[1] | 1 | MODULE poisfft_mod |
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| 2 | |
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[1036] | 3 | !--------------------------------------------------------------------------------! |
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| 4 | ! This file is part of PALM. |
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| 5 | ! |
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| 6 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
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| 7 | ! of the GNU General Public License as published by the Free Software Foundation, |
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| 8 | ! either version 3 of the License, or (at your option) any later version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2012 Leibniz University Hannover |
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| 18 | !--------------------------------------------------------------------------------! |
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| 19 | ! |
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[484] | 20 | ! Current revisions: |
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[1] | 21 | ! ----------------- |
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[1107] | 22 | ! |
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[1] | 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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[3] | 26 | ! $Id: poisfft.f90 1107 2013-03-04 06:23:14Z raasch $ |
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[77] | 27 | ! |
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[1107] | 28 | ! 1106 2013-03-04 05:31:38Z raasch |
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| 29 | ! routines fftx, ffty, fftxp, fftyp removed, calls replaced by fft_x, fft_y, |
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| 30 | ! in the 1D-decomposition routines fft_x, ffty are replaced by fft_x_1d, |
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| 31 | ! fft_y_1d |
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| 32 | ! |
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[1104] | 33 | ! 1103 2013-02-20 02:15:53Z raasch |
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| 34 | ! tri, ar, and ar1 arguments in tridia-routines (2d) are removed because they |
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| 35 | ! sometimes cause segmentation faults with intel 12.1 compiler |
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| 36 | ! |
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[1093] | 37 | ! 1092 2013-02-02 11:24:22Z raasch |
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| 38 | ! unused variables removed |
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| 39 | ! |
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[1037] | 40 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 41 | ! code put under GPL (PALM 3.9) |
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| 42 | ! |
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[1014] | 43 | ! 2012-09-21 07:03:55Z raasch |
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| 44 | ! FLOAT type conversion replaced by REAL |
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| 45 | ! |
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[1004] | 46 | ! 1003 2012-09-14 14:35:53Z raasch |
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| 47 | ! indices nxa, nya, etc. replaced by nx, ny, etc. |
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| 48 | ! |
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[941] | 49 | ! 940 2012-07-09 14:31:00Z raasch |
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| 50 | ! special handling of tri-array as an argument in tridia_1dd routines switched |
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| 51 | ! off because it caused segmentation faults with intel 12.1 compiler |
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| 52 | ! |
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[878] | 53 | ! 877 2012-04-03 11:21:44Z suehring |
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| 54 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
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| 55 | ! pressure at the top of the model domain. |
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| 56 | ! |
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[810] | 57 | ! 809 2012-01-30 13:32:58Z maronga |
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| 58 | ! Bugfix: replaced .AND. and .NOT. with && and ! in the preprocessor directives |
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| 59 | ! |
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[808] | 60 | ! 807 2012-01-25 11:53:51Z maronga |
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| 61 | ! New cpp directive "__check" implemented which is used by check_namelist_files |
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| 62 | ! (most of the code is unneeded by check_namelist_files). |
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| 63 | ! |
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[764] | 64 | ! 763 2011-10-06 09:32:09Z suehring |
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| 65 | ! Comment added concerning the last change. |
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| 66 | ! |
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[762] | 67 | ! 761 2011-10-05 17:58:52Z suehring |
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| 68 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
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| 69 | ! pressure at the top of the model domain. |
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| 70 | ! |
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[697] | 71 | ! 696 2011-03-18 07:03:49Z raasch |
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| 72 | ! work_fftx removed from PRIVATE clauses in fftx_tr_xy and tr_yx_fftx |
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| 73 | ! |
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[684] | 74 | ! 683 2011-02-09 14:25:15Z raasch |
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| 75 | ! openMP parallelization for 2d-domain-decomposition |
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| 76 | ! |
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[668] | 77 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 78 | ! ddzu replaced by ddzu_pres due to changes in zu(0) |
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| 79 | ! |
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[623] | 80 | ! 622 2010-12-10 08:08:13Z raasch |
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| 81 | ! optional barriers included in order to speed up collective operations |
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| 82 | ! |
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[392] | 83 | ! 377 2009-09-04 11:09:00Z raasch |
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| 84 | ! __lcmuk changed to __lc to avoid problems with Intel compiler on sgi-ice |
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| 85 | ! |
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[198] | 86 | ! 164 2008-05-15 08:46:15Z raasch |
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| 87 | ! Arguments removed from transpose routines |
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| 88 | ! |
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[139] | 89 | ! 128 2007-10-26 13:11:14Z raasch |
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| 90 | ! Bugfix: wavenumber calculation for even nx in routines maketri |
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| 91 | ! |
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[90] | 92 | ! 85 2007-05-11 09:35:14Z raasch |
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| 93 | ! Bugfix: work_fft*_vec removed from some PRIVATE-declarations |
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| 94 | ! |
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[77] | 95 | ! 76 2007-03-29 00:58:32Z raasch |
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| 96 | ! Tridiagonal coefficients adjusted for Neumann boundary conditions both at |
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| 97 | ! the bottom and the top. |
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| 98 | ! |
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[3] | 99 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 100 | ! |
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[1] | 101 | ! Revision 1.24 2006/08/04 15:00:24 raasch |
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| 102 | ! Default setting of the thread number tn in case of not using OpenMP |
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| 103 | ! |
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| 104 | ! Revision 1.23 2006/02/23 12:48:38 raasch |
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| 105 | ! Additional compiler directive in routine tridia_1dd for preventing loop |
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| 106 | ! exchange on NEC-SX6 |
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| 107 | ! |
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| 108 | ! Revision 1.20 2004/04/30 12:38:09 raasch |
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| 109 | ! Parts of former poisfft_hybrid moved to this subroutine, |
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| 110 | ! former subroutine changed to a module, renaming of FFT-subroutines and |
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| 111 | ! -module, FFTs completely substituted by calls of fft_x and fft_y, |
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| 112 | ! NAG fft used in the non-parallel case completely removed, l in maketri |
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| 113 | ! is now a 1d-array, variables passed by modules instead of using parameter |
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| 114 | ! lists, enlarged transposition arrays introduced |
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| 115 | ! |
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| 116 | ! Revision 1.1 1997/07/24 11:24:14 raasch |
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| 117 | ! Initial revision |
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| 118 | ! |
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| 119 | ! |
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| 120 | ! Description: |
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| 121 | ! ------------ |
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| 122 | ! See below. |
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| 123 | !------------------------------------------------------------------------------! |
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| 124 | |
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| 125 | !--------------------------------------------------------------------------! |
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| 126 | ! poisfft ! |
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| 127 | ! ! |
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| 128 | ! Original version: Stephan Siano (pois3d) ! |
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| 129 | ! ! |
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| 130 | ! Institute of Meteorology and Climatology, University of Hannover ! |
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| 131 | ! Germany ! |
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| 132 | ! ! |
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| 133 | ! Version as of July 23,1996 ! |
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| 134 | ! ! |
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| 135 | ! ! |
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| 136 | ! Version for parallel computers: Siegfried Raasch ! |
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| 137 | ! ! |
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| 138 | ! Version as of July 03,1997 ! |
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| 139 | ! ! |
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| 140 | ! Solves the Poisson equation with a 2D spectral method ! |
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| 141 | ! d^2 p / dx^2 + d^2 p / dy^2 + d^2 p / dz^2 = s ! |
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| 142 | ! ! |
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| 143 | ! Input: ! |
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| 144 | ! real ar contains in the (nnx,nny,nnz) elements, ! |
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| 145 | ! starting from the element (1,nys,nxl), the ! |
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| 146 | ! values for s ! |
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| 147 | ! real work Temporary array ! |
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| 148 | ! ! |
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| 149 | ! Output: ! |
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| 150 | ! real ar contains the solution for p ! |
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| 151 | !--------------------------------------------------------------------------! |
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| 152 | |
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| 153 | USE fft_xy |
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| 154 | USE indices |
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| 155 | USE transpose_indices |
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| 156 | |
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| 157 | IMPLICIT NONE |
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| 158 | |
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| 159 | PRIVATE |
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[807] | 160 | |
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[809] | 161 | #if ! defined ( __check ) |
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[1] | 162 | PUBLIC poisfft, poisfft_init |
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| 163 | |
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| 164 | INTERFACE poisfft |
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| 165 | MODULE PROCEDURE poisfft |
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| 166 | END INTERFACE poisfft |
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| 167 | |
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| 168 | INTERFACE poisfft_init |
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| 169 | MODULE PROCEDURE poisfft_init |
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| 170 | END INTERFACE poisfft_init |
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[807] | 171 | #else |
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| 172 | PUBLIC poisfft_init |
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[1] | 173 | |
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[807] | 174 | INTERFACE poisfft_init |
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| 175 | MODULE PROCEDURE poisfft_init |
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| 176 | END INTERFACE poisfft_init |
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| 177 | #endif |
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| 178 | |
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[1] | 179 | CONTAINS |
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| 180 | |
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| 181 | SUBROUTINE poisfft_init |
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| 182 | |
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| 183 | CALL fft_init |
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| 184 | |
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| 185 | END SUBROUTINE poisfft_init |
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| 186 | |
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[809] | 187 | #if ! defined ( __check ) |
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[1] | 188 | SUBROUTINE poisfft( ar, work ) |
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| 189 | |
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| 190 | USE cpulog |
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| 191 | USE interfaces |
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| 192 | USE pegrid |
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| 193 | |
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| 194 | IMPLICIT NONE |
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| 195 | |
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[1003] | 196 | REAL, DIMENSION(1:nz,nys:nyn,nxl:nxr) :: ar, work |
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[1] | 197 | |
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| 198 | |
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| 199 | CALL cpu_log( log_point_s(3), 'poisfft', 'start' ) |
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| 200 | |
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| 201 | ! |
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| 202 | !-- Two-dimensional Fourier Transformation in x- and y-direction. |
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| 203 | #if defined( __parallel ) |
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| 204 | IF ( pdims(2) == 1 ) THEN |
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| 205 | |
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| 206 | ! |
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| 207 | !-- 1d-domain-decomposition along x: |
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| 208 | !-- FFT along y and transposition y --> x |
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| 209 | CALL ffty_tr_yx( ar, work, ar ) |
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| 210 | |
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| 211 | ! |
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| 212 | !-- FFT along x, solving the tridiagonal system and backward FFT |
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| 213 | CALL fftx_tri_fftx( ar ) |
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| 214 | |
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| 215 | ! |
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| 216 | !-- Transposition x --> y and backward FFT along y |
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| 217 | CALL tr_xy_ffty( ar, work, ar ) |
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| 218 | |
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| 219 | ELSEIF ( pdims(1) == 1 ) THEN |
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| 220 | |
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| 221 | ! |
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| 222 | !-- 1d-domain-decomposition along y: |
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| 223 | !-- FFT along x and transposition x --> y |
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| 224 | CALL fftx_tr_xy( ar, work, ar ) |
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| 225 | |
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| 226 | ! |
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| 227 | !-- FFT along y, solving the tridiagonal system and backward FFT |
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| 228 | CALL ffty_tri_ffty( ar ) |
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| 229 | |
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| 230 | ! |
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| 231 | !-- Transposition y --> x and backward FFT along x |
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| 232 | CALL tr_yx_fftx( ar, work, ar ) |
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| 233 | |
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| 234 | ELSE |
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| 235 | |
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| 236 | ! |
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| 237 | !-- 2d-domain-decomposition |
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| 238 | !-- Transposition z --> x |
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| 239 | CALL cpu_log( log_point_s(5), 'transpo forward', 'start' ) |
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[164] | 240 | CALL transpose_zx( ar, work, ar ) |
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[1] | 241 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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| 242 | |
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| 243 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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[1106] | 244 | CALL fft_x( ar, 'forward' ) |
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[1] | 245 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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| 246 | |
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| 247 | ! |
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| 248 | !-- Transposition x --> y |
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| 249 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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[164] | 250 | CALL transpose_xy( ar, work, ar ) |
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[1] | 251 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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| 252 | |
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| 253 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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[1106] | 254 | CALL fft_y( ar, 'forward' ) |
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[1] | 255 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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| 256 | |
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| 257 | ! |
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| 258 | !-- Transposition y --> z |
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| 259 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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[164] | 260 | CALL transpose_yz( ar, work, ar ) |
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[1] | 261 | CALL cpu_log( log_point_s(5), 'transpo forward', 'stop' ) |
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| 262 | |
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| 263 | ! |
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[1106] | 264 | !-- Solve the tridiagonal equation system along z |
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[1] | 265 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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| 266 | CALL tridia( ar ) |
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| 267 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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| 268 | |
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| 269 | ! |
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| 270 | !-- Inverse Fourier Transformation |
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| 271 | !-- Transposition z --> y |
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| 272 | CALL cpu_log( log_point_s(8), 'transpo invers', 'start' ) |
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[164] | 273 | CALL transpose_zy( ar, work, ar ) |
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[1] | 274 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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| 275 | |
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| 276 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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[1106] | 277 | CALL fft_y( ar, 'backward' ) |
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[1] | 278 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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| 279 | |
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| 280 | ! |
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| 281 | !-- Transposition y --> x |
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| 282 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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[164] | 283 | CALL transpose_yx( ar, work, ar ) |
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[1] | 284 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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| 285 | |
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| 286 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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[1106] | 287 | CALL fft_x( ar, 'backward' ) |
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[1] | 288 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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| 289 | |
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| 290 | ! |
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| 291 | !-- Transposition x --> z |
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| 292 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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[164] | 293 | CALL transpose_xz( ar, work, ar ) |
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[1] | 294 | CALL cpu_log( log_point_s(8), 'transpo invers', 'stop' ) |
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| 295 | |
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| 296 | ENDIF |
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| 297 | |
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| 298 | #else |
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| 299 | |
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| 300 | ! |
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| 301 | !-- Two-dimensional Fourier Transformation along x- and y-direction. |
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[1106] | 302 | CALL cpu_log( log_point_s(5), 'transpo forward', 'start' ) |
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| 303 | !$acc data copyin( ar, work ) |
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| 304 | CALL transpose_zx( ar, work, ar ) |
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| 305 | !$acc update host( ar ) |
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| 306 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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| 307 | |
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| 308 | |
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[1] | 309 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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[1106] | 310 | CALL fft_x( ar, 'forward' ) |
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[1] | 311 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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[1106] | 312 | |
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| 313 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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| 314 | CALL transpose_xy( ar, work, ar ) |
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| 315 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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| 316 | |
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[1] | 317 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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[1106] | 318 | CALL fft_y( ar, 'forward' ) |
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[1] | 319 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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| 320 | |
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| 321 | ! |
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[1106] | 322 | !-- Solve the tridiagonal equation system along z |
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| 323 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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| 324 | CALL transpose_yz( ar, work, ar ) |
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| 325 | CALL cpu_log( log_point_s(5), 'transpo forward', 'stop' ) |
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| 326 | |
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[1] | 327 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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| 328 | CALL tridia( ar ) |
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| 329 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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| 330 | |
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[1106] | 331 | CALL cpu_log( log_point_s(8), 'transpo invers', 'start' ) |
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| 332 | CALL transpose_zy( ar, work, ar ) |
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| 333 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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| 334 | |
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[1] | 335 | ! |
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| 336 | !-- Inverse Fourier Transformation. |
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| 337 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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[1106] | 338 | CALL fft_y( ar, 'backward' ) |
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[1] | 339 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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[1106] | 340 | |
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| 341 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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| 342 | CALL transpose_yx( ar, work, ar ) |
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| 343 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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| 344 | |
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[1] | 345 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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[1106] | 346 | CALL fft_x( ar, 'backward' ) |
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[1] | 347 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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| 348 | |
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[1106] | 349 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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| 350 | CALL transpose_xz( ar, work, ar ) |
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| 351 | CALL cpu_log( log_point_s(8), 'transpo invers', 'stop' ) |
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| 352 | |
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| 353 | !$acc end data |
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| 354 | |
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[1] | 355 | #endif |
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| 356 | |
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| 357 | CALL cpu_log( log_point_s(3), 'poisfft', 'stop' ) |
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| 358 | |
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| 359 | END SUBROUTINE poisfft |
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| 360 | |
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| 361 | |
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| 362 | |
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| 363 | SUBROUTINE tridia( ar ) |
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| 364 | |
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| 365 | !------------------------------------------------------------------------------! |
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| 366 | ! solves the linear system of equations: |
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| 367 | ! |
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| 368 | ! -(4 pi^2(i^2/(dx^2*nnx^2)+j^2/(dy^2*nny^2))+ |
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| 369 | ! 1/(dzu(k)*dzw(k))+1/(dzu(k-1)*dzw(k)))*p(i,j,k)+ |
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| 370 | ! 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) |
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| 371 | ! |
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| 372 | ! by using the Thomas algorithm |
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| 373 | !------------------------------------------------------------------------------! |
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| 374 | |
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| 375 | USE arrays_3d |
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| 376 | |
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| 377 | IMPLICIT NONE |
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| 378 | |
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| 379 | INTEGER :: i, j, k, nnyh |
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| 380 | |
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| 381 | REAL, DIMENSION(nxl_z:nxr_z,0:nz-1) :: ar1 |
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| 382 | REAL, DIMENSION(5,nxl_z:nxr_z,0:nz-1) :: tri |
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| 383 | |
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[1003] | 384 | REAL :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) |
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[1] | 385 | |
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| 386 | |
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| 387 | nnyh = (ny+1) / 2 |
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| 388 | |
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| 389 | ! |
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| 390 | !-- Define constant elements of the tridiagonal matrix. |
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[683] | 391 | !$OMP PARALLEL PRIVATE ( k, i ) |
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| 392 | !$OMP DO |
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[1] | 393 | DO k = 0, nz-1 |
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| 394 | DO i = nxl_z, nxr_z |
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[667] | 395 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
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| 396 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
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[1] | 397 | ENDDO |
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| 398 | ENDDO |
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[683] | 399 | !$OMP END PARALLEL |
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[1] | 400 | |
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| 401 | #if defined( __parallel ) |
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| 402 | ! |
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| 403 | !-- Repeat for all y-levels. |
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[683] | 404 | !$OMP PARALLEL FIRSTPRIVATE( tri ) PRIVATE ( ar1, j ) |
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| 405 | !$OMP DO |
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[1] | 406 | DO j = nys_z, nyn_z |
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| 407 | IF ( j <= nnyh ) THEN |
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[1103] | 408 | CALL maketri( j ) |
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[1] | 409 | ELSE |
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[1103] | 410 | CALL maketri( ny+1-j ) |
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[1] | 411 | ENDIF |
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[1103] | 412 | CALL split |
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| 413 | CALL substi( j ) |
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[1] | 414 | ENDDO |
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[683] | 415 | !$OMP END PARALLEL |
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[1] | 416 | #else |
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| 417 | ! |
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| 418 | !-- First y-level. |
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[1103] | 419 | CALL maketri( nys_z ) |
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| 420 | CALL split |
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| 421 | CALL substi( 0 ) |
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[1] | 422 | |
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| 423 | ! |
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| 424 | !-- Further y-levels. |
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| 425 | DO j = 1, nnyh - 1 |
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[1103] | 426 | CALL maketri( j ) |
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| 427 | CALL split |
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| 428 | CALL substi( j ) |
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| 429 | CALL substi( ny+1-j ) |
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[1] | 430 | ENDDO |
---|
[1103] | 431 | CALL maketri( nnyh ) |
---|
| 432 | CALL split |
---|
| 433 | CALL substi( nnyh+nys ) |
---|
[1] | 434 | #endif |
---|
| 435 | |
---|
| 436 | CONTAINS |
---|
| 437 | |
---|
[1103] | 438 | SUBROUTINE maketri( j ) |
---|
[1] | 439 | |
---|
| 440 | !------------------------------------------------------------------------------! |
---|
| 441 | ! Computes the i- and j-dependent component of the matrix |
---|
| 442 | !------------------------------------------------------------------------------! |
---|
| 443 | |
---|
| 444 | USE arrays_3d |
---|
| 445 | USE constants |
---|
| 446 | USE control_parameters |
---|
| 447 | USE grid_variables |
---|
| 448 | |
---|
| 449 | IMPLICIT NONE |
---|
| 450 | |
---|
| 451 | INTEGER :: i, j, k, nnxh |
---|
| 452 | REAL :: a, c |
---|
| 453 | REAL :: ll(nxl_z:nxr_z) |
---|
| 454 | |
---|
| 455 | |
---|
| 456 | nnxh = ( nx + 1 ) / 2 |
---|
| 457 | |
---|
| 458 | ! |
---|
| 459 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
---|
| 460 | !-- Fourier space. The coefficients are computed following the method of |
---|
| 461 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
---|
| 462 | !-- Siano's original version by discretizing the Poisson equation, |
---|
| 463 | !-- before it is Fourier-transformed |
---|
| 464 | #if defined( __parallel ) |
---|
| 465 | DO i = nxl_z, nxr_z |
---|
[128] | 466 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
---|
[1] | 467 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
---|
[1013] | 468 | REAL( nx+1 ) ) ) / ( dx * dx ) + & |
---|
[1] | 469 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
[1013] | 470 | REAL( ny+1 ) ) ) / ( dy * dy ) |
---|
[1] | 471 | ELSE |
---|
| 472 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
[1013] | 473 | REAL( nx+1 ) ) ) / ( dx * dx ) + & |
---|
[1] | 474 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
[1013] | 475 | REAL( ny+1 ) ) ) / ( dy * dy ) |
---|
[1] | 476 | ENDIF |
---|
| 477 | DO k = 0,nz-1 |
---|
[667] | 478 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
| 479 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
[1] | 480 | tri(1,i,k) = a + c - ll(i) |
---|
| 481 | ENDDO |
---|
| 482 | ENDDO |
---|
| 483 | #else |
---|
| 484 | DO i = 0, nnxh |
---|
[1013] | 485 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / REAL( nx+1 ) ) ) / & |
---|
[1] | 486 | ( dx * dx ) + & |
---|
[1013] | 487 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / REAL( ny+1 ) ) ) / & |
---|
[1] | 488 | ( dy * dy ) |
---|
| 489 | DO k = 0, nz-1 |
---|
[667] | 490 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
| 491 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
[1] | 492 | tri(1,i,k) = a + c - ll(i) |
---|
| 493 | IF ( i >= 1 .and. i < nnxh ) THEN |
---|
| 494 | tri(1,nx+1-i,k) = tri(1,i,k) |
---|
| 495 | ENDIF |
---|
| 496 | ENDDO |
---|
| 497 | ENDDO |
---|
| 498 | #endif |
---|
| 499 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
| 500 | DO i = nxl_z, nxr_z |
---|
| 501 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
| 502 | ENDDO |
---|
| 503 | ENDIF |
---|
| 504 | IF ( ibc_p_t == 1 ) THEN |
---|
| 505 | DO i = nxl_z, nxr_z |
---|
| 506 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
| 507 | ENDDO |
---|
| 508 | ENDIF |
---|
| 509 | |
---|
| 510 | END SUBROUTINE maketri |
---|
| 511 | |
---|
| 512 | |
---|
[1103] | 513 | SUBROUTINE substi( j ) |
---|
[1] | 514 | |
---|
| 515 | !------------------------------------------------------------------------------! |
---|
| 516 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
| 517 | !------------------------------------------------------------------------------! |
---|
| 518 | |
---|
[76] | 519 | USE control_parameters |
---|
| 520 | |
---|
[1] | 521 | IMPLICIT NONE |
---|
| 522 | |
---|
| 523 | INTEGER :: i, j, k |
---|
| 524 | |
---|
| 525 | ! |
---|
| 526 | !-- Forward substitution. |
---|
| 527 | DO i = nxl_z, nxr_z |
---|
| 528 | ar1(i,0) = ar(i,j,1) |
---|
| 529 | ENDDO |
---|
| 530 | DO k = 1, nz - 1 |
---|
| 531 | DO i = nxl_z, nxr_z |
---|
| 532 | ar1(i,k) = ar(i,j,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
| 533 | ENDDO |
---|
| 534 | ENDDO |
---|
| 535 | |
---|
| 536 | ! |
---|
[877] | 537 | !-- Backward substitution |
---|
| 538 | !-- Note, the 1.0E-20 in the denominator is due to avoid divisions |
---|
| 539 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
| 540 | !-- the model domain. |
---|
[1] | 541 | DO i = nxl_z, nxr_z |
---|
[877] | 542 | ar(i,j,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
[1] | 543 | ENDDO |
---|
| 544 | DO k = nz-2, 0, -1 |
---|
| 545 | DO i = nxl_z, nxr_z |
---|
| 546 | ar(i,j,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,j,k+2) ) & |
---|
| 547 | / tri(4,i,k) |
---|
| 548 | ENDDO |
---|
| 549 | ENDDO |
---|
| 550 | |
---|
[76] | 551 | ! |
---|
| 552 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
| 553 | !-- The respective values of ar should be zero at all k-levels if |
---|
| 554 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
| 555 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
| 556 | IF ( j == 0 .AND. nxl_z == 0 ) THEN |
---|
| 557 | DO k = 1, nz |
---|
| 558 | ar(nxl_z,j,k) = 0.0 |
---|
| 559 | ENDDO |
---|
| 560 | ENDIF |
---|
| 561 | ENDIF |
---|
| 562 | |
---|
[1] | 563 | END SUBROUTINE substi |
---|
| 564 | |
---|
| 565 | |
---|
[1103] | 566 | SUBROUTINE split |
---|
[1] | 567 | |
---|
| 568 | !------------------------------------------------------------------------------! |
---|
| 569 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
| 570 | !------------------------------------------------------------------------------! |
---|
| 571 | |
---|
| 572 | IMPLICIT NONE |
---|
| 573 | |
---|
| 574 | INTEGER :: i, k |
---|
| 575 | |
---|
| 576 | ! |
---|
| 577 | !-- Splitting. |
---|
| 578 | DO i = nxl_z, nxr_z |
---|
| 579 | tri(4,i,0) = tri(1,i,0) |
---|
| 580 | ENDDO |
---|
| 581 | DO k = 1, nz-1 |
---|
| 582 | DO i = nxl_z, nxr_z |
---|
| 583 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
| 584 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
| 585 | ENDDO |
---|
| 586 | ENDDO |
---|
| 587 | |
---|
| 588 | END SUBROUTINE split |
---|
| 589 | |
---|
| 590 | END SUBROUTINE tridia |
---|
| 591 | |
---|
| 592 | |
---|
| 593 | #if defined( __parallel ) |
---|
| 594 | SUBROUTINE ffty_tr_yx( f_in, work, f_out ) |
---|
| 595 | |
---|
| 596 | !------------------------------------------------------------------------------! |
---|
| 597 | ! Fourier-transformation along y with subsequent transposition y --> x for |
---|
| 598 | ! a 1d-decomposition along x |
---|
| 599 | ! |
---|
| 600 | ! ATTENTION: The performance of this routine is much faster on the NEC-SX6, |
---|
| 601 | ! if the first index of work_ffty_vec is odd. Otherwise |
---|
| 602 | ! memory bank conflicts may occur (especially if the index is a |
---|
| 603 | ! multiple of 128). That's why work_ffty_vec is dimensioned as |
---|
| 604 | ! 0:ny+1. |
---|
| 605 | ! Of course, this will not work if users are using an odd number |
---|
| 606 | ! of gridpoints along y. |
---|
| 607 | !------------------------------------------------------------------------------! |
---|
| 608 | |
---|
| 609 | USE control_parameters |
---|
| 610 | USE cpulog |
---|
| 611 | USE indices |
---|
| 612 | USE interfaces |
---|
| 613 | USE pegrid |
---|
| 614 | USE transpose_indices |
---|
| 615 | |
---|
| 616 | IMPLICIT NONE |
---|
| 617 | |
---|
| 618 | INTEGER :: i, iend, iouter, ir, j, k |
---|
| 619 | INTEGER, PARAMETER :: stridex = 4 |
---|
| 620 | |
---|
| 621 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
| 622 | #if defined( __nec ) |
---|
| 623 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
| 624 | #endif |
---|
[1003] | 625 | REAL, DIMENSION(1:nz,0:ny,nxl:nxr) :: f_in |
---|
| 626 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: f_out |
---|
| 627 | REAL, DIMENSION(nxl:nxr,1:nz,0:ny) :: work |
---|
[1] | 628 | |
---|
| 629 | ! |
---|
| 630 | !-- Carry out the FFT along y, where all data are present due to the |
---|
| 631 | !-- 1d-decomposition along x. Resort the data in a way that x becomes |
---|
| 632 | !-- the first index. |
---|
[1106] | 633 | CALL cpu_log( log_point_s(7), 'fft_y_1d', 'start' ) |
---|
[1] | 634 | |
---|
| 635 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 636 | #if defined( __nec ) |
---|
| 637 | ! |
---|
| 638 | !-- Code optimized for vector processors |
---|
[85] | 639 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 640 | !$OMP DO |
---|
| 641 | DO i = nxl, nxr |
---|
| 642 | |
---|
| 643 | DO j = 0, ny |
---|
| 644 | DO k = 1, nz |
---|
| 645 | work_ffty_vec(j,k,i) = f_in(k,j,i) |
---|
| 646 | ENDDO |
---|
| 647 | ENDDO |
---|
| 648 | |
---|
| 649 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'forward' ) |
---|
| 650 | |
---|
| 651 | ENDDO |
---|
| 652 | |
---|
| 653 | !$OMP DO |
---|
| 654 | DO k = 1, nz |
---|
| 655 | DO j = 0, ny |
---|
| 656 | DO i = nxl, nxr |
---|
| 657 | work(i,k,j) = work_ffty_vec(j,k,i) |
---|
| 658 | ENDDO |
---|
| 659 | ENDDO |
---|
| 660 | ENDDO |
---|
| 661 | !$OMP END PARALLEL |
---|
| 662 | #endif |
---|
| 663 | |
---|
| 664 | ELSE |
---|
| 665 | |
---|
| 666 | ! |
---|
| 667 | !-- Cache optimized code. |
---|
| 668 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
| 669 | !-- loop for better cache performance |
---|
| 670 | !$OMP PARALLEL PRIVATE (i,iend,iouter,ir,j,k,work_ffty) |
---|
| 671 | !$OMP DO |
---|
| 672 | DO iouter = nxl, nxr, stridex |
---|
| 673 | |
---|
| 674 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
| 675 | |
---|
| 676 | DO k = 1, nz |
---|
| 677 | |
---|
| 678 | DO i = iouter, iend |
---|
| 679 | |
---|
| 680 | ir = i-iouter+1 ! counter within a stride |
---|
| 681 | DO j = 0, ny |
---|
| 682 | work_ffty(j,ir) = f_in(k,j,i) |
---|
| 683 | ENDDO |
---|
| 684 | ! |
---|
| 685 | !-- FFT along y |
---|
[1106] | 686 | CALL fft_y_1d( work_ffty(:,ir), 'forward' ) |
---|
[1] | 687 | |
---|
| 688 | ENDDO |
---|
| 689 | |
---|
| 690 | ! |
---|
| 691 | !-- Resort |
---|
| 692 | DO j = 0, ny |
---|
| 693 | DO i = iouter, iend |
---|
| 694 | work(i,k,j) = work_ffty(j,i-iouter+1) |
---|
| 695 | ENDDO |
---|
| 696 | ENDDO |
---|
| 697 | |
---|
| 698 | ENDDO |
---|
| 699 | |
---|
| 700 | ENDDO |
---|
| 701 | !$OMP END PARALLEL |
---|
| 702 | |
---|
| 703 | ENDIF |
---|
[1106] | 704 | CALL cpu_log( log_point_s(7), 'fft_y_1d', 'pause' ) |
---|
[1] | 705 | |
---|
| 706 | ! |
---|
| 707 | !-- Transpose array |
---|
| 708 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 709 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 710 | CALL MPI_ALLTOALL( work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 711 | f_out(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 712 | comm1dx, ierr ) |
---|
| 713 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 714 | |
---|
| 715 | END SUBROUTINE ffty_tr_yx |
---|
| 716 | |
---|
| 717 | |
---|
| 718 | SUBROUTINE tr_xy_ffty( f_in, work, f_out ) |
---|
| 719 | |
---|
| 720 | !------------------------------------------------------------------------------! |
---|
| 721 | ! Transposition x --> y with a subsequent backward Fourier transformation for |
---|
| 722 | ! a 1d-decomposition along x |
---|
| 723 | !------------------------------------------------------------------------------! |
---|
| 724 | |
---|
| 725 | USE control_parameters |
---|
| 726 | USE cpulog |
---|
| 727 | USE indices |
---|
| 728 | USE interfaces |
---|
| 729 | USE pegrid |
---|
| 730 | USE transpose_indices |
---|
| 731 | |
---|
| 732 | IMPLICIT NONE |
---|
| 733 | |
---|
| 734 | INTEGER :: i, iend, iouter, ir, j, k |
---|
| 735 | INTEGER, PARAMETER :: stridex = 4 |
---|
| 736 | |
---|
| 737 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
| 738 | #if defined( __nec ) |
---|
| 739 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
| 740 | #endif |
---|
[1003] | 741 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: f_in |
---|
| 742 | REAL, DIMENSION(1:nz,0:ny,nxl:nxr) :: f_out |
---|
| 743 | REAL, DIMENSION(nxl:nxr,1:nz,0:ny) :: work |
---|
[1] | 744 | |
---|
| 745 | ! |
---|
| 746 | !-- Transpose array |
---|
| 747 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 748 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 749 | CALL MPI_ALLTOALL( f_in(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 750 | work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 751 | comm1dx, ierr ) |
---|
| 752 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 753 | |
---|
| 754 | ! |
---|
| 755 | !-- Resort the data in a way that y becomes the first index and carry out the |
---|
| 756 | !-- backward fft along y. |
---|
[1106] | 757 | CALL cpu_log( log_point_s(7), 'fft_y_1d', 'continue' ) |
---|
[1] | 758 | |
---|
| 759 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 760 | #if defined( __nec ) |
---|
| 761 | ! |
---|
| 762 | !-- Code optimized for vector processors |
---|
[85] | 763 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 764 | !$OMP DO |
---|
| 765 | DO k = 1, nz |
---|
| 766 | DO j = 0, ny |
---|
| 767 | DO i = nxl, nxr |
---|
| 768 | work_ffty_vec(j,k,i) = work(i,k,j) |
---|
| 769 | ENDDO |
---|
| 770 | ENDDO |
---|
| 771 | ENDDO |
---|
| 772 | |
---|
| 773 | !$OMP DO |
---|
| 774 | DO i = nxl, nxr |
---|
| 775 | |
---|
| 776 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'backward' ) |
---|
| 777 | |
---|
| 778 | DO j = 0, ny |
---|
| 779 | DO k = 1, nz |
---|
| 780 | f_out(k,j,i) = work_ffty_vec(j,k,i) |
---|
| 781 | ENDDO |
---|
| 782 | ENDDO |
---|
| 783 | |
---|
| 784 | ENDDO |
---|
| 785 | !$OMP END PARALLEL |
---|
| 786 | #endif |
---|
| 787 | |
---|
| 788 | ELSE |
---|
| 789 | |
---|
| 790 | ! |
---|
| 791 | !-- Cache optimized code. |
---|
| 792 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
| 793 | !-- loop for better cache performance |
---|
| 794 | !$OMP PARALLEL PRIVATE ( i, iend, iouter, ir, j, k, work_ffty ) |
---|
| 795 | !$OMP DO |
---|
| 796 | DO iouter = nxl, nxr, stridex |
---|
| 797 | |
---|
| 798 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
| 799 | |
---|
| 800 | DO k = 1, nz |
---|
| 801 | ! |
---|
| 802 | !-- Resort |
---|
| 803 | DO j = 0, ny |
---|
| 804 | DO i = iouter, iend |
---|
| 805 | work_ffty(j,i-iouter+1) = work(i,k,j) |
---|
| 806 | ENDDO |
---|
| 807 | ENDDO |
---|
| 808 | |
---|
| 809 | DO i = iouter, iend |
---|
| 810 | |
---|
| 811 | ! |
---|
| 812 | !-- FFT along y |
---|
| 813 | ir = i-iouter+1 ! counter within a stride |
---|
[1106] | 814 | CALL fft_y_1d( work_ffty(:,ir), 'backward' ) |
---|
[1] | 815 | |
---|
| 816 | DO j = 0, ny |
---|
| 817 | f_out(k,j,i) = work_ffty(j,ir) |
---|
| 818 | ENDDO |
---|
| 819 | ENDDO |
---|
| 820 | |
---|
| 821 | ENDDO |
---|
| 822 | |
---|
| 823 | ENDDO |
---|
| 824 | !$OMP END PARALLEL |
---|
| 825 | |
---|
| 826 | ENDIF |
---|
| 827 | |
---|
[1106] | 828 | CALL cpu_log( log_point_s(7), 'fft_y_1d', 'stop' ) |
---|
[1] | 829 | |
---|
| 830 | END SUBROUTINE tr_xy_ffty |
---|
| 831 | |
---|
| 832 | |
---|
| 833 | SUBROUTINE fftx_tri_fftx( ar ) |
---|
| 834 | |
---|
| 835 | !------------------------------------------------------------------------------! |
---|
| 836 | ! FFT along x, solution of the tridiagonal system and backward FFT for |
---|
| 837 | ! a 1d-decomposition along x |
---|
| 838 | ! |
---|
| 839 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
| 840 | ! with OpenMP (for possible necessary changes see the original |
---|
| 841 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
| 842 | !------------------------------------------------------------------------------! |
---|
| 843 | |
---|
| 844 | USE control_parameters |
---|
| 845 | USE cpulog |
---|
| 846 | USE grid_variables |
---|
| 847 | USE indices |
---|
| 848 | USE interfaces |
---|
| 849 | USE pegrid |
---|
| 850 | USE transpose_indices |
---|
| 851 | |
---|
| 852 | IMPLICIT NONE |
---|
| 853 | |
---|
| 854 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
| 855 | |
---|
[1003] | 856 | REAL, DIMENSION(0:nx) :: work_fftx |
---|
| 857 | REAL, DIMENSION(0:nx,1:nz) :: work_trix |
---|
| 858 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: ar |
---|
| 859 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
[1] | 860 | |
---|
| 861 | |
---|
[1106] | 862 | CALL cpu_log( log_point_s(33), 'fft_x_1d + tridia', 'start' ) |
---|
[1] | 863 | |
---|
| 864 | ALLOCATE( tri(5,0:nx,0:nz-1,0:threads_per_task-1) ) |
---|
| 865 | |
---|
| 866 | tn = 0 ! Default thread number in case of one thread |
---|
| 867 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_fftx, work_trix ) |
---|
| 868 | DO j = nys_x, nyn_x |
---|
| 869 | |
---|
| 870 | !$ tn = omp_get_thread_num() |
---|
| 871 | |
---|
| 872 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 873 | ! |
---|
| 874 | !-- Code optimized for vector processors |
---|
| 875 | DO k = 1, nz |
---|
| 876 | |
---|
| 877 | m = 0 |
---|
| 878 | DO n = 1, pdims(1) |
---|
[1003] | 879 | DO i = 1, nnx |
---|
[1] | 880 | work_trix(m,k) = ar(i,k,j,n) |
---|
| 881 | m = m + 1 |
---|
| 882 | ENDDO |
---|
| 883 | ENDDO |
---|
| 884 | |
---|
| 885 | ENDDO |
---|
| 886 | |
---|
| 887 | CALL fft_x_m( work_trix, 'forward' ) |
---|
| 888 | |
---|
| 889 | ELSE |
---|
| 890 | ! |
---|
| 891 | !-- Cache optimized code |
---|
| 892 | DO k = 1, nz |
---|
| 893 | |
---|
| 894 | m = 0 |
---|
| 895 | DO n = 1, pdims(1) |
---|
[1003] | 896 | DO i = 1, nnx |
---|
[1] | 897 | work_fftx(m) = ar(i,k,j,n) |
---|
| 898 | m = m + 1 |
---|
| 899 | ENDDO |
---|
| 900 | ENDDO |
---|
| 901 | |
---|
[1106] | 902 | CALL fft_x_1d( work_fftx, 'forward' ) |
---|
[1] | 903 | |
---|
| 904 | DO i = 0, nx |
---|
| 905 | work_trix(i,k) = work_fftx(i) |
---|
| 906 | ENDDO |
---|
| 907 | |
---|
| 908 | ENDDO |
---|
| 909 | |
---|
| 910 | ENDIF |
---|
| 911 | |
---|
| 912 | ! |
---|
| 913 | !-- Solve the linear equation system |
---|
| 914 | CALL tridia_1dd( ddx2, ddy2, nx, ny, j, work_trix, tri(:,:,:,tn) ) |
---|
| 915 | |
---|
| 916 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 917 | ! |
---|
| 918 | !-- Code optimized for vector processors |
---|
| 919 | CALL fft_x_m( work_trix, 'backward' ) |
---|
| 920 | |
---|
| 921 | DO k = 1, nz |
---|
| 922 | |
---|
| 923 | m = 0 |
---|
| 924 | DO n = 1, pdims(1) |
---|
[1003] | 925 | DO i = 1, nnx |
---|
[1] | 926 | ar(i,k,j,n) = work_trix(m,k) |
---|
| 927 | m = m + 1 |
---|
| 928 | ENDDO |
---|
| 929 | ENDDO |
---|
| 930 | |
---|
| 931 | ENDDO |
---|
| 932 | |
---|
| 933 | ELSE |
---|
| 934 | ! |
---|
| 935 | !-- Cache optimized code |
---|
| 936 | DO k = 1, nz |
---|
| 937 | |
---|
| 938 | DO i = 0, nx |
---|
| 939 | work_fftx(i) = work_trix(i,k) |
---|
| 940 | ENDDO |
---|
| 941 | |
---|
[1106] | 942 | CALL fft_x_1d( work_fftx, 'backward' ) |
---|
[1] | 943 | |
---|
| 944 | m = 0 |
---|
| 945 | DO n = 1, pdims(1) |
---|
[1003] | 946 | DO i = 1, nnx |
---|
[1] | 947 | ar(i,k,j,n) = work_fftx(m) |
---|
| 948 | m = m + 1 |
---|
| 949 | ENDDO |
---|
| 950 | ENDDO |
---|
| 951 | |
---|
| 952 | ENDDO |
---|
| 953 | |
---|
| 954 | ENDIF |
---|
| 955 | |
---|
| 956 | ENDDO |
---|
| 957 | |
---|
| 958 | DEALLOCATE( tri ) |
---|
| 959 | |
---|
[1106] | 960 | CALL cpu_log( log_point_s(33), 'fft_x_1d + tridia', 'stop' ) |
---|
[1] | 961 | |
---|
| 962 | END SUBROUTINE fftx_tri_fftx |
---|
| 963 | |
---|
| 964 | |
---|
| 965 | SUBROUTINE fftx_tr_xy( f_in, work, f_out ) |
---|
| 966 | |
---|
| 967 | !------------------------------------------------------------------------------! |
---|
| 968 | ! Fourier-transformation along x with subsequent transposition x --> y for |
---|
| 969 | ! a 1d-decomposition along y |
---|
| 970 | ! |
---|
| 971 | ! ATTENTION: The NEC-branch of this routine may significantly profit from |
---|
| 972 | ! further optimizations. So far, performance is much worse than |
---|
| 973 | ! for routine ffty_tr_yx (more than three times slower). |
---|
| 974 | !------------------------------------------------------------------------------! |
---|
| 975 | |
---|
| 976 | USE control_parameters |
---|
| 977 | USE cpulog |
---|
| 978 | USE indices |
---|
| 979 | USE interfaces |
---|
| 980 | USE pegrid |
---|
| 981 | USE transpose_indices |
---|
| 982 | |
---|
| 983 | IMPLICIT NONE |
---|
| 984 | |
---|
| 985 | INTEGER :: i, j, k |
---|
| 986 | |
---|
[1003] | 987 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
| 988 | REAL, DIMENSION(1:nz,nys:nyn,0:nx) :: f_in |
---|
| 989 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: f_out |
---|
| 990 | REAL, DIMENSION(nys:nyn,1:nz,0:nx) :: work |
---|
[1] | 991 | |
---|
| 992 | ! |
---|
| 993 | !-- Carry out the FFT along x, where all data are present due to the |
---|
| 994 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
| 995 | !-- the first index. |
---|
[1106] | 996 | CALL cpu_log( log_point_s(4), 'fft_x_1d', 'start' ) |
---|
[1] | 997 | |
---|
| 998 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 999 | ! |
---|
| 1000 | !-- Code for vector processors |
---|
[85] | 1001 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 1002 | !$OMP DO |
---|
| 1003 | DO i = 0, nx |
---|
| 1004 | |
---|
| 1005 | DO j = nys, nyn |
---|
| 1006 | DO k = 1, nz |
---|
| 1007 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
| 1008 | ENDDO |
---|
| 1009 | ENDDO |
---|
| 1010 | |
---|
| 1011 | ENDDO |
---|
| 1012 | |
---|
| 1013 | !$OMP DO |
---|
| 1014 | DO j = nys, nyn |
---|
| 1015 | |
---|
| 1016 | CALL fft_x_m( work_fftx(:,:,j), 'forward' ) |
---|
| 1017 | |
---|
| 1018 | DO k = 1, nz |
---|
| 1019 | DO i = 0, nx |
---|
| 1020 | work(j,k,i) = work_fftx(i,k,j) |
---|
| 1021 | ENDDO |
---|
| 1022 | ENDDO |
---|
| 1023 | |
---|
| 1024 | ENDDO |
---|
| 1025 | !$OMP END PARALLEL |
---|
| 1026 | |
---|
| 1027 | ELSE |
---|
| 1028 | |
---|
| 1029 | ! |
---|
| 1030 | !-- Cache optimized code (there might be still a potential for better |
---|
| 1031 | !-- optimization). |
---|
[696] | 1032 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
[1] | 1033 | !$OMP DO |
---|
| 1034 | DO i = 0, nx |
---|
| 1035 | |
---|
| 1036 | DO j = nys, nyn |
---|
| 1037 | DO k = 1, nz |
---|
| 1038 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
| 1039 | ENDDO |
---|
| 1040 | ENDDO |
---|
| 1041 | |
---|
| 1042 | ENDDO |
---|
| 1043 | |
---|
| 1044 | !$OMP DO |
---|
| 1045 | DO j = nys, nyn |
---|
| 1046 | DO k = 1, nz |
---|
| 1047 | |
---|
[1106] | 1048 | CALL fft_x_1d( work_fftx(0:nx,k,j), 'forward' ) |
---|
[1] | 1049 | |
---|
| 1050 | DO i = 0, nx |
---|
| 1051 | work(j,k,i) = work_fftx(i,k,j) |
---|
| 1052 | ENDDO |
---|
| 1053 | ENDDO |
---|
| 1054 | |
---|
| 1055 | ENDDO |
---|
| 1056 | !$OMP END PARALLEL |
---|
| 1057 | |
---|
| 1058 | ENDIF |
---|
[1106] | 1059 | CALL cpu_log( log_point_s(4), 'fft_x_1d', 'pause' ) |
---|
[1] | 1060 | |
---|
| 1061 | ! |
---|
| 1062 | !-- Transpose array |
---|
| 1063 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 1064 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 1065 | CALL MPI_ALLTOALL( work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 1066 | f_out(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 1067 | comm1dy, ierr ) |
---|
| 1068 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 1069 | |
---|
| 1070 | END SUBROUTINE fftx_tr_xy |
---|
| 1071 | |
---|
| 1072 | |
---|
| 1073 | SUBROUTINE tr_yx_fftx( f_in, work, f_out ) |
---|
| 1074 | |
---|
| 1075 | !------------------------------------------------------------------------------! |
---|
| 1076 | ! Transposition y --> x with a subsequent backward Fourier transformation for |
---|
| 1077 | ! a 1d-decomposition along x |
---|
| 1078 | !------------------------------------------------------------------------------! |
---|
| 1079 | |
---|
| 1080 | USE control_parameters |
---|
| 1081 | USE cpulog |
---|
| 1082 | USE indices |
---|
| 1083 | USE interfaces |
---|
| 1084 | USE pegrid |
---|
| 1085 | USE transpose_indices |
---|
| 1086 | |
---|
| 1087 | IMPLICIT NONE |
---|
| 1088 | |
---|
| 1089 | INTEGER :: i, j, k |
---|
| 1090 | |
---|
[1003] | 1091 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
| 1092 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: f_in |
---|
| 1093 | REAL, DIMENSION(1:nz,nys:nyn,0:nx) :: f_out |
---|
| 1094 | REAL, DIMENSION(nys:nyn,1:nz,0:nx) :: work |
---|
[1] | 1095 | |
---|
| 1096 | ! |
---|
| 1097 | !-- Transpose array |
---|
| 1098 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 1099 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 1100 | CALL MPI_ALLTOALL( f_in(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 1101 | work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 1102 | comm1dy, ierr ) |
---|
| 1103 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 1104 | |
---|
| 1105 | ! |
---|
| 1106 | !-- Carry out the FFT along x, where all data are present due to the |
---|
| 1107 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
| 1108 | !-- the first index. |
---|
[1106] | 1109 | CALL cpu_log( log_point_s(4), 'fft_x_1d', 'continue' ) |
---|
[1] | 1110 | |
---|
| 1111 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1112 | ! |
---|
| 1113 | !-- Code optimized for vector processors |
---|
[85] | 1114 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 1115 | !$OMP DO |
---|
| 1116 | DO j = nys, nyn |
---|
| 1117 | |
---|
| 1118 | DO k = 1, nz |
---|
| 1119 | DO i = 0, nx |
---|
| 1120 | work_fftx(i,k,j) = work(j,k,i) |
---|
| 1121 | ENDDO |
---|
| 1122 | ENDDO |
---|
| 1123 | |
---|
| 1124 | CALL fft_x_m( work_fftx(:,:,j), 'backward' ) |
---|
| 1125 | |
---|
| 1126 | ENDDO |
---|
| 1127 | |
---|
| 1128 | !$OMP DO |
---|
| 1129 | DO i = 0, nx |
---|
| 1130 | DO j = nys, nyn |
---|
| 1131 | DO k = 1, nz |
---|
| 1132 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
| 1133 | ENDDO |
---|
| 1134 | ENDDO |
---|
| 1135 | ENDDO |
---|
| 1136 | !$OMP END PARALLEL |
---|
| 1137 | |
---|
| 1138 | ELSE |
---|
| 1139 | |
---|
| 1140 | ! |
---|
| 1141 | !-- Cache optimized code (there might be still a potential for better |
---|
| 1142 | !-- optimization). |
---|
[696] | 1143 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
[1] | 1144 | !$OMP DO |
---|
| 1145 | DO j = nys, nyn |
---|
| 1146 | DO k = 1, nz |
---|
| 1147 | |
---|
| 1148 | DO i = 0, nx |
---|
| 1149 | work_fftx(i,k,j) = work(j,k,i) |
---|
| 1150 | ENDDO |
---|
| 1151 | |
---|
[1106] | 1152 | CALL fft_x_1d( work_fftx(0:nx,k,j), 'backward' ) |
---|
[1] | 1153 | |
---|
| 1154 | ENDDO |
---|
| 1155 | ENDDO |
---|
| 1156 | |
---|
| 1157 | !$OMP DO |
---|
| 1158 | DO i = 0, nx |
---|
| 1159 | DO j = nys, nyn |
---|
| 1160 | DO k = 1, nz |
---|
| 1161 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
| 1162 | ENDDO |
---|
| 1163 | ENDDO |
---|
| 1164 | ENDDO |
---|
| 1165 | !$OMP END PARALLEL |
---|
| 1166 | |
---|
| 1167 | ENDIF |
---|
[1106] | 1168 | CALL cpu_log( log_point_s(4), 'fft_x_1d', 'stop' ) |
---|
[1] | 1169 | |
---|
| 1170 | END SUBROUTINE tr_yx_fftx |
---|
| 1171 | |
---|
| 1172 | |
---|
| 1173 | SUBROUTINE ffty_tri_ffty( ar ) |
---|
| 1174 | |
---|
| 1175 | !------------------------------------------------------------------------------! |
---|
| 1176 | ! FFT along y, solution of the tridiagonal system and backward FFT for |
---|
| 1177 | ! a 1d-decomposition along y |
---|
| 1178 | ! |
---|
| 1179 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
| 1180 | ! with OpenMP (for possible necessary changes see the original |
---|
| 1181 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
| 1182 | !------------------------------------------------------------------------------! |
---|
| 1183 | |
---|
| 1184 | USE control_parameters |
---|
| 1185 | USE cpulog |
---|
| 1186 | USE grid_variables |
---|
| 1187 | USE indices |
---|
| 1188 | USE interfaces |
---|
| 1189 | USE pegrid |
---|
| 1190 | USE transpose_indices |
---|
| 1191 | |
---|
| 1192 | IMPLICIT NONE |
---|
| 1193 | |
---|
| 1194 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
| 1195 | |
---|
[1003] | 1196 | REAL, DIMENSION(0:ny) :: work_ffty |
---|
| 1197 | REAL, DIMENSION(0:ny,1:nz) :: work_triy |
---|
| 1198 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: ar |
---|
| 1199 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
[1] | 1200 | |
---|
| 1201 | |
---|
[1106] | 1202 | CALL cpu_log( log_point_s(39), 'fft_y_1d + tridia', 'start' ) |
---|
[1] | 1203 | |
---|
| 1204 | ALLOCATE( tri(5,0:ny,0:nz-1,0:threads_per_task-1) ) |
---|
| 1205 | |
---|
| 1206 | tn = 0 ! Default thread number in case of one thread |
---|
[696] | 1207 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_ffty, work_triy ) |
---|
[1] | 1208 | DO i = nxl_y, nxr_y |
---|
| 1209 | |
---|
| 1210 | !$ tn = omp_get_thread_num() |
---|
| 1211 | |
---|
| 1212 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1213 | ! |
---|
| 1214 | !-- Code optimized for vector processors |
---|
| 1215 | DO k = 1, nz |
---|
| 1216 | |
---|
| 1217 | m = 0 |
---|
| 1218 | DO n = 1, pdims(2) |
---|
[1003] | 1219 | DO j = 1, nny |
---|
[1] | 1220 | work_triy(m,k) = ar(j,k,i,n) |
---|
| 1221 | m = m + 1 |
---|
| 1222 | ENDDO |
---|
| 1223 | ENDDO |
---|
| 1224 | |
---|
| 1225 | ENDDO |
---|
| 1226 | |
---|
| 1227 | CALL fft_y_m( work_triy, ny, 'forward' ) |
---|
| 1228 | |
---|
| 1229 | ELSE |
---|
| 1230 | ! |
---|
| 1231 | !-- Cache optimized code |
---|
| 1232 | DO k = 1, nz |
---|
| 1233 | |
---|
| 1234 | m = 0 |
---|
| 1235 | DO n = 1, pdims(2) |
---|
[1003] | 1236 | DO j = 1, nny |
---|
[1] | 1237 | work_ffty(m) = ar(j,k,i,n) |
---|
| 1238 | m = m + 1 |
---|
| 1239 | ENDDO |
---|
| 1240 | ENDDO |
---|
| 1241 | |
---|
[1106] | 1242 | CALL fft_y_1d( work_ffty, 'forward' ) |
---|
[1] | 1243 | |
---|
| 1244 | DO j = 0, ny |
---|
| 1245 | work_triy(j,k) = work_ffty(j) |
---|
| 1246 | ENDDO |
---|
| 1247 | |
---|
| 1248 | ENDDO |
---|
| 1249 | |
---|
| 1250 | ENDIF |
---|
| 1251 | |
---|
| 1252 | ! |
---|
| 1253 | !-- Solve the linear equation system |
---|
| 1254 | CALL tridia_1dd( ddy2, ddx2, ny, nx, i, work_triy, tri(:,:,:,tn) ) |
---|
| 1255 | |
---|
| 1256 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1257 | ! |
---|
| 1258 | !-- Code optimized for vector processors |
---|
| 1259 | CALL fft_y_m( work_triy, ny, 'backward' ) |
---|
| 1260 | |
---|
| 1261 | DO k = 1, nz |
---|
| 1262 | |
---|
| 1263 | m = 0 |
---|
| 1264 | DO n = 1, pdims(2) |
---|
[1003] | 1265 | DO j = 1, nny |
---|
[1] | 1266 | ar(j,k,i,n) = work_triy(m,k) |
---|
| 1267 | m = m + 1 |
---|
| 1268 | ENDDO |
---|
| 1269 | ENDDO |
---|
| 1270 | |
---|
| 1271 | ENDDO |
---|
| 1272 | |
---|
| 1273 | ELSE |
---|
| 1274 | ! |
---|
| 1275 | !-- Cache optimized code |
---|
| 1276 | DO k = 1, nz |
---|
| 1277 | |
---|
| 1278 | DO j = 0, ny |
---|
| 1279 | work_ffty(j) = work_triy(j,k) |
---|
| 1280 | ENDDO |
---|
| 1281 | |
---|
[1106] | 1282 | CALL fft_y_1d( work_ffty, 'backward' ) |
---|
[1] | 1283 | |
---|
| 1284 | m = 0 |
---|
| 1285 | DO n = 1, pdims(2) |
---|
[1003] | 1286 | DO j = 1, nny |
---|
[1] | 1287 | ar(j,k,i,n) = work_ffty(m) |
---|
| 1288 | m = m + 1 |
---|
| 1289 | ENDDO |
---|
| 1290 | ENDDO |
---|
| 1291 | |
---|
| 1292 | ENDDO |
---|
| 1293 | |
---|
| 1294 | ENDIF |
---|
| 1295 | |
---|
| 1296 | ENDDO |
---|
| 1297 | |
---|
| 1298 | DEALLOCATE( tri ) |
---|
| 1299 | |
---|
[1106] | 1300 | CALL cpu_log( log_point_s(39), 'fft_y_1d + tridia', 'stop' ) |
---|
[1] | 1301 | |
---|
| 1302 | END SUBROUTINE ffty_tri_ffty |
---|
| 1303 | |
---|
| 1304 | |
---|
| 1305 | SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri ) |
---|
| 1306 | |
---|
| 1307 | !------------------------------------------------------------------------------! |
---|
| 1308 | ! Solves the linear system of equations for a 1d-decomposition along x (see |
---|
| 1309 | ! tridia) |
---|
| 1310 | ! |
---|
[940] | 1311 | ! Attention: when using the intel compilers older than 12.0, array tri must |
---|
| 1312 | ! be passed as an argument to the contained subroutines. Otherwise |
---|
| 1313 | ! addres faults will occur. This feature can be activated with |
---|
| 1314 | ! cpp-switch __intel11 |
---|
[1] | 1315 | ! On NEC, tri should not be passed (except for routine substi_1dd) |
---|
| 1316 | ! because this causes very bad performance. |
---|
| 1317 | !------------------------------------------------------------------------------! |
---|
| 1318 | |
---|
| 1319 | USE arrays_3d |
---|
| 1320 | USE control_parameters |
---|
| 1321 | |
---|
| 1322 | USE pegrid |
---|
| 1323 | |
---|
| 1324 | IMPLICIT NONE |
---|
| 1325 | |
---|
| 1326 | INTEGER :: i, j, k, nnyh, nx, ny, omp_get_thread_num, tn |
---|
| 1327 | |
---|
| 1328 | REAL :: ddx2, ddy2 |
---|
| 1329 | |
---|
| 1330 | REAL, DIMENSION(0:nx,1:nz) :: ar |
---|
| 1331 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1332 | |
---|
| 1333 | |
---|
| 1334 | nnyh = ( ny + 1 ) / 2 |
---|
| 1335 | |
---|
| 1336 | ! |
---|
| 1337 | !-- Define constant elements of the tridiagonal matrix. |
---|
| 1338 | !-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2, |
---|
| 1339 | !-- the exchanged loops create bank conflicts. The following directive |
---|
| 1340 | !-- prohibits loop exchange and the loops perform much better. |
---|
| 1341 | ! tn = omp_get_thread_num() |
---|
| 1342 | ! WRITE( 120+tn, * ) '+++ id=',myid,' nx=',nx,' thread=', omp_get_thread_num() |
---|
[82] | 1343 | ! CALL local_flush( 120+tn ) |
---|
[1] | 1344 | !CDIR NOLOOPCHG |
---|
| 1345 | DO k = 0, nz-1 |
---|
| 1346 | DO i = 0,nx |
---|
[667] | 1347 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
---|
| 1348 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
---|
[1] | 1349 | ENDDO |
---|
| 1350 | ENDDO |
---|
| 1351 | ! WRITE( 120+tn, * ) '+++ id=',myid,' end of first tridia loop thread=', omp_get_thread_num() |
---|
[82] | 1352 | ! CALL local_flush( 120+tn ) |
---|
[1] | 1353 | |
---|
| 1354 | IF ( j <= nnyh ) THEN |
---|
[940] | 1355 | #if defined( __intel11 ) |
---|
[1] | 1356 | CALL maketri_1dd( j, tri ) |
---|
| 1357 | #else |
---|
| 1358 | CALL maketri_1dd( j ) |
---|
| 1359 | #endif |
---|
| 1360 | ELSE |
---|
[940] | 1361 | #if defined( __intel11 ) |
---|
[1] | 1362 | CALL maketri_1dd( ny+1-j, tri ) |
---|
| 1363 | #else |
---|
| 1364 | CALL maketri_1dd( ny+1-j ) |
---|
| 1365 | #endif |
---|
| 1366 | ENDIF |
---|
[940] | 1367 | #if defined( __intel11 ) |
---|
[1] | 1368 | CALL split_1dd( tri ) |
---|
| 1369 | #else |
---|
| 1370 | CALL split_1dd |
---|
| 1371 | #endif |
---|
| 1372 | CALL substi_1dd( ar, tri ) |
---|
| 1373 | |
---|
| 1374 | CONTAINS |
---|
| 1375 | |
---|
[940] | 1376 | #if defined( __intel11 ) |
---|
[1] | 1377 | SUBROUTINE maketri_1dd( j, tri ) |
---|
| 1378 | #else |
---|
| 1379 | SUBROUTINE maketri_1dd( j ) |
---|
| 1380 | #endif |
---|
| 1381 | |
---|
| 1382 | !------------------------------------------------------------------------------! |
---|
| 1383 | ! computes the i- and j-dependent component of the matrix |
---|
| 1384 | !------------------------------------------------------------------------------! |
---|
| 1385 | |
---|
| 1386 | USE constants |
---|
| 1387 | |
---|
| 1388 | IMPLICIT NONE |
---|
| 1389 | |
---|
| 1390 | INTEGER :: i, j, k, nnxh |
---|
| 1391 | REAL :: a, c |
---|
| 1392 | |
---|
| 1393 | REAL, DIMENSION(0:nx) :: l |
---|
| 1394 | |
---|
[940] | 1395 | #if defined( __intel11 ) |
---|
[1] | 1396 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1397 | #endif |
---|
| 1398 | |
---|
| 1399 | |
---|
| 1400 | nnxh = ( nx + 1 ) / 2 |
---|
| 1401 | ! |
---|
| 1402 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
---|
| 1403 | !-- Fourier space. The coefficients are computed following the method of |
---|
| 1404 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
---|
| 1405 | !-- Siano's original version by discretizing the Poisson equation, |
---|
| 1406 | !-- before it is Fourier-transformed |
---|
| 1407 | DO i = 0, nx |
---|
[128] | 1408 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
---|
[1] | 1409 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
---|
[1013] | 1410 | REAL( nx+1 ) ) ) * ddx2 + & |
---|
[1] | 1411 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
[1013] | 1412 | REAL( ny+1 ) ) ) * ddy2 |
---|
[1] | 1413 | ELSE |
---|
| 1414 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
[1013] | 1415 | REAL( nx+1 ) ) ) * ddx2 + & |
---|
[1] | 1416 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
[1013] | 1417 | REAL( ny+1 ) ) ) * ddy2 |
---|
[1] | 1418 | ENDIF |
---|
| 1419 | ENDDO |
---|
| 1420 | |
---|
| 1421 | DO k = 0, nz-1 |
---|
| 1422 | DO i = 0, nx |
---|
[667] | 1423 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
| 1424 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
[1] | 1425 | tri(1,i,k) = a + c - l(i) |
---|
| 1426 | ENDDO |
---|
| 1427 | ENDDO |
---|
| 1428 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
| 1429 | DO i = 0, nx |
---|
| 1430 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
| 1431 | ENDDO |
---|
| 1432 | ENDIF |
---|
| 1433 | IF ( ibc_p_t == 1 ) THEN |
---|
| 1434 | DO i = 0, nx |
---|
| 1435 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
| 1436 | ENDDO |
---|
| 1437 | ENDIF |
---|
| 1438 | |
---|
| 1439 | END SUBROUTINE maketri_1dd |
---|
| 1440 | |
---|
| 1441 | |
---|
[940] | 1442 | #if defined( __intel11 ) |
---|
[1] | 1443 | SUBROUTINE split_1dd( tri ) |
---|
| 1444 | #else |
---|
| 1445 | SUBROUTINE split_1dd |
---|
| 1446 | #endif |
---|
| 1447 | |
---|
| 1448 | !------------------------------------------------------------------------------! |
---|
| 1449 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
| 1450 | !------------------------------------------------------------------------------! |
---|
| 1451 | |
---|
| 1452 | IMPLICIT NONE |
---|
| 1453 | |
---|
| 1454 | INTEGER :: i, k |
---|
| 1455 | |
---|
[940] | 1456 | #if defined( __intel11 ) |
---|
[1] | 1457 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1458 | #endif |
---|
| 1459 | |
---|
| 1460 | |
---|
| 1461 | ! |
---|
| 1462 | !-- Splitting |
---|
| 1463 | DO i = 0, nx |
---|
| 1464 | tri(4,i,0) = tri(1,i,0) |
---|
| 1465 | ENDDO |
---|
| 1466 | DO k = 1, nz-1 |
---|
| 1467 | DO i = 0, nx |
---|
| 1468 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
| 1469 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
| 1470 | ENDDO |
---|
| 1471 | ENDDO |
---|
| 1472 | |
---|
| 1473 | END SUBROUTINE split_1dd |
---|
| 1474 | |
---|
| 1475 | |
---|
| 1476 | SUBROUTINE substi_1dd( ar, tri ) |
---|
| 1477 | |
---|
| 1478 | !------------------------------------------------------------------------------! |
---|
| 1479 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
| 1480 | !------------------------------------------------------------------------------! |
---|
| 1481 | |
---|
| 1482 | IMPLICIT NONE |
---|
| 1483 | |
---|
[76] | 1484 | INTEGER :: i, k |
---|
[1] | 1485 | |
---|
| 1486 | REAL, DIMENSION(0:nx,nz) :: ar |
---|
| 1487 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
| 1488 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1489 | |
---|
| 1490 | ! |
---|
| 1491 | !-- Forward substitution |
---|
| 1492 | DO i = 0, nx |
---|
| 1493 | ar1(i,0) = ar(i,1) |
---|
| 1494 | ENDDO |
---|
| 1495 | DO k = 1, nz-1 |
---|
| 1496 | DO i = 0, nx |
---|
| 1497 | ar1(i,k) = ar(i,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
| 1498 | ENDDO |
---|
| 1499 | ENDDO |
---|
| 1500 | |
---|
| 1501 | ! |
---|
| 1502 | !-- Backward substitution |
---|
[763] | 1503 | !-- Note, the add of 1.0E-20 in the denominator is due to avoid divisions |
---|
| 1504 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
| 1505 | !-- the model domain. |
---|
[1] | 1506 | DO i = 0, nx |
---|
[761] | 1507 | ar(i,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
[1] | 1508 | ENDDO |
---|
| 1509 | DO k = nz-2, 0, -1 |
---|
| 1510 | DO i = 0, nx |
---|
| 1511 | ar(i,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,k+2) ) & |
---|
| 1512 | / tri(4,i,k) |
---|
| 1513 | ENDDO |
---|
| 1514 | ENDDO |
---|
| 1515 | |
---|
[76] | 1516 | ! |
---|
| 1517 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
| 1518 | !-- The respective values of ar should be zero at all k-levels if |
---|
| 1519 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
| 1520 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
| 1521 | IF ( j == 0 ) THEN |
---|
| 1522 | DO k = 1, nz |
---|
| 1523 | ar(0,k) = 0.0 |
---|
| 1524 | ENDDO |
---|
| 1525 | ENDIF |
---|
| 1526 | ENDIF |
---|
| 1527 | |
---|
[1] | 1528 | END SUBROUTINE substi_1dd |
---|
| 1529 | |
---|
| 1530 | END SUBROUTINE tridia_1dd |
---|
| 1531 | |
---|
| 1532 | #endif |
---|
[807] | 1533 | #endif |
---|
[1] | 1534 | END MODULE poisfft_mod |
---|