model/src/ini_cg2d.F

C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.19 1998/09/06 17:35:20 cnh Exp $

#include "CPP_OPTIONS.h"

CStartOfInterface
      SUBROUTINE INI_CG2D( myThid )
C     /==========================================================\
C     | SUBROUTINE INI_CG2D                                      |
C     | o Initialise 2d conjugate gradient solver operators.     |
C     |==========================================================|
C     | These arrays are purely a function of the basin geom.    |
C     | We set then here once and them use then repeatedly.      |
C     \==========================================================/

C     === Global variables ===
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "DYNVARS.h"
#include "CG2D.h"

C     === Routine arguments ===
C     myThid - Thread no. that called this routine.
      INTEGER myThid
CEndOfInterface

C     === Local variables ===
C     xG, yG - Global coordinate location.
C     zG
C     iG, jG - Global coordinate index
C     bi,bj  - Loop counters
C     faceArea - Temporary used to hold cell face areas.
C     I,J,K
C     myNorm - Work variable used in clculating normalisation factor
      CHARACTER*(MAX_LEN_MBUF) msgBuf
      INTEGER bi, bj
      INTEGER I,  J, K
      _RL     faceArea
      _RS     myNorm
      _RL     aC, aCw, aCs

C--   Initialise laplace operator
C     aW2d: integral in Z Ax/dX
C     aS2d: integral in Z Ay/dY
      myNorm = 0. _d 0
      DO bj=myByLo(myThid),myByHi(myThid)
       DO bi=myBxLo(myThid),myBxHi(myThid)
        DO J=1,sNy
         DO I=1,sNx
          aW2d(I,J,bi,bj) = 0. _d 0
          aS2d(I,J,bi,bj) = 0. _d 0
         ENDDO
        ENDDO
        DO K=1,Nr
         DO J=1,sNy
          DO I=1,sNx
           faceArea = _dyG(I,J,bi,bj)*drF(K)
     &               *_hFacW(I,J,K,bi,bj)
           aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj) + 
     &      gBaro*faceArea*recip_dxC(I,J,bi,bj)
           faceArea = _dxG(I,J,bi,bj)*drF(K)
     &               *_hFacS(I,J,K,bi,bj)
           aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj) + 
     &      gBaro*faceArea*recip_dyC(I,J,bi,bj)
          ENDDO
         ENDDO
        ENDDO
        DO J=1,sNy
         DO I=1,sNx
          myNorm = MAX(ABS(aW2d(I,J,bi,bj)),myNorm)
          myNorm = MAX(ABS(aS2d(I,J,bi,bj)),myNorm)
         ENDDO
        ENDDO
       ENDDO
      ENDDO
      cg2dNbuf(1,myThid) = myNorm
      _GLOBAL_MAX_R4( cg2dNbuf, myNorm, myThid )
      IF ( cg2dNbuf(1,1) .NE. 0. _d 0 ) THEN
       myNorm = 1. _d 0/cg2dNbuf(1,1)
      ELSE
       myNorm = 1. _d 0
      ENDIF
       cg2dNorm = myNorm
      _BEGIN_MASTER( myThid )
CcnhDebugStarts
       WRITE(msgBuf,'(A,E40.25)') '// CG2D normalisation factor = ', 
     &               cg2dNorm
       CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
       WRITE(msgBuf,*) '                               '
       CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
CcnhDebugEnds
      _END_MASTER( myThid )
      DO bj=myByLo(myThid),myByHi(myThid)
       DO bi=myBxLo(myThid),myBxHi(myThid)
        DO J=1,sNy
         DO I=1,sNx
          aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj)*myNorm
          aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj)*myNorm
         ENDDO
        ENDDO
       ENDDO
      ENDDO
      
C--   Update overlap regions
CcnhDebugStarts
C     CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.1' , 1, myThid )
C     CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.1' , 1, myThid )
CcnhDebugEnds
      _EXCH_XY_R4(aW2d, myThid)
      _EXCH_XY_R4(aS2d, myThid)
CcnhDebugStarts
      CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.2' , 1, myThid )
      CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.2' , 1, myThid )
CcnhDebugEnds

C--   Initialise preconditioner
C     Note. 20th May 1998
C           I made a weird discovery! In the model paper we argue
C           for the form of the preconditioner used here ( see
C           A Finite-volume, Incompressible Navier-Stokes Model
C           ...., Marshall et. al ). The algebra gives a simple
C           0.5 factor for the averaging of ac and aCw to get a
C           symmettric pre-conditioner. By using a factor of 0.51
C           i.e. scaling the off-diagonal terms in the
C           preconditioner down slightly I managed to get the
C           number of iterations for convergence in a test case to
C           drop form 192 -> 134! Need to investigate this further!
C           For now I have introduced a parameter cg2dpcOffDFac which
C           defaults to 0.51 but can be set at runtime.
      DO bj=myByLo(myThid),myByHi(myThid)
       DO bi=myBxLo(myThid),myBxHi(myThid)
        DO J=1,sNy
         DO I=1,sNx
          pC(I,J,bi,bj) = 1. _d 0
          aC = -(
     &     aW2d(I,J,bi,bj) + aW2d(I+1,J  ,bi,bj)
     &    +aS2d(I,J,bi,bj) + aS2D(I  ,J+1,bi,bj)
     &    +freeSurfFac*myNorm* horiVertRatio*
     &     rA(I,J,bi,bj)/deltaTMom/deltaTMom
     &    )
          aCs = -(
     &     aW2d(I,J-1,bi,bj) + aW2d(I+1,J-1,bi,bj)
     &    +aS2d(I,J-1,bi,bj) + aS2d(I  ,J  ,bi,bj)
     &    +freeSurfFac*myNorm* horiVertRatio*
     &     rA(I,J-1,bi,bj)/deltaTMom/deltaTMom
     &    )
          aCw = -(
     &     aW2d(I-1,J,bi,bj) + aW2d(I  ,J  ,bi,bj)
     &    +aS2d(I-1,J,bi,bj) + aS2d(I-1,J+1,bi,bj)
     &    +freeSurfFac*myNorm* horiVertRatio*
     &     rA(I-1,J,bi,bj)/deltaTMom/deltaTMom
     &    )
          IF ( aC .EQ. 0. ) THEN
            pC(I,J,bi,bj) = 0. _d 0
          ELSE
           pC(I,J,bi,bj) =  1. _d 0 / aC
          ENDIF
          IF ( aC + aCw .EQ. 0. ) THEN
           pW(I,J,bi,bj) = 0.
          ELSE
           pW(I,J,bi,bj) = 
     &     -aW2d(I  ,J  ,bi,bj)/((cg2dpcOffDFac *(aCw+aC))**2 )
          ENDIF
          IF ( aC + aCs .EQ. 0. ) THEN
           pS(I,J,bi,bj) = 0.
          ELSE
           pS(I,J,bi,bj) =
     &     -aS2d(I  ,J  ,bi,bj)/((cg2dpcOffDFac *(aCs+aC))**2 )
          ENDIF
C         pC(I,J,bi,bj) = 1.
C         pW(I,J,bi,bj) = 0.
C         pS(I,J,bi,bj) = 0.
         ENDDO
        ENDDO
       ENDDO
      ENDDO
C--   Update overlap regions
      _EXCH_XY_R4(pC, myThid)
      _EXCH_XY_R4(pW, myThid)
      _EXCH_XY_R4(pS, myThid)
CcnhDebugStarts
      CALL PLOT_FIELD_XYRS( pC, 'pC   INI_CG2D.2' , 1, myThid )
      CALL PLOT_FIELD_XYRS( pW, 'pW   INI_CG2D.2' , 1, myThid )
      CALL PLOT_FIELD_XYRS( pS, 'pS   INI_CG2D.2' , 1, myThid )
CcnhDebugEnds

C--   Set default values for initial guess and RHS
      IF ( startTime .EQ. 0 ) THEN
       DO bj=myByLo(myThid),myByHi(myThid)
        DO bi=myBxLo(myThid),myBxHi(myThid)
         DO J=1,sNy
          DO I=1,sNx
           cg2d_x(I,J,bi,bj) = 0. _d 0
           cg2d_b(I,J,bi,bj) = 0. _d 0
#ifdef ALLOW_CD
           cg2d_xNM1(I,J,bi,bj) = 0. _d 0
#endif
          ENDDO
         ENDDO
        ENDDO
       ENDDO
C--    Update overlap regions
       _EXCH_XY_R8(cg2d_x, myThid)
       _EXCH_XY_R8(cg2d_b, myThid)
#ifdef ALLOW_CD
       _EXCH_XY_R8(cg2d_xNM1, myThid)
#endif
      ENDIF

      RETURN
      END
1	cnh	1.20	C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.19 1998/09/06 17:35:20 cnh Exp $
2	cnh	1.1
3	adcroft	1.13	#include "CPP_OPTIONS.h"
4	cnh	1.1
5			CStartOfInterface
6			SUBROUTINE INI_CG2D( myThid )
7			C /==========================================================\
8			C \| SUBROUTINE INI_CG2D \|
9			C \| o Initialise 2d conjugate gradient solver operators. \|
10			C \|==========================================================\|
11			C \| These arrays are purely a function of the basin geom. \|
12			C \| We set then here once and them use then repeatedly. \|
13			C \==========================================================/
14
15			C === Global variables ===
16			#include "SIZE.h"
17			#include "EEPARAMS.h"
18			#include "PARAMS.h"
19			#include "GRID.h"
20	cnh	1.12	#include "DYNVARS.h"
21	cnh	1.1	#include "CG2D.h"
22
23			C === Routine arguments ===
24			C myThid - Thread no. that called this routine.
25			INTEGER myThid
26			CEndOfInterface
27
28			C === Local variables ===
29			C xG, yG - Global coordinate location.
30			C zG
31			C iG, jG - Global coordinate index
32			C bi,bj - Loop counters
33			C faceArea - Temporary used to hold cell face areas.
34			C I,J,K
35			C myNorm - Work variable used in clculating normalisation factor
36			CHARACTER*(MAX_LEN_MBUF) msgBuf
37			INTEGER bi, bj
38			INTEGER I, J, K
39	cnh	1.7	_RL faceArea
40	cnh	1.15	_RS myNorm
41	cnh	1.4	_RL aC, aCw, aCs
42	cnh	1.1
43			C-- Initialise laplace operator
44			C aW2d: integral in Z Ax/dX
45			C aS2d: integral in Z Ay/dY
46			myNorm = 0. _d 0
47			DO bj=myByLo(myThid),myByHi(myThid)
48			DO bi=myBxLo(myThid),myBxHi(myThid)
49			DO J=1,sNy
50			DO I=1,sNx
51			aW2d(I,J,bi,bj) = 0. _d 0
52			aS2d(I,J,bi,bj) = 0. _d 0
53			ENDDO
54			ENDDO
55	cnh	1.17	DO K=1,Nr
56	cnh	1.1	DO J=1,sNy
57			DO I=1,sNx
58	cnh	1.20	faceArea = _dyG(I,J,bi,bj)*drF(K)
59			& *_hFacW(I,J,K,bi,bj)
60	cnh	1.1	aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj) +
61	cnh	1.17	& gBarofaceArearecip_dxC(I,J,bi,bj)
62	cnh	1.20	faceArea = _dxG(I,J,bi,bj)*drF(K)
63			& *_hFacS(I,J,K,bi,bj)
64	cnh	1.1	aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj) +
65	cnh	1.17	& gBarofaceArearecip_dyC(I,J,bi,bj)
66	cnh	1.1	ENDDO
67			ENDDO
68			ENDDO
69			DO J=1,sNy
70			DO I=1,sNx
71			myNorm = MAX(ABS(aW2d(I,J,bi,bj)),myNorm)
72			myNorm = MAX(ABS(aS2d(I,J,bi,bj)),myNorm)
73			ENDDO
74			ENDDO
75			ENDDO
76			ENDDO
77			cg2dNbuf(1,myThid) = myNorm
78	adcroft	1.16	_GLOBAL_MAX_R4( cg2dNbuf, myNorm, myThid )
79	cnh	1.1	IF ( cg2dNbuf(1,1) .NE. 0. _d 0 ) THEN
80			myNorm = 1. _d 0/cg2dNbuf(1,1)
81			ELSE
82			myNorm = 1. _d 0
83			ENDIF
84	cnh	1.5	cg2dNorm = myNorm
85	cnh	1.1	_BEGIN_MASTER( myThid )
86			CcnhDebugStarts
87	cnh	1.20	WRITE(msgBuf,'(A,E40.25)') '// CG2D normalisation factor = ',
88			& cg2dNorm
89	cnh	1.3	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
90			WRITE(msgBuf,*) ' '
91	cnh	1.1	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
92			CcnhDebugEnds
93			_END_MASTER( myThid )
94			DO bj=myByLo(myThid),myByHi(myThid)
95			DO bi=myBxLo(myThid),myBxHi(myThid)
96			DO J=1,sNy
97			DO I=1,sNx
98			aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj)*myNorm
99			aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj)*myNorm
100			ENDDO
101			ENDDO
102			ENDDO
103			ENDDO
104
105			C-- Update overlap regions
106			CcnhDebugStarts
107	cnh	1.14	C CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.1' , 1, myThid )
108			C CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.1' , 1, myThid )
109	cnh	1.1	CcnhDebugEnds
110			_EXCH_XY_R4(aW2d, myThid)
111			_EXCH_XY_R4(aS2d, myThid)
112			CcnhDebugStarts
113	cnh	1.18	CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.2' , 1, myThid )
114			CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.2' , 1, myThid )
115	cnh	1.1	CcnhDebugEnds
116
117			C-- Initialise preconditioner
118	cnh	1.4	C Note. 20th May 1998
119			C I made a weird discovery! In the model paper we argue
120			C for the form of the preconditioner used here ( see
121			C A Finite-volume, Incompressible Navier-Stokes Model
122			C ...., Marshall et. al ). The algebra gives a simple
123			C 0.5 factor for the averaging of ac and aCw to get a
124			C symmettric pre-conditioner. By using a factor of 0.51
125			C i.e. scaling the off-diagonal terms in the
126			C preconditioner down slightly I managed to get the
127			C number of iterations for convergence in a test case to
128			C drop form 192 -> 134! Need to investigate this further!
129			C For now I have introduced a parameter cg2dpcOffDFac which
130			C defaults to 0.51 but can be set at runtime.
131	cnh	1.1	DO bj=myByLo(myThid),myByHi(myThid)
132			DO bi=myBxLo(myThid),myBxHi(myThid)
133			DO J=1,sNy
134			DO I=1,sNx
135			pC(I,J,bi,bj) = 1. _d 0
136	cnh	1.4	aC = -(
137			& aW2d(I,J,bi,bj) + aW2d(I+1,J ,bi,bj)
138			& +aS2d(I,J,bi,bj) + aS2D(I ,J+1,bi,bj)
139	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
140	cnh	1.17	& rA(I,J,bi,bj)/deltaTMom/deltaTMom
141	cnh	1.4	& )
142			aCs = -(
143			& aW2d(I,J-1,bi,bj) + aW2d(I+1,J-1,bi,bj)
144			& +aS2d(I,J-1,bi,bj) + aS2d(I ,J ,bi,bj)
145	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
146	cnh	1.17	& rA(I,J-1,bi,bj)/deltaTMom/deltaTMom
147	cnh	1.4	& )
148			aCw = -(
149			& aW2d(I-1,J,bi,bj) + aW2d(I ,J ,bi,bj)
150			& +aS2d(I-1,J,bi,bj) + aS2d(I-1,J+1,bi,bj)
151	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
152	cnh	1.17	& rA(I-1,J,bi,bj)/deltaTMom/deltaTMom
153	cnh	1.4	& )
154			IF ( aC .EQ. 0. ) THEN
155			pC(I,J,bi,bj) = 0. _d 0
156			ELSE
157			pC(I,J,bi,bj) = 1. _d 0 / aC
158			ENDIF
159			IF ( aC + aCw .EQ. 0. ) THEN
160			pW(I,J,bi,bj) = 0.
161			ELSE
162			pW(I,J,bi,bj) =
163			& -aW2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCw+aC))*2 )
164			ENDIF
165			IF ( aC + aCs .EQ. 0. ) THEN
166			pS(I,J,bi,bj) = 0.
167			ELSE
168			pS(I,J,bi,bj) =
169			& -aS2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCs+aC))*2 )
170			ENDIF
171	cnh	1.6	C pC(I,J,bi,bj) = 1.
172			C pW(I,J,bi,bj) = 0.
173			C pS(I,J,bi,bj) = 0.
174	cnh	1.1	ENDDO
175			ENDDO
176			ENDDO
177			ENDDO
178			C-- Update overlap regions
179			_EXCH_XY_R4(pC, myThid)
180			_EXCH_XY_R4(pW, myThid)
181			_EXCH_XY_R4(pS, myThid)
182	cnh	1.18	CcnhDebugStarts
183			CALL PLOT_FIELD_XYRS( pC, 'pC INI_CG2D.2' , 1, myThid )
184			CALL PLOT_FIELD_XYRS( pW, 'pW INI_CG2D.2' , 1, myThid )
185			CALL PLOT_FIELD_XYRS( pS, 'pS INI_CG2D.2' , 1, myThid )
186			CcnhDebugEnds
187	cnh	1.1
188	cnh	1.5	C-- Set default values for initial guess and RHS
189	cnh	1.4	IF ( startTime .EQ. 0 ) THEN
190			DO bj=myByLo(myThid),myByHi(myThid)
191			DO bi=myBxLo(myThid),myBxHi(myThid)
192			DO J=1,sNy
193			DO I=1,sNx
194			cg2d_x(I,J,bi,bj) = 0. _d 0
195	cnh	1.5	cg2d_b(I,J,bi,bj) = 0. _d 0
196	cnh	1.12	#ifdef ALLOW_CD
197			cg2d_xNM1(I,J,bi,bj) = 0. _d 0
198			#endif
199	cnh	1.4	ENDDO
200	cnh	1.1	ENDDO
201			ENDDO
202			ENDDO
203	cnh	1.4	C-- Update overlap regions
204			_EXCH_XY_R8(cg2d_x, myThid)
205	cnh	1.5	_EXCH_XY_R8(cg2d_b, myThid)
206	cnh	1.12	#ifdef ALLOW_CD
207			_EXCH_XY_R8(cg2d_xNM1, myThid)
208			#endif
209	cnh	1.4	ENDIF
210	cnh	1.1
211			RETURN
212			END