/[MITgcm]/MITgcm/pkg/seaice/seaice_jfnk.F
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revision 1.10 by mlosch, Mon Nov 26 08:04:50 2012 UTC revision 1.19 by mlosch, Mon Feb 25 10:44:10 2013 UTC
# Line 3  C $Name$ Line 3  C $Name$
3    
4  #include "SEAICE_OPTIONS.h"  #include "SEAICE_OPTIONS.h"
5    
6    C--  File seaice_jfnk.F: seaice jfnk dynamical solver S/R:
7    C--   Contents
8    C--   o SEAICE_JFNK
9    C--   o SEAICE_JFNK_UPDATE
10    
11  CBOP  CBOP
12  C     !ROUTINE: SEAICE_JFNK  C     !ROUTINE: SEAICE_JFNK
13  C     !INTERFACE:  C     !INTERFACE:
# Line 10  C     !INTERFACE: Line 15  C     !INTERFACE:
15    
16  C     !DESCRIPTION: \bv  C     !DESCRIPTION: \bv
17  C     *==========================================================*  C     *==========================================================*
18  C     | SUBROUTINE SEAICE_JFKF  C     | SUBROUTINE SEAICE_JFNK
19  C     | o Ice dynamics using a Jacobian-free Newton-Krylov solver  C     | o Ice dynamics using a Jacobian-free Newton-Krylov solver
20  C     |   following J.-F. Lemieux et al. Improving the numerical  C     |   following J.-F. Lemieux et al. Improving the numerical
21  C     |   convergence of viscous-plastic sea ice models with the  C     |   convergence of viscous-plastic sea ice models with the
# Line 55  C     !FUNCTIONS: Line 60  C     !FUNCTIONS:
60        LOGICAL  DIFFERENT_MULTIPLE        LOGICAL  DIFFERENT_MULTIPLE
61        EXTERNAL DIFFERENT_MULTIPLE        EXTERNAL DIFFERENT_MULTIPLE
62    
63    C     !LOCAL VARIABLES:
64    C     === Local variables ===
65  C     i,j,bi,bj :: loop indices  C     i,j,bi,bj :: loop indices
66        INTEGER i,j,bi,bj        INTEGER i,j,bi,bj
67  C     loop indices  C     loop indices
68        INTEGER newtonIter        INTEGER newtonIter
69        INTEGER krylovIter, krylovFails        INTEGER krylovIter, krylovFails
70        INTEGER totalKrylovItersLoc        INTEGER totalKrylovItersLoc, totalNewtonItersLoc
71  C     FGMRES flag that determines amount of output messages of fgmres  C     FGMRES flag that determines amount of output messages of fgmres
72        INTEGER iOutFGMRES        INTEGER iOutFGMRES
73  C     FGMRES flag that indicates what fgmres wants us to do next  C     FGMRES flag that indicates what fgmres wants us to do next
74        INTEGER iCode        INTEGER iCode
75        _RL     JFNKresidual, JFNKresidualTile(nSx,nSy)        _RL     JFNKresidual
76        _RL     JFNKresidualKm1        _RL     JFNKresidualKm1
77  C     parameters to compute convergence criterion  C     parameters to compute convergence criterion
78        _RL     phi_e, alp_e, JFNKgamma_lin        _RL     phi_e, alp_e, JFNKgamma_lin
# Line 80  C Line 87  C
87  C     u/vIceRes :: residual of sea-ice momentum equations  C     u/vIceRes :: residual of sea-ice momentum equations
88        _RL uIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)        _RL uIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
89        _RL vIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)        _RL vIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
90    C     vector version of the residuals
91          _RL resTmp (nVec,1,nSx,nSy)
92  C     du/vIce   :: ice velocity increment to be added to u/vIce  C     du/vIce   :: ice velocity increment to be added to u/vIce
93        _RL duIce  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)        _RL duIce  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
94        _RL dvIce  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)        _RL dvIce  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
# Line 103  C     Initialise Line 112  C     Initialise
112        recip_deltaT        = 1. _d 0 / SEAICE_deltaTdyn        recip_deltaT        = 1. _d 0 / SEAICE_deltaTdyn
113    
114        iOutFGMRES=0        iOutFGMRES=0
115  C     iOutFgmres=1 gives a little bit of output  C     with iOutFgmres=1, seaice_fgmres prints the residual at each iteration
116        IF ( debugLevel.GE.debLevA .AND.        IF ( debugLevel.GE.debLevC .AND.
117       &     DIFFERENT_MULTIPLE( SEAICE_monFreq, myTime, deltaTClock ) )       &     DIFFERENT_MULTIPLE( SEAICE_monFreq, myTime, deltaTClock ) )
118       &     iOutFGMRES=1       &     iOutFGMRES=1
119    
# Line 140  C     Start nonlinear Newton iteration: Line 149  C     Start nonlinear Newton iteration:
149         newtonIter = newtonIter + 1         newtonIter = newtonIter + 1
150  C     Compute initial residual F(u), (includes computation of global  C     Compute initial residual F(u), (includes computation of global
151  C     variables DWATN, zeta, and eta)  C     variables DWATN, zeta, and eta)
152         CALL SEAICE_CALC_RESIDUAL(         IF ( newtonIter .EQ. 1 ) CALL SEAICE_JFNK_UPDATE(
153       I      uIce, vIce,       I      duIce, dvIce,
154       O      uIceRes, vIceRes,       U      uIce, vIce, JFNKresidual,
155       I      newtonIter, 0, myTime, myIter, myThid )       O      uIceRes, vIceRes,
156         CALL EXCH_UV_XY_RL( uIceRes, vIceRes,.TRUE.,myThid)       I      newtonIter, myTime, myIter, myThid )
157  C     local copies of precomputed coefficients that are to stay  C     local copies of precomputed coefficients that are to stay
158  C     constant for the preconditioner  C     constant for the preconditioner
159         DO bj=myByLo(myThid),myByHi(myThid)         DO bj=myByLo(myThid),myByHi(myThid)
# Line 159  C     constant for the preconditioner Line 168  C     constant for the preconditioner
168           ENDDO           ENDDO
169          ENDDO          ENDDO
170         ENDDO         ENDDO
 C      
        DO bj=myByLo(myThid),myByHi(myThid)  
         DO bi=myBxLo(myThid),myBxHi(myThid)  
          JFNKresidualTile(bi,bj) = 0. _d 0  
          DO J=1,sNy  
           DO I=1,sNx  
 #ifdef CG2D_SINGLECPU_SUM  
            JFNKlocalBuf(I,J,bi,bj) =  
 #else  
            JFNKresidualTile(bi,bj) = JFNKresidualTile(bi,bj) +  
 #endif  
      &          uIceRes(I,J,bi,bj)*uIceRes(I,J,bi,bj) +  
      &          vIceRes(I,J,bi,bj)*vIceRes(I,J,bi,bj)  
           ENDDO  
          ENDDO  
         ENDDO  
        ENDDO  
        JFNKresidual = 0. _d 0  
 #ifdef CG2D_SINGLECPU_SUM  
        CALL GLOBAL_SUM_SINGLECPU_RL(  
      &         JFNKlocalBuf,JFNKresidual, 0, 0, myThid)  
 #else  
        CALL GLOBAL_SUM_TILE_RL( JFNKresidualTile,JFNKresidual,myThid )  
 #endif  
        JFNKresidual = SQRT(JFNKresidual)  
171  C     compute convergence criterion for linear preconditioned FGMRES  C     compute convergence criterion for linear preconditioned FGMRES
172         JFNKgamma_lin = JFNKgamma_lin_max         JFNKgamma_lin = JFNKgamma_lin_max
173         IF ( newtonIter.GT.1.AND.newtonIter.LE.100         IF ( newtonIter.GT.1.AND.newtonIter.LE.SEAICE_JFNK_tolIter
174       &      .AND.JFNKresidual.LT.JFNKres_t ) THEN       &      .AND.JFNKresidual.LT.JFNKres_t ) THEN
175  C     Eisenstat, 1996, equ.(2.6)        C     Eisenstat, 1996, equ.(2.6)      
176          phi_e = 1. _d 0          phi_e = 1. _d 0
# Line 205  C     krylovIter is mapped into "its" in Line 189  C     krylovIter is mapped into "its" in
189  C     in that routine  C     in that routine
190         krylovIter    = 0         krylovIter    = 0
191         iCode         = 0         iCode         = 0
        IF ( debugLevel.GE.debLevA ) THEN    
         _BEGIN_MASTER( myThid )  
         WRITE(msgBuf,'(2A,2(1XI6),2E12.5)')  
      &       ' S/R SEAICE_JFNK: newtonIter,',  
      &       ' total newtonIter, JFNKgamma_lin, initial norm = ',  
      &       newtonIter,SEAICEnewtonIterMax*(myIter-nIter0)+newtonIter,  
      &       JFNKgamma_lin, JFNKresidual  
         CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,  
      &       SQUEEZE_RIGHT, myThid )  
         _END_MASTER( myThid )  
        ENDIF  
192  C  C
193         JFNKconverged = JFNKresidual.LT.JFNKtol         JFNKconverged = JFNKresidual.LT.JFNKtol
194  C  C
# Line 261  C     End of Krylov iterate Line 234  C     End of Krylov iterate
234  C     some output diagnostics  C     some output diagnostics
235          IF ( debugLevel.GE.debLevA ) THEN          IF ( debugLevel.GE.debLevA ) THEN
236           _BEGIN_MASTER( myThid )           _BEGIN_MASTER( myThid )
237             totalNewtonItersLoc =
238         &        SEAICEnewtonIterMax*(myIter-nIter0)+newtonIter
239             WRITE(msgBuf,'(2A,2(1XI6),2E12.5)')
240         &        ' S/R SEAICE_JFNK: Newton iterate / total, ',
241         &        'JFNKgamma_lin, initial norm = ',
242         &        newtonIter, totalNewtonItersLoc,
243         &        JFNKgamma_lin,JFNKresidual
244             CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,
245         &        SQUEEZE_RIGHT, myThid )
246           WRITE(msgBuf,'(3(A,I6))')           WRITE(msgBuf,'(3(A,I6))')
247       &        ' S/R SEAICE_JFNK: Newton iterate / total = ', newtonIter,       &        ' S/R SEAICE_JFNK: Newton iterate / total = ',newtonIter,
248       &        ' / ', SEAICEnewtonIterMax*(myIter-nIter0)+newtonIter,       &        ' / ', totalNewtonItersLoc,
249       &        ', Nb. of FGMRES iterations = ', krylovIter       &        ', Nb. of FGMRES iterations = ', krylovIter
250           CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,           CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,
251       &        SQUEEZE_RIGHT, myThid )       &        SQUEEZE_RIGHT, myThid )
# Line 272  C     some output diagnostics Line 254  C     some output diagnostics
254          IF ( krylovIter.EQ.SEAICEkrylovIterMax ) THEN          IF ( krylovIter.EQ.SEAICEkrylovIterMax ) THEN
255           krylovFails = krylovFails + 1           krylovFails = krylovFails + 1
256          ENDIF          ENDIF
257    C     Set the stopping criterion for the Newton iteration and the
258    C     criterion for the transition from accurate to approximate FGMRES
259            IF ( newtonIter .EQ. 1 ) THEN
260             JFNKtol=JFNKgamma_nonlin*JFNKresidual
261             IF ( JFNKres_tFac .NE. UNSET_RL )
262         &        JFNKres_t = JFNKresidual * JFNKres_tFac
263            ENDIF
264  C     Update linear solution vector and return to Newton iteration  C     Update linear solution vector and return to Newton iteration
265    C     Do a linesearch if necessary, and compute a new residual.
266    C     Note that it should be possible to do the following operations
267    C     at the beginning of the Newton iteration, thereby saving us from
268    C     the extra call of seaice_jfnk_update, but unfortunately that
269    C     changes the results, so we leave the stuff here for now.
270            CALL SEAICE_JFNK_UPDATE(
271         I       duIce, dvIce,
272         U       uIce, vIce, JFNKresidual,
273         O       uIceRes, vIceRes,
274         I       newtonIter, myTime, myIter, myThid )
275    C     reset du/vIce here instead of setting sol = 0 in seaice_fgmres_driver
276          DO bj=myByLo(myThid),myByHi(myThid)          DO bj=myByLo(myThid),myByHi(myThid)
277           DO bi=myBxLo(myThid),myBxHi(myThid)           DO bi=myBxLo(myThid),myBxHi(myThid)
278            DO J=1-Oly,sNy+Oly            DO J=1-Oly,sNy+Oly
279             DO I=1-Olx,sNx+Olx             DO I=1-Olx,sNx+Olx
             uIce(I,J,bi,bj) = uIce(I,J,bi,bj)+duIce(I,J,bi,bj)  
             vIce(I,J,bi,bj) = vIce(I,J,bi,bj)+dvIce(I,J,bi,bj)  
 C     reset du/vIce here instead of setting sol = 0 in seaice_fgmres_driver  
280              duIce(I,J,bi,bj)= 0. _d 0              duIce(I,J,bi,bj)= 0. _d 0
281              dvIce(I,J,bi,bj)= 0. _d 0              dvIce(I,J,bi,bj)= 0. _d 0
282             ENDDO             ENDDO
283            ENDDO            ENDDO
284           ENDDO           ENDDO
285          ENDDO          ENDDO
 C     Set the stopping criterion for the Newton iteration  
         IF ( newtonIter .EQ. 1 ) JFNKtol=JFNKgamma_nonlin*JFNKresidual  
286         ENDIF         ENDIF
287  C     end of Newton iterate  C     end of Newton iterate
288        ENDDO        ENDDO
# Line 357  C     Decide whether it is time to dump Line 352  C     Decide whether it is time to dump
352       &' // ======================================================='       &' // ======================================================='
353         CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,         CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,
354       &      SQUEEZE_RIGHT, myThid )       &      SQUEEZE_RIGHT, myThid )
355         WRITE(msgBuf,'(A)') ' // Begin JFNK statistics'         WRITE(msgBuf,'(A)') ' // End JFNK statistics'
356         CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,         CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,
357       &      SQUEEZE_RIGHT, myThid )       &      SQUEEZE_RIGHT, myThid )
358         WRITE(msgBuf,'(A)')         WRITE(msgBuf,'(A)')
# Line 402  C     Print more debugging information Line 397  C     Print more debugging information
397         _END_MASTER( myThid )         _END_MASTER( myThid )
398        ENDIF        ENDIF
399    
400          RETURN
401          END
402    
403    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
404    CBOP
405    C     !ROUTINE: SEAICE_JFNK_UPDATE
406    C     !INTERFACE:
407    
408          SUBROUTINE SEAICE_JFNK_UPDATE(
409         I     duIce, dvIce,
410         U     uIce, vIce, JFNKresidual,
411         O     uIceRes, vIceRes,
412         I     newtonIter, myTime, myIter, myThid )
413    
414    C     !DESCRIPTION: \bv
415    C     *==========================================================*
416    C     | SUBROUTINE SEAICE_JFNK_UPDATE
417    C     | o Update velocities with incremental solutions of FGMRES
418    C     | o compute residual of updated solutions and do
419    C     | o linesearch:
420    C     |   reduce update until residual is smaller than previous
421    C     |   one (input)
422    C     *==========================================================*
423    C     | written by Martin Losch, Jan 2013
424    C     *==========================================================*
425    C     \ev
426    
427    C     !USES:
428          IMPLICIT NONE
429    
430    C     === Global variables ===
431    #include "SIZE.h"
432    #include "EEPARAMS.h"
433    #include "PARAMS.h"
434    #include "SEAICE_SIZE.h"
435    #include "SEAICE_PARAMS.h"
436    
437    C     !INPUT/OUTPUT PARAMETERS:
438    C     === Routine arguments ===
439    C     myTime :: Simulation time
440    C     myIter :: Simulation timestep number
441    C     myThid :: my Thread Id. number
442    C     newtonIter :: current iterate of Newton iteration
443          _RL     myTime
444          INTEGER myIter
445          INTEGER myThid
446          INTEGER newtonIter
447    C     JFNKresidual :: Residual at the beginning of the FGMRES iteration,
448    C                     changes with newtonIter (updated)
449          _RL     JFNKresidual
450    C     du/vIce   :: ice velocity increment to be added to u/vIce (input)
451          _RL duIce  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
452          _RL dvIce  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
453    C     u/vIce    :: ice velocity increment to be added to u/vIce (updated)
454          _RL uIce   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
455          _RL vIce   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
456    C     u/vIceRes :: residual of sea-ice momentum equations (output)
457          _RL uIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
458          _RL vIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
459    
460    C     !LOCAL VARIABLES:
461    C     === Local variables ===
462    C     i,j,bi,bj :: loop indices
463          INTEGER i,j,bi,bj
464          INTEGER l
465          _RL     resLoc, facLS
466          LOGICAL doLineSearch
467    C     nVec    :: size of the input vector(s)
468    C     vector version of the residuals
469          INTEGER nVec
470          PARAMETER ( nVec  = 2*sNx*sNy )
471          _RL resTmp (nVec,1,nSx,nSy)
472    C
473          CHARACTER*(MAX_LEN_MBUF) msgBuf
474    CEOP
475    
476    C     Initialise some local variables
477          l = 0
478          resLoc = JFNKresidual
479          facLS = 1. _d 0
480          doLineSearch = .TRUE.
481          DO WHILE ( doLineSearch )
482    C     Create update
483           DO bj=myByLo(myThid),myByHi(myThid)
484            DO bi=myBxLo(myThid),myBxHi(myThid)
485             DO J=1-Oly,sNy+Oly
486              DO I=1-Olx,sNx+Olx
487               uIce(I,J,bi,bj) = uIce(I,J,bi,bj)+facLS*duIce(I,J,bi,bj)
488               vIce(I,J,bi,bj) = vIce(I,J,bi,bj)+facLS*dvIce(I,J,bi,bj)
489              ENDDO
490             ENDDO
491            ENDDO
492           ENDDO
493    C     Compute current residual F(u), (includes re-computation of global
494    C     variables DWATN, zeta, and eta, i.e. they are different after this)
495           CALL SEAICE_CALC_RESIDUAL(
496         I      uIce, vIce,
497         O      uIceRes, vIceRes,
498         I      newtonIter, 0, myTime, myIter, myThid )
499    C     Important: Compute the norm of the residual using the same scalar
500    C     product that SEAICE_FGMRES does
501           CALL SEAICE_MAP2VEC(nVec,uIceRes,vIceRes,resTmp,.TRUE.,myThid)
502           CALL SEAICE_SCALPROD(nVec,1,1,1,resTmp,resTmp,resLoc,myThid)
503           resLoc = SQRT(resLoc)
504    C     Determine, if we need more iterations
505           doLineSearch = resLoc .GE. JFNKresidual
506    C     Limit the maximum number of iterations arbitrarily to four
507           doLineSearch = doLineSearch .AND. l .LT. 4
508    C     For the first iteration du/vIce = 0 and there will be no
509    C     improvement of the residual possible, so we do only the first
510    C     iteration
511           IF ( newtonIter .EQ. 1 ) doLineSearch = .FALSE.
512    C     Only start a linesearch after some Newton iterations
513           IF ( newtonIter .LE. SEAICE_JFNK_lsIter ) doLineSearch = .FALSE.
514    C     Increment counter
515           l = l + 1
516    C     some output diagnostics
517           IF ( debugLevel.GE.debLevA .AND. doLineSearch ) THEN
518            _BEGIN_MASTER( myThid )
519            WRITE(msgBuf,'(2A,2(1XI6),3E12.5)')
520         &       ' S/R SEAICE_JFNK_UPDATE: Newton iter, LSiter, ',
521         &       'facLS, JFNKresidual, resLoc = ',
522         &        newtonIter, l, facLS, JFNKresidual, resLoc
523            CALL PRINT_MESSAGE( msgBuf, standardMessageUnit,
524         &       SQUEEZE_RIGHT, myThid )
525            _END_MASTER( myThid )
526           ENDIF
527    C     Get ready for the next iteration: after adding du/vIce in the first
528    C     iteration, we substract 0.5*du/vIce from u/vIce in the next
529    C     iterations, 0.25*du/vIce in the second, etc.
530           facLS = - 0.5 _d 0 * ABS(facLS)
531          ENDDO
532    C     This is the new residual
533          JFNKresidual = resLoc
534    
535  #endif /* SEAICE_ALLOW_DYNAMICS and SEAICE_CGRID and SEAICE_ALLOW_JFNK */  #endif /* SEAICE_ALLOW_DYNAMICS and SEAICE_CGRID and SEAICE_ALLOW_JFNK */
536    
537        RETURN        RETURN
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