| 1 |
SUBROUTINE CG2D |
| 2 |
C /==========================================================\ |
| 3 |
C | SUBROUTINE CG2D | |
| 4 |
C | o Two-dimensional grid problem conjugate-gradient | |
| 5 |
C | inverter (with preconditioner). | |
| 6 |
C |==========================================================| |
| 7 |
C | Con. grad is an iterative procedure for solving Ax = b. | |
| 8 |
C | It requires the A be symmetric. | |
| 9 |
C | This implementation assumes A is a five-diagonal | |
| 10 |
C | matrix of the form that arises in the discrete | |
| 11 |
C | representation of the del^2 operator in a | |
| 12 |
C | two-dimensional space. | |
| 13 |
C | Notes: | |
| 14 |
C | ====== | |
| 15 |
C | This implementation can support shared-memory | |
| 16 |
C | multi-threaded execution. In order to do this COMMON | |
| 17 |
C | blocks are used for many of the arrays - even ones that | |
| 18 |
C | are only used for intermedaite results. This design is | |
| 19 |
C | OK if you want to all the threads to collaborate on | |
| 20 |
C | solving the same problem. On the other hand if you want | |
| 21 |
C | the threads to solve several different problems | |
| 22 |
C | concurrently this implementation will not work. | |
| 23 |
C \==========================================================/ |
| 24 |
IMPLICIT NONE |
| 25 |
|
| 26 |
C === Global data === |
| 27 |
#include "SIZE.h" |
| 28 |
#include "EEPARAMS.h" |
| 29 |
#include "PARAMS.h" |
| 30 |
#include "CG2D.h" |
| 31 |
|
| 32 |
C === Routine arguments === |
| 33 |
C myThid - Thread on which I am working. |
| 34 |
INTEGER myThid |
| 35 |
|
| 36 |
C === Local variables ==== |
| 37 |
C actualIts - Number of iterations taken |
| 38 |
C actualResidual - residual |
| 39 |
C bi - Block index in X and Y. |
| 40 |
C bj |
| 41 |
C etaN - Used in computing search directions |
| 42 |
C etaNM1 suffix N and NM1 denote current and |
| 43 |
C beta previous iterations respectively. |
| 44 |
C alpha |
| 45 |
C sumRHS - Sum of right-hand-side. Sometimes this is a |
| 46 |
C useful debuggin/trouble shooting diagnostic. |
| 47 |
C For neumann problems sumRHS needs to be ~0. |
| 48 |
C or they converge at a non-zero residual. |
| 49 |
C err - Measure of residual of Ax - b, usually the norm. |
| 50 |
C I, J, N - Loop counters ( N counts CG iterations ) |
| 51 |
INTEGER actualIts |
| 52 |
REAL actualResidual |
| 53 |
INTEGER bi, bj |
| 54 |
INTEGER I, J, N |
| 55 |
REAL err |
| 56 |
REAL errSum |
| 57 |
REAL etaN |
| 58 |
REAL etaNM1 |
| 59 |
REAL etaNSum |
| 60 |
REAL beta |
| 61 |
REAL alpha |
| 62 |
REAL alphaSum |
| 63 |
REAL sumRHS |
| 64 |
REAL temp |
| 65 |
|
| 66 |
C-- Initialise inverter |
| 67 |
etaNM1 = 1. D0 |
| 68 |
|
| 69 |
C-- Initial residual calculation |
| 70 |
err = 0. _d 0 |
| 71 |
sumRHS = 0. _d 0 |
| 72 |
DO J=1,sNy |
| 73 |
DO I=1,sNx |
| 74 |
cg2d_s(I,J) = 0. |
| 75 |
cg2d_r(I,J) = cg2d_b(I,J) - |
| 76 |
& ( aW2d(I ,J )*cg2d_x(I-1,J )+aW2d(I+1,J )*cg2d_x(I+1,J ) |
| 77 |
& +aS2d(I ,J )*cg2d_x(I ,J-1)+aS2d(I ,J+1)*cg2d_x(I ,J+1) |
| 78 |
& -aW2d(I ,J )*cg2d_x(I ,J )-aW2d(I+1,J )*cg2d_x(I ,J ) |
| 79 |
& -aS2d(I ,J )*cg2d_x(I ,J )-aS2d(I ,J+1)*cg2d_x(I ,J ) |
| 80 |
& ) |
| 81 |
err = err + cg2d_r(I,J)*cg2d_r(I,J) |
| 82 |
sumRHS = sumRHS + cg2d_b(I,J) |
| 83 |
ENDDO |
| 84 |
ENDDO |
| 85 |
CALL EXCH_XY_R8( cg2d_r ) |
| 86 |
CALL EXCH_XY_R8( cg2d_s ) |
| 87 |
CALL GSUM_R8( temp, err ) |
| 88 |
err = temp |
| 89 |
CALL GSUM_R8( temp, sumRHS ) |
| 90 |
sumRHS = temp |
| 91 |
|
| 92 |
actualIts = 0 |
| 93 |
actualResidual = SQRT(err) |
| 94 |
WRITE(6,*) ' CG2D iters, err = ', actualIts, actualResidual |
| 95 |
IF ( actualResidual .EQ. 0. ) STOP 'ABNORMAL END: RESIDUAL 0' |
| 96 |
|
| 97 |
C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
| 98 |
DO 10 N=1, cg2dMaxIters |
| 99 |
C-- Solve preconditioning equation and update |
| 100 |
C-- conjugate direction vector "s". |
| 101 |
etaN = 0. _d 0 |
| 102 |
DO J=1,sNy |
| 103 |
DO I=1,sNx |
| 104 |
cg2d_q(I,J) = |
| 105 |
& pW(I ,J )*cg2d_r(I-1,J )+pW(I+1,J )*cg2d_r(I+1,J ) |
| 106 |
& +pS(I ,J )*cg2d_r(I ,J-1)+pS(I ,J+1)*cg2d_r(I ,J+1) |
| 107 |
& +pC(I ,J )*cg2d_r(I ,J ) |
| 108 |
etaN = etaN+cg2d_q(I,J)*cg2d_r(I,J) |
| 109 |
ENDDO |
| 110 |
ENDDO |
| 111 |
|
| 112 |
CALL GSUM_R8( temp, etaN ) |
| 113 |
etaN = temp |
| 114 |
beta = etaN/etaNM1 |
| 115 |
etaNM1 = etaN |
| 116 |
|
| 117 |
DO J=1,sNy |
| 118 |
DO I=1,sNx |
| 119 |
cg2d_s(I,J) = cg2d_q(I,J) + beta*cg2d_s(I,J) |
| 120 |
ENDDO |
| 121 |
ENDDO |
| 122 |
|
| 123 |
C-- Do exchanges that require messages i.e. between |
| 124 |
C-- processes. |
| 125 |
CALL EXCH_XY_R8( cg2d_s ) |
| 126 |
|
| 127 |
C-- Ten extra exchanges |
| 128 |
#ifdef TEN_EXTRA_EXCHS |
| 129 |
CALL EXCH_XY_R8( cg2d_s ) |
| 130 |
CALL EXCH_XY_R8( cg2d_s ) |
| 131 |
CALL EXCH_XY_R8( cg2d_s ) |
| 132 |
CALL EXCH_XY_R8( cg2d_s ) |
| 133 |
CALL EXCH_XY_R8( cg2d_s ) |
| 134 |
CALL EXCH_XY_R8( cg2d_s ) |
| 135 |
CALL EXCH_XY_R8( cg2d_s ) |
| 136 |
CALL EXCH_XY_R8( cg2d_s ) |
| 137 |
CALL EXCH_XY_R8( cg2d_s ) |
| 138 |
CALL EXCH_XY_R8( cg2d_s ) |
| 139 |
#endif |
| 140 |
|
| 141 |
C== Evaluate laplace operator on conjugate gradient vector |
| 142 |
C== q = A.s |
| 143 |
alpha = 0. _d 0 |
| 144 |
DO J=1,sNy |
| 145 |
DO I=1,sNx |
| 146 |
cg2d_q(I,J) = |
| 147 |
& aW2d(I ,J )*cg2d_s(I-1,J )+aW2d(I+1,J )*cg2d_s(I+1,J ) |
| 148 |
& +aS2d(I ,J )*cg2d_s(I ,J-1)+aS2d(I ,J+1)*cg2d_s(I ,J+1) |
| 149 |
& -aW2d(I ,J )*cg2d_s(I ,J )-aW2d(I+1,J )*cg2d_s(I ,J ) |
| 150 |
& -aS2d(I ,J )*cg2d_s(I ,J )-aS2d(I ,J+1)*cg2d_s(I ,J ) |
| 151 |
alpha = alpha+cg2d_s(I,J)*cg2d_q(I,J) |
| 152 |
ENDDO |
| 153 |
ENDDO |
| 154 |
CALL GSUM_R8( temp, alpha ) |
| 155 |
|
| 156 |
#ifdef HUNDRED_EXTRA_SUMS |
| 157 |
C-- Hundred extra global sums |
| 158 |
CALL GSUM_R8( temp, alpha ) |
| 159 |
CALL GSUM_R8( temp, alpha ) |
| 160 |
CALL GSUM_R8( temp, alpha ) |
| 161 |
CALL GSUM_R8( temp, alpha ) |
| 162 |
CALL GSUM_R8( temp, alpha ) |
| 163 |
CALL GSUM_R8( temp, alpha ) |
| 164 |
CALL GSUM_R8( temp, alpha ) |
| 165 |
CALL GSUM_R8( temp, alpha ) |
| 166 |
CALL GSUM_R8( temp, alpha ) |
| 167 |
CALL GSUM_R8( temp, alpha ) |
| 168 |
CALL GSUM_R8( temp, alpha ) |
| 169 |
CALL GSUM_R8( temp, alpha ) |
| 170 |
CALL GSUM_R8( temp, alpha ) |
| 171 |
CALL GSUM_R8( temp, alpha ) |
| 172 |
CALL GSUM_R8( temp, alpha ) |
| 173 |
CALL GSUM_R8( temp, alpha ) |
| 174 |
CALL GSUM_R8( temp, alpha ) |
| 175 |
CALL GSUM_R8( temp, alpha ) |
| 176 |
CALL GSUM_R8( temp, alpha ) |
| 177 |
CALL GSUM_R8( temp, alpha ) |
| 178 |
CALL GSUM_R8( temp, alpha ) |
| 179 |
CALL GSUM_R8( temp, alpha ) |
| 180 |
CALL GSUM_R8( temp, alpha ) |
| 181 |
CALL GSUM_R8( temp, alpha ) |
| 182 |
CALL GSUM_R8( temp, alpha ) |
| 183 |
CALL GSUM_R8( temp, alpha ) |
| 184 |
CALL GSUM_R8( temp, alpha ) |
| 185 |
CALL GSUM_R8( temp, alpha ) |
| 186 |
CALL GSUM_R8( temp, alpha ) |
| 187 |
CALL GSUM_R8( temp, alpha ) |
| 188 |
CALL GSUM_R8( temp, alpha ) |
| 189 |
CALL GSUM_R8( temp, alpha ) |
| 190 |
CALL GSUM_R8( temp, alpha ) |
| 191 |
CALL GSUM_R8( temp, alpha ) |
| 192 |
CALL GSUM_R8( temp, alpha ) |
| 193 |
CALL GSUM_R8( temp, alpha ) |
| 194 |
CALL GSUM_R8( temp, alpha ) |
| 195 |
CALL GSUM_R8( temp, alpha ) |
| 196 |
CALL GSUM_R8( temp, alpha ) |
| 197 |
CALL GSUM_R8( temp, alpha ) |
| 198 |
CALL GSUM_R8( temp, alpha ) |
| 199 |
CALL GSUM_R8( temp, alpha ) |
| 200 |
CALL GSUM_R8( temp, alpha ) |
| 201 |
CALL GSUM_R8( temp, alpha ) |
| 202 |
CALL GSUM_R8( temp, alpha ) |
| 203 |
CALL GSUM_R8( temp, alpha ) |
| 204 |
CALL GSUM_R8( temp, alpha ) |
| 205 |
CALL GSUM_R8( temp, alpha ) |
| 206 |
CALL GSUM_R8( temp, alpha ) |
| 207 |
CALL GSUM_R8( temp, alpha ) |
| 208 |
CALL GSUM_R8( temp, alpha ) |
| 209 |
CALL GSUM_R8( temp, alpha ) |
| 210 |
CALL GSUM_R8( temp, alpha ) |
| 211 |
CALL GSUM_R8( temp, alpha ) |
| 212 |
CALL GSUM_R8( temp, alpha ) |
| 213 |
CALL GSUM_R8( temp, alpha ) |
| 214 |
CALL GSUM_R8( temp, alpha ) |
| 215 |
CALL GSUM_R8( temp, alpha ) |
| 216 |
CALL GSUM_R8( temp, alpha ) |
| 217 |
CALL GSUM_R8( temp, alpha ) |
| 218 |
CALL GSUM_R8( temp, alpha ) |
| 219 |
CALL GSUM_R8( temp, alpha ) |
| 220 |
CALL GSUM_R8( temp, alpha ) |
| 221 |
CALL GSUM_R8( temp, alpha ) |
| 222 |
CALL GSUM_R8( temp, alpha ) |
| 223 |
CALL GSUM_R8( temp, alpha ) |
| 224 |
CALL GSUM_R8( temp, alpha ) |
| 225 |
CALL GSUM_R8( temp, alpha ) |
| 226 |
CALL GSUM_R8( temp, alpha ) |
| 227 |
CALL GSUM_R8( temp, alpha ) |
| 228 |
CALL GSUM_R8( temp, alpha ) |
| 229 |
CALL GSUM_R8( temp, alpha ) |
| 230 |
CALL GSUM_R8( temp, alpha ) |
| 231 |
CALL GSUM_R8( temp, alpha ) |
| 232 |
CALL GSUM_R8( temp, alpha ) |
| 233 |
CALL GSUM_R8( temp, alpha ) |
| 234 |
CALL GSUM_R8( temp, alpha ) |
| 235 |
CALL GSUM_R8( temp, alpha ) |
| 236 |
CALL GSUM_R8( temp, alpha ) |
| 237 |
CALL GSUM_R8( temp, alpha ) |
| 238 |
CALL GSUM_R8( temp, alpha ) |
| 239 |
CALL GSUM_R8( temp, alpha ) |
| 240 |
CALL GSUM_R8( temp, alpha ) |
| 241 |
CALL GSUM_R8( temp, alpha ) |
| 242 |
CALL GSUM_R8( temp, alpha ) |
| 243 |
CALL GSUM_R8( temp, alpha ) |
| 244 |
CALL GSUM_R8( temp, alpha ) |
| 245 |
CALL GSUM_R8( temp, alpha ) |
| 246 |
CALL GSUM_R8( temp, alpha ) |
| 247 |
CALL GSUM_R8( temp, alpha ) |
| 248 |
CALL GSUM_R8( temp, alpha ) |
| 249 |
CALL GSUM_R8( temp, alpha ) |
| 250 |
CALL GSUM_R8( temp, alpha ) |
| 251 |
CALL GSUM_R8( temp, alpha ) |
| 252 |
CALL GSUM_R8( temp, alpha ) |
| 253 |
CALL GSUM_R8( temp, alpha ) |
| 254 |
CALL GSUM_R8( temp, alpha ) |
| 255 |
CALL GSUM_R8( temp, alpha ) |
| 256 |
CALL GSUM_R8( temp, alpha ) |
| 257 |
CALL GSUM_R8( temp, alpha ) |
| 258 |
#endif |
| 259 |
|
| 260 |
alpha = temp |
| 261 |
alpha = etaN/alpha |
| 262 |
|
| 263 |
C== Update solution and residual vectors |
| 264 |
C Now compute "interior" points. |
| 265 |
err = 0. _d 0 |
| 266 |
DO J=1,sNy |
| 267 |
DO I=1,sNx |
| 268 |
cg2d_x(I,J)=cg2d_x(I,J)+alpha*cg2d_s(I,J) |
| 269 |
cg2d_r(I,J)=cg2d_r(I,J)-alpha*cg2d_q(I,J) |
| 270 |
err = err+cg2d_r(I,J)*cg2d_r(I,J) |
| 271 |
ENDDO |
| 272 |
ENDDO |
| 273 |
|
| 274 |
CALL GSUM_R8( temp, err ) |
| 275 |
|
| 276 |
err = temp |
| 277 |
err = SQRT(err) |
| 278 |
actualIts = N |
| 279 |
actualResidual = err |
| 280 |
CcnhDebugStarts |
| 281 |
C WRITE(6,*) ' CG2D iters, err = ', actualIts, actualResidual |
| 282 |
CcnhDebugEnds |
| 283 |
IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
| 284 |
CALL EXCH_XY_R8(cg2d_r ) |
| 285 |
10 CONTINUE |
| 286 |
11 CONTINUE |
| 287 |
CALL EXCH_XY_R8(cg2d_x ) |
| 288 |
WRITE(6,*) ' CG2D iters, err = ', actualIts, actualResidual |
| 289 |
|
| 290 |
C Calc Ax to check result |
| 291 |
DO J=1,sNy |
| 292 |
DO I=1,sNx |
| 293 |
cg2d_Ax(I,J) = |
| 294 |
& ( aW2d(I ,J )*cg2d_x(I-1,J )+aW2d(I+1,J )*cg2d_x(I+1,J ) |
| 295 |
& +aS2d(I ,J )*cg2d_x(I ,J-1)+aS2d(I ,J+1)*cg2d_x(I ,J+1) |
| 296 |
& -aW2d(I ,J )*cg2d_x(I ,J )-aW2d(I+1,J )*cg2d_x(I ,J ) |
| 297 |
& -aS2d(I ,J )*cg2d_x(I ,J )-aS2d(I ,J+1)*cg2d_x(I ,J ) |
| 298 |
& ) |
| 299 |
cg2d_r(I,J) = cg2d_b(I,J)-cg2d_Ax(I,J) |
| 300 |
ENDDO |
| 301 |
ENDDO |
| 302 |
CALL EXCH_XY_R8(cg2d_Ax ) |
| 303 |
CALL EXCH_XY_R8(cg2d_r ) |
| 304 |
|
| 305 |
END |
Parent Directory
| 
Revision Log
| 
Revision Graph