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C $Header: /u/gcmpack/models/MITgcmUV/model/src/cg3d.F,v 1.9 2001/05/14 21:33:30 heimbach 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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#define VERBOSE |
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|
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SUBROUTINE CG3D( |
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I myThid ) |
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C /==========================================================\ |
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C | SUBROUTINE CG3D | |
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C | o Three-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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IMPLICIT NONE |
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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 "CG3D.h" |
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|
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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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|
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#ifdef ALLOW_NONHYDROSTATIC |
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|
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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, K, it3d |
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INTEGER KM1, KP1 |
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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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_RL topLevTerm |
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|
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C-- Initialise inverter |
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eta_qrNM1 = 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 K=1,Nr |
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DO J=1,sNy |
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DO I=1,sNx |
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cg3d_b(I,J,K,bi,bj) = cg3d_b(I,J,K,bi,bj)*cg3dNorm |
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rhsMax = MAX(ABS(cg3d_b(I,J,K,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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ENDDO |
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_GLOBAL_MAX_R8( rhsMax, myThid ) |
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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 K=1,Nr |
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DO J=1,sNy |
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DO I=1,sNx |
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cg3d_b(I,J,K,bi,bj) = cg3d_b(I,J,K,bi,bj)*rhsNorm |
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cg3d_x(I,J,K,bi,bj) = cg3d_x(I,J,K,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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ENDDO |
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|
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C-- Update overlaps |
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_EXCH_XYZ_R8( cg3d_b, myThid ) |
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_EXCH_XYZ_R8( cg3d_x, myThid ) |
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|
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C-- Initial residual calculation (with free-Surface term) |
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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 K=1,Nr |
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KM1 = K-1 |
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IF ( K .EQ. 1 ) KM1 = 1 |
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KP1 = K+1 |
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IF ( K .EQ. Nr ) KP1 = 1 |
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topLevTerm = 0. |
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IF ( K .EQ. 1) topLevTerm = freeSurfFac*cg3dNorm* |
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& (horiVertRatio/gravity)/deltaTMom/deltaTMom |
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DO J=1,sNy |
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DO I=1,sNx |
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cg3d_s(I,J,K,bi,bj) = 0. |
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cg3d_r(I,J,K,bi,bj) = cg3d_b(I,J,K,bi,bj) -( 0. |
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& +aW3d(I ,J ,K ,bi,bj)*cg3d_x(I-1,J ,K ,bi,bj) |
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& +aW3d(I+1,J ,K ,bi,bj)*cg3d_x(I+1,J ,K ,bi,bj) |
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& +aS3d(I ,J ,K ,bi,bj)*cg3d_x(I ,J-1,K ,bi,bj) |
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& +aS3d(I ,J+1,K ,bi,bj)*cg3d_x(I ,J+1,K ,bi,bj) |
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& +aV3d(I ,J ,K ,bi,bj)*cg3d_x(I ,J ,KM1,bi,bj) |
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& +aV3d(I ,J ,KP1,bi,bj)*cg3d_x(I ,J ,KP1,bi,bj) |
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& -aW3d(I ,J ,K ,bi,bj)*cg3d_x(I ,J ,K ,bi,bj) |
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& -aW3d(I+1,J ,K ,bi,bj)*cg3d_x(I ,J ,K ,bi,bj) |
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& -aS3d(I ,J ,K ,bi,bj)*cg3d_x(I ,J ,K ,bi,bj) |
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& -aS3d(I ,J+1,K ,bi,bj)*cg3d_x(I ,J ,K ,bi,bj) |
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& -aV3d(I ,J ,K ,bi,bj)*cg3d_x(I ,J ,K ,bi,bj) |
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& -aV3d(I ,J ,KP1,bi,bj)*cg3d_x(I ,J ,K ,bi,bj) |
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& -topLevTerm*_rA(I,J,bi,bj)*cg3d_x(I,J,K,bi,bj) |
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& ) |
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err = err |
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& +cg3d_r(I,J,K,bi,bj)*cg3d_r(I,J,K,bi,bj) |
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sumRHS = sumRHS |
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& +cg3d_b(I,J,K,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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ENDDO |
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C _EXCH_XYZ_R8( cg3d_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 = Nr |
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CALL EXCH_RL( cg3d_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_XYZ_R8( cg3d_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 = Nr |
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CALL EXCH_RL( cg3d_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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_GLOBAL_SUM_R8( sumRHS, myThid ) |
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_GLOBAL_SUM_R8( err , myThid ) |
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|
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_BEGIN_MASTER( myThid ) |
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write(*,'(A,1PE30.14)') ' cg3d: Sum(rhs) = ',sumRHS |
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_END_MASTER( ) |
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|
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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(*,'(A,I6,1PE30.14)') ' CG3D iters, err = ', |
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& 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 it3d=1, cg3dMaxIters |
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|
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CcnhDebugStarts |
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#ifdef VERBOSE |
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IF ( mod(it3d-1,10).EQ.0) |
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& WRITE(*,*) ' CG3D: Iteration ',it3d-1, |
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& ' residual = ',actualResidual |
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#endif |
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CcnhDebugEnds |
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IF ( actualResidual .LT. cg3dTargetResidual ) 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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C Note. On the next to loops over all tiles the inner loop ranges |
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C in sNx and sNy are expanded by 1 to avoid a communication |
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C step. However this entails a bit of gynamastics because we only |
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C want eta_qrN for the interior points. |
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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 K=1,1 |
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DO J=1-1,sNy+1 |
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DO I=1-1,sNx+1 |
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cg3d_q(I,J,K,bi,bj) = |
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& zMC(I ,J ,K,bi,bj)*cg3d_r(I ,J ,K,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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DO K=2,Nr |
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DO J=1-1,sNy+1 |
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DO I=1-1,sNx+1 |
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cg3d_q(I,J,K,bi,bj) = |
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& zMC(I,J,K,bi,bj)*(cg3d_r(I,J,K ,bi,bj) |
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& -zML(I,J,K,bi,bj)*cg3d_q(I,J,K-1,bi,bj)) |
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ENDDO |
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ENDDO |
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ENDDO |
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DO K=Nr,Nr |
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caja IF (Nr .GT. 1) THEN |
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caja DO J=1-1,sNy+1 |
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caja DO I=1-1,sNx+1 |
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caja cg3d_q(I,J,K,bi,bj) = |
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caja & zMC(i,j,k,bi,bj)*(cg3d_r(i,j,k ,bi,bj) |
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caja & -zML(i,j,k,bi,bj)*cg3d_q(i,j,k-1,bi,bj)) |
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caja ENDDO |
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caja ENDDO |
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caja ENDIF |
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DO J=1,sNy |
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DO I=1,sNx |
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eta_qrN = eta_qrN |
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& +cg3d_q(I,J,K,bi,bj)*cg3d_r(I,J,K,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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DO K=Nr-1,1,-1 |
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DO J=1-1,sNy+1 |
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DO I=1-1,sNx+1 |
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cg3d_q(I,J,K,bi,bj) = |
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& cg3d_q(I,J,K,bi,bj) |
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& -zMU(I,J,K,bi,bj)*cg3d_q(I,J,K+1,bi,bj) |
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ENDDO |
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ENDDO |
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DO J=1,sNy |
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DO I=1,sNx |
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eta_qrN = eta_qrN |
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& +cg3d_q(I,J,K,bi,bj)*cg3d_r(I,J,K,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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ENDDO |
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caja |
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caja eta_qrN=0. |
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caja DO bj=myByLo(myThid),myByHi(myThid) |
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caja DO bi=myBxLo(myThid),myBxHi(myThid) |
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caja DO K=1,Nr |
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caja DO J=1,sNy |
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caja DO I=1,sNx |
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caja eta_qrN = eta_qrN |
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caja & +cg3d_q(I,J,K,bi,bj)*cg3d_r(I,J,K,bi,bj) |
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caja ENDDO |
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caja ENDDO |
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caja ENDDO |
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caja ENDDO |
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caja ENDDO |
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caja |
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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(*,*) ' CG3D: Iteration ',it3d-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(*,*) ' CG3D: Iteration ',it3d-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 K=1,Nr |
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DO J=1-1,sNy+1 |
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DO I=1-1,sNx+1 |
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cg3d_s(I,J,K,bi,bj) = cg3d_q(I,J,K,bi,bj) |
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& + cgBeta*cg3d_s(I,J,K,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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ENDDO |
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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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topLevTerm = freeSurfFac*cg3dNorm* |
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& (horiVertRatio/gravity)/deltaTMom/deltaTMom |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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IF ( Nr .GT. 1 ) THEN |
| 319 |
DO K=1,1 |
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DO J=1,sNy |
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DO I=1,sNx |
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cg3d_q(I,J,K,bi,bj) = |
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& aW3d(I ,J ,K ,bi,bj)*cg3d_s(I-1,J ,K ,bi,bj) |
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& +aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I+1,J ,K ,bi,bj) |
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& +aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J-1,K ,bi,bj) |
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& +aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J+1,K ,bi,bj) |
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& +aV3d(I ,J ,K+1,bi,bj)*cg3d_s(I ,J ,K+1,bi,bj) |
| 328 |
& -aW3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
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& -aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 330 |
& -aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 331 |
& -aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 332 |
& -aV3d(I ,J ,K+1,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 333 |
& -topLevTerm*_rA(I,J,bi,bj)*cg3d_s(I,J,K,bi,bj) |
| 334 |
alpha = alpha+cg3d_s(I,J,K,bi,bj)*cg3d_q(I,J,K,bi,bj) |
| 335 |
ENDDO |
| 336 |
ENDDO |
| 337 |
ENDDO |
| 338 |
ELSE |
| 339 |
DO K=1,1 |
| 340 |
DO J=1,sNy |
| 341 |
DO I=1,sNx |
| 342 |
cg3d_q(I,J,K,bi,bj) = |
| 343 |
& aW3d(I ,J ,K ,bi,bj)*cg3d_s(I-1,J ,K ,bi,bj) |
| 344 |
& +aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I+1,J ,K ,bi,bj) |
| 345 |
& +aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J-1,K ,bi,bj) |
| 346 |
& +aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J+1,K ,bi,bj) |
| 347 |
& -aW3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 348 |
& -aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 349 |
& -aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 350 |
& -aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 351 |
& -topLevTerm*_rA(I,J,bi,bj)*cg3d_s(I,J,K,bi,bj) |
| 352 |
alpha = alpha+cg3d_s(I,J,K,bi,bj)*cg3d_q(I,J,K,bi,bj) |
| 353 |
ENDDO |
| 354 |
ENDDO |
| 355 |
ENDDO |
| 356 |
ENDIF |
| 357 |
DO K=2,Nr-1 |
| 358 |
DO J=1,sNy |
| 359 |
DO I=1,sNx |
| 360 |
cg3d_q(I,J,K,bi,bj) = |
| 361 |
& aW3d(I ,J ,K ,bi,bj)*cg3d_s(I-1,J ,K ,bi,bj) |
| 362 |
& +aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I+1,J ,K ,bi,bj) |
| 363 |
& +aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J-1,K ,bi,bj) |
| 364 |
& +aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J+1,K ,bi,bj) |
| 365 |
& +aV3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K-1,bi,bj) |
| 366 |
& +aV3d(I ,J ,K+1,bi,bj)*cg3d_s(I ,J ,K+1,bi,bj) |
| 367 |
& -aW3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 368 |
& -aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 369 |
& -aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 370 |
& -aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 371 |
& -aV3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 372 |
& -aV3d(I ,J ,K+1,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 373 |
alpha = alpha+cg3d_s(I,J,K,bi,bj)*cg3d_q(I,J,K,bi,bj) |
| 374 |
ENDDO |
| 375 |
ENDDO |
| 376 |
ENDDO |
| 377 |
IF ( Nr .GT. 1 ) THEN |
| 378 |
DO K=Nr,Nr |
| 379 |
DO J=1,sNy |
| 380 |
DO I=1,sNx |
| 381 |
cg3d_q(I,J,K,bi,bj) = |
| 382 |
& aW3d(I ,J ,K ,bi,bj)*cg3d_s(I-1,J ,K ,bi,bj) |
| 383 |
& +aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I+1,J ,K ,bi,bj) |
| 384 |
& +aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J-1,K ,bi,bj) |
| 385 |
& +aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J+1,K ,bi,bj) |
| 386 |
& +aV3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K-1,bi,bj) |
| 387 |
& -aW3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 388 |
& -aW3d(I+1,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 389 |
& -aS3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 390 |
& -aS3d(I ,J+1,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 391 |
& -aV3d(I ,J ,K ,bi,bj)*cg3d_s(I ,J ,K ,bi,bj) |
| 392 |
alpha = alpha+cg3d_s(I,J,K,bi,bj)*cg3d_q(I,J,K,bi,bj) |
| 393 |
ENDDO |
| 394 |
ENDDO |
| 395 |
ENDDO |
| 396 |
ENDIF |
| 397 |
ENDDO |
| 398 |
ENDDO |
| 399 |
_GLOBAL_SUM_R8(alpha,myThid) |
| 400 |
CcnhDebugStarts |
| 401 |
C WRITE(*,*) ' CG3D: Iteration ',it3d-1,' SUM(s*q)= ',alpha |
| 402 |
CcnhDebugEnds |
| 403 |
alpha = eta_qrN/alpha |
| 404 |
CcnhDebugStarts |
| 405 |
C WRITE(*,*) ' CG3D: Iteration ',it3d-1,' alpha= ',alpha |
| 406 |
CcnhDebugEnds |
| 407 |
|
| 408 |
C== Update solution and residual vectors |
| 409 |
C Now compute "interior" points. |
| 410 |
err = 0. _d 0 |
| 411 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 412 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 413 |
DO K=1,Nr |
| 414 |
DO J=1,sNy |
| 415 |
DO I=1,sNx |
| 416 |
cg3d_x(I,J,K,bi,bj)=cg3d_x(I,J,K,bi,bj) |
| 417 |
& +alpha*cg3d_s(I,J,K,bi,bj) |
| 418 |
cg3d_r(I,J,K,bi,bj)=cg3d_r(I,J,K,bi,bj) |
| 419 |
& -alpha*cg3d_q(I,J,K,bi,bj) |
| 420 |
err = err+cg3d_r(I,J,K,bi,bj)*cg3d_r(I,J,K,bi,bj) |
| 421 |
ENDDO |
| 422 |
ENDDO |
| 423 |
ENDDO |
| 424 |
ENDDO |
| 425 |
ENDDO |
| 426 |
|
| 427 |
_GLOBAL_SUM_R8( err , myThid ) |
| 428 |
err = SQRT(err) |
| 429 |
actualIts = it3d |
| 430 |
actualResidual = err |
| 431 |
IF ( actualResidual .LT. cg3dTargetResidual ) GOTO 11 |
| 432 |
C _EXCH_XYZ_R8(cg3d_r, myThid ) |
| 433 |
OLw = 1 |
| 434 |
OLe = 1 |
| 435 |
OLn = 1 |
| 436 |
OLs = 1 |
| 437 |
exchWidthX = 1 |
| 438 |
exchWidthY = 1 |
| 439 |
myNz = Nr |
| 440 |
CALL EXCH_RL( cg3d_r, |
| 441 |
I OLw, OLe, OLs, OLn, myNz, |
| 442 |
I exchWidthX, exchWidthY, |
| 443 |
I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
| 444 |
|
| 445 |
10 CONTINUE |
| 446 |
11 CONTINUE |
| 447 |
|
| 448 |
C-- Un-normalise the answer |
| 449 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 450 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 451 |
DO K=1,Nr |
| 452 |
DO J=1,sNy |
| 453 |
DO I=1,sNx |
| 454 |
cg3d_x(I,J,K,bi,bj) = cg3d_x(I,J,K,bi,bj)/rhsNorm |
| 455 |
ENDDO |
| 456 |
ENDDO |
| 457 |
ENDDO |
| 458 |
ENDDO |
| 459 |
ENDDO |
| 460 |
|
| 461 |
Cadj _EXCH_XYZ_R8(cg3d_x, myThid ) |
| 462 |
_BEGIN_MASTER( myThid ) |
| 463 |
WRITE(*,'(A,I6,1PE30.14)') ' CG3D iters, err = ', |
| 464 |
& actualIts, actualResidual |
| 465 |
_END_MASTER( ) |
| 466 |
|
| 467 |
#endif /* ALLOW_NONHYDROSTATIC */ |
| 468 |
|
| 469 |
RETURN |
| 470 |
END |
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