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C $Header: /u/gcmpack/models/MITgcmUV/model/src/cg2d.F,v 1.5 1998/05/30 02:10:16 cnh Exp $ |
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#include "CPP_EEOPTIONS.h" |
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|
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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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|
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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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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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|
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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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|
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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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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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|
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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_XYR8( cg2d_b, 'CG2D.1 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*_zA(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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_EXCH_XY_R8( cg2d_r, myThid ) |
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_EXCH_XY_R8( cg2d_s, myThid ) |
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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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C write(0,*) 'cg2d: Sum(rhs) = ',sumRHS |
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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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WRITE(0,*) ' CG2D iters, err = ', actualIts, actualResidual |
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_END_MASTER( ) |
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|
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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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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' residual = ',actualResidual |
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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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& 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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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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|
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C-- Do exchanges that require messages i.e. between |
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C-- processes. |
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_EXCH_XY_R8( cg2d_s, myThid ) |
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C== Evaluate laplace operator on conjugate gradient vector |
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C== q = A.s |
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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) |
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& -aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J ,bi,bj) |
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& -freeSurfFac*_zA(i,j,bi,bj)* |
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& cg2d_s(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
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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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|
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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) |
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DO J=1,sNy |
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DO I=1,sNx |
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cg2d_x(I,J,bi,bj)=cg2d_x(I,J,bi,bj)+alpha*cg2d_s(I,J,bi,bj) |
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cg2d_r(I,J,bi,bj)=cg2d_r(I,J,bi,bj)-alpha*cg2d_q(I,J,bi,bj) |
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err = err+cg2d_r(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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errBuf(1,myThid) = err |
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_GLOBAL_SUM_R8( errBuf , err , myThid ) |
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err = errBuf(1,1) |
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err = SQRT(err) |
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actualIts = it2d |
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actualResidual = err |
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IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
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_EXCH_XY_R8(cg2d_r, myThid ) |
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10 CONTINUE |
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11 CONTINUE |
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|
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C-- Un-normalise the answer |
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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_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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|
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_EXCH_XY_R8(cg2d_x, myThid ) |
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_BEGIN_MASTER( myThid ) |
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WRITE(0,*) ' CG2D iters, err = ', actualIts, actualResidual |
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_END_MASTER( ) |
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|
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CcnhDebugStarts |
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C CALL PLOT_FIELD_XYR8( cg2d_x, 'CALC_MOM_RHS CG2D_X' , 1, myThid ) |
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C err = 0. _d 0 |
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C DO bj=myByLo(myThid),myByHi(myThid) |
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C DO bi=myBxLo(myThid),myBxHi(myThid) |
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C DO J=1,sNy |
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C DO I=1,sNx |
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C cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
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C & (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
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C & +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
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C & +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
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C & +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
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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 err = err + |
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C & cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
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C ENDDO |
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C ENDDO |
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C ENDDO |
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C ENDDO |
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C errBuf(1,myThid) = err |
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C _GLOBAL_SUM_R8( errBuf , err , myThid ) |
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C err = errBuf(1,1) |
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C write(0,*) 'cg2d: Ax - b = ',SQRT(err) |
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CcnhDebugEnds |
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|
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|
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END |
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