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C $Header: $ |
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C $Name: $ |
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|
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#include "SEAICE_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: SEAICE_JFNK |
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C !INTERFACE: |
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SUBROUTINE SEAICE_JFNK( myTime, myIter, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE SEAICE_JFKF |
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C | o Ice dynamics using a Jacobian-free Newton-Krylov solver |
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C | following J.-F. Lemieux et al. Improving the numerical |
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C | convergence of viscous-plastic sea ice models with the |
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C | Jacobian-free Newton-Krylov method. J. Comp. Phys. 229, |
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C | 2840-2852 (2010). |
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C | o The logic follows JFs code. |
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C *==========================================================* |
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C | written by Martin Losch, Oct 2012 |
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C *==========================================================* |
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C \ev |
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|
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C !USES: |
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IMPLICIT NONE |
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|
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C === Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "DYNVARS.h" |
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#include "GRID.h" |
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#include "SEAICE_SIZE.h" |
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#include "SEAICE_PARAMS.h" |
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#include "SEAICE.h" |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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# include "tamc.h" |
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#endif |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C === Routine arguments === |
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C myTime :: Simulation time |
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C myIter :: Simulation timestep number |
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C myThid :: my Thread Id. number |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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|
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#if ( (defined SEAICE_CGRID) && \ |
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(defined SEAICE_ALLOW_JFNK) && \ |
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(defined SEAICE_ALLOW_DYNAMICS) ) |
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|
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C i,j,bi,bj :: loop indices |
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INTEGER i,j,bi,bj |
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C loop indices |
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INTEGER newtonIter, newtonIterFail |
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INTEGER krylovIter, krylovIterFail |
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INTEGER totalKrylovIter |
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C FGMRES flag that indicates what to do next |
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INTEGER iCode |
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_RL JFNKresidual, JFNKresidualTile(nSx,nSy) |
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_RL JFNKresidualKm1 |
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C parameters to compute convergence criterion |
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_RL phi_e, alp_e, JFNKgamma_lin |
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_RL FGMRESeps |
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_RL JFNKtol |
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C |
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_RL recip_deltaT |
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LOGICAL JFNKconverged, krylovConverged |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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C |
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C u/vIceRes :: residual of sea-ice momentum equations |
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_RL uIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL vIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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C du/vIce :: ice velocity increment to be added to u/vIce |
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_RL duIce (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL dvIce (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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C precomputed (= constant per Newton iteration) versions of |
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C zeta, eta, and DWATN |
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_RL zetaPre(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL etaPre (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL dwatPre(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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CEOP |
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|
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C Initialise |
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newtonIter = 0 |
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newtonIterFail = 0 |
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krylovIterFail = 0 |
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totalKrylovIter = 0 |
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JFNKconverged = .FALSE. |
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JFNKtol = 0. _d 0 |
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JFNKresidual = 0. _d 0 |
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JFNKresidualKm1 = 0. _d 0 |
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FGMRESeps = 0. _d 0 |
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recip_deltaT = 1. _d 0 / SEAICE_deltaTdyn |
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C |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO J=1-Oly,sNy+Oly |
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DO I=1-Olx,sNx+Olx |
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uIceRes(I,J,bi,bj) = 0. _d 0 |
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vIceRes(I,J,bi,bj) = 0. _d 0 |
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duIce (I,J,bi,bj) = 0. _d 0 |
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dvIce (I,J,bi,bj) = 0. _d 0 |
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uIceNm1(I,J,bi,bj) = uIce(I,J,bi,bj) |
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vIceNm1(I,J,bi,bj) = vIce(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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C Compute things that do no change during the Newton iteration: |
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C sea-surface tilt and wind stress: |
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C FORCEX/Y0 - mass*(u/vIceNm1)/deltaT |
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DO J=1-Oly,sNy+Oly |
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DO I=1-Olx,sNx+Olx |
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FORCEX(I,J,bi,bj) = FORCEX0(I,J,bi,bj) |
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& + seaiceMassU(I,J,bi,bj)*uIceNm1(I,J,bi,bj)*recip_deltaT |
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FORCEY(I,J,bi,bj) = FORCEY0(I,J,bi,bj) |
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& + seaiceMassV(I,J,bi,bj)*vIceNm1(I,J,bi,bj)*recip_deltaT |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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C Start nonlinear Newton iteration: outer loop iteration |
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DO WHILE ( newtonIter.LT.SEAICEnewtonIterMax .AND. |
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& .NOT.JFNKconverged ) |
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newtonIter = newtonIter + 1 |
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C Compute initial residual F(u), (includes computation of global |
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C variables DWATN, zeta, and eta) |
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CALL SEAICE_CALC_RESIDUAL( |
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I uIce, vIce, |
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O uIceRes, vIceRes, |
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I newtonIter, 0, myTime, myIter, myThid ) |
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C local copies of precomputed coefficients that are to stay |
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C constant for the preconditioner |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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zetaPre(I,J,bi,bj) = zeta(I,J,bi,bj) |
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etaPre(I,J,bi,bj) = eta(I,J,bi,bj) |
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dwatPre(I,J,bi,bj) = DWATN(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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C |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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JFNKresidualTile(bi,bj) = 0. _d 0 |
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DO J=1,sNy |
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DO I=1,sNx |
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#ifdef CG2D_SINGLECPU_SUM |
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JFNKlocalBuf(I,J,bi,bj) = |
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#else |
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JFNKresidualTile(bi,bj) = JFNKresidualTile(bi,bj) + |
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#endif |
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& uIceRes(I,J,bi,bj)*uIceRes(I,J,bi,bj) + |
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& vIceRes(I,J,bi,bj)*vIceRes(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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JFNKresidual = 0. _d 0 |
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#ifdef CG2D_SINGLECPU_SUM |
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CALL GLOBAL_SUM_SINGLECPU_RL( |
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& JFNKlocalBuf,JFNKresidual, 0, 0, myThid) |
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#else |
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CALL GLOBAL_SUM_TILE_RL( JFNKresidualTile,JFNKresidual,myThid ) |
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#endif |
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JFNKresidual = SQRT(JFNKresidual) |
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C compute convergence criterion for linear preconditioned FGMRES |
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JFNKgamma_lin = JFNKgamma_lin_max |
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IF ( newtonIter.GT.1.AND.newtonIter.LE.100 |
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& .AND.JFNKresidual.LT.JFNKres_t ) THEN |
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C Eisenstat, 1996, equ.(2.6) |
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phi_e = 1. _d 0 |
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alp_e = 1. _d 0 |
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JFNKgamma_lin = phi_e*( JFNKresidual/JFNKresidualKm1 )**alp_e |
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JFNKgamma_lin = min(JFNKgamma_lin_max, JFNKgamma_lin) |
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JFNKgamma_lin = max(JFNKgamma_lin_min, JFNKgamma_lin) |
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ENDIF |
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C save the residual for the next iteration |
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JFNKresidualKm1 = JFNKresidual |
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C |
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C The Krylov iteration using FGMRES, the preconditioner is LSOR |
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C for now. The code is adapted from SEAICE_LSR, but heavily stripped |
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C down. |
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C krylovIter is mapped into "its" in seaice_fgmres and is incremented |
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C in that routine |
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krylovIter = 0 |
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iCode = 0 |
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IF ( debugLevel.GE.debLevA ) THEN |
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WRITE(msgBuf,'(2A,2(1XI6),2E12.5)') |
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& ' S/R SEAICE_JFNK: newtonIter,', |
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& ' total newtonIter, JFNKgamma_lin, initial norm = ', |
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& newtonIter, SEAICEnewtonIterMax*myIter+newtonIter, |
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& JFNKgamma_lin, JFNKresidual |
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT, myThid ) |
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ENDIF |
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C |
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JFNKconverged = JFNKresidual.LT.JFNKtol |
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C |
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C do Krylov loop only if convergence is not reached |
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C |
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IF ( .NOT.JFNKconverged ) THEN |
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C |
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C start Krylov iteration (FGMRES) |
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C |
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krylovConverged = .FALSE. |
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FGMRESeps = JFNKgamma_lin * JFNKresidual |
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DO WHILE ( .NOT.krylovConverged ) |
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C solution vector sol = du/vIce |
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C residual vector (rhs) Fu = u/vIceRes |
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C output work vectors wk1, -> input work vector wk2 |
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C |
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CALL EXCH_UV_XY_RL( uIceRes, vIceRes,.TRUE.,myThid) |
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CALL EXCH_UV_XY_RL( duIce, dvIce,.TRUE.,myThid) |
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CALL SEAICE_FGMRES_DRIVER( |
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I uIceRes, vIceRes, |
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U duIce, dvIce, iCode, |
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I FGMRESeps, |
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I newtonIter, krylovIter, myTime, myIter, myThid ) |
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C FGMRES returns iCode either asking for an new preconditioned vector |
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C or product of matrix (Jacobian) times vector. For iCode = 0, terminate |
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C iteration |
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IF (iCode.EQ.1) THEN |
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C Call preconditioner |
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CALL SEAICE_PRECONDITIONER( |
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U duIce, dvIce, |
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I zetaPre, etaPre, dwatPre, |
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I newtonIter, krylovIter, myTime, myIter, myThid ) |
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ELSEIF (iCode.GE.2) THEN |
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C Compute Jacobian times vector |
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CALL SEAICE_JACVEC( |
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I uIce, vIce, uIceRes, vIceRes, |
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U duIce, dvIce, |
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I newtonIter, krylovIter, myTime, myIter, myThid ) |
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ENDIF |
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krylovConverged = iCode.EQ.0 |
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C End of Krylov iterate |
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ENDDO |
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totalKrylovIter = totalKrylovIter + krylovIter |
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C some output diagnostics |
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IF ( debugLevel.GE.debLevA ) THEN |
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WRITE(msgBuf,'(3(A,I6))') |
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& ' S/R SEAICE_JFNK: Newton iterate / total = ', newtonIter, |
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& ' / ', SEAICEnewtonIterMax*myIter+newtonIter, |
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& ', Nb. of FGMRES iterations = ', krylovIter |
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT, myThid ) |
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ENDIF |
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IF ( krylovIter.EQ.SEAICEkrylovIterMax ) THEN |
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krylovIterFail = krylovIterFail + 1 |
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ENDIF |
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C Update linear solution vector and return to Newton iteration |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO J=1-Oly,sNy+Oly |
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DO I=1-Olx,sNx+Olx |
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uIce(I,J,bi,bj) = uIce(I,J,bi,bj)+duIce(I,J,bi,bj) |
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vIce(I,J,bi,bj) = vIce(I,J,bi,bj)+dvIce(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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C Set the stopping criterion for the Newton iteration |
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IF ( newtonIter .EQ. 1 ) JFNKtol=JFNKgamma_nonlin*JFNKresidual |
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ENDIF |
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C end of Newton iterate |
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ENDDO |
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C some output diagnostics |
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IF ( debugLevel.GE.debLevA ) THEN |
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C Record failure |
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IF ( newtonIter .EQ. SEAICEnewtonIterMax ) THEN |
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newtonIterFail = newtonIterFail + 1 |
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WRITE(msgBuf,'(A,I10)') |
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& ' S/R SEAICE_JFNK: JFNK did not converge in timestep ', |
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& myIter |
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT, myThid ) |
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ENDIF |
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IF ( krylovIterFail .GT. 0 ) THEN |
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WRITE(msgBuf,'(A,I4,A,I10)') |
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& ' S/R SEAICE_JFNK: FGMRES did not converge ', |
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& krylovIterFail, ' times in timestep ', myIter |
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT, myThid ) |
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ENDIF |
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WRITE(msgBuf,'(A,I6)') |
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& ' S/R SEAICE_JFNK: Total number FGMRES iterations = ', |
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& totalKrylovIter |
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT, myThid ) |
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|
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ENDIF |
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|
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#endif /* SEAICE_ALLOW_DYNAMICS and SEAICE_CGRID and SEAICE_ALLOW_JFNK */ |
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|
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RETURN |
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END |
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