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/*@@
@header DXZDG_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,z
The macro is defined in terms of standard variables in
@seefile DXZDG_declare.h
The macro uses @seefile DXDG_guts.h , @seefile DZDG_guts.h and
@seefile DXDG_declare.h , @seefile DZDG_declare.h
@enddesc
@@*/
#ifndef DXZDG_GUTS
#define DXZDG_GUTS
#include "DXDG_guts.h"
#include "DZDG_guts.h"
#ifdef FCODE
#include "ADM_Derivative.h"
/* Factor involving 2nd derivative of conformal factor, nowadays zero */
DXZDG_FAC = 0
/* Now calculate the second deriatives */
if (local_spatial_order.eq.2) then
DXZDG_DXZDGXX = DZDCG_DZDCGXX*DXDG_FAC + DXDCG_DXDCGXX*DZDG_FAC \
+ DXZDG_FAC*DXDG_GXX + DXDG_PSI4*ADM_DXZ_2(gxx,i,j,k)
DXZDG_DXZDGXY = DZDCG_DZDCGXY*DXDG_FAC + DXDCG_DXDCGXY*DZDG_FAC \
+ DXZDG_FAC*DXDG_GXY + DXDG_PSI4*ADM_DXZ_2(gxy,i,j,k)
DXZDG_DXZDGXZ = DZDCG_DZDCGXZ*DXDG_FAC + DXDCG_DXDCGXZ*DZDG_FAC \
+ DXZDG_FAC*DXDG_GXZ + DXDG_PSI4*ADM_DXZ_2(gxz,i,j,k)
DXZDG_DXZDGYY = DZDCG_DZDCGYY*DXDG_FAC + DXDCG_DXDCGYY*DZDG_FAC \
+ DXZDG_FAC*DXDG_GYY + DXDG_PSI4*ADM_DXZ_2(gyy,i,j,k)
DXZDG_DXZDGYZ = DZDCG_DZDCGYZ*DXDG_FAC + DXDCG_DXDCGYZ*DZDG_FAC \
+ DXZDG_FAC*DXDG_GYZ + DXDG_PSI4*ADM_DXZ_2(gyz,i,j,k)
DXZDG_DXZDGZZ = DZDCG_DZDCGZZ*DXDG_FAC + DXDCG_DXDCGZZ*DZDG_FAC \
+ DXZDG_FAC*DXDG_GZZ + DXDG_PSI4*ADM_DXZ_2(gzz,i,j,k)
else
DXZDG_DXZDGXX = DZDCG_DZDCGXX*DXDG_FAC + DXDCG_DXDCGXX*DZDG_FAC \
+ DXZDG_FAC*DXDG_GXX + DXDG_PSI4*ADM_DXZ_4(gxx,i,j,k)
DXZDG_DXZDGXY = DZDCG_DZDCGXY*DXDG_FAC + DXDCG_DXDCGXY*DZDG_FAC \
+ DXZDG_FAC*DXDG_GXY + DXDG_PSI4*ADM_DXZ_4(gxy,i,j,k)
DXZDG_DXZDGXZ = DZDCG_DZDCGXZ*DXDG_FAC + DXDCG_DXDCGXZ*DZDG_FAC \
+ DXZDG_FAC*DXDG_GXZ + DXDG_PSI4*ADM_DXZ_4(gxz,i,j,k)
DXZDG_DXZDGYY = DZDCG_DZDCGYY*DXDG_FAC + DXDCG_DXDCGYY*DZDG_FAC \
+ DXZDG_FAC*DXDG_GYY + DXDG_PSI4*ADM_DXZ_4(gyy,i,j,k)
DXZDG_DXZDGYZ = DZDCG_DZDCGYZ*DXDG_FAC + DXDCG_DXDCGYZ*DZDG_FAC \
+ DXZDG_FAC*DXDG_GYZ + DXDG_PSI4*ADM_DXZ_4(gyz,i,j,k)
DXZDG_DXZDGZZ = DZDCG_DZDCGZZ*DXDG_FAC + DXDCG_DXDCGZZ*DZDG_FAC \
+ DXZDG_FAC*DXDG_GZZ + DXDG_PSI4*ADM_DXZ_4(gzz,i,j,k)
end if
#endif
#ifdef CCODE
/* Factor involving 2nd derivative of conformal factor, nowadays zero */
DXZDG_FAC = 0;
/* Now calculate the second deriatives */
DXZDG_DXZDGXX = DZDCG_DZDCGXX*DXDG_FAC+DXDCG_DXDCGXX*DZDG_FAC+DXZDG_FAC*DXDG_GXX+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXX_IPKP-DXZDG_GXX_IPKM-DXZDG_GXX_IMKP+
DXZDG_GXX_IMKM);
DXZDG_DXZDGXY = DZDCG_DZDCGXY*DXDG_FAC+DXDCG_DXDCGXY*DZDG_FAC+DXZDG_FAC*DXDG_GXY+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXY_IPKP-DXZDG_GXY_IPKM-DXZDG_GXY_IMKP+
DXZDG_GXY_IMKM);
DXZDG_DXZDGXZ = DZDCG_DZDCGXZ*DXDG_FAC+DXDCG_DXDCGXZ*DZDG_FAC+DXZDG_FAC*DXDG_GXZ+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GXZ_IPKP-DXZDG_GXZ_IPKM-DXZDG_GXZ_IMKP+
DXZDG_GXZ_IMKM);
DXZDG_DXZDGYY = DZDCG_DZDCGYY*DXDG_FAC+DXDCG_DXDCGYY*DZDG_FAC+DXZDG_FAC*DXDG_GYY+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GYY_IPKP-DXZDG_GYY_IPKM-DXZDG_GYY_IMKP+
DXZDG_GYY_IMKM);
DXZDG_DXZDGYZ = DZDCG_DZDCGYZ*DXDG_FAC+DXDCG_DXDCGYZ*DZDG_FAC+DXZDG_FAC*DXDG_GYZ+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GYZ_IPKP-DXZDG_GYZ_IPKM-DXZDG_GYZ_IMKP+
DXZDG_GYZ_IMKM);
DXZDG_DXZDGZZ = DZDCG_DZDCGZZ*DXDG_FAC+DXDCG_DXDCGZZ*DZDG_FAC+DXZDG_FAC*DXDG_GZZ+
DXDG_PSI4*DXZDG_OO4DXDZ*(DXZDG_GZZ_IPKP-DXZDG_GZZ_IPKM-DXZDG_GZZ_IMKP+
DXZDG_GZZ_IMKM);
#endif
#endif
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