1 |
adcroft |
1.19 |
C $Header: /u/gcmpack/models/MITgcmUV/model/src/cg2d.F,v 1.18 1998/12/09 16:11:51 adcroft Exp $ |
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cnh |
1.1 |
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cnh |
1.16 |
#include "CPP_OPTIONS.h" |
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cnh |
1.1 |
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5 |
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SUBROUTINE CG2D( |
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cnh |
1.14 |
I cg2d_b, |
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U cg2d_x, |
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cnh |
1.1 |
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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adcroft |
1.18 |
IMPLICIT NONE |
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cnh |
1.1 |
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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 |
1.14 |
#include "CG2D_INTERNAL.h" |
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cnh |
1.1 |
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40 |
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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 |
43 |
cnh |
1.14 |
_RL cg2d_x(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL cg2d_b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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cnh |
1.1 |
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C === Local variables ==== |
48 |
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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 |
63 |
cnh |
1.14 |
_RL actualResidual |
64 |
cnh |
1.1 |
INTEGER bi, bj |
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INTEGER I, J, it2d |
66 |
cnh |
1.14 |
_RL err |
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_RL etaN |
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_RL etaNM1 |
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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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cnh |
1.1 |
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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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84 |
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 |
90 |
cnh |
1.15 |
etaNBuf(1,myThid) = 0. _d 0 |
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errBuf(1,myThid) = 0. _d 0 |
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sumRHSBuf(1,myThid) = 0. _d 0 |
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etaNM1 = 1. _d 0 |
94 |
cnh |
1.1 |
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95 |
cnh |
1.10 |
CcnhDebugStarts |
96 |
cnh |
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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cnh |
1.12 |
C suff = 'unnormalised' |
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C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
100 |
cnh |
1.14 |
C STOP |
101 |
cnh |
1.10 |
CcnhDebugEnds |
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103 |
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) |
107 |
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DO J=1,sNy |
108 |
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DO I=1,sNx |
109 |
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cg2d_b(I,J,bi,bj) = cg2d_b(I,J,bi,bj)*cg2dNorm |
110 |
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rhsMax = MAX(ABS(cg2d_b(I,J,bi,bj)),rhsMax) |
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ENDDO |
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ENDDO |
113 |
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ENDDO |
114 |
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ENDDO |
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rhsMaxBuf(1,myThid) = rhsMax |
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_GLOBAL_MAX_R8( rhsMaxbuf, rhsMax, myThid ) |
117 |
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rhsMax = rhsMaxBuf(1,1) |
118 |
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rhsNorm = 1. _d 0 |
119 |
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IF ( rhsMax .NE. 0. ) rhsNorm = 1. _d 0 / rhsMax |
120 |
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DO bj=myByLo(myThid),myByHi(myThid) |
121 |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
122 |
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DO J=1,sNy |
123 |
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DO I=1,sNx |
124 |
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cg2d_b(I,J,bi,bj) = cg2d_b(I,J,bi,bj)*rhsNorm |
125 |
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cg2d_x(I,J,bi,bj) = cg2d_x(I,J,bi,bj)*rhsNorm |
126 |
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ENDDO |
127 |
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ENDDO |
128 |
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ENDDO |
129 |
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ENDDO |
130 |
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131 |
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C-- Update overlaps |
132 |
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_EXCH_XY_R8( cg2d_b, myThid ) |
133 |
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_EXCH_XY_R8( cg2d_x, myThid ) |
134 |
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CcnhDebugStarts |
135 |
cnh |
1.11 |
C CALL PLOT_FIELD_XYRL( cg2d_b, 'CG2D.1 CG2D_B' , 1, myThid ) |
136 |
cnh |
1.12 |
C suff = 'normalised' |
137 |
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C CALL WRITE_FLD_XY_RL ( 'cg2d_b.',suff, cg2d_b, 1, myThid) |
138 |
cnh |
1.1 |
CcnhDebugEnds |
139 |
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140 |
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C-- Initial residual calculation |
141 |
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err = 0. _d 0 |
142 |
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sumRHS = 0. _d 0 |
143 |
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DO bj=myByLo(myThid),myByHi(myThid) |
144 |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
145 |
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DO J=1,sNy |
146 |
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DO I=1,sNx |
147 |
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cg2d_s(I,J,bi,bj) = 0. |
148 |
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cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
149 |
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& (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
150 |
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& +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
151 |
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& +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
152 |
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& +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
153 |
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& -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
154 |
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& -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
155 |
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& -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
156 |
cnh |
1.4 |
& -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj) |
157 |
cnh |
1.10 |
& -freeSurfFac*_rA(i,j,bi,bj)* horiVertRatio* |
158 |
cnh |
1.4 |
& cg2d_x(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
159 |
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& ) |
160 |
cnh |
1.1 |
err = err + |
161 |
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& cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
162 |
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sumRHS = sumRHS + |
163 |
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& cg2d_b(I,J,bi,bj) |
164 |
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ENDDO |
165 |
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ENDDO |
166 |
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ENDDO |
167 |
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ENDDO |
168 |
cnh |
1.13 |
C _EXCH_XY_R8( cg2d_r, myThid ) |
169 |
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OLw = 1 |
170 |
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OLe = 1 |
171 |
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OLn = 1 |
172 |
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OLs = 1 |
173 |
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exchWidthX = 1 |
174 |
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exchWidthY = 1 |
175 |
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myNz = 1 |
176 |
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CALL EXCH_RL( cg2d_r, |
177 |
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I OLw, OLe, OLs, OLn, myNz, |
178 |
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I exchWidthX, exchWidthY, |
179 |
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I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
180 |
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C _EXCH_XY_R8( cg2d_s, myThid ) |
181 |
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OLw = 1 |
182 |
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OLe = 1 |
183 |
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OLn = 1 |
184 |
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OLs = 1 |
185 |
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exchWidthX = 1 |
186 |
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exchWidthY = 1 |
187 |
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myNz = 1 |
188 |
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CALL EXCH_RL( cg2d_s, |
189 |
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I OLw, OLe, OLs, OLn, myNz, |
190 |
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I exchWidthX, exchWidthY, |
191 |
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I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
192 |
cnh |
1.1 |
sumRHSBuf(1,myThid) = sumRHS |
193 |
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_GLOBAL_SUM_R8( sumRHSBuf , sumRHS, myThid ) |
194 |
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sumRHS = sumRHSBuf(1,1) |
195 |
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errBuf(1,myThid) = err |
196 |
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C WRITE(6,*) ' mythid, err = ', mythid, SQRT(err) |
197 |
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_GLOBAL_SUM_R8( errBuf , err , myThid ) |
198 |
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err = errBuf(1,1) |
199 |
cnh |
1.13 |
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200 |
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_BEGIN_MASTER( myThid ) |
201 |
adcroft |
1.19 |
write(0,'(A,1PE30.14)') ' cg2d: Sum(rhs) = ',sumRHS |
202 |
cnh |
1.13 |
_END_MASTER( ) |
203 |
cnh |
1.1 |
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204 |
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actualIts = 0 |
205 |
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actualResidual = SQRT(err) |
206 |
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C _BARRIER |
207 |
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_BEGIN_MASTER( myThid ) |
208 |
adcroft |
1.17 |
WRITE(0,'(A,I6,1PE30.14)') ' CG2D iters, err = ', |
209 |
cnh |
1.14 |
& actualIts, actualResidual |
210 |
cnh |
1.1 |
_END_MASTER( ) |
211 |
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212 |
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C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
213 |
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DO 10 it2d=1, cg2dMaxIters |
214 |
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215 |
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CcnhDebugStarts |
216 |
cnh |
1.14 |
C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' residual = ', |
217 |
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C & actualResidual |
218 |
cnh |
1.1 |
CcnhDebugEnds |
219 |
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IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
220 |
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C-- Solve preconditioning equation and update |
221 |
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C-- conjugate direction vector "s". |
222 |
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etaN = 0. _d 0 |
223 |
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DO bj=myByLo(myThid),myByHi(myThid) |
224 |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
225 |
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DO J=1,sNy |
226 |
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DO I=1,sNx |
227 |
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cg2d_q(I,J,bi,bj) = |
228 |
cnh |
1.3 |
& pC(I ,J ,bi,bj)*cg2d_r(I ,J ,bi,bj) |
229 |
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& +pW(I ,J ,bi,bj)*cg2d_r(I-1,J ,bi,bj) |
230 |
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& +pW(I+1,J ,bi,bj)*cg2d_r(I+1,J ,bi,bj) |
231 |
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& +pS(I ,J ,bi,bj)*cg2d_r(I ,J-1,bi,bj) |
232 |
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& +pS(I ,J+1,bi,bj)*cg2d_r(I ,J+1,bi,bj) |
233 |
cnh |
1.4 |
CcnhDebugStarts |
234 |
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C cg2d_q(I,J,bi,bj) = cg2d_r(I ,J ,bi,bj) |
235 |
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CcnhDebugEnds |
236 |
cnh |
1.1 |
etaN = etaN |
237 |
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& +cg2d_q(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
238 |
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ENDDO |
239 |
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ENDDO |
240 |
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ENDDO |
241 |
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ENDDO |
242 |
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243 |
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etanBuf(1,myThid) = etaN |
244 |
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_GLOBAL_SUM_R8(etaNbuf,etaN, myThid) |
245 |
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etaN = etaNBuf(1,1) |
246 |
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CcnhDebugStarts |
247 |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' etaN = ',etaN |
248 |
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CcnhDebugEnds |
249 |
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cgBeta = etaN/etaNM1 |
250 |
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CcnhDebugStarts |
251 |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' beta = ',cgBeta |
252 |
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CcnhDebugEnds |
253 |
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etaNM1 = etaN |
254 |
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255 |
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DO bj=myByLo(myThid),myByHi(myThid) |
256 |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
257 |
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DO J=1,sNy |
258 |
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DO I=1,sNx |
259 |
cnh |
1.14 |
cg2d_s(I,J,bi,bj) = cg2d_q(I,J,bi,bj) |
260 |
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& + cgBeta*cg2d_s(I,J,bi,bj) |
261 |
cnh |
1.1 |
ENDDO |
262 |
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ENDDO |
263 |
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ENDDO |
264 |
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ENDDO |
265 |
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266 |
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C-- Do exchanges that require messages i.e. between |
267 |
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C-- processes. |
268 |
cnh |
1.13 |
C _EXCH_XY_R8( cg2d_s, myThid ) |
269 |
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OLw = 1 |
270 |
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OLe = 1 |
271 |
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OLn = 1 |
272 |
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OLs = 1 |
273 |
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exchWidthX = 1 |
274 |
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exchWidthY = 1 |
275 |
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myNz = 1 |
276 |
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CALL EXCH_RL( cg2d_s, |
277 |
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I OLw, OLe, OLs, OLn, myNz, |
278 |
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I exchWidthX, exchWidthY, |
279 |
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I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
280 |
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281 |
cnh |
1.1 |
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282 |
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C== Evaluate laplace operator on conjugate gradient vector |
283 |
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C== q = A.s |
284 |
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alpha = 0. _d 0 |
285 |
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DO bj=myByLo(myThid),myByHi(myThid) |
286 |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
287 |
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DO J=1,sNy |
288 |
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DO I=1,sNx |
289 |
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cg2d_q(I,J,bi,bj) = |
290 |
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& aW2d(I ,J ,bi,bj)*cg2d_s(I-1,J ,bi,bj) |
291 |
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& +aW2d(I+1,J ,bi,bj)*cg2d_s(I+1,J ,bi,bj) |
292 |
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& +aS2d(I ,J ,bi,bj)*cg2d_s(I ,J-1,bi,bj) |
293 |
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& +aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J+1,bi,bj) |
294 |
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& -aW2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
295 |
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& -aW2d(I+1,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
296 |
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& -aS2d(I ,J ,bi,bj)*cg2d_s(I ,J ,bi,bj) |
297 |
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& -aS2d(I ,J+1,bi,bj)*cg2d_s(I ,J ,bi,bj) |
298 |
cnh |
1.10 |
& -freeSurfFac*_rA(i,j,bi,bj)* horiVertRatio* |
299 |
cnh |
1.4 |
& cg2d_s(I ,J ,bi,bj)/deltaTMom/deltaTMom*cg2dNorm |
300 |
cnh |
1.1 |
alpha = alpha+cg2d_s(I,J,bi,bj)*cg2d_q(I,J,bi,bj) |
301 |
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ENDDO |
302 |
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ENDDO |
303 |
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ENDDO |
304 |
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ENDDO |
305 |
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alphaBuf(1,myThid) = alpha |
306 |
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_GLOBAL_SUM_R8(alphaBuf,alpha,myThid) |
307 |
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alpha = alphaBuf(1,1) |
308 |
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CcnhDebugStarts |
309 |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' SUM(s*q)= ',alpha |
310 |
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CcnhDebugEnds |
311 |
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alpha = etaN/alpha |
312 |
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CcnhDebugStarts |
313 |
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C WRITE(0,*) ' CG2D: Iteration ',it2d-1,' alpha= ',alpha |
314 |
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CcnhDebugEnds |
315 |
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316 |
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C== Update solution and residual vectors |
317 |
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C Now compute "interior" points. |
318 |
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err = 0. _d 0 |
319 |
|
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DO bj=myByLo(myThid),myByHi(myThid) |
320 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
321 |
|
|
DO J=1,sNy |
322 |
|
|
DO I=1,sNx |
323 |
|
|
cg2d_x(I,J,bi,bj)=cg2d_x(I,J,bi,bj)+alpha*cg2d_s(I,J,bi,bj) |
324 |
|
|
cg2d_r(I,J,bi,bj)=cg2d_r(I,J,bi,bj)-alpha*cg2d_q(I,J,bi,bj) |
325 |
|
|
err = err+cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
326 |
|
|
ENDDO |
327 |
|
|
ENDDO |
328 |
|
|
ENDDO |
329 |
|
|
ENDDO |
330 |
|
|
|
331 |
|
|
errBuf(1,myThid) = err |
332 |
|
|
_GLOBAL_SUM_R8( errBuf , err , myThid ) |
333 |
|
|
err = errBuf(1,1) |
334 |
|
|
err = SQRT(err) |
335 |
|
|
actualIts = it2d |
336 |
|
|
actualResidual = err |
337 |
|
|
IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
338 |
cnh |
1.13 |
C _EXCH_XY_R8(cg2d_r, myThid ) |
339 |
|
|
OLw = 1 |
340 |
|
|
OLe = 1 |
341 |
|
|
OLn = 1 |
342 |
|
|
OLs = 1 |
343 |
|
|
exchWidthX = 1 |
344 |
|
|
exchWidthY = 1 |
345 |
|
|
myNz = 1 |
346 |
|
|
CALL EXCH_RL( cg2d_r, |
347 |
|
|
I OLw, OLe, OLs, OLn, myNz, |
348 |
|
|
I exchWidthX, exchWidthY, |
349 |
|
|
I FORWARD_SIMULATION, EXCH_IGNORE_CORNERS, myThid ) |
350 |
|
|
|
351 |
cnh |
1.1 |
10 CONTINUE |
352 |
|
|
11 CONTINUE |
353 |
|
|
|
354 |
|
|
C-- Un-normalise the answer |
355 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
356 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
357 |
|
|
DO J=1,sNy |
358 |
|
|
DO I=1,sNx |
359 |
|
|
cg2d_x(I ,J ,bi,bj) = cg2d_x(I ,J ,bi,bj)/rhsNorm |
360 |
|
|
ENDDO |
361 |
|
|
ENDDO |
362 |
|
|
ENDDO |
363 |
|
|
ENDDO |
364 |
|
|
|
365 |
|
|
_EXCH_XY_R8(cg2d_x, myThid ) |
366 |
cnh |
1.6 |
_BEGIN_MASTER( myThid ) |
367 |
adcroft |
1.17 |
WRITE(0,'(A,I6,1PE30.14)') ' CG2D iters, err = ', |
368 |
cnh |
1.14 |
& actualIts, actualResidual |
369 |
cnh |
1.6 |
_END_MASTER( ) |
370 |
cnh |
1.1 |
|
371 |
|
|
CcnhDebugStarts |
372 |
cnh |
1.7 |
C CALL PLOT_FIELD_XYRL( cg2d_x, 'CALC_MOM_RHS CG2D_X' , 1, myThid ) |
373 |
cnh |
1.1 |
C err = 0. _d 0 |
374 |
|
|
C DO bj=myByLo(myThid),myByHi(myThid) |
375 |
|
|
C DO bi=myBxLo(myThid),myBxHi(myThid) |
376 |
|
|
C DO J=1,sNy |
377 |
|
|
C DO I=1,sNx |
378 |
|
|
C cg2d_r(I,J,bi,bj) = cg2d_b(I,J,bi,bj) - |
379 |
|
|
C & (aW2d(I ,J ,bi,bj)*cg2d_x(I-1,J ,bi,bj) |
380 |
|
|
C & +aW2d(I+1,J ,bi,bj)*cg2d_x(I+1,J ,bi,bj) |
381 |
|
|
C & +aS2d(I ,J ,bi,bj)*cg2d_x(I ,J-1,bi,bj) |
382 |
|
|
C & +aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J+1,bi,bj) |
383 |
|
|
C & -aW2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
384 |
|
|
C & -aW2d(I+1,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
385 |
|
|
C & -aS2d(I ,J ,bi,bj)*cg2d_x(I ,J ,bi,bj) |
386 |
|
|
C & -aS2d(I ,J+1,bi,bj)*cg2d_x(I ,J ,bi,bj)) |
387 |
|
|
C err = err + |
388 |
|
|
C & cg2d_r(I,J,bi,bj)*cg2d_r(I,J,bi,bj) |
389 |
|
|
C ENDDO |
390 |
|
|
C ENDDO |
391 |
|
|
C ENDDO |
392 |
|
|
C ENDDO |
393 |
|
|
C errBuf(1,myThid) = err |
394 |
|
|
C _GLOBAL_SUM_R8( errBuf , err , myThid ) |
395 |
|
|
C err = errBuf(1,1) |
396 |
|
|
C write(0,*) 'cg2d: Ax - b = ',SQRT(err) |
397 |
|
|
CcnhDebugEnds |
398 |
|
|
|
399 |
adcroft |
1.19 |
RETURN |
400 |
cnh |
1.1 |
END |