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/*@@
@header DXYDG_guts.h
@date Jun 98
@author Gabrielle Allen
@desc
Macro to calculate the (first and) second derivatives of the
physical metric with respect to x,y
The macro is defined in terms of standard variables in
@seefile DXYDG_declare.h
The macro uses @seefile DXDG_guts.h , @seefile DYDG_guts.h and
@seefile DXDG_declare.h , @seefile DYDG_declare.h
@enddesc
@@*/
#ifndef DXYDG_GUTS
#define DXYDG_DECLARE
#include "DXDG_guts.h"
#include "DYDG_guts.h"
#ifdef FCODE
#include "ADM_Derivative.h"
/* Factor involving 2nd derivative of conformal factor */
IF (conformal_state .eq. 0) THEN
DXYDG_FAC = 0
ELSE
DXYDG_FAC = DXDG_PSI4*(4*DXYDG_DXYDPSI_O_PSI + \
12*DXDG_DXDPSI_O_PSI*DYDG_DYDPSI_O_PSI)
ENDIF
/* Now calculate the second deriatives */
if (local_spatial_order.eq.2) then
DXYDG_DXYDGXX = DYDCG_DYDCGXX*DXDG_FAC + DXDCG_DXDCGXX*DYDG_FAC \
+ DXYDG_FAC*DXDG_GXX + DXDG_PSI4*ADM_DXY_2(gxx,i,j,k)
DXYDG_DXYDGXY = DYDCG_DYDCGXY*DXDG_FAC + DXDCG_DXDCGXY*DYDG_FAC \
+ DXYDG_FAC*DXDG_GXY + DXDG_PSI4*ADM_DXY_2(gxy,i,j,k)
DXYDG_DXYDGXZ = DYDCG_DYDCGXZ*DXDG_FAC + DXDCG_DXDCGXZ*DYDG_FAC \
+ DXYDG_FAC*DXDG_GXZ + DXDG_PSI4*ADM_DXY_2(gxz,i,j,k)
DXYDG_DXYDGYY = DYDCG_DYDCGYY*DXDG_FAC + DXDCG_DXDCGYY*DYDG_FAC \
+ DXYDG_FAC*DXDG_GYY + DXDG_PSI4*ADM_DXY_2(gyy,i,j,k)
DXYDG_DXYDGYZ = DYDCG_DYDCGYZ*DXDG_FAC + DXDCG_DXDCGYZ*DYDG_FAC \
+ DXYDG_FAC*DXDG_GYZ + DXDG_PSI4*ADM_DXY_2(gyz,i,j,k)
DXYDG_DXYDGZZ = DYDCG_DYDCGZZ*DXDG_FAC + DXDCG_DXDCGZZ*DYDG_FAC \
+ DXYDG_FAC*DXDG_GZZ + DXDG_PSI4*ADM_DXY_2(gzz,i,j,k)
else
DXYDG_DXYDGXX = DYDCG_DYDCGXX*DXDG_FAC + DXDCG_DXDCGXX*DYDG_FAC \
+ DXYDG_FAC*DXDG_GXX + DXDG_PSI4*ADM_DXY_4(gxx,i,j,k)
DXYDG_DXYDGXY = DYDCG_DYDCGXY*DXDG_FAC + DXDCG_DXDCGXY*DYDG_FAC \
+ DXYDG_FAC*DXDG_GXY + DXDG_PSI4*ADM_DXY_4(gxy,i,j,k)
DXYDG_DXYDGXZ = DYDCG_DYDCGXZ*DXDG_FAC + DXDCG_DXDCGXZ*DYDG_FAC \
+ DXYDG_FAC*DXDG_GXZ + DXDG_PSI4*ADM_DXY_4(gxz,i,j,k)
DXYDG_DXYDGYY = DYDCG_DYDCGYY*DXDG_FAC + DXDCG_DXDCGYY*DYDG_FAC \
+ DXYDG_FAC*DXDG_GYY + DXDG_PSI4*ADM_DXY_4(gyy,i,j,k)
DXYDG_DXYDGYZ = DYDCG_DYDCGYZ*DXDG_FAC + DXDCG_DXDCGYZ*DYDG_FAC \
+ DXYDG_FAC*DXDG_GYZ + DXDG_PSI4*ADM_DXY_4(gyz,i,j,k)
DXYDG_DXYDGZZ = DYDCG_DYDCGZZ*DXDG_FAC + DXDCG_DXDCGZZ*DYDG_FAC \
+ DXYDG_FAC*DXDG_GZZ + DXDG_PSI4*ADM_DXY_4(gzz,i,j,k)
end if
#endif
#ifdef CCODE
/* Factor involving 2nd derivative of conformal factor */
DXYDG_FAC = ((*conformal_state == 0)?0:
DXDG_PSI4*(4*DXYDG_DXYDPSI_O_PSI + 12*DXDG_DXDPSI_O_PSI*DYDG_DYDPSI_O_PSI));
/* Now calculate the second deriatives */
DXYDG_DXYDGXX = DYDCG_DYDCGXX*DXDG_FAC+DXDCG_DXDCGXX*DYDG_FAC+DXYDG_FAC*DXDG_GXX
+DXDG_PSI4*DXYDG_OO4DXDY*
(DXYDG_GXX_IPJP-DXYDG_GXX_IPJM-DXYDG_GXX_IMJP+DXYDG_GXX_IMJM);
DXYDG_DXYDGXY = DYDCG_DYDCGXY*DXDG_FAC+DXDCG_DXDCGXY*DYDG_FAC+DXYDG_FAC*DXDG_GXY
+DXDG_PSI4*DXYDG_OO4DXDY*
(DXYDG_GXY_IPJP-DXYDG_GXY_IPJM-DXYDG_GXY_IMJP+DXYDG_GXY_IMJM);
DXYDG_DXYDGXZ = DYDCG_DYDCGXZ*DXDG_FAC+DXDCG_DXDCGXZ*DYDG_FAC+DXYDG_FAC*DXDG_GXZ
+DXDG_PSI4*DXYDG_OO4DXDY*
(DXYDG_GXZ_IPJP-DXYDG_GXZ_IPJM-DXYDG_GXZ_IMJP+DXYDG_GXZ_IMJM);
DXYDG_DXYDGYY = DYDCG_DYDCGYY*DXDG_FAC+DXDCG_DXDCGYY*DYDG_FAC+DXYDG_FAC*DXDG_GYY
+DXDG_PSI4*DXYDG_OO4DXDY*
(DXYDG_GYY_IPJP-DXYDG_GYY_IPJM-DXYDG_GYY_IMJP+DXYDG_GYY_IMJM);
DXYDG_DXYDGYZ = DYDCG_DYDCGYZ*DXDG_FAC+DXDCG_DXDCGYZ*DYDG_FAC+DXYDG_FAC*DXDG_GYZ
+DXDG_PSI4*DXYDG_OO4DXDY*
(DXYDG_GYZ_IPJP-DXYDG_GYZ_IPJM-DXYDG_GYZ_IMJP+DXYDG_GYZ_IMJM);
DXYDG_DXYDGZZ = DYDCG_DYDCGZZ*DXDG_FAC+DXDCG_DXDCGZZ*DYDG_FAC+DXYDG_FAC*DXDG_GZZ
+DXDG_PSI4*DXYDG_OO4DXDY*
(DXYDG_GZZ_IPJP-DXYDG_GZZ_IPJM-DXYDG_GZZ_IMJP+DXYDG_GZZ_IMJM);
#endif
#endif
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