model/src/ini_cg2d.F

C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.21 1998/11/06 22:44:46 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"
#include "OBCS.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
        IF (openBoundaries) THEN
         DO I=1,sNx
          IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj),bi,bj)=0.
          IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj)+1,bi,bj)=0.
          IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj)+1,bi,bj)=0.
          IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj),bi,bj)=0.
         ENDDO
         DO J=1,sNy
          IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj),J,bi,bj)=0.
          IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj)+1,J,bi,bj)=0.
          IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj)+1,J,bi,bj)=0.
          IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj),J,bi,bj)=0.
         ENDDO
        ENDIF
        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 INCLUDE_CD_CODE
           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 INCLUDE_CD_CODE
       _EXCH_XY_R8(cg2d_xNM1, myThid)
#endif
      ENDIF

      RETURN
      END
1	adcroft	1.22	C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.21 1998/11/06 22:44:46 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	adcroft	1.22	#include "OBCS.h"
23	cnh	1.1
24			C === Routine arguments ===
25			C myThid - Thread no. that called this routine.
26			INTEGER myThid
27			CEndOfInterface
28
29			C === Local variables ===
30			C xG, yG - Global coordinate location.
31			C zG
32			C iG, jG - Global coordinate index
33			C bi,bj - Loop counters
34			C faceArea - Temporary used to hold cell face areas.
35			C I,J,K
36			C myNorm - Work variable used in clculating normalisation factor
37			CHARACTER*(MAX_LEN_MBUF) msgBuf
38			INTEGER bi, bj
39			INTEGER I, J, K
40	cnh	1.7	_RL faceArea
41	cnh	1.15	_RS myNorm
42	cnh	1.4	_RL aC, aCw, aCs
43	cnh	1.1
44			C-- Initialise laplace operator
45			C aW2d: integral in Z Ax/dX
46			C aS2d: integral in Z Ay/dY
47			myNorm = 0. _d 0
48			DO bj=myByLo(myThid),myByHi(myThid)
49			DO bi=myBxLo(myThid),myBxHi(myThid)
50			DO J=1,sNy
51			DO I=1,sNx
52			aW2d(I,J,bi,bj) = 0. _d 0
53			aS2d(I,J,bi,bj) = 0. _d 0
54			ENDDO
55			ENDDO
56	cnh	1.17	DO K=1,Nr
57	cnh	1.1	DO J=1,sNy
58			DO I=1,sNx
59	cnh	1.20	faceArea = _dyG(I,J,bi,bj)*drF(K)
60			& *_hFacW(I,J,K,bi,bj)
61	cnh	1.1	aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj) +
62	cnh	1.17	& gBarofaceArearecip_dxC(I,J,bi,bj)
63	cnh	1.20	faceArea = _dxG(I,J,bi,bj)*drF(K)
64			& *_hFacS(I,J,K,bi,bj)
65	cnh	1.1	aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj) +
66	cnh	1.17	& gBarofaceArearecip_dyC(I,J,bi,bj)
67	cnh	1.1	ENDDO
68			ENDDO
69			ENDDO
70	adcroft	1.22	IF (openBoundaries) THEN
71			DO I=1,sNx
72			IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj),bi,bj)=0.
73			IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj)+1,bi,bj)=0.
74			IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj)+1,bi,bj)=0.
75			IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj),bi,bj)=0.
76			ENDDO
77			DO J=1,sNy
78			IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj),J,bi,bj)=0.
79			IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj)+1,J,bi,bj)=0.
80			IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj)+1,J,bi,bj)=0.
81			IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj),J,bi,bj)=0.
82			ENDDO
83			ENDIF
84	cnh	1.1	DO J=1,sNy
85			DO I=1,sNx
86			myNorm = MAX(ABS(aW2d(I,J,bi,bj)),myNorm)
87			myNorm = MAX(ABS(aS2d(I,J,bi,bj)),myNorm)
88			ENDDO
89			ENDDO
90			ENDDO
91			ENDDO
92			cg2dNbuf(1,myThid) = myNorm
93	adcroft	1.16	_GLOBAL_MAX_R4( cg2dNbuf, myNorm, myThid )
94	cnh	1.1	IF ( cg2dNbuf(1,1) .NE. 0. _d 0 ) THEN
95			myNorm = 1. _d 0/cg2dNbuf(1,1)
96			ELSE
97			myNorm = 1. _d 0
98			ENDIF
99	cnh	1.5	cg2dNorm = myNorm
100	cnh	1.1	_BEGIN_MASTER( myThid )
101			CcnhDebugStarts
102	cnh	1.20	WRITE(msgBuf,'(A,E40.25)') '// CG2D normalisation factor = ',
103			& cg2dNorm
104	cnh	1.3	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
105			WRITE(msgBuf,*) ' '
106	cnh	1.1	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
107			CcnhDebugEnds
108			_END_MASTER( myThid )
109			DO bj=myByLo(myThid),myByHi(myThid)
110			DO bi=myBxLo(myThid),myBxHi(myThid)
111			DO J=1,sNy
112			DO I=1,sNx
113			aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj)*myNorm
114			aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj)*myNorm
115			ENDDO
116			ENDDO
117			ENDDO
118			ENDDO
119
120			C-- Update overlap regions
121			CcnhDebugStarts
122	cnh	1.14	C CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.1' , 1, myThid )
123			C CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.1' , 1, myThid )
124	cnh	1.1	CcnhDebugEnds
125			_EXCH_XY_R4(aW2d, myThid)
126			_EXCH_XY_R4(aS2d, myThid)
127			CcnhDebugStarts
128	cnh	1.18	CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.2' , 1, myThid )
129			CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.2' , 1, myThid )
130	cnh	1.1	CcnhDebugEnds
131
132			C-- Initialise preconditioner
133	cnh	1.4	C Note. 20th May 1998
134			C I made a weird discovery! In the model paper we argue
135			C for the form of the preconditioner used here ( see
136			C A Finite-volume, Incompressible Navier-Stokes Model
137			C ...., Marshall et. al ). The algebra gives a simple
138			C 0.5 factor for the averaging of ac and aCw to get a
139			C symmettric pre-conditioner. By using a factor of 0.51
140			C i.e. scaling the off-diagonal terms in the
141			C preconditioner down slightly I managed to get the
142			C number of iterations for convergence in a test case to
143			C drop form 192 -> 134! Need to investigate this further!
144			C For now I have introduced a parameter cg2dpcOffDFac which
145			C defaults to 0.51 but can be set at runtime.
146	cnh	1.1	DO bj=myByLo(myThid),myByHi(myThid)
147			DO bi=myBxLo(myThid),myBxHi(myThid)
148			DO J=1,sNy
149			DO I=1,sNx
150			pC(I,J,bi,bj) = 1. _d 0
151	cnh	1.4	aC = -(
152			& aW2d(I,J,bi,bj) + aW2d(I+1,J ,bi,bj)
153			& +aS2d(I,J,bi,bj) + aS2D(I ,J+1,bi,bj)
154	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
155	cnh	1.17	& rA(I,J,bi,bj)/deltaTMom/deltaTMom
156	cnh	1.4	& )
157			aCs = -(
158			& aW2d(I,J-1,bi,bj) + aW2d(I+1,J-1,bi,bj)
159			& +aS2d(I,J-1,bi,bj) + aS2d(I ,J ,bi,bj)
160	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
161	cnh	1.17	& rA(I,J-1,bi,bj)/deltaTMom/deltaTMom
162	cnh	1.4	& )
163			aCw = -(
164			& aW2d(I-1,J,bi,bj) + aW2d(I ,J ,bi,bj)
165			& +aS2d(I-1,J,bi,bj) + aS2d(I-1,J+1,bi,bj)
166	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
167	cnh	1.17	& rA(I-1,J,bi,bj)/deltaTMom/deltaTMom
168	cnh	1.4	& )
169			IF ( aC .EQ. 0. ) THEN
170			pC(I,J,bi,bj) = 0. _d 0
171			ELSE
172			pC(I,J,bi,bj) = 1. _d 0 / aC
173			ENDIF
174			IF ( aC + aCw .EQ. 0. ) THEN
175			pW(I,J,bi,bj) = 0.
176			ELSE
177			pW(I,J,bi,bj) =
178			& -aW2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCw+aC))*2 )
179			ENDIF
180			IF ( aC + aCs .EQ. 0. ) THEN
181			pS(I,J,bi,bj) = 0.
182			ELSE
183			pS(I,J,bi,bj) =
184			& -aS2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCs+aC))*2 )
185			ENDIF
186	cnh	1.6	C pC(I,J,bi,bj) = 1.
187			C pW(I,J,bi,bj) = 0.
188			C pS(I,J,bi,bj) = 0.
189	cnh	1.1	ENDDO
190			ENDDO
191			ENDDO
192			ENDDO
193			C-- Update overlap regions
194			_EXCH_XY_R4(pC, myThid)
195			_EXCH_XY_R4(pW, myThid)
196			_EXCH_XY_R4(pS, myThid)
197	cnh	1.18	CcnhDebugStarts
198			CALL PLOT_FIELD_XYRS( pC, 'pC INI_CG2D.2' , 1, myThid )
199			CALL PLOT_FIELD_XYRS( pW, 'pW INI_CG2D.2' , 1, myThid )
200			CALL PLOT_FIELD_XYRS( pS, 'pS INI_CG2D.2' , 1, myThid )
201			CcnhDebugEnds
202	cnh	1.1
203	cnh	1.5	C-- Set default values for initial guess and RHS
204	cnh	1.4	IF ( startTime .EQ. 0 ) THEN
205			DO bj=myByLo(myThid),myByHi(myThid)
206			DO bi=myBxLo(myThid),myBxHi(myThid)
207			DO J=1,sNy
208			DO I=1,sNx
209			cg2d_x(I,J,bi,bj) = 0. _d 0
210	cnh	1.5	cg2d_b(I,J,bi,bj) = 0. _d 0
211	cnh	1.21	#ifdef INCLUDE_CD_CODE
212	cnh	1.12	cg2d_xNM1(I,J,bi,bj) = 0. _d 0
213			#endif
214	cnh	1.4	ENDDO
215	cnh	1.1	ENDDO
216			ENDDO
217			ENDDO
218	cnh	1.4	C-- Update overlap regions
219			_EXCH_XY_R8(cg2d_x, myThid)
220	cnh	1.5	_EXCH_XY_R8(cg2d_b, myThid)
221	cnh	1.21	#ifdef INCLUDE_CD_CODE
222	cnh	1.12	_EXCH_XY_R8(cg2d_xNM1, myThid)
223			#endif
224	cnh	1.4	ENDIF
225	cnh	1.1
226			RETURN
227			END