1 | MODULE poisfft_mod |
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2 | |
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3 | !------------------------------------------------------------------------------! |
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4 | ! Current revisions: |
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5 | ! ----------------- |
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6 | ! |
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7 | ! |
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8 | ! Former revisions: |
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9 | ! ----------------- |
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10 | ! $Id: poisfft.f90 810 2012-01-30 13:40:12Z maronga $ |
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11 | ! |
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12 | ! 809 2012-01-30 13:32:58Z maronga |
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13 | ! Bugfix: replaced .AND. and .NOT. with && and ! in the preprocessor directives |
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14 | ! |
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15 | ! 807 2012-01-25 11:53:51Z maronga |
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16 | ! New cpp directive "__check" implemented which is used by check_namelist_files |
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17 | ! (most of the code is unneeded by check_namelist_files). |
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18 | ! |
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19 | ! 763 2011-10-06 09:32:09Z suehring |
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20 | ! Comment added concerning the last change. |
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21 | ! |
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22 | ! 761 2011-10-05 17:58:52Z suehring |
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23 | ! Bugfix: Avoid divisions by zero in case of using a 'neumann' bc for the |
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24 | ! pressure at the top of the model domain. |
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25 | ! |
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26 | ! 696 2011-03-18 07:03:49Z raasch |
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27 | ! work_fftx removed from PRIVATE clauses in fftx_tr_xy and tr_yx_fftx |
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28 | ! |
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29 | ! 683 2011-02-09 14:25:15Z raasch |
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30 | ! openMP parallelization for 2d-domain-decomposition |
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31 | ! |
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32 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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33 | ! ddzu replaced by ddzu_pres due to changes in zu(0) |
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34 | ! |
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35 | ! 622 2010-12-10 08:08:13Z raasch |
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36 | ! optional barriers included in order to speed up collective operations |
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37 | ! |
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38 | ! 377 2009-09-04 11:09:00Z raasch |
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39 | ! __lcmuk changed to __lc to avoid problems with Intel compiler on sgi-ice |
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40 | ! |
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41 | ! 164 2008-05-15 08:46:15Z raasch |
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42 | ! Arguments removed from transpose routines |
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43 | ! |
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44 | ! 128 2007-10-26 13:11:14Z raasch |
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45 | ! Bugfix: wavenumber calculation for even nx in routines maketri |
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46 | ! |
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47 | ! 85 2007-05-11 09:35:14Z raasch |
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48 | ! Bugfix: work_fft*_vec removed from some PRIVATE-declarations |
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49 | ! |
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50 | ! 76 2007-03-29 00:58:32Z raasch |
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51 | ! Tridiagonal coefficients adjusted for Neumann boundary conditions both at |
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52 | ! the bottom and the top. |
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53 | ! |
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54 | ! RCS Log replace by Id keyword, revision history cleaned up |
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55 | ! |
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56 | ! Revision 1.24 2006/08/04 15:00:24 raasch |
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57 | ! Default setting of the thread number tn in case of not using OpenMP |
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58 | ! |
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59 | ! Revision 1.23 2006/02/23 12:48:38 raasch |
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60 | ! Additional compiler directive in routine tridia_1dd for preventing loop |
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61 | ! exchange on NEC-SX6 |
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62 | ! |
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63 | ! Revision 1.20 2004/04/30 12:38:09 raasch |
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64 | ! Parts of former poisfft_hybrid moved to this subroutine, |
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65 | ! former subroutine changed to a module, renaming of FFT-subroutines and |
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66 | ! -module, FFTs completely substituted by calls of fft_x and fft_y, |
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67 | ! NAG fft used in the non-parallel case completely removed, l in maketri |
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68 | ! is now a 1d-array, variables passed by modules instead of using parameter |
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69 | ! lists, enlarged transposition arrays introduced |
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70 | ! |
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71 | ! Revision 1.1 1997/07/24 11:24:14 raasch |
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72 | ! Initial revision |
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73 | ! |
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74 | ! |
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75 | ! Description: |
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76 | ! ------------ |
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77 | ! See below. |
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78 | !------------------------------------------------------------------------------! |
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79 | |
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80 | !--------------------------------------------------------------------------! |
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81 | ! poisfft ! |
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82 | ! ! |
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83 | ! Original version: Stephan Siano (pois3d) ! |
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84 | ! ! |
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85 | ! Institute of Meteorology and Climatology, University of Hannover ! |
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86 | ! Germany ! |
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87 | ! ! |
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88 | ! Version as of July 23,1996 ! |
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89 | ! ! |
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90 | ! ! |
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91 | ! Version for parallel computers: Siegfried Raasch ! |
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92 | ! ! |
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93 | ! Version as of July 03,1997 ! |
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94 | ! ! |
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95 | ! Solves the Poisson equation with a 2D spectral method ! |
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96 | ! d^2 p / dx^2 + d^2 p / dy^2 + d^2 p / dz^2 = s ! |
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97 | ! ! |
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98 | ! Input: ! |
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99 | ! real ar contains in the (nnx,nny,nnz) elements, ! |
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100 | ! starting from the element (1,nys,nxl), the ! |
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101 | ! values for s ! |
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102 | ! real work Temporary array ! |
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103 | ! ! |
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104 | ! Output: ! |
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105 | ! real ar contains the solution for p ! |
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106 | !--------------------------------------------------------------------------! |
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107 | |
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108 | USE fft_xy |
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109 | USE indices |
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110 | USE transpose_indices |
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111 | |
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112 | IMPLICIT NONE |
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113 | |
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114 | PRIVATE |
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115 | |
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116 | #if ! defined ( __check ) |
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117 | PUBLIC poisfft, poisfft_init |
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118 | |
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119 | INTERFACE poisfft |
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120 | MODULE PROCEDURE poisfft |
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121 | END INTERFACE poisfft |
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122 | |
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123 | INTERFACE poisfft_init |
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124 | MODULE PROCEDURE poisfft_init |
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125 | END INTERFACE poisfft_init |
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126 | #else |
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127 | PUBLIC poisfft_init |
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128 | |
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129 | INTERFACE poisfft_init |
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130 | MODULE PROCEDURE poisfft_init |
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131 | END INTERFACE poisfft_init |
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132 | #endif |
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133 | |
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134 | CONTAINS |
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135 | |
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136 | SUBROUTINE poisfft_init |
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137 | |
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138 | CALL fft_init |
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139 | |
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140 | END SUBROUTINE poisfft_init |
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141 | |
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142 | #if ! defined ( __check ) |
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143 | SUBROUTINE poisfft( ar, work ) |
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144 | |
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145 | USE cpulog |
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146 | USE interfaces |
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147 | USE pegrid |
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148 | |
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149 | IMPLICIT NONE |
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150 | |
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151 | REAL, DIMENSION(1:nza,nys:nyna,nxl:nxra) :: ar, work |
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152 | |
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153 | |
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154 | CALL cpu_log( log_point_s(3), 'poisfft', 'start' ) |
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155 | |
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156 | ! |
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157 | !-- Two-dimensional Fourier Transformation in x- and y-direction. |
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158 | #if defined( __parallel ) |
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159 | IF ( pdims(2) == 1 ) THEN |
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160 | |
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161 | ! |
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162 | !-- 1d-domain-decomposition along x: |
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163 | !-- FFT along y and transposition y --> x |
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164 | CALL ffty_tr_yx( ar, work, ar ) |
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165 | |
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166 | ! |
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167 | !-- FFT along x, solving the tridiagonal system and backward FFT |
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168 | CALL fftx_tri_fftx( ar ) |
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169 | |
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170 | ! |
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171 | !-- Transposition x --> y and backward FFT along y |
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172 | CALL tr_xy_ffty( ar, work, ar ) |
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173 | |
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174 | ELSEIF ( pdims(1) == 1 ) THEN |
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175 | |
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176 | ! |
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177 | !-- 1d-domain-decomposition along y: |
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178 | !-- FFT along x and transposition x --> y |
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179 | CALL fftx_tr_xy( ar, work, ar ) |
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180 | |
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181 | ! |
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182 | !-- FFT along y, solving the tridiagonal system and backward FFT |
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183 | CALL ffty_tri_ffty( ar ) |
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184 | |
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185 | ! |
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186 | !-- Transposition y --> x and backward FFT along x |
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187 | CALL tr_yx_fftx( ar, work, ar ) |
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188 | |
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189 | ELSE |
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190 | |
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191 | ! |
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192 | !-- 2d-domain-decomposition |
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193 | !-- Transposition z --> x |
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194 | CALL cpu_log( log_point_s(5), 'transpo forward', 'start' ) |
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195 | CALL transpose_zx( ar, work, ar ) |
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196 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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197 | |
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198 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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199 | CALL fftxp( ar, 'forward' ) |
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200 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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201 | |
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202 | ! |
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203 | !-- Transposition x --> y |
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204 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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205 | CALL transpose_xy( ar, work, ar ) |
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206 | CALL cpu_log( log_point_s(5), 'transpo forward', 'pause' ) |
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207 | |
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208 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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209 | CALL fftyp( ar, 'forward' ) |
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210 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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211 | |
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212 | ! |
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213 | !-- Transposition y --> z |
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214 | CALL cpu_log( log_point_s(5), 'transpo forward', 'continue' ) |
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215 | CALL transpose_yz( ar, work, ar ) |
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216 | CALL cpu_log( log_point_s(5), 'transpo forward', 'stop' ) |
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217 | |
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218 | ! |
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219 | !-- Solve the Poisson equation in z-direction in cartesian space. |
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220 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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221 | CALL tridia( ar ) |
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222 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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223 | |
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224 | ! |
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225 | !-- Inverse Fourier Transformation |
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226 | !-- Transposition z --> y |
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227 | CALL cpu_log( log_point_s(8), 'transpo invers', 'start' ) |
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228 | CALL transpose_zy( ar, work, ar ) |
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229 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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230 | |
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231 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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232 | CALL fftyp( ar, 'backward' ) |
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233 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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234 | |
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235 | ! |
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236 | !-- Transposition y --> x |
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237 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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238 | CALL transpose_yx( ar, work, ar ) |
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239 | CALL cpu_log( log_point_s(8), 'transpo invers', 'pause' ) |
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240 | |
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241 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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242 | CALL fftxp( ar, 'backward' ) |
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243 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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244 | |
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245 | ! |
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246 | !-- Transposition x --> z |
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247 | CALL cpu_log( log_point_s(8), 'transpo invers', 'continue' ) |
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248 | CALL transpose_xz( ar, work, ar ) |
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249 | CALL cpu_log( log_point_s(8), 'transpo invers', 'stop' ) |
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250 | |
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251 | ENDIF |
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252 | |
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253 | #else |
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254 | |
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255 | ! |
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256 | !-- Two-dimensional Fourier Transformation along x- and y-direction. |
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257 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
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258 | CALL fftx( ar, 'forward' ) |
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259 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
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260 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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261 | CALL ffty( ar, 'forward' ) |
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262 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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263 | |
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264 | ! |
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265 | !-- Solve the Poisson equation in z-direction in cartesian space. |
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266 | CALL cpu_log( log_point_s(6), 'tridia', 'start' ) |
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267 | CALL tridia( ar ) |
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268 | CALL cpu_log( log_point_s(6), 'tridia', 'stop' ) |
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269 | |
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270 | ! |
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271 | !-- Inverse Fourier Transformation. |
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272 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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273 | CALL ffty( ar, 'backward' ) |
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274 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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275 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
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276 | CALL fftx( ar, 'backward' ) |
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277 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
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278 | |
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279 | #endif |
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280 | |
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281 | CALL cpu_log( log_point_s(3), 'poisfft', 'stop' ) |
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282 | |
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283 | END SUBROUTINE poisfft |
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284 | |
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285 | |
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286 | |
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287 | SUBROUTINE tridia( ar ) |
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288 | |
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289 | !------------------------------------------------------------------------------! |
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290 | ! solves the linear system of equations: |
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291 | ! |
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292 | ! -(4 pi^2(i^2/(dx^2*nnx^2)+j^2/(dy^2*nny^2))+ |
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293 | ! 1/(dzu(k)*dzw(k))+1/(dzu(k-1)*dzw(k)))*p(i,j,k)+ |
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294 | ! 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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295 | ! |
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296 | ! by using the Thomas algorithm |
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297 | !------------------------------------------------------------------------------! |
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298 | |
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299 | USE arrays_3d |
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300 | |
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301 | IMPLICIT NONE |
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302 | |
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303 | INTEGER :: i, j, k, nnyh |
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304 | |
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305 | REAL, DIMENSION(nxl_z:nxr_z,0:nz-1) :: ar1 |
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306 | REAL, DIMENSION(5,nxl_z:nxr_z,0:nz-1) :: tri |
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307 | |
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308 | #if defined( __parallel ) |
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309 | REAL :: ar(nxl_z:nxr_za,nys_z:nyn_za,1:nza) |
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310 | #else |
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311 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
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312 | #endif |
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313 | |
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314 | |
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315 | nnyh = (ny+1) / 2 |
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316 | |
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317 | ! |
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318 | !-- Define constant elements of the tridiagonal matrix. |
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319 | !$OMP PARALLEL PRIVATE ( k, i ) |
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320 | !$OMP DO |
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321 | DO k = 0, nz-1 |
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322 | DO i = nxl_z, nxr_z |
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323 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
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324 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
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325 | ENDDO |
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326 | ENDDO |
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327 | !$OMP END PARALLEL |
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328 | |
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329 | #if defined( __parallel ) |
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330 | ! |
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331 | !-- Repeat for all y-levels. |
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332 | !$OMP PARALLEL FIRSTPRIVATE( tri ) PRIVATE ( ar1, j ) |
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333 | !$OMP DO |
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334 | DO j = nys_z, nyn_z |
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335 | IF ( j <= nnyh ) THEN |
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336 | CALL maketri( tri, j ) |
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337 | ELSE |
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338 | CALL maketri( tri, ny+1-j ) |
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339 | ENDIF |
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340 | CALL split( tri ) |
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341 | CALL substi( ar, ar1, tri, j ) |
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342 | ENDDO |
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343 | !$OMP END PARALLEL |
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344 | #else |
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345 | ! |
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346 | !-- First y-level. |
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347 | CALL maketri( tri, nys_z ) |
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348 | CALL split( tri ) |
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349 | CALL substi( ar, ar1, tri, 0 ) |
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350 | |
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351 | ! |
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352 | !-- Further y-levels. |
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353 | DO j = 1, nnyh - 1 |
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354 | CALL maketri( tri, j ) |
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355 | CALL split( tri ) |
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356 | CALL substi( ar, ar1, tri, j ) |
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357 | CALL substi( ar, ar1, tri, ny+1-j ) |
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358 | ENDDO |
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359 | CALL maketri( tri, nnyh ) |
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360 | CALL split( tri ) |
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361 | CALL substi( ar, ar1, tri, nnyh+nys ) |
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362 | #endif |
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363 | |
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364 | CONTAINS |
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365 | |
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366 | SUBROUTINE maketri( tri, j ) |
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367 | |
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368 | !------------------------------------------------------------------------------! |
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369 | ! Computes the i- and j-dependent component of the matrix |
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370 | !------------------------------------------------------------------------------! |
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371 | |
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372 | USE arrays_3d |
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373 | USE constants |
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374 | USE control_parameters |
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375 | USE grid_variables |
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376 | |
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377 | IMPLICIT NONE |
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378 | |
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379 | INTEGER :: i, j, k, nnxh |
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380 | REAL :: a, c |
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381 | REAL :: ll(nxl_z:nxr_z) |
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382 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
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383 | |
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384 | |
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385 | nnxh = ( nx + 1 ) / 2 |
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386 | |
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387 | ! |
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388 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
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389 | !-- Fourier space. The coefficients are computed following the method of |
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390 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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391 | !-- Siano's original version by discretizing the Poisson equation, |
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392 | !-- before it is Fourier-transformed |
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393 | #if defined( __parallel ) |
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394 | DO i = nxl_z, nxr_z |
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395 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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396 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
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397 | FLOAT( nx+1 ) ) ) / ( dx * dx ) + & |
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398 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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399 | FLOAT( ny+1 ) ) ) / ( dy * dy ) |
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400 | ELSE |
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401 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
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402 | FLOAT( nx+1 ) ) ) / ( dx * dx ) + & |
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403 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
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404 | FLOAT( ny+1 ) ) ) / ( dy * dy ) |
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405 | ENDIF |
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406 | DO k = 0,nz-1 |
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407 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
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408 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
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409 | tri(1,i,k) = a + c - ll(i) |
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410 | ENDDO |
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411 | ENDDO |
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412 | #else |
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413 | DO i = 0, nnxh |
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414 | ll(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / FLOAT( nx+1 ) ) ) / & |
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415 | ( dx * dx ) + & |
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416 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / FLOAT( ny+1 ) ) ) / & |
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417 | ( dy * dy ) |
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418 | DO k = 0, nz-1 |
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419 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
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420 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
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421 | tri(1,i,k) = a + c - ll(i) |
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422 | IF ( i >= 1 .and. i < nnxh ) THEN |
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423 | tri(1,nx+1-i,k) = tri(1,i,k) |
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424 | ENDIF |
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425 | ENDDO |
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426 | ENDDO |
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427 | #endif |
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428 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
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429 | DO i = nxl_z, nxr_z |
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430 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
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431 | ENDDO |
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432 | ENDIF |
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433 | IF ( ibc_p_t == 1 ) THEN |
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434 | DO i = nxl_z, nxr_z |
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435 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
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436 | ENDDO |
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437 | ENDIF |
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438 | |
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439 | END SUBROUTINE maketri |
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440 | |
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441 | |
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442 | SUBROUTINE substi( ar, ar1, tri, j ) |
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443 | |
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444 | !------------------------------------------------------------------------------! |
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445 | ! Substitution (Forward and Backward) (Thomas algorithm) |
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446 | !------------------------------------------------------------------------------! |
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447 | |
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448 | USE control_parameters |
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449 | |
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450 | IMPLICIT NONE |
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451 | |
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452 | INTEGER :: i, j, k |
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453 | REAL :: ar1(nxl_z:nxr_z,0:nz-1) |
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454 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
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455 | #if defined( __parallel ) |
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456 | REAL :: ar(nxl_z:nxr_za,nys_z:nyn_za,1:nza) |
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457 | #else |
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458 | REAL :: ar(1:nz,nys_z:nyn_z,nxl_z:nxr_z) |
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459 | #endif |
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460 | |
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461 | ! |
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462 | !-- Forward substitution. |
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463 | DO i = nxl_z, nxr_z |
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464 | #if defined( __parallel ) |
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465 | ar1(i,0) = ar(i,j,1) |
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466 | #else |
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467 | ar1(i,0) = ar(1,j,i) |
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468 | #endif |
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469 | ENDDO |
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470 | DO k = 1, nz - 1 |
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471 | DO i = nxl_z, nxr_z |
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472 | #if defined( __parallel ) |
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473 | ar1(i,k) = ar(i,j,k+1) - tri(5,i,k) * ar1(i,k-1) |
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474 | #else |
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475 | ar1(i,k) = ar(k+1,j,i) - tri(5,i,k) * ar1(i,k-1) |
---|
476 | #endif |
---|
477 | ENDDO |
---|
478 | ENDDO |
---|
479 | |
---|
480 | ! |
---|
481 | !-- Backward substitution. |
---|
482 | DO i = nxl_z, nxr_z |
---|
483 | #if defined( __parallel ) |
---|
484 | ar(i,j,nz) = ar1(i,nz-1) / tri(4,i,nz-1) |
---|
485 | #else |
---|
486 | ar(nz,j,i) = ar1(i,nz-1) / tri(4,i,nz-1) |
---|
487 | #endif |
---|
488 | ENDDO |
---|
489 | DO k = nz-2, 0, -1 |
---|
490 | DO i = nxl_z, nxr_z |
---|
491 | #if defined( __parallel ) |
---|
492 | ar(i,j,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,j,k+2) ) & |
---|
493 | / tri(4,i,k) |
---|
494 | #else |
---|
495 | ar(k+1,j,i) = ( ar1(i,k) - tri(3,i,k) * ar(k+2,j,i) ) & |
---|
496 | / tri(4,i,k) |
---|
497 | #endif |
---|
498 | ENDDO |
---|
499 | ENDDO |
---|
500 | |
---|
501 | ! |
---|
502 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
503 | !-- The respective values of ar should be zero at all k-levels if |
---|
504 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
505 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
506 | IF ( j == 0 .AND. nxl_z == 0 ) THEN |
---|
507 | #if defined( __parallel ) |
---|
508 | DO k = 1, nz |
---|
509 | ar(nxl_z,j,k) = 0.0 |
---|
510 | ENDDO |
---|
511 | #else |
---|
512 | DO k = 1, nz |
---|
513 | ar(k,j,nxl_z) = 0.0 |
---|
514 | ENDDO |
---|
515 | #endif |
---|
516 | ENDIF |
---|
517 | ENDIF |
---|
518 | |
---|
519 | END SUBROUTINE substi |
---|
520 | |
---|
521 | |
---|
522 | SUBROUTINE split( tri ) |
---|
523 | |
---|
524 | !------------------------------------------------------------------------------! |
---|
525 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
526 | !------------------------------------------------------------------------------! |
---|
527 | |
---|
528 | IMPLICIT NONE |
---|
529 | |
---|
530 | INTEGER :: i, k |
---|
531 | REAL :: tri(5,nxl_z:nxr_z,0:nz-1) |
---|
532 | |
---|
533 | ! |
---|
534 | !-- Splitting. |
---|
535 | DO i = nxl_z, nxr_z |
---|
536 | tri(4,i,0) = tri(1,i,0) |
---|
537 | ENDDO |
---|
538 | DO k = 1, nz-1 |
---|
539 | DO i = nxl_z, nxr_z |
---|
540 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
541 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
542 | ENDDO |
---|
543 | ENDDO |
---|
544 | |
---|
545 | END SUBROUTINE split |
---|
546 | |
---|
547 | END SUBROUTINE tridia |
---|
548 | |
---|
549 | |
---|
550 | #if defined( __parallel ) |
---|
551 | SUBROUTINE fftxp( ar, direction ) |
---|
552 | |
---|
553 | !------------------------------------------------------------------------------! |
---|
554 | ! Fourier-transformation along x-direction Parallelized version |
---|
555 | !------------------------------------------------------------------------------! |
---|
556 | |
---|
557 | IMPLICIT NONE |
---|
558 | |
---|
559 | CHARACTER (LEN=*) :: direction |
---|
560 | INTEGER :: j, k |
---|
561 | REAL :: ar(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa) |
---|
562 | |
---|
563 | ! |
---|
564 | !-- Performing the fft with one of the methods implemented |
---|
565 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
566 | !$OMP DO |
---|
567 | DO k = nzb_x, nzt_x |
---|
568 | DO j = nys_x, nyn_x |
---|
569 | CALL fft_x( ar(0:nx,j,k), direction ) |
---|
570 | ENDDO |
---|
571 | ENDDO |
---|
572 | !$OMP END PARALLEL |
---|
573 | |
---|
574 | END SUBROUTINE fftxp |
---|
575 | |
---|
576 | #else |
---|
577 | SUBROUTINE fftx( ar, direction ) |
---|
578 | |
---|
579 | !------------------------------------------------------------------------------! |
---|
580 | ! Fourier-transformation along x-direction Non parallel version |
---|
581 | !------------------------------------------------------------------------------! |
---|
582 | |
---|
583 | IMPLICIT NONE |
---|
584 | |
---|
585 | CHARACTER (LEN=*) :: direction |
---|
586 | INTEGER :: i, j, k |
---|
587 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
588 | |
---|
589 | ! |
---|
590 | !-- Performing the fft with one of the methods implemented |
---|
591 | !$OMP PARALLEL PRIVATE ( j, k ) |
---|
592 | !$OMP DO |
---|
593 | DO k = 1, nz |
---|
594 | DO j = 0, ny |
---|
595 | CALL fft_x( ar(k,j,0:nx), direction ) |
---|
596 | ENDDO |
---|
597 | ENDDO |
---|
598 | !$OMP END PARALLEL |
---|
599 | |
---|
600 | END SUBROUTINE fftx |
---|
601 | #endif |
---|
602 | |
---|
603 | |
---|
604 | #if defined( __parallel ) |
---|
605 | SUBROUTINE fftyp( ar, direction ) |
---|
606 | |
---|
607 | !------------------------------------------------------------------------------! |
---|
608 | ! Fourier-transformation along y-direction Parallelized version |
---|
609 | !------------------------------------------------------------------------------! |
---|
610 | |
---|
611 | IMPLICIT NONE |
---|
612 | |
---|
613 | CHARACTER (LEN=*) :: direction |
---|
614 | INTEGER :: i, k |
---|
615 | REAL :: ar(0:nya,nxl_y:nxr_ya,nzb_y:nzt_ya) |
---|
616 | |
---|
617 | ! |
---|
618 | !-- Performing the fft with one of the methods implemented |
---|
619 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
620 | !$OMP DO |
---|
621 | DO k = nzb_y, nzt_y |
---|
622 | DO i = nxl_y, nxr_y |
---|
623 | CALL fft_y( ar(0:ny,i,k), direction ) |
---|
624 | ENDDO |
---|
625 | ENDDO |
---|
626 | !$OMP END PARALLEL |
---|
627 | |
---|
628 | END SUBROUTINE fftyp |
---|
629 | |
---|
630 | #else |
---|
631 | SUBROUTINE ffty( ar, direction ) |
---|
632 | |
---|
633 | !------------------------------------------------------------------------------! |
---|
634 | ! Fourier-transformation along y-direction Non parallel version |
---|
635 | !------------------------------------------------------------------------------! |
---|
636 | |
---|
637 | IMPLICIT NONE |
---|
638 | |
---|
639 | CHARACTER (LEN=*) :: direction |
---|
640 | INTEGER :: i, k |
---|
641 | REAL :: ar(1:nz,0:ny,0:nx) |
---|
642 | |
---|
643 | ! |
---|
644 | !-- Performing the fft with one of the methods implemented |
---|
645 | !$OMP PARALLEL PRIVATE ( i, k ) |
---|
646 | !$OMP DO |
---|
647 | DO k = 1, nz |
---|
648 | DO i = 0, nx |
---|
649 | CALL fft_y( ar(k,0:ny,i), direction ) |
---|
650 | ENDDO |
---|
651 | ENDDO |
---|
652 | !$OMP END PARALLEL |
---|
653 | |
---|
654 | END SUBROUTINE ffty |
---|
655 | #endif |
---|
656 | |
---|
657 | #if defined( __parallel ) |
---|
658 | SUBROUTINE ffty_tr_yx( f_in, work, f_out ) |
---|
659 | |
---|
660 | !------------------------------------------------------------------------------! |
---|
661 | ! Fourier-transformation along y with subsequent transposition y --> x for |
---|
662 | ! a 1d-decomposition along x |
---|
663 | ! |
---|
664 | ! ATTENTION: The performance of this routine is much faster on the NEC-SX6, |
---|
665 | ! if the first index of work_ffty_vec is odd. Otherwise |
---|
666 | ! memory bank conflicts may occur (especially if the index is a |
---|
667 | ! multiple of 128). That's why work_ffty_vec is dimensioned as |
---|
668 | ! 0:ny+1. |
---|
669 | ! Of course, this will not work if users are using an odd number |
---|
670 | ! of gridpoints along y. |
---|
671 | !------------------------------------------------------------------------------! |
---|
672 | |
---|
673 | USE control_parameters |
---|
674 | USE cpulog |
---|
675 | USE indices |
---|
676 | USE interfaces |
---|
677 | USE pegrid |
---|
678 | USE transpose_indices |
---|
679 | |
---|
680 | IMPLICIT NONE |
---|
681 | |
---|
682 | INTEGER :: i, iend, iouter, ir, j, k |
---|
683 | INTEGER, PARAMETER :: stridex = 4 |
---|
684 | |
---|
685 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
686 | #if defined( __nec ) |
---|
687 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
688 | #endif |
---|
689 | REAL, DIMENSION(1:nza,0:nya,nxl:nxra) :: f_in |
---|
690 | REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: f_out |
---|
691 | REAL, DIMENSION(nxl:nxra,1:nza,0:nya) :: work |
---|
692 | |
---|
693 | ! |
---|
694 | !-- Carry out the FFT along y, where all data are present due to the |
---|
695 | !-- 1d-decomposition along x. Resort the data in a way that x becomes |
---|
696 | !-- the first index. |
---|
697 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
---|
698 | |
---|
699 | IF ( host(1:3) == 'nec' ) THEN |
---|
700 | #if defined( __nec ) |
---|
701 | ! |
---|
702 | !-- Code optimized for vector processors |
---|
703 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
704 | !$OMP DO |
---|
705 | DO i = nxl, nxr |
---|
706 | |
---|
707 | DO j = 0, ny |
---|
708 | DO k = 1, nz |
---|
709 | work_ffty_vec(j,k,i) = f_in(k,j,i) |
---|
710 | ENDDO |
---|
711 | ENDDO |
---|
712 | |
---|
713 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'forward' ) |
---|
714 | |
---|
715 | ENDDO |
---|
716 | |
---|
717 | !$OMP DO |
---|
718 | DO k = 1, nz |
---|
719 | DO j = 0, ny |
---|
720 | DO i = nxl, nxr |
---|
721 | work(i,k,j) = work_ffty_vec(j,k,i) |
---|
722 | ENDDO |
---|
723 | ENDDO |
---|
724 | ENDDO |
---|
725 | !$OMP END PARALLEL |
---|
726 | #endif |
---|
727 | |
---|
728 | ELSE |
---|
729 | |
---|
730 | ! |
---|
731 | !-- Cache optimized code. |
---|
732 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
733 | !-- loop for better cache performance |
---|
734 | !$OMP PARALLEL PRIVATE (i,iend,iouter,ir,j,k,work_ffty) |
---|
735 | !$OMP DO |
---|
736 | DO iouter = nxl, nxr, stridex |
---|
737 | |
---|
738 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
739 | |
---|
740 | DO k = 1, nz |
---|
741 | |
---|
742 | DO i = iouter, iend |
---|
743 | |
---|
744 | ir = i-iouter+1 ! counter within a stride |
---|
745 | DO j = 0, ny |
---|
746 | work_ffty(j,ir) = f_in(k,j,i) |
---|
747 | ENDDO |
---|
748 | ! |
---|
749 | !-- FFT along y |
---|
750 | CALL fft_y( work_ffty(:,ir), 'forward' ) |
---|
751 | |
---|
752 | ENDDO |
---|
753 | |
---|
754 | ! |
---|
755 | !-- Resort |
---|
756 | DO j = 0, ny |
---|
757 | DO i = iouter, iend |
---|
758 | work(i,k,j) = work_ffty(j,i-iouter+1) |
---|
759 | ENDDO |
---|
760 | ENDDO |
---|
761 | |
---|
762 | ENDDO |
---|
763 | |
---|
764 | ENDDO |
---|
765 | !$OMP END PARALLEL |
---|
766 | |
---|
767 | ENDIF |
---|
768 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
---|
769 | |
---|
770 | ! |
---|
771 | !-- Transpose array |
---|
772 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
773 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
774 | CALL MPI_ALLTOALL( work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
775 | f_out(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
776 | comm1dx, ierr ) |
---|
777 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
778 | |
---|
779 | END SUBROUTINE ffty_tr_yx |
---|
780 | |
---|
781 | |
---|
782 | SUBROUTINE tr_xy_ffty( f_in, work, f_out ) |
---|
783 | |
---|
784 | !------------------------------------------------------------------------------! |
---|
785 | ! Transposition x --> y with a subsequent backward Fourier transformation for |
---|
786 | ! a 1d-decomposition along x |
---|
787 | !------------------------------------------------------------------------------! |
---|
788 | |
---|
789 | USE control_parameters |
---|
790 | USE cpulog |
---|
791 | USE indices |
---|
792 | USE interfaces |
---|
793 | USE pegrid |
---|
794 | USE transpose_indices |
---|
795 | |
---|
796 | IMPLICIT NONE |
---|
797 | |
---|
798 | INTEGER :: i, iend, iouter, ir, j, k |
---|
799 | INTEGER, PARAMETER :: stridex = 4 |
---|
800 | |
---|
801 | REAL, DIMENSION(0:ny,stridex) :: work_ffty |
---|
802 | #if defined( __nec ) |
---|
803 | REAL, DIMENSION(0:ny+1,1:nz,nxl:nxr) :: work_ffty_vec |
---|
804 | #endif |
---|
805 | REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: f_in |
---|
806 | REAL, DIMENSION(1:nza,0:nya,nxl:nxra) :: f_out |
---|
807 | REAL, DIMENSION(nxl:nxra,1:nza,0:nya) :: work |
---|
808 | |
---|
809 | ! |
---|
810 | !-- Transpose array |
---|
811 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
812 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
813 | CALL MPI_ALLTOALL( f_in(1,1,nys_x,1), sendrecvcount_xy, MPI_REAL, & |
---|
814 | work(nxl,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
815 | comm1dx, ierr ) |
---|
816 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
817 | |
---|
818 | ! |
---|
819 | !-- Resort the data in a way that y becomes the first index and carry out the |
---|
820 | !-- backward fft along y. |
---|
821 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
---|
822 | |
---|
823 | IF ( host(1:3) == 'nec' ) THEN |
---|
824 | #if defined( __nec ) |
---|
825 | ! |
---|
826 | !-- Code optimized for vector processors |
---|
827 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
828 | !$OMP DO |
---|
829 | DO k = 1, nz |
---|
830 | DO j = 0, ny |
---|
831 | DO i = nxl, nxr |
---|
832 | work_ffty_vec(j,k,i) = work(i,k,j) |
---|
833 | ENDDO |
---|
834 | ENDDO |
---|
835 | ENDDO |
---|
836 | |
---|
837 | !$OMP DO |
---|
838 | DO i = nxl, nxr |
---|
839 | |
---|
840 | CALL fft_y_m( work_ffty_vec(:,:,i), ny+1, 'backward' ) |
---|
841 | |
---|
842 | DO j = 0, ny |
---|
843 | DO k = 1, nz |
---|
844 | f_out(k,j,i) = work_ffty_vec(j,k,i) |
---|
845 | ENDDO |
---|
846 | ENDDO |
---|
847 | |
---|
848 | ENDDO |
---|
849 | !$OMP END PARALLEL |
---|
850 | #endif |
---|
851 | |
---|
852 | ELSE |
---|
853 | |
---|
854 | ! |
---|
855 | !-- Cache optimized code. |
---|
856 | !-- The i-(x-)direction is split into a strided outer loop and an inner |
---|
857 | !-- loop for better cache performance |
---|
858 | !$OMP PARALLEL PRIVATE ( i, iend, iouter, ir, j, k, work_ffty ) |
---|
859 | !$OMP DO |
---|
860 | DO iouter = nxl, nxr, stridex |
---|
861 | |
---|
862 | iend = MIN( iouter+stridex-1, nxr ) ! Upper bound for inner i loop |
---|
863 | |
---|
864 | DO k = 1, nz |
---|
865 | ! |
---|
866 | !-- Resort |
---|
867 | DO j = 0, ny |
---|
868 | DO i = iouter, iend |
---|
869 | work_ffty(j,i-iouter+1) = work(i,k,j) |
---|
870 | ENDDO |
---|
871 | ENDDO |
---|
872 | |
---|
873 | DO i = iouter, iend |
---|
874 | |
---|
875 | ! |
---|
876 | !-- FFT along y |
---|
877 | ir = i-iouter+1 ! counter within a stride |
---|
878 | CALL fft_y( work_ffty(:,ir), 'backward' ) |
---|
879 | |
---|
880 | DO j = 0, ny |
---|
881 | f_out(k,j,i) = work_ffty(j,ir) |
---|
882 | ENDDO |
---|
883 | ENDDO |
---|
884 | |
---|
885 | ENDDO |
---|
886 | |
---|
887 | ENDDO |
---|
888 | !$OMP END PARALLEL |
---|
889 | |
---|
890 | ENDIF |
---|
891 | |
---|
892 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
---|
893 | |
---|
894 | END SUBROUTINE tr_xy_ffty |
---|
895 | |
---|
896 | |
---|
897 | SUBROUTINE fftx_tri_fftx( ar ) |
---|
898 | |
---|
899 | !------------------------------------------------------------------------------! |
---|
900 | ! FFT along x, solution of the tridiagonal system and backward FFT for |
---|
901 | ! a 1d-decomposition along x |
---|
902 | ! |
---|
903 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
904 | ! with OpenMP (for possible necessary changes see the original |
---|
905 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
906 | !------------------------------------------------------------------------------! |
---|
907 | |
---|
908 | USE control_parameters |
---|
909 | USE cpulog |
---|
910 | USE grid_variables |
---|
911 | USE indices |
---|
912 | USE interfaces |
---|
913 | USE pegrid |
---|
914 | USE transpose_indices |
---|
915 | |
---|
916 | IMPLICIT NONE |
---|
917 | |
---|
918 | character(len=3) :: myth_char |
---|
919 | |
---|
920 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
921 | |
---|
922 | REAL, DIMENSION(0:nx) :: work_fftx |
---|
923 | REAL, DIMENSION(0:nx,1:nz) :: work_trix |
---|
924 | REAL, DIMENSION(nnx,1:nza,nys_x:nyn_xa,pdims(1)) :: ar |
---|
925 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
926 | |
---|
927 | |
---|
928 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'start' ) |
---|
929 | |
---|
930 | ALLOCATE( tri(5,0:nx,0:nz-1,0:threads_per_task-1) ) |
---|
931 | |
---|
932 | tn = 0 ! Default thread number in case of one thread |
---|
933 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_fftx, work_trix ) |
---|
934 | DO j = nys_x, nyn_x |
---|
935 | |
---|
936 | !$ tn = omp_get_thread_num() |
---|
937 | |
---|
938 | IF ( host(1:3) == 'nec' ) THEN |
---|
939 | ! |
---|
940 | !-- Code optimized for vector processors |
---|
941 | DO k = 1, nz |
---|
942 | |
---|
943 | m = 0 |
---|
944 | DO n = 1, pdims(1) |
---|
945 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
946 | work_trix(m,k) = ar(i,k,j,n) |
---|
947 | m = m + 1 |
---|
948 | ENDDO |
---|
949 | ENDDO |
---|
950 | |
---|
951 | ENDDO |
---|
952 | |
---|
953 | CALL fft_x_m( work_trix, 'forward' ) |
---|
954 | |
---|
955 | ELSE |
---|
956 | ! |
---|
957 | !-- Cache optimized code |
---|
958 | DO k = 1, nz |
---|
959 | |
---|
960 | m = 0 |
---|
961 | DO n = 1, pdims(1) |
---|
962 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
963 | work_fftx(m) = ar(i,k,j,n) |
---|
964 | m = m + 1 |
---|
965 | ENDDO |
---|
966 | ENDDO |
---|
967 | |
---|
968 | CALL fft_x( work_fftx, 'forward' ) |
---|
969 | |
---|
970 | DO i = 0, nx |
---|
971 | work_trix(i,k) = work_fftx(i) |
---|
972 | ENDDO |
---|
973 | |
---|
974 | ENDDO |
---|
975 | |
---|
976 | ENDIF |
---|
977 | |
---|
978 | ! |
---|
979 | !-- Solve the linear equation system |
---|
980 | CALL tridia_1dd( ddx2, ddy2, nx, ny, j, work_trix, tri(:,:,:,tn) ) |
---|
981 | |
---|
982 | IF ( host(1:3) == 'nec' ) THEN |
---|
983 | ! |
---|
984 | !-- Code optimized for vector processors |
---|
985 | CALL fft_x_m( work_trix, 'backward' ) |
---|
986 | |
---|
987 | DO k = 1, nz |
---|
988 | |
---|
989 | m = 0 |
---|
990 | DO n = 1, pdims(1) |
---|
991 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
992 | ar(i,k,j,n) = work_trix(m,k) |
---|
993 | m = m + 1 |
---|
994 | ENDDO |
---|
995 | ENDDO |
---|
996 | |
---|
997 | ENDDO |
---|
998 | |
---|
999 | ELSE |
---|
1000 | ! |
---|
1001 | !-- Cache optimized code |
---|
1002 | DO k = 1, nz |
---|
1003 | |
---|
1004 | DO i = 0, nx |
---|
1005 | work_fftx(i) = work_trix(i,k) |
---|
1006 | ENDDO |
---|
1007 | |
---|
1008 | CALL fft_x( work_fftx, 'backward' ) |
---|
1009 | |
---|
1010 | m = 0 |
---|
1011 | DO n = 1, pdims(1) |
---|
1012 | DO i = 1, nnx_pe( n-1 ) ! WARN: pcoord(i) should be used!! |
---|
1013 | ar(i,k,j,n) = work_fftx(m) |
---|
1014 | m = m + 1 |
---|
1015 | ENDDO |
---|
1016 | ENDDO |
---|
1017 | |
---|
1018 | ENDDO |
---|
1019 | |
---|
1020 | ENDIF |
---|
1021 | |
---|
1022 | ENDDO |
---|
1023 | |
---|
1024 | DEALLOCATE( tri ) |
---|
1025 | |
---|
1026 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'stop' ) |
---|
1027 | |
---|
1028 | END SUBROUTINE fftx_tri_fftx |
---|
1029 | |
---|
1030 | |
---|
1031 | SUBROUTINE fftx_tr_xy( f_in, work, f_out ) |
---|
1032 | |
---|
1033 | !------------------------------------------------------------------------------! |
---|
1034 | ! Fourier-transformation along x with subsequent transposition x --> y for |
---|
1035 | ! a 1d-decomposition along y |
---|
1036 | ! |
---|
1037 | ! ATTENTION: The NEC-branch of this routine may significantly profit from |
---|
1038 | ! further optimizations. So far, performance is much worse than |
---|
1039 | ! for routine ffty_tr_yx (more than three times slower). |
---|
1040 | !------------------------------------------------------------------------------! |
---|
1041 | |
---|
1042 | USE control_parameters |
---|
1043 | USE cpulog |
---|
1044 | USE indices |
---|
1045 | USE interfaces |
---|
1046 | USE pegrid |
---|
1047 | USE transpose_indices |
---|
1048 | |
---|
1049 | IMPLICIT NONE |
---|
1050 | |
---|
1051 | INTEGER :: i, j, k |
---|
1052 | |
---|
1053 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
1054 | REAL, DIMENSION(1:nza,nys:nyna,0:nxa) :: f_in |
---|
1055 | REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: f_out |
---|
1056 | REAL, DIMENSION(nys:nyna,1:nza,0:nxa) :: work |
---|
1057 | |
---|
1058 | ! |
---|
1059 | !-- Carry out the FFT along x, where all data are present due to the |
---|
1060 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
1061 | !-- the first index. |
---|
1062 | CALL cpu_log( log_point_s(4), 'fft_x', 'start' ) |
---|
1063 | |
---|
1064 | IF ( host(1:3) == 'nec' ) THEN |
---|
1065 | ! |
---|
1066 | !-- Code for vector processors |
---|
1067 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
1068 | !$OMP DO |
---|
1069 | DO i = 0, nx |
---|
1070 | |
---|
1071 | DO j = nys, nyn |
---|
1072 | DO k = 1, nz |
---|
1073 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
1074 | ENDDO |
---|
1075 | ENDDO |
---|
1076 | |
---|
1077 | ENDDO |
---|
1078 | |
---|
1079 | !$OMP DO |
---|
1080 | DO j = nys, nyn |
---|
1081 | |
---|
1082 | CALL fft_x_m( work_fftx(:,:,j), 'forward' ) |
---|
1083 | |
---|
1084 | DO k = 1, nz |
---|
1085 | DO i = 0, nx |
---|
1086 | work(j,k,i) = work_fftx(i,k,j) |
---|
1087 | ENDDO |
---|
1088 | ENDDO |
---|
1089 | |
---|
1090 | ENDDO |
---|
1091 | !$OMP END PARALLEL |
---|
1092 | |
---|
1093 | ELSE |
---|
1094 | |
---|
1095 | ! |
---|
1096 | !-- Cache optimized code (there might be still a potential for better |
---|
1097 | !-- optimization). |
---|
1098 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
1099 | !$OMP DO |
---|
1100 | DO i = 0, nx |
---|
1101 | |
---|
1102 | DO j = nys, nyn |
---|
1103 | DO k = 1, nz |
---|
1104 | work_fftx(i,k,j) = f_in(k,j,i) |
---|
1105 | ENDDO |
---|
1106 | ENDDO |
---|
1107 | |
---|
1108 | ENDDO |
---|
1109 | |
---|
1110 | !$OMP DO |
---|
1111 | DO j = nys, nyn |
---|
1112 | DO k = 1, nz |
---|
1113 | |
---|
1114 | CALL fft_x( work_fftx(0:nx,k,j), 'forward' ) |
---|
1115 | |
---|
1116 | DO i = 0, nx |
---|
1117 | work(j,k,i) = work_fftx(i,k,j) |
---|
1118 | ENDDO |
---|
1119 | ENDDO |
---|
1120 | |
---|
1121 | ENDDO |
---|
1122 | !$OMP END PARALLEL |
---|
1123 | |
---|
1124 | ENDIF |
---|
1125 | CALL cpu_log( log_point_s(4), 'fft_x', 'pause' ) |
---|
1126 | |
---|
1127 | ! |
---|
1128 | !-- Transpose array |
---|
1129 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
1130 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
1131 | CALL MPI_ALLTOALL( work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
1132 | f_out(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
1133 | comm1dy, ierr ) |
---|
1134 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
1135 | |
---|
1136 | END SUBROUTINE fftx_tr_xy |
---|
1137 | |
---|
1138 | |
---|
1139 | SUBROUTINE tr_yx_fftx( f_in, work, f_out ) |
---|
1140 | |
---|
1141 | !------------------------------------------------------------------------------! |
---|
1142 | ! Transposition y --> x with a subsequent backward Fourier transformation for |
---|
1143 | ! a 1d-decomposition along x |
---|
1144 | !------------------------------------------------------------------------------! |
---|
1145 | |
---|
1146 | USE control_parameters |
---|
1147 | USE cpulog |
---|
1148 | USE indices |
---|
1149 | USE interfaces |
---|
1150 | USE pegrid |
---|
1151 | USE transpose_indices |
---|
1152 | |
---|
1153 | IMPLICIT NONE |
---|
1154 | |
---|
1155 | INTEGER :: i, j, k |
---|
1156 | |
---|
1157 | REAL, DIMENSION(0:nx,1:nz,nys:nyn) :: work_fftx |
---|
1158 | REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: f_in |
---|
1159 | REAL, DIMENSION(1:nza,nys:nyna,0:nxa) :: f_out |
---|
1160 | REAL, DIMENSION(nys:nyna,1:nza,0:nxa) :: work |
---|
1161 | |
---|
1162 | ! |
---|
1163 | !-- Transpose array |
---|
1164 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
1165 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
---|
1166 | CALL MPI_ALLTOALL( f_in(1,1,nxl_y,1), sendrecvcount_xy, MPI_REAL, & |
---|
1167 | work(nys,1,0), sendrecvcount_xy, MPI_REAL, & |
---|
1168 | comm1dy, ierr ) |
---|
1169 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
1170 | |
---|
1171 | ! |
---|
1172 | !-- Carry out the FFT along x, where all data are present due to the |
---|
1173 | !-- 1d-decomposition along y. Resort the data in a way that y becomes |
---|
1174 | !-- the first index. |
---|
1175 | CALL cpu_log( log_point_s(4), 'fft_x', 'continue' ) |
---|
1176 | |
---|
1177 | IF ( host(1:3) == 'nec' ) THEN |
---|
1178 | ! |
---|
1179 | !-- Code optimized for vector processors |
---|
1180 | !$OMP PARALLEL PRIVATE ( i, j, k ) |
---|
1181 | !$OMP DO |
---|
1182 | DO j = nys, nyn |
---|
1183 | |
---|
1184 | DO k = 1, nz |
---|
1185 | DO i = 0, nx |
---|
1186 | work_fftx(i,k,j) = work(j,k,i) |
---|
1187 | ENDDO |
---|
1188 | ENDDO |
---|
1189 | |
---|
1190 | CALL fft_x_m( work_fftx(:,:,j), 'backward' ) |
---|
1191 | |
---|
1192 | ENDDO |
---|
1193 | |
---|
1194 | !$OMP DO |
---|
1195 | DO i = 0, nx |
---|
1196 | DO j = nys, nyn |
---|
1197 | DO k = 1, nz |
---|
1198 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
1199 | ENDDO |
---|
1200 | ENDDO |
---|
1201 | ENDDO |
---|
1202 | !$OMP END PARALLEL |
---|
1203 | |
---|
1204 | ELSE |
---|
1205 | |
---|
1206 | ! |
---|
1207 | !-- Cache optimized code (there might be still a potential for better |
---|
1208 | !-- optimization). |
---|
1209 | !$OMP PARALLEL PRIVATE (i,j,k) |
---|
1210 | !$OMP DO |
---|
1211 | DO j = nys, nyn |
---|
1212 | DO k = 1, nz |
---|
1213 | |
---|
1214 | DO i = 0, nx |
---|
1215 | work_fftx(i,k,j) = work(j,k,i) |
---|
1216 | ENDDO |
---|
1217 | |
---|
1218 | CALL fft_x( work_fftx(0:nx,k,j), 'backward' ) |
---|
1219 | |
---|
1220 | ENDDO |
---|
1221 | ENDDO |
---|
1222 | |
---|
1223 | !$OMP DO |
---|
1224 | DO i = 0, nx |
---|
1225 | DO j = nys, nyn |
---|
1226 | DO k = 1, nz |
---|
1227 | f_out(k,j,i) = work_fftx(i,k,j) |
---|
1228 | ENDDO |
---|
1229 | ENDDO |
---|
1230 | ENDDO |
---|
1231 | !$OMP END PARALLEL |
---|
1232 | |
---|
1233 | ENDIF |
---|
1234 | CALL cpu_log( log_point_s(4), 'fft_x', 'stop' ) |
---|
1235 | |
---|
1236 | END SUBROUTINE tr_yx_fftx |
---|
1237 | |
---|
1238 | |
---|
1239 | SUBROUTINE ffty_tri_ffty( ar ) |
---|
1240 | |
---|
1241 | !------------------------------------------------------------------------------! |
---|
1242 | ! FFT along y, solution of the tridiagonal system and backward FFT for |
---|
1243 | ! a 1d-decomposition along y |
---|
1244 | ! |
---|
1245 | ! WARNING: this subroutine may still not work for hybrid parallelization |
---|
1246 | ! with OpenMP (for possible necessary changes see the original |
---|
1247 | ! routine poisfft_hybrid, developed by Klaus Ketelsen, May 2002) |
---|
1248 | !------------------------------------------------------------------------------! |
---|
1249 | |
---|
1250 | USE control_parameters |
---|
1251 | USE cpulog |
---|
1252 | USE grid_variables |
---|
1253 | USE indices |
---|
1254 | USE interfaces |
---|
1255 | USE pegrid |
---|
1256 | USE transpose_indices |
---|
1257 | |
---|
1258 | IMPLICIT NONE |
---|
1259 | |
---|
1260 | INTEGER :: i, j, k, m, n, omp_get_thread_num, tn |
---|
1261 | |
---|
1262 | REAL, DIMENSION(0:ny) :: work_ffty |
---|
1263 | REAL, DIMENSION(0:ny,1:nz) :: work_triy |
---|
1264 | REAL, DIMENSION(nny,1:nza,nxl_y:nxr_ya,pdims(2)) :: ar |
---|
1265 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
---|
1266 | |
---|
1267 | |
---|
1268 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'start' ) |
---|
1269 | |
---|
1270 | ALLOCATE( tri(5,0:ny,0:nz-1,0:threads_per_task-1) ) |
---|
1271 | |
---|
1272 | tn = 0 ! Default thread number in case of one thread |
---|
1273 | !$OMP PARALLEL DO PRIVATE ( i, j, k, m, n, tn, work_ffty, work_triy ) |
---|
1274 | DO i = nxl_y, nxr_y |
---|
1275 | |
---|
1276 | !$ tn = omp_get_thread_num() |
---|
1277 | |
---|
1278 | IF ( host(1:3) == 'nec' ) THEN |
---|
1279 | ! |
---|
1280 | !-- Code optimized for vector processors |
---|
1281 | DO k = 1, nz |
---|
1282 | |
---|
1283 | m = 0 |
---|
1284 | DO n = 1, pdims(2) |
---|
1285 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1286 | work_triy(m,k) = ar(j,k,i,n) |
---|
1287 | m = m + 1 |
---|
1288 | ENDDO |
---|
1289 | ENDDO |
---|
1290 | |
---|
1291 | ENDDO |
---|
1292 | |
---|
1293 | CALL fft_y_m( work_triy, ny, 'forward' ) |
---|
1294 | |
---|
1295 | ELSE |
---|
1296 | ! |
---|
1297 | !-- Cache optimized code |
---|
1298 | DO k = 1, nz |
---|
1299 | |
---|
1300 | m = 0 |
---|
1301 | DO n = 1, pdims(2) |
---|
1302 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1303 | work_ffty(m) = ar(j,k,i,n) |
---|
1304 | m = m + 1 |
---|
1305 | ENDDO |
---|
1306 | ENDDO |
---|
1307 | |
---|
1308 | CALL fft_y( work_ffty, 'forward' ) |
---|
1309 | |
---|
1310 | DO j = 0, ny |
---|
1311 | work_triy(j,k) = work_ffty(j) |
---|
1312 | ENDDO |
---|
1313 | |
---|
1314 | ENDDO |
---|
1315 | |
---|
1316 | ENDIF |
---|
1317 | |
---|
1318 | ! |
---|
1319 | !-- Solve the linear equation system |
---|
1320 | CALL tridia_1dd( ddy2, ddx2, ny, nx, i, work_triy, tri(:,:,:,tn) ) |
---|
1321 | |
---|
1322 | IF ( host(1:3) == 'nec' ) THEN |
---|
1323 | ! |
---|
1324 | !-- Code optimized for vector processors |
---|
1325 | CALL fft_y_m( work_triy, ny, 'backward' ) |
---|
1326 | |
---|
1327 | DO k = 1, nz |
---|
1328 | |
---|
1329 | m = 0 |
---|
1330 | DO n = 1, pdims(2) |
---|
1331 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1332 | ar(j,k,i,n) = work_triy(m,k) |
---|
1333 | m = m + 1 |
---|
1334 | ENDDO |
---|
1335 | ENDDO |
---|
1336 | |
---|
1337 | ENDDO |
---|
1338 | |
---|
1339 | ELSE |
---|
1340 | ! |
---|
1341 | !-- Cache optimized code |
---|
1342 | DO k = 1, nz |
---|
1343 | |
---|
1344 | DO j = 0, ny |
---|
1345 | work_ffty(j) = work_triy(j,k) |
---|
1346 | ENDDO |
---|
1347 | |
---|
1348 | CALL fft_y( work_ffty, 'backward' ) |
---|
1349 | |
---|
1350 | m = 0 |
---|
1351 | DO n = 1, pdims(2) |
---|
1352 | DO j = 1, nny_pe( n-1 ) ! WARN: pcoord(j) should be used!! |
---|
1353 | ar(j,k,i,n) = work_ffty(m) |
---|
1354 | m = m + 1 |
---|
1355 | ENDDO |
---|
1356 | ENDDO |
---|
1357 | |
---|
1358 | ENDDO |
---|
1359 | |
---|
1360 | ENDIF |
---|
1361 | |
---|
1362 | ENDDO |
---|
1363 | |
---|
1364 | DEALLOCATE( tri ) |
---|
1365 | |
---|
1366 | CALL cpu_log( log_point_s(39), 'fft_y + tridia', 'stop' ) |
---|
1367 | |
---|
1368 | END SUBROUTINE ffty_tri_ffty |
---|
1369 | |
---|
1370 | |
---|
1371 | SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri ) |
---|
1372 | |
---|
1373 | !------------------------------------------------------------------------------! |
---|
1374 | ! Solves the linear system of equations for a 1d-decomposition along x (see |
---|
1375 | ! tridia) |
---|
1376 | ! |
---|
1377 | ! Attention: when using the intel compiler, array tri must be passed as an |
---|
1378 | ! argument to the contained subroutines. Otherwise addres faults |
---|
1379 | ! will occur. |
---|
1380 | ! On NEC, tri should not be passed (except for routine substi_1dd) |
---|
1381 | ! because this causes very bad performance. |
---|
1382 | !------------------------------------------------------------------------------! |
---|
1383 | |
---|
1384 | USE arrays_3d |
---|
1385 | USE control_parameters |
---|
1386 | |
---|
1387 | USE pegrid |
---|
1388 | |
---|
1389 | IMPLICIT NONE |
---|
1390 | |
---|
1391 | INTEGER :: i, j, k, nnyh, nx, ny, omp_get_thread_num, tn |
---|
1392 | |
---|
1393 | REAL :: ddx2, ddy2 |
---|
1394 | |
---|
1395 | REAL, DIMENSION(0:nx,1:nz) :: ar |
---|
1396 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
1397 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1398 | |
---|
1399 | |
---|
1400 | nnyh = ( ny + 1 ) / 2 |
---|
1401 | |
---|
1402 | ! |
---|
1403 | !-- Define constant elements of the tridiagonal matrix. |
---|
1404 | !-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2, |
---|
1405 | !-- the exchanged loops create bank conflicts. The following directive |
---|
1406 | !-- prohibits loop exchange and the loops perform much better. |
---|
1407 | ! tn = omp_get_thread_num() |
---|
1408 | ! WRITE( 120+tn, * ) '+++ id=',myid,' nx=',nx,' thread=', omp_get_thread_num() |
---|
1409 | ! CALL local_flush( 120+tn ) |
---|
1410 | !CDIR NOLOOPCHG |
---|
1411 | DO k = 0, nz-1 |
---|
1412 | DO i = 0,nx |
---|
1413 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
---|
1414 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
---|
1415 | ENDDO |
---|
1416 | ENDDO |
---|
1417 | ! WRITE( 120+tn, * ) '+++ id=',myid,' end of first tridia loop thread=', omp_get_thread_num() |
---|
1418 | ! CALL local_flush( 120+tn ) |
---|
1419 | |
---|
1420 | IF ( j <= nnyh ) THEN |
---|
1421 | #if defined( __lc ) |
---|
1422 | CALL maketri_1dd( j, tri ) |
---|
1423 | #else |
---|
1424 | CALL maketri_1dd( j ) |
---|
1425 | #endif |
---|
1426 | ELSE |
---|
1427 | #if defined( __lc ) |
---|
1428 | CALL maketri_1dd( ny+1-j, tri ) |
---|
1429 | #else |
---|
1430 | CALL maketri_1dd( ny+1-j ) |
---|
1431 | #endif |
---|
1432 | ENDIF |
---|
1433 | #if defined( __lc ) |
---|
1434 | CALL split_1dd( tri ) |
---|
1435 | #else |
---|
1436 | CALL split_1dd |
---|
1437 | #endif |
---|
1438 | CALL substi_1dd( ar, tri ) |
---|
1439 | |
---|
1440 | CONTAINS |
---|
1441 | |
---|
1442 | #if defined( __lc ) |
---|
1443 | SUBROUTINE maketri_1dd( j, tri ) |
---|
1444 | #else |
---|
1445 | SUBROUTINE maketri_1dd( j ) |
---|
1446 | #endif |
---|
1447 | |
---|
1448 | !------------------------------------------------------------------------------! |
---|
1449 | ! computes the i- and j-dependent component of the matrix |
---|
1450 | !------------------------------------------------------------------------------! |
---|
1451 | |
---|
1452 | USE constants |
---|
1453 | |
---|
1454 | IMPLICIT NONE |
---|
1455 | |
---|
1456 | INTEGER :: i, j, k, nnxh |
---|
1457 | REAL :: a, c |
---|
1458 | |
---|
1459 | REAL, DIMENSION(0:nx) :: l |
---|
1460 | |
---|
1461 | #if defined( __lc ) |
---|
1462 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1463 | #endif |
---|
1464 | |
---|
1465 | |
---|
1466 | nnxh = ( nx + 1 ) / 2 |
---|
1467 | ! |
---|
1468 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
---|
1469 | !-- Fourier space. The coefficients are computed following the method of |
---|
1470 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
---|
1471 | !-- Siano's original version by discretizing the Poisson equation, |
---|
1472 | !-- before it is Fourier-transformed |
---|
1473 | DO i = 0, nx |
---|
1474 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
---|
1475 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
---|
1476 | FLOAT( nx+1 ) ) ) * ddx2 + & |
---|
1477 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
1478 | FLOAT( ny+1 ) ) ) * ddy2 |
---|
1479 | ELSE |
---|
1480 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
1481 | FLOAT( nx+1 ) ) ) * ddx2 + & |
---|
1482 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
1483 | FLOAT( ny+1 ) ) ) * ddy2 |
---|
1484 | ENDIF |
---|
1485 | ENDDO |
---|
1486 | |
---|
1487 | DO k = 0, nz-1 |
---|
1488 | DO i = 0, nx |
---|
1489 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
1490 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
1491 | tri(1,i,k) = a + c - l(i) |
---|
1492 | ENDDO |
---|
1493 | ENDDO |
---|
1494 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
1495 | DO i = 0, nx |
---|
1496 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
1497 | ENDDO |
---|
1498 | ENDIF |
---|
1499 | IF ( ibc_p_t == 1 ) THEN |
---|
1500 | DO i = 0, nx |
---|
1501 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
1502 | ENDDO |
---|
1503 | ENDIF |
---|
1504 | |
---|
1505 | END SUBROUTINE maketri_1dd |
---|
1506 | |
---|
1507 | |
---|
1508 | #if defined( __lc ) |
---|
1509 | SUBROUTINE split_1dd( tri ) |
---|
1510 | #else |
---|
1511 | SUBROUTINE split_1dd |
---|
1512 | #endif |
---|
1513 | |
---|
1514 | !------------------------------------------------------------------------------! |
---|
1515 | ! Splitting of the tridiagonal matrix (Thomas algorithm) |
---|
1516 | !------------------------------------------------------------------------------! |
---|
1517 | |
---|
1518 | IMPLICIT NONE |
---|
1519 | |
---|
1520 | INTEGER :: i, k |
---|
1521 | |
---|
1522 | #if defined( __lc ) |
---|
1523 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1524 | #endif |
---|
1525 | |
---|
1526 | |
---|
1527 | ! |
---|
1528 | !-- Splitting |
---|
1529 | DO i = 0, nx |
---|
1530 | tri(4,i,0) = tri(1,i,0) |
---|
1531 | ENDDO |
---|
1532 | DO k = 1, nz-1 |
---|
1533 | DO i = 0, nx |
---|
1534 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
1535 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
1536 | ENDDO |
---|
1537 | ENDDO |
---|
1538 | |
---|
1539 | END SUBROUTINE split_1dd |
---|
1540 | |
---|
1541 | |
---|
1542 | SUBROUTINE substi_1dd( ar, tri ) |
---|
1543 | |
---|
1544 | !------------------------------------------------------------------------------! |
---|
1545 | ! Substitution (Forward and Backward) (Thomas algorithm) |
---|
1546 | !------------------------------------------------------------------------------! |
---|
1547 | |
---|
1548 | IMPLICIT NONE |
---|
1549 | |
---|
1550 | INTEGER :: i, k |
---|
1551 | |
---|
1552 | REAL, DIMENSION(0:nx,nz) :: ar |
---|
1553 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
1554 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
1555 | |
---|
1556 | ! |
---|
1557 | !-- Forward substitution |
---|
1558 | DO i = 0, nx |
---|
1559 | ar1(i,0) = ar(i,1) |
---|
1560 | ENDDO |
---|
1561 | DO k = 1, nz-1 |
---|
1562 | DO i = 0, nx |
---|
1563 | ar1(i,k) = ar(i,k+1) - tri(5,i,k) * ar1(i,k-1) |
---|
1564 | ENDDO |
---|
1565 | ENDDO |
---|
1566 | |
---|
1567 | ! |
---|
1568 | !-- Backward substitution |
---|
1569 | !-- Note, the add of 1.0E-20 in the denominator is due to avoid divisions |
---|
1570 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
---|
1571 | !-- the model domain. |
---|
1572 | DO i = 0, nx |
---|
1573 | ar(i,nz) = ar1(i,nz-1) / ( tri(4,i,nz-1) + 1.0E-20 ) |
---|
1574 | ENDDO |
---|
1575 | DO k = nz-2, 0, -1 |
---|
1576 | DO i = 0, nx |
---|
1577 | ar(i,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,k+2) ) & |
---|
1578 | / tri(4,i,k) |
---|
1579 | ENDDO |
---|
1580 | ENDDO |
---|
1581 | |
---|
1582 | ! |
---|
1583 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
---|
1584 | !-- The respective values of ar should be zero at all k-levels if |
---|
1585 | !-- acceleration of horizontally averaged vertical velocity is zero. |
---|
1586 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
---|
1587 | IF ( j == 0 ) THEN |
---|
1588 | DO k = 1, nz |
---|
1589 | ar(0,k) = 0.0 |
---|
1590 | ENDDO |
---|
1591 | ENDIF |
---|
1592 | ENDIF |
---|
1593 | |
---|
1594 | END SUBROUTINE substi_1dd |
---|
1595 | |
---|
1596 | END SUBROUTINE tridia_1dd |
---|
1597 | |
---|
1598 | #endif |
---|
1599 | #endif |
---|
1600 | END MODULE poisfft_mod |
---|