[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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[1093] | 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 1093 2013-02-02 12:58:49Z raasch $ |
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[77] | 27 | ! |
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[1093] | 28 | ! 1092 2013-02-02 11:24:22Z raasch |
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| 29 | ! unused variables removed |
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| 30 | ! |
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[1037] | 31 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 32 | ! code put under GPL (PALM 3.9) |
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| 33 | ! |
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[1014] | 34 | ! 2012-09-21 07:03:55Z raasch |
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| 35 | ! FLOAT type conversion replaced by REAL |
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| 36 | ! |
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[1004] | 37 | ! 1003 2012-09-14 14:35:53Z raasch |
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| 38 | ! indices nxa, nya, etc. replaced by nx, ny, etc. |
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| 39 | ! |
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[941] | 40 | ! 940 2012-07-09 14:31:00Z raasch |
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| 41 | ! special handling of tri-array as an argument in tridia_1dd routines switched |
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| 42 | ! off because it caused segmentation faults with intel 12.1 compiler |
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| 43 | ! |
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[878] | 44 | ! 877 2012-04-03 11:21:44Z suehring |
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| 45 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
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| 46 | ! pressure at the top of the model domain. |
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| 47 | ! |
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[810] | 48 | ! 809 2012-01-30 13:32:58Z maronga |
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| 49 | ! Bugfix: replaced .AND. and .NOT. with && and ! in the preprocessor directives |
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| 50 | ! |
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[808] | 51 | ! 807 2012-01-25 11:53:51Z maronga |
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| 52 | ! New cpp directive "__check" implemented which is used by check_namelist_files |
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| 53 | ! (most of the code is unneeded by check_namelist_files). |
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| 54 | ! |
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[764] | 55 | ! 763 2011-10-06 09:32:09Z suehring |
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| 56 | ! Comment added concerning the last change. |
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| 57 | ! |
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[762] | 58 | ! 761 2011-10-05 17:58:52Z suehring |
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| 59 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
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| 60 | ! pressure at the top of the model domain. |
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| 61 | ! |
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[697] | 62 | ! 696 2011-03-18 07:03:49Z raasch |
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| 63 | ! work_fftx removed from PRIVATE clauses in fftx_tr_xy and tr_yx_fftx |
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| 64 | ! |
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[684] | 65 | ! 683 2011-02-09 14:25:15Z raasch |
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| 66 | ! openMP parallelization for 2d-domain-decomposition |
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| 67 | ! |
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[668] | 68 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 69 | ! ddzu replaced by ddzu_pres due to changes in zu(0) |
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| 70 | ! |
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[623] | 71 | ! 622 2010-12-10 08:08:13Z raasch |
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| 72 | ! optional barriers included in order to speed up collective operations |
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| 73 | ! |
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[392] | 74 | ! 377 2009-09-04 11:09:00Z raasch |
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| 75 | ! __lcmuk changed to __lc to avoid problems with Intel compiler on sgi-ice |
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| 76 | ! |
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[198] | 77 | ! 164 2008-05-15 08:46:15Z raasch |
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| 78 | ! Arguments removed from transpose routines |
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| 79 | ! |
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[139] | 80 | ! 128 2007-10-26 13:11:14Z raasch |
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| 81 | ! Bugfix: wavenumber calculation for even nx in routines maketri |
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| 82 | ! |
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[90] | 83 | ! 85 2007-05-11 09:35:14Z raasch |
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| 84 | ! Bugfix: work_fft*_vec removed from some PRIVATE-declarations |
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| 85 | ! |
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[77] | 86 | ! 76 2007-03-29 00:58:32Z raasch |
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| 87 | ! Tridiagonal coefficients adjusted for Neumann boundary conditions both at |
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| 88 | ! the bottom and the top. |
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| 89 | ! |
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[3] | 90 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 91 | ! |
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[1] | 92 | ! Revision 1.24 2006/08/04 15:00:24 raasch |
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| 93 | ! Default setting of the thread number tn in case of not using OpenMP |
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| 94 | ! |
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| 95 | ! Revision 1.23 2006/02/23 12:48:38 raasch |
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| 96 | ! Additional compiler directive in routine tridia_1dd for preventing loop |
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| 97 | ! exchange on NEC-SX6 |
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| 98 | ! |
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| 99 | ! Revision 1.20 2004/04/30 12:38:09 raasch |
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| 100 | ! Parts of former poisfft_hybrid moved to this subroutine, |
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| 101 | ! former subroutine changed to a module, renaming of FFT-subroutines and |
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| 102 | ! -module, FFTs completely substituted by calls of fft_x and fft_y, |
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| 103 | ! NAG fft used in the non-parallel case completely removed, l in maketri |
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| 104 | ! is now a 1d-array, variables passed by modules instead of using parameter |
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| 105 | ! lists, enlarged transposition arrays introduced |
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| 106 | ! |
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| 107 | ! Revision 1.1 1997/07/24 11:24:14 raasch |
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| 108 | ! Initial revision |
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| 109 | ! |
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| 110 | ! |
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| 111 | ! Description: |
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| 112 | ! ------------ |
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| 113 | ! See below. |
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| 114 | !------------------------------------------------------------------------------! |
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| 115 | |
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| 116 | !--------------------------------------------------------------------------! |
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| 117 | ! poisfft ! |
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| 118 | ! ! |
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| 119 | ! Original version: Stephan Siano (pois3d) ! |
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| 120 | ! ! |
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| 121 | ! Institute of Meteorology and Climatology, University of Hannover ! |
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| 122 | ! Germany ! |
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| 123 | ! ! |
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| 124 | ! Version as of July 23,1996 ! |
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| 125 | ! ! |
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| 126 | ! ! |
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| 127 | ! Version for parallel computers: Siegfried Raasch ! |
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| 128 | ! ! |
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| 129 | ! Version as of July 03,1997 ! |
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| 130 | ! ! |
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| 131 | ! Solves the Poisson equation with a 2D spectral method ! |
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| 132 | ! d^2 p / dx^2 + d^2 p / dy^2 + d^2 p / dz^2 = s ! |
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| 133 | ! ! |
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| 134 | ! Input: ! |
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| 135 | ! real ar contains in the (nnx,nny,nnz) elements, ! |
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| 136 | ! starting from the element (1,nys,nxl), the ! |
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| 137 | ! values for s ! |
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| 138 | ! real work Temporary array ! |
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| 139 | ! ! |
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| 140 | ! Output: ! |
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| 141 | ! real ar contains the solution for p ! |
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| 142 | !--------------------------------------------------------------------------! |
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| 143 | |
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| 144 | USE fft_xy |
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| 145 | USE indices |
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| 146 | USE transpose_indices |
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| 147 | |
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| 148 | IMPLICIT NONE |
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| 149 | |
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| 150 | PRIVATE |
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[807] | 151 | |
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[809] | 152 | #if ! defined ( __check ) |
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[1] | 153 | PUBLIC poisfft, poisfft_init |
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| 154 | |
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| 155 | INTERFACE poisfft |
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| 156 | MODULE PROCEDURE poisfft |
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| 157 | END INTERFACE poisfft |
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| 158 | |
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| 159 | INTERFACE poisfft_init |
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| 160 | MODULE PROCEDURE poisfft_init |
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| 161 | END INTERFACE poisfft_init |
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[807] | 162 | #else |
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| 163 | PUBLIC poisfft_init |
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[1] | 164 | |
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[807] | 165 | INTERFACE poisfft_init |
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| 166 | MODULE PROCEDURE poisfft_init |
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| 167 | END INTERFACE poisfft_init |
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| 168 | #endif |
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| 169 | |
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[1] | 170 | CONTAINS |
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| 171 | |
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| 172 | SUBROUTINE poisfft_init |
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| 173 | |
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| 174 | CALL fft_init |
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| 175 | |
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| 176 | END SUBROUTINE poisfft_init |
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| 177 | |
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[809] | 178 | #if ! defined ( __check ) |
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[1] | 179 | SUBROUTINE poisfft( ar, work ) |
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| 180 | |
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| 181 | USE cpulog |
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| 182 | USE interfaces |
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| 183 | USE pegrid |
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| 184 | |
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| 185 | IMPLICIT NONE |
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| 186 | |
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[1003] | 187 | REAL, DIMENSION(1:nz,nys:nyn,nxl:nxr) :: ar, work |
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[1] | 188 | |
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| 189 | |
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| 190 | CALL cpu_log( log_point_s(3), 'poisfft', 'start' ) |
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| 191 | |
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| 192 | ! |
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| 193 | !-- Two-dimensional Fourier Transformation in x- and y-direction. |
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| 194 | #if defined( __parallel ) |
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| 195 | IF ( pdims(2) == 1 ) THEN |
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| 196 | |
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| 197 | ! |
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| 198 | !-- 1d-domain-decomposition along x: |
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| 199 | !-- FFT along y and transposition y --> x |
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| 200 | CALL ffty_tr_yx( ar, work, ar ) |
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| 201 | |
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| 202 | ! |
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| 203 | !-- FFT along x, solving the tridiagonal system and backward FFT |
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| 204 | CALL fftx_tri_fftx( ar ) |
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| 205 | |
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| 206 | ! |
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| 207 | !-- Transposition x --> y and backward FFT along y |
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| 208 | CALL tr_xy_ffty( ar, work, ar ) |
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| 209 | |
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| 210 | ELSEIF ( pdims(1) == 1 ) THEN |
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| 211 | |
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| 212 | ! |
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| 213 | !-- 1d-domain-decomposition along y: |
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| 214 | !-- FFT along x and transposition x --> y |
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| 215 | CALL fftx_tr_xy( ar, work, ar ) |
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| 216 | |
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| 217 | ! |
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| 218 | !-- FFT along y, solving the tridiagonal system and backward FFT |
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| 219 | CALL ffty_tri_ffty( ar ) |
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| 220 | |
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| 221 | ! |
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| 222 | !-- Transposition y --> x and backward FFT along x |
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| 223 | CALL tr_yx_fftx( ar, work, ar ) |
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| 224 | |
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| 225 | ELSE |
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| 226 | |
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| 227 | ! |
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| 228 | !-- 2d-domain-decomposition |
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| 229 | !-- Transposition z --> x |
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| 230 | CALL cpu_log( log_point_s(5), 'transpo forward', 'start' ) |
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[164] | 231 | CALL transpose_zx( ar, work, ar ) |
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[1] | 232 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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| 233 | |
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| 234 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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| 235 | CALL fftxp( ar, 'forward' ) |
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| 236 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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| 237 | |
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| 238 | ! |
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| 239 | !-- Transposition x --> y |
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| 240 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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[164] | 241 | CALL transpose_xy( ar, work, ar ) |
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[1] | 242 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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| 243 | |
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| 244 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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| 245 | CALL fftyp( ar, 'forward' ) |
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| 246 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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| 247 | |
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| 248 | ! |
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| 249 | !-- Transposition y --> z |
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| 250 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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[164] | 251 | CALL transpose_yz( ar, work, ar ) |
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[1] | 252 | CALL cpu_log( log_point_s(5), 'transpo forward', 'stop' ) |
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| 253 | |
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| 254 | ! |
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| 255 | !-- Solve the Poisson equation in z-direction in cartesian space. |
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| 256 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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| 257 | CALL tridia( ar ) |
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| 258 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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| 259 | |
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| 260 | ! |
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| 261 | !-- Inverse Fourier Transformation |
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| 262 | !-- Transposition z --> y |
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| 263 | CALL cpu_log( log_point_s(8), 'transpo invers', 'start' ) |
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[164] | 264 | CALL transpose_zy( ar, work, ar ) |
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[1] | 265 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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| 266 | |
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| 267 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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| 268 | CALL fftyp( ar, 'backward' ) |
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| 269 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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| 270 | |
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| 271 | ! |
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| 272 | !-- Transposition y --> x |
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| 273 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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[164] | 274 | CALL transpose_yx( ar, work, ar ) |
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[1] | 275 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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| 276 | |
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| 277 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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| 278 | CALL fftxp( ar, 'backward' ) |
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| 279 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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| 280 | |
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| 281 | ! |
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| 282 | !-- Transposition x --> z |
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| 283 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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[164] | 284 | CALL transpose_xz( ar, work, ar ) |
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[1] | 285 | CALL cpu_log( log_point_s(8), 'transpo invers', 'stop' ) |
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| 286 | |
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| 287 | ENDIF |
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| 288 | |
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| 289 | #else |
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| 290 | |
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| 291 | ! |
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| 292 | !-- Two-dimensional Fourier Transformation along x- and y-direction. |
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| 293 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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| 294 | CALL fftx( ar, 'forward' ) |
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| 295 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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| 296 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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| 297 | CALL ffty( ar, 'forward' ) |
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| 298 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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| 299 | |
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| 300 | ! |
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| 301 | !-- Solve the Poisson equation in z-direction in cartesian space. |
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| 302 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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| 303 | CALL tridia( ar ) |
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| 304 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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| 305 | |
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| 306 | ! |
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| 307 | !-- Inverse Fourier Transformation. |
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| 308 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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| 309 | CALL ffty( ar, 'backward' ) |
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| 310 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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| 311 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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| 312 | CALL fftx( ar, 'backward' ) |
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| 313 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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| 314 | |
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| 315 | #endif |
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| 316 | |
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| 317 | CALL cpu_log( log_point_s(3), 'poisfft', 'stop' ) |
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| 318 | |
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| 319 | END SUBROUTINE poisfft |
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| 320 | |
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| 321 | |
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| 322 | |
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| 323 | SUBROUTINE tridia( ar ) |
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| 324 | |
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| 325 | !------------------------------------------------------------------------------! |
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| 326 | ! solves the linear system of equations: |
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| 327 | ! |
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| 328 | ! -(4 pi^2(i^2/(dx^2*nnx^2)+j^2/(dy^2*nny^2))+ |
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| 329 | ! 1/(dzu(k)*dzw(k))+1/(dzu(k-1)*dzw(k)))*p(i,j,k)+ |
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| 330 | ! 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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| 331 | ! |
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| 332 | ! by using the Thomas algorithm |
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| 333 | !------------------------------------------------------------------------------! |
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| 334 | |
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| 335 | USE arrays_3d |
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| 336 | |
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| 337 | IMPLICIT NONE |
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| 338 | |
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| 339 | INTEGER :: i, j, k, nnyh |
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| 340 | |
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| 341 | REAL, DIMENSION(nxl_z:nxr_z,0:nz-1) :: ar1 |
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| 342 | REAL, DIMENSION(5,nxl_z:nxr_z,0:nz-1) :: tri |
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| 343 | |
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| 344 | #if defined( __parallel ) |
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[1003] | 345 | REAL :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) |
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[1] | 346 | #else |
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| 347 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
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| 348 | #endif |
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| 349 | |
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| 350 | |
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| 351 | nnyh = (ny+1) / 2 |
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| 352 | |
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| 353 | ! |
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| 354 | !-- Define constant elements of the tridiagonal matrix. |
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[683] | 355 | !$OMP PARALLEL PRIVATE ( k, i ) |
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| 356 | !$OMP DO |
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[1] | 357 | DO k = 0, nz-1 |
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| 358 | DO i = nxl_z, nxr_z |
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[667] | 359 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
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| 360 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
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[1] | 361 | ENDDO |
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| 362 | ENDDO |
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[683] | 363 | !$OMP END PARALLEL |
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[1] | 364 | |
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| 365 | #if defined( __parallel ) |
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| 366 | ! |
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| 367 | !-- Repeat for all y-levels. |
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[683] | 368 | !$OMP PARALLEL FIRSTPRIVATE( tri ) PRIVATE ( ar1, j ) |
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| 369 | !$OMP DO |
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[1] | 370 | DO j = nys_z, nyn_z |
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| 371 | IF ( j <= nnyh ) THEN |
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| 372 | CALL maketri( tri, j ) |
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| 373 | ELSE |
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| 374 | CALL maketri( tri, ny+1-j ) |
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| 375 | ENDIF |
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| 376 | CALL split( tri ) |
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| 377 | CALL substi( ar, ar1, tri, j ) |
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| 378 | ENDDO |
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[683] | 379 | !$OMP END PARALLEL |
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[1] | 380 | #else |
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| 381 | ! |
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| 382 | !-- First y-level. |
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| 383 | CALL maketri( tri, nys_z ) |
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| 384 | CALL split( tri ) |
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| 385 | CALL substi( ar, ar1, tri, 0 ) |
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| 386 | |
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| 387 | ! |
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| 388 | !-- Further y-levels. |
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| 389 | DO j = 1, nnyh - 1 |
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| 390 | CALL maketri( tri, j ) |
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| 391 | CALL split( tri ) |
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| 392 | CALL substi( ar, ar1, tri, j ) |
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| 393 | CALL substi( ar, ar1, tri, ny+1-j ) |
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| 394 | ENDDO |
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| 395 | CALL maketri( tri, nnyh ) |
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| 396 | CALL split( tri ) |
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| 397 | CALL substi( ar, ar1, tri, nnyh+nys ) |
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| 398 | #endif |
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| 399 | |
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| 400 | CONTAINS |
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| 401 | |
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| 402 | SUBROUTINE maketri( tri, j ) |
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| 403 | |
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| 404 | !------------------------------------------------------------------------------! |
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| 405 | ! Computes the i- and j-dependent component of the matrix |
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| 406 | !------------------------------------------------------------------------------! |
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| 407 | |
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| 408 | USE arrays_3d |
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| 409 | USE constants |
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| 410 | USE control_parameters |
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| 411 | USE grid_variables |
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| 412 | |
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| 413 | IMPLICIT NONE |
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| 414 | |
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| 415 | INTEGER :: i, j, k, nnxh |
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| 416 | REAL :: a, c |
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| 417 | REAL :: ll(nxl_z:nxr_z) |
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| 418 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
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| 419 | |
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| 420 | |
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| 421 | nnxh = ( nx + 1 ) / 2 |
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| 422 | |
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| 423 | ! |
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| 424 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
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| 425 | !-- Fourier space. The coefficients are computed following the method of |
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| 426 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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| 427 | !-- Siano's original version by discretizing the Poisson equation, |
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| 428 | !-- before it is Fourier-transformed |
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| 429 | #if defined( __parallel ) |
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| 430 | DO i = nxl_z, nxr_z |
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[128] | 431 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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[1] | 432 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
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[1013] | 433 | REAL( nx+1 ) ) ) / ( dx * dx ) + & |
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[1] | 434 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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[1013] | 435 | REAL( ny+1 ) ) ) / ( dy * dy ) |
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[1] | 436 | ELSE |
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| 437 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
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[1013] | 438 | REAL( nx+1 ) ) ) / ( dx * dx ) + & |
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[1] | 439 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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[1013] | 440 | REAL( ny+1 ) ) ) / ( dy * dy ) |
---|
[1] | 441 | ENDIF |
---|
| 442 | DO k = 0,nz-1 |
---|
[667] | 443 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
| 444 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
[1] | 445 | tri(1,i,k) = a + c - ll(i) |
---|
| 446 | ENDDO |
---|
| 447 | ENDDO |
---|
| 448 | #else |
---|
| 449 | DO i = 0, nnxh |
---|
[1013] | 450 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / REAL( nx+1 ) ) ) / & |
---|
[1] | 451 | ( dx * dx ) + & |
---|
[1013] | 452 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / REAL( ny+1 ) ) ) / & |
---|
[1] | 453 | ( dy * dy ) |
---|
| 454 | DO k = 0, nz-1 |
---|
[667] | 455 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
| 456 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
[1] | 457 | tri(1,i,k) = a + c - ll(i) |
---|
| 458 | IF ( i >= 1 .and. i < nnxh ) THEN |
---|
| 459 | tri(1,nx+1-i,k) = tri(1,i,k) |
---|
| 460 | ENDIF |
---|
| 461 | ENDDO |
---|
| 462 | ENDDO |
---|
| 463 | #endif |
---|
| 464 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
| 465 | DO i = nxl_z, nxr_z |
---|
| 466 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
| 467 | ENDDO |
---|
| 468 | ENDIF |
---|
| 469 | IF ( ibc_p_t == 1 ) THEN |
---|
| 470 | DO i = nxl_z, nxr_z |
---|
| 471 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
| 472 | ENDDO |
---|
| 473 | ENDIF |
---|
| 474 | |
---|
| 475 | END SUBROUTINE maketri |
---|
| 476 | |
---|
| 477 | |
---|
| 478 | SUBROUTINE substi( ar, ar1, tri, j ) |
---|
| 479 | |
---|
| 480 | !------------------------------------------------------------------------------! |
---|
| 481 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
| 482 | !------------------------------------------------------------------------------! |
---|
| 483 | |
---|
[76] | 484 | USE control_parameters |
---|
| 485 | |
---|
[1] | 486 | IMPLICIT NONE |
---|
| 487 | |
---|
| 488 | INTEGER :: i, j, k |
---|
| 489 | REAL :: ar1(nxl_z:nxr_z,0:nz-1) |
---|
| 490 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
| 491 | #if defined( __parallel ) |
---|
[1003] | 492 | REAL :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) |
---|
[1] | 493 | #else |
---|
| 494 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
---|
| 495 | #endif |
---|
| 496 | |
---|
| 497 | ! |
---|
| 498 | !-- Forward substitution. |
---|
| 499 | DO i = nxl_z, nxr_z |
---|
| 500 | #if defined( __parallel ) |
---|
| 501 | ar1(i,0) = ar(i,j,1) |
---|
| 502 | #else |
---|
| 503 | ar1(i,0) = ar(1,j,i) |
---|
| 504 | #endif |
---|
| 505 | ENDDO |
---|
| 506 | DO k = 1, nz - 1 |
---|
| 507 | DO i = nxl_z, nxr_z |
---|
| 508 | #if defined( __parallel ) |
---|
| 509 | ar1(i,k) = ar(i,j,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
| 510 | #else |
---|
| 511 | ar1(i,k) = ar(k+1,j,i) - tri(5,i,k) * ar1(i,k-1) |
---|
| 512 | #endif |
---|
| 513 | ENDDO |
---|
| 514 | ENDDO |
---|
| 515 | |
---|
| 516 | ! |
---|
[877] | 517 | !-- Backward substitution |
---|
| 518 | !-- Note, the 1.0E-20 in the denominator is due to avoid divisions |
---|
| 519 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
| 520 | !-- the model domain. |
---|
[1] | 521 | DO i = nxl_z, nxr_z |
---|
| 522 | #if defined( __parallel ) |
---|
[877] | 523 | ar(i,j,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
[1] | 524 | #else |
---|
[877] | 525 | ar(nz,j,i) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
[1] | 526 | #endif |
---|
| 527 | ENDDO |
---|
| 528 | DO k = nz-2, 0, -1 |
---|
| 529 | DO i = nxl_z, nxr_z |
---|
| 530 | #if defined( __parallel ) |
---|
| 531 | ar(i,j,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,j,k+2) ) & |
---|
| 532 | / tri(4,i,k) |
---|
| 533 | #else |
---|
| 534 | ar(k+1,j,i) = ( ar1(i,k) - tri(3,i,k) * ar(k+2,j,i) ) & |
---|
| 535 | / tri(4,i,k) |
---|
| 536 | #endif |
---|
| 537 | ENDDO |
---|
| 538 | ENDDO |
---|
| 539 | |
---|
[76] | 540 | ! |
---|
| 541 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
| 542 | !-- The respective values of ar should be zero at all k-levels if |
---|
| 543 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
| 544 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
| 545 | IF ( j == 0 .AND. nxl_z == 0 ) THEN |
---|
| 546 | #if defined( __parallel ) |
---|
| 547 | DO k = 1, nz |
---|
| 548 | ar(nxl_z,j,k) = 0.0 |
---|
| 549 | ENDDO |
---|
| 550 | #else |
---|
| 551 | DO k = 1, nz |
---|
| 552 | ar(k,j,nxl_z) = 0.0 |
---|
| 553 | ENDDO |
---|
| 554 | #endif |
---|
| 555 | ENDIF |
---|
| 556 | ENDIF |
---|
| 557 | |
---|
[1] | 558 | END SUBROUTINE substi |
---|
| 559 | |
---|
| 560 | |
---|
| 561 | SUBROUTINE split( tri ) |
---|
| 562 | |
---|
| 563 | !------------------------------------------------------------------------------! |
---|
| 564 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
| 565 | !------------------------------------------------------------------------------! |
---|
| 566 | |
---|
| 567 | IMPLICIT NONE |
---|
| 568 | |
---|
| 569 | INTEGER :: i, k |
---|
| 570 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
| 571 | |
---|
| 572 | ! |
---|
| 573 | !-- Splitting. |
---|
| 574 | DO i = nxl_z, nxr_z |
---|
| 575 | tri(4,i,0) = tri(1,i,0) |
---|
| 576 | ENDDO |
---|
| 577 | DO k = 1, nz-1 |
---|
| 578 | DO i = nxl_z, nxr_z |
---|
| 579 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
| 580 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
| 581 | ENDDO |
---|
| 582 | ENDDO |
---|
| 583 | |
---|
| 584 | END SUBROUTINE split |
---|
| 585 | |
---|
| 586 | END SUBROUTINE tridia |
---|
| 587 | |
---|
| 588 | |
---|
| 589 | #if defined( __parallel ) |
---|
| 590 | SUBROUTINE fftxp( ar, direction ) |
---|
| 591 | |
---|
| 592 | !------------------------------------------------------------------------------! |
---|
| 593 | ! Fourier-transformation along x-direction Parallelized version |
---|
| 594 | !------------------------------------------------------------------------------! |
---|
| 595 | |
---|
| 596 | IMPLICIT NONE |
---|
| 597 | |
---|
| 598 | CHARACTER (LEN=*) :: direction |
---|
| 599 | INTEGER :: j, k |
---|
[1003] | 600 | REAL :: ar(0:nx,nys_x:nyn_x,nzb_x:nzt_x) |
---|
[1] | 601 | |
---|
| 602 | ! |
---|
| 603 | !-- Performing the fft with one of the methods implemented |
---|
[683] | 604 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
| 605 | !$OMP DO |
---|
[1] | 606 | DO k = nzb_x, nzt_x |
---|
| 607 | DO j = nys_x, nyn_x |
---|
| 608 | CALL fft_x( ar(0:nx,j,k), direction ) |
---|
| 609 | ENDDO |
---|
| 610 | ENDDO |
---|
[683] | 611 | !$OMP END PARALLEL |
---|
[1] | 612 | |
---|
| 613 | END SUBROUTINE fftxp |
---|
| 614 | |
---|
| 615 | #else |
---|
| 616 | SUBROUTINE fftx( ar, direction ) |
---|
| 617 | |
---|
| 618 | !------------------------------------------------------------------------------! |
---|
| 619 | ! Fourier-transformation along x-direction Non parallel version |
---|
| 620 | !------------------------------------------------------------------------------! |
---|
| 621 | |
---|
| 622 | IMPLICIT NONE |
---|
| 623 | |
---|
| 624 | CHARACTER (LEN=*) :: direction |
---|
| 625 | INTEGER :: i, j, k |
---|
| 626 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
| 627 | |
---|
| 628 | ! |
---|
| 629 | !-- Performing the fft with one of the methods implemented |
---|
[683] | 630 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
| 631 | !$OMP DO |
---|
[1] | 632 | DO k = 1, nz |
---|
| 633 | DO j = 0, ny |
---|
| 634 | CALL fft_x( ar(k,j,0:nx), direction ) |
---|
| 635 | ENDDO |
---|
| 636 | ENDDO |
---|
[683] | 637 | !$OMP END PARALLEL |
---|
[1] | 638 | |
---|
| 639 | END SUBROUTINE fftx |
---|
| 640 | #endif |
---|
| 641 | |
---|
| 642 | |
---|
| 643 | #if defined( __parallel ) |
---|
| 644 | SUBROUTINE fftyp( ar, direction ) |
---|
| 645 | |
---|
| 646 | !------------------------------------------------------------------------------! |
---|
| 647 | ! Fourier-transformation along y-direction Parallelized version |
---|
| 648 | !------------------------------------------------------------------------------! |
---|
| 649 | |
---|
| 650 | IMPLICIT NONE |
---|
| 651 | |
---|
| 652 | CHARACTER (LEN=*) :: direction |
---|
| 653 | INTEGER :: i, k |
---|
[1003] | 654 | REAL :: ar(0:ny,nxl_y:nxr_y,nzb_y:nzt_y) |
---|
[1] | 655 | |
---|
| 656 | ! |
---|
| 657 | !-- Performing the fft with one of the methods implemented |
---|
[683] | 658 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
| 659 | !$OMP DO |
---|
[1] | 660 | DO k = nzb_y, nzt_y |
---|
| 661 | DO i = nxl_y, nxr_y |
---|
| 662 | CALL fft_y( ar(0:ny,i,k), direction ) |
---|
| 663 | ENDDO |
---|
| 664 | ENDDO |
---|
[683] | 665 | !$OMP END PARALLEL |
---|
[1] | 666 | |
---|
| 667 | END SUBROUTINE fftyp |
---|
| 668 | |
---|
| 669 | #else |
---|
| 670 | SUBROUTINE ffty( ar, direction ) |
---|
| 671 | |
---|
| 672 | !------------------------------------------------------------------------------! |
---|
| 673 | ! Fourier-transformation along y-direction Non parallel version |
---|
| 674 | !------------------------------------------------------------------------------! |
---|
| 675 | |
---|
| 676 | IMPLICIT NONE |
---|
| 677 | |
---|
| 678 | CHARACTER (LEN=*) :: direction |
---|
| 679 | INTEGER :: i, k |
---|
| 680 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
| 681 | |
---|
| 682 | ! |
---|
| 683 | !-- Performing the fft with one of the methods implemented |
---|
[683] | 684 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
| 685 | !$OMP DO |
---|
[1] | 686 | DO k = 1, nz |
---|
| 687 | DO i = 0, nx |
---|
| 688 | CALL fft_y( ar(k,0:ny,i), direction ) |
---|
| 689 | ENDDO |
---|
| 690 | ENDDO |
---|
[683] | 691 | !$OMP END PARALLEL |
---|
[1] | 692 | |
---|
| 693 | END SUBROUTINE ffty |
---|
| 694 | #endif |
---|
| 695 | |
---|
| 696 | #if defined( __parallel ) |
---|
| 697 | SUBROUTINE ffty_tr_yx( f_in, work, f_out ) |
---|
| 698 | |
---|
| 699 | !------------------------------------------------------------------------------! |
---|
| 700 | ! Fourier-transformation along y with subsequent transposition y --> x for |
---|
| 701 | ! a 1d-decomposition along x |
---|
| 702 | ! |
---|
| 703 | ! ATTENTION: The performance of this routine is much faster on the NEC-SX6, |
---|
| 704 | ! if the first index of work_ffty_vec is odd. Otherwise |
---|
| 705 | ! memory bank conflicts may occur (especially if the index is a |
---|
| 706 | ! multiple of 128). That's why work_ffty_vec is dimensioned as |
---|
| 707 | ! 0:ny+1. |
---|
| 708 | ! Of course, this will not work if users are using an odd number |
---|
| 709 | ! of gridpoints along y. |
---|
| 710 | !------------------------------------------------------------------------------! |
---|
| 711 | |
---|
| 712 | USE control_parameters |
---|
| 713 | USE cpulog |
---|
| 714 | USE indices |
---|
| 715 | USE interfaces |
---|
| 716 | USE pegrid |
---|
| 717 | USE transpose_indices |
---|
| 718 | |
---|
| 719 | IMPLICIT NONE |
---|
| 720 | |
---|
| 721 | INTEGER :: i, iend, iouter, ir, j, k |
---|
| 722 | INTEGER, PARAMETER :: stridex = 4 |
---|
| 723 | |
---|
| 724 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
| 725 | #if defined( __nec ) |
---|
| 726 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
| 727 | #endif |
---|
[1003] | 728 | REAL, DIMENSION(1:nz,0:ny,nxl:nxr) :: f_in |
---|
| 729 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: f_out |
---|
| 730 | REAL, DIMENSION(nxl:nxr,1:nz,0:ny) :: work |
---|
[1] | 731 | |
---|
| 732 | ! |
---|
| 733 | !-- Carry out the FFT along y, where all data are present due to the |
---|
| 734 | !-- 1d-decomposition along x. Resort the data in a way that x becomes |
---|
| 735 | !-- the first index. |
---|
| 736 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
---|
| 737 | |
---|
| 738 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 739 | #if defined( __nec ) |
---|
| 740 | ! |
---|
| 741 | !-- Code optimized for vector processors |
---|
[85] | 742 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 743 | !$OMP DO |
---|
| 744 | DO i = nxl, nxr |
---|
| 745 | |
---|
| 746 | DO j = 0, ny |
---|
| 747 | DO k = 1, nz |
---|
| 748 | work_ffty_vec(j,k,i) = f_in(k,j,i) |
---|
| 749 | ENDDO |
---|
| 750 | ENDDO |
---|
| 751 | |
---|
| 752 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'forward' ) |
---|
| 753 | |
---|
| 754 | ENDDO |
---|
| 755 | |
---|
| 756 | !$OMP DO |
---|
| 757 | DO k = 1, nz |
---|
| 758 | DO j = 0, ny |
---|
| 759 | DO i = nxl, nxr |
---|
| 760 | work(i,k,j) = work_ffty_vec(j,k,i) |
---|
| 761 | ENDDO |
---|
| 762 | ENDDO |
---|
| 763 | ENDDO |
---|
| 764 | !$OMP END PARALLEL |
---|
| 765 | #endif |
---|
| 766 | |
---|
| 767 | ELSE |
---|
| 768 | |
---|
| 769 | ! |
---|
| 770 | !-- Cache optimized code. |
---|
| 771 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
| 772 | !-- loop for better cache performance |
---|
| 773 | !$OMP PARALLEL PRIVATE (i,iend,iouter,ir,j,k,work_ffty) |
---|
| 774 | !$OMP DO |
---|
| 775 | DO iouter = nxl, nxr, stridex |
---|
| 776 | |
---|
| 777 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
| 778 | |
---|
| 779 | DO k = 1, nz |
---|
| 780 | |
---|
| 781 | DO i = iouter, iend |
---|
| 782 | |
---|
| 783 | ir = i-iouter+1 ! counter within a stride |
---|
| 784 | DO j = 0, ny |
---|
| 785 | work_ffty(j,ir) = f_in(k,j,i) |
---|
| 786 | ENDDO |
---|
| 787 | ! |
---|
| 788 | !-- FFT along y |
---|
| 789 | CALL fft_y( work_ffty(:,ir), 'forward' ) |
---|
| 790 | |
---|
| 791 | ENDDO |
---|
| 792 | |
---|
| 793 | ! |
---|
| 794 | !-- Resort |
---|
| 795 | DO j = 0, ny |
---|
| 796 | DO i = iouter, iend |
---|
| 797 | work(i,k,j) = work_ffty(j,i-iouter+1) |
---|
| 798 | ENDDO |
---|
| 799 | ENDDO |
---|
| 800 | |
---|
| 801 | ENDDO |
---|
| 802 | |
---|
| 803 | ENDDO |
---|
| 804 | !$OMP END PARALLEL |
---|
| 805 | |
---|
| 806 | ENDIF |
---|
| 807 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
---|
| 808 | |
---|
| 809 | ! |
---|
| 810 | !-- Transpose array |
---|
| 811 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 812 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 813 | CALL MPI_ALLTOALL( work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 814 | f_out(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 815 | comm1dx, ierr ) |
---|
| 816 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 817 | |
---|
| 818 | END SUBROUTINE ffty_tr_yx |
---|
| 819 | |
---|
| 820 | |
---|
| 821 | SUBROUTINE tr_xy_ffty( f_in, work, f_out ) |
---|
| 822 | |
---|
| 823 | !------------------------------------------------------------------------------! |
---|
| 824 | ! Transposition x --> y with a subsequent backward Fourier transformation for |
---|
| 825 | ! a 1d-decomposition along x |
---|
| 826 | !------------------------------------------------------------------------------! |
---|
| 827 | |
---|
| 828 | USE control_parameters |
---|
| 829 | USE cpulog |
---|
| 830 | USE indices |
---|
| 831 | USE interfaces |
---|
| 832 | USE pegrid |
---|
| 833 | USE transpose_indices |
---|
| 834 | |
---|
| 835 | IMPLICIT NONE |
---|
| 836 | |
---|
| 837 | INTEGER :: i, iend, iouter, ir, j, k |
---|
| 838 | INTEGER, PARAMETER :: stridex = 4 |
---|
| 839 | |
---|
| 840 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
| 841 | #if defined( __nec ) |
---|
| 842 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
| 843 | #endif |
---|
[1003] | 844 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: f_in |
---|
| 845 | REAL, DIMENSION(1:nz,0:ny,nxl:nxr) :: f_out |
---|
| 846 | REAL, DIMENSION(nxl:nxr,1:nz,0:ny) :: work |
---|
[1] | 847 | |
---|
| 848 | ! |
---|
| 849 | !-- Transpose array |
---|
| 850 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 851 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 852 | CALL MPI_ALLTOALL( f_in(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 853 | work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 854 | comm1dx, ierr ) |
---|
| 855 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 856 | |
---|
| 857 | ! |
---|
| 858 | !-- Resort the data in a way that y becomes the first index and carry out the |
---|
| 859 | !-- backward fft along y. |
---|
| 860 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
---|
| 861 | |
---|
| 862 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 863 | #if defined( __nec ) |
---|
| 864 | ! |
---|
| 865 | !-- Code optimized for vector processors |
---|
[85] | 866 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 867 | !$OMP DO |
---|
| 868 | DO k = 1, nz |
---|
| 869 | DO j = 0, ny |
---|
| 870 | DO i = nxl, nxr |
---|
| 871 | work_ffty_vec(j,k,i) = work(i,k,j) |
---|
| 872 | ENDDO |
---|
| 873 | ENDDO |
---|
| 874 | ENDDO |
---|
| 875 | |
---|
| 876 | !$OMP DO |
---|
| 877 | DO i = nxl, nxr |
---|
| 878 | |
---|
| 879 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'backward' ) |
---|
| 880 | |
---|
| 881 | DO j = 0, ny |
---|
| 882 | DO k = 1, nz |
---|
| 883 | f_out(k,j,i) = work_ffty_vec(j,k,i) |
---|
| 884 | ENDDO |
---|
| 885 | ENDDO |
---|
| 886 | |
---|
| 887 | ENDDO |
---|
| 888 | !$OMP END PARALLEL |
---|
| 889 | #endif |
---|
| 890 | |
---|
| 891 | ELSE |
---|
| 892 | |
---|
| 893 | ! |
---|
| 894 | !-- Cache optimized code. |
---|
| 895 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
| 896 | !-- loop for better cache performance |
---|
| 897 | !$OMP PARALLEL PRIVATE ( i, iend, iouter, ir, j, k, work_ffty ) |
---|
| 898 | !$OMP DO |
---|
| 899 | DO iouter = nxl, nxr, stridex |
---|
| 900 | |
---|
| 901 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
| 902 | |
---|
| 903 | DO k = 1, nz |
---|
| 904 | ! |
---|
| 905 | !-- Resort |
---|
| 906 | DO j = 0, ny |
---|
| 907 | DO i = iouter, iend |
---|
| 908 | work_ffty(j,i-iouter+1) = work(i,k,j) |
---|
| 909 | ENDDO |
---|
| 910 | ENDDO |
---|
| 911 | |
---|
| 912 | DO i = iouter, iend |
---|
| 913 | |
---|
| 914 | ! |
---|
| 915 | !-- FFT along y |
---|
| 916 | ir = i-iouter+1 ! counter within a stride |
---|
| 917 | CALL fft_y( work_ffty(:,ir), 'backward' ) |
---|
| 918 | |
---|
| 919 | DO j = 0, ny |
---|
| 920 | f_out(k,j,i) = work_ffty(j,ir) |
---|
| 921 | ENDDO |
---|
| 922 | ENDDO |
---|
| 923 | |
---|
| 924 | ENDDO |
---|
| 925 | |
---|
| 926 | ENDDO |
---|
| 927 | !$OMP END PARALLEL |
---|
| 928 | |
---|
| 929 | ENDIF |
---|
| 930 | |
---|
| 931 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
---|
| 932 | |
---|
| 933 | END SUBROUTINE tr_xy_ffty |
---|
| 934 | |
---|
| 935 | |
---|
| 936 | SUBROUTINE fftx_tri_fftx( ar ) |
---|
| 937 | |
---|
| 938 | !------------------------------------------------------------------------------! |
---|
| 939 | ! FFT along x, solution of the tridiagonal system and backward FFT for |
---|
| 940 | ! a 1d-decomposition along x |
---|
| 941 | ! |
---|
| 942 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
| 943 | ! with OpenMP (for possible necessary changes see the original |
---|
| 944 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
| 945 | !------------------------------------------------------------------------------! |
---|
| 946 | |
---|
| 947 | USE control_parameters |
---|
| 948 | USE cpulog |
---|
| 949 | USE grid_variables |
---|
| 950 | USE indices |
---|
| 951 | USE interfaces |
---|
| 952 | USE pegrid |
---|
| 953 | USE transpose_indices |
---|
| 954 | |
---|
| 955 | IMPLICIT NONE |
---|
| 956 | |
---|
| 957 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
| 958 | |
---|
[1003] | 959 | REAL, DIMENSION(0:nx) :: work_fftx |
---|
| 960 | REAL, DIMENSION(0:nx,1:nz) :: work_trix |
---|
| 961 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: ar |
---|
| 962 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
[1] | 963 | |
---|
| 964 | |
---|
| 965 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'start' ) |
---|
| 966 | |
---|
| 967 | ALLOCATE( tri(5,0:nx,0:nz-1,0:threads_per_task-1) ) |
---|
| 968 | |
---|
| 969 | tn = 0 ! Default thread number in case of one thread |
---|
| 970 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_fftx, work_trix ) |
---|
| 971 | DO j = nys_x, nyn_x |
---|
| 972 | |
---|
| 973 | !$ tn = omp_get_thread_num() |
---|
| 974 | |
---|
| 975 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 976 | ! |
---|
| 977 | !-- Code optimized for vector processors |
---|
| 978 | DO k = 1, nz |
---|
| 979 | |
---|
| 980 | m = 0 |
---|
| 981 | DO n = 1, pdims(1) |
---|
[1003] | 982 | DO i = 1, nnx |
---|
[1] | 983 | work_trix(m,k) = ar(i,k,j,n) |
---|
| 984 | m = m + 1 |
---|
| 985 | ENDDO |
---|
| 986 | ENDDO |
---|
| 987 | |
---|
| 988 | ENDDO |
---|
| 989 | |
---|
| 990 | CALL fft_x_m( work_trix, 'forward' ) |
---|
| 991 | |
---|
| 992 | ELSE |
---|
| 993 | ! |
---|
| 994 | !-- Cache optimized code |
---|
| 995 | DO k = 1, nz |
---|
| 996 | |
---|
| 997 | m = 0 |
---|
| 998 | DO n = 1, pdims(1) |
---|
[1003] | 999 | DO i = 1, nnx |
---|
[1] | 1000 | work_fftx(m) = ar(i,k,j,n) |
---|
| 1001 | m = m + 1 |
---|
| 1002 | ENDDO |
---|
| 1003 | ENDDO |
---|
| 1004 | |
---|
| 1005 | CALL fft_x( work_fftx, 'forward' ) |
---|
| 1006 | |
---|
| 1007 | DO i = 0, nx |
---|
| 1008 | work_trix(i,k) = work_fftx(i) |
---|
| 1009 | ENDDO |
---|
| 1010 | |
---|
| 1011 | ENDDO |
---|
| 1012 | |
---|
| 1013 | ENDIF |
---|
| 1014 | |
---|
| 1015 | ! |
---|
| 1016 | !-- Solve the linear equation system |
---|
| 1017 | CALL tridia_1dd( ddx2, ddy2, nx, ny, j, work_trix, tri(:,:,:,tn) ) |
---|
| 1018 | |
---|
| 1019 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1020 | ! |
---|
| 1021 | !-- Code optimized for vector processors |
---|
| 1022 | CALL fft_x_m( work_trix, 'backward' ) |
---|
| 1023 | |
---|
| 1024 | DO k = 1, nz |
---|
| 1025 | |
---|
| 1026 | m = 0 |
---|
| 1027 | DO n = 1, pdims(1) |
---|
[1003] | 1028 | DO i = 1, nnx |
---|
[1] | 1029 | ar(i,k,j,n) = work_trix(m,k) |
---|
| 1030 | m = m + 1 |
---|
| 1031 | ENDDO |
---|
| 1032 | ENDDO |
---|
| 1033 | |
---|
| 1034 | ENDDO |
---|
| 1035 | |
---|
| 1036 | ELSE |
---|
| 1037 | ! |
---|
| 1038 | !-- Cache optimized code |
---|
| 1039 | DO k = 1, nz |
---|
| 1040 | |
---|
| 1041 | DO i = 0, nx |
---|
| 1042 | work_fftx(i) = work_trix(i,k) |
---|
| 1043 | ENDDO |
---|
| 1044 | |
---|
| 1045 | CALL fft_x( work_fftx, 'backward' ) |
---|
| 1046 | |
---|
| 1047 | m = 0 |
---|
| 1048 | DO n = 1, pdims(1) |
---|
[1003] | 1049 | DO i = 1, nnx |
---|
[1] | 1050 | ar(i,k,j,n) = work_fftx(m) |
---|
| 1051 | m = m + 1 |
---|
| 1052 | ENDDO |
---|
| 1053 | ENDDO |
---|
| 1054 | |
---|
| 1055 | ENDDO |
---|
| 1056 | |
---|
| 1057 | ENDIF |
---|
| 1058 | |
---|
| 1059 | ENDDO |
---|
| 1060 | |
---|
| 1061 | DEALLOCATE( tri ) |
---|
| 1062 | |
---|
| 1063 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'stop' ) |
---|
| 1064 | |
---|
| 1065 | END SUBROUTINE fftx_tri_fftx |
---|
| 1066 | |
---|
| 1067 | |
---|
| 1068 | SUBROUTINE fftx_tr_xy( f_in, work, f_out ) |
---|
| 1069 | |
---|
| 1070 | !------------------------------------------------------------------------------! |
---|
| 1071 | ! Fourier-transformation along x with subsequent transposition x --> y for |
---|
| 1072 | ! a 1d-decomposition along y |
---|
| 1073 | ! |
---|
| 1074 | ! ATTENTION: The NEC-branch of this routine may significantly profit from |
---|
| 1075 | ! further optimizations. So far, performance is much worse than |
---|
| 1076 | ! for routine ffty_tr_yx (more than three times slower). |
---|
| 1077 | !------------------------------------------------------------------------------! |
---|
| 1078 | |
---|
| 1079 | USE control_parameters |
---|
| 1080 | USE cpulog |
---|
| 1081 | USE indices |
---|
| 1082 | USE interfaces |
---|
| 1083 | USE pegrid |
---|
| 1084 | USE transpose_indices |
---|
| 1085 | |
---|
| 1086 | IMPLICIT NONE |
---|
| 1087 | |
---|
| 1088 | INTEGER :: i, j, k |
---|
| 1089 | |
---|
[1003] | 1090 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
| 1091 | REAL, DIMENSION(1:nz,nys:nyn,0:nx) :: f_in |
---|
| 1092 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: f_out |
---|
| 1093 | REAL, DIMENSION(nys:nyn,1:nz,0:nx) :: work |
---|
[1] | 1094 | |
---|
| 1095 | ! |
---|
| 1096 | !-- Carry out the FFT along x, where all data are present due to the |
---|
| 1097 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
| 1098 | !-- the first index. |
---|
| 1099 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
---|
| 1100 | |
---|
| 1101 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1102 | ! |
---|
| 1103 | !-- Code for vector processors |
---|
[85] | 1104 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 1105 | !$OMP DO |
---|
| 1106 | DO i = 0, nx |
---|
| 1107 | |
---|
| 1108 | DO j = nys, nyn |
---|
| 1109 | DO k = 1, nz |
---|
| 1110 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
| 1111 | ENDDO |
---|
| 1112 | ENDDO |
---|
| 1113 | |
---|
| 1114 | ENDDO |
---|
| 1115 | |
---|
| 1116 | !$OMP DO |
---|
| 1117 | DO j = nys, nyn |
---|
| 1118 | |
---|
| 1119 | CALL fft_x_m( work_fftx(:,:,j), 'forward' ) |
---|
| 1120 | |
---|
| 1121 | DO k = 1, nz |
---|
| 1122 | DO i = 0, nx |
---|
| 1123 | work(j,k,i) = work_fftx(i,k,j) |
---|
| 1124 | ENDDO |
---|
| 1125 | ENDDO |
---|
| 1126 | |
---|
| 1127 | ENDDO |
---|
| 1128 | !$OMP END PARALLEL |
---|
| 1129 | |
---|
| 1130 | ELSE |
---|
| 1131 | |
---|
| 1132 | ! |
---|
| 1133 | !-- Cache optimized code (there might be still a potential for better |
---|
| 1134 | !-- optimization). |
---|
[696] | 1135 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
[1] | 1136 | !$OMP DO |
---|
| 1137 | DO i = 0, nx |
---|
| 1138 | |
---|
| 1139 | DO j = nys, nyn |
---|
| 1140 | DO k = 1, nz |
---|
| 1141 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
| 1142 | ENDDO |
---|
| 1143 | ENDDO |
---|
| 1144 | |
---|
| 1145 | ENDDO |
---|
| 1146 | |
---|
| 1147 | !$OMP DO |
---|
| 1148 | DO j = nys, nyn |
---|
| 1149 | DO k = 1, nz |
---|
| 1150 | |
---|
| 1151 | CALL fft_x( work_fftx(0:nx,k,j), 'forward' ) |
---|
| 1152 | |
---|
| 1153 | DO i = 0, nx |
---|
| 1154 | work(j,k,i) = work_fftx(i,k,j) |
---|
| 1155 | ENDDO |
---|
| 1156 | ENDDO |
---|
| 1157 | |
---|
| 1158 | ENDDO |
---|
| 1159 | !$OMP END PARALLEL |
---|
| 1160 | |
---|
| 1161 | ENDIF |
---|
| 1162 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
---|
| 1163 | |
---|
| 1164 | ! |
---|
| 1165 | !-- Transpose array |
---|
| 1166 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 1167 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 1168 | CALL MPI_ALLTOALL( work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 1169 | f_out(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 1170 | comm1dy, ierr ) |
---|
| 1171 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 1172 | |
---|
| 1173 | END SUBROUTINE fftx_tr_xy |
---|
| 1174 | |
---|
| 1175 | |
---|
| 1176 | SUBROUTINE tr_yx_fftx( f_in, work, f_out ) |
---|
| 1177 | |
---|
| 1178 | !------------------------------------------------------------------------------! |
---|
| 1179 | ! Transposition y --> x with a subsequent backward Fourier transformation for |
---|
| 1180 | ! a 1d-decomposition along x |
---|
| 1181 | !------------------------------------------------------------------------------! |
---|
| 1182 | |
---|
| 1183 | USE control_parameters |
---|
| 1184 | USE cpulog |
---|
| 1185 | USE indices |
---|
| 1186 | USE interfaces |
---|
| 1187 | USE pegrid |
---|
| 1188 | USE transpose_indices |
---|
| 1189 | |
---|
| 1190 | IMPLICIT NONE |
---|
| 1191 | |
---|
| 1192 | INTEGER :: i, j, k |
---|
| 1193 | |
---|
[1003] | 1194 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
| 1195 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: f_in |
---|
| 1196 | REAL, DIMENSION(1:nz,nys:nyn,0:nx) :: f_out |
---|
| 1197 | REAL, DIMENSION(nys:nyn,1:nz,0:nx) :: work |
---|
[1] | 1198 | |
---|
| 1199 | ! |
---|
| 1200 | !-- Transpose array |
---|
| 1201 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
[622] | 1202 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
[1] | 1203 | CALL MPI_ALLTOALL( f_in(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
| 1204 | work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
| 1205 | comm1dy, ierr ) |
---|
| 1206 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
| 1207 | |
---|
| 1208 | ! |
---|
| 1209 | !-- Carry out the FFT along x, where all data are present due to the |
---|
| 1210 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
| 1211 | !-- the first index. |
---|
| 1212 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
---|
| 1213 | |
---|
| 1214 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1215 | ! |
---|
| 1216 | !-- Code optimized for vector processors |
---|
[85] | 1217 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
[1] | 1218 | !$OMP DO |
---|
| 1219 | DO j = nys, nyn |
---|
| 1220 | |
---|
| 1221 | DO k = 1, nz |
---|
| 1222 | DO i = 0, nx |
---|
| 1223 | work_fftx(i,k,j) = work(j,k,i) |
---|
| 1224 | ENDDO |
---|
| 1225 | ENDDO |
---|
| 1226 | |
---|
| 1227 | CALL fft_x_m( work_fftx(:,:,j), 'backward' ) |
---|
| 1228 | |
---|
| 1229 | ENDDO |
---|
| 1230 | |
---|
| 1231 | !$OMP DO |
---|
| 1232 | DO i = 0, nx |
---|
| 1233 | DO j = nys, nyn |
---|
| 1234 | DO k = 1, nz |
---|
| 1235 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
| 1236 | ENDDO |
---|
| 1237 | ENDDO |
---|
| 1238 | ENDDO |
---|
| 1239 | !$OMP END PARALLEL |
---|
| 1240 | |
---|
| 1241 | ELSE |
---|
| 1242 | |
---|
| 1243 | ! |
---|
| 1244 | !-- Cache optimized code (there might be still a potential for better |
---|
| 1245 | !-- optimization). |
---|
[696] | 1246 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
[1] | 1247 | !$OMP DO |
---|
| 1248 | DO j = nys, nyn |
---|
| 1249 | DO k = 1, nz |
---|
| 1250 | |
---|
| 1251 | DO i = 0, nx |
---|
| 1252 | work_fftx(i,k,j) = work(j,k,i) |
---|
| 1253 | ENDDO |
---|
| 1254 | |
---|
| 1255 | CALL fft_x( work_fftx(0:nx,k,j), 'backward' ) |
---|
| 1256 | |
---|
| 1257 | ENDDO |
---|
| 1258 | ENDDO |
---|
| 1259 | |
---|
| 1260 | !$OMP DO |
---|
| 1261 | DO i = 0, nx |
---|
| 1262 | DO j = nys, nyn |
---|
| 1263 | DO k = 1, nz |
---|
| 1264 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
| 1265 | ENDDO |
---|
| 1266 | ENDDO |
---|
| 1267 | ENDDO |
---|
| 1268 | !$OMP END PARALLEL |
---|
| 1269 | |
---|
| 1270 | ENDIF |
---|
| 1271 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
---|
| 1272 | |
---|
| 1273 | END SUBROUTINE tr_yx_fftx |
---|
| 1274 | |
---|
| 1275 | |
---|
| 1276 | SUBROUTINE ffty_tri_ffty( ar ) |
---|
| 1277 | |
---|
| 1278 | !------------------------------------------------------------------------------! |
---|
| 1279 | ! FFT along y, solution of the tridiagonal system and backward FFT for |
---|
| 1280 | ! a 1d-decomposition along y |
---|
| 1281 | ! |
---|
| 1282 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
| 1283 | ! with OpenMP (for possible necessary changes see the original |
---|
| 1284 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
| 1285 | !------------------------------------------------------------------------------! |
---|
| 1286 | |
---|
| 1287 | USE control_parameters |
---|
| 1288 | USE cpulog |
---|
| 1289 | USE grid_variables |
---|
| 1290 | USE indices |
---|
| 1291 | USE interfaces |
---|
| 1292 | USE pegrid |
---|
| 1293 | USE transpose_indices |
---|
| 1294 | |
---|
| 1295 | IMPLICIT NONE |
---|
| 1296 | |
---|
| 1297 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
| 1298 | |
---|
[1003] | 1299 | REAL, DIMENSION(0:ny) :: work_ffty |
---|
| 1300 | REAL, DIMENSION(0:ny,1:nz) :: work_triy |
---|
| 1301 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: ar |
---|
| 1302 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
[1] | 1303 | |
---|
| 1304 | |
---|
| 1305 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'start' ) |
---|
| 1306 | |
---|
| 1307 | ALLOCATE( tri(5,0:ny,0:nz-1,0:threads_per_task-1) ) |
---|
| 1308 | |
---|
| 1309 | tn = 0 ! Default thread number in case of one thread |
---|
[696] | 1310 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_ffty, work_triy ) |
---|
[1] | 1311 | DO i = nxl_y, nxr_y |
---|
| 1312 | |
---|
| 1313 | !$ tn = omp_get_thread_num() |
---|
| 1314 | |
---|
| 1315 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1316 | ! |
---|
| 1317 | !-- Code optimized for vector processors |
---|
| 1318 | DO k = 1, nz |
---|
| 1319 | |
---|
| 1320 | m = 0 |
---|
| 1321 | DO n = 1, pdims(2) |
---|
[1003] | 1322 | DO j = 1, nny |
---|
[1] | 1323 | work_triy(m,k) = ar(j,k,i,n) |
---|
| 1324 | m = m + 1 |
---|
| 1325 | ENDDO |
---|
| 1326 | ENDDO |
---|
| 1327 | |
---|
| 1328 | ENDDO |
---|
| 1329 | |
---|
| 1330 | CALL fft_y_m( work_triy, ny, 'forward' ) |
---|
| 1331 | |
---|
| 1332 | ELSE |
---|
| 1333 | ! |
---|
| 1334 | !-- Cache optimized code |
---|
| 1335 | DO k = 1, nz |
---|
| 1336 | |
---|
| 1337 | m = 0 |
---|
| 1338 | DO n = 1, pdims(2) |
---|
[1003] | 1339 | DO j = 1, nny |
---|
[1] | 1340 | work_ffty(m) = ar(j,k,i,n) |
---|
| 1341 | m = m + 1 |
---|
| 1342 | ENDDO |
---|
| 1343 | ENDDO |
---|
| 1344 | |
---|
| 1345 | CALL fft_y( work_ffty, 'forward' ) |
---|
| 1346 | |
---|
| 1347 | DO j = 0, ny |
---|
| 1348 | work_triy(j,k) = work_ffty(j) |
---|
| 1349 | ENDDO |
---|
| 1350 | |
---|
| 1351 | ENDDO |
---|
| 1352 | |
---|
| 1353 | ENDIF |
---|
| 1354 | |
---|
| 1355 | ! |
---|
| 1356 | !-- Solve the linear equation system |
---|
| 1357 | CALL tridia_1dd( ddy2, ddx2, ny, nx, i, work_triy, tri(:,:,:,tn) ) |
---|
| 1358 | |
---|
| 1359 | IF ( host(1:3) == 'nec' ) THEN |
---|
| 1360 | ! |
---|
| 1361 | !-- Code optimized for vector processors |
---|
| 1362 | CALL fft_y_m( work_triy, ny, 'backward' ) |
---|
| 1363 | |
---|
| 1364 | DO k = 1, nz |
---|
| 1365 | |
---|
| 1366 | m = 0 |
---|
| 1367 | DO n = 1, pdims(2) |
---|
[1003] | 1368 | DO j = 1, nny |
---|
[1] | 1369 | ar(j,k,i,n) = work_triy(m,k) |
---|
| 1370 | m = m + 1 |
---|
| 1371 | ENDDO |
---|
| 1372 | ENDDO |
---|
| 1373 | |
---|
| 1374 | ENDDO |
---|
| 1375 | |
---|
| 1376 | ELSE |
---|
| 1377 | ! |
---|
| 1378 | !-- Cache optimized code |
---|
| 1379 | DO k = 1, nz |
---|
| 1380 | |
---|
| 1381 | DO j = 0, ny |
---|
| 1382 | work_ffty(j) = work_triy(j,k) |
---|
| 1383 | ENDDO |
---|
| 1384 | |
---|
| 1385 | CALL fft_y( work_ffty, 'backward' ) |
---|
| 1386 | |
---|
| 1387 | m = 0 |
---|
| 1388 | DO n = 1, pdims(2) |
---|
[1003] | 1389 | DO j = 1, nny |
---|
[1] | 1390 | ar(j,k,i,n) = work_ffty(m) |
---|
| 1391 | m = m + 1 |
---|
| 1392 | ENDDO |
---|
| 1393 | ENDDO |
---|
| 1394 | |
---|
| 1395 | ENDDO |
---|
| 1396 | |
---|
| 1397 | ENDIF |
---|
| 1398 | |
---|
| 1399 | ENDDO |
---|
| 1400 | |
---|
| 1401 | DEALLOCATE( tri ) |
---|
| 1402 | |
---|
| 1403 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'stop' ) |
---|
| 1404 | |
---|
| 1405 | END SUBROUTINE ffty_tri_ffty |
---|
| 1406 | |
---|
| 1407 | |
---|
| 1408 | SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri ) |
---|
| 1409 | |
---|
| 1410 | !------------------------------------------------------------------------------! |
---|
| 1411 | ! Solves the linear system of equations for a 1d-decomposition along x (see |
---|
| 1412 | ! tridia) |
---|
| 1413 | ! |
---|
[940] | 1414 | ! Attention: when using the intel compilers older than 12.0, array tri must |
---|
| 1415 | ! be passed as an argument to the contained subroutines. Otherwise |
---|
| 1416 | ! addres faults will occur. This feature can be activated with |
---|
| 1417 | ! cpp-switch __intel11 |
---|
[1] | 1418 | ! On NEC, tri should not be passed (except for routine substi_1dd) |
---|
| 1419 | ! because this causes very bad performance. |
---|
| 1420 | !------------------------------------------------------------------------------! |
---|
| 1421 | |
---|
| 1422 | USE arrays_3d |
---|
| 1423 | USE control_parameters |
---|
| 1424 | |
---|
| 1425 | USE pegrid |
---|
| 1426 | |
---|
| 1427 | IMPLICIT NONE |
---|
| 1428 | |
---|
| 1429 | INTEGER :: i, j, k, nnyh, nx, ny, omp_get_thread_num, tn |
---|
| 1430 | |
---|
| 1431 | REAL :: ddx2, ddy2 |
---|
| 1432 | |
---|
| 1433 | REAL, DIMENSION(0:nx,1:nz) :: ar |
---|
| 1434 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1435 | |
---|
| 1436 | |
---|
| 1437 | nnyh = ( ny + 1 ) / 2 |
---|
| 1438 | |
---|
| 1439 | ! |
---|
| 1440 | !-- Define constant elements of the tridiagonal matrix. |
---|
| 1441 | !-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2, |
---|
| 1442 | !-- the exchanged loops create bank conflicts. The following directive |
---|
| 1443 | !-- prohibits loop exchange and the loops perform much better. |
---|
| 1444 | ! tn = omp_get_thread_num() |
---|
| 1445 | ! WRITE( 120+tn, * ) '+++ id=',myid,' nx=',nx,' thread=', omp_get_thread_num() |
---|
[82] | 1446 | ! CALL local_flush( 120+tn ) |
---|
[1] | 1447 | !CDIR NOLOOPCHG |
---|
| 1448 | DO k = 0, nz-1 |
---|
| 1449 | DO i = 0,nx |
---|
[667] | 1450 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
---|
| 1451 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
---|
[1] | 1452 | ENDDO |
---|
| 1453 | ENDDO |
---|
| 1454 | ! WRITE( 120+tn, * ) '+++ id=',myid,' end of first tridia loop thread=', omp_get_thread_num() |
---|
[82] | 1455 | ! CALL local_flush( 120+tn ) |
---|
[1] | 1456 | |
---|
| 1457 | IF ( j <= nnyh ) THEN |
---|
[940] | 1458 | #if defined( __intel11 ) |
---|
[1] | 1459 | CALL maketri_1dd( j, tri ) |
---|
| 1460 | #else |
---|
| 1461 | CALL maketri_1dd( j ) |
---|
| 1462 | #endif |
---|
| 1463 | ELSE |
---|
[940] | 1464 | #if defined( __intel11 ) |
---|
[1] | 1465 | CALL maketri_1dd( ny+1-j, tri ) |
---|
| 1466 | #else |
---|
| 1467 | CALL maketri_1dd( ny+1-j ) |
---|
| 1468 | #endif |
---|
| 1469 | ENDIF |
---|
[940] | 1470 | #if defined( __intel11 ) |
---|
[1] | 1471 | CALL split_1dd( tri ) |
---|
| 1472 | #else |
---|
| 1473 | CALL split_1dd |
---|
| 1474 | #endif |
---|
| 1475 | CALL substi_1dd( ar, tri ) |
---|
| 1476 | |
---|
| 1477 | CONTAINS |
---|
| 1478 | |
---|
[940] | 1479 | #if defined( __intel11 ) |
---|
[1] | 1480 | SUBROUTINE maketri_1dd( j, tri ) |
---|
| 1481 | #else |
---|
| 1482 | SUBROUTINE maketri_1dd( j ) |
---|
| 1483 | #endif |
---|
| 1484 | |
---|
| 1485 | !------------------------------------------------------------------------------! |
---|
| 1486 | ! computes the i- and j-dependent component of the matrix |
---|
| 1487 | !------------------------------------------------------------------------------! |
---|
| 1488 | |
---|
| 1489 | USE constants |
---|
| 1490 | |
---|
| 1491 | IMPLICIT NONE |
---|
| 1492 | |
---|
| 1493 | INTEGER :: i, j, k, nnxh |
---|
| 1494 | REAL :: a, c |
---|
| 1495 | |
---|
| 1496 | REAL, DIMENSION(0:nx) :: l |
---|
| 1497 | |
---|
[940] | 1498 | #if defined( __intel11 ) |
---|
[1] | 1499 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1500 | #endif |
---|
| 1501 | |
---|
| 1502 | |
---|
| 1503 | nnxh = ( nx + 1 ) / 2 |
---|
| 1504 | ! |
---|
| 1505 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
---|
| 1506 | !-- Fourier space. The coefficients are computed following the method of |
---|
| 1507 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
---|
| 1508 | !-- Siano's original version by discretizing the Poisson equation, |
---|
| 1509 | !-- before it is Fourier-transformed |
---|
| 1510 | DO i = 0, nx |
---|
[128] | 1511 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
---|
[1] | 1512 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
---|
[1013] | 1513 | REAL( nx+1 ) ) ) * ddx2 + & |
---|
[1] | 1514 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
[1013] | 1515 | REAL( ny+1 ) ) ) * ddy2 |
---|
[1] | 1516 | ELSE |
---|
| 1517 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
[1013] | 1518 | REAL( nx+1 ) ) ) * ddx2 + & |
---|
[1] | 1519 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
[1013] | 1520 | REAL( ny+1 ) ) ) * ddy2 |
---|
[1] | 1521 | ENDIF |
---|
| 1522 | ENDDO |
---|
| 1523 | |
---|
| 1524 | DO k = 0, nz-1 |
---|
| 1525 | DO i = 0, nx |
---|
[667] | 1526 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
| 1527 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
[1] | 1528 | tri(1,i,k) = a + c - l(i) |
---|
| 1529 | ENDDO |
---|
| 1530 | ENDDO |
---|
| 1531 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
| 1532 | DO i = 0, nx |
---|
| 1533 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
| 1534 | ENDDO |
---|
| 1535 | ENDIF |
---|
| 1536 | IF ( ibc_p_t == 1 ) THEN |
---|
| 1537 | DO i = 0, nx |
---|
| 1538 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
| 1539 | ENDDO |
---|
| 1540 | ENDIF |
---|
| 1541 | |
---|
| 1542 | END SUBROUTINE maketri_1dd |
---|
| 1543 | |
---|
| 1544 | |
---|
[940] | 1545 | #if defined( __intel11 ) |
---|
[1] | 1546 | SUBROUTINE split_1dd( tri ) |
---|
| 1547 | #else |
---|
| 1548 | SUBROUTINE split_1dd |
---|
| 1549 | #endif |
---|
| 1550 | |
---|
| 1551 | !------------------------------------------------------------------------------! |
---|
| 1552 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
| 1553 | !------------------------------------------------------------------------------! |
---|
| 1554 | |
---|
| 1555 | IMPLICIT NONE |
---|
| 1556 | |
---|
| 1557 | INTEGER :: i, k |
---|
| 1558 | |
---|
[940] | 1559 | #if defined( __intel11 ) |
---|
[1] | 1560 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1561 | #endif |
---|
| 1562 | |
---|
| 1563 | |
---|
| 1564 | ! |
---|
| 1565 | !-- Splitting |
---|
| 1566 | DO i = 0, nx |
---|
| 1567 | tri(4,i,0) = tri(1,i,0) |
---|
| 1568 | ENDDO |
---|
| 1569 | DO k = 1, nz-1 |
---|
| 1570 | DO i = 0, nx |
---|
| 1571 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
| 1572 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
| 1573 | ENDDO |
---|
| 1574 | ENDDO |
---|
| 1575 | |
---|
| 1576 | END SUBROUTINE split_1dd |
---|
| 1577 | |
---|
| 1578 | |
---|
| 1579 | SUBROUTINE substi_1dd( ar, tri ) |
---|
| 1580 | |
---|
| 1581 | !------------------------------------------------------------------------------! |
---|
| 1582 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
| 1583 | !------------------------------------------------------------------------------! |
---|
| 1584 | |
---|
| 1585 | IMPLICIT NONE |
---|
| 1586 | |
---|
[76] | 1587 | INTEGER :: i, k |
---|
[1] | 1588 | |
---|
| 1589 | REAL, DIMENSION(0:nx,nz) :: ar |
---|
| 1590 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
| 1591 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
| 1592 | |
---|
| 1593 | ! |
---|
| 1594 | !-- Forward substitution |
---|
| 1595 | DO i = 0, nx |
---|
| 1596 | ar1(i,0) = ar(i,1) |
---|
| 1597 | ENDDO |
---|
| 1598 | DO k = 1, nz-1 |
---|
| 1599 | DO i = 0, nx |
---|
| 1600 | ar1(i,k) = ar(i,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
| 1601 | ENDDO |
---|
| 1602 | ENDDO |
---|
| 1603 | |
---|
| 1604 | ! |
---|
| 1605 | !-- Backward substitution |
---|
[763] | 1606 | !-- Note, the add of 1.0E-20 in the denominator is due to avoid divisions |
---|
| 1607 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
| 1608 | !-- the model domain. |
---|
[1] | 1609 | DO i = 0, nx |
---|
[761] | 1610 | ar(i,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
[1] | 1611 | ENDDO |
---|
| 1612 | DO k = nz-2, 0, -1 |
---|
| 1613 | DO i = 0, nx |
---|
| 1614 | ar(i,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,k+2) ) & |
---|
| 1615 | / tri(4,i,k) |
---|
| 1616 | ENDDO |
---|
| 1617 | ENDDO |
---|
| 1618 | |
---|
[76] | 1619 | ! |
---|
| 1620 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
| 1621 | !-- The respective values of ar should be zero at all k-levels if |
---|
| 1622 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
| 1623 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
| 1624 | IF ( j == 0 ) THEN |
---|
| 1625 | DO k = 1, nz |
---|
| 1626 | ar(0,k) = 0.0 |
---|
| 1627 | ENDDO |
---|
| 1628 | ENDIF |
---|
| 1629 | ENDIF |
---|
| 1630 | |
---|
[1] | 1631 | END SUBROUTINE substi_1dd |
---|
| 1632 | |
---|
| 1633 | END SUBROUTINE tridia_1dd |
---|
| 1634 | |
---|
| 1635 | #endif |
---|
[807] | 1636 | #endif |
---|
[1] | 1637 | END MODULE poisfft_mod |
---|