1 | MODULE poisfft_mod |
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2 | |
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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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20 | ! Current revisions: |
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21 | ! ----------------- |
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22 | ! |
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23 | ! |
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24 | ! Former revisions: |
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25 | ! ----------------- |
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26 | ! $Id: poisfft.f90 1036 2012-10-22 13:43:42Z raasch $ |
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27 | ! |
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28 | ! 2012-09-21 07:03:55Z raasch |
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29 | ! FLOAT type conversion replaced by REAL |
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30 | ! |
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31 | ! 1003 2012-09-14 14:35:53Z raasch |
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32 | ! indices nxa, nya, etc. replaced by nx, ny, etc. |
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33 | ! |
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34 | ! 940 2012-07-09 14:31:00Z raasch |
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35 | ! special handling of tri-array as an argument in tridia_1dd routines switched |
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36 | ! off because it caused segmentation faults with intel 12.1 compiler |
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37 | ! |
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38 | ! 877 2012-04-03 11:21:44Z suehring |
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39 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
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40 | ! pressure at the top of the model domain. |
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41 | ! |
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42 | ! 809 2012-01-30 13:32:58Z maronga |
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43 | ! Bugfix: replaced .AND. and .NOT. with && and ! in the preprocessor directives |
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44 | ! |
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45 | ! 807 2012-01-25 11:53:51Z maronga |
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46 | ! New cpp directive "__check" implemented which is used by check_namelist_files |
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47 | ! (most of the code is unneeded by check_namelist_files). |
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48 | ! |
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49 | ! 763 2011-10-06 09:32:09Z suehring |
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50 | ! Comment added concerning the last change. |
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51 | ! |
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52 | ! 761 2011-10-05 17:58:52Z suehring |
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53 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
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54 | ! pressure at the top of the model domain. |
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55 | ! |
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56 | ! 696 2011-03-18 07:03:49Z raasch |
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57 | ! work_fftx removed from PRIVATE clauses in fftx_tr_xy and tr_yx_fftx |
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58 | ! |
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59 | ! 683 2011-02-09 14:25:15Z raasch |
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60 | ! openMP parallelization for 2d-domain-decomposition |
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61 | ! |
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62 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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63 | ! ddzu replaced by ddzu_pres due to changes in zu(0) |
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64 | ! |
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65 | ! 622 2010-12-10 08:08:13Z raasch |
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66 | ! optional barriers included in order to speed up collective operations |
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67 | ! |
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68 | ! 377 2009-09-04 11:09:00Z raasch |
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69 | ! __lcmuk changed to __lc to avoid problems with Intel compiler on sgi-ice |
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70 | ! |
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71 | ! 164 2008-05-15 08:46:15Z raasch |
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72 | ! Arguments removed from transpose routines |
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73 | ! |
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74 | ! 128 2007-10-26 13:11:14Z raasch |
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75 | ! Bugfix: wavenumber calculation for even nx in routines maketri |
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76 | ! |
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77 | ! 85 2007-05-11 09:35:14Z raasch |
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78 | ! Bugfix: work_fft*_vec removed from some PRIVATE-declarations |
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79 | ! |
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80 | ! 76 2007-03-29 00:58:32Z raasch |
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81 | ! Tridiagonal coefficients adjusted for Neumann boundary conditions both at |
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82 | ! the bottom and the top. |
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83 | ! |
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84 | ! RCS Log replace by Id keyword, revision history cleaned up |
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85 | ! |
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86 | ! Revision 1.24 2006/08/04 15:00:24 raasch |
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87 | ! Default setting of the thread number tn in case of not using OpenMP |
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88 | ! |
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89 | ! Revision 1.23 2006/02/23 12:48:38 raasch |
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90 | ! Additional compiler directive in routine tridia_1dd for preventing loop |
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91 | ! exchange on NEC-SX6 |
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92 | ! |
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93 | ! Revision 1.20 2004/04/30 12:38:09 raasch |
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94 | ! Parts of former poisfft_hybrid moved to this subroutine, |
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95 | ! former subroutine changed to a module, renaming of FFT-subroutines and |
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96 | ! -module, FFTs completely substituted by calls of fft_x and fft_y, |
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97 | ! NAG fft used in the non-parallel case completely removed, l in maketri |
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98 | ! is now a 1d-array, variables passed by modules instead of using parameter |
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99 | ! lists, enlarged transposition arrays introduced |
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100 | ! |
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101 | ! Revision 1.1 1997/07/24 11:24:14 raasch |
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102 | ! Initial revision |
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103 | ! |
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104 | ! |
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105 | ! Description: |
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106 | ! ------------ |
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107 | ! See below. |
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108 | !------------------------------------------------------------------------------! |
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109 | |
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110 | !--------------------------------------------------------------------------! |
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111 | ! poisfft ! |
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112 | ! ! |
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113 | ! Original version: Stephan Siano (pois3d) ! |
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114 | ! ! |
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115 | ! Institute of Meteorology and Climatology, University of Hannover ! |
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116 | ! Germany ! |
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117 | ! ! |
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118 | ! Version as of July 23,1996 ! |
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119 | ! ! |
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120 | ! ! |
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121 | ! Version for parallel computers: Siegfried Raasch ! |
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122 | ! ! |
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123 | ! Version as of July 03,1997 ! |
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124 | ! ! |
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125 | ! Solves the Poisson equation with a 2D spectral method ! |
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126 | ! d^2 p / dx^2 + d^2 p / dy^2 + d^2 p / dz^2 = s ! |
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127 | ! ! |
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128 | ! Input: ! |
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129 | ! real ar contains in the (nnx,nny,nnz) elements, ! |
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130 | ! starting from the element (1,nys,nxl), the ! |
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131 | ! values for s ! |
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132 | ! real work Temporary array ! |
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133 | ! ! |
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134 | ! Output: ! |
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135 | ! real ar contains the solution for p ! |
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136 | !--------------------------------------------------------------------------! |
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137 | |
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138 | USE fft_xy |
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139 | USE indices |
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140 | USE transpose_indices |
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141 | |
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142 | IMPLICIT NONE |
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143 | |
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144 | PRIVATE |
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145 | |
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146 | #if ! defined ( __check ) |
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147 | PUBLIC poisfft, poisfft_init |
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148 | |
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149 | INTERFACE poisfft |
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150 | MODULE PROCEDURE poisfft |
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151 | END INTERFACE poisfft |
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152 | |
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153 | INTERFACE poisfft_init |
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154 | MODULE PROCEDURE poisfft_init |
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155 | END INTERFACE poisfft_init |
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156 | #else |
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157 | PUBLIC poisfft_init |
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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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162 | #endif |
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163 | |
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164 | CONTAINS |
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165 | |
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166 | SUBROUTINE poisfft_init |
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167 | |
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168 | CALL fft_init |
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169 | |
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170 | END SUBROUTINE poisfft_init |
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171 | |
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172 | #if ! defined ( __check ) |
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173 | SUBROUTINE poisfft( ar, work ) |
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174 | |
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175 | USE cpulog |
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176 | USE interfaces |
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177 | USE pegrid |
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178 | |
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179 | IMPLICIT NONE |
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180 | |
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181 | REAL, DIMENSION(1:nz,nys:nyn,nxl:nxr) :: ar, work |
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182 | |
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183 | |
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184 | CALL cpu_log( log_point_s(3), 'poisfft', 'start' ) |
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185 | |
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186 | ! |
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187 | !-- Two-dimensional Fourier Transformation in x- and y-direction. |
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188 | #if defined( __parallel ) |
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189 | IF ( pdims(2) == 1 ) THEN |
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190 | |
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191 | ! |
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192 | !-- 1d-domain-decomposition along x: |
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193 | !-- FFT along y and transposition y --> x |
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194 | CALL ffty_tr_yx( ar, work, ar ) |
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195 | |
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196 | ! |
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197 | !-- FFT along x, solving the tridiagonal system and backward FFT |
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198 | CALL fftx_tri_fftx( ar ) |
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199 | |
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200 | ! |
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201 | !-- Transposition x --> y and backward FFT along y |
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202 | CALL tr_xy_ffty( ar, work, ar ) |
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203 | |
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204 | ELSEIF ( pdims(1) == 1 ) THEN |
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205 | |
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206 | ! |
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207 | !-- 1d-domain-decomposition along y: |
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208 | !-- FFT along x and transposition x --> y |
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209 | CALL fftx_tr_xy( ar, work, ar ) |
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210 | |
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211 | ! |
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212 | !-- FFT along y, solving the tridiagonal system and backward FFT |
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213 | CALL ffty_tri_ffty( ar ) |
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214 | |
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215 | ! |
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216 | !-- Transposition y --> x and backward FFT along x |
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217 | CALL tr_yx_fftx( ar, work, ar ) |
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218 | |
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219 | ELSE |
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220 | |
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221 | ! |
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222 | !-- 2d-domain-decomposition |
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223 | !-- Transposition z --> x |
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224 | CALL cpu_log( log_point_s(5), 'transpo forward', 'start' ) |
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225 | CALL transpose_zx( ar, work, ar ) |
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226 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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227 | |
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228 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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229 | CALL fftxp( ar, 'forward' ) |
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230 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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231 | |
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232 | ! |
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233 | !-- Transposition x --> y |
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234 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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235 | CALL transpose_xy( ar, work, ar ) |
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236 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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237 | |
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238 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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239 | CALL fftyp( ar, 'forward' ) |
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240 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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241 | |
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242 | ! |
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243 | !-- Transposition y --> z |
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244 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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245 | CALL transpose_yz( ar, work, ar ) |
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246 | CALL cpu_log( log_point_s(5), 'transpo forward', 'stop' ) |
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247 | |
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248 | ! |
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249 | !-- Solve the Poisson equation in z-direction in cartesian space. |
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250 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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251 | CALL tridia( ar ) |
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252 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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253 | |
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254 | ! |
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255 | !-- Inverse Fourier Transformation |
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256 | !-- Transposition z --> y |
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257 | CALL cpu_log( log_point_s(8), 'transpo invers', 'start' ) |
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258 | CALL transpose_zy( ar, work, ar ) |
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259 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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260 | |
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261 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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262 | CALL fftyp( ar, 'backward' ) |
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263 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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264 | |
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265 | ! |
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266 | !-- Transposition y --> x |
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267 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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268 | CALL transpose_yx( ar, work, ar ) |
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269 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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270 | |
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271 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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272 | CALL fftxp( ar, 'backward' ) |
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273 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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274 | |
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275 | ! |
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276 | !-- Transposition x --> z |
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277 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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278 | CALL transpose_xz( ar, work, ar ) |
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279 | CALL cpu_log( log_point_s(8), 'transpo invers', 'stop' ) |
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280 | |
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281 | ENDIF |
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282 | |
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283 | #else |
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284 | |
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285 | ! |
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286 | !-- Two-dimensional Fourier Transformation along x- and y-direction. |
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287 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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288 | CALL fftx( ar, 'forward' ) |
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289 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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290 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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291 | CALL ffty( ar, 'forward' ) |
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292 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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293 | |
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294 | ! |
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295 | !-- Solve the Poisson equation in z-direction in cartesian space. |
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296 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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297 | CALL tridia( ar ) |
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298 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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299 | |
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300 | ! |
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301 | !-- Inverse Fourier Transformation. |
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302 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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303 | CALL ffty( ar, 'backward' ) |
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304 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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305 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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306 | CALL fftx( ar, 'backward' ) |
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307 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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308 | |
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309 | #endif |
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310 | |
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311 | CALL cpu_log( log_point_s(3), 'poisfft', 'stop' ) |
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312 | |
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313 | END SUBROUTINE poisfft |
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314 | |
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315 | |
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316 | |
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317 | SUBROUTINE tridia( ar ) |
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318 | |
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319 | !------------------------------------------------------------------------------! |
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320 | ! solves the linear system of equations: |
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321 | ! |
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322 | ! -(4 pi^2(i^2/(dx^2*nnx^2)+j^2/(dy^2*nny^2))+ |
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323 | ! 1/(dzu(k)*dzw(k))+1/(dzu(k-1)*dzw(k)))*p(i,j,k)+ |
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324 | ! 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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325 | ! |
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326 | ! by using the Thomas algorithm |
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327 | !------------------------------------------------------------------------------! |
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328 | |
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329 | USE arrays_3d |
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330 | |
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331 | IMPLICIT NONE |
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332 | |
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333 | INTEGER :: i, j, k, nnyh |
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334 | |
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335 | REAL, DIMENSION(nxl_z:nxr_z,0:nz-1) :: ar1 |
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336 | REAL, DIMENSION(5,nxl_z:nxr_z,0:nz-1) :: tri |
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337 | |
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338 | #if defined( __parallel ) |
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339 | REAL :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) |
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340 | #else |
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341 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
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342 | #endif |
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343 | |
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344 | |
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345 | nnyh = (ny+1) / 2 |
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346 | |
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347 | ! |
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348 | !-- Define constant elements of the tridiagonal matrix. |
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349 | !$OMP PARALLEL PRIVATE ( k, i ) |
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350 | !$OMP DO |
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351 | DO k = 0, nz-1 |
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352 | DO i = nxl_z, nxr_z |
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353 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
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354 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
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355 | ENDDO |
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356 | ENDDO |
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357 | !$OMP END PARALLEL |
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358 | |
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359 | #if defined( __parallel ) |
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360 | ! |
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361 | !-- Repeat for all y-levels. |
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362 | !$OMP PARALLEL FIRSTPRIVATE( tri ) PRIVATE ( ar1, j ) |
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363 | !$OMP DO |
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364 | DO j = nys_z, nyn_z |
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365 | IF ( j <= nnyh ) THEN |
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366 | CALL maketri( tri, j ) |
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367 | ELSE |
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368 | CALL maketri( tri, ny+1-j ) |
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369 | ENDIF |
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370 | CALL split( tri ) |
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371 | CALL substi( ar, ar1, tri, j ) |
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372 | ENDDO |
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373 | !$OMP END PARALLEL |
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374 | #else |
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375 | ! |
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376 | !-- First y-level. |
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377 | CALL maketri( tri, nys_z ) |
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378 | CALL split( tri ) |
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379 | CALL substi( ar, ar1, tri, 0 ) |
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380 | |
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381 | ! |
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382 | !-- Further y-levels. |
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383 | DO j = 1, nnyh - 1 |
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384 | CALL maketri( tri, j ) |
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385 | CALL split( tri ) |
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386 | CALL substi( ar, ar1, tri, j ) |
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387 | CALL substi( ar, ar1, tri, ny+1-j ) |
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388 | ENDDO |
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389 | CALL maketri( tri, nnyh ) |
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390 | CALL split( tri ) |
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391 | CALL substi( ar, ar1, tri, nnyh+nys ) |
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392 | #endif |
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393 | |
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394 | CONTAINS |
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395 | |
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396 | SUBROUTINE maketri( tri, j ) |
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397 | |
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398 | !------------------------------------------------------------------------------! |
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399 | ! Computes the i- and j-dependent component of the matrix |
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400 | !------------------------------------------------------------------------------! |
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401 | |
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402 | USE arrays_3d |
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403 | USE constants |
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404 | USE control_parameters |
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405 | USE grid_variables |
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406 | |
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407 | IMPLICIT NONE |
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408 | |
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409 | INTEGER :: i, j, k, nnxh |
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410 | REAL :: a, c |
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411 | REAL :: ll(nxl_z:nxr_z) |
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412 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
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413 | |
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414 | |
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415 | nnxh = ( nx + 1 ) / 2 |
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416 | |
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417 | ! |
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418 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
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419 | !-- Fourier space. The coefficients are computed following the method of |
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420 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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421 | !-- Siano's original version by discretizing the Poisson equation, |
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422 | !-- before it is Fourier-transformed |
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423 | #if defined( __parallel ) |
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424 | DO i = nxl_z, nxr_z |
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425 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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426 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
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427 | REAL( nx+1 ) ) ) / ( dx * dx ) + & |
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428 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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429 | REAL( ny+1 ) ) ) / ( dy * dy ) |
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430 | ELSE |
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431 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
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432 | REAL( nx+1 ) ) ) / ( dx * dx ) + & |
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433 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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434 | REAL( ny+1 ) ) ) / ( dy * dy ) |
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435 | ENDIF |
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436 | DO k = 0,nz-1 |
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437 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
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438 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
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439 | tri(1,i,k) = a + c - ll(i) |
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440 | ENDDO |
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441 | ENDDO |
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442 | #else |
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443 | DO i = 0, nnxh |
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444 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / REAL( nx+1 ) ) ) / & |
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445 | ( dx * dx ) + & |
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446 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / REAL( ny+1 ) ) ) / & |
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447 | ( dy * dy ) |
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448 | DO k = 0, nz-1 |
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449 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
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450 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
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451 | tri(1,i,k) = a + c - ll(i) |
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452 | IF ( i >= 1 .and. i < nnxh ) THEN |
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453 | tri(1,nx+1-i,k) = tri(1,i,k) |
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454 | ENDIF |
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455 | ENDDO |
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456 | ENDDO |
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457 | #endif |
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458 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
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459 | DO i = nxl_z, nxr_z |
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460 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
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461 | ENDDO |
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462 | ENDIF |
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463 | IF ( ibc_p_t == 1 ) THEN |
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464 | DO i = nxl_z, nxr_z |
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465 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
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466 | ENDDO |
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467 | ENDIF |
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468 | |
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469 | END SUBROUTINE maketri |
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470 | |
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471 | |
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472 | SUBROUTINE substi( ar, ar1, tri, j ) |
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473 | |
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474 | !------------------------------------------------------------------------------! |
---|
475 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
476 | !------------------------------------------------------------------------------! |
---|
477 | |
---|
478 | USE control_parameters |
---|
479 | |
---|
480 | IMPLICIT NONE |
---|
481 | |
---|
482 | INTEGER :: i, j, k |
---|
483 | REAL :: ar1(nxl_z:nxr_z,0:nz-1) |
---|
484 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
485 | #if defined( __parallel ) |
---|
486 | REAL :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) |
---|
487 | #else |
---|
488 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
---|
489 | #endif |
---|
490 | |
---|
491 | ! |
---|
492 | !-- Forward substitution. |
---|
493 | DO i = nxl_z, nxr_z |
---|
494 | #if defined( __parallel ) |
---|
495 | ar1(i,0) = ar(i,j,1) |
---|
496 | #else |
---|
497 | ar1(i,0) = ar(1,j,i) |
---|
498 | #endif |
---|
499 | ENDDO |
---|
500 | DO k = 1, nz - 1 |
---|
501 | DO i = nxl_z, nxr_z |
---|
502 | #if defined( __parallel ) |
---|
503 | ar1(i,k) = ar(i,j,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
504 | #else |
---|
505 | ar1(i,k) = ar(k+1,j,i) - tri(5,i,k) * ar1(i,k-1) |
---|
506 | #endif |
---|
507 | ENDDO |
---|
508 | ENDDO |
---|
509 | |
---|
510 | ! |
---|
511 | !-- Backward substitution |
---|
512 | !-- Note, the 1.0E-20 in the denominator is due to avoid divisions |
---|
513 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
514 | !-- the model domain. |
---|
515 | DO i = nxl_z, nxr_z |
---|
516 | #if defined( __parallel ) |
---|
517 | ar(i,j,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
518 | #else |
---|
519 | ar(nz,j,i) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
520 | #endif |
---|
521 | ENDDO |
---|
522 | DO k = nz-2, 0, -1 |
---|
523 | DO i = nxl_z, nxr_z |
---|
524 | #if defined( __parallel ) |
---|
525 | ar(i,j,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,j,k+2) ) & |
---|
526 | / tri(4,i,k) |
---|
527 | #else |
---|
528 | ar(k+1,j,i) = ( ar1(i,k) - tri(3,i,k) * ar(k+2,j,i) ) & |
---|
529 | / tri(4,i,k) |
---|
530 | #endif |
---|
531 | ENDDO |
---|
532 | ENDDO |
---|
533 | |
---|
534 | ! |
---|
535 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
536 | !-- The respective values of ar should be zero at all k-levels if |
---|
537 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
538 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
539 | IF ( j == 0 .AND. nxl_z == 0 ) THEN |
---|
540 | #if defined( __parallel ) |
---|
541 | DO k = 1, nz |
---|
542 | ar(nxl_z,j,k) = 0.0 |
---|
543 | ENDDO |
---|
544 | #else |
---|
545 | DO k = 1, nz |
---|
546 | ar(k,j,nxl_z) = 0.0 |
---|
547 | ENDDO |
---|
548 | #endif |
---|
549 | ENDIF |
---|
550 | ENDIF |
---|
551 | |
---|
552 | END SUBROUTINE substi |
---|
553 | |
---|
554 | |
---|
555 | SUBROUTINE split( tri ) |
---|
556 | |
---|
557 | !------------------------------------------------------------------------------! |
---|
558 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
559 | !------------------------------------------------------------------------------! |
---|
560 | |
---|
561 | IMPLICIT NONE |
---|
562 | |
---|
563 | INTEGER :: i, k |
---|
564 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
565 | |
---|
566 | ! |
---|
567 | !-- Splitting. |
---|
568 | DO i = nxl_z, nxr_z |
---|
569 | tri(4,i,0) = tri(1,i,0) |
---|
570 | ENDDO |
---|
571 | DO k = 1, nz-1 |
---|
572 | DO i = nxl_z, nxr_z |
---|
573 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
574 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
575 | ENDDO |
---|
576 | ENDDO |
---|
577 | |
---|
578 | END SUBROUTINE split |
---|
579 | |
---|
580 | END SUBROUTINE tridia |
---|
581 | |
---|
582 | |
---|
583 | #if defined( __parallel ) |
---|
584 | SUBROUTINE fftxp( ar, direction ) |
---|
585 | |
---|
586 | !------------------------------------------------------------------------------! |
---|
587 | ! Fourier-transformation along x-direction Parallelized version |
---|
588 | !------------------------------------------------------------------------------! |
---|
589 | |
---|
590 | IMPLICIT NONE |
---|
591 | |
---|
592 | CHARACTER (LEN=*) :: direction |
---|
593 | INTEGER :: j, k |
---|
594 | REAL :: ar(0:nx,nys_x:nyn_x,nzb_x:nzt_x) |
---|
595 | |
---|
596 | ! |
---|
597 | !-- Performing the fft with one of the methods implemented |
---|
598 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
599 | !$OMP DO |
---|
600 | DO k = nzb_x, nzt_x |
---|
601 | DO j = nys_x, nyn_x |
---|
602 | CALL fft_x( ar(0:nx,j,k), direction ) |
---|
603 | ENDDO |
---|
604 | ENDDO |
---|
605 | !$OMP END PARALLEL |
---|
606 | |
---|
607 | END SUBROUTINE fftxp |
---|
608 | |
---|
609 | #else |
---|
610 | SUBROUTINE fftx( ar, direction ) |
---|
611 | |
---|
612 | !------------------------------------------------------------------------------! |
---|
613 | ! Fourier-transformation along x-direction Non parallel version |
---|
614 | !------------------------------------------------------------------------------! |
---|
615 | |
---|
616 | IMPLICIT NONE |
---|
617 | |
---|
618 | CHARACTER (LEN=*) :: direction |
---|
619 | INTEGER :: i, j, k |
---|
620 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
621 | |
---|
622 | ! |
---|
623 | !-- Performing the fft with one of the methods implemented |
---|
624 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
625 | !$OMP DO |
---|
626 | DO k = 1, nz |
---|
627 | DO j = 0, ny |
---|
628 | CALL fft_x( ar(k,j,0:nx), direction ) |
---|
629 | ENDDO |
---|
630 | ENDDO |
---|
631 | !$OMP END PARALLEL |
---|
632 | |
---|
633 | END SUBROUTINE fftx |
---|
634 | #endif |
---|
635 | |
---|
636 | |
---|
637 | #if defined( __parallel ) |
---|
638 | SUBROUTINE fftyp( ar, direction ) |
---|
639 | |
---|
640 | !------------------------------------------------------------------------------! |
---|
641 | ! Fourier-transformation along y-direction Parallelized version |
---|
642 | !------------------------------------------------------------------------------! |
---|
643 | |
---|
644 | IMPLICIT NONE |
---|
645 | |
---|
646 | CHARACTER (LEN=*) :: direction |
---|
647 | INTEGER :: i, k |
---|
648 | REAL :: ar(0:ny,nxl_y:nxr_y,nzb_y:nzt_y) |
---|
649 | |
---|
650 | ! |
---|
651 | !-- Performing the fft with one of the methods implemented |
---|
652 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
653 | !$OMP DO |
---|
654 | DO k = nzb_y, nzt_y |
---|
655 | DO i = nxl_y, nxr_y |
---|
656 | CALL fft_y( ar(0:ny,i,k), direction ) |
---|
657 | ENDDO |
---|
658 | ENDDO |
---|
659 | !$OMP END PARALLEL |
---|
660 | |
---|
661 | END SUBROUTINE fftyp |
---|
662 | |
---|
663 | #else |
---|
664 | SUBROUTINE ffty( ar, direction ) |
---|
665 | |
---|
666 | !------------------------------------------------------------------------------! |
---|
667 | ! Fourier-transformation along y-direction Non parallel version |
---|
668 | !------------------------------------------------------------------------------! |
---|
669 | |
---|
670 | IMPLICIT NONE |
---|
671 | |
---|
672 | CHARACTER (LEN=*) :: direction |
---|
673 | INTEGER :: i, k |
---|
674 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
675 | |
---|
676 | ! |
---|
677 | !-- Performing the fft with one of the methods implemented |
---|
678 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
679 | !$OMP DO |
---|
680 | DO k = 1, nz |
---|
681 | DO i = 0, nx |
---|
682 | CALL fft_y( ar(k,0:ny,i), direction ) |
---|
683 | ENDDO |
---|
684 | ENDDO |
---|
685 | !$OMP END PARALLEL |
---|
686 | |
---|
687 | END SUBROUTINE ffty |
---|
688 | #endif |
---|
689 | |
---|
690 | #if defined( __parallel ) |
---|
691 | SUBROUTINE ffty_tr_yx( f_in, work, f_out ) |
---|
692 | |
---|
693 | !------------------------------------------------------------------------------! |
---|
694 | ! Fourier-transformation along y with subsequent transposition y --> x for |
---|
695 | ! a 1d-decomposition along x |
---|
696 | ! |
---|
697 | ! ATTENTION: The performance of this routine is much faster on the NEC-SX6, |
---|
698 | ! if the first index of work_ffty_vec is odd. Otherwise |
---|
699 | ! memory bank conflicts may occur (especially if the index is a |
---|
700 | ! multiple of 128). That's why work_ffty_vec is dimensioned as |
---|
701 | ! 0:ny+1. |
---|
702 | ! Of course, this will not work if users are using an odd number |
---|
703 | ! of gridpoints along y. |
---|
704 | !------------------------------------------------------------------------------! |
---|
705 | |
---|
706 | USE control_parameters |
---|
707 | USE cpulog |
---|
708 | USE indices |
---|
709 | USE interfaces |
---|
710 | USE pegrid |
---|
711 | USE transpose_indices |
---|
712 | |
---|
713 | IMPLICIT NONE |
---|
714 | |
---|
715 | INTEGER :: i, iend, iouter, ir, j, k |
---|
716 | INTEGER, PARAMETER :: stridex = 4 |
---|
717 | |
---|
718 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
719 | #if defined( __nec ) |
---|
720 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
721 | #endif |
---|
722 | REAL, DIMENSION(1:nz,0:ny,nxl:nxr) :: f_in |
---|
723 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: f_out |
---|
724 | REAL, DIMENSION(nxl:nxr,1:nz,0:ny) :: work |
---|
725 | |
---|
726 | ! |
---|
727 | !-- Carry out the FFT along y, where all data are present due to the |
---|
728 | !-- 1d-decomposition along x. Resort the data in a way that x becomes |
---|
729 | !-- the first index. |
---|
730 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
---|
731 | |
---|
732 | IF ( host(1:3) == 'nec' ) THEN |
---|
733 | #if defined( __nec ) |
---|
734 | ! |
---|
735 | !-- Code optimized for vector processors |
---|
736 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
737 | !$OMP DO |
---|
738 | DO i = nxl, nxr |
---|
739 | |
---|
740 | DO j = 0, ny |
---|
741 | DO k = 1, nz |
---|
742 | work_ffty_vec(j,k,i) = f_in(k,j,i) |
---|
743 | ENDDO |
---|
744 | ENDDO |
---|
745 | |
---|
746 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'forward' ) |
---|
747 | |
---|
748 | ENDDO |
---|
749 | |
---|
750 | !$OMP DO |
---|
751 | DO k = 1, nz |
---|
752 | DO j = 0, ny |
---|
753 | DO i = nxl, nxr |
---|
754 | work(i,k,j) = work_ffty_vec(j,k,i) |
---|
755 | ENDDO |
---|
756 | ENDDO |
---|
757 | ENDDO |
---|
758 | !$OMP END PARALLEL |
---|
759 | #endif |
---|
760 | |
---|
761 | ELSE |
---|
762 | |
---|
763 | ! |
---|
764 | !-- Cache optimized code. |
---|
765 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
766 | !-- loop for better cache performance |
---|
767 | !$OMP PARALLEL PRIVATE (i,iend,iouter,ir,j,k,work_ffty) |
---|
768 | !$OMP DO |
---|
769 | DO iouter = nxl, nxr, stridex |
---|
770 | |
---|
771 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
772 | |
---|
773 | DO k = 1, nz |
---|
774 | |
---|
775 | DO i = iouter, iend |
---|
776 | |
---|
777 | ir = i-iouter+1 ! counter within a stride |
---|
778 | DO j = 0, ny |
---|
779 | work_ffty(j,ir) = f_in(k,j,i) |
---|
780 | ENDDO |
---|
781 | ! |
---|
782 | !-- FFT along y |
---|
783 | CALL fft_y( work_ffty(:,ir), 'forward' ) |
---|
784 | |
---|
785 | ENDDO |
---|
786 | |
---|
787 | ! |
---|
788 | !-- Resort |
---|
789 | DO j = 0, ny |
---|
790 | DO i = iouter, iend |
---|
791 | work(i,k,j) = work_ffty(j,i-iouter+1) |
---|
792 | ENDDO |
---|
793 | ENDDO |
---|
794 | |
---|
795 | ENDDO |
---|
796 | |
---|
797 | ENDDO |
---|
798 | !$OMP END PARALLEL |
---|
799 | |
---|
800 | ENDIF |
---|
801 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
---|
802 | |
---|
803 | ! |
---|
804 | !-- Transpose array |
---|
805 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
806 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
807 | CALL MPI_ALLTOALL( work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
808 | f_out(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
809 | comm1dx, ierr ) |
---|
810 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
811 | |
---|
812 | END SUBROUTINE ffty_tr_yx |
---|
813 | |
---|
814 | |
---|
815 | SUBROUTINE tr_xy_ffty( f_in, work, f_out ) |
---|
816 | |
---|
817 | !------------------------------------------------------------------------------! |
---|
818 | ! Transposition x --> y with a subsequent backward Fourier transformation for |
---|
819 | ! a 1d-decomposition along x |
---|
820 | !------------------------------------------------------------------------------! |
---|
821 | |
---|
822 | USE control_parameters |
---|
823 | USE cpulog |
---|
824 | USE indices |
---|
825 | USE interfaces |
---|
826 | USE pegrid |
---|
827 | USE transpose_indices |
---|
828 | |
---|
829 | IMPLICIT NONE |
---|
830 | |
---|
831 | INTEGER :: i, iend, iouter, ir, j, k |
---|
832 | INTEGER, PARAMETER :: stridex = 4 |
---|
833 | |
---|
834 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
835 | #if defined( __nec ) |
---|
836 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
837 | #endif |
---|
838 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: f_in |
---|
839 | REAL, DIMENSION(1:nz,0:ny,nxl:nxr) :: f_out |
---|
840 | REAL, DIMENSION(nxl:nxr,1:nz,0:ny) :: work |
---|
841 | |
---|
842 | ! |
---|
843 | !-- Transpose array |
---|
844 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
845 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
846 | CALL MPI_ALLTOALL( f_in(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
847 | work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
848 | comm1dx, ierr ) |
---|
849 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
850 | |
---|
851 | ! |
---|
852 | !-- Resort the data in a way that y becomes the first index and carry out the |
---|
853 | !-- backward fft along y. |
---|
854 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
---|
855 | |
---|
856 | IF ( host(1:3) == 'nec' ) THEN |
---|
857 | #if defined( __nec ) |
---|
858 | ! |
---|
859 | !-- Code optimized for vector processors |
---|
860 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
861 | !$OMP DO |
---|
862 | DO k = 1, nz |
---|
863 | DO j = 0, ny |
---|
864 | DO i = nxl, nxr |
---|
865 | work_ffty_vec(j,k,i) = work(i,k,j) |
---|
866 | ENDDO |
---|
867 | ENDDO |
---|
868 | ENDDO |
---|
869 | |
---|
870 | !$OMP DO |
---|
871 | DO i = nxl, nxr |
---|
872 | |
---|
873 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'backward' ) |
---|
874 | |
---|
875 | DO j = 0, ny |
---|
876 | DO k = 1, nz |
---|
877 | f_out(k,j,i) = work_ffty_vec(j,k,i) |
---|
878 | ENDDO |
---|
879 | ENDDO |
---|
880 | |
---|
881 | ENDDO |
---|
882 | !$OMP END PARALLEL |
---|
883 | #endif |
---|
884 | |
---|
885 | ELSE |
---|
886 | |
---|
887 | ! |
---|
888 | !-- Cache optimized code. |
---|
889 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
890 | !-- loop for better cache performance |
---|
891 | !$OMP PARALLEL PRIVATE ( i, iend, iouter, ir, j, k, work_ffty ) |
---|
892 | !$OMP DO |
---|
893 | DO iouter = nxl, nxr, stridex |
---|
894 | |
---|
895 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
896 | |
---|
897 | DO k = 1, nz |
---|
898 | ! |
---|
899 | !-- Resort |
---|
900 | DO j = 0, ny |
---|
901 | DO i = iouter, iend |
---|
902 | work_ffty(j,i-iouter+1) = work(i,k,j) |
---|
903 | ENDDO |
---|
904 | ENDDO |
---|
905 | |
---|
906 | DO i = iouter, iend |
---|
907 | |
---|
908 | ! |
---|
909 | !-- FFT along y |
---|
910 | ir = i-iouter+1 ! counter within a stride |
---|
911 | CALL fft_y( work_ffty(:,ir), 'backward' ) |
---|
912 | |
---|
913 | DO j = 0, ny |
---|
914 | f_out(k,j,i) = work_ffty(j,ir) |
---|
915 | ENDDO |
---|
916 | ENDDO |
---|
917 | |
---|
918 | ENDDO |
---|
919 | |
---|
920 | ENDDO |
---|
921 | !$OMP END PARALLEL |
---|
922 | |
---|
923 | ENDIF |
---|
924 | |
---|
925 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
---|
926 | |
---|
927 | END SUBROUTINE tr_xy_ffty |
---|
928 | |
---|
929 | |
---|
930 | SUBROUTINE fftx_tri_fftx( ar ) |
---|
931 | |
---|
932 | !------------------------------------------------------------------------------! |
---|
933 | ! FFT along x, solution of the tridiagonal system and backward FFT for |
---|
934 | ! a 1d-decomposition along x |
---|
935 | ! |
---|
936 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
937 | ! with OpenMP (for possible necessary changes see the original |
---|
938 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
939 | !------------------------------------------------------------------------------! |
---|
940 | |
---|
941 | USE control_parameters |
---|
942 | USE cpulog |
---|
943 | USE grid_variables |
---|
944 | USE indices |
---|
945 | USE interfaces |
---|
946 | USE pegrid |
---|
947 | USE transpose_indices |
---|
948 | |
---|
949 | IMPLICIT NONE |
---|
950 | |
---|
951 | character(len=3) :: myth_char |
---|
952 | |
---|
953 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
954 | |
---|
955 | REAL, DIMENSION(0:nx) :: work_fftx |
---|
956 | REAL, DIMENSION(0:nx,1:nz) :: work_trix |
---|
957 | REAL, DIMENSION(nnx,1:nz,nys_x:nyn_x,pdims(1)) :: ar |
---|
958 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
959 | |
---|
960 | |
---|
961 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'start' ) |
---|
962 | |
---|
963 | ALLOCATE( tri(5,0:nx,0:nz-1,0:threads_per_task-1) ) |
---|
964 | |
---|
965 | tn = 0 ! Default thread number in case of one thread |
---|
966 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_fftx, work_trix ) |
---|
967 | DO j = nys_x, nyn_x |
---|
968 | |
---|
969 | !$ tn = omp_get_thread_num() |
---|
970 | |
---|
971 | IF ( host(1:3) == 'nec' ) THEN |
---|
972 | ! |
---|
973 | !-- Code optimized for vector processors |
---|
974 | DO k = 1, nz |
---|
975 | |
---|
976 | m = 0 |
---|
977 | DO n = 1, pdims(1) |
---|
978 | DO i = 1, nnx |
---|
979 | work_trix(m,k) = ar(i,k,j,n) |
---|
980 | m = m + 1 |
---|
981 | ENDDO |
---|
982 | ENDDO |
---|
983 | |
---|
984 | ENDDO |
---|
985 | |
---|
986 | CALL fft_x_m( work_trix, 'forward' ) |
---|
987 | |
---|
988 | ELSE |
---|
989 | ! |
---|
990 | !-- Cache optimized code |
---|
991 | DO k = 1, nz |
---|
992 | |
---|
993 | m = 0 |
---|
994 | DO n = 1, pdims(1) |
---|
995 | DO i = 1, nnx |
---|
996 | work_fftx(m) = ar(i,k,j,n) |
---|
997 | m = m + 1 |
---|
998 | ENDDO |
---|
999 | ENDDO |
---|
1000 | |
---|
1001 | CALL fft_x( work_fftx, 'forward' ) |
---|
1002 | |
---|
1003 | DO i = 0, nx |
---|
1004 | work_trix(i,k) = work_fftx(i) |
---|
1005 | ENDDO |
---|
1006 | |
---|
1007 | ENDDO |
---|
1008 | |
---|
1009 | ENDIF |
---|
1010 | |
---|
1011 | ! |
---|
1012 | !-- Solve the linear equation system |
---|
1013 | CALL tridia_1dd( ddx2, ddy2, nx, ny, j, work_trix, tri(:,:,:,tn) ) |
---|
1014 | |
---|
1015 | IF ( host(1:3) == 'nec' ) THEN |
---|
1016 | ! |
---|
1017 | !-- Code optimized for vector processors |
---|
1018 | CALL fft_x_m( work_trix, 'backward' ) |
---|
1019 | |
---|
1020 | DO k = 1, nz |
---|
1021 | |
---|
1022 | m = 0 |
---|
1023 | DO n = 1, pdims(1) |
---|
1024 | DO i = 1, nnx |
---|
1025 | ar(i,k,j,n) = work_trix(m,k) |
---|
1026 | m = m + 1 |
---|
1027 | ENDDO |
---|
1028 | ENDDO |
---|
1029 | |
---|
1030 | ENDDO |
---|
1031 | |
---|
1032 | ELSE |
---|
1033 | ! |
---|
1034 | !-- Cache optimized code |
---|
1035 | DO k = 1, nz |
---|
1036 | |
---|
1037 | DO i = 0, nx |
---|
1038 | work_fftx(i) = work_trix(i,k) |
---|
1039 | ENDDO |
---|
1040 | |
---|
1041 | CALL fft_x( work_fftx, 'backward' ) |
---|
1042 | |
---|
1043 | m = 0 |
---|
1044 | DO n = 1, pdims(1) |
---|
1045 | DO i = 1, nnx |
---|
1046 | ar(i,k,j,n) = work_fftx(m) |
---|
1047 | m = m + 1 |
---|
1048 | ENDDO |
---|
1049 | ENDDO |
---|
1050 | |
---|
1051 | ENDDO |
---|
1052 | |
---|
1053 | ENDIF |
---|
1054 | |
---|
1055 | ENDDO |
---|
1056 | |
---|
1057 | DEALLOCATE( tri ) |
---|
1058 | |
---|
1059 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'stop' ) |
---|
1060 | |
---|
1061 | END SUBROUTINE fftx_tri_fftx |
---|
1062 | |
---|
1063 | |
---|
1064 | SUBROUTINE fftx_tr_xy( f_in, work, f_out ) |
---|
1065 | |
---|
1066 | !------------------------------------------------------------------------------! |
---|
1067 | ! Fourier-transformation along x with subsequent transposition x --> y for |
---|
1068 | ! a 1d-decomposition along y |
---|
1069 | ! |
---|
1070 | ! ATTENTION: The NEC-branch of this routine may significantly profit from |
---|
1071 | ! further optimizations. So far, performance is much worse than |
---|
1072 | ! for routine ffty_tr_yx (more than three times slower). |
---|
1073 | !------------------------------------------------------------------------------! |
---|
1074 | |
---|
1075 | USE control_parameters |
---|
1076 | USE cpulog |
---|
1077 | USE indices |
---|
1078 | USE interfaces |
---|
1079 | USE pegrid |
---|
1080 | USE transpose_indices |
---|
1081 | |
---|
1082 | IMPLICIT NONE |
---|
1083 | |
---|
1084 | INTEGER :: i, j, k |
---|
1085 | |
---|
1086 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
1087 | REAL, DIMENSION(1:nz,nys:nyn,0:nx) :: f_in |
---|
1088 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: f_out |
---|
1089 | REAL, DIMENSION(nys:nyn,1:nz,0:nx) :: work |
---|
1090 | |
---|
1091 | ! |
---|
1092 | !-- Carry out the FFT along x, where all data are present due to the |
---|
1093 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
1094 | !-- the first index. |
---|
1095 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
---|
1096 | |
---|
1097 | IF ( host(1:3) == 'nec' ) THEN |
---|
1098 | ! |
---|
1099 | !-- Code for vector processors |
---|
1100 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
1101 | !$OMP DO |
---|
1102 | DO i = 0, nx |
---|
1103 | |
---|
1104 | DO j = nys, nyn |
---|
1105 | DO k = 1, nz |
---|
1106 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
1107 | ENDDO |
---|
1108 | ENDDO |
---|
1109 | |
---|
1110 | ENDDO |
---|
1111 | |
---|
1112 | !$OMP DO |
---|
1113 | DO j = nys, nyn |
---|
1114 | |
---|
1115 | CALL fft_x_m( work_fftx(:,:,j), 'forward' ) |
---|
1116 | |
---|
1117 | DO k = 1, nz |
---|
1118 | DO i = 0, nx |
---|
1119 | work(j,k,i) = work_fftx(i,k,j) |
---|
1120 | ENDDO |
---|
1121 | ENDDO |
---|
1122 | |
---|
1123 | ENDDO |
---|
1124 | !$OMP END PARALLEL |
---|
1125 | |
---|
1126 | ELSE |
---|
1127 | |
---|
1128 | ! |
---|
1129 | !-- Cache optimized code (there might be still a potential for better |
---|
1130 | !-- optimization). |
---|
1131 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
1132 | !$OMP DO |
---|
1133 | DO i = 0, nx |
---|
1134 | |
---|
1135 | DO j = nys, nyn |
---|
1136 | DO k = 1, nz |
---|
1137 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
1138 | ENDDO |
---|
1139 | ENDDO |
---|
1140 | |
---|
1141 | ENDDO |
---|
1142 | |
---|
1143 | !$OMP DO |
---|
1144 | DO j = nys, nyn |
---|
1145 | DO k = 1, nz |
---|
1146 | |
---|
1147 | CALL fft_x( work_fftx(0:nx,k,j), 'forward' ) |
---|
1148 | |
---|
1149 | DO i = 0, nx |
---|
1150 | work(j,k,i) = work_fftx(i,k,j) |
---|
1151 | ENDDO |
---|
1152 | ENDDO |
---|
1153 | |
---|
1154 | ENDDO |
---|
1155 | !$OMP END PARALLEL |
---|
1156 | |
---|
1157 | ENDIF |
---|
1158 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
---|
1159 | |
---|
1160 | ! |
---|
1161 | !-- Transpose array |
---|
1162 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
1163 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
1164 | CALL MPI_ALLTOALL( work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
1165 | f_out(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
1166 | comm1dy, ierr ) |
---|
1167 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
1168 | |
---|
1169 | END SUBROUTINE fftx_tr_xy |
---|
1170 | |
---|
1171 | |
---|
1172 | SUBROUTINE tr_yx_fftx( f_in, work, f_out ) |
---|
1173 | |
---|
1174 | !------------------------------------------------------------------------------! |
---|
1175 | ! Transposition y --> x with a subsequent backward Fourier transformation for |
---|
1176 | ! a 1d-decomposition along x |
---|
1177 | !------------------------------------------------------------------------------! |
---|
1178 | |
---|
1179 | USE control_parameters |
---|
1180 | USE cpulog |
---|
1181 | USE indices |
---|
1182 | USE interfaces |
---|
1183 | USE pegrid |
---|
1184 | USE transpose_indices |
---|
1185 | |
---|
1186 | IMPLICIT NONE |
---|
1187 | |
---|
1188 | INTEGER :: i, j, k |
---|
1189 | |
---|
1190 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
1191 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: f_in |
---|
1192 | REAL, DIMENSION(1:nz,nys:nyn,0:nx) :: f_out |
---|
1193 | REAL, DIMENSION(nys:nyn,1:nz,0:nx) :: work |
---|
1194 | |
---|
1195 | ! |
---|
1196 | !-- Transpose array |
---|
1197 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
1198 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
1199 | CALL MPI_ALLTOALL( f_in(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
1200 | work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
1201 | comm1dy, ierr ) |
---|
1202 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
1203 | |
---|
1204 | ! |
---|
1205 | !-- Carry out the FFT along x, where all data are present due to the |
---|
1206 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
1207 | !-- the first index. |
---|
1208 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
---|
1209 | |
---|
1210 | IF ( host(1:3) == 'nec' ) THEN |
---|
1211 | ! |
---|
1212 | !-- Code optimized for vector processors |
---|
1213 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
1214 | !$OMP DO |
---|
1215 | DO j = nys, nyn |
---|
1216 | |
---|
1217 | DO k = 1, nz |
---|
1218 | DO i = 0, nx |
---|
1219 | work_fftx(i,k,j) = work(j,k,i) |
---|
1220 | ENDDO |
---|
1221 | ENDDO |
---|
1222 | |
---|
1223 | CALL fft_x_m( work_fftx(:,:,j), 'backward' ) |
---|
1224 | |
---|
1225 | ENDDO |
---|
1226 | |
---|
1227 | !$OMP DO |
---|
1228 | DO i = 0, nx |
---|
1229 | DO j = nys, nyn |
---|
1230 | DO k = 1, nz |
---|
1231 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
1232 | ENDDO |
---|
1233 | ENDDO |
---|
1234 | ENDDO |
---|
1235 | !$OMP END PARALLEL |
---|
1236 | |
---|
1237 | ELSE |
---|
1238 | |
---|
1239 | ! |
---|
1240 | !-- Cache optimized code (there might be still a potential for better |
---|
1241 | !-- optimization). |
---|
1242 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
1243 | !$OMP DO |
---|
1244 | DO j = nys, nyn |
---|
1245 | DO k = 1, nz |
---|
1246 | |
---|
1247 | DO i = 0, nx |
---|
1248 | work_fftx(i,k,j) = work(j,k,i) |
---|
1249 | ENDDO |
---|
1250 | |
---|
1251 | CALL fft_x( work_fftx(0:nx,k,j), 'backward' ) |
---|
1252 | |
---|
1253 | ENDDO |
---|
1254 | ENDDO |
---|
1255 | |
---|
1256 | !$OMP DO |
---|
1257 | DO i = 0, nx |
---|
1258 | DO j = nys, nyn |
---|
1259 | DO k = 1, nz |
---|
1260 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
1261 | ENDDO |
---|
1262 | ENDDO |
---|
1263 | ENDDO |
---|
1264 | !$OMP END PARALLEL |
---|
1265 | |
---|
1266 | ENDIF |
---|
1267 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
---|
1268 | |
---|
1269 | END SUBROUTINE tr_yx_fftx |
---|
1270 | |
---|
1271 | |
---|
1272 | SUBROUTINE ffty_tri_ffty( ar ) |
---|
1273 | |
---|
1274 | !------------------------------------------------------------------------------! |
---|
1275 | ! FFT along y, solution of the tridiagonal system and backward FFT for |
---|
1276 | ! a 1d-decomposition along y |
---|
1277 | ! |
---|
1278 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
1279 | ! with OpenMP (for possible necessary changes see the original |
---|
1280 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
1281 | !------------------------------------------------------------------------------! |
---|
1282 | |
---|
1283 | USE control_parameters |
---|
1284 | USE cpulog |
---|
1285 | USE grid_variables |
---|
1286 | USE indices |
---|
1287 | USE interfaces |
---|
1288 | USE pegrid |
---|
1289 | USE transpose_indices |
---|
1290 | |
---|
1291 | IMPLICIT NONE |
---|
1292 | |
---|
1293 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
1294 | |
---|
1295 | REAL, DIMENSION(0:ny) :: work_ffty |
---|
1296 | REAL, DIMENSION(0:ny,1:nz) :: work_triy |
---|
1297 | REAL, DIMENSION(nny,1:nz,nxl_y:nxr_y,pdims(2)) :: ar |
---|
1298 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
1299 | |
---|
1300 | |
---|
1301 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'start' ) |
---|
1302 | |
---|
1303 | ALLOCATE( tri(5,0:ny,0:nz-1,0:threads_per_task-1) ) |
---|
1304 | |
---|
1305 | tn = 0 ! Default thread number in case of one thread |
---|
1306 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_ffty, work_triy ) |
---|
1307 | DO i = nxl_y, nxr_y |
---|
1308 | |
---|
1309 | !$ tn = omp_get_thread_num() |
---|
1310 | |
---|
1311 | IF ( host(1:3) == 'nec' ) THEN |
---|
1312 | ! |
---|
1313 | !-- Code optimized for vector processors |
---|
1314 | DO k = 1, nz |
---|
1315 | |
---|
1316 | m = 0 |
---|
1317 | DO n = 1, pdims(2) |
---|
1318 | DO j = 1, nny |
---|
1319 | work_triy(m,k) = ar(j,k,i,n) |
---|
1320 | m = m + 1 |
---|
1321 | ENDDO |
---|
1322 | ENDDO |
---|
1323 | |
---|
1324 | ENDDO |
---|
1325 | |
---|
1326 | CALL fft_y_m( work_triy, ny, 'forward' ) |
---|
1327 | |
---|
1328 | ELSE |
---|
1329 | ! |
---|
1330 | !-- Cache optimized code |
---|
1331 | DO k = 1, nz |
---|
1332 | |
---|
1333 | m = 0 |
---|
1334 | DO n = 1, pdims(2) |
---|
1335 | DO j = 1, nny |
---|
1336 | work_ffty(m) = ar(j,k,i,n) |
---|
1337 | m = m + 1 |
---|
1338 | ENDDO |
---|
1339 | ENDDO |
---|
1340 | |
---|
1341 | CALL fft_y( work_ffty, 'forward' ) |
---|
1342 | |
---|
1343 | DO j = 0, ny |
---|
1344 | work_triy(j,k) = work_ffty(j) |
---|
1345 | ENDDO |
---|
1346 | |
---|
1347 | ENDDO |
---|
1348 | |
---|
1349 | ENDIF |
---|
1350 | |
---|
1351 | ! |
---|
1352 | !-- Solve the linear equation system |
---|
1353 | CALL tridia_1dd( ddy2, ddx2, ny, nx, i, work_triy, tri(:,:,:,tn) ) |
---|
1354 | |
---|
1355 | IF ( host(1:3) == 'nec' ) THEN |
---|
1356 | ! |
---|
1357 | !-- Code optimized for vector processors |
---|
1358 | CALL fft_y_m( work_triy, ny, 'backward' ) |
---|
1359 | |
---|
1360 | DO k = 1, nz |
---|
1361 | |
---|
1362 | m = 0 |
---|
1363 | DO n = 1, pdims(2) |
---|
1364 | DO j = 1, nny |
---|
1365 | ar(j,k,i,n) = work_triy(m,k) |
---|
1366 | m = m + 1 |
---|
1367 | ENDDO |
---|
1368 | ENDDO |
---|
1369 | |
---|
1370 | ENDDO |
---|
1371 | |
---|
1372 | ELSE |
---|
1373 | ! |
---|
1374 | !-- Cache optimized code |
---|
1375 | DO k = 1, nz |
---|
1376 | |
---|
1377 | DO j = 0, ny |
---|
1378 | work_ffty(j) = work_triy(j,k) |
---|
1379 | ENDDO |
---|
1380 | |
---|
1381 | CALL fft_y( work_ffty, 'backward' ) |
---|
1382 | |
---|
1383 | m = 0 |
---|
1384 | DO n = 1, pdims(2) |
---|
1385 | DO j = 1, nny |
---|
1386 | ar(j,k,i,n) = work_ffty(m) |
---|
1387 | m = m + 1 |
---|
1388 | ENDDO |
---|
1389 | ENDDO |
---|
1390 | |
---|
1391 | ENDDO |
---|
1392 | |
---|
1393 | ENDIF |
---|
1394 | |
---|
1395 | ENDDO |
---|
1396 | |
---|
1397 | DEALLOCATE( tri ) |
---|
1398 | |
---|
1399 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'stop' ) |
---|
1400 | |
---|
1401 | END SUBROUTINE ffty_tri_ffty |
---|
1402 | |
---|
1403 | |
---|
1404 | SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri ) |
---|
1405 | |
---|
1406 | !------------------------------------------------------------------------------! |
---|
1407 | ! Solves the linear system of equations for a 1d-decomposition along x (see |
---|
1408 | ! tridia) |
---|
1409 | ! |
---|
1410 | ! Attention: when using the intel compilers older than 12.0, array tri must |
---|
1411 | ! be passed as an argument to the contained subroutines. Otherwise |
---|
1412 | ! addres faults will occur. This feature can be activated with |
---|
1413 | ! cpp-switch __intel11 |
---|
1414 | ! On NEC, tri should not be passed (except for routine substi_1dd) |
---|
1415 | ! because this causes very bad performance. |
---|
1416 | !------------------------------------------------------------------------------! |
---|
1417 | |
---|
1418 | USE arrays_3d |
---|
1419 | USE control_parameters |
---|
1420 | |
---|
1421 | USE pegrid |
---|
1422 | |
---|
1423 | IMPLICIT NONE |
---|
1424 | |
---|
1425 | INTEGER :: i, j, k, nnyh, nx, ny, omp_get_thread_num, tn |
---|
1426 | |
---|
1427 | REAL :: ddx2, ddy2 |
---|
1428 | |
---|
1429 | REAL, DIMENSION(0:nx,1:nz) :: ar |
---|
1430 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
1431 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1432 | |
---|
1433 | |
---|
1434 | nnyh = ( ny + 1 ) / 2 |
---|
1435 | |
---|
1436 | ! |
---|
1437 | !-- Define constant elements of the tridiagonal matrix. |
---|
1438 | !-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2, |
---|
1439 | !-- the exchanged loops create bank conflicts. The following directive |
---|
1440 | !-- prohibits loop exchange and the loops perform much better. |
---|
1441 | ! tn = omp_get_thread_num() |
---|
1442 | ! WRITE( 120+tn, * ) '+++ id=',myid,' nx=',nx,' thread=', omp_get_thread_num() |
---|
1443 | ! CALL local_flush( 120+tn ) |
---|
1444 | !CDIR NOLOOPCHG |
---|
1445 | DO k = 0, nz-1 |
---|
1446 | DO i = 0,nx |
---|
1447 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
---|
1448 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
---|
1449 | ENDDO |
---|
1450 | ENDDO |
---|
1451 | ! WRITE( 120+tn, * ) '+++ id=',myid,' end of first tridia loop thread=', omp_get_thread_num() |
---|
1452 | ! CALL local_flush( 120+tn ) |
---|
1453 | |
---|
1454 | IF ( j <= nnyh ) THEN |
---|
1455 | #if defined( __intel11 ) |
---|
1456 | CALL maketri_1dd( j, tri ) |
---|
1457 | #else |
---|
1458 | CALL maketri_1dd( j ) |
---|
1459 | #endif |
---|
1460 | ELSE |
---|
1461 | #if defined( __intel11 ) |
---|
1462 | CALL maketri_1dd( ny+1-j, tri ) |
---|
1463 | #else |
---|
1464 | CALL maketri_1dd( ny+1-j ) |
---|
1465 | #endif |
---|
1466 | ENDIF |
---|
1467 | #if defined( __intel11 ) |
---|
1468 | CALL split_1dd( tri ) |
---|
1469 | #else |
---|
1470 | CALL split_1dd |
---|
1471 | #endif |
---|
1472 | CALL substi_1dd( ar, tri ) |
---|
1473 | |
---|
1474 | CONTAINS |
---|
1475 | |
---|
1476 | #if defined( __intel11 ) |
---|
1477 | SUBROUTINE maketri_1dd( j, tri ) |
---|
1478 | #else |
---|
1479 | SUBROUTINE maketri_1dd( j ) |
---|
1480 | #endif |
---|
1481 | |
---|
1482 | !------------------------------------------------------------------------------! |
---|
1483 | ! computes the i- and j-dependent component of the matrix |
---|
1484 | !------------------------------------------------------------------------------! |
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1485 | |
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1486 | USE constants |
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1487 | |
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1488 | IMPLICIT NONE |
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1489 | |
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1490 | INTEGER :: i, j, k, nnxh |
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1491 | REAL :: a, c |
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1492 | |
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1493 | REAL, DIMENSION(0:nx) :: l |
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1494 | |
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1495 | #if defined( __intel11 ) |
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1496 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
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1497 | #endif |
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1498 | |
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1499 | |
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1500 | nnxh = ( nx + 1 ) / 2 |
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1501 | ! |
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1502 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
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1503 | !-- Fourier space. The coefficients are computed following the method of |
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1504 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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1505 | !-- Siano's original version by discretizing the Poisson equation, |
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1506 | !-- before it is Fourier-transformed |
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1507 | DO i = 0, nx |
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1508 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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1509 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
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1510 | REAL( nx+1 ) ) ) * ddx2 + & |
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1511 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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1512 | REAL( ny+1 ) ) ) * ddy2 |
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1513 | ELSE |
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1514 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
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1515 | REAL( nx+1 ) ) ) * ddx2 + & |
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1516 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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1517 | REAL( ny+1 ) ) ) * ddy2 |
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1518 | ENDIF |
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1519 | ENDDO |
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1520 | |
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1521 | DO k = 0, nz-1 |
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1522 | DO i = 0, nx |
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1523 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
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1524 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
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1525 | tri(1,i,k) = a + c - l(i) |
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1526 | ENDDO |
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1527 | ENDDO |
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1528 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
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1529 | DO i = 0, nx |
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1530 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
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1531 | ENDDO |
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1532 | ENDIF |
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1533 | IF ( ibc_p_t == 1 ) THEN |
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1534 | DO i = 0, nx |
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1535 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
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1536 | ENDDO |
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1537 | ENDIF |
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1538 | |
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1539 | END SUBROUTINE maketri_1dd |
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1540 | |
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1541 | |
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1542 | #if defined( __intel11 ) |
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1543 | SUBROUTINE split_1dd( tri ) |
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1544 | #else |
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1545 | SUBROUTINE split_1dd |
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1546 | #endif |
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1547 | |
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1548 | !------------------------------------------------------------------------------! |
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1549 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
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1550 | !------------------------------------------------------------------------------! |
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1551 | |
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1552 | IMPLICIT NONE |
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1553 | |
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1554 | INTEGER :: i, k |
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1555 | |
---|
1556 | #if defined( __intel11 ) |
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1557 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1558 | #endif |
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1559 | |
---|
1560 | |
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1561 | ! |
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1562 | !-- Splitting |
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1563 | DO i = 0, nx |
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1564 | tri(4,i,0) = tri(1,i,0) |
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1565 | ENDDO |
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1566 | DO k = 1, nz-1 |
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1567 | DO i = 0, nx |
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1568 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
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1569 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
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1570 | ENDDO |
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1571 | ENDDO |
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1572 | |
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1573 | END SUBROUTINE split_1dd |
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1574 | |
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1575 | |
---|
1576 | SUBROUTINE substi_1dd( ar, tri ) |
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1577 | |
---|
1578 | !------------------------------------------------------------------------------! |
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1579 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
1580 | !------------------------------------------------------------------------------! |
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1581 | |
---|
1582 | IMPLICIT NONE |
---|
1583 | |
---|
1584 | INTEGER :: i, k |
---|
1585 | |
---|
1586 | REAL, DIMENSION(0:nx,nz) :: ar |
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1587 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
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1588 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
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1589 | |
---|
1590 | ! |
---|
1591 | !-- Forward substitution |
---|
1592 | DO i = 0, nx |
---|
1593 | ar1(i,0) = ar(i,1) |
---|
1594 | ENDDO |
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1595 | DO k = 1, nz-1 |
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1596 | DO i = 0, nx |
---|
1597 | ar1(i,k) = ar(i,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
1598 | ENDDO |
---|
1599 | ENDDO |
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1600 | |
---|
1601 | ! |
---|
1602 | !-- Backward substitution |
---|
1603 | !-- Note, the add of 1.0E-20 in the denominator is due to avoid divisions |
---|
1604 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
1605 | !-- the model domain. |
---|
1606 | DO i = 0, nx |
---|
1607 | ar(i,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
1608 | ENDDO |
---|
1609 | DO k = nz-2, 0, -1 |
---|
1610 | DO i = 0, nx |
---|
1611 | ar(i,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,k+2) ) & |
---|
1612 | / tri(4,i,k) |
---|
1613 | ENDDO |
---|
1614 | ENDDO |
---|
1615 | |
---|
1616 | ! |
---|
1617 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
1618 | !-- The respective values of ar should be zero at all k-levels if |
---|
1619 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
1620 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
1621 | IF ( j == 0 ) THEN |
---|
1622 | DO k = 1, nz |
---|
1623 | ar(0,k) = 0.0 |
---|
1624 | ENDDO |
---|
1625 | ENDIF |
---|
1626 | ENDIF |
---|
1627 | |
---|
1628 | END SUBROUTINE substi_1dd |
---|
1629 | |
---|
1630 | END SUBROUTINE tridia_1dd |
---|
1631 | |
---|
1632 | #endif |
---|
1633 | #endif |
---|
1634 | END MODULE poisfft_mod |
---|