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C $Header: /u/gcmpack/MITgcm/model/src/cg2d.F,v 1.53 2009/07/11 22:00:40 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 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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C myThid :: Thread on which I am working. |
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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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#ifdef CG2D_SINGLECPU_SUM |
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_RL localBuf(1:sNx,1:sNy,nSx,nSy) |
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#endif |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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LOGICAL printResidual |
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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_RL( 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_RL( rhsMax, myThid ) |
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rhsMax=1. |
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#else |
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_GLOBAL_MAX_RL( 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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c CALL EXCH_XY_RL( cg2d_b, myThid ) |
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CALL EXCH_XY_RL( 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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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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cg2d_s(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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#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) |
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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) |
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& ) |
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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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#ifdef CG2D_SINGLECPU_SUM |
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localBuf(I,J,bi,bj) = cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
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#else |
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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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#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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CALL EXCH_S3D_RL( cg2d_r, 1, myThid ) |
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#ifdef CG2D_SINGLECPU_SUM |
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CALL GLOBAL_SUM_SINGLECPU_RL(localBuf, err, 0, 0, myThid) |
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CALL GLOBAL_SUM_SINGLECPU_RL(cg2d_b, sumRHS, OLx, OLy, myThid) |
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#else |
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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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#endif |
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err = SQRT(err) |
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actualIts = 0 |
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actualResidual = err |
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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 = printResidualFreq.GE.1 |
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WRITE(standardmessageunit,'(A,1P2E22.14)') |
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& ' cg2d: Sum(rhs),rhsMax = ', sumRHS,rhsMax |
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_END_MASTER( myThid ) |
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ENDIF |
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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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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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#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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cg2d_q(I,J,bi,bj) = |
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& pC(I ,J ,bi,bj)*cg2d_r(I ,J ,bi,bj) |
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& +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) |
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& +pS(I ,J ,bi,bj)*cg2d_r(I ,J-1,bi,bj) |
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& +pS(I ,J+1,bi,bj)*cg2d_r(I ,J+1,bi,bj) |
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CcnhDebugStarts |
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C cg2d_q(I,J,bi,bj) = cg2d_r(I ,J ,bi,bj) |
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CcnhDebugEnds |
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#ifdef CG2D_SINGLECPU_SUM |
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localBuf(I,J,bi,bj) = |
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& cg2d_q(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
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#else |
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eta_qrNtile(bi,bj) = eta_qrNtile(bi,bj) |
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& +cg2d_q(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
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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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|
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#ifdef CG2D_SINGLECPU_SUM |
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CALL GLOBAL_SUM_SINGLECPU_RL( localBuf,eta_qrN,0,0,myThid ) |
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#else |
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CALL GLOBAL_SUM_TILE_RL( eta_qrNtile,eta_qrN,myThid ) |
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#endif |
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CcnhDebugStarts |
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C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' eta_qrN = ',eta_qrN |
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CcnhDebugEnds |
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cgBeta = eta_qrN/eta_qrNM1 |
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CcnhDebugStarts |
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C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' beta = ',cgBeta |
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CcnhDebugEnds |
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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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cg2d_s(I,J,bi,bj) = cg2d_q(I,J,bi,bj) |
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& + cgBeta*cg2d_s(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( cg2d_s, 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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#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 |
| 308 |
DO I=1,sNx |
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c ks = kSurfC(I,J,bi,bj) |
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cg2d_q(I,J,bi,bj) = |
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& aW2d(I ,J ,bi,bj)*cg2d_s(I-1,J ,bi,bj) |
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& +aW2d(I+1,J ,bi,bj)*cg2d_s(I+1,J ,bi,bj) |
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& +aS2d(I ,J ,bi,bj)*cg2d_s(I ,J-1,bi,bj) |
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& +aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J+1,bi,bj) |
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& +aC2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
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c & -aW2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 317 |
c & -aW2d(I+1,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 318 |
c & -aS2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 319 |
c & -aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 320 |
c & -freeSurfFac*_rA(i,j,bi,bj)*deepFac2F(ks)*recip_Bo(i,j,bi,bj) |
| 321 |
c & *cg2d_s(I ,J ,bi,bj) |
| 322 |
c & /deltaTMom/deltaTfreesurf*cg2dNorm |
| 323 |
#ifdef CG2D_SINGLECPU_SUM |
| 324 |
localBuf(I,J,bi,bj) = cg2d_s(I,J,bi,bj)*cg2d_q(I,J,bi,bj) |
| 325 |
#else |
| 326 |
alphaTile(bi,bj) = alphaTile(bi,bj) |
| 327 |
& + cg2d_s(I,J,bi,bj)*cg2d_q(I,J,bi,bj) |
| 328 |
#endif |
| 329 |
ENDDO |
| 330 |
ENDDO |
| 331 |
ENDDO |
| 332 |
ENDDO |
| 333 |
#ifdef CG2D_SINGLECPU_SUM |
| 334 |
CALL GLOBAL_SUM_SINGLECPU_RL(localBuf, alpha, 0, 0, myThid) |
| 335 |
#else |
| 336 |
CALL GLOBAL_SUM_TILE_RL( alphaTile, alpha, myThid ) |
| 337 |
#endif |
| 338 |
CcnhDebugStarts |
| 339 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' SUM(s*q)= ',alpha |
| 340 |
CcnhDebugEnds |
| 341 |
alpha = eta_qrN/alpha |
| 342 |
CcnhDebugStarts |
| 343 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' alpha= ',alpha |
| 344 |
CcnhDebugEnds |
| 345 |
|
| 346 |
C== Update solution and residual vectors |
| 347 |
C Now compute "interior" points. |
| 348 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 349 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 350 |
errTile(bi,bj) = 0. _d 0 |
| 351 |
DO J=1,sNy |
| 352 |
DO I=1,sNx |
| 353 |
cg2d_x(I,J,bi,bj)=cg2d_x(I,J,bi,bj)+alpha*cg2d_s(I,J,bi,bj) |
| 354 |
cg2d_r(I,J,bi,bj)=cg2d_r(I,J,bi,bj)-alpha*cg2d_q(I,J,bi,bj) |
| 355 |
#ifdef CG2D_SINGLECPU_SUM |
| 356 |
localBuf(I,J,bi,bj) = cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 357 |
#else |
| 358 |
errTile(bi,bj) = errTile(bi,bj) |
| 359 |
& + cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 360 |
#endif |
| 361 |
ENDDO |
| 362 |
ENDDO |
| 363 |
ENDDO |
| 364 |
ENDDO |
| 365 |
|
| 366 |
#ifdef CG2D_SINGLECPU_SUM |
| 367 |
CALL GLOBAL_SUM_SINGLECPU_RL(localBuf, err, 0, 0, myThid) |
| 368 |
#else |
| 369 |
CALL GLOBAL_SUM_TILE_RL( errTile, err, myThid ) |
| 370 |
#endif |
| 371 |
err = SQRT(err) |
| 372 |
actualIts = it2d |
| 373 |
actualResidual = err |
| 374 |
IF ( printResidual ) THEN |
| 375 |
IF ( MOD( it2d-1, printResidualFreq ).EQ.0 ) THEN |
| 376 |
WRITE(msgBuf,'(A,I6,A,1PE21.14)') |
| 377 |
& ' cg2d: iter=', actualIts, ' ; resid.= ', actualResidual |
| 378 |
CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
| 379 |
& SQUEEZE_RIGHT, myThid ) |
| 380 |
ENDIF |
| 381 |
ENDIF |
| 382 |
IF ( err .LT. cg2dTolerance ) GOTO 11 |
| 383 |
|
| 384 |
CALL EXCH_S3D_RL( cg2d_r, 1, myThid ) |
| 385 |
|
| 386 |
10 CONTINUE |
| 387 |
11 CONTINUE |
| 388 |
|
| 389 |
IF (cg2dNormaliseRHS) THEN |
| 390 |
C-- Un-normalise the answer |
| 391 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 392 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 393 |
DO J=1,sNy |
| 394 |
DO I=1,sNx |
| 395 |
cg2d_x(I ,J ,bi,bj) = cg2d_x(I ,J ,bi,bj)/rhsNorm |
| 396 |
ENDDO |
| 397 |
ENDDO |
| 398 |
ENDDO |
| 399 |
ENDDO |
| 400 |
ENDIF |
| 401 |
|
| 402 |
C The following exchange was moved up to solve_for_pressure |
| 403 |
C for compatibility with TAMC. |
| 404 |
C _EXCH_XY_RL(cg2d_x, myThid ) |
| 405 |
|
| 406 |
C-- Return parameters to caller |
| 407 |
lastResidual = actualResidual |
| 408 |
numIters = actualIts |
| 409 |
|
| 410 |
CcnhDebugStarts |
| 411 |
C CALL PLOT_FIELD_XYRL( cg2d_x, 'CALC_MOM_RHS CG2D_X' , 1, myThid ) |
| 412 |
C err = 0. _d 0 |
| 413 |
C DO bj=myByLo(myThid),myByHi(myThid) |
| 414 |
C DO bi=myBxLo(myThid),myBxHi(myThid) |
| 415 |
C DO J=1,sNy |
| 416 |
C DO I=1,sNx |
| 417 |
C cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
| 418 |
C & (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
| 419 |
C & +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
| 420 |
C & +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
| 421 |
C & +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
| 422 |
C & -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 423 |
C & -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 424 |
C & -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 425 |
C & -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj)) |
| 426 |
C err = err + |
| 427 |
C & cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 428 |
C ENDDO |
| 429 |
C ENDDO |
| 430 |
C ENDDO |
| 431 |
C ENDDO |
| 432 |
C _GLOBAL_SUM_RL( err , myThid ) |
| 433 |
C write(*,*) 'cg2d: Ax - b = ',SQRT(err) |
| 434 |
CcnhDebugEnds |
| 435 |
|
| 436 |
RETURN |
| 437 |
END |
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