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