------------------------------------------------------------------------------! |
---|
1230 | |
---|
1231 | USE control_parameters |
---|
1232 | USE cpulog |
---|
1233 | USE grid_variables |
---|
1234 | USE indices |
---|
1235 | USE interfaces |
---|
1236 | USE pegrid |
---|
1237 | USE transpose_indices |
---|
1238 | |
---|
1239 | IMPLICIT NONE |
---|
1240 | |
---|
1241 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
1242 | |
---|
1243 | REAL, DIMENSION(0:ny) :: work_ffty |
---|
1244 | REAL, DIMENSION(0:ny,1:nz) :: work_triy |
---|
1245 | REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: ar |
---|
1246 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
1247 | |
---|
1248 | |
---|
1249 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'start' ) |
---|
1250 | |
---|
1251 | ALLOCATE( tri(5,0:ny,0:nz-1,0:threads_per_task-1) ) |
---|
1252 | |
---|
1253 | tn = 0 ! Default thread number in case of one thread |
---|
1254 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_ffty, work_triy ) |
---|
1255 | DO i = nxl_y, nxr_y |
---|
1256 | |
---|
1257 | !$ tn = omp_get_thread_num() |
---|
1258 | |
---|
1259 | IF ( host(1:3) == 'nec' ) THEN |
---|
1260 | ! |
---|
1261 | !-- Code optimized for vector processors |
---|
1262 | DO k = 1, nz |
---|
1263 | |
---|
1264 | m = 0 |
---|
1265 | DO n = 1, pdims(2) |
---|
1266 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1267 | work_triy(m,k) = ar(j,k,i,n) |
---|
1268 | m = m + 1 |
---|
1269 | ENDDO |
---|
1270 | ENDDO |
---|
1271 | |
---|
1272 | ENDDO |
---|
1273 | |
---|
1274 | CALL fft_y_m( work_triy, ny, 'forward' ) |
---|
1275 | |
---|
1276 | ELSE |
---|
1277 | ! |
---|
1278 | !-- Cache optimized code |
---|
1279 | DO k = 1, nz |
---|
1280 | |
---|
1281 | m = 0 |
---|
1282 | DO n = 1, pdims(2) |
---|
1283 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1284 | work_ffty(m) = ar(j,k,i,n) |
---|
1285 | m = m + 1 |
---|
1286 | ENDDO |
---|
1287 | ENDDO |
---|
1288 | |
---|
1289 | CALL fft_y( work_ffty, 'forward' ) |
---|
1290 | |
---|
1291 | DO j = 0, ny |
---|
1292 | work_triy(j,k) = work_ffty(j) |
---|
1293 | ENDDO |
---|
1294 | |
---|
1295 | ENDDO |
---|
1296 | |
---|
1297 | ENDIF |
---|
1298 | |
---|
1299 | ! |
---|
1300 | !-- Solve the linear equation system |
---|
1301 | CALL tridia_1dd( ddy2, ddx2, ny, nx, i, work_triy, tri(:,:,:,tn) ) |
---|
1302 | |
---|
1303 | IF ( host(1:3) == 'nec' ) THEN |
---|
1304 | ! |
---|
1305 | !-- Code optimized for vector processors |
---|
1306 | CALL fft_y_m( work_triy, ny, 'backward' ) |
---|
1307 | |
---|
1308 | DO k = 1, nz |
---|
1309 | |
---|
1310 | m = 0 |
---|
1311 | DO n = 1, pdims(2) |
---|
1312 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1313 | ar(j,k,i,n) = work_triy(m,k) |
---|
1314 | m = m + 1 |
---|
1315 | ENDDO |
---|
1316 | ENDDO |
---|
1317 | |
---|
1318 | ENDDO |
---|
1319 | |
---|
1320 | ELSE |
---|
1321 | ! |
---|
1322 | !-- Cache optimized code |
---|
1323 | DO k = 1, nz |
---|
1324 | |
---|
1325 | DO j = 0, ny |
---|
1326 | work_ffty(j) = work_triy(j,k) |
---|
1327 | ENDDO |
---|
1328 | |
---|
1329 | CALL fft_y( work_ffty, 'backward' ) |
---|
1330 | |
---|
1331 | m = 0 |
---|
1332 | DO n = 1, pdims(2) |
---|
1333 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1334 | ar(j,k,i,n) = work_ffty(m) |
---|
1335 | m = m + 1 |
---|
1336 | ENDDO |
---|
1337 | ENDDO |
---|
1338 | |
---|
1339 | ENDDO |
---|
1340 | |
---|
1341 | ENDIF |
---|
1342 | |
---|
1343 | ENDDO |
---|
1344 | |
---|
1345 | DEALLOCATE( tri ) |
---|
1346 | |
---|
1347 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'stop' ) |
---|
1348 | |
---|
1349 | END SUBROUTINE ffty_tri_ffty |
---|
1350 | |
---|
1351 | |
---|
1352 | SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri ) |
---|
1353 | |
---|
1354 | !------------------------------------------------------------------------------! |
---|
1355 | ! Solves the linear system of equations for a 1d-decomposition along x (see |
---|
1356 | ! tridia) |
---|
1357 | ! |
---|
1358 | ! Attention: when using the intel compiler, array tri must be passed as an |
---|
1359 | ! argument to the contained subroutines. Otherwise addres faults |
---|
1360 | ! will occur. |
---|
1361 | ! On NEC, tri should not be passed (except for routine substi_1dd) |
---|
1362 | ! because this causes very bad performance. |
---|
1363 | !------------------------------------------------------------------------------! |
---|
1364 | |
---|
1365 | USE arrays_3d |
---|
1366 | USE control_parameters |
---|
1367 | |
---|
1368 | USE pegrid |
---|
1369 | |
---|
1370 | IMPLICIT NONE |
---|
1371 | |
---|
1372 | INTEGER :: i, j, k, nnyh, nx, ny, omp_get_thread_num, tn |
---|
1373 | |
---|
1374 | REAL :: ddx2, ddy2 |
---|
1375 | |
---|
1376 | REAL, DIMENSION(0:nx,1:nz) :: ar |
---|
1377 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
1378 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1379 | |
---|
1380 | |
---|
1381 | nnyh = ( ny + 1 ) / 2 |
---|
1382 | |
---|
1383 | ! |
---|
1384 | !-- Define constant elements of the tridiagonal matrix. |
---|
1385 | !-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2, |
---|
1386 | !-- the exchanged loops create bank conflicts. The following directive |
---|
1387 | !-- prohibits loop exchange and the loops perform much better. |
---|
1388 | ! tn = omp_get_thread_num() |
---|
1389 | ! WRITE( 120+tn, * ) '+++ id=',myid,' nx=',nx,' thread=', omp_get_thread_num() |
---|
1390 | ! CALL local_flush( 120+tn ) |
---|
1391 | !CDIR NOLOOPCHG |
---|
1392 | DO k = 0, nz-1 |
---|
1393 | DO i = 0,nx |
---|
1394 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
---|
1395 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
---|
1396 | ENDDO |
---|
1397 | ENDDO |
---|
1398 | ! WRITE( 120+tn, * ) '+++ id=',myid,' end of first tridia loop thread=', omp_get_thread_num() |
---|
1399 | ! CALL local_flush( 120+tn ) |
---|
1400 | |
---|
1401 | IF ( j <= nnyh ) THEN |
---|
1402 | #if defined( __lc ) |
---|
1403 | CALL maketri_1dd( j, tri ) |
---|
1404 | #else |
---|
1405 | CALL maketri_1dd( j ) |
---|
1406 | #endif |
---|
1407 | ELSE |
---|
1408 | #if defined( __lc ) |
---|
1409 | CALL maketri_1dd( ny+1-j, tri ) |
---|
1410 | #else |
---|
1411 | CALL maketri_1dd( ny+1-j ) |
---|
1412 | #endif |
---|
1413 | ENDIF |
---|
1414 | #if defined( __lc ) |
---|
1415 | CALL split_1dd( tri ) |
---|
1416 | #else |
---|
1417 | CALL split_1dd |
---|
1418 | #endif |
---|
1419 | CALL substi_1dd( ar, tri ) |
---|
1420 | |
---|
1421 | CONTAINS |
---|
1422 | |
---|
1423 | #if defined( __lc ) |
---|
1424 | SUBROUTINE maketri_1dd( j, tri ) |
---|
1425 | #else |
---|
1426 | SUBROUTINE maketri_1dd( j ) |
---|
1427 | #endif |
---|
1428 | |
---|
1429 | !------------------------------------------------------------------------------! |
---|
1430 | ! computes the i- and j-dependent component of the matrix |
---|
1431 | !------------------------------------------------------------------------------! |
---|
1432 | |
---|
1433 | USE constants |
---|
1434 | |
---|
1435 | IMPLICIT NONE |
---|
1436 | |
---|
1437 | INTEGER :: i, j, k, nnxh |
---|
1438 | REAL :: a, c |
---|
1439 | |
---|
1440 | REAL, DIMENSION(0:nx) :: l |
---|
1441 | |
---|
1442 | #if defined( __lc ) |
---|
1443 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1444 | #endif |
---|
1445 | |
---|
1446 | |
---|
1447 | nnxh = ( nx + 1 ) / 2 |
---|
1448 | ! |
---|
1449 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
---|
1450 | !-- Fourier space. The coefficients are computed following the method of |
---|
1451 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
---|
1452 | !-- Siano's original version by discretizing the Poisson equation, |
---|
1453 | !-- before it is Fourier-transformed |
---|
1454 | DO i = 0, nx |
---|
1455 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
---|
1456 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
---|
1457 | FLOAT( nx+1 ) ) ) * ddx2 + & |
---|
1458 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
1459 | FLOAT( ny+1 ) ) ) * ddy2 |
---|
1460 | ELSE |
---|
1461 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
1462 | FLOAT( nx+1 ) ) ) * ddx2 + & |
---|
1463 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
1464 | FLOAT( ny+1 ) ) ) * ddy2 |
---|
1465 | ENDIF |
---|
1466 | ENDDO |
---|
1467 | |
---|
1468 | DO k = 0, nz-1 |
---|
1469 | DO i = 0, nx |
---|
1470 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
1471 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
1472 | tri(1,i,k) = a + c - l(i) |
---|
1473 | ENDDO |
---|
1474 | ENDDO |
---|
1475 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
1476 | DO i = 0, nx |
---|
1477 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
1478 | ENDDO |
---|
1479 | ENDIF |
---|
1480 | IF ( ibc_p_t == 1 ) THEN |
---|
1481 | DO i = 0, nx |
---|
1482 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
1483 | ENDDO |
---|
1484 | ENDIF |
---|
1485 | |
---|
1486 | END SUBROUTINE maketri_1dd |
---|
1487 | |
---|
1488 | |
---|
1489 | #if defined( __lc ) |
---|
1490 | SUBROUTINE split_1dd( tri ) |
---|
1491 | #else |
---|
1492 | SUBROUTINE split_1dd |
---|
1493 | #endif |
---|
1494 | |
---|
1495 | !------------------------------------------------------------------------------! |
---|
1496 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
1497 | !------------------------------------------------------------------------------! |
---|
1498 | |
---|
1499 | IMPLICIT NONE |
---|
1500 | |
---|
1501 | INTEGER :: i, k |
---|
1502 | |
---|
1503 | #if defined( __lc ) |
---|
1504 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1505 | #endif |
---|
1506 | |
---|
1507 | |
---|
1508 | ! |
---|
1509 | !-- Splitting |
---|
1510 | DO i = 0, nx |
---|
1511 | tri(4,i,0) = tri(1,i,0) |
---|
1512 | ENDDO |
---|
1513 | DO k = 1, nz-1 |
---|
1514 | DO i = 0, nx |
---|
1515 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
1516 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
1517 | ENDDO |
---|
1518 | ENDDO |
---|
1519 | |
---|
1520 | END SUBROUTINE split_1dd |
---|
1521 | |
---|
1522 | |
---|
1523 | SUBROUTINE substi_1dd( ar, tri ) |
---|
1524 | |
---|
1525 | !------------------------------------------------------------------------------! |
---|
1526 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
1527 | !------------------------------------------------------------------------------! |
---|
1528 | |
---|
1529 | IMPLICIT NONE |
---|
1530 | |
---|
1531 | INTEGER :: i, k |
---|
1532 | |
---|
1533 | REAL, DIMENSION(0:nx,nz) :: ar |
---|
1534 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
1535 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1536 | |
---|
1537 | ! |
---|
1538 | !-- Forward substitution |
---|
1539 | DO i = 0, nx |
---|
1540 | ar1(i,0) = ar(i,1) |
---|
1541 | ENDDO |
---|
1542 | DO k = 1, nz-1 |
---|
1543 | DO i = 0, nx |
---|
1544 | ar1(i,k) = ar(i,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
1545 | ENDDO |
---|
1546 | ENDDO |
---|
1547 | |
---|
1548 | ! |
---|
1549 | !-- Backward substitution |
---|
1550 | !-- Note, the add of 1.0E-20 in the denominator is due to avoid divisions |
---|
1551 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
1552 | !-- the model domain. |
---|
1553 | DO i = 0, nx |
---|
1554 | ar(i,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
1555 | ENDDO |
---|
1556 | DO k = nz-2, 0, -1 |
---|
1557 | DO i = 0, nx |
---|
1558 | ar(i,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,k+2) ) & |
---|
1559 | / tri(4,i,k) |
---|
1560 | ENDDO |
---|
1561 | ENDDO |
---|
1562 | |
---|
1563 | ! |
---|
1564 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
1565 | !-- The respective values of ar should be zero at all k-levels if |
---|
1566 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
1567 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
1568 | IF ( j == 0 ) THEN |
---|
1569 | DO k = 1, nz |
---|
1570 | ar(0,k) = 0.0 |
---|
1571 | ENDDO |
---|
1572 | ENDIF |
---|
1573 | ENDIF |
---|
1574 | |
---|
1575 | END SUBROUTINE substi_1dd |
---|
1576 | |
---|
1577 | END SUBROUTINE tridia_1dd |
---|
1578 | |
---|
1579 | #endif |
---|
1580 | |
---|
1581 | END MODULE poisfft_mod |
---|