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C $Header: /u/gcmpack/MITgcm/pkg/diagnostics/diag_cg2d.F,v 1.5 2012/03/19 18:22:09 jmc Exp $ |
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C $Name: $ |
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|
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#include "DIAG_OPTIONS.h" |
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#undef DEBUG_DIAG_CG2D |
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|
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CBOP |
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C !ROUTINE: DIAG_CG2D |
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C !INTERFACE: |
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SUBROUTINE DIAG_CG2D( |
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I aW2d, aS2d, b2d, |
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I offDiagFactor, residCriter, |
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O firstResidual, minResidual, lastResidual, |
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U x2d, numIters, |
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O nIterMin, |
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I printResidFrq, myThid ) |
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE CG2D |
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C | o Two-dimensional grid problem conjugate-gradient |
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C | inverter (with preconditioner). |
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C *==========================================================* |
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C | Con. grad is an iterative procedure for solving Ax = b. |
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C | It requires the A be symmetric. |
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C | This implementation assumes A is a five-diagonal |
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C | matrix of the form that arises in the discrete |
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C | representation of the del^2 operator in a |
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C | two-dimensional space. |
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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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C === Global data === |
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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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|
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C !INPUT/OUTPUT PARAMETERS: |
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C === Routine arguments === |
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C b2d :: The source term or "right hand side" |
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C x2d :: The solution |
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C offDiagFactor :: preconditioner off-diagonal factor |
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C residCriter :: residual target for convergence |
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C firstResidual :: the initial residual before any iterations |
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C minResidual :: the lowest residual reached |
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C lastResidual :: the actual residual reached |
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C numIters :: Entry: the maximum number of iterations allowed |
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C Exit: the actual number of iterations used |
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C nIterMin :: iteration number corresponding to lowest residual |
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C printResidFrq :: Frequency for printing residual in CG iterations |
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C myThid :: my Thread Id number |
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_RS aW2d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RS aS2d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL b2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL residCriter |
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_RL offDiagFactor |
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_RL firstResidual |
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_RL minResidual |
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_RL lastResidual |
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_RL x2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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INTEGER numIters |
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INTEGER nIterMin |
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INTEGER printResidFrq |
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INTEGER myThid |
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|
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C !LOCAL VARIABLES: |
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C === Local variables ==== |
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C bi, bj :: tile indices |
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C eta_qrN :: Used in computing search directions |
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C eta_qrNM1 suffix N and NM1 denote current and |
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C cgBeta previous iterations respectively. |
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C alpha |
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C sumRHS :: Sum of right-hand-side. Sometimes this is a |
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C useful debuggin/trouble shooting diagnostic. |
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C For neumann problems sumRHS needs to be ~0. |
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C or they converge at a non-zero residual. |
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C err :: Measure of current residual of Ax - b, usually the norm. |
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C i, j, it2d :: Loop counters ( it2d counts CG iterations ) |
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INTEGER bi, bj |
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INTEGER i, j, it2d |
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_RL err, errTile(nSx,nSy) |
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_RL eta_qrN, eta_qrNtile(nSx,nSy) |
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_RL eta_qrNM1 |
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_RL cgBeta |
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_RL alpha, alphaTile(nSx,nSy) |
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_RL sumRHS, sumRHStile(nSx,nSy) |
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_RL pW_tmp, pS_tmp |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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LOGICAL printResidual |
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CEOP |
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_RS aC2d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RS pW (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RS pS (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RS pC (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL q2d(0:sNx+1,0:sNy+1,nSx,nSy) |
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#ifdef DEBUG_DIAG_CG2D |
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CHARACTER*(10) sufx |
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_RL r2d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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#else |
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_RL r2d(0:sNx+1,0:sNy+1,nSx,nSy) |
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#endif |
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_RL s2d(0:sNx+1,0:sNy+1,nSx,nSy) |
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_RL x2dm(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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|
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#ifdef ALLOW_DEBUG |
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IF (debugMode) CALL DEBUG_ENTER('DIAG_CG2D',myThid) |
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#endif |
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|
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C-- Set matrice main diagnonal: |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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C- Initialise overlap regions (in case EXCH call do not fill them all) |
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DO j = 1-OLy,sNy+OLy |
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DO i = 1-OLx,sNx+OLx |
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aC2d(i,j,bi,bj) = 0. |
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ENDDO |
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ENDDO |
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DO j=1,sNy |
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DO i=1,sNx |
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aC2d(i,j,bi,bj) = -( ( aW2d(i,j,bi,bj)+aW2d(i+1,j,bi,bj) ) |
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& +( aS2d(i,j,bi,bj)+aS2d(i,j+1,bi,bj) ) |
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& ) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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CALL EXCH_XY_RS(aC2d, myThid) |
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|
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C-- Initialise 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,sNy+1 |
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DO i=1,sNx+1 |
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IF ( aC2d(i,j,bi,bj) .EQ. 0. ) THEN |
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pC(i,j,bi,bj) = 1. _d 0 |
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ELSE |
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pC(i,j,bi,bj) = 1. _d 0 / aC2d(i,j,bi,bj) |
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ENDIF |
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pW_tmp = aC2d(i,j,bi,bj)+aC2d(i-1,j,bi,bj) |
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IF ( pW_tmp .EQ. 0. ) THEN |
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pW(i,j,bi,bj) = 0. |
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ELSE |
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pW(i,j,bi,bj) = -aW2d(i,j,bi,bj)*offDiagFactor |
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& *4. _d 0/( pW_tmp*pW_tmp ) |
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ENDIF |
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pS_tmp = aC2d(i,j,bi,bj)+aC2d(i,j-1,bi,bj) |
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IF ( pS_tmp .EQ. 0. ) THEN |
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pS(i,j,bi,bj) = 0. |
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ELSE |
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pS(i,j,bi,bj) = -aS2d(i,j,bi,bj)*offDiagFactor |
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& *4. _d 0/( pS_tmp*pS_tmp ) |
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ENDIF |
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c pC(i,j,bi,bj) = 1. |
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c pW(i,j,bi,bj) = 0. |
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c pS(i,j,bi,bj) = 0. |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C-- Initialise inverter |
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eta_qrNM1 = 1. _d 0 |
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|
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CALL EXCH_XY_RL( x2d, myThid ) |
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|
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C-- Initial residual calculation |
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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=0,sNy+1 |
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DO i=0,sNx+1 |
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r2d(i,j,bi,bj) = 0. |
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s2d(i,j,bi,bj) = 0. |
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x2dm(i,j,bi,bj) = x2d(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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sumRHStile(bi,bj) = 0. _d 0 |
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errTile(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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r2d(i,j,bi,bj) = b2d(i,j,bi,bj) - |
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& (aW2d(i ,j ,bi,bj)*x2d(i-1,j ,bi,bj) |
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& +aW2d(i+1,j ,bi,bj)*x2d(i+1,j ,bi,bj) |
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& +aS2d(i ,j ,bi,bj)*x2d(i ,j-1,bi,bj) |
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& +aS2d(i ,j+1,bi,bj)*x2d(i ,j+1,bi,bj) |
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& +aC2d(i ,j ,bi,bj)*x2d(i ,j ,bi,bj) |
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& ) |
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errTile(bi,bj) = errTile(bi,bj) |
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& + r2d(i,j,bi,bj)*r2d(i,j,bi,bj) |
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sumRHStile(bi,bj) = sumRHStile(bi,bj) + b2d(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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#ifdef DEBUG_DIAG_CG2D |
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CALL EXCH_XY_RL ( r2d, myThid ) |
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#else |
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CALL EXCH_S3D_RL( r2d, 1, myThid ) |
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#endif |
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CALL GLOBAL_SUM_TILE_RL( errTile, err, myThid ) |
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IF ( printResidFrq.GE.1 ) |
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& CALL GLOBAL_SUM_TILE_RL( sumRHStile, sumRHS, myThid ) |
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err = SQRT(err) |
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it2d = 0 |
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firstResidual = err |
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minResidual = err |
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nIterMin = it2d |
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|
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printResidual = .FALSE. |
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IF ( debugLevel .GE. debLevZero ) THEN |
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_BEGIN_MASTER( myThid ) |
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printResidual = printResidFrq.GE.1 |
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IF ( printResidual ) THEN |
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WRITE(msgBuf,'(2A,I6,A,1PE17.9,A,1PE14.6)')' diag_cg2d:', |
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& ' iter=', it2d, ' ; resid.=', err, ' ; sumRHS=', sumRHS |
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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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_END_MASTER( myThid ) |
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ENDIF |
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#ifdef DEBUG_DIAG_CG2D |
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IF ( printResidFrq.GE.1 ) THEN |
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WRITE(sufx,'(I10.10)') 0 |
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CALL WRITE_FLD_XY_RL( 'r2d.',sufx, r2d, 1, myThid ) |
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ENDIF |
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#endif |
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|
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IF ( err .LT. residCriter ) GOTO 11 |
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|
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C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
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DO 10 it2d=1, numIters |
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|
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C-- Solve preconditioning equation and update |
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C-- conjugate direction vector "s". |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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eta_qrNtile(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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q2d(i,j,bi,bj) = |
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& pC(i ,j ,bi,bj)*r2d(i ,j ,bi,bj) |
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& +pW(i ,j ,bi,bj)*r2d(i-1,j ,bi,bj) |
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& +pW(i+1,j ,bi,bj)*r2d(i+1,j ,bi,bj) |
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& +pS(i ,j ,bi,bj)*r2d(i ,j-1,bi,bj) |
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& +pS(i ,j+1,bi,bj)*r2d(i ,j+1,bi,bj) |
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eta_qrNtile(bi,bj) = eta_qrNtile(bi,bj) |
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& +q2d(i,j,bi,bj)*r2d(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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|
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CALL GLOBAL_SUM_TILE_RL( eta_qrNtile,eta_qrN,myThid ) |
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cgBeta = eta_qrN/eta_qrNM1 |
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eta_qrNM1 = eta_qrN |
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|
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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,sNy |
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DO i=1,sNx |
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s2d(i,j,bi,bj) = q2d(i,j,bi,bj) |
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& + cgBeta*s2d(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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|
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C-- Do exchanges that require messages i.e. between processes. |
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CALL EXCH_S3D_RL( s2d, 1, myThid ) |
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|
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C== Evaluate laplace operator on conjugate gradient vector |
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C== q = A.s |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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alphaTile(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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q2d(i,j,bi,bj) = |
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& aW2d(i ,j ,bi,bj)*s2d(i-1,j ,bi,bj) |
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& +aW2d(i+1,j ,bi,bj)*s2d(i+1,j ,bi,bj) |
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& +aS2d(i ,j ,bi,bj)*s2d(i ,j-1,bi,bj) |
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& +aS2d(i ,j+1,bi,bj)*s2d(i ,j+1,bi,bj) |
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& +aC2d(i ,j ,bi,bj)*s2d(i ,j ,bi,bj) |
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alphaTile(bi,bj) = alphaTile(bi,bj) |
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& + s2d(i,j,bi,bj)*q2d(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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CALL GLOBAL_SUM_TILE_RL( alphaTile, alpha, myThid ) |
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alpha = eta_qrN/alpha |
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|
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C== Update solution and residual vectors |
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C Now compute "interior" points. |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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errTile(bi,bj) = 0. _d 0 |
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DO j=1,sNy |
| 299 |
DO i=1,sNx |
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x2d(i,j,bi,bj)=x2d(i,j,bi,bj)+alpha*s2d(i,j,bi,bj) |
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r2d(i,j,bi,bj)=r2d(i,j,bi,bj)-alpha*q2d(i,j,bi,bj) |
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errTile(bi,bj) = errTile(bi,bj) |
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& + r2d(i,j,bi,bj)*r2d(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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|
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CALL GLOBAL_SUM_TILE_RL( errTile, err, myThid ) |
| 310 |
err = SQRT(err) |
| 311 |
IF ( printResidual ) THEN |
| 312 |
IF ( MOD( it2d-1, printResidFrq ).EQ.0 ) THEN |
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WRITE(msgBuf,'(A,I6,A,1PE17.9)') |
| 314 |
& ' diag_cg2d: iter=', it2d, ' ; resid.=', err |
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
| 316 |
& SQUEEZE_RIGHT, myThid ) |
| 317 |
ENDIF |
| 318 |
ENDIF |
| 319 |
IF ( err .LT. residCriter ) GOTO 11 |
| 320 |
IF ( err .LT. minResidual ) THEN |
| 321 |
C- Store lowest residual solution |
| 322 |
minResidual = err |
| 323 |
nIterMin = it2d |
| 324 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 325 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 326 |
DO j=1,sNy |
| 327 |
DO i=1,sNx |
| 328 |
x2dm(i,j,bi,bj) = x2d(i,j,bi,bj) |
| 329 |
ENDDO |
| 330 |
ENDDO |
| 331 |
ENDDO |
| 332 |
ENDDO |
| 333 |
ENDIF |
| 334 |
|
| 335 |
#ifdef DEBUG_DIAG_CG2D |
| 336 |
CALL EXCH_XY_RL( r2d, myThid ) |
| 337 |
IF ( printResidFrq.GE.1 ) THEN |
| 338 |
WRITE(sufx,'(I10.10)') it2d |
| 339 |
CALL WRITE_FLD_XY_RL( 'r2d.',sufx, r2d, 1, myThid ) |
| 340 |
CALL WRITE_FLD_XY_RL( 'x2d.',sufx, x2d, 1, myThid ) |
| 341 |
ENDIF |
| 342 |
#else |
| 343 |
CALL EXCH_S3D_RL( r2d, 1, myThid ) |
| 344 |
#endif |
| 345 |
|
| 346 |
10 CONTINUE |
| 347 |
it2d = numIters |
| 348 |
11 CONTINUE |
| 349 |
|
| 350 |
C-- Return parameters to caller |
| 351 |
lastResidual = err |
| 352 |
numIters = it2d |
| 353 |
|
| 354 |
IF ( err .GT. minResidual ) THEN |
| 355 |
C- use the lowest residual solution (instead of current one <-> last residual) |
| 356 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 357 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 358 |
DO j=1,sNy |
| 359 |
DO i=1,sNx |
| 360 |
x2d(i,j,bi,bj) = x2dm(i,j,bi,bj) |
| 361 |
ENDDO |
| 362 |
ENDDO |
| 363 |
ENDDO |
| 364 |
ENDDO |
| 365 |
ENDIF |
| 366 |
c CALL EXCH_XY_RL( x2d, myThid ) |
| 367 |
|
| 368 |
#ifdef ALLOW_DEBUG |
| 369 |
IF (debugMode) CALL DEBUG_LEAVE('DIAG_CG2D',myThid) |
| 370 |
#endif |
| 371 |
|
| 372 |
RETURN |
| 373 |
END |
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