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C $Header: /u/gcmpack/MITgcm/model/src/cg2d.F,v 1.48 2007/09/04 14:54:57 jmc Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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#ifdef TARGET_NEC_SX |
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C set a sensible default for the outer loop unrolling parameter that can |
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C be overriden in the Makefile with the DEFINES macro or in CPP_OPTIONS.h |
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#ifndef CG2D_OUTERLOOPITERS |
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# define CG2D_OUTERLOOPITERS 10 |
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#endif |
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#endif /* TARGET_NEC_SX */ |
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|
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CBOP |
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C !ROUTINE: CG2D |
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C !INTERFACE: |
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SUBROUTINE CG2D( |
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I cg2d_b, |
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U cg2d_x, |
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O firstResidual, |
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O lastResidual, |
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U 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 | Notes: |
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C | ====== |
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C | This implementation can support shared-memory |
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C | multi-threaded execution. In order to do this COMMON |
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C | blocks are used for many of the arrays - even ones that |
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C | are only used for intermedaite results. This design is |
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C | OK if you want to all the threads to collaborate on |
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C | solving the same problem. On the other hand if you want |
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C | the threads to solve several different problems |
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C | concurrently this implementation will not work. |
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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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#include "CG2D.h" |
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c#include "GRID.h" |
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c#include "SURFACE.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 myThid :: Thread on which I am working. |
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C cg2d_b :: The source term or "right hand side" |
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C cg2d_x :: 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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_RL cg2d_b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL cg2d_x(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL firstResidual |
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_RL lastResidual |
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INTEGER numIters |
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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 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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c INTEGER ks |
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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 rhsMax |
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_RL rhsNorm |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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CEOP |
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|
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|
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CcnhDebugStarts |
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C CHARACTER*(MAX_LEN_FNAM) suff |
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CcnhDebugEnds |
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|
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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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CcnhDebugStarts |
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C _EXCH_XY_R8( cg2d_b, myThid ) |
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C CALL PLOT_FIELD_XYRL( cg2d_b, 'CG2D.0 CG2D_B' , 1, myThid ) |
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C suff = 'unnormalised' |
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C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
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C STOP |
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CcnhDebugEnds |
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|
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C-- Normalise RHS |
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rhsMax = 0. _d 0 |
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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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cg2d_b(I,J,bi,bj) = cg2d_b(I,J,bi,bj)*cg2dNorm |
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rhsMax = MAX(ABS(cg2d_b(I,J,bi,bj)),rhsMax) |
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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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IF (cg2dNormaliseRHS) THEN |
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C- Normalise RHS : |
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#ifdef LETS_MAKE_JAM |
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C _GLOBAL_MAX_R8( rhsMax, myThid ) |
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rhsMax=1. |
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#else |
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_GLOBAL_MAX_R8( rhsMax, myThid ) |
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#endif |
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rhsNorm = 1. _d 0 |
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IF ( rhsMax .NE. 0. ) rhsNorm = 1. _d 0 / rhsMax |
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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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cg2d_b(I,J,bi,bj) = cg2d_b(I,J,bi,bj)*rhsNorm |
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cg2d_x(I,J,bi,bj) = cg2d_x(I,J,bi,bj)*rhsNorm |
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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- end Normalise RHS |
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ENDIF |
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|
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C-- Update overlaps |
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_EXCH_XY_R8( cg2d_b, myThid ) |
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_EXCH_XY_R8( cg2d_x, myThid ) |
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CcnhDebugStarts |
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C CALL PLOT_FIELD_XYRL( cg2d_b, 'CG2D.1 CG2D_B' , 1, myThid ) |
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C suff = 'normalised' |
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C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
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CcnhDebugEnds |
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|
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C-- Initial residual calculation |
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err = 0. _d 0 |
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sumRHS = 0. _d 0 |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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sumRHStile(bi,bj) = 0. _d 0 |
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errTile(bi,bj) = 0. _d 0 |
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#ifdef TARGET_NEC_SX |
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!CDIR OUTERUNROLL=CG2D_OUTERLOOPITERS |
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#endif /* TARGET_NEC_SX */ |
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DO J=1,sNy |
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DO I=1,sNx |
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c ks = ksurfC(I,J,bi,bj) |
180 |
cg2d_s(I,J,bi,bj) = 0. |
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cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
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& (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
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& +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
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& +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
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& +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
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& +aC2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
187 |
& ) |
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c & -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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c & -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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c & -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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c & -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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c & -freeSurfFac*_rA(i,j,bi,bj)*deepFac2F(ks)*recip_Bo(i,j,bi,bj) |
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c & *cg2d_x(I ,J ,bi,bj) |
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c & /deltaTMom/deltaTfreesurf*cg2dNorm |
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c & ) |
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errTile(bi,bj) = errTile(bi,bj) |
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& + cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
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sumRHStile(bi,bj) = sumRHStile(bi,bj) + cg2d_b(I,J,bi,bj) |
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ENDDO |
200 |
ENDDO |
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c sumRHS = sumRHS + sumRHStile(bi,bj) |
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c err = err + errTile(bi,bj) |
203 |
ENDDO |
204 |
ENDDO |
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#ifdef LETS_MAKE_JAM |
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CALL EXCH_XY_O1_R8_JAM( cg2d_r ) |
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#else |
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CALL EXCH_XY_RL( cg2d_r, myThid ) |
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#endif |
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#ifdef LETS_MAKE_JAM |
211 |
CALL EXCH_XY_O1_R8_JAM( cg2d_s ) |
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#else |
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CALL EXCH_XY_RL( cg2d_s, myThid ) |
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#endif |
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c _GLOBAL_SUM_R8( sumRHS, myThid ) |
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c _GLOBAL_SUM_R8( err , myThid ) |
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CALL GLOBAL_SUM_TILE_RL( sumRHStile, sumRHS, myThid ) |
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CALL GLOBAL_SUM_TILE_RL( errTile, err, myThid ) |
219 |
err = SQRT(err) |
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actualIts = 0 |
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actualResidual = err |
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|
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IF ( debugLevel .GE. debLevZero ) THEN |
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_BEGIN_MASTER( myThid ) |
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WRITE(standardmessageunit,'(A,1P2E22.14)') |
226 |
& ' cg2d: Sum(rhs),rhsMax = ', sumRHS,rhsMax |
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_END_MASTER( myThid ) |
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ENDIF |
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C _BARRIER |
230 |
c _BEGIN_MASTER( myThid ) |
231 |
c WRITE(standardmessageunit,'(A,I6,1PE30.14)') |
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c & ' CG2D iters, err = ', |
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c & actualIts, actualResidual |
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c _END_MASTER( myThid ) |
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firstResidual=actualResidual |
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|
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IF ( err .LT. cg2dTolerance ) 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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CcnhDebugStarts |
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C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' residual = ', |
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C & actualResidual |
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CcnhDebugEnds |
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C-- Solve preconditioning equation and update |
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C-- conjugate direction vector "s". |
248 |
eta_qrN = 0. _d 0 |
249 |
DO bj=myByLo(myThid),myByHi(myThid) |
250 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
251 |
eta_qrNtile(bi,bj) = 0. _d 0 |
252 |
#ifdef TARGET_NEC_SX |
253 |
!CDIR OUTERUNROLL=CG2D_OUTERLOOPITERS |
254 |
#endif /* TARGET_NEC_SX */ |
255 |
DO J=1,sNy |
256 |
DO I=1,sNx |
257 |
cg2d_q(I,J,bi,bj) = |
258 |
& pC(I ,J ,bi,bj)*cg2d_r(I ,J ,bi,bj) |
259 |
& +pW(I ,J ,bi,bj)*cg2d_r(I-1,J ,bi,bj) |
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& +pW(I+1,J ,bi,bj)*cg2d_r(I+1,J ,bi,bj) |
261 |
& +pS(I ,J ,bi,bj)*cg2d_r(I ,J-1,bi,bj) |
262 |
& +pS(I ,J+1,bi,bj)*cg2d_r(I ,J+1,bi,bj) |
263 |
CcnhDebugStarts |
264 |
C cg2d_q(I,J,bi,bj) = cg2d_r(I ,J ,bi,bj) |
265 |
CcnhDebugEnds |
266 |
eta_qrNtile(bi,bj) = eta_qrNtile(bi,bj) |
267 |
& +cg2d_q(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
268 |
ENDDO |
269 |
ENDDO |
270 |
c eta_qrN = eta_qrN + eta_qrNtile(bi,bj) |
271 |
ENDDO |
272 |
ENDDO |
273 |
|
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c _GLOBAL_SUM_R8(eta_qrN, myThid) |
275 |
CALL GLOBAL_SUM_TILE_RL( eta_qrNtile,eta_qrN,myThid ) |
276 |
CcnhDebugStarts |
277 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' eta_qrN = ',eta_qrN |
278 |
CcnhDebugEnds |
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cgBeta = eta_qrN/eta_qrNM1 |
280 |
CcnhDebugStarts |
281 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' beta = ',cgBeta |
282 |
CcnhDebugEnds |
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eta_qrNM1 = eta_qrN |
284 |
|
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DO bj=myByLo(myThid),myByHi(myThid) |
286 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
287 |
DO J=1,sNy |
288 |
DO I=1,sNx |
289 |
cg2d_s(I,J,bi,bj) = cg2d_q(I,J,bi,bj) |
290 |
& + cgBeta*cg2d_s(I,J,bi,bj) |
291 |
ENDDO |
292 |
ENDDO |
293 |
ENDDO |
294 |
ENDDO |
295 |
|
296 |
C-- Do exchanges that require messages i.e. between |
297 |
C-- processes. |
298 |
C _EXCH_XY_R8( cg2d_s, myThid ) |
299 |
#ifdef LETS_MAKE_JAM |
300 |
CALL EXCH_XY_O1_R8_JAM( cg2d_s ) |
301 |
#else |
302 |
CALL EXCH_XY_RL( cg2d_s, myThid ) |
303 |
#endif |
304 |
|
305 |
C== Evaluate laplace operator on conjugate gradient vector |
306 |
C== q = A.s |
307 |
alpha = 0. _d 0 |
308 |
DO bj=myByLo(myThid),myByHi(myThid) |
309 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
310 |
alphaTile(bi,bj) = 0. _d 0 |
311 |
#ifdef TARGET_NEC_SX |
312 |
!CDIR OUTERUNROLL=CG2D_OUTERLOOPITERS |
313 |
#endif /* TARGET_NEC_SX */ |
314 |
DO J=1,sNy |
315 |
DO I=1,sNx |
316 |
c ks = ksurfC(I,J,bi,bj) |
317 |
cg2d_q(I,J,bi,bj) = |
318 |
& aW2d(I ,J ,bi,bj)*cg2d_s(I-1,J ,bi,bj) |
319 |
& +aW2d(I+1,J ,bi,bj)*cg2d_s(I+1,J ,bi,bj) |
320 |
& +aS2d(I ,J ,bi,bj)*cg2d_s(I ,J-1,bi,bj) |
321 |
& +aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J+1,bi,bj) |
322 |
& +aC2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
323 |
c & -aW2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
324 |
c & -aW2d(I+1,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
325 |
c & -aS2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
326 |
c & -aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J ,bi,bj) |
327 |
c & -freeSurfFac*_rA(i,j,bi,bj)*deepFac2F(ks)*recip_Bo(i,j,bi,bj) |
328 |
c & *cg2d_s(I ,J ,bi,bj) |
329 |
c & /deltaTMom/deltaTfreesurf*cg2dNorm |
330 |
alphaTile(bi,bj) = alphaTile(bi,bj) |
331 |
& + cg2d_s(I,J,bi,bj)*cg2d_q(I,J,bi,bj) |
332 |
ENDDO |
333 |
ENDDO |
334 |
c alpha = alpha + alphaTile(bi,bj) |
335 |
ENDDO |
336 |
ENDDO |
337 |
c _GLOBAL_SUM_R8(alpha,myThid) |
338 |
CALL GLOBAL_SUM_TILE_RL( alphaTile, alpha, myThid ) |
339 |
CcnhDebugStarts |
340 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' SUM(s*q)= ',alpha |
341 |
CcnhDebugEnds |
342 |
alpha = eta_qrN/alpha |
343 |
CcnhDebugStarts |
344 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' alpha= ',alpha |
345 |
CcnhDebugEnds |
346 |
|
347 |
C== Update solution and residual vectors |
348 |
C Now compute "interior" points. |
349 |
err = 0. _d 0 |
350 |
DO bj=myByLo(myThid),myByHi(myThid) |
351 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
352 |
errTile(bi,bj) = 0. _d 0 |
353 |
DO J=1,sNy |
354 |
DO I=1,sNx |
355 |
cg2d_x(I,J,bi,bj)=cg2d_x(I,J,bi,bj)+alpha*cg2d_s(I,J,bi,bj) |
356 |
cg2d_r(I,J,bi,bj)=cg2d_r(I,J,bi,bj)-alpha*cg2d_q(I,J,bi,bj) |
357 |
errTile(bi,bj) = errTile(bi,bj) |
358 |
& + cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
359 |
ENDDO |
360 |
ENDDO |
361 |
c err = err + errTile(bi,bj) |
362 |
ENDDO |
363 |
ENDDO |
364 |
|
365 |
c _GLOBAL_SUM_R8( err , myThid ) |
366 |
CALL GLOBAL_SUM_TILE_RL( errTile, err, myThid ) |
367 |
err = SQRT(err) |
368 |
actualIts = it2d |
369 |
actualResidual = err |
370 |
IF ( debugLevel.GT.debLevB ) THEN |
371 |
c IF ( DIFFERENT_MULTIPLE(monitorFreq,myTime,deltaTClock) |
372 |
c & ) THEN |
373 |
_BEGIN_MASTER( myThid ) |
374 |
WRITE(msgBuf,'(A,I6,A,1PE21.14)') |
375 |
& ' cg2d: iter=', actualIts, ' ; resid.= ', actualResidual |
376 |
CALL PRINT_MESSAGE(msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1) |
377 |
_END_MASTER( myThid ) |
378 |
c ENDIF |
379 |
ENDIF |
380 |
IF ( err .LT. cg2dTolerance ) GOTO 11 |
381 |
|
382 |
#ifdef LETS_MAKE_JAM |
383 |
CALL EXCH_XY_O1_R8_JAM( cg2d_r ) |
384 |
#else |
385 |
CALL EXCH_XY_RL( cg2d_r, myThid ) |
386 |
#endif |
387 |
|
388 |
10 CONTINUE |
389 |
11 CONTINUE |
390 |
|
391 |
IF (cg2dNormaliseRHS) THEN |
392 |
C-- Un-normalise the answer |
393 |
DO bj=myByLo(myThid),myByHi(myThid) |
394 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
395 |
DO J=1,sNy |
396 |
DO I=1,sNx |
397 |
cg2d_x(I ,J ,bi,bj) = cg2d_x(I ,J ,bi,bj)/rhsNorm |
398 |
ENDDO |
399 |
ENDDO |
400 |
ENDDO |
401 |
ENDDO |
402 |
ENDIF |
403 |
|
404 |
C The following exchange was moved up to solve_for_pressure |
405 |
C for compatibility with TAMC. |
406 |
C _EXCH_XY_R8(cg2d_x, myThid ) |
407 |
c _BEGIN_MASTER( myThid ) |
408 |
c WRITE(*,'(A,I6,1PE30.14)') ' CG2D iters, err = ', |
409 |
c & actualIts, actualResidual |
410 |
c _END_MASTER( myThid ) |
411 |
|
412 |
C-- Return parameters to caller |
413 |
lastResidual=actualResidual |
414 |
numIters=actualIts |
415 |
|
416 |
CcnhDebugStarts |
417 |
C CALL PLOT_FIELD_XYRL( cg2d_x, 'CALC_MOM_RHS CG2D_X' , 1, myThid ) |
418 |
C err = 0. _d 0 |
419 |
C DO bj=myByLo(myThid),myByHi(myThid) |
420 |
C DO bi=myBxLo(myThid),myBxHi(myThid) |
421 |
C DO J=1,sNy |
422 |
C DO I=1,sNx |
423 |
C cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
424 |
C & (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
425 |
C & +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
426 |
C & +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
427 |
C & +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
428 |
C & -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
429 |
C & -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
430 |
C & -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
431 |
C & -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj)) |
432 |
C err = err + |
433 |
C & cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
434 |
C ENDDO |
435 |
C ENDDO |
436 |
C ENDDO |
437 |
C ENDDO |
438 |
C _GLOBAL_SUM_R8( err , myThid ) |
439 |
C write(*,*) 'cg2d: Ax - b = ',SQRT(err) |
440 |
CcnhDebugEnds |
441 |
|
442 |
RETURN |
443 |
END |