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cnh |
1.13 |
C $Header: /u/gcmpack/models/MITgcmUV/model/src/cg2d.F,v 1.12 1998/09/08 01:37:49 cnh Exp $ |
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cnh |
1.1 |
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#include "CPP_EEOPTIONS.h" |
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SUBROUTINE CG2D( |
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I myThid ) |
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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 === 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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cnh |
1.4 |
#include "GRID.h" |
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cnh |
1.1 |
#include "CG2D.h" |
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C === Routine arguments === |
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C myThid - Thread on which I am working. |
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INTEGER myThid |
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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 etaN - Used in computing search directions |
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C etaNM1 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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REAL actualResidual |
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INTEGER bi, bj |
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INTEGER I, J, it2d |
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REAL err |
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REAL etaN |
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REAL etaNM1 |
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REAL cgBeta |
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REAL alpha |
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REAL sumRHS |
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REAL rhsMax |
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REAL rhsNorm |
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cnh |
1.13 |
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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cnh |
1.12 |
CcnhDebugStarts |
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CHARACTER*(MAX_LEN_FNAM) suff |
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CcnhDebugEnds |
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cnh |
1.1 |
C-- Initialise inverter |
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etaNBuf(1,myThid) = 0. D0 |
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errBuf(1,myThid) = 0. D0 |
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sumRHSBuf(1,myThid) = 0. D0 |
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etaNM1 = 1. D0 |
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cnh |
1.10 |
CcnhDebugStarts |
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1.11 |
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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1.12 |
C suff = 'unnormalised' |
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C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
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cnh |
1.10 |
CcnhDebugEnds |
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cnh |
1.1 |
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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rhsMaxBuf(1,myThid) = rhsMax |
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_GLOBAL_MAX_R8( rhsMaxbuf, rhsMax, myThid ) |
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rhsMax = rhsMaxBuf(1,1) |
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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-- 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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cnh |
1.11 |
C CALL PLOT_FIELD_XYRL( cg2d_b, 'CG2D.1 CG2D_B' , 1, myThid ) |
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cnh |
1.12 |
C suff = 'normalised' |
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C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
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cnh |
1.1 |
CcnhDebugEnds |
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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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cnh |
1.4 |
& -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj) |
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cnh |
1.10 |
& -freeSurfFac*_rA(i,j,bi,bj)* horiVertRatio* |
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cnh |
1.4 |
& cg2d_x(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
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& ) |
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cnh |
1.1 |
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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cnh |
1.13 |
C _EXCH_XY_R8( cg2d_r, myThid ) |
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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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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_IGNORE_CORNERS, myThid ) |
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C _EXCH_XY_R8( cg2d_s, myThid ) |
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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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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_IGNORE_CORNERS, myThid ) |
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cnh |
1.1 |
sumRHSBuf(1,myThid) = sumRHS |
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_GLOBAL_SUM_R8( sumRHSBuf , sumRHS, myThid ) |
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sumRHS = sumRHSBuf(1,1) |
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errBuf(1,myThid) = err |
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C WRITE(6,*) ' mythid, err = ', mythid, SQRT(err) |
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_GLOBAL_SUM_R8( errBuf , err , myThid ) |
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err = errBuf(1,1) |
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cnh |
1.13 |
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_BEGIN_MASTER( myThid ) |
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cnh |
1.9 |
write(0,*) 'cg2d: Sum(rhs) = ',sumRHS |
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cnh |
1.13 |
_END_MASTER( ) |
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cnh |
1.1 |
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actualIts = 0 |
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actualResidual = SQRT(err) |
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C _BARRIER |
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_BEGIN_MASTER( myThid ) |
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cnh |
1.6 |
WRITE(0,*) ' CG2D iters, err = ', actualIts, actualResidual |
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cnh |
1.1 |
_END_MASTER( ) |
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C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
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DO 10 it2d=1, cg2dMaxIters |
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CcnhDebugStarts |
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cnh |
1.10 |
C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' residual = ',actualResidual |
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cnh |
1.1 |
CcnhDebugEnds |
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IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
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C-- Solve preconditioning equation and update |
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C-- conjugate direction vector "s". |
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etaN = 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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cnh |
1.3 |
& 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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cnh |
1.4 |
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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cnh |
1.1 |
etaN = etaN |
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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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etanBuf(1,myThid) = etaN |
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_GLOBAL_SUM_R8(etaNbuf,etaN, myThid) |
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etaN = etaNBuf(1,1) |
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CcnhDebugStarts |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' etaN = ',etaN |
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CcnhDebugEnds |
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cgBeta = etaN/etaNM1 |
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CcnhDebugStarts |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' beta = ',cgBeta |
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CcnhDebugEnds |
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etaNM1 = etaN |
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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) + 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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C-- Do exchanges that require messages i.e. between |
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C-- processes. |
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cnh |
1.13 |
C _EXCH_XY_R8( cg2d_s, myThid ) |
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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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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_IGNORE_CORNERS, myThid ) |
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cnh |
1.1 |
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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) |
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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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& 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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& -aW2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
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& -aW2d(I+1,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
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& -aS2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 287 |
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& -aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J ,bi,bj) |
| 288 |
cnh |
1.10 |
& -freeSurfFac*_rA(i,j,bi,bj)* horiVertRatio* |
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cnh |
1.4 |
& cg2d_s(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
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cnh |
1.1 |
alpha = alpha+cg2d_s(I,J,bi,bj)*cg2d_q(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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alphaBuf(1,myThid) = alpha |
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_GLOBAL_SUM_R8(alphaBuf,alpha,myThid) |
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alpha = alphaBuf(1,1) |
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CcnhDebugStarts |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' SUM(s*q)= ',alpha |
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CcnhDebugEnds |
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alpha = etaN/alpha |
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CcnhDebugStarts |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' alpha= ',alpha |
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CcnhDebugEnds |
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C== Update solution and residual vectors |
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C Now compute "interior" points. |
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err = 0. _d 0 |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
| 311 |
|
|
DO J=1,sNy |
| 312 |
|
|
DO I=1,sNx |
| 313 |
|
|
cg2d_x(I,J,bi,bj)=cg2d_x(I,J,bi,bj)+alpha*cg2d_s(I,J,bi,bj) |
| 314 |
|
|
cg2d_r(I,J,bi,bj)=cg2d_r(I,J,bi,bj)-alpha*cg2d_q(I,J,bi,bj) |
| 315 |
|
|
err = err+cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 316 |
|
|
ENDDO |
| 317 |
|
|
ENDDO |
| 318 |
|
|
ENDDO |
| 319 |
|
|
ENDDO |
| 320 |
|
|
|
| 321 |
|
|
errBuf(1,myThid) = err |
| 322 |
|
|
_GLOBAL_SUM_R8( errBuf , err , myThid ) |
| 323 |
|
|
err = errBuf(1,1) |
| 324 |
|
|
err = SQRT(err) |
| 325 |
|
|
actualIts = it2d |
| 326 |
|
|
actualResidual = err |
| 327 |
|
|
IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
| 328 |
cnh |
1.13 |
C _EXCH_XY_R8(cg2d_r, myThid ) |
| 329 |
|
|
OLw = 1 |
| 330 |
|
|
OLe = 1 |
| 331 |
|
|
OLn = 1 |
| 332 |
|
|
OLs = 1 |
| 333 |
|
|
exchWidthX = 1 |
| 334 |
|
|
exchWidthY = 1 |
| 335 |
|
|
myNz = 1 |
| 336 |
|
|
CALL EXCH_RL( cg2d_r, |
| 337 |
|
|
I OLw, OLe, OLs, OLn, myNz, |
| 338 |
|
|
I exchWidthX, exchWidthY, |
| 339 |
|
|
I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
| 340 |
|
|
|
| 341 |
cnh |
1.1 |
10 CONTINUE |
| 342 |
|
|
11 CONTINUE |
| 343 |
|
|
|
| 344 |
|
|
C-- Un-normalise the answer |
| 345 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
| 346 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 347 |
|
|
DO J=1,sNy |
| 348 |
|
|
DO I=1,sNx |
| 349 |
|
|
cg2d_x(I ,J ,bi,bj) = cg2d_x(I ,J ,bi,bj)/rhsNorm |
| 350 |
|
|
ENDDO |
| 351 |
|
|
ENDDO |
| 352 |
|
|
ENDDO |
| 353 |
|
|
ENDDO |
| 354 |
|
|
|
| 355 |
|
|
_EXCH_XY_R8(cg2d_x, myThid ) |
| 356 |
cnh |
1.6 |
_BEGIN_MASTER( myThid ) |
| 357 |
|
|
WRITE(0,*) ' CG2D iters, err = ', actualIts, actualResidual |
| 358 |
|
|
_END_MASTER( ) |
| 359 |
cnh |
1.1 |
|
| 360 |
|
|
CcnhDebugStarts |
| 361 |
cnh |
1.7 |
C CALL PLOT_FIELD_XYRL( cg2d_x, 'CALC_MOM_RHS CG2D_X' , 1, myThid ) |
| 362 |
cnh |
1.1 |
C err = 0. _d 0 |
| 363 |
|
|
C DO bj=myByLo(myThid),myByHi(myThid) |
| 364 |
|
|
C DO bi=myBxLo(myThid),myBxHi(myThid) |
| 365 |
|
|
C DO J=1,sNy |
| 366 |
|
|
C DO I=1,sNx |
| 367 |
|
|
C cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
| 368 |
|
|
C & (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
| 369 |
|
|
C & +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
| 370 |
|
|
C & +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
| 371 |
|
|
C & +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
| 372 |
|
|
C & -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 373 |
|
|
C & -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 374 |
|
|
C & -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
| 375 |
|
|
C & -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj)) |
| 376 |
|
|
C err = err + |
| 377 |
|
|
C & cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
| 378 |
|
|
C ENDDO |
| 379 |
|
|
C ENDDO |
| 380 |
|
|
C ENDDO |
| 381 |
|
|
C ENDDO |
| 382 |
|
|
C errBuf(1,myThid) = err |
| 383 |
|
|
C _GLOBAL_SUM_R8( errBuf , err , myThid ) |
| 384 |
|
|
C err = errBuf(1,1) |
| 385 |
|
|
C write(0,*) 'cg2d: Ax - b = ',SQRT(err) |
| 386 |
|
|
CcnhDebugEnds |
| 387 |
|
|
|
| 388 |
|
|
|
| 389 |
|
|
END |
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