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jmc |
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C $Header: /u/gcmpack/MITgcm/model/src/cg2d.F,v 1.54 2011/06/08 01:46:34 jmc Exp $ |
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C $Name: $ |
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#include "DIAG_OPTIONS.h" |
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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 residCriter, |
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O firstResidual, lastResidual, |
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U x2d, numIters, |
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I 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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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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c#include "CG2D.h" |
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c#include "GRID.h" |
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c#include "SURFACE.h" |
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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 firstResidual :: the initial residual before any iterations |
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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 myThid :: Thread on which I am working. |
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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 firstResidual |
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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 myThid |
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C !LOCAL VARIABLES: |
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C === Local variables ==== |
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C actualIts :: Number of iterations taken |
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C actualResidual :: residual |
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C bi, bj :: Block index in X and Y. |
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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 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 actualIts |
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_RL actualResidual |
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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(1-1:sNx+1,1-1:sNy+1,nSx,nSy) |
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_RL r2d(1-1:sNx+1,1-1:sNy+1,nSx,nSy) |
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_RL s2d(1-1:sNx+1,1-1:sNy+1,nSx,nSy) |
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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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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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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) |
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& /( (cg2dpcOffDFac*pW_tmp)**2 ) |
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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) |
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& /( (cg2dpcOffDFac*pS_tmp)**2 ) |
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ENDIF |
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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-- Initialise inverter |
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eta_qrNM1 = 1. _d 0 |
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CALL EXCH_XY_RL( x2d, myThid ) |
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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=1-1,sNy+1 |
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DO i=1-1,sNx+1 |
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s2d(i,j,bi,bj) = 0. |
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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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CALL EXCH_S3D_RL( r2d, 1, myThid ) |
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CALL GLOBAL_SUM_TILE_RL( errTile, err, myThid ) |
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CALL GLOBAL_SUM_TILE_RL( sumRHStile, sumRHS, myThid ) |
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err = SQRT(err) |
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actualIts = 0 |
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actualResidual = err |
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firstResidual = err |
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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 = printResidualFreq.GE.1 |
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c WRITE(standardmessageunit,'(A,1P2E22.14)') |
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c & ' diag_cg2d: Sum(rhs),rhsMax = ', sumRHS, rhsMax |
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_END_MASTER( myThid ) |
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ENDIF |
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IF ( err .LT. residCriter ) GOTO 11 |
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C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
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DO 10 it2d=1, numIters |
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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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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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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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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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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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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 |
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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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CALL GLOBAL_SUM_TILE_RL( errTile, err, myThid ) |
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err = SQRT(err) |
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actualIts = it2d |
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actualResidual = err |
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IF ( printResidual ) THEN |
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IF ( MOD( it2d-1, printResidualFreq ).EQ.0 ) THEN |
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WRITE(msgBuf,'(A,I6,A,1PE21.14)') |
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& ' diag_cg2d: iter=', actualIts, ' ; resid.= ', actualResidual |
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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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ENDIF |
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IF ( err .LT. residCriter ) GOTO 11 |
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CALL EXCH_S3D_RL( r2d, 1, myThid ) |
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10 CONTINUE |
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11 CONTINUE |
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c CALL EXCH_XY_RL( x2d, myThid ) |
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C-- Return parameters to caller |
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lastResidual = actualResidual |
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numIters = actualIts |
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RETURN |
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END |
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