| 1 |
C $Header: /u/gcmpack/models/MITgcmUV/model/src/cg2d.F,v 1.17 1998/11/30 23:45:24 adcroft Exp $ |
| 2 |
|
| 3 |
#include "CPP_OPTIONS.h" |
| 4 |
|
| 5 |
SUBROUTINE CG2D( |
| 6 |
I cg2d_b, |
| 7 |
U cg2d_x, |
| 8 |
I myThid ) |
| 9 |
C /==========================================================\ |
| 10 |
C | SUBROUTINE CG2D | |
| 11 |
C | o Two-dimensional grid problem conjugate-gradient | |
| 12 |
C | inverter (with preconditioner). | |
| 13 |
C |==========================================================| |
| 14 |
C | Con. grad is an iterative procedure for solving Ax = b. | |
| 15 |
C | It requires the A be symmetric. | |
| 16 |
C | This implementation assumes A is a five-diagonal | |
| 17 |
C | matrix of the form that arises in the discrete | |
| 18 |
C | representation of the del^2 operator in a | |
| 19 |
C | two-dimensional space. | |
| 20 |
C | Notes: | |
| 21 |
C | ====== | |
| 22 |
C | This implementation can support shared-memory | |
| 23 |
C | multi-threaded execution. In order to do this COMMON | |
| 24 |
C | blocks are used for many of the arrays - even ones that | |
| 25 |
C | are only used for intermedaite results. This design is | |
| 26 |
C | OK if you want to all the threads to collaborate on | |
| 27 |
C | solving the same problem. On the other hand if you want | |
| 28 |
C | the threads to solve several different problems | |
| 29 |
C | concurrently this implementation will not work. | |
| 30 |
C \==========================================================/ |
| 31 |
IMPLICIT NONE |
| 32 |
|
| 33 |
C === Global data === |
| 34 |
#include "SIZE.h" |
| 35 |
#include "EEPARAMS.h" |
| 36 |
#include "PARAMS.h" |
| 37 |
#include "GRID.h" |
| 38 |
#include "CG2D_INTERNAL.h" |
| 39 |
|
| 40 |
C === Routine arguments === |
| 41 |
C myThid - Thread on which I am working. |
| 42 |
INTEGER myThid |
| 43 |
_RL cg2d_x(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
| 44 |
_RL cg2d_b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
| 45 |
|
| 46 |
|
| 47 |
C === Local variables ==== |
| 48 |
C actualIts - Number of iterations taken |
| 49 |
C actualResidual - residual |
| 50 |
C bi - Block index in X and Y. |
| 51 |
C bj |
| 52 |
C etaN - Used in computing search directions |
| 53 |
C etaNM1 suffix N and NM1 denote current and |
| 54 |
C cgBeta previous iterations respectively. |
| 55 |
C alpha |
| 56 |
C sumRHS - Sum of right-hand-side. Sometimes this is a |
| 57 |
C useful debuggin/trouble shooting diagnostic. |
| 58 |
C For neumann problems sumRHS needs to be ~0. |
| 59 |
C or they converge at a non-zero residual. |
| 60 |
C err - Measure of residual of Ax - b, usually the norm. |
| 61 |
C I, J, N - Loop counters ( N counts CG iterations ) |
| 62 |
INTEGER actualIts |
| 63 |
_RL actualResidual |
| 64 |
INTEGER bi, bj |
| 65 |
INTEGER I, J, it2d |
| 66 |
_RL err |
| 67 |
_RL etaN |
| 68 |
_RL etaNM1 |
| 69 |
_RL cgBeta |
| 70 |
_RL alpha |
| 71 |
_RL sumRHS |
| 72 |
_RL rhsMax |
| 73 |
_RL rhsNorm |
| 74 |
|
| 75 |
INTEGER OLw |
| 76 |
INTEGER OLe |
| 77 |
INTEGER OLn |
| 78 |
INTEGER OLs |
| 79 |
INTEGER exchWidthX |
| 80 |
INTEGER exchWidthY |
| 81 |
INTEGER myNz |
| 82 |
|
| 83 |
|
| 84 |
CcnhDebugStarts |
| 85 |
CHARACTER*(MAX_LEN_FNAM) suff |
| 86 |
CcnhDebugEnds |
| 87 |
|
| 88 |
|
| 89 |
C-- Initialise inverter |
| 90 |
etaNBuf(1,myThid) = 0. _d 0 |
| 91 |
errBuf(1,myThid) = 0. _d 0 |
| 92 |
sumRHSBuf(1,myThid) = 0. _d 0 |
| 93 |
etaNM1 = 1. _d 0 |
| 94 |
|
| 95 |
CcnhDebugStarts |
| 96 |
C _EXCH_XY_R8( cg2d_b, myThid ) |
| 97 |
C CALL PLOT_FIELD_XYRL( cg2d_b, 'CG2D.0 CG2D_B' , 1, myThid ) |
| 98 |
C suff = 'unnormalised' |
| 99 |
C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
| 100 |
C STOP |
| 101 |
CcnhDebugEnds |
| 102 |
|
| 103 |
C-- Normalise RHS |
| 104 |
rhsMax = 0. _d 0 |
| 105 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 106 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 107 |
DO J=1,sNy |
| 108 |
DO I=1,sNx |
| 109 |
cg2d_b(I,J,bi,bj) = cg2d_b(I,J,bi,bj)*cg2dNorm |
| 110 |
rhsMax = MAX(ABS(cg2d_b(I,J,bi,bj)),rhsMax) |
| 111 |
ENDDO |
| 112 |
ENDDO |
| 113 |
ENDDO |
| 114 |
ENDDO |
| 115 |
rhsMaxBuf(1,myThid) = rhsMax |
| 116 |
_GLOBAL_MAX_R8( rhsMaxbuf, rhsMax, myThid ) |
| 117 |
rhsMax = rhsMaxBuf(1,1) |
| 118 |
rhsNorm = 1. _d 0 |
| 119 |
IF ( rhsMax .NE. 0. ) rhsNorm = 1. _d 0 / rhsMax |
| 120 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 121 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 122 |
DO J=1,sNy |
| 123 |
DO I=1,sNx |
| 124 |
cg2d_b(I,J,bi,bj) = cg2d_b(I,J,bi,bj)*rhsNorm |
| 125 |
cg2d_x(I,J,bi,bj) = cg2d_x(I,J,bi,bj)*rhsNorm |
| 126 |
ENDDO |
| 127 |
ENDDO |
| 128 |
ENDDO |
| 129 |
ENDDO |
| 130 |
|
| 131 |
C-- Update overlaps |
| 132 |
_EXCH_XY_R8( cg2d_b, myThid ) |
| 133 |
_EXCH_XY_R8( cg2d_x, myThid ) |
| 134 |
CcnhDebugStarts |
| 135 |
C CALL PLOT_FIELD_XYRL( cg2d_b, 'CG2D.1 CG2D_B' , 1, myThid ) |
| 136 |
C suff = 'normalised' |
| 137 |
C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
| 138 |
CcnhDebugEnds |
| 139 |
|
| 140 |
C-- Initial residual calculation |
| 141 |
err = 0. _d 0 |
| 142 |
sumRHS = 0. _d 0 |
| 143 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 144 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 145 |
DO J=1,sNy |
| 146 |
DO I=1,sNx |
| 147 |
cg2d_s(I,J,bi,bj) = 0. |
| 148 |
cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
| 149 |
& (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
| 150 |
& +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
| 151 |
& +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
| 152 |
& +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
| 153 |
& -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 154 |
& -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 155 |
& -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 156 |
& -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 157 |
& -freeSurfFac*_rA(i,j,bi,bj)* horiVertRatio* |
| 158 |
& cg2d_x(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
| 159 |
& ) |
| 160 |
err = err + |
| 161 |
& cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 162 |
sumRHS = sumRHS + |
| 163 |
& cg2d_b(I,J,bi,bj) |
| 164 |
ENDDO |
| 165 |
ENDDO |
| 166 |
ENDDO |
| 167 |
ENDDO |
| 168 |
C _EXCH_XY_R8( cg2d_r, myThid ) |
| 169 |
OLw = 1 |
| 170 |
OLe = 1 |
| 171 |
OLn = 1 |
| 172 |
OLs = 1 |
| 173 |
exchWidthX = 1 |
| 174 |
exchWidthY = 1 |
| 175 |
myNz = 1 |
| 176 |
CALL EXCH_RL( cg2d_r, |
| 177 |
I OLw, OLe, OLs, OLn, myNz, |
| 178 |
I exchWidthX, exchWidthY, |
| 179 |
I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
| 180 |
C _EXCH_XY_R8( cg2d_s, myThid ) |
| 181 |
OLw = 1 |
| 182 |
OLe = 1 |
| 183 |
OLn = 1 |
| 184 |
OLs = 1 |
| 185 |
exchWidthX = 1 |
| 186 |
exchWidthY = 1 |
| 187 |
myNz = 1 |
| 188 |
CALL EXCH_RL( cg2d_s, |
| 189 |
I OLw, OLe, OLs, OLn, myNz, |
| 190 |
I exchWidthX, exchWidthY, |
| 191 |
I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
| 192 |
sumRHSBuf(1,myThid) = sumRHS |
| 193 |
_GLOBAL_SUM_R8( sumRHSBuf , sumRHS, myThid ) |
| 194 |
sumRHS = sumRHSBuf(1,1) |
| 195 |
errBuf(1,myThid) = err |
| 196 |
C WRITE(6,*) ' mythid, err = ', mythid, SQRT(err) |
| 197 |
_GLOBAL_SUM_R8( errBuf , err , myThid ) |
| 198 |
err = errBuf(1,1) |
| 199 |
|
| 200 |
_BEGIN_MASTER( myThid ) |
| 201 |
write(0,'(A,1PE30.14)') 'cg2d: Sum(rhs) = ',sumRHS |
| 202 |
_END_MASTER( ) |
| 203 |
|
| 204 |
actualIts = 0 |
| 205 |
actualResidual = SQRT(err) |
| 206 |
C _BARRIER |
| 207 |
_BEGIN_MASTER( myThid ) |
| 208 |
WRITE(0,'(A,I6,1PE30.14)') ' CG2D iters, err = ', |
| 209 |
& actualIts, actualResidual |
| 210 |
_END_MASTER( ) |
| 211 |
|
| 212 |
C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
| 213 |
DO 10 it2d=1, cg2dMaxIters |
| 214 |
|
| 215 |
CcnhDebugStarts |
| 216 |
C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' residual = ', |
| 217 |
C & actualResidual |
| 218 |
CcnhDebugEnds |
| 219 |
IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
| 220 |
C-- Solve preconditioning equation and update |
| 221 |
C-- conjugate direction vector "s". |
| 222 |
etaN = 0. _d 0 |
| 223 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 224 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 225 |
DO J=1,sNy |
| 226 |
DO I=1,sNx |
| 227 |
cg2d_q(I,J,bi,bj) = |
| 228 |
& pC(I ,J ,bi,bj)*cg2d_r(I ,J ,bi,bj) |
| 229 |
& +pW(I ,J ,bi,bj)*cg2d_r(I-1,J ,bi,bj) |
| 230 |
& +pW(I+1,J ,bi,bj)*cg2d_r(I+1,J ,bi,bj) |
| 231 |
& +pS(I ,J ,bi,bj)*cg2d_r(I ,J-1,bi,bj) |
| 232 |
& +pS(I ,J+1,bi,bj)*cg2d_r(I ,J+1,bi,bj) |
| 233 |
CcnhDebugStarts |
| 234 |
C cg2d_q(I,J,bi,bj) = cg2d_r(I ,J ,bi,bj) |
| 235 |
CcnhDebugEnds |
| 236 |
etaN = etaN |
| 237 |
& +cg2d_q(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 238 |
ENDDO |
| 239 |
ENDDO |
| 240 |
ENDDO |
| 241 |
ENDDO |
| 242 |
|
| 243 |
etanBuf(1,myThid) = etaN |
| 244 |
_GLOBAL_SUM_R8(etaNbuf,etaN, myThid) |
| 245 |
etaN = etaNBuf(1,1) |
| 246 |
CcnhDebugStarts |
| 247 |
C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' etaN = ',etaN |
| 248 |
CcnhDebugEnds |
| 249 |
cgBeta = etaN/etaNM1 |
| 250 |
CcnhDebugStarts |
| 251 |
C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' beta = ',cgBeta |
| 252 |
CcnhDebugEnds |
| 253 |
etaNM1 = etaN |
| 254 |
|
| 255 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 256 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 257 |
DO J=1,sNy |
| 258 |
DO I=1,sNx |
| 259 |
cg2d_s(I,J,bi,bj) = cg2d_q(I,J,bi,bj) |
| 260 |
& + cgBeta*cg2d_s(I,J,bi,bj) |
| 261 |
ENDDO |
| 262 |
ENDDO |
| 263 |
ENDDO |
| 264 |
ENDDO |
| 265 |
|
| 266 |
C-- Do exchanges that require messages i.e. between |
| 267 |
C-- processes. |
| 268 |
C _EXCH_XY_R8( cg2d_s, myThid ) |
| 269 |
OLw = 1 |
| 270 |
OLe = 1 |
| 271 |
OLn = 1 |
| 272 |
OLs = 1 |
| 273 |
exchWidthX = 1 |
| 274 |
exchWidthY = 1 |
| 275 |
myNz = 1 |
| 276 |
CALL EXCH_RL( cg2d_s, |
| 277 |
I OLw, OLe, OLs, OLn, myNz, |
| 278 |
I exchWidthX, exchWidthY, |
| 279 |
I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
| 280 |
|
| 281 |
|
| 282 |
C== Evaluate laplace operator on conjugate gradient vector |
| 283 |
C== q = A.s |
| 284 |
alpha = 0. _d 0 |
| 285 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 286 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 287 |
DO J=1,sNy |
| 288 |
DO I=1,sNx |
| 289 |
cg2d_q(I,J,bi,bj) = |
| 290 |
& aW2d(I ,J ,bi,bj)*cg2d_s(I-1,J ,bi,bj) |
| 291 |
& +aW2d(I+1,J ,bi,bj)*cg2d_s(I+1,J ,bi,bj) |
| 292 |
& +aS2d(I ,J ,bi,bj)*cg2d_s(I ,J-1,bi,bj) |
| 293 |
& +aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J+1,bi,bj) |
| 294 |
& -aW2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 295 |
& -aW2d(I+1,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 296 |
& -aS2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 297 |
& -aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 298 |
& -freeSurfFac*_rA(i,j,bi,bj)* horiVertRatio* |
| 299 |
& cg2d_s(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
| 300 |
alpha = alpha+cg2d_s(I,J,bi,bj)*cg2d_q(I,J,bi,bj) |
| 301 |
ENDDO |
| 302 |
ENDDO |
| 303 |
ENDDO |
| 304 |
ENDDO |
| 305 |
alphaBuf(1,myThid) = alpha |
| 306 |
_GLOBAL_SUM_R8(alphaBuf,alpha,myThid) |
| 307 |
alpha = alphaBuf(1,1) |
| 308 |
CcnhDebugStarts |
| 309 |
C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' SUM(s*q)= ',alpha |
| 310 |
CcnhDebugEnds |
| 311 |
alpha = etaN/alpha |
| 312 |
CcnhDebugStarts |
| 313 |
C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' alpha= ',alpha |
| 314 |
CcnhDebugEnds |
| 315 |
|
| 316 |
C== Update solution and residual vectors |
| 317 |
C Now compute "interior" points. |
| 318 |
err = 0. _d 0 |
| 319 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 320 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 321 |
DO J=1,sNy |
| 322 |
DO I=1,sNx |
| 323 |
cg2d_x(I,J,bi,bj)=cg2d_x(I,J,bi,bj)+alpha*cg2d_s(I,J,bi,bj) |
| 324 |
cg2d_r(I,J,bi,bj)=cg2d_r(I,J,bi,bj)-alpha*cg2d_q(I,J,bi,bj) |
| 325 |
err = err+cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 326 |
ENDDO |
| 327 |
ENDDO |
| 328 |
ENDDO |
| 329 |
ENDDO |
| 330 |
|
| 331 |
errBuf(1,myThid) = err |
| 332 |
_GLOBAL_SUM_R8( errBuf , err , myThid ) |
| 333 |
err = errBuf(1,1) |
| 334 |
err = SQRT(err) |
| 335 |
actualIts = it2d |
| 336 |
actualResidual = err |
| 337 |
IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
| 338 |
C _EXCH_XY_R8(cg2d_r, myThid ) |
| 339 |
OLw = 1 |
| 340 |
OLe = 1 |
| 341 |
OLn = 1 |
| 342 |
OLs = 1 |
| 343 |
exchWidthX = 1 |
| 344 |
exchWidthY = 1 |
| 345 |
myNz = 1 |
| 346 |
CALL EXCH_RL( cg2d_r, |
| 347 |
I OLw, OLe, OLs, OLn, myNz, |
| 348 |
I exchWidthX, exchWidthY, |
| 349 |
I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
| 350 |
|
| 351 |
10 CONTINUE |
| 352 |
11 CONTINUE |
| 353 |
|
| 354 |
C-- Un-normalise the answer |
| 355 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 356 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 357 |
DO J=1,sNy |
| 358 |
DO I=1,sNx |
| 359 |
cg2d_x(I ,J ,bi,bj) = cg2d_x(I ,J ,bi,bj)/rhsNorm |
| 360 |
ENDDO |
| 361 |
ENDDO |
| 362 |
ENDDO |
| 363 |
ENDDO |
| 364 |
|
| 365 |
_EXCH_XY_R8(cg2d_x, myThid ) |
| 366 |
_BEGIN_MASTER( myThid ) |
| 367 |
WRITE(0,'(A,I6,1PE30.14)') ' CG2D iters, err = ', |
| 368 |
& actualIts, actualResidual |
| 369 |
_END_MASTER( ) |
| 370 |
|
| 371 |
CcnhDebugStarts |
| 372 |
C CALL PLOT_FIELD_XYRL( cg2d_x, 'CALC_MOM_RHS CG2D_X' , 1, myThid ) |
| 373 |
C err = 0. _d 0 |
| 374 |
C DO bj=myByLo(myThid),myByHi(myThid) |
| 375 |
C DO bi=myBxLo(myThid),myBxHi(myThid) |
| 376 |
C DO J=1,sNy |
| 377 |
C DO I=1,sNx |
| 378 |
C cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
| 379 |
C & (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
| 380 |
C & +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
| 381 |
C & +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
| 382 |
C & +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
| 383 |
C & -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 384 |
C & -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 385 |
C & -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 386 |
C & -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj)) |
| 387 |
C err = err + |
| 388 |
C & cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 389 |
C ENDDO |
| 390 |
C ENDDO |
| 391 |
C ENDDO |
| 392 |
C ENDDO |
| 393 |
C errBuf(1,myThid) = err |
| 394 |
C _GLOBAL_SUM_R8( errBuf , err , myThid ) |
| 395 |
C err = errBuf(1,1) |
| 396 |
C write(0,*) 'cg2d: Ax - b = ',SQRT(err) |
| 397 |
CcnhDebugEnds |
| 398 |
|
| 399 |
|
| 400 |
END |
Parent Directory
| 
Revision Log
| 
Revision Graph