model/src/ini_cg2d.F

C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.27.2.1 2001/01/30 21:02:59 adcroft 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     \==========================================================/
      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	adcroft	1.28	C $Header: /u/gcmpack/models/MITgcmUV/model/src/ini_cg2d.F,v 1.27.2.1 2001/01/30 21:02:59 adcroft 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	adcroft	1.23	IMPLICIT NONE
15	cnh	1.1
16			C === Global variables ===
17			#include "SIZE.h"
18			#include "EEPARAMS.h"
19			#include "PARAMS.h"
20			#include "GRID.h"
21	cnh	1.12	#include "DYNVARS.h"
22	cnh	1.1	#include "CG2D.h"
23	adcroft	1.26	#ifdef ALLOW_OBCS
24	adcroft	1.22	#include "OBCS.h"
25	adcroft	1.26	#endif
26	cnh	1.1
27			C === Routine arguments ===
28			C myThid - Thread no. that called this routine.
29			INTEGER myThid
30			CEndOfInterface
31
32			C === Local variables ===
33			C xG, yG - Global coordinate location.
34			C zG
35			C iG, jG - Global coordinate index
36			C bi,bj - Loop counters
37			C faceArea - Temporary used to hold cell face areas.
38			C I,J,K
39			C myNorm - Work variable used in clculating normalisation factor
40			CHARACTER*(MAX_LEN_MBUF) msgBuf
41			INTEGER bi, bj
42			INTEGER I, J, K
43	cnh	1.7	_RL faceArea
44	cnh	1.15	_RS myNorm
45	cnh	1.4	_RL aC, aCw, aCs
46	cnh	1.1
47			C-- Initialise laplace operator
48			C aW2d: integral in Z Ax/dX
49			C aS2d: integral in Z Ay/dY
50			myNorm = 0. _d 0
51			DO bj=myByLo(myThid),myByHi(myThid)
52			DO bi=myBxLo(myThid),myBxHi(myThid)
53			DO J=1,sNy
54			DO I=1,sNx
55			aW2d(I,J,bi,bj) = 0. _d 0
56			aS2d(I,J,bi,bj) = 0. _d 0
57			ENDDO
58			ENDDO
59	cnh	1.17	DO K=1,Nr
60	cnh	1.1	DO J=1,sNy
61			DO I=1,sNx
62	cnh	1.20	faceArea = _dyG(I,J,bi,bj)*drF(K)
63			& *_hFacW(I,J,K,bi,bj)
64	cnh	1.1	aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj) +
65	cnh	1.17	& gBarofaceArearecip_dxC(I,J,bi,bj)
66	cnh	1.20	faceArea = _dxG(I,J,bi,bj)*drF(K)
67			& *_hFacS(I,J,K,bi,bj)
68	cnh	1.1	aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj) +
69	cnh	1.17	& gBarofaceArearecip_dyC(I,J,bi,bj)
70	cnh	1.1	ENDDO
71			ENDDO
72			ENDDO
73	adcroft	1.26	#ifdef ALLOW_OBCS
74	adcroft	1.28	IF (useOBCS) THEN
75	adcroft	1.22	DO I=1,sNx
76			IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj),bi,bj)=0.
77			IF (OB_Jn(I,bi,bj).NE.0) aS2d(I,OB_Jn(I,bi,bj)+1,bi,bj)=0.
78			IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj)+1,bi,bj)=0.
79			IF (OB_Js(I,bi,bj).NE.0) aS2d(I,OB_Js(I,bi,bj),bi,bj)=0.
80			ENDDO
81			DO J=1,sNy
82			IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj),J,bi,bj)=0.
83			IF (OB_Ie(J,bi,bj).NE.0) aW2d(OB_Ie(J,bi,bj)+1,J,bi,bj)=0.
84			IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj)+1,J,bi,bj)=0.
85			IF (OB_Iw(J,bi,bj).NE.0) aW2d(OB_Iw(J,bi,bj),J,bi,bj)=0.
86			ENDDO
87			ENDIF
88	adcroft	1.26	#endif
89	cnh	1.1	DO J=1,sNy
90			DO I=1,sNx
91			myNorm = MAX(ABS(aW2d(I,J,bi,bj)),myNorm)
92			myNorm = MAX(ABS(aS2d(I,J,bi,bj)),myNorm)
93			ENDDO
94			ENDDO
95			ENDDO
96			ENDDO
97	adcroft	1.25	_GLOBAL_MAX_R4( myNorm, myThid )
98			IF ( myNorm .NE. 0. _d 0 ) THEN
99			myNorm = 1. _d 0/myNorm
100	cnh	1.1	ELSE
101			myNorm = 1. _d 0
102			ENDIF
103	cnh	1.5	cg2dNorm = myNorm
104	cnh	1.1	_BEGIN_MASTER( myThid )
105			CcnhDebugStarts
106	cnh	1.20	WRITE(msgBuf,'(A,E40.25)') '// CG2D normalisation factor = ',
107			& cg2dNorm
108	cnh	1.3	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
109			WRITE(msgBuf,*) ' '
110	cnh	1.1	CALL PRINT_MESSAGE( msgBuf,standardMessageUnit,SQUEEZE_RIGHT,1)
111			CcnhDebugEnds
112			_END_MASTER( myThid )
113			DO bj=myByLo(myThid),myByHi(myThid)
114			DO bi=myBxLo(myThid),myBxHi(myThid)
115			DO J=1,sNy
116			DO I=1,sNx
117			aW2d(I,J,bi,bj) = aW2d(I,J,bi,bj)*myNorm
118			aS2d(I,J,bi,bj) = aS2d(I,J,bi,bj)*myNorm
119			ENDDO
120			ENDDO
121			ENDDO
122			ENDDO
123
124			C-- Update overlap regions
125			CcnhDebugStarts
126	cnh	1.14	C CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.1' , 1, myThid )
127			C CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.1' , 1, myThid )
128	cnh	1.1	CcnhDebugEnds
129			_EXCH_XY_R4(aW2d, myThid)
130			_EXCH_XY_R4(aS2d, myThid)
131			CcnhDebugStarts
132	adcroft	1.24	C CALL PLOT_FIELD_XYRS( aW2d, 'AW2D INI_CG2D.2' , 1, myThid )
133			C CALL PLOT_FIELD_XYRS( aS2d, 'AS2D INI_CG2D.2' , 1, myThid )
134	cnh	1.1	CcnhDebugEnds
135
136			C-- Initialise preconditioner
137	cnh	1.4	C Note. 20th May 1998
138			C I made a weird discovery! In the model paper we argue
139			C for the form of the preconditioner used here ( see
140			C A Finite-volume, Incompressible Navier-Stokes Model
141			C ...., Marshall et. al ). The algebra gives a simple
142			C 0.5 factor for the averaging of ac and aCw to get a
143			C symmettric pre-conditioner. By using a factor of 0.51
144			C i.e. scaling the off-diagonal terms in the
145			C preconditioner down slightly I managed to get the
146			C number of iterations for convergence in a test case to
147			C drop form 192 -> 134! Need to investigate this further!
148			C For now I have introduced a parameter cg2dpcOffDFac which
149			C defaults to 0.51 but can be set at runtime.
150	cnh	1.1	DO bj=myByLo(myThid),myByHi(myThid)
151			DO bi=myBxLo(myThid),myBxHi(myThid)
152			DO J=1,sNy
153			DO I=1,sNx
154			pC(I,J,bi,bj) = 1. _d 0
155	cnh	1.4	aC = -(
156			& aW2d(I,J,bi,bj) + aW2d(I+1,J ,bi,bj)
157	adcroft	1.24	& +aS2d(I,J,bi,bj) + aS2d(I ,J+1,bi,bj)
158	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
159	cnh	1.17	& rA(I,J,bi,bj)/deltaTMom/deltaTMom
160	cnh	1.4	& )
161			aCs = -(
162			& aW2d(I,J-1,bi,bj) + aW2d(I+1,J-1,bi,bj)
163			& +aS2d(I,J-1,bi,bj) + aS2d(I ,J ,bi,bj)
164	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
165	cnh	1.17	& rA(I,J-1,bi,bj)/deltaTMom/deltaTMom
166	cnh	1.4	& )
167			aCw = -(
168			& aW2d(I-1,J,bi,bj) + aW2d(I ,J ,bi,bj)
169			& +aS2d(I-1,J,bi,bj) + aS2d(I-1,J+1,bi,bj)
170	cnh	1.19	& +freeSurfFacmyNorm horiVertRatio*
171	cnh	1.17	& rA(I-1,J,bi,bj)/deltaTMom/deltaTMom
172	cnh	1.4	& )
173			IF ( aC .EQ. 0. ) THEN
174	adcroft	1.27	pC(I,J,bi,bj) = 1. _d 0
175	cnh	1.4	ELSE
176			pC(I,J,bi,bj) = 1. _d 0 / aC
177			ENDIF
178			IF ( aC + aCw .EQ. 0. ) THEN
179			pW(I,J,bi,bj) = 0.
180			ELSE
181			pW(I,J,bi,bj) =
182			& -aW2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCw+aC))*2 )
183			ENDIF
184			IF ( aC + aCs .EQ. 0. ) THEN
185			pS(I,J,bi,bj) = 0.
186			ELSE
187			pS(I,J,bi,bj) =
188			& -aS2d(I ,J ,bi,bj)/((cg2dpcOffDFac (aCs+aC))*2 )
189			ENDIF
190	cnh	1.6	C pC(I,J,bi,bj) = 1.
191			C pW(I,J,bi,bj) = 0.
192			C pS(I,J,bi,bj) = 0.
193	cnh	1.1	ENDDO
194			ENDDO
195			ENDDO
196			ENDDO
197			C-- Update overlap regions
198			_EXCH_XY_R4(pC, myThid)
199			_EXCH_XY_R4(pW, myThid)
200			_EXCH_XY_R4(pS, myThid)
201	cnh	1.18	CcnhDebugStarts
202	adcroft	1.24	C CALL PLOT_FIELD_XYRS( pC, 'pC INI_CG2D.2' , 1, myThid )
203			C CALL PLOT_FIELD_XYRS( pW, 'pW INI_CG2D.2' , 1, myThid )
204			C CALL PLOT_FIELD_XYRS( pS, 'pS INI_CG2D.2' , 1, myThid )
205	cnh	1.18	CcnhDebugEnds
206	cnh	1.1
207	cnh	1.5	C-- Set default values for initial guess and RHS
208	cnh	1.4	IF ( startTime .EQ. 0 ) THEN
209			DO bj=myByLo(myThid),myByHi(myThid)
210			DO bi=myBxLo(myThid),myBxHi(myThid)
211			DO J=1,sNy
212			DO I=1,sNx
213			cg2d_x(I,J,bi,bj) = 0. _d 0
214	cnh	1.5	cg2d_b(I,J,bi,bj) = 0. _d 0
215	cnh	1.21	#ifdef INCLUDE_CD_CODE
216	cnh	1.12	cg2d_xNM1(I,J,bi,bj) = 0. _d 0
217			#endif
218	cnh	1.4	ENDDO
219	cnh	1.1	ENDDO
220			ENDDO
221			ENDDO
222	cnh	1.4	C-- Update overlap regions
223			_EXCH_XY_R8(cg2d_x, myThid)
224	cnh	1.5	_EXCH_XY_R8(cg2d_b, myThid)
225	cnh	1.21	#ifdef INCLUDE_CD_CODE
226	cnh	1.12	_EXCH_XY_R8(cg2d_xNM1, myThid)
227			#endif
228	cnh	1.4	ENDIF
229	cnh	1.1
230			RETURN
231			END