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C $Header: /u/gcmpack/models/MITgcmUV/model/src/cg2d.F,v 1.33 2001/05/29 14:01:36 adcroft Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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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 "GRID.h" |
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#include "CG2D.h" |
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#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 - Block index in X and Y. |
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C bj |
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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, N - Loop counters ( N 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 |
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_RL eta_qrN |
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_RL eta_qrNM1 |
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_RL cgBeta |
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_RL alpha |
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_RL sumRHS |
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_RL rhsMax |
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_RL rhsNorm |
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|
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INTEGER OLw |
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INTEGER OLe |
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INTEGER OLn |
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INTEGER OLs |
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INTEGER exchWidthX |
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INTEGER exchWidthY |
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INTEGER myNz |
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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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Catm rhsMax=1. |
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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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DO J=1,sNy |
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DO I=1,sNx |
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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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& -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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& -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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& -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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& -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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& -freeSurfFac*_rA(i,j,bi,bj)*recip_Bo(i,j,bi,bj)* |
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& cg2d_x(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
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& ) |
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err = err + |
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& cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
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sumRHS = sumRHS + |
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& cg2d_b(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 _EXCH_XY_R8( cg2d_r, myThid ) |
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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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OLw = 1 |
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OLe = 1 |
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OLn = 1 |
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OLs = 1 |
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exchWidthX = 1 |
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exchWidthY = 1 |
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myNz = 1 |
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IF (useCubedSphereExchange) THEN |
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CALL EXCH_RL_CUBE( cg2d_r, |
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I OLw, OLe, OLs, OLn, myNz, |
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I exchWidthX, exchWidthY, |
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I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
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ELSE |
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CALL EXCH_RL( cg2d_r, |
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I OLw, OLe, OLs, OLn, myNz, |
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I exchWidthX, exchWidthY, |
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I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
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ENDIF |
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#endif |
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C _EXCH_XY_R8( cg2d_s, myThid ) |
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#ifdef LETS_MAKE_JAM |
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CALL EXCH_XY_O1_R8_JAM( cg2d_s ) |
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#else |
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OLw = 1 |
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OLe = 1 |
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OLn = 1 |
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OLs = 1 |
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exchWidthX = 1 |
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exchWidthY = 1 |
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myNz = 1 |
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IF (useCubedSphereExchange) THEN |
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CALL EXCH_RL_CUBE( cg2d_s, |
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I OLw, OLe, OLs, OLn, myNz, |
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I exchWidthX, exchWidthY, |
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I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
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ELSE |
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CALL EXCH_RL( cg2d_s, |
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I OLw, OLe, OLs, OLn, myNz, |
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I exchWidthX, exchWidthY, |
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I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
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ENDIF |
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#endif |
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_GLOBAL_SUM_R8( sumRHS, myThid ) |
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_GLOBAL_SUM_R8( err , myThid ) |
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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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_BEGIN_MASTER( myThid ) |
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write(*,'(A,1P2E22.14)')' cg2d: Sum(rhs),rhsMax = ', |
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& sumRHS,rhsMax |
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_END_MASTER( ) |
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C _BARRIER |
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c _BEGIN_MASTER( myThid ) |
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c WRITE(*,'(A,I6,1PE30.14)') ' CG2D iters, err = ', |
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c & actualIts, actualResidual |
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c _END_MASTER( ) |
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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". |
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eta_qrN = 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_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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eta_qrN = eta_qrN |
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& +cg2d_q(I,J,bi,bj)*cg2d_r(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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_GLOBAL_SUM_R8(eta_qrN, myThid) |
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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 |
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C-- processes. |
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C _EXCH_XY_R8( cg2d_s, myThid ) |
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#ifdef LETS_MAKE_JAM |
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CALL EXCH_XY_O1_R8_JAM( cg2d_s ) |
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#else |
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OLw = 1 |
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OLe = 1 |
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OLn = 1 |
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OLs = 1 |
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exchWidthX = 1 |
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exchWidthY = 1 |
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myNz = 1 |
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IF (useCubedSphereExchange) THEN |
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CALL EXCH_RL_CUBE( cg2d_s, |
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I OLw, OLe, OLs, OLn, myNz, |
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I exchWidthX, exchWidthY, |
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I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
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ELSE |
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CALL EXCH_RL( cg2d_s, |
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I OLw, OLe, OLs, OLn, myNz, |
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I exchWidthX, exchWidthY, |
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I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
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ENDIF |
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#endif |
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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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alpha = 0. _d 0 |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
| 343 |
DO J=1,sNy |
| 344 |
DO I=1,sNx |
| 345 |
cg2d_q(I,J,bi,bj) = |
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& aW2d(I ,J ,bi,bj)*cg2d_s(I-1,J ,bi,bj) |
| 347 |
& +aW2d(I+1,J ,bi,bj)*cg2d_s(I+1,J ,bi,bj) |
| 348 |
& +aS2d(I ,J ,bi,bj)*cg2d_s(I ,J-1,bi,bj) |
| 349 |
& +aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J+1,bi,bj) |
| 350 |
& -aW2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 351 |
& -aW2d(I+1,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 352 |
& -aS2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 353 |
& -aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 354 |
& -freeSurfFac*_rA(i,j,bi,bj)*recip_Bo(i,j,bi,bj)* |
| 355 |
& cg2d_s(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
| 356 |
alpha = alpha+cg2d_s(I,J,bi,bj)*cg2d_q(I,J,bi,bj) |
| 357 |
ENDDO |
| 358 |
ENDDO |
| 359 |
ENDDO |
| 360 |
ENDDO |
| 361 |
_GLOBAL_SUM_R8(alpha,myThid) |
| 362 |
CcnhDebugStarts |
| 363 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' SUM(s*q)= ',alpha |
| 364 |
CcnhDebugEnds |
| 365 |
alpha = eta_qrN/alpha |
| 366 |
CcnhDebugStarts |
| 367 |
C WRITE(*,*) ' CG2D: Iteration ',it2d-1,' alpha= ',alpha |
| 368 |
CcnhDebugEnds |
| 369 |
|
| 370 |
C== Update solution and residual vectors |
| 371 |
C Now compute "interior" points. |
| 372 |
err = 0. _d 0 |
| 373 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 374 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 375 |
DO J=1,sNy |
| 376 |
DO I=1,sNx |
| 377 |
cg2d_x(I,J,bi,bj)=cg2d_x(I,J,bi,bj)+alpha*cg2d_s(I,J,bi,bj) |
| 378 |
cg2d_r(I,J,bi,bj)=cg2d_r(I,J,bi,bj)-alpha*cg2d_q(I,J,bi,bj) |
| 379 |
err = err+cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 380 |
ENDDO |
| 381 |
ENDDO |
| 382 |
ENDDO |
| 383 |
ENDDO |
| 384 |
|
| 385 |
_GLOBAL_SUM_R8( err , myThid ) |
| 386 |
err = SQRT(err) |
| 387 |
actualIts = it2d |
| 388 |
actualResidual = err |
| 389 |
IF ( err .LT. cg2dTolerance ) GOTO 11 |
| 390 |
C _EXCH_XY_R8(cg2d_r, myThid ) |
| 391 |
#ifdef LETS_MAKE_JAM |
| 392 |
CALL EXCH_XY_O1_R8_JAM( cg2d_r ) |
| 393 |
#else |
| 394 |
OLw = 1 |
| 395 |
OLe = 1 |
| 396 |
OLn = 1 |
| 397 |
OLs = 1 |
| 398 |
exchWidthX = 1 |
| 399 |
exchWidthY = 1 |
| 400 |
myNz = 1 |
| 401 |
IF (useCubedSphereExchange) THEN |
| 402 |
CALL EXCH_RL_CUBE( cg2d_r, |
| 403 |
I OLw, OLe, OLs, OLn, myNz, |
| 404 |
I exchWidthX, exchWidthY, |
| 405 |
I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
| 406 |
ELSE |
| 407 |
CALL EXCH_RL( cg2d_r, |
| 408 |
I OLw, OLe, OLs, OLn, myNz, |
| 409 |
I exchWidthX, exchWidthY, |
| 410 |
I FORWARD_SIMULATION, EXCH_UPDATE_CORNERS, myThid ) |
| 411 |
ENDIF |
| 412 |
#endif |
| 413 |
|
| 414 |
10 CONTINUE |
| 415 |
11 CONTINUE |
| 416 |
|
| 417 |
IF (cg2dNormaliseRHS) THEN |
| 418 |
C-- Un-normalise the answer |
| 419 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 420 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 421 |
DO J=1,sNy |
| 422 |
DO I=1,sNx |
| 423 |
cg2d_x(I ,J ,bi,bj) = cg2d_x(I ,J ,bi,bj)/rhsNorm |
| 424 |
ENDDO |
| 425 |
ENDDO |
| 426 |
ENDDO |
| 427 |
ENDDO |
| 428 |
ENDIF |
| 429 |
|
| 430 |
C The following exchange was moved up to solve_for_pressure |
| 431 |
C for compatibility with TAMC. |
| 432 |
C _EXCH_XY_R8(cg2d_x, myThid ) |
| 433 |
c _BEGIN_MASTER( myThid ) |
| 434 |
c WRITE(*,'(A,I6,1PE30.14)') ' CG2D iters, err = ', |
| 435 |
c & actualIts, actualResidual |
| 436 |
c _END_MASTER( ) |
| 437 |
|
| 438 |
C-- Return parameters to caller |
| 439 |
lastResidual=actualResidual |
| 440 |
numIters=actualIts |
| 441 |
|
| 442 |
CcnhDebugStarts |
| 443 |
C CALL PLOT_FIELD_XYRL( cg2d_x, 'CALC_MOM_RHS CG2D_X' , 1, myThid ) |
| 444 |
C err = 0. _d 0 |
| 445 |
C DO bj=myByLo(myThid),myByHi(myThid) |
| 446 |
C DO bi=myBxLo(myThid),myBxHi(myThid) |
| 447 |
C DO J=1,sNy |
| 448 |
C DO I=1,sNx |
| 449 |
C cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
| 450 |
C & (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
| 451 |
C & +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
| 452 |
C & +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
| 453 |
C & +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
| 454 |
C & -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 455 |
C & -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 456 |
C & -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 457 |
C & -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj)) |
| 458 |
C err = err + |
| 459 |
C & cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 460 |
C ENDDO |
| 461 |
C ENDDO |
| 462 |
C ENDDO |
| 463 |
C ENDDO |
| 464 |
C _GLOBAL_SUM_R8( err , myThid ) |
| 465 |
C write(*,*) 'cg2d: Ax - b = ',SQRT(err) |
| 466 |
CcnhDebugEnds |
| 467 |
|
| 468 |
RETURN |
| 469 |
END |
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