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Last-Modified: Sat, 6 Dec 2024 06:11:57 GMT Content-Type: text/plain #include "SEAICE_OPTIONS.h" #ifdef ALLOW_AUTODIFF # include "AUTODIFF_OPTIONS.h" #endif C-- File seaice_krylov.F: seaice krylov dynamical solver S/R: CBOP C !ROUTINE: SEAICE_KRYLOV C !INTERFACE: SUBROUTINE SEAICE_KRYLOV( myTime, myIter, myThid ) C !DESCRIPTION: \bv C *==========================================================* C | SUBROUTINE SEAICE_KRYLOV C | o Picard solver for ice dynamics using a preconditioned C | KRYLOV (Generalized Minimum RESidual=GMRES) method for C | solving the linearised system following J.-F. Lemieux C | et al., JGR 113, doi:10.1029/2007JC004680, 2008. C *==========================================================* C | written by Martin Losch, Jan 2016 C *==========================================================* C \ev C !USES: IMPLICIT NONE C === Global variables === #include "SIZE.h" #include "EEPARAMS.h" #include "PARAMS.h" #include "DYNVARS.h" #include "GRID.h" #include "SEAICE_SIZE.h" #include "SEAICE_PARAMS.h" #include "SEAICE.h" C !INPUT/OUTPUT PARAMETERS: C === Routine arguments === C myTime :: Simulation time C myIter :: Simulation timestep number C myThid :: my Thread Id. number _RL myTime INTEGER myIter INTEGER myThid #if ( defined SEAICE_CGRID && defined SEAICE_ALLOW_KRYLOV ) C !FUNCTIONS: LOGICAL DIFFERENT_MULTIPLE EXTERNAL DIFFERENT_MULTIPLE C !LOCAL VARIABLES: C === Local variables === C i,j,bi,bj :: loop indices INTEGER i,j,bi,bj C loop indices INTEGER picardIter INTEGER krylovIter, krylovFails INTEGER krylovIterMax, picardIterMax INTEGER totalKrylovItersLoc, totalPicardItersLoc C FGMRES parameters C im :: size of Krylov space C ifgmres :: interation counter INTEGER im PARAMETER ( im = 50 ) INTEGER ifgmres C FGMRES flag that determines amount of output messages of fgmres INTEGER iOutFGMRES C FGMRES flag that indicates what fgmres wants us to do next INTEGER iCode _RL picardResidual _RL picardResidualKm1 C parameters to compute convergence criterion _RL krylovLinTol _RL FGMRESeps _RL picardTol C backward differences extrapolation factors _RL bdfFac, bdfAlpha C _RL recip_deltaT LOGICAL picardConverged, krylovConverged LOGICAL writeNow CHARACTER*(MAX_LEN_MBUF) msgBuf _RL uIceLin(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) _RL vIceLin(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) C extra time level required for backward difference time stepping _RL duIcNm1(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) _RL dvIcNm1(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) C u/vWork :: work arrays _RL uWork (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) _RL vWork (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) C u/vIceLHS :: left hand side of momentum equation (A*x) _RL uIceLHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) _RL vIceLHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) C u/vIceRHS :: right hand side of momentum equation (b) _RL uIceRHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) _RL vIceRHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) C helper array _RL resTmp (nVec,1,nSx,nSy) C work arrays _RL rhs(nVec,nSx,nSy), sol(nVec,nSx,nSy) _RL vv(nVec,im+1,nSx,nSy), w(nVec,im,nSx,nSy) _RL wk1(nVec,nSx,nSy), wk2(nVec,nSx,nSy) CEOP C Initialise picardIter = 0 krylovFails = 0 totalKrylovItersLoc = 0 picardConverged = .FALSE. picardTol = 0. _d 0 picardResidual = 0. _d 0 picardResidualKm1 = 0. _d 0 FGMRESeps = 0. _d 0 recip_deltaT = 1. _d 0 / SEAICE_deltaTdyn krylovIterMax = SEAICElinearIterMax picardIterMax = SEAICEnonLinIterMax IF ( SEAICEusePicardAsPrecon ) THEN krylovIterMax = SEAICEpreconlinIter picardIterMax = SEAICEpreconNL_Iter ENDIF iOutFGMRES=0 C with iOutFgmres=1, seaice_fgmres prints the residual at each iteration IF ( debugLevel.GE.debLevC .AND. & .NOT.SEAICEusePicardAsPrecon .AND. & DIFFERENT_MULTIPLE( SEAICE_monFreq, myTime, deltaTClock ) ) & iOutFGMRES=1 C backward difference extrapolation factors bdfFac = 0. _d 0 IF ( SEAICEuseBDF2 ) THEN IF ( myIter.EQ.nIter0 .AND. SEAICEmomStartBDF.EQ.0 ) THEN bdfFac = 0. _d 0 ELSE bdfFac = 0.5 _d 0 ENDIF ENDIF bdfAlpha = 1. _d 0 + bdfFac DO bj=myByLo(myThid),myByHi(myThid) DO bi=myBxLo(myThid),myBxHi(myThid) DO J=1-OLy,sNy+OLy DO I=1-OLx,sNx+OLx uIceLHS(I,J,bi,bj) = 0. _d 0 vIceLHS(I,J,bi,bj) = 0. _d 0 uIceRHS(I,J,bi,bj) = 0. _d 0 vIceRHS(I,J,bi,bj) = 0. _d 0 ENDDO ENDDO C cycle ice velocities DO J=1-OLy,sNy+OLy DO I=1-OLx,sNx+OLx duIcNm1(I,J,bi,bj) = uIce(I,J,bi,bj) * bdfAlpha & + ( uIce(I,J,bi,bj) - uIceNm1(I,J,bi,bj) ) * bdfFac dvIcNm1(I,J,bi,bj) = vIce(I,J,bi,bj) * bdfAlpha & + ( vIce(I,J,bi,bj) - vIceNm1(I,J,bi,bj) ) * bdfFac uIceNm1(I,J,bi,bj) = uIce(I,J,bi,bj) vIceNm1(I,J,bi,bj) = vIce(I,J,bi,bj) uIceLin(I,J,bi,bj) = uIce(I,J,bi,bj) vIceLin(I,J,bi,bj) = vIce(I,J,bi,bj) ENDDO ENDDO C Compute things that do no change during the OL iteration: C sea-surface tilt and wind stress: C FORCEX/Y0 - mass*(1.5*u/vIceNm1+0.5*(u/vIceNm1-u/vIceNm2))/deltaT DO J=1-OLy,sNy+OLy DO I=1-OLx,sNx+OLx FORCEX(I,J,bi,bj) = FORCEX0(I,J,bi,bj) & + seaiceMassU(I,J,bi,bj)*duIcNm1(I,J,bi,bj)*recip_deltaT FORCEY(I,J,bi,bj) = FORCEY0(I,J,bi,bj) & + seaiceMassV(I,J,bi,bj)*dvIcNm1(I,J,bi,bj)*recip_deltaT ENDDO ENDDO CML ENDIF ENDDO ENDDO C Start nonlinear Picard iteration: outer loop iteration DO WHILE ( picardIter.LT.picardIterMax .AND. & .NOT.picardConverged ) picardIter = picardIter + 1 C smooth ice velocities in time for computation of C the non-linear drag coefficents DO bj=myByLo(myThid),myByHi(myThid) DO bi=myBxLo(myThid),myBxHi(myThid) DO j=1-OLy,sNy+OLy DO i=1-OLx,sNx+OLx uIceLin(I,J,bi,bj) = 0.5 _d 0 * & (uIce(I,J,bi,bj) + uIceLin(I,J,bi,bj)) vIceLin(I,J,bi,bj) = 0.5 _d 0 * & (vIce(I,J,bi,bj) + vIceLin(I,J,bi,bj)) ENDDO ENDDO ENDDO ENDDO C u/vIce have changed in Picard iteration so that new drag C coefficients and viscosities are required (that will not change in C the Krylov iteration) CALL SEAICE_OCEANDRAG_COEFFS( I uIceLin, vIceLin, HEFFM, O DWATN, I 0, myTime, myIter, myThid ) #ifdef SEAICE_ALLOW_BOTTOMDRAG CALL SEAICE_BOTTOMDRAG_COEFFS( I uIceLin, vIceLin, HEFFM, #ifdef SEAICE_ITD I HEFFITD, AREAITD, AREA, #else I HEFF, AREA, #endif O CbotC, I 0, myTime, myIter, myThid ) #endif /* SEAICE_ALLOW_BOTTOMDRAG */ CALL SEAICE_CALC_STRAINRATES( I uIceLin, vIceLin, O e11, e22, e12, I 0, myTime, myIter, myThid ) CALL SEAICE_CALC_VISCOSITIES( I e11, e22, e12, SEAICE_zMin, SEAICE_zMax, HEFFM, press0, I tensileStrFac, O eta, etaZ, zeta, zetaZ, press, deltaC, I 0, myTime, myIter, myThid ) C compute rhs that does not change during Krylov iteration CALL SEAICE_CALC_RHS( O uIceRHS, vIceRHS, I picardIter, 0, myTime, myIter, myThid ) C compute rhs for initial residual CALL SEAICE_CALC_LHS( I uIce, vIce, O uIceLHS, vIceLHS, I picardIter, myTime, myIter, myThid ) C Calculate the residual DO bj=myByLo(myThid),myByHi(myThid) DO bi=myBxLo(myThid),myBxHi(myThid) DO J=1,sNy DO I=1,sNx uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj) - uIceRHS(I,J,bi,bj) vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj) - vIceRHS(I,J,bi,bj) C save u/vIceLin as k-2nd step for linearization (does not work properly) CML uIceLin(I,J,bi,bj) = uIce(I,J,bi,bj) CML vIceLin(I,J,bi,bj) = vIce(I,J,bi,bj) ENDDO ENDDO ENDDO ENDDO C Important: Compute the norm of the residual using the same scalar C product that SEAICE_FGMRES does CALL SEAICE_MAP2VEC(nVec,uIceLHS,vIceLHS,resTmp,.TRUE.,myThid) CALL SEAICE_SCALPROD(nVec,1,1,1,resTmp,resTmp, & picardResidual,myThid) picardResidual = SQRT(picardResidual) C compute convergence criterion for linear preconditioned FGMRES krylovLinTol = JFNKgamma_lin_max C the best method is still not clear to me C this is described in Lemieux et al 2008 CML IF ( picardIter .EQ. 1 ) krylovLinTol = 1./10. CML IF ( picardIter .EQ. 2 ) krylovLinTol = 1./20. CML IF ( picardIter .EQ. 3 ) krylovLinTol = 1./20. CML IF ( picardIter .EQ. 4 ) krylovLinTol = 1./30. CML IF ( picardIter .EQ. 5 ) krylovLinTol = 1./30. CML IF ( picardIter .EQ. 6 ) krylovLinTol = 1./30. CML IF ( picardIter .EQ. 7 ) krylovLinTol = 1./30. CML IF ( picardIter .EQ. 8 ) krylovLinTol = 1./40. CML IF ( picardIter .EQ. 9 ) krylovLinTol = 1./50. CML IF ( picardIter .GT. 9 ) krylovLinTol = 1./80. C this is used with the JFNK solver, but the Picard-Krylov solver C converges too slowly for this scheme CML IF ( picardIter.GT.1.AND.picardResidual.LT.JFNKres_t ) THEN CMLC Eisenstat and Walker (1996), eq.(2.6) CML krylovLinTol = SEAICE_JFNKphi CML & *( picardResidual/picardResidualKm1 )**SEAICE_JFNKalpha CML krylovLinTol = min(JFNKgamma_lin_max, krylovLinTol) CML krylovLinTol = max(JFNKgamma_lin_min, krylovLinTol) CML ENDIF CML krylovLinTol = 1. _d -1 C save the residual for the next iteration picardResidualKm1 = picardResidual C The Krylov iteration uses FGMRES, the preconditioner is LSOR C for now. The code is adapted from SEAICE_LSR, but heavily stripped C down. C krylovIter is mapped into "its" in seaice_fgmres and is incremented C in that routine krylovIter = 0 iCode = 0 picardConverged = picardResidual.LT.picardTol & .OR.picardResidual.EQ.0. _d 0 C do Krylov loop only if convergence is not reached IF ( .NOT.picardConverged ) THEN C start Krylov iteration (FGMRES) krylovConverged = .FALSE. FGMRESeps = krylovLinTol * picardResidual CALL SEAICE_MAP2VEC(nVec,uIce,vIce,sol,.TRUE.,myThid) CALL SEAICE_MAP2VEC(nVec,uIceRHS,vIceRHS,rhs,.TRUE.,myThid) DO bj=myByLo(myThid),myByHi(myThid) DO bi=myBxLo(myThid),myBxHi(myThid) DO j=1-OLy,sNy+OLy DO i=1-OLx,sNx+OLx uWork(i,j,bi,bj) = 0. _d 0 vWork(i,j,bi,bj) = 0. _d 0 ENDDO ENDDO ENDDO ENDDO DO WHILE ( .NOT.krylovConverged ) C solution vector sol = u/vIce C residual vector (rhs) Fu = u/vIceRHS C output work vectors wk1, -> input work vector wk2 C map results to wk2 CALL SEAICE_MAP2VEC(nVec,uWork,vWork,wk2,.TRUE.,myThid) CALL SEAICE_FGMRES (nVec,im,rhs,sol,ifgmres,krylovIter, U vv,w,wk1,wk2, I FGMRESeps,krylovIterMax,iOutFGMRES, U iCode, I myThid) C IF ( iCode .EQ. 0 ) THEN C map sol(ution) vector to u/vIce CALL SEAICE_MAP2VEC(nVec,uIce,vIce,sol,.FALSE.,myThid) CALL EXCH_UV_XY_RL( uIce, vIce,.TRUE.,myThid) ELSE C map work vector to du/vIce to either compute a preconditioner C solution (wk1=rhs) or a matrix times wk1 CALL SEAICE_MAP2VEC(nVec,uWork,vWork,wk1,.FALSE.,myThid) CALL EXCH_UV_XY_RL( uWork, vWork,.TRUE.,myThid) ENDIF C FGMRES returns iCode either asking for an new preconditioned vector C or product of matrix times vector. For iCode = 0, terminate C iteration IF (iCode.EQ.1) THEN C Call preconditioner IF ( SEAICEpreconLinIter .GT. 0 ) & CALL SEAICE_PRECONDITIONER( U uWork, vWork, I zeta, eta, etaZ, zetaZ, dwatn, I picardIter, krylovIter, myTime, myIter, myThid ) ELSEIF (iCode.GE.2) THEN C Compute lhs of equations (A*x) CALL SEAICE_CALC_STRAINRATES( I uWork, vWork, O e11, e22, e12, I krylovIter, myTime, myIter, myThid ) CALL SEAICE_CALC_LHS( I uWork, vWork, O uIceLHS, vIceLHS, I picardIter, myTime, myIter, myThid ) DO bj=myByLo(myThid),myByHi(myThid) DO bi=myBxLo(myThid),myBxHi(myThid) DO j=1-OLy,sNy+OLy DO i=1-OLx,sNx+OLx uWork(i,j,bi,bj) = uIceLHS(i,j,bi,bj) vWork(i,j,bi,bj) = vIceLHS(i,j,bi,bj) ENDDO ENDDO ENDDO ENDDO ENDIF krylovConverged = iCode.EQ.0 C End of Krylov iterate ENDDO totalKrylovItersLoc = totalKrylovItersLoc + krylovIter C some output diagnostics IF ( debugLevel.GE.debLevA & .AND. .NOT.SEAICEusePicardAsPrecon ) THEN _BEGIN_MASTER( myThid ) totalPicardItersLoc = & picardIterMax*(myIter-nIter0)+picardIter WRITE(msgBuf,'(2A,2(1XI6),2E12.5)') & ' S/R SEAICE_KRYLOV: Picard iterate / total, ', & 'KRYLOVgamma_lin, initial norm = ', & picardIter, totalPicardItersLoc, & krylovLinTol,picardResidual CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(3(A,I6))') & ' S/R SEAICE_KRYLOV: Picard iterate / total = ', & picardIter, ' / ', totalPicardItersLoc, & ', Nb. of FGMRES iterations = ', krylovIter CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) _END_MASTER( myThid ) ENDIF IF ( krylovIter.EQ.krylovIterMax ) THEN krylovFails = krylovFails + 1 ENDIF C Set the stopping criterion for the Picard iteration and the C criterion for the transition from accurate to approximate FGMRES IF ( picardIter .EQ. 1 ) THEN picardTol=SEAICEnonLinTol*picardResidual IF ( JFNKres_tFac .NE. UNSET_RL ) & JFNKres_t = picardResidual * JFNKres_tFac ENDIF ENDIF C end of Picard iterate ENDDO C-- Output diagnostics IF ( SEAICE_monFreq .GT. 0. _d 0 ) THEN C Only Master Thread updates counters in common block: _BEGIN_MASTER(myThid) C Cumulate some diagnostic counters for the Krylov solver totalJFNKtimeSteps = totalJFNKtimeSteps + 1 totalNewtonIters = totalNewtonIters + picardIter totalKrylovIters = totalKrylovIters + totalKrylovItersLoc C Record failure totalKrylovFails = totalKrylovFails + krylovFails IF ( picardIter .EQ. picardIterMax ) THEN totalNewtonfails = totalNewtonfails + 1 ENDIF _END_MASTER( myThid ) ENDIF C Decide whether it is time to dump and reset the counter writeNow = DIFFERENT_MULTIPLE(SEAICE_monFreq, & myTime+deltaTClock, deltaTClock) #ifdef ALLOW_CAL IF ( useCAL ) THEN CALL CAL_TIME2DUMP( I zeroRL, SEAICE_monFreq, deltaTClock, U writeNow, I myTime+deltaTClock, myIter+1, myThid ) ENDIF #endif IF ( writeNow ) THEN _BEGIN_MASTER( myThid ) WRITE(msgBuf,'(A)') &' // =======================================================' CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A)') ' // Begin KRYLOV statistics' CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A)') &' // =======================================================' CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A,I10)') & ' %KRYLOV_MON: time step = ', myIter+1 CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A,I10)') & ' %KRYLOV_MON: Nb. of time steps = ', & totalJFNKtimeSteps CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A,I10)') & ' %KRYLOV_MON: Nb. of Picard steps = ', totalNewtonIters CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A,I10)') & ' %KRYLOV_MON: Nb. of Krylov steps = ', totalKrylovIters CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A,I10)') & ' %KRYLOV_MON: Nb. of Picard failures = ', totalNewtonfails CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A,I10)') & ' %KRYLOV_MON: Nb. of Krylov failures = ', totalKrylovFails CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A)') &' // =======================================================' CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A)') ' // End KRYLOV statistics' CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) WRITE(msgBuf,'(A)') &' // =======================================================' CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) C Reset and start again totalJFNKtimeSteps = 0 totalNewtonIters = 0 totalKrylovIters = 0 totalKrylovFails = 0 totalNewtonfails = 0 _END_MASTER( myThid ) ENDIF C Print more debugging information IF ( debugLevel.GE.debLevA & .AND. .NOT.SEAICEusePicardAsPrecon ) THEN IF ( picardIter .EQ. picardIterMax ) THEN _BEGIN_MASTER( myThid ) WRITE(msgBuf,'(A,I10)') & ' S/R SEAICE_KRYLOV: Solver did not converge in timestep ', & myIter+1 CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) _END_MASTER( myThid ) ENDIF IF ( krylovFails .GT. 0 ) THEN _BEGIN_MASTER( myThid ) WRITE(msgBuf,'(A,I4,A,I10)') & ' S/R SEAICE_KRYLOV: FGMRES did not converge ', & krylovFails, ' times in timestep ', myIter+1 CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) _END_MASTER( myThid ) ENDIF _BEGIN_MASTER( myThid ) WRITE(msgBuf,'(A,I6,A,I10)') & ' S/R SEAICE_KRYLOV: Total number FGMRES iterations = ', & totalKrylovItersLoc, ' in timestep ', myIter+1 CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, & SQUEEZE_RIGHT, myThid ) _END_MASTER( myThid ) ENDIF #endif /* SEAICE_CGRID and SEAICE_ALLOW_KRYLOV */ RETURN END

** Warning **Issuing rollback() due to DESTROY without explicit disconnect() of DBD::mysql::db handle dbname=MITgcm at /usr/local/share/lxr/lib/LXR/Common.pm line 1224.

Warning
Issuing rollback() due to DESTROY without explicit disconnect() of DBD::mysql::db handle dbname=MITgcm at /usr/local/share/lxr/lib/LXR/Common.pm line 1224.