model/src/ini_cg2d.F

C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.28 2001/02/02 21:04:48 adcroft Exp $
C $Name: $

#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     \==========================================================/
      IMPLICIT NONE

C     === Global variables ===
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "DYNVARS.h"
#include "CG2D.h"
#ifdef ALLOW_OBCS
#include "OBCS.h"
#endif

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
#ifdef ALLOW_OBCS
        IF (useOBCS) 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
#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
      _GLOBAL_MAX_R4( myNorm, myThid )
      IF ( myNorm .NE. 0. _d 0 ) THEN
       myNorm = 1. _d 0/myNorm
      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
C     CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.2' , 1, myThid )
C     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) = 1. _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
C     CALL PLOT_FIELD_XYRS( pC, 'pC   INI_CG2D.2' , 1, myThid )
C     CALL PLOT_FIELD_XYRS( pW, 'pW   INI_CG2D.2' , 1, myThid )
C     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	cnh	1.29	C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.28 2001/02/02 21:04:48 adcroft Exp $
2			C $Name: $
3	cnh	1.1
4	adcroft	1.13	#include "CPP_OPTIONS.h"
5	cnh	1.1
6			CStartOfInterface
7			SUBROUTINE INI_CG2D( myThid )
8			C /==========================================================\
9			C \| SUBROUTINE INI_CG2D \|
10			C \| o Initialise 2d conjugate gradient solver operators. \|
11			C \|==========================================================\|
12			C \| These arrays are purely a function of the basin geom. \|
13			C \| We set then here once and them use then repeatedly. \|
14			C \==========================================================/
15	adcroft	1.23	IMPLICIT NONE
16	cnh	1.1
17			C === Global variables ===
18			#include "SIZE.h"
19			#include "EEPARAMS.h"
20			#include "PARAMS.h"
21			#include "GRID.h"
22	cnh	1.12	#include "DYNVARS.h"
23	cnh	1.1	#include "CG2D.h"
24	adcroft	1.26	#ifdef ALLOW_OBCS
25	adcroft	1.22	#include "OBCS.h"
26	adcroft	1.26	#endif
27	cnh	1.1
28			C === Routine arguments ===
29			C myThid - Thread no. that called this routine.
30			INTEGER myThid
31			CEndOfInterface
32
33			C === Local variables ===
34			C xG, yG - Global coordinate location.
35			C zG
36			C iG, jG - Global coordinate index
37			C bi,bj - Loop counters
38			C faceArea - Temporary used to hold cell face areas.
39			C I,J,K
40			C myNorm - Work variable used in clculating normalisation factor
41			CHARACTER*(MAX_LEN_MBUF) msgBuf
42			INTEGER bi, bj
43			INTEGER I, J, K
44	cnh	1.7	_RL faceArea
45	cnh	1.15	_RS myNorm
46	cnh	1.4	_RL aC, aCw, aCs
47	cnh	1.1
48			C-- Initialise laplace operator
49			C aW2d: integral in Z Ax/dX
50			C aS2d: integral in Z Ay/dY
51			myNorm = 0. _d 0
52			DO bj=myByLo(myThid),myByHi(myThid)
53			DO bi=myBxLo(myThid),myBxHi(myThid)
54			DO J=1,sNy
55			DO I=1,sNx
56			aW2d(I,J,bi,bj) = 0. _d 0
57			aS2d(I,J,bi,bj) = 0. _d 0
58			ENDDO
59			ENDDO
60	cnh	1.17	DO K=1,Nr
61	cnh	1.1	DO J=1,sNy
62			DO I=1,sNx
63	cnh	1.20	faceArea = _dyG(I,J,bi,bj)*drF(K)
64			& *_hFacW(I,J,K,bi,bj)
65	cnh	1.1	aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj) +
66	cnh	1.17	& gBarofaceArearecip_dxC(I,J,bi,bj)
67	cnh	1.20	faceArea = _dxG(I,J,bi,bj)*drF(K)
68			& *_hFacS(I,J,K,bi,bj)
69	cnh	1.1	aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj) +
70	cnh	1.17	& gBarofaceArearecip_dyC(I,J,bi,bj)
71	cnh	1.1	ENDDO
72			ENDDO
73			ENDDO
74	adcroft	1.26	#ifdef ALLOW_OBCS
75	adcroft	1.28	IF (useOBCS) THEN
76	adcroft	1.22	DO I=1,sNx
77			IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj),bi,bj)=0.
78			IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj)+1,bi,bj)=0.
79			IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj)+1,bi,bj)=0.
80			IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj),bi,bj)=0.
81			ENDDO
82			DO J=1,sNy
83			IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj),J,bi,bj)=0.
84			IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj)+1,J,bi,bj)=0.
85			IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj)+1,J,bi,bj)=0.
86			IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj),J,bi,bj)=0.
87			ENDDO
88			ENDIF
89	adcroft	1.26	#endif
90	cnh	1.1	DO J=1,sNy
91			DO I=1,sNx
92			myNorm = MAX(ABS(aW2d(I,J,bi,bj)),myNorm)
93			myNorm = MAX(ABS(aS2d(I,J,bi,bj)),myNorm)
94			ENDDO
95			ENDDO
96			ENDDO
97			ENDDO
98	adcroft	1.25	_GLOBAL_MAX_R4( myNorm, myThid )
99			IF ( myNorm .NE. 0. _d 0 ) THEN
100			myNorm = 1. _d 0/myNorm
101	cnh	1.1	ELSE
102			myNorm = 1. _d 0
103			ENDIF
104	cnh	1.5	cg2dNorm = myNorm
105	cnh	1.1	_BEGIN_MASTER( myThid )
106			CcnhDebugStarts
107	cnh	1.20	WRITE(msgBuf,'(A,E40.25)') '// CG2D normalisation factor = ',
108			& cg2dNorm
109	cnh	1.3	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
110			WRITE(msgBuf,*) ' '
111	cnh	1.1	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
112			CcnhDebugEnds
113			_END_MASTER( myThid )
114			DO bj=myByLo(myThid),myByHi(myThid)
115			DO bi=myBxLo(myThid),myBxHi(myThid)
116			DO J=1,sNy
117			DO I=1,sNx
118			aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj)*myNorm
119			aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj)*myNorm
120			ENDDO
121			ENDDO
122			ENDDO
123			ENDDO
124
125			C-- Update overlap regions
126			CcnhDebugStarts
127	cnh	1.14	C CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.1' , 1, myThid )
128			C CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.1' , 1, myThid )
129	cnh	1.1	CcnhDebugEnds
130			_EXCH_XY_R4(aW2d, myThid)
131			_EXCH_XY_R4(aS2d, myThid)
132			CcnhDebugStarts
133	adcroft	1.24	C CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.2' , 1, myThid )
134			C CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.2' , 1, myThid )
135	cnh	1.1	CcnhDebugEnds
136
137			C-- Initialise preconditioner
138	cnh	1.4	C Note. 20th May 1998
139			C I made a weird discovery! In the model paper we argue
140			C for the form of the preconditioner used here ( see
141			C A Finite-volume, Incompressible Navier-Stokes Model
142			C ...., Marshall et. al ). The algebra gives a simple
143			C 0.5 factor for the averaging of ac and aCw to get a
144			C symmettric pre-conditioner. By using a factor of 0.51
145			C i.e. scaling the off-diagonal terms in the
146			C preconditioner down slightly I managed to get the
147			C number of iterations for convergence in a test case to
148			C drop form 192 -> 134! Need to investigate this further!
149			C For now I have introduced a parameter cg2dpcOffDFac which
150			C defaults to 0.51 but can be set at runtime.
151	cnh	1.1	DO bj=myByLo(myThid),myByHi(myThid)
152			DO bi=myBxLo(myThid),myBxHi(myThid)
153			DO J=1,sNy
154			DO I=1,sNx
155			pC(I,J,bi,bj) = 1. _d 0
156	cnh	1.4	aC = -(
157			& aW2d(I,J,bi,bj) + aW2d(I+1,J ,bi,bj)
158	adcroft	1.24	& +aS2d(I,J,bi,bj) + aS2d(I ,J+1,bi,bj)
159	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
160	cnh	1.17	& rA(I,J,bi,bj)/deltaTMom/deltaTMom
161	cnh	1.4	& )
162			aCs = -(
163			& aW2d(I,J-1,bi,bj) + aW2d(I+1,J-1,bi,bj)
164			& +aS2d(I,J-1,bi,bj) + aS2d(I ,J ,bi,bj)
165	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
166	cnh	1.17	& rA(I,J-1,bi,bj)/deltaTMom/deltaTMom
167	cnh	1.4	& )
168			aCw = -(
169			& aW2d(I-1,J,bi,bj) + aW2d(I ,J ,bi,bj)
170			& +aS2d(I-1,J,bi,bj) + aS2d(I-1,J+1,bi,bj)
171	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
172	cnh	1.17	& rA(I-1,J,bi,bj)/deltaTMom/deltaTMom
173	cnh	1.4	& )
174			IF ( aC .EQ. 0. ) THEN
175	adcroft	1.27	pC(I,J,bi,bj) = 1. _d 0
176	cnh	1.4	ELSE
177			pC(I,J,bi,bj) = 1. _d 0 / aC
178			ENDIF
179			IF ( aC + aCw .EQ. 0. ) THEN
180			pW(I,J,bi,bj) = 0.
181			ELSE
182			pW(I,J,bi,bj) =
183			& -aW2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCw+aC))*2 )
184			ENDIF
185			IF ( aC + aCs .EQ. 0. ) THEN
186			pS(I,J,bi,bj) = 0.
187			ELSE
188			pS(I,J,bi,bj) =
189			& -aS2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCs+aC))*2 )
190			ENDIF
191	cnh	1.6	C pC(I,J,bi,bj) = 1.
192			C pW(I,J,bi,bj) = 0.
193			C pS(I,J,bi,bj) = 0.
194	cnh	1.1	ENDDO
195			ENDDO
196			ENDDO
197			ENDDO
198			C-- Update overlap regions
199			_EXCH_XY_R4(pC, myThid)
200			_EXCH_XY_R4(pW, myThid)
201			_EXCH_XY_R4(pS, myThid)
202	cnh	1.18	CcnhDebugStarts
203	adcroft	1.24	C CALL PLOT_FIELD_XYRS( pC, 'pC INI_CG2D.2' , 1, myThid )
204			C CALL PLOT_FIELD_XYRS( pW, 'pW INI_CG2D.2' , 1, myThid )
205			C CALL PLOT_FIELD_XYRS( pS, 'pS INI_CG2D.2' , 1, myThid )
206	cnh	1.18	CcnhDebugEnds
207	cnh	1.1
208	cnh	1.5	C-- Set default values for initial guess and RHS
209	cnh	1.4	IF ( startTime .EQ. 0 ) THEN
210			DO bj=myByLo(myThid),myByHi(myThid)
211			DO bi=myBxLo(myThid),myBxHi(myThid)
212			DO J=1,sNy
213			DO I=1,sNx
214			cg2d_x(I,J,bi,bj) = 0. _d 0
215	cnh	1.5	cg2d_b(I,J,bi,bj) = 0. _d 0
216	cnh	1.21	#ifdef INCLUDE_CD_CODE
217	cnh	1.12	cg2d_xNM1(I,J,bi,bj) = 0. _d 0
218			#endif
219	cnh	1.4	ENDDO
220	cnh	1.1	ENDDO
221			ENDDO
222			ENDDO
223	cnh	1.4	C-- Update overlap regions
224			_EXCH_XY_R8(cg2d_x, myThid)
225	cnh	1.5	_EXCH_XY_R8(cg2d_b, myThid)
226	cnh	1.21	#ifdef INCLUDE_CD_CODE
227	cnh	1.12	_EXCH_XY_R8(cg2d_xNM1, myThid)
228			#endif
229	cnh	1.4	ENDIF
230	cnh	1.1
231			RETURN
232			END