diff options
| -rw-r--r-- | ML_ADM/src/Differencing.h | 24 | ||||
| -rw-r--r-- | ML_ADM/src/ML_ADM_RHS.c | 552 | ||||
| -rw-r--r-- | ML_ADM/src/ML_ADM_constraints.c | 438 | ||||
| -rw-r--r-- | ML_BSSN/src/Differencing.h | 24 | ||||
| -rw-r--r-- | ML_BSSN/src/ML_BSSN_RHS.c | 1690 | ||||
| -rw-r--r-- | ML_BSSN/src/ML_BSSN_constraints.c | 722 | ||||
| -rw-r--r-- | ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c | 144 | ||||
| -rw-r--r-- | m/McLachlan.m | 25 | ||||
| -rwxr-xr-x | m/McLachlan.sh | 5 | ||||
| -rw-r--r-- | par/ks_bssn_0_8th.par | 172 | ||||
| -rw-r--r-- | par/ks_bssn_1_8th.par | 172 | ||||
| -rw-r--r-- | par/ks_bssn_2_8th.par | 172 |
12 files changed, 2332 insertions, 1808 deletions
diff --git a/ML_ADM/src/Differencing.h b/ML_ADM/src/Differencing.h index 7ada6a7..876855b 100644 --- a/ML_ADM/src/Differencing.h +++ b/ML_ADM/src/Differencing.h @@ -1,12 +1,12 @@ -#define PDstandard4th1(u,i,j,k) (p1o12dx*(-8*u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)])) -#define PDstandard4th2(u,i,j,k) (p1o12dy*(-8*u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)])) -#define PDstandard4th3(u,i,j,k) (p1o12dz*(-8*u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)])) -#define PDstandard4th11(u,i,j,k) (pm1o12dx2*(-16*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) -#define PDstandard4th22(u,i,j,k) (pm1o12dy2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) -#define PDstandard4th33(u,i,j,k) (pm1o12dz2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) -#define PDstandard4th12(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) -#define PDstandard4th13(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) -#define PDstandard4th21(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) -#define PDstandard4th23(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) -#define PDstandard4th31(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) -#define PDstandard4th32(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) +#define PDstandardNth1(u,i,j,k) (p1o12dx*(-8*u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)])) +#define PDstandardNth2(u,i,j,k) (p1o12dy*(-8*u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)])) +#define PDstandardNth3(u,i,j,k) (p1o12dz*(-8*u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)])) +#define PDstandardNth11(u,i,j,k) (pm1o12dx2*(-16*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) +#define PDstandardNth22(u,i,j,k) (pm1o12dy2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) +#define PDstandardNth33(u,i,j,k) (pm1o12dz2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) +#define PDstandardNth12(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) +#define PDstandardNth13(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) +#define PDstandardNth21(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) +#define PDstandardNth23(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) +#define PDstandardNth31(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) +#define PDstandardNth32(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) diff --git a/ML_ADM/src/ML_ADM_RHS.c b/ML_ADM/src/ML_ADM_RHS.c index cc16858..20b9f39 100644 --- a/ML_ADM/src/ML_ADM_RHS.c +++ b/ML_ADM/src/ML_ADM_RHS.c @@ -114,105 +114,105 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ /* Declare precomputed derivatives*/ /* Declare derivatives */ - CCTK_REAL PDstandard4th1alpha = INITVALUE; - CCTK_REAL PDstandard4th2alpha = INITVALUE; - CCTK_REAL PDstandard4th3alpha = INITVALUE; - CCTK_REAL PDstandard4th11alpha = INITVALUE; - CCTK_REAL PDstandard4th22alpha = INITVALUE; - CCTK_REAL PDstandard4th33alpha = INITVALUE; - CCTK_REAL PDstandard4th12alpha = INITVALUE; - CCTK_REAL PDstandard4th13alpha = INITVALUE; - CCTK_REAL PDstandard4th23alpha = INITVALUE; - CCTK_REAL PDstandard4th1beta1 = INITVALUE; - CCTK_REAL PDstandard4th2beta1 = INITVALUE; - CCTK_REAL PDstandard4th3beta1 = INITVALUE; - CCTK_REAL PDstandard4th1beta2 = INITVALUE; - CCTK_REAL PDstandard4th2beta2 = INITVALUE; - CCTK_REAL PDstandard4th3beta2 = INITVALUE; - CCTK_REAL PDstandard4th1beta3 = INITVALUE; - CCTK_REAL PDstandard4th2beta3 = INITVALUE; - CCTK_REAL PDstandard4th3beta3 = INITVALUE; - CCTK_REAL PDstandard4th1g11 = INITVALUE; - CCTK_REAL PDstandard4th2g11 = INITVALUE; - CCTK_REAL PDstandard4th3g11 = INITVALUE; - CCTK_REAL PDstandard4th22g11 = INITVALUE; - CCTK_REAL PDstandard4th33g11 = INITVALUE; - CCTK_REAL PDstandard4th12g11 = INITVALUE; - CCTK_REAL PDstandard4th13g11 = INITVALUE; - CCTK_REAL PDstandard4th21g11 = INITVALUE; - CCTK_REAL PDstandard4th23g11 = INITVALUE; - CCTK_REAL PDstandard4th31g11 = INITVALUE; - CCTK_REAL PDstandard4th32g11 = INITVALUE; - CCTK_REAL PDstandard4th1g12 = INITVALUE; - CCTK_REAL PDstandard4th2g12 = INITVALUE; - CCTK_REAL PDstandard4th3g12 = INITVALUE; - CCTK_REAL PDstandard4th33g12 = INITVALUE; - CCTK_REAL PDstandard4th12g12 = INITVALUE; - CCTK_REAL PDstandard4th13g12 = INITVALUE; - CCTK_REAL PDstandard4th21g12 = INITVALUE; - CCTK_REAL PDstandard4th23g12 = INITVALUE; - CCTK_REAL PDstandard4th31g12 = INITVALUE; - CCTK_REAL PDstandard4th32g12 = INITVALUE; - CCTK_REAL PDstandard4th1g13 = INITVALUE; - CCTK_REAL PDstandard4th2g13 = INITVALUE; - CCTK_REAL PDstandard4th3g13 = INITVALUE; - CCTK_REAL PDstandard4th22g13 = INITVALUE; - CCTK_REAL PDstandard4th12g13 = INITVALUE; - CCTK_REAL PDstandard4th13g13 = INITVALUE; - CCTK_REAL PDstandard4th21g13 = INITVALUE; - CCTK_REAL PDstandard4th23g13 = INITVALUE; - CCTK_REAL PDstandard4th31g13 = INITVALUE; - CCTK_REAL PDstandard4th32g13 = INITVALUE; - CCTK_REAL PDstandard4th1g22 = INITVALUE; - CCTK_REAL PDstandard4th2g22 = INITVALUE; - CCTK_REAL PDstandard4th3g22 = INITVALUE; - CCTK_REAL PDstandard4th11g22 = INITVALUE; - CCTK_REAL PDstandard4th33g22 = INITVALUE; - CCTK_REAL PDstandard4th12g22 = INITVALUE; - CCTK_REAL PDstandard4th13g22 = INITVALUE; - CCTK_REAL PDstandard4th21g22 = INITVALUE; - CCTK_REAL PDstandard4th23g22 = INITVALUE; - CCTK_REAL PDstandard4th31g22 = INITVALUE; - CCTK_REAL PDstandard4th32g22 = INITVALUE; - CCTK_REAL PDstandard4th1g23 = INITVALUE; - CCTK_REAL PDstandard4th2g23 = INITVALUE; - CCTK_REAL PDstandard4th3g23 = INITVALUE; - CCTK_REAL PDstandard4th11g23 = INITVALUE; - CCTK_REAL PDstandard4th12g23 = INITVALUE; - CCTK_REAL PDstandard4th13g23 = INITVALUE; - CCTK_REAL PDstandard4th21g23 = INITVALUE; - CCTK_REAL PDstandard4th23g23 = INITVALUE; - CCTK_REAL PDstandard4th31g23 = INITVALUE; - CCTK_REAL PDstandard4th32g23 = INITVALUE; - CCTK_REAL PDstandard4th1g33 = INITVALUE; - CCTK_REAL PDstandard4th2g33 = INITVALUE; - CCTK_REAL PDstandard4th3g33 = INITVALUE; - CCTK_REAL PDstandard4th11g33 = INITVALUE; - CCTK_REAL PDstandard4th22g33 = INITVALUE; - CCTK_REAL PDstandard4th12g33 = INITVALUE; - CCTK_REAL PDstandard4th13g33 = INITVALUE; - CCTK_REAL PDstandard4th21g33 = INITVALUE; - CCTK_REAL PDstandard4th23g33 = INITVALUE; - CCTK_REAL PDstandard4th31g33 = INITVALUE; - CCTK_REAL PDstandard4th32g33 = INITVALUE; - CCTK_REAL PDstandard4th1K11 = INITVALUE; - CCTK_REAL PDstandard4th2K11 = INITVALUE; - CCTK_REAL PDstandard4th3K11 = INITVALUE; - CCTK_REAL PDstandard4th1K12 = INITVALUE; - CCTK_REAL PDstandard4th2K12 = INITVALUE; - CCTK_REAL PDstandard4th3K12 = INITVALUE; - CCTK_REAL PDstandard4th1K13 = INITVALUE; - CCTK_REAL PDstandard4th2K13 = INITVALUE; - CCTK_REAL PDstandard4th3K13 = INITVALUE; - CCTK_REAL PDstandard4th1K22 = INITVALUE; - CCTK_REAL PDstandard4th2K22 = INITVALUE; - CCTK_REAL PDstandard4th3K22 = INITVALUE; - CCTK_REAL PDstandard4th1K23 = INITVALUE; - CCTK_REAL PDstandard4th2K23 = INITVALUE; - CCTK_REAL PDstandard4th3K23 = INITVALUE; - CCTK_REAL PDstandard4th1K33 = INITVALUE; - CCTK_REAL PDstandard4th2K33 = INITVALUE; - CCTK_REAL PDstandard4th3K33 = INITVALUE; + CCTK_REAL PDstandardNth1alpha = INITVALUE; + CCTK_REAL PDstandardNth2alpha = INITVALUE; + CCTK_REAL PDstandardNth3alpha = INITVALUE; + CCTK_REAL PDstandardNth11alpha = INITVALUE; + CCTK_REAL PDstandardNth22alpha = INITVALUE; + CCTK_REAL PDstandardNth33alpha = INITVALUE; + CCTK_REAL PDstandardNth12alpha = INITVALUE; + CCTK_REAL PDstandardNth13alpha = INITVALUE; + CCTK_REAL PDstandardNth23alpha = INITVALUE; + CCTK_REAL PDstandardNth1beta1 = INITVALUE; + CCTK_REAL PDstandardNth2beta1 = INITVALUE; + CCTK_REAL PDstandardNth3beta1 = INITVALUE; + CCTK_REAL PDstandardNth1beta2 = INITVALUE; + CCTK_REAL PDstandardNth2beta2 = INITVALUE; + CCTK_REAL PDstandardNth3beta2 = INITVALUE; + CCTK_REAL PDstandardNth1beta3 = INITVALUE; + CCTK_REAL PDstandardNth2beta3 = INITVALUE; + CCTK_REAL PDstandardNth3beta3 = INITVALUE; + CCTK_REAL PDstandardNth1g11 = INITVALUE; + CCTK_REAL PDstandardNth2g11 = INITVALUE; + CCTK_REAL PDstandardNth3g11 = INITVALUE; + CCTK_REAL PDstandardNth22g11 = INITVALUE; + CCTK_REAL PDstandardNth33g11 = INITVALUE; + CCTK_REAL PDstandardNth12g11 = INITVALUE; + CCTK_REAL PDstandardNth13g11 = INITVALUE; + CCTK_REAL PDstandardNth21g11 = INITVALUE; + CCTK_REAL PDstandardNth23g11 = INITVALUE; + CCTK_REAL PDstandardNth31g11 = INITVALUE; + CCTK_REAL PDstandardNth32g11 = INITVALUE; + CCTK_REAL PDstandardNth1g12 = INITVALUE; + CCTK_REAL PDstandardNth2g12 = INITVALUE; + CCTK_REAL PDstandardNth3g12 = INITVALUE; + CCTK_REAL PDstandardNth33g12 = INITVALUE; + CCTK_REAL PDstandardNth12g12 = INITVALUE; + CCTK_REAL PDstandardNth13g12 = INITVALUE; + CCTK_REAL PDstandardNth21g12 = INITVALUE; + CCTK_REAL PDstandardNth23g12 = INITVALUE; + CCTK_REAL PDstandardNth31g12 = INITVALUE; + CCTK_REAL PDstandardNth32g12 = INITVALUE; + CCTK_REAL PDstandardNth1g13 = INITVALUE; + CCTK_REAL PDstandardNth2g13 = INITVALUE; + CCTK_REAL PDstandardNth3g13 = INITVALUE; + CCTK_REAL PDstandardNth22g13 = INITVALUE; + CCTK_REAL PDstandardNth12g13 = INITVALUE; + CCTK_REAL PDstandardNth13g13 = INITVALUE; + CCTK_REAL PDstandardNth21g13 = INITVALUE; + CCTK_REAL PDstandardNth23g13 = INITVALUE; + CCTK_REAL PDstandardNth31g13 = INITVALUE; + CCTK_REAL PDstandardNth32g13 = INITVALUE; + CCTK_REAL PDstandardNth1g22 = INITVALUE; + CCTK_REAL PDstandardNth2g22 = INITVALUE; + CCTK_REAL PDstandardNth3g22 = INITVALUE; + CCTK_REAL PDstandardNth11g22 = INITVALUE; + CCTK_REAL PDstandardNth33g22 = INITVALUE; + CCTK_REAL PDstandardNth12g22 = INITVALUE; + CCTK_REAL PDstandardNth13g22 = INITVALUE; + CCTK_REAL PDstandardNth21g22 = INITVALUE; + CCTK_REAL PDstandardNth23g22 = INITVALUE; + CCTK_REAL PDstandardNth31g22 = INITVALUE; + CCTK_REAL PDstandardNth32g22 = INITVALUE; + CCTK_REAL PDstandardNth1g23 = INITVALUE; + CCTK_REAL PDstandardNth2g23 = INITVALUE; + CCTK_REAL PDstandardNth3g23 = INITVALUE; + CCTK_REAL PDstandardNth11g23 = INITVALUE; + CCTK_REAL PDstandardNth12g23 = INITVALUE; + CCTK_REAL PDstandardNth13g23 = INITVALUE; + CCTK_REAL PDstandardNth21g23 = INITVALUE; + CCTK_REAL PDstandardNth23g23 = INITVALUE; + CCTK_REAL PDstandardNth31g23 = INITVALUE; + CCTK_REAL PDstandardNth32g23 = INITVALUE; + CCTK_REAL PDstandardNth1g33 = INITVALUE; + CCTK_REAL PDstandardNth2g33 = INITVALUE; + CCTK_REAL PDstandardNth3g33 = INITVALUE; + CCTK_REAL PDstandardNth11g33 = INITVALUE; + CCTK_REAL PDstandardNth22g33 = INITVALUE; + CCTK_REAL PDstandardNth12g33 = INITVALUE; + CCTK_REAL PDstandardNth13g33 = INITVALUE; + CCTK_REAL PDstandardNth21g33 = INITVALUE; + CCTK_REAL PDstandardNth23g33 = INITVALUE; + CCTK_REAL PDstandardNth31g33 = INITVALUE; + CCTK_REAL PDstandardNth32g33 = INITVALUE; + CCTK_REAL PDstandardNth1K11 = INITVALUE; + CCTK_REAL PDstandardNth2K11 = INITVALUE; + CCTK_REAL PDstandardNth3K11 = INITVALUE; + CCTK_REAL PDstandardNth1K12 = INITVALUE; + CCTK_REAL PDstandardNth2K12 = INITVALUE; + CCTK_REAL PDstandardNth3K12 = INITVALUE; + CCTK_REAL PDstandardNth1K13 = INITVALUE; + CCTK_REAL PDstandardNth2K13 = INITVALUE; + CCTK_REAL PDstandardNth3K13 = INITVALUE; + CCTK_REAL PDstandardNth1K22 = INITVALUE; + CCTK_REAL PDstandardNth2K22 = INITVALUE; + CCTK_REAL PDstandardNth3K22 = INITVALUE; + CCTK_REAL PDstandardNth1K23 = INITVALUE; + CCTK_REAL PDstandardNth2K23 = INITVALUE; + CCTK_REAL PDstandardNth3K23 = INITVALUE; + CCTK_REAL PDstandardNth1K33 = INITVALUE; + CCTK_REAL PDstandardNth2K33 = INITVALUE; + CCTK_REAL PDstandardNth3K33 = INITVALUE; /* Assign local copies of grid functions */ alphaL = alpha[index]; @@ -237,81 +237,81 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ /* Include user supplied include files */ /* Precompute derivatives (new style) */ - PDstandard4th1alpha = PDstandard4th1(alpha, i, j, k); - PDstandard4th2alpha = PDstandard4th2(alpha, i, j, k); - PDstandard4th3alpha = PDstandard4th3(alpha, i, j, k); - PDstandard4th11alpha = PDstandard4th11(alpha, i, j, k); - PDstandard4th22alpha = PDstandard4th22(alpha, i, j, k); - PDstandard4th33alpha = PDstandard4th33(alpha, i, j, k); - PDstandard4th12alpha = PDstandard4th12(alpha, i, j, k); - PDstandard4th13alpha = PDstandard4th13(alpha, i, j, k); - PDstandard4th23alpha = PDstandard4th23(alpha, i, j, k); - PDstandard4th1beta1 = PDstandard4th1(beta1, i, j, k); - PDstandard4th2beta1 = PDstandard4th2(beta1, i, j, k); - PDstandard4th3beta1 = PDstandard4th3(beta1, i, j, k); - PDstandard4th1beta2 = PDstandard4th1(beta2, i, j, k); - PDstandard4th2beta2 = PDstandard4th2(beta2, i, j, k); - PDstandard4th3beta2 = PDstandard4th3(beta2, i, j, k); - PDstandard4th1beta3 = PDstandard4th1(beta3, i, j, k); - PDstandard4th2beta3 = PDstandard4th2(beta3, i, j, k); - PDstandard4th3beta3 = PDstandard4th3(beta3, i, j, k); - PDstandard4th1g11 = PDstandard4th1(g11, i, j, k); - PDstandard4th2g11 = PDstandard4th2(g11, i, j, k); - PDstandard4th3g11 = PDstandard4th3(g11, i, j, k); - PDstandard4th22g11 = PDstandard4th22(g11, i, j, k); - PDstandard4th33g11 = PDstandard4th33(g11, i, j, k); - PDstandard4th23g11 = PDstandard4th23(g11, i, j, k); - PDstandard4th1g12 = PDstandard4th1(g12, i, j, k); - PDstandard4th2g12 = PDstandard4th2(g12, i, j, k); - PDstandard4th3g12 = PDstandard4th3(g12, i, j, k); - PDstandard4th33g12 = PDstandard4th33(g12, i, j, k); - PDstandard4th12g12 = PDstandard4th12(g12, i, j, k); - PDstandard4th13g12 = PDstandard4th13(g12, i, j, k); - PDstandard4th23g12 = PDstandard4th23(g12, i, j, k); - PDstandard4th1g13 = PDstandard4th1(g13, i, j, k); - PDstandard4th2g13 = PDstandard4th2(g13, i, j, k); - PDstandard4th3g13 = PDstandard4th3(g13, i, j, k); - PDstandard4th22g13 = PDstandard4th22(g13, i, j, k); - PDstandard4th12g13 = PDstandard4th12(g13, i, j, k); - PDstandard4th13g13 = PDstandard4th13(g13, i, j, k); - PDstandard4th23g13 = PDstandard4th23(g13, i, j, k); - PDstandard4th1g22 = PDstandard4th1(g22, i, j, k); - PDstandard4th2g22 = PDstandard4th2(g22, i, j, k); - PDstandard4th3g22 = PDstandard4th3(g22, i, j, k); - PDstandard4th11g22 = PDstandard4th11(g22, i, j, k); - PDstandard4th33g22 = PDstandard4th33(g22, i, j, k); - PDstandard4th13g22 = PDstandard4th13(g22, i, j, k); - PDstandard4th1g23 = PDstandard4th1(g23, i, j, k); - PDstandard4th2g23 = PDstandard4th2(g23, i, j, k); - PDstandard4th3g23 = PDstandard4th3(g23, i, j, k); - PDstandard4th11g23 = PDstandard4th11(g23, i, j, k); - PDstandard4th12g23 = PDstandard4th12(g23, i, j, k); - PDstandard4th13g23 = PDstandard4th13(g23, i, j, k); - PDstandard4th23g23 = PDstandard4th23(g23, i, j, k); - PDstandard4th1g33 = PDstandard4th1(g33, i, j, k); - PDstandard4th2g33 = PDstandard4th2(g33, i, j, k); - PDstandard4th3g33 = PDstandard4th3(g33, i, j, k); - PDstandard4th11g33 = PDstandard4th11(g33, i, j, k); - PDstandard4th22g33 = PDstandard4th22(g33, i, j, k); - PDstandard4th12g33 = PDstandard4th12(g33, i, j, k); - PDstandard4th1K11 = PDstandard4th1(K11, i, j, k); - PDstandard4th2K11 = PDstandard4th2(K11, i, j, k); - PDstandard4th3K11 = PDstandard4th3(K11, i, j, k); - PDstandard4th1K12 = PDstandard4th1(K12, i, j, k); - PDstandard4th2K12 = PDstandard4th2(K12, i, j, k); - PDstandard4th3K12 = PDstandard4th3(K12, i, j, k); - PDstandard4th1K13 = PDstandard4th1(K13, i, j, k); - PDstandard4th2K13 = PDstandard4th2(K13, i, j, k); - PDstandard4th3K13 = PDstandard4th3(K13, i, j, k); - PDstandard4th1K22 = PDstandard4th1(K22, i, j, k); - PDstandard4th2K22 = PDstandard4th2(K22, i, j, k); - PDstandard4th3K22 = PDstandard4th3(K22, i, j, k); - PDstandard4th1K23 = PDstandard4th1(K23, i, j, k); - PDstandard4th2K23 = PDstandard4th2(K23, i, j, k); - PDstandard4th3K23 = PDstandard4th3(K23, i, j, k); - PDstandard4th1K33 = PDstandard4th1(K33, i, j, k); - PDstandard4th2K33 = PDstandard4th2(K33, i, j, k); - PDstandard4th3K33 = PDstandard4th3(K33, i, j, k); + PDstandardNth1alpha = PDstandardNth1(alpha, i, j, k); + PDstandardNth2alpha = PDstandardNth2(alpha, i, j, k); + PDstandardNth3alpha = PDstandardNth3(alpha, i, j, k); + PDstandardNth11alpha = PDstandardNth11(alpha, i, j, k); + PDstandardNth22alpha = PDstandardNth22(alpha, i, j, k); + PDstandardNth33alpha = PDstandardNth33(alpha, i, j, k); + PDstandardNth12alpha = PDstandardNth12(alpha, i, j, k); + PDstandardNth13alpha = PDstandardNth13(alpha, i, j, k); + PDstandardNth23alpha = PDstandardNth23(alpha, i, j, k); + PDstandardNth1beta1 = PDstandardNth1(beta1, i, j, k); + PDstandardNth2beta1 = PDstandardNth2(beta1, i, j, k); + PDstandardNth3beta1 = PDstandardNth3(beta1, i, j, k); + PDstandardNth1beta2 = PDstandardNth1(beta2, i, j, k); + PDstandardNth2beta2 = PDstandardNth2(beta2, i, j, k); + PDstandardNth3beta2 = PDstandardNth3(beta2, i, j, k); + PDstandardNth1beta3 = PDstandardNth1(beta3, i, j, k); + PDstandardNth2beta3 = PDstandardNth2(beta3, i, j, k); + PDstandardNth3beta3 = PDstandardNth3(beta3, i, j, k); + PDstandardNth1g11 = PDstandardNth1(g11, i, j, k); + PDstandardNth2g11 = PDstandardNth2(g11, i, j, k); + PDstandardNth3g11 = PDstandardNth3(g11, i, j, k); + PDstandardNth22g11 = PDstandardNth22(g11, i, j, k); + PDstandardNth33g11 = PDstandardNth33(g11, i, j, k); + PDstandardNth23g11 = PDstandardNth23(g11, i, j, k); + PDstandardNth1g12 = PDstandardNth1(g12, i, j, k); + PDstandardNth2g12 = PDstandardNth2(g12, i, j, k); + PDstandardNth3g12 = PDstandardNth3(g12, i, j, k); + PDstandardNth33g12 = PDstandardNth33(g12, i, j, k); + PDstandardNth12g12 = PDstandardNth12(g12, i, j, k); + PDstandardNth13g12 = PDstandardNth13(g12, i, j, k); + PDstandardNth23g12 = PDstandardNth23(g12, i, j, k); + PDstandardNth1g13 = PDstandardNth1(g13, i, j, k); + PDstandardNth2g13 = PDstandardNth2(g13, i, j, k); + PDstandardNth3g13 = PDstandardNth3(g13, i, j, k); + PDstandardNth22g13 = PDstandardNth22(g13, i, j, k); + PDstandardNth12g13 = PDstandardNth12(g13, i, j, k); + PDstandardNth13g13 = PDstandardNth13(g13, i, j, k); + PDstandardNth23g13 = PDstandardNth23(g13, i, j, k); + PDstandardNth1g22 = PDstandardNth1(g22, i, j, k); + PDstandardNth2g22 = PDstandardNth2(g22, i, j, k); + PDstandardNth3g22 = PDstandardNth3(g22, i, j, k); + PDstandardNth11g22 = PDstandardNth11(g22, i, j, k); + PDstandardNth33g22 = PDstandardNth33(g22, i, j, k); + PDstandardNth13g22 = PDstandardNth13(g22, i, j, k); + PDstandardNth1g23 = PDstandardNth1(g23, i, j, k); + PDstandardNth2g23 = PDstandardNth2(g23, i, j, k); + PDstandardNth3g23 = PDstandardNth3(g23, i, j, k); + PDstandardNth11g23 = PDstandardNth11(g23, i, j, k); + PDstandardNth12g23 = PDstandardNth12(g23, i, j, k); + PDstandardNth13g23 = PDstandardNth13(g23, i, j, k); + PDstandardNth23g23 = PDstandardNth23(g23, i, j, k); + PDstandardNth1g33 = PDstandardNth1(g33, i, j, k); + PDstandardNth2g33 = PDstandardNth2(g33, i, j, k); + PDstandardNth3g33 = PDstandardNth3(g33, i, j, k); + PDstandardNth11g33 = PDstandardNth11(g33, i, j, k); + PDstandardNth22g33 = PDstandardNth22(g33, i, j, k); + PDstandardNth12g33 = PDstandardNth12(g33, i, j, k); + PDstandardNth1K11 = PDstandardNth1(K11, i, j, k); + PDstandardNth2K11 = PDstandardNth2(K11, i, j, k); + PDstandardNth3K11 = PDstandardNth3(K11, i, j, k); + PDstandardNth1K12 = PDstandardNth1(K12, i, j, k); + PDstandardNth2K12 = PDstandardNth2(K12, i, j, k); + PDstandardNth3K12 = PDstandardNth3(K12, i, j, k); + PDstandardNth1K13 = PDstandardNth1(K13, i, j, k); + PDstandardNth2K13 = PDstandardNth2(K13, i, j, k); + PDstandardNth3K13 = PDstandardNth3(K13, i, j, k); + PDstandardNth1K22 = PDstandardNth1(K22, i, j, k); + PDstandardNth2K22 = PDstandardNth2(K22, i, j, k); + PDstandardNth3K22 = PDstandardNth3(K22, i, j, k); + PDstandardNth1K23 = PDstandardNth1(K23, i, j, k); + PDstandardNth2K23 = PDstandardNth2(K23, i, j, k); + PDstandardNth3K23 = PDstandardNth3(K23, i, j, k); + PDstandardNth1K33 = PDstandardNth1(K33, i, j, k); + PDstandardNth2K33 = PDstandardNth2(K33, i, j, k); + PDstandardNth3K33 = PDstandardNth3(K33, i, j, k); /* Precompute derivatives (old style) */ @@ -330,97 +330,97 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ gu33 = INV(detg)*(g11L*g22L - SQR(g12L)); - G111 = khalf*(gu11*PDstandard4th1g11 + 2*(gu21*PDstandard4th1g12 + gu31*PDstandard4th1g13) - gu21*PDstandard4th2g11 - - gu31*PDstandard4th3g11); + G111 = khalf*(gu11*PDstandardNth1g11 + 2*(gu21*PDstandardNth1g12 + gu31*PDstandardNth1g13) - gu21*PDstandardNth2g11 - + gu31*PDstandardNth3g11); - G211 = khalf*(gu21*PDstandard4th1g11 + 2*(gu22*PDstandard4th1g12 + gu32*PDstandard4th1g13) - gu22*PDstandard4th2g11 - - gu32*PDstandard4th3g11); + G211 = khalf*(gu21*PDstandardNth1g11 + 2*(gu22*PDstandardNth1g12 + gu32*PDstandardNth1g13) - gu22*PDstandardNth2g11 - + gu32*PDstandardNth3g11); - G311 = khalf*(gu31*PDstandard4th1g11 + 2*(gu32*PDstandard4th1g12 + gu33*PDstandard4th1g13) - gu32*PDstandard4th2g11 - - gu33*PDstandard4th3g11); + G311 = khalf*(gu31*PDstandardNth1g11 + 2*(gu32*PDstandardNth1g12 + gu33*PDstandardNth1g13) - gu32*PDstandardNth2g11 - + gu33*PDstandardNth3g11); - G112 = khalf*(gu21*PDstandard4th1g22 + gu11*PDstandard4th2g11 + - gu31*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); + G112 = khalf*(gu21*PDstandardNth1g22 + gu11*PDstandardNth2g11 + + gu31*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - G212 = khalf*(gu22*PDstandard4th1g22 + gu21*PDstandard4th2g11 + - gu32*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); + G212 = khalf*(gu22*PDstandardNth1g22 + gu21*PDstandardNth2g11 + + gu32*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - G312 = khalf*(gu32*PDstandard4th1g22 + gu31*PDstandard4th2g11 + - gu33*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); + G312 = khalf*(gu32*PDstandardNth1g22 + gu31*PDstandardNth2g11 + + gu33*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - G113 = khalf*(gu31*PDstandard4th1g33 + gu11*PDstandard4th3g11 + - gu21*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); + G113 = khalf*(gu31*PDstandardNth1g33 + gu11*PDstandardNth3g11 + + gu21*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - G213 = khalf*(gu32*PDstandard4th1g33 + gu21*PDstandard4th3g11 + - gu22*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); + G213 = khalf*(gu32*PDstandardNth1g33 + gu21*PDstandardNth3g11 + + gu22*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - G313 = khalf*(gu33*PDstandard4th1g33 + gu31*PDstandard4th3g11 + - gu32*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); + G313 = khalf*(gu33*PDstandardNth1g33 + gu31*PDstandardNth3g11 + + gu32*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - G122 = khalf*(gu11*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu21*PDstandard4th2g22 + - gu31*(2*PDstandard4th2g23 - PDstandard4th3g22)); + G122 = khalf*(gu11*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu21*PDstandardNth2g22 + + gu31*(2*PDstandardNth2g23 - PDstandardNth3g22)); - G222 = khalf*(gu21*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu22*PDstandard4th2g22 + - gu32*(2*PDstandard4th2g23 - PDstandard4th3g22)); + G222 = khalf*(gu21*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu22*PDstandardNth2g22 + + gu32*(2*PDstandardNth2g23 - PDstandardNth3g22)); - G322 = khalf*(gu31*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu32*PDstandard4th2g22 + - gu33*(2*PDstandard4th2g23 - PDstandard4th3g22)); + G322 = khalf*(gu31*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu32*PDstandardNth2g22 + + gu33*(2*PDstandardNth2g23 - PDstandardNth3g22)); - G123 = khalf*(gu31*PDstandard4th2g33 + gu11*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + - gu21*PDstandard4th3g22); + G123 = khalf*(gu31*PDstandardNth2g33 + gu11*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu21*PDstandardNth3g22); - G223 = khalf*(gu32*PDstandard4th2g33 + gu21*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + - gu22*PDstandard4th3g22); + G223 = khalf*(gu32*PDstandardNth2g33 + gu21*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu22*PDstandardNth3g22); - G323 = khalf*(gu33*PDstandard4th2g33 + gu31*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + - gu32*PDstandard4th3g22); + G323 = khalf*(gu33*PDstandardNth2g33 + gu31*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu32*PDstandardNth3g22); - G133 = khalf*(-(gu11*PDstandard4th1g33) - gu21*PDstandard4th2g33 + 2*gu11*PDstandard4th3g13 + - 2*gu21*PDstandard4th3g23 + gu31*PDstandard4th3g33); + G133 = khalf*(-(gu11*PDstandardNth1g33) - gu21*PDstandardNth2g33 + 2*gu11*PDstandardNth3g13 + + 2*gu21*PDstandardNth3g23 + gu31*PDstandardNth3g33); - G233 = khalf*(-(gu21*PDstandard4th1g33) - gu22*PDstandard4th2g33 + 2*gu21*PDstandard4th3g13 + - 2*gu22*PDstandard4th3g23 + gu32*PDstandard4th3g33); + G233 = khalf*(-(gu21*PDstandardNth1g33) - gu22*PDstandardNth2g33 + 2*gu21*PDstandardNth3g13 + + 2*gu22*PDstandardNth3g23 + gu32*PDstandardNth3g33); - G333 = khalf*(-(gu31*PDstandard4th1g33) - gu32*PDstandard4th2g33 + 2*gu31*PDstandard4th3g13 + - 2*gu32*PDstandard4th3g23 + gu33*PDstandard4th3g33); + G333 = khalf*(-(gu31*PDstandardNth1g33) - gu32*PDstandardNth2g33 + 2*gu31*PDstandardNth3g13 + + 2*gu32*PDstandardNth3g23 + gu33*PDstandardNth3g33); - R11 = khalf*(4*G213*G312 + G211*(2*G112 - 2*G222 - 2*G323) + G311*(2*G113 - 2*G333) - gu22*PDstandard4th11g22 - - 2*(G111*G212 + G223*G311 + G111*G313 + gu32*PDstandard4th11g23) - gu33*PDstandard4th11g33 + - 2*gu22*PDstandard4th12g12 + 2*gu32*PDstandard4th12g13 + 2*gu32*PDstandard4th13g12 + 2*gu33*PDstandard4th13g13 - - gu22*PDstandard4th22g11 - 2*gu32*PDstandard4th23g11 - gu33*PDstandard4th33g11 + 2*SQR(G212) + 2*SQR(G313)); + R11 = khalf*(4*G213*G312 + G211*(2*G112 - 2*G222 - 2*G323) + G311*(2*G113 - 2*G333) - gu22*PDstandardNth11g22 - + 2*(G111*G212 + G223*G311 + G111*G313 + gu32*PDstandardNth11g23) - gu33*PDstandardNth11g33 + + 2*gu22*PDstandardNth12g12 + 2*gu32*PDstandardNth12g13 + 2*gu32*PDstandardNth13g12 + 2*gu33*PDstandardNth13g13 - + gu22*PDstandardNth22g11 - 2*gu32*PDstandardNth23g11 - gu33*PDstandardNth33g11 + 2*SQR(G212) + 2*SQR(G313)); R12 = khalf*(2*(G122*G211 + G123*G311 + G213*G322 + G313*G323) - - 2*(G112*G212 + G112*G313 + G212*G323 + G312*G333 + gu21*PDstandard4th12g12) - gu32*PDstandard4th12g23 - - gu33*PDstandard4th12g33 + gu31*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12) + - gu32*PDstandard4th13g22 + gu33*PDstandard4th13g23 + gu21*(PDstandard4th11g22 + PDstandard4th22g11) + - gu32*PDstandard4th22g13 + gu31*PDstandard4th23g11 - gu32*PDstandard4th23g12 + gu33*PDstandard4th23g13 - - gu33*PDstandard4th33g12); + 2*(G112*G212 + G112*G313 + G212*G323 + G312*G333 + gu21*PDstandardNth12g12) - gu32*PDstandardNth12g23 - + gu33*PDstandardNth12g33 + gu31*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12) + + gu32*PDstandardNth13g22 + gu33*PDstandardNth13g23 + gu21*(PDstandardNth11g22 + PDstandardNth22g11) + + gu32*PDstandardNth22g13 + gu31*PDstandardNth23g11 - gu32*PDstandardNth23g12 + gu33*PDstandardNth23g13 - + gu33*PDstandardNth33g12); R13 = khalf*(2*(G123*G211 + G212*G223 + G133*G311 + G233*G312) - - 2*(G213*G222 + G223*G313 + G113*(G212 + G313) + gu31*PDstandard4th13g13) + - gu21*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12 + PDstandard4th23g11) + - gu22*(PDstandard4th12g23 - PDstandard4th13g22 - PDstandard4th22g13 + PDstandard4th23g12) + - gu31*(PDstandard4th11g33 + PDstandard4th33g11) + - gu32*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12)); + 2*(G213*G222 + G223*G313 + G113*(G212 + G313) + gu31*PDstandardNth13g13) + + gu21*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12 + PDstandardNth23g11) + + gu22*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) + + gu31*(PDstandardNth11g33 + PDstandardNth33g11) + + gu32*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12)); R22 = khalf*(4*G123*G312 + G122*(2*G212 - 2*(G111 + G313)) + G322*(2*G223 - 2*G333) - - 2*(G113*G322 + G222*(G112 + G323) + gu31*PDstandard4th13g22) + - gu11*(-PDstandard4th11g22 + 2*PDstandard4th12g12 - PDstandard4th22g11) + - gu31*(-2*PDstandard4th22g13 + 2*(PDstandard4th12g23 + PDstandard4th23g12)) + - gu33*(-PDstandard4th22g33 + 2*PDstandard4th23g23 - PDstandard4th33g22) + 2*(SQR(G112) + SQR(G323))); + 2*(G113*G322 + G222*(G112 + G323) + gu31*PDstandardNth13g22) + + gu11*(-PDstandardNth11g22 + 2*PDstandardNth12g12 - PDstandardNth22g11) + + gu31*(-2*PDstandardNth22g13 + 2*(PDstandardNth12g23 + PDstandardNth23g12)) + + gu33*(-PDstandardNth22g33 + 2*PDstandardNth23g23 - PDstandardNth33g22) + 2*(SQR(G112) + SQR(G323))); R23 = khalf*(2*(G112*G113 + G122*G213 + G133*G312 + G233*G322) + - gu11*(-PDstandard4th11g23 + PDstandard4th12g13 + PDstandard4th13g12 - PDstandard4th23g11) + - gu21*(-PDstandard4th12g23 + PDstandard4th13g22 + PDstandard4th22g13 - PDstandard4th23g12) - - 2*(G111*G123 + G113*G323 + G223*(G112 + G323) + gu32*PDstandard4th23g23) + - gu31*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12) + - gu32*(PDstandard4th22g33 + PDstandard4th33g22)); - - R33 = khalf*(4*G123*G213 - gu11*PDstandard4th11g33 - - 2*(G111*G133 + G133*G212 + G112*G233 + G222*G233 + G113*G333 + G223*G333 + gu21*PDstandard4th12g33) + - 2*(G133*G313 + G233*G323 + gu11*PDstandard4th13g13) + 2*gu21*PDstandard4th13g23 - gu22*PDstandard4th22g33 + - 2*gu21*PDstandard4th23g13 + 2*gu22*PDstandard4th23g23 - gu11*PDstandard4th33g11 - 2*gu21*PDstandard4th33g12 - - gu22*PDstandard4th33g22 + 2*SQR(G113) + 2*SQR(G223)); + gu11*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) + + gu21*(-PDstandardNth12g23 + PDstandardNth13g22 + PDstandardNth22g13 - PDstandardNth23g12) - + 2*(G111*G123 + G113*G323 + G223*(G112 + G323) + gu32*PDstandardNth23g23) + + gu31*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12) + + gu32*(PDstandardNth22g33 + PDstandardNth33g22)); + + R33 = khalf*(4*G123*G213 - gu11*PDstandardNth11g33 - + 2*(G111*G133 + G133*G212 + G112*G233 + G222*G233 + G113*G333 + G223*G333 + gu21*PDstandardNth12g33) + + 2*(G133*G313 + G233*G323 + gu11*PDstandardNth13g13) + 2*gu21*PDstandardNth13g23 - gu22*PDstandardNth22g33 + + 2*gu21*PDstandardNth23g13 + 2*gu22*PDstandardNth23g23 - gu11*PDstandardNth33g11 - 2*gu21*PDstandardNth33g12 - + gu22*PDstandardNth33g22 + 2*SQR(G113) + 2*SQR(G223)); Km11 = gu11*K11L + gu21*K12L + gu31*K13L; @@ -442,57 +442,57 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ trK = Km11 + Km22 + Km33; - g11rhsL = -2*alphaL*K11L + 2*(g11L*PDstandard4th1beta1 + g12L*PDstandard4th1beta2 + g13L*PDstandard4th1beta3) + - beta1L*PDstandard4th1g11 + beta2L*PDstandard4th2g11 + beta3L*PDstandard4th3g11; + g11rhsL = -2*alphaL*K11L + 2*(g11L*PDstandardNth1beta1 + g12L*PDstandardNth1beta2 + g13L*PDstandardNth1beta3) + + beta1L*PDstandardNth1g11 + beta2L*PDstandardNth2g11 + beta3L*PDstandardNth3g11; - g12rhsL = -2*alphaL*K12L + g22L*PDstandard4th1beta2 + g23L*PDstandard4th1beta3 + beta1L*PDstandard4th1g12 + - g11L*PDstandard4th2beta1 + g12L*(PDstandard4th1beta1 + PDstandard4th2beta2) + g13L*PDstandard4th2beta3 + - beta2L*PDstandard4th2g12 + beta3L*PDstandard4th3g12; + g12rhsL = -2*alphaL*K12L + g22L*PDstandardNth1beta2 + g23L*PDstandardNth1beta3 + beta1L*PDstandardNth1g12 + + g11L*PDstandardNth2beta1 + g12L*(PDstandardNth1beta1 + PDstandardNth2beta2) + g13L*PDstandardNth2beta3 + + beta2L*PDstandardNth2g12 + beta3L*PDstandardNth3g12; - g13rhsL = -2*alphaL*K13L + g23L*PDstandard4th1beta2 + g33L*PDstandard4th1beta3 + beta1L*PDstandard4th1g13 + - beta2L*PDstandard4th2g13 + g11L*PDstandard4th3beta1 + g12L*PDstandard4th3beta2 + - g13L*(PDstandard4th1beta1 + PDstandard4th3beta3) + beta3L*PDstandard4th3g13; + g13rhsL = -2*alphaL*K13L + g23L*PDstandardNth1beta2 + g33L*PDstandardNth1beta3 + beta1L*PDstandardNth1g13 + + beta2L*PDstandardNth2g13 + g11L*PDstandardNth3beta1 + g12L*PDstandardNth3beta2 + + g13L*(PDstandardNth1beta1 + PDstandardNth3beta3) + beta3L*PDstandardNth3g13; - g22rhsL = -2*alphaL*K22L + beta1L*PDstandard4th1g22 + - 2*(g12L*PDstandard4th2beta1 + g22L*PDstandard4th2beta2 + g23L*PDstandard4th2beta3) + beta2L*PDstandard4th2g22 + - beta3L*PDstandard4th3g22; + g22rhsL = -2*alphaL*K22L + beta1L*PDstandardNth1g22 + + 2*(g12L*PDstandardNth2beta1 + g22L*PDstandardNth2beta2 + g23L*PDstandardNth2beta3) + beta2L*PDstandardNth2g22 + + beta3L*PDstandardNth3g22; - g23rhsL = -2*alphaL*K23L + beta1L*PDstandard4th1g23 + g13L*PDstandard4th2beta1 + g33L*PDstandard4th2beta3 + - beta2L*PDstandard4th2g23 + g12L*PDstandard4th3beta1 + g22L*PDstandard4th3beta2 + - g23L*(PDstandard4th2beta2 + PDstandard4th3beta3) + beta3L*PDstandard4th3g23; + g23rhsL = -2*alphaL*K23L + beta1L*PDstandardNth1g23 + g13L*PDstandardNth2beta1 + g33L*PDstandardNth2beta3 + + beta2L*PDstandardNth2g23 + g12L*PDstandardNth3beta1 + g22L*PDstandardNth3beta2 + + g23L*(PDstandardNth2beta2 + PDstandardNth3beta3) + beta3L*PDstandardNth3g23; - g33rhsL = -2*alphaL*K33L + beta1L*PDstandard4th1g33 + beta2L*PDstandard4th2g33 + - 2*(g13L*PDstandard4th3beta1 + g23L*PDstandard4th3beta2 + g33L*PDstandard4th3beta3) + beta3L*PDstandard4th3g33; + g33rhsL = -2*alphaL*K33L + beta1L*PDstandardNth1g33 + beta2L*PDstandardNth2g33 + + 2*(g13L*PDstandardNth3beta1 + g23L*PDstandardNth3beta2 + g33L*PDstandardNth3beta3) + beta3L*PDstandardNth3g33; - K11rhsL = -PDstandard4th11alpha + G111*PDstandard4th1alpha + - 2*(K11L*PDstandard4th1beta1 + K12L*PDstandard4th1beta2 + K13L*PDstandard4th1beta3) + beta1L*PDstandard4th1K11 + - G211*PDstandard4th2alpha + beta2L*PDstandard4th2K11 + G311*PDstandard4th3alpha + beta3L*PDstandard4th3K11 + + K11rhsL = -PDstandardNth11alpha + G111*PDstandardNth1alpha + + 2*(K11L*PDstandardNth1beta1 + K12L*PDstandardNth1beta2 + K13L*PDstandardNth1beta3) + beta1L*PDstandardNth1K11 + + G211*PDstandardNth2alpha + beta2L*PDstandardNth2K11 + G311*PDstandardNth3alpha + beta3L*PDstandardNth3K11 + alphaL*(-2*(K11L*Km11 + K12L*Km21 + K13L*Km31) + R11 + K11L*trK); - K12rhsL = -PDstandard4th12alpha + G112*PDstandard4th1alpha + K22L*PDstandard4th1beta2 + K23L*PDstandard4th1beta3 + - beta1L*PDstandard4th1K12 + G212*PDstandard4th2alpha + K11L*PDstandard4th2beta1 + - K12L*(PDstandard4th1beta1 + PDstandard4th2beta2) + K13L*PDstandard4th2beta3 + beta2L*PDstandard4th2K12 + - G312*PDstandard4th3alpha + beta3L*PDstandard4th3K12 + + K12rhsL = -PDstandardNth12alpha + G112*PDstandardNth1alpha + K22L*PDstandardNth1beta2 + K23L*PDstandardNth1beta3 + + beta1L*PDstandardNth1K12 + G212*PDstandardNth2alpha + K11L*PDstandardNth2beta1 + + K12L*(PDstandardNth1beta1 + PDstandardNth2beta2) + K13L*PDstandardNth2beta3 + beta2L*PDstandardNth2K12 + + G312*PDstandardNth3alpha + beta3L*PDstandardNth3K12 + alphaL*(-2*(K11L*Km12 + K12L*Km22 + K13L*Km32) + R12 + K12L*trK); - K13rhsL = -PDstandard4th13alpha + G113*PDstandard4th1alpha + K23L*PDstandard4th1beta2 + K33L*PDstandard4th1beta3 + - beta1L*PDstandard4th1K13 + G213*PDstandard4th2alpha + beta2L*PDstandard4th2K13 + G313*PDstandard4th3alpha + - K11L*PDstandard4th3beta1 + K12L*PDstandard4th3beta2 + K13L*(PDstandard4th1beta1 + PDstandard4th3beta3) + - beta3L*PDstandard4th3K13 + alphaL*(-2*(K11L*Km13 + K12L*Km23 + K13L*Km33) + R13 + K13L*trK); + K13rhsL = -PDstandardNth13alpha + G113*PDstandardNth1alpha + K23L*PDstandardNth1beta2 + K33L*PDstandardNth1beta3 + + beta1L*PDstandardNth1K13 + G213*PDstandardNth2alpha + beta2L*PDstandardNth2K13 + G313*PDstandardNth3alpha + + K11L*PDstandardNth3beta1 + K12L*PDstandardNth3beta2 + K13L*(PDstandardNth1beta1 + PDstandardNth3beta3) + + beta3L*PDstandardNth3K13 + alphaL*(-2*(K11L*Km13 + K12L*Km23 + K13L*Km33) + R13 + K13L*trK); - K22rhsL = G122*PDstandard4th1alpha + beta1L*PDstandard4th1K22 - PDstandard4th22alpha + G222*PDstandard4th2alpha + - 2*(K12L*PDstandard4th2beta1 + K22L*PDstandard4th2beta2 + K23L*PDstandard4th2beta3) + beta2L*PDstandard4th2K22 + - G322*PDstandard4th3alpha + beta3L*PDstandard4th3K22 + + K22rhsL = G122*PDstandardNth1alpha + beta1L*PDstandardNth1K22 - PDstandardNth22alpha + G222*PDstandardNth2alpha + + 2*(K12L*PDstandardNth2beta1 + K22L*PDstandardNth2beta2 + K23L*PDstandardNth2beta3) + beta2L*PDstandardNth2K22 + + G322*PDstandardNth3alpha + beta3L*PDstandardNth3K22 + alphaL*(-2*(K12L*Km12 + K22L*Km22 + K23L*Km32) + R22 + K22L*trK); - K23rhsL = G123*PDstandard4th1alpha + beta1L*PDstandard4th1K23 - PDstandard4th23alpha + G223*PDstandard4th2alpha + - K13L*PDstandard4th2beta1 + K33L*PDstandard4th2beta3 + beta2L*PDstandard4th2K23 + G323*PDstandard4th3alpha + - K12L*PDstandard4th3beta1 + K22L*PDstandard4th3beta2 + K23L*(PDstandard4th2beta2 + PDstandard4th3beta3) + - beta3L*PDstandard4th3K23 + alphaL*(-2*(K12L*Km13 + K22L*Km23 + K23L*Km33) + R23 + K23L*trK); + K23rhsL = G123*PDstandardNth1alpha + beta1L*PDstandardNth1K23 - PDstandardNth23alpha + G223*PDstandardNth2alpha + + K13L*PDstandardNth2beta1 + K33L*PDstandardNth2beta3 + beta2L*PDstandardNth2K23 + G323*PDstandardNth3alpha + + K12L*PDstandardNth3beta1 + K22L*PDstandardNth3beta2 + K23L*(PDstandardNth2beta2 + PDstandardNth3beta3) + + beta3L*PDstandardNth3K23 + alphaL*(-2*(K12L*Km13 + K22L*Km23 + K23L*Km33) + R23 + K23L*trK); - K33rhsL = G133*PDstandard4th1alpha + beta1L*PDstandard4th1K33 + G233*PDstandard4th2alpha + beta2L*PDstandard4th2K33 - - PDstandard4th33alpha + G333*PDstandard4th3alpha + - 2*(K13L*PDstandard4th3beta1 + K23L*PDstandard4th3beta2 + K33L*PDstandard4th3beta3) + beta3L*PDstandard4th3K33 + + K33rhsL = G133*PDstandardNth1alpha + beta1L*PDstandardNth1K33 + G233*PDstandardNth2alpha + beta2L*PDstandardNth2K33 - + PDstandardNth33alpha + G333*PDstandardNth3alpha + + 2*(K13L*PDstandardNth3beta1 + K23L*PDstandardNth3beta2 + K33L*PDstandardNth3beta3) + beta3L*PDstandardNth3K33 + alphaL*(-2*(K13L*Km13 + K23L*Km23 + K33L*Km33) + R33 + K33L*trK); alpharhsL = 0; diff --git a/ML_ADM/src/ML_ADM_constraints.c b/ML_ADM/src/ML_ADM_constraints.c index f373870..389568d 100644 --- a/ML_ADM/src/ML_ADM_constraints.c +++ b/ML_ADM/src/ML_ADM_constraints.c @@ -113,84 +113,84 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL /* Declare precomputed derivatives*/ /* Declare derivatives */ - CCTK_REAL PDstandard4th1g11 = INITVALUE; - CCTK_REAL PDstandard4th2g11 = INITVALUE; - CCTK_REAL PDstandard4th3g11 = INITVALUE; - CCTK_REAL PDstandard4th22g11 = INITVALUE; - CCTK_REAL PDstandard4th33g11 = INITVALUE; - CCTK_REAL PDstandard4th12g11 = INITVALUE; - CCTK_REAL PDstandard4th13g11 = INITVALUE; - CCTK_REAL PDstandard4th21g11 = INITVALUE; - CCTK_REAL PDstandard4th23g11 = INITVALUE; - CCTK_REAL PDstandard4th31g11 = INITVALUE; - CCTK_REAL PDstandard4th32g11 = INITVALUE; - CCTK_REAL PDstandard4th1g12 = INITVALUE; - CCTK_REAL PDstandard4th2g12 = INITVALUE; - CCTK_REAL PDstandard4th3g12 = INITVALUE; - CCTK_REAL PDstandard4th33g12 = INITVALUE; - CCTK_REAL PDstandard4th12g12 = INITVALUE; - CCTK_REAL PDstandard4th13g12 = INITVALUE; - CCTK_REAL PDstandard4th21g12 = INITVALUE; - CCTK_REAL PDstandard4th23g12 = INITVALUE; - CCTK_REAL PDstandard4th31g12 = INITVALUE; - CCTK_REAL PDstandard4th32g12 = INITVALUE; - CCTK_REAL PDstandard4th1g13 = INITVALUE; - CCTK_REAL PDstandard4th2g13 = INITVALUE; - CCTK_REAL PDstandard4th3g13 = INITVALUE; - CCTK_REAL PDstandard4th22g13 = INITVALUE; - CCTK_REAL PDstandard4th12g13 = INITVALUE; - CCTK_REAL PDstandard4th13g13 = INITVALUE; - CCTK_REAL PDstandard4th21g13 = INITVALUE; - CCTK_REAL PDstandard4th23g13 = INITVALUE; - CCTK_REAL PDstandard4th31g13 = INITVALUE; - CCTK_REAL PDstandard4th32g13 = INITVALUE; - CCTK_REAL PDstandard4th1g22 = INITVALUE; - CCTK_REAL PDstandard4th2g22 = INITVALUE; - CCTK_REAL PDstandard4th3g22 = INITVALUE; - CCTK_REAL PDstandard4th11g22 = INITVALUE; - CCTK_REAL PDstandard4th33g22 = INITVALUE; - CCTK_REAL PDstandard4th12g22 = INITVALUE; - CCTK_REAL PDstandard4th13g22 = INITVALUE; - CCTK_REAL PDstandard4th21g22 = INITVALUE; - CCTK_REAL PDstandard4th23g22 = INITVALUE; - CCTK_REAL PDstandard4th31g22 = INITVALUE; - CCTK_REAL PDstandard4th32g22 = INITVALUE; - CCTK_REAL PDstandard4th1g23 = INITVALUE; - CCTK_REAL PDstandard4th2g23 = INITVALUE; - CCTK_REAL PDstandard4th3g23 = INITVALUE; - CCTK_REAL PDstandard4th11g23 = INITVALUE; - CCTK_REAL PDstandard4th12g23 = INITVALUE; - CCTK_REAL PDstandard4th13g23 = INITVALUE; - CCTK_REAL PDstandard4th21g23 = INITVALUE; - CCTK_REAL PDstandard4th23g23 = INITVALUE; - CCTK_REAL PDstandard4th31g23 = INITVALUE; - CCTK_REAL PDstandard4th32g23 = INITVALUE; - CCTK_REAL PDstandard4th1g33 = INITVALUE; - CCTK_REAL PDstandard4th2g33 = INITVALUE; - CCTK_REAL PDstandard4th3g33 = INITVALUE; - CCTK_REAL PDstandard4th11g33 = INITVALUE; - CCTK_REAL PDstandard4th22g33 = INITVALUE; - CCTK_REAL PDstandard4th12g33 = INITVALUE; - CCTK_REAL PDstandard4th13g33 = INITVALUE; - CCTK_REAL PDstandard4th21g33 = INITVALUE; - CCTK_REAL PDstandard4th23g33 = INITVALUE; - CCTK_REAL PDstandard4th31g33 = INITVALUE; - CCTK_REAL PDstandard4th32g33 = INITVALUE; - CCTK_REAL PDstandard4th2K11 = INITVALUE; - CCTK_REAL PDstandard4th3K11 = INITVALUE; - CCTK_REAL PDstandard4th1K12 = INITVALUE; - CCTK_REAL PDstandard4th2K12 = INITVALUE; - CCTK_REAL PDstandard4th3K12 = INITVALUE; - CCTK_REAL PDstandard4th1K13 = INITVALUE; - CCTK_REAL PDstandard4th2K13 = INITVALUE; - CCTK_REAL PDstandard4th3K13 = INITVALUE; - CCTK_REAL PDstandard4th1K22 = INITVALUE; - CCTK_REAL PDstandard4th3K22 = INITVALUE; - CCTK_REAL PDstandard4th1K23 = INITVALUE; - CCTK_REAL PDstandard4th2K23 = INITVALUE; - CCTK_REAL PDstandard4th3K23 = INITVALUE; - CCTK_REAL PDstandard4th1K33 = INITVALUE; - CCTK_REAL PDstandard4th2K33 = INITVALUE; + CCTK_REAL PDstandardNth1g11 = INITVALUE; + CCTK_REAL PDstandardNth2g11 = INITVALUE; + CCTK_REAL PDstandardNth3g11 = INITVALUE; + CCTK_REAL PDstandardNth22g11 = INITVALUE; + CCTK_REAL PDstandardNth33g11 = INITVALUE; + CCTK_REAL PDstandardNth12g11 = INITVALUE; + CCTK_REAL PDstandardNth13g11 = INITVALUE; + CCTK_REAL PDstandardNth21g11 = INITVALUE; + CCTK_REAL PDstandardNth23g11 = INITVALUE; + CCTK_REAL PDstandardNth31g11 = INITVALUE; + CCTK_REAL PDstandardNth32g11 = INITVALUE; + CCTK_REAL PDstandardNth1g12 = INITVALUE; + CCTK_REAL PDstandardNth2g12 = INITVALUE; + CCTK_REAL PDstandardNth3g12 = INITVALUE; + CCTK_REAL PDstandardNth33g12 = INITVALUE; + CCTK_REAL PDstandardNth12g12 = INITVALUE; + CCTK_REAL PDstandardNth13g12 = INITVALUE; + CCTK_REAL PDstandardNth21g12 = INITVALUE; + CCTK_REAL PDstandardNth23g12 = INITVALUE; + CCTK_REAL PDstandardNth31g12 = INITVALUE; + CCTK_REAL PDstandardNth32g12 = INITVALUE; + CCTK_REAL PDstandardNth1g13 = INITVALUE; + CCTK_REAL PDstandardNth2g13 = INITVALUE; + CCTK_REAL PDstandardNth3g13 = INITVALUE; + CCTK_REAL PDstandardNth22g13 = INITVALUE; + CCTK_REAL PDstandardNth12g13 = INITVALUE; + CCTK_REAL PDstandardNth13g13 = INITVALUE; + CCTK_REAL PDstandardNth21g13 = INITVALUE; + CCTK_REAL PDstandardNth23g13 = INITVALUE; + CCTK_REAL PDstandardNth31g13 = INITVALUE; + CCTK_REAL PDstandardNth32g13 = INITVALUE; + CCTK_REAL PDstandardNth1g22 = INITVALUE; + CCTK_REAL PDstandardNth2g22 = INITVALUE; + CCTK_REAL PDstandardNth3g22 = INITVALUE; + CCTK_REAL PDstandardNth11g22 = INITVALUE; + CCTK_REAL PDstandardNth33g22 = INITVALUE; + CCTK_REAL PDstandardNth12g22 = INITVALUE; + CCTK_REAL PDstandardNth13g22 = INITVALUE; + CCTK_REAL PDstandardNth21g22 = INITVALUE; + CCTK_REAL PDstandardNth23g22 = INITVALUE; + CCTK_REAL PDstandardNth31g22 = INITVALUE; + CCTK_REAL PDstandardNth32g22 = INITVALUE; + CCTK_REAL PDstandardNth1g23 = INITVALUE; + CCTK_REAL PDstandardNth2g23 = INITVALUE; + CCTK_REAL PDstandardNth3g23 = INITVALUE; + CCTK_REAL PDstandardNth11g23 = INITVALUE; + CCTK_REAL PDstandardNth12g23 = INITVALUE; + CCTK_REAL PDstandardNth13g23 = INITVALUE; + CCTK_REAL PDstandardNth21g23 = INITVALUE; + CCTK_REAL PDstandardNth23g23 = INITVALUE; + CCTK_REAL PDstandardNth31g23 = INITVALUE; + CCTK_REAL PDstandardNth32g23 = INITVALUE; + CCTK_REAL PDstandardNth1g33 = INITVALUE; + CCTK_REAL PDstandardNth2g33 = INITVALUE; + CCTK_REAL PDstandardNth3g33 = INITVALUE; + CCTK_REAL PDstandardNth11g33 = INITVALUE; + CCTK_REAL PDstandardNth22g33 = INITVALUE; + CCTK_REAL PDstandardNth12g33 = INITVALUE; + CCTK_REAL PDstandardNth13g33 = INITVALUE; + CCTK_REAL PDstandardNth21g33 = INITVALUE; + CCTK_REAL PDstandardNth23g33 = INITVALUE; + CCTK_REAL PDstandardNth31g33 = INITVALUE; + CCTK_REAL PDstandardNth32g33 = INITVALUE; + CCTK_REAL PDstandardNth2K11 = INITVALUE; + CCTK_REAL PDstandardNth3K11 = INITVALUE; + CCTK_REAL PDstandardNth1K12 = INITVALUE; + CCTK_REAL PDstandardNth2K12 = INITVALUE; + CCTK_REAL PDstandardNth3K12 = INITVALUE; + CCTK_REAL PDstandardNth1K13 = INITVALUE; + CCTK_REAL PDstandardNth2K13 = INITVALUE; + CCTK_REAL PDstandardNth3K13 = INITVALUE; + CCTK_REAL PDstandardNth1K22 = INITVALUE; + CCTK_REAL PDstandardNth3K22 = INITVALUE; + CCTK_REAL PDstandardNth1K23 = INITVALUE; + CCTK_REAL PDstandardNth2K23 = INITVALUE; + CCTK_REAL PDstandardNth3K23 = INITVALUE; + CCTK_REAL PDstandardNth1K33 = INITVALUE; + CCTK_REAL PDstandardNth2K33 = INITVALUE; /* Assign local copies of grid functions */ g11L = g11[index]; @@ -211,60 +211,60 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL /* Include user supplied include files */ /* Precompute derivatives (new style) */ - PDstandard4th1g11 = PDstandard4th1(g11, i, j, k); - PDstandard4th2g11 = PDstandard4th2(g11, i, j, k); - PDstandard4th3g11 = PDstandard4th3(g11, i, j, k); - PDstandard4th22g11 = PDstandard4th22(g11, i, j, k); - PDstandard4th33g11 = PDstandard4th33(g11, i, j, k); - PDstandard4th23g11 = PDstandard4th23(g11, i, j, k); - PDstandard4th1g12 = PDstandard4th1(g12, i, j, k); - PDstandard4th2g12 = PDstandard4th2(g12, i, j, k); - PDstandard4th3g12 = PDstandard4th3(g12, i, j, k); - PDstandard4th33g12 = PDstandard4th33(g12, i, j, k); - PDstandard4th12g12 = PDstandard4th12(g12, i, j, k); - PDstandard4th13g12 = PDstandard4th13(g12, i, j, k); - PDstandard4th23g12 = PDstandard4th23(g12, i, j, k); - PDstandard4th1g13 = PDstandard4th1(g13, i, j, k); - PDstandard4th2g13 = PDstandard4th2(g13, i, j, k); - PDstandard4th3g13 = PDstandard4th3(g13, i, j, k); - PDstandard4th22g13 = PDstandard4th22(g13, i, j, k); - PDstandard4th12g13 = PDstandard4th12(g13, i, j, k); - PDstandard4th13g13 = PDstandard4th13(g13, i, j, k); - PDstandard4th23g13 = PDstandard4th23(g13, i, j, k); - PDstandard4th1g22 = PDstandard4th1(g22, i, j, k); - PDstandard4th2g22 = PDstandard4th2(g22, i, j, k); - PDstandard4th3g22 = PDstandard4th3(g22, i, j, k); - PDstandard4th11g22 = PDstandard4th11(g22, i, j, k); - PDstandard4th33g22 = PDstandard4th33(g22, i, j, k); - PDstandard4th13g22 = PDstandard4th13(g22, i, j, k); - PDstandard4th1g23 = PDstandard4th1(g23, i, j, k); - PDstandard4th2g23 = PDstandard4th2(g23, i, j, k); - PDstandard4th3g23 = PDstandard4th3(g23, i, j, k); - PDstandard4th11g23 = PDstandard4th11(g23, i, j, k); - PDstandard4th12g23 = PDstandard4th12(g23, i, j, k); - PDstandard4th13g23 = PDstandard4th13(g23, i, j, k); - PDstandard4th23g23 = PDstandard4th23(g23, i, j, k); - PDstandard4th1g33 = PDstandard4th1(g33, i, j, k); - PDstandard4th2g33 = PDstandard4th2(g33, i, j, k); - PDstandard4th3g33 = PDstandard4th3(g33, i, j, k); - PDstandard4th11g33 = PDstandard4th11(g33, i, j, k); - PDstandard4th22g33 = PDstandard4th22(g33, i, j, k); - PDstandard4th12g33 = PDstandard4th12(g33, i, j, k); - PDstandard4th2K11 = PDstandard4th2(K11, i, j, k); - PDstandard4th3K11 = PDstandard4th3(K11, i, j, k); - PDstandard4th1K12 = PDstandard4th1(K12, i, j, k); - PDstandard4th2K12 = PDstandard4th2(K12, i, j, k); - PDstandard4th3K12 = PDstandard4th3(K12, i, j, k); - PDstandard4th1K13 = PDstandard4th1(K13, i, j, k); - PDstandard4th2K13 = PDstandard4th2(K13, i, j, k); - PDstandard4th3K13 = PDstandard4th3(K13, i, j, k); - PDstandard4th1K22 = PDstandard4th1(K22, i, j, k); - PDstandard4th3K22 = PDstandard4th3(K22, i, j, k); - PDstandard4th1K23 = PDstandard4th1(K23, i, j, k); - PDstandard4th2K23 = PDstandard4th2(K23, i, j, k); - PDstandard4th3K23 = PDstandard4th3(K23, i, j, k); - PDstandard4th1K33 = PDstandard4th1(K33, i, j, k); - PDstandard4th2K33 = PDstandard4th2(K33, i, j, k); + PDstandardNth1g11 = PDstandardNth1(g11, i, j, k); + PDstandardNth2g11 = PDstandardNth2(g11, i, j, k); + PDstandardNth3g11 = PDstandardNth3(g11, i, j, k); + PDstandardNth22g11 = PDstandardNth22(g11, i, j, k); + PDstandardNth33g11 = PDstandardNth33(g11, i, j, k); + PDstandardNth23g11 = PDstandardNth23(g11, i, j, k); + PDstandardNth1g12 = PDstandardNth1(g12, i, j, k); + PDstandardNth2g12 = PDstandardNth2(g12, i, j, k); + PDstandardNth3g12 = PDstandardNth3(g12, i, j, k); + PDstandardNth33g12 = PDstandardNth33(g12, i, j, k); + PDstandardNth12g12 = PDstandardNth12(g12, i, j, k); + PDstandardNth13g12 = PDstandardNth13(g12, i, j, k); + PDstandardNth23g12 = PDstandardNth23(g12, i, j, k); + PDstandardNth1g13 = PDstandardNth1(g13, i, j, k); + PDstandardNth2g13 = PDstandardNth2(g13, i, j, k); + PDstandardNth3g13 = PDstandardNth3(g13, i, j, k); + PDstandardNth22g13 = PDstandardNth22(g13, i, j, k); + PDstandardNth12g13 = PDstandardNth12(g13, i, j, k); + PDstandardNth13g13 = PDstandardNth13(g13, i, j, k); + PDstandardNth23g13 = PDstandardNth23(g13, i, j, k); + PDstandardNth1g22 = PDstandardNth1(g22, i, j, k); + PDstandardNth2g22 = PDstandardNth2(g22, i, j, k); + PDstandardNth3g22 = PDstandardNth3(g22, i, j, k); + PDstandardNth11g22 = PDstandardNth11(g22, i, j, k); + PDstandardNth33g22 = PDstandardNth33(g22, i, j, k); + PDstandardNth13g22 = PDstandardNth13(g22, i, j, k); + PDstandardNth1g23 = PDstandardNth1(g23, i, j, k); + PDstandardNth2g23 = PDstandardNth2(g23, i, j, k); + PDstandardNth3g23 = PDstandardNth3(g23, i, j, k); + PDstandardNth11g23 = PDstandardNth11(g23, i, j, k); + PDstandardNth12g23 = PDstandardNth12(g23, i, j, k); + PDstandardNth13g23 = PDstandardNth13(g23, i, j, k); + PDstandardNth23g23 = PDstandardNth23(g23, i, j, k); + PDstandardNth1g33 = PDstandardNth1(g33, i, j, k); + PDstandardNth2g33 = PDstandardNth2(g33, i, j, k); + PDstandardNth3g33 = PDstandardNth3(g33, i, j, k); + PDstandardNth11g33 = PDstandardNth11(g33, i, j, k); + PDstandardNth22g33 = PDstandardNth22(g33, i, j, k); + PDstandardNth12g33 = PDstandardNth12(g33, i, j, k); + PDstandardNth2K11 = PDstandardNth2(K11, i, j, k); + PDstandardNth3K11 = PDstandardNth3(K11, i, j, k); + PDstandardNth1K12 = PDstandardNth1(K12, i, j, k); + PDstandardNth2K12 = PDstandardNth2(K12, i, j, k); + PDstandardNth3K12 = PDstandardNth3(K12, i, j, k); + PDstandardNth1K13 = PDstandardNth1(K13, i, j, k); + PDstandardNth2K13 = PDstandardNth2(K13, i, j, k); + PDstandardNth3K13 = PDstandardNth3(K13, i, j, k); + PDstandardNth1K22 = PDstandardNth1(K22, i, j, k); + PDstandardNth3K22 = PDstandardNth3(K22, i, j, k); + PDstandardNth1K23 = PDstandardNth1(K23, i, j, k); + PDstandardNth2K23 = PDstandardNth2(K23, i, j, k); + PDstandardNth3K23 = PDstandardNth3(K23, i, j, k); + PDstandardNth1K33 = PDstandardNth1(K33, i, j, k); + PDstandardNth2K33 = PDstandardNth2(K33, i, j, k); /* Precompute derivatives (old style) */ @@ -283,95 +283,95 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL gu33 = INV(detg)*(g11L*g22L - SQR(g12L)); - G111 = khalf*(gu11*PDstandard4th1g11 + 2*(gu21*PDstandard4th1g12 + gu31*PDstandard4th1g13) - gu21*PDstandard4th2g11 - - gu31*PDstandard4th3g11); + G111 = khalf*(gu11*PDstandardNth1g11 + 2*(gu21*PDstandardNth1g12 + gu31*PDstandardNth1g13) - gu21*PDstandardNth2g11 - + gu31*PDstandardNth3g11); - G211 = khalf*(gu21*PDstandard4th1g11 + 2*(gu22*PDstandard4th1g12 + gu32*PDstandard4th1g13) - gu22*PDstandard4th2g11 - - gu32*PDstandard4th3g11); + G211 = khalf*(gu21*PDstandardNth1g11 + 2*(gu22*PDstandardNth1g12 + gu32*PDstandardNth1g13) - gu22*PDstandardNth2g11 - + gu32*PDstandardNth3g11); - G311 = khalf*(gu31*PDstandard4th1g11 + 2*(gu32*PDstandard4th1g12 + gu33*PDstandard4th1g13) - gu32*PDstandard4th2g11 - - gu33*PDstandard4th3g11); + G311 = khalf*(gu31*PDstandardNth1g11 + 2*(gu32*PDstandardNth1g12 + gu33*PDstandardNth1g13) - gu32*PDstandardNth2g11 - + gu33*PDstandardNth3g11); - G112 = khalf*(gu21*PDstandard4th1g22 + gu11*PDstandard4th2g11 + - gu31*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); + G112 = khalf*(gu21*PDstandardNth1g22 + gu11*PDstandardNth2g11 + + gu31*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - G212 = khalf*(gu22*PDstandard4th1g22 + gu21*PDstandard4th2g11 + - gu32*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); + G212 = khalf*(gu22*PDstandardNth1g22 + gu21*PDstandardNth2g11 + + gu32*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - G312 = khalf*(gu32*PDstandard4th1g22 + gu31*PDstandard4th2g11 + - gu33*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); + G312 = khalf*(gu32*PDstandardNth1g22 + gu31*PDstandardNth2g11 + + gu33*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - G113 = khalf*(gu31*PDstandard4th1g33 + gu11*PDstandard4th3g11 + - gu21*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); + G113 = khalf*(gu31*PDstandardNth1g33 + gu11*PDstandardNth3g11 + + gu21*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - G213 = khalf*(gu32*PDstandard4th1g33 + gu21*PDstandard4th3g11 + - gu22*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); + G213 = khalf*(gu32*PDstandardNth1g33 + gu21*PDstandardNth3g11 + + gu22*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - G313 = khalf*(gu33*PDstandard4th1g33 + gu31*PDstandard4th3g11 + - gu32*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); + G313 = khalf*(gu33*PDstandardNth1g33 + gu31*PDstandardNth3g11 + + gu32*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - G122 = khalf*(gu11*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu21*PDstandard4th2g22 + - gu31*(2*PDstandard4th2g23 - PDstandard4th3g22)); + G122 = khalf*(gu11*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu21*PDstandardNth2g22 + + gu31*(2*PDstandardNth2g23 - PDstandardNth3g22)); - G222 = khalf*(gu21*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu22*PDstandard4th2g22 + - gu32*(2*PDstandard4th2g23 - PDstandard4th3g22)); + G222 = khalf*(gu21*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu22*PDstandardNth2g22 + + gu32*(2*PDstandardNth2g23 - PDstandardNth3g22)); - G322 = khalf*(gu31*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu32*PDstandard4th2g22 + - gu33*(2*PDstandard4th2g23 - PDstandard4th3g22)); + G322 = khalf*(gu31*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu32*PDstandardNth2g22 + + gu33*(2*PDstandardNth2g23 - PDstandardNth3g22)); - G123 = khalf*(gu31*PDstandard4th2g33 + gu11*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + - gu21*PDstandard4th3g22); + G123 = khalf*(gu31*PDstandardNth2g33 + gu11*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu21*PDstandardNth3g22); - G223 = khalf*(gu32*PDstandard4th2g33 + gu21*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + - gu22*PDstandard4th3g22); + G223 = khalf*(gu32*PDstandardNth2g33 + gu21*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu22*PDstandardNth3g22); - G323 = khalf*(gu33*PDstandard4th2g33 + gu31*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + - gu32*PDstandard4th3g22); + G323 = khalf*(gu33*PDstandardNth2g33 + gu31*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu32*PDstandardNth3g22); - G133 = khalf*(-(gu11*PDstandard4th1g33) - gu21*PDstandard4th2g33 + 2*gu11*PDstandard4th3g13 + - 2*gu21*PDstandard4th3g23 + gu31*PDstandard4th3g33); + G133 = khalf*(-(gu11*PDstandardNth1g33) - gu21*PDstandardNth2g33 + 2*gu11*PDstandardNth3g13 + + 2*gu21*PDstandardNth3g23 + gu31*PDstandardNth3g33); - G233 = khalf*(-(gu21*PDstandard4th1g33) - gu22*PDstandard4th2g33 + 2*gu21*PDstandard4th3g13 + - 2*gu22*PDstandard4th3g23 + gu32*PDstandard4th3g33); + G233 = khalf*(-(gu21*PDstandardNth1g33) - gu22*PDstandardNth2g33 + 2*gu21*PDstandardNth3g13 + + 2*gu22*PDstandardNth3g23 + gu32*PDstandardNth3g33); - G333 = khalf*(-(gu31*PDstandard4th1g33) - gu32*PDstandard4th2g33 + 2*gu31*PDstandard4th3g13 + - 2*gu32*PDstandard4th3g23 + gu33*PDstandard4th3g33); + G333 = khalf*(-(gu31*PDstandardNth1g33) - gu32*PDstandardNth2g33 + 2*gu31*PDstandardNth3g13 + + 2*gu32*PDstandardNth3g23 + gu33*PDstandardNth3g33); - R11 = khalf*(-(gu22*PDstandard4th11g22) - 2*(G111*G122 + G111*G133 + G211*G222 + G211*G233 + G311*G322 + G311*G333 + - gu32*PDstandard4th11g23) - gu33*PDstandard4th11g33 + 2*gu22*PDstandard4th12g12 + 2*gu32*PDstandard4th12g13 + - 2*gu32*PDstandard4th13g12 + 2*gu33*PDstandard4th13g13 - gu22*PDstandard4th22g11 - 2*gu32*PDstandard4th23g11 - - gu33*PDstandard4th33g11 + 2*SQR(G112) + 2*SQR(G113) + 2*SQR(G212) + 2*SQR(G213) + 2*SQR(G312) + 2*SQR(G313)); + R11 = khalf*(-(gu22*PDstandardNth11g22) - 2*(G111*G122 + G111*G133 + G211*G222 + G211*G233 + G311*G322 + G311*G333 + + gu32*PDstandardNth11g23) - gu33*PDstandardNth11g33 + 2*gu22*PDstandardNth12g12 + 2*gu32*PDstandardNth12g13 + + 2*gu32*PDstandardNth13g12 + 2*gu33*PDstandardNth13g13 - gu22*PDstandardNth22g11 - 2*gu32*PDstandardNth23g11 - + gu33*PDstandardNth33g11 + 2*SQR(G112) + 2*SQR(G113) + 2*SQR(G212) + 2*SQR(G213) + 2*SQR(G312) + 2*SQR(G313)); - R12 = khalf*(2*(G113*G123 + G213*G223 + G313*G323) - 2*(G112*G133 + G212*G233 + G312*G333 + gu21*PDstandard4th12g12) - - gu32*PDstandard4th12g23 - gu33*PDstandard4th12g33 + - gu31*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12) + gu32*PDstandard4th13g22 + - gu33*PDstandard4th13g23 + gu21*(PDstandard4th11g22 + PDstandard4th22g11) + gu32*PDstandard4th22g13 + - gu31*PDstandard4th23g11 - gu32*PDstandard4th23g12 + gu33*PDstandard4th23g13 - gu33*PDstandard4th33g12); + R12 = khalf*(2*(G113*G123 + G213*G223 + G313*G323) - 2*(G112*G133 + G212*G233 + G312*G333 + gu21*PDstandardNth12g12) - + gu32*PDstandardNth12g23 - gu33*PDstandardNth12g33 + + gu31*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12) + gu32*PDstandardNth13g22 + + gu33*PDstandardNth13g23 + gu21*(PDstandardNth11g22 + PDstandardNth22g11) + gu32*PDstandardNth22g13 + + gu31*PDstandardNth23g11 - gu32*PDstandardNth23g12 + gu33*PDstandardNth23g13 - gu33*PDstandardNth33g12); - R13 = khalf*(2*(G112*G123 + G212*G223 + G312*G323) - 2*(G113*G122 + G213*G222 + G313*G322 + gu31*PDstandard4th13g13) + - gu21*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12 + PDstandard4th23g11) + - gu22*(PDstandard4th12g23 - PDstandard4th13g22 - PDstandard4th22g13 + PDstandard4th23g12) + - gu31*(PDstandard4th11g33 + PDstandard4th33g11) + - gu32*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12)); + R13 = khalf*(2*(G112*G123 + G212*G223 + G312*G323) - 2*(G113*G122 + G213*G222 + G313*G322 + gu31*PDstandardNth13g13) + + gu21*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12 + PDstandardNth23g11) + + gu22*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) + + gu31*(PDstandardNth11g33 + PDstandardNth33g11) + + gu32*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12)); - R22 = khalf*(-2*(G122*(G111 + G133) + G222*(G211 + G233) + G322*(G311 + G333) + gu31*PDstandard4th13g22) + - gu11*(-PDstandard4th11g22 + 2*PDstandard4th12g12 - PDstandard4th22g11) + - gu31*(-2*PDstandard4th22g13 + 2*(PDstandard4th12g23 + PDstandard4th23g12)) + - gu33*(-PDstandard4th22g33 + 2*PDstandard4th23g23 - PDstandard4th33g22) + + R22 = khalf*(-2*(G122*(G111 + G133) + G222*(G211 + G233) + G322*(G311 + G333) + gu31*PDstandardNth13g22) + + gu11*(-PDstandardNth11g22 + 2*PDstandardNth12g12 - PDstandardNth22g11) + + gu31*(-2*PDstandardNth22g13 + 2*(PDstandardNth12g23 + PDstandardNth23g12)) + + gu33*(-PDstandardNth22g33 + 2*PDstandardNth23g23 - PDstandardNth33g22) + 2*(SQR(G112) + SQR(G123) + SQR(G212) + SQR(G223) + SQR(G312) + SQR(G323))); R23 = khalf*(2*(G112*G113 + G212*G213 + G312*G313) + - gu11*(-PDstandard4th11g23 + PDstandard4th12g13 + PDstandard4th13g12 - PDstandard4th23g11) + - gu21*(-PDstandard4th12g23 + PDstandard4th13g22 + PDstandard4th22g13 - PDstandard4th23g12) - - 2*(G111*G123 + G211*G223 + G311*G323 + gu32*PDstandard4th23g23) + - gu31*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12) + - gu32*(PDstandard4th22g33 + PDstandard4th33g22)); + gu11*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) + + gu21*(-PDstandardNth12g23 + PDstandardNth13g22 + PDstandardNth22g13 - PDstandardNth23g12) - + 2*(G111*G123 + G211*G223 + G311*G323 + gu32*PDstandardNth23g23) + + gu31*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12) + + gu32*(PDstandardNth22g33 + PDstandardNth33g22)); - R33 = khalf*(gu11*(-PDstandard4th11g33 + 2*PDstandard4th13g13 - PDstandard4th33g11) - + R33 = khalf*(gu11*(-PDstandardNth11g33 + 2*PDstandardNth13g13 - PDstandardNth33g11) - 2*((G111 + G122)*G133 + (G211 + G222)*G233 + (G311 + G322)*G333 + - gu21*(PDstandard4th12g33 + PDstandard4th33g12)) + - gu22*(-PDstandard4th22g33 + 2*PDstandard4th23g23 - PDstandard4th33g22) + - 2*(gu21*(PDstandard4th13g23 + PDstandard4th23g13) + SQR(G113) + SQR(G123) + SQR(G213) + SQR(G223) + SQR(G313) + + gu21*(PDstandardNth12g33 + PDstandardNth33g12)) + + gu22*(-PDstandardNth22g33 + 2*PDstandardNth23g23 - PDstandardNth33g22) + + 2*(gu21*(PDstandardNth13g23 + PDstandardNth23g13) + SQR(G113) + SQR(G123) + SQR(G213) + SQR(G223) + SQR(G313) + SQR(G323))); trR = gu11*R11 + gu22*R22 + 2*(gu21*R12 + gu31*R13 + gu32*R23) + gu33*R33; @@ -398,31 +398,31 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL HL = -2*(Km12*Km21 + Km13*Km31 + Km23*Km32) + trR - SQR(Km11) - SQR(Km22) - SQR(Km33) + SQR(trK); - M1L = gu21*(-(G112*K11L) + G111*K12L - G212*K12L - G312*K13L + G211*K22L + G311*K23L - PDstandard4th1K12 + - PDstandard4th2K11) + gu22*(-(G122*K11L) + G112*K12L - G222*K12L - G322*K13L + G212*K22L + G312*K23L - - PDstandard4th1K22 + PDstandard4th2K12) + gu31* - (-(G113*K11L) - G213*K12L + G111*K13L - G313*K13L + G211*K23L + G311*K33L - PDstandard4th1K13 + PDstandard4th3K11)\ + M1L = gu21*(-(G112*K11L) + G111*K12L - G212*K12L - G312*K13L + G211*K22L + G311*K23L - PDstandardNth1K12 + + PDstandardNth2K11) + gu22*(-(G122*K11L) + G112*K12L - G222*K12L - G322*K13L + G212*K22L + G312*K23L - + PDstandardNth1K22 + PDstandardNth2K12) + gu31* + (-(G113*K11L) - G213*K12L + G111*K13L - G313*K13L + G211*K23L + G311*K33L - PDstandardNth1K13 + PDstandardNth3K11)\ + gu32*(G113*K12L + G112*K13L + G213*K22L + (G212 + G313)*K23L + G312*K33L - - 2*(G123*K11L + G223*K12L + G323*K13L + PDstandard4th1K23) + PDstandard4th2K13 + PDstandard4th3K12) + - gu33*(-(G133*K11L) - G233*K12L + G113*K13L - G333*K13L + G213*K23L + G313*K33L - PDstandard4th1K33 + - PDstandard4th3K13); - - M2L = gu11*(G112*K11L + (-G111 + G212)*K12L + G312*K13L - G211*K22L - G311*K23L + PDstandard4th1K12 - - PDstandard4th2K11) + gu21*(G122*K11L + (-G112 + G222)*K12L + G322*K13L - G212*K22L - G312*K23L + - PDstandard4th1K22 - PDstandard4th2K12) + gu31* - (G123*K11L + (-2*G113 + G223)*K12L + (G112 + G323)*K13L + G212*K23L + G312*K33L + PDstandard4th1K23 - - 2*(G213*K22L + G313*K23L + PDstandard4th2K13) + PDstandard4th3K12) + - gu32*(-(G123*K12L) + G122*K13L - G223*K22L + G222*K23L - G323*K23L + G322*K33L - PDstandard4th2K23 + - PDstandard4th3K22) + gu33*(-(G133*K12L) + G123*K13L - G233*K22L + G223*K23L - G333*K23L + G323*K33L - - PDstandard4th2K33 + PDstandard4th3K23); - - M3L = gu11*(G113*K11L + G213*K12L + (-G111 + G313)*K13L - G211*K23L - G311*K33L + PDstandard4th1K13 - - PDstandard4th3K11) + gu21*(G123*K11L + (G113 + G223)*K12L + (-2*G112 + G323)*K13L + G213*K22L + - (-2*G212 + G313)*K23L + PDstandard4th1K23 + PDstandard4th2K13 - 2*(G312*K33L + PDstandard4th3K12)) + - gu31*(G133*K11L + G233*K12L + (-G113 + G333)*K13L - G213*K23L - G313*K33L + PDstandard4th1K33 - - PDstandard4th3K13) + gu22*(G123*K12L - G122*K13L + G223*K22L - G222*K23L + G323*K23L - G322*K33L + - PDstandard4th2K23 - PDstandard4th3K22) + gu32* - (G133*K12L - G123*K13L + G233*K22L - G223*K23L + G333*K23L - G323*K33L + PDstandard4th2K33 - PDstandard4th3K23); + 2*(G123*K11L + G223*K12L + G323*K13L + PDstandardNth1K23) + PDstandardNth2K13 + PDstandardNth3K12) + + gu33*(-(G133*K11L) - G233*K12L + G113*K13L - G333*K13L + G213*K23L + G313*K33L - PDstandardNth1K33 + + PDstandardNth3K13); + + M2L = gu11*(G112*K11L + (-G111 + G212)*K12L + G312*K13L - G211*K22L - G311*K23L + PDstandardNth1K12 - + PDstandardNth2K11) + gu21*(G122*K11L + (-G112 + G222)*K12L + G322*K13L - G212*K22L - G312*K23L + + PDstandardNth1K22 - PDstandardNth2K12) + gu31* + (G123*K11L + (-2*G113 + G223)*K12L + (G112 + G323)*K13L + G212*K23L + G312*K33L + PDstandardNth1K23 - + 2*(G213*K22L + G313*K23L + PDstandardNth2K13) + PDstandardNth3K12) + + gu32*(-(G123*K12L) + G122*K13L - G223*K22L + G222*K23L - G323*K23L + G322*K33L - PDstandardNth2K23 + + PDstandardNth3K22) + gu33*(-(G133*K12L) + G123*K13L - G233*K22L + G223*K23L - G333*K23L + G323*K33L - + PDstandardNth2K33 + PDstandardNth3K23); + + M3L = gu11*(G113*K11L + G213*K12L + (-G111 + G313)*K13L - G211*K23L - G311*K33L + PDstandardNth1K13 - + PDstandardNth3K11) + gu21*(G123*K11L + (G113 + G223)*K12L + (-2*G112 + G323)*K13L + G213*K22L + + (-2*G212 + G313)*K23L + PDstandardNth1K23 + PDstandardNth2K13 - 2*(G312*K33L + PDstandardNth3K12)) + + gu31*(G133*K11L + G233*K12L + (-G113 + G333)*K13L - G213*K23L - G313*K33L + PDstandardNth1K33 - + PDstandardNth3K13) + gu22*(G123*K12L - G122*K13L + G223*K22L - G222*K23L + G323*K23L - G322*K33L + + PDstandardNth2K23 - PDstandardNth3K22) + gu32* + (G133*K12L - G123*K13L + G233*K22L - G223*K23L + G333*K23L - G323*K33L + PDstandardNth2K33 - PDstandardNth3K23); /* Copy local copies back to grid functions */ diff --git a/ML_BSSN/src/Differencing.h b/ML_BSSN/src/Differencing.h index 7ada6a7..876855b 100644 --- a/ML_BSSN/src/Differencing.h +++ b/ML_BSSN/src/Differencing.h @@ -1,12 +1,12 @@ -#define PDstandard4th1(u,i,j,k) (p1o12dx*(-8*u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)])) -#define PDstandard4th2(u,i,j,k) (p1o12dy*(-8*u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)])) -#define PDstandard4th3(u,i,j,k) (p1o12dz*(-8*u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)])) -#define PDstandard4th11(u,i,j,k) (pm1o12dx2*(-16*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) -#define PDstandard4th22(u,i,j,k) (pm1o12dy2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) -#define PDstandard4th33(u,i,j,k) (pm1o12dz2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) -#define PDstandard4th12(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) -#define PDstandard4th13(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) -#define PDstandard4th21(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) -#define PDstandard4th23(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) -#define PDstandard4th31(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) -#define PDstandard4th32(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) +#define PDstandardNth1(u,i,j,k) (p1o12dx*(-8*u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)])) +#define PDstandardNth2(u,i,j,k) (p1o12dy*(-8*u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)])) +#define PDstandardNth3(u,i,j,k) (p1o12dz*(-8*u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + 8*u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)])) +#define PDstandardNth11(u,i,j,k) (pm1o12dx2*(-16*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) +#define PDstandardNth22(u,i,j,k) (pm1o12dy2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) +#define PDstandardNth33(u,i,j,k) (pm1o12dz2*(-16*(u[CCTK_GFINDEX3D(cctkGH,i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,j,2 + k)] + 30*u[CCTK_GFINDEX3D(cctkGH,i,j,k)])) +#define PDstandardNth12(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) +#define PDstandardNth13(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) +#define PDstandardNth21(u,i,j,k) (p1o144dxdy*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-1 + j,k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,1 + j,k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,-1 + j,k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-1 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,1 + j,k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,-2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,2 + j,k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,-2 + j,k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,2 + j,k)])) +#define PDstandardNth23(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) +#define PDstandardNth31(u,i,j,k) (p1o144dxdz*(-64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,-1 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,1 + i,j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,-2 + i,j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,2 + i,j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,2 + i,j,2 + k)])) +#define PDstandardNth32(u,i,j,k) (p1o144dydz*(-64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-1 + k)]) + 64*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,1 + k)]) + 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-1 + k)]) - 8*(u[CCTK_GFINDEX3D(cctkGH,i,-1 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,1 + j,2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-1 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,1 + k)]) + u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,-2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,-2 + j,2 + k)] - u[CCTK_GFINDEX3D(cctkGH,i,2 + j,-2 + k)] + u[CCTK_GFINDEX3D(cctkGH,i,2 + j,2 + k)])) diff --git a/ML_BSSN/src/ML_BSSN_RHS.c b/ML_BSSN/src/ML_BSSN_RHS.c index c0bc0c5..1ecae65 100644 --- a/ML_BSSN/src/ML_BSSN_RHS.c +++ b/ML_BSSN/src/ML_BSSN_RHS.c @@ -147,168 +147,168 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal /* Declare precomputed derivatives*/ /* Declare derivatives */ - CCTK_REAL PDstandard4th1alpha = INITVALUE; - CCTK_REAL PDstandard4th2alpha = INITVALUE; - CCTK_REAL PDstandard4th3alpha = INITVALUE; - CCTK_REAL PDstandard4th11alpha = INITVALUE; - CCTK_REAL PDstandard4th22alpha = INITVALUE; - CCTK_REAL PDstandard4th33alpha = INITVALUE; - CCTK_REAL PDstandard4th12alpha = INITVALUE; - CCTK_REAL PDstandard4th13alpha = INITVALUE; - CCTK_REAL PDstandard4th21alpha = INITVALUE; - CCTK_REAL PDstandard4th23alpha = INITVALUE; - CCTK_REAL PDstandard4th31alpha = INITVALUE; - CCTK_REAL PDstandard4th32alpha = INITVALUE; - CCTK_REAL PDstandard4th1At11 = INITVALUE; - CCTK_REAL PDstandard4th2At11 = INITVALUE; - CCTK_REAL PDstandard4th3At11 = INITVALUE; - CCTK_REAL PDstandard4th1At12 = INITVALUE; - CCTK_REAL PDstandard4th2At12 = INITVALUE; - CCTK_REAL PDstandard4th3At12 = INITVALUE; - CCTK_REAL PDstandard4th1At13 = INITVALUE; - CCTK_REAL PDstandard4th2At13 = INITVALUE; - CCTK_REAL PDstandard4th3At13 = INITVALUE; - CCTK_REAL PDstandard4th1At22 = INITVALUE; - CCTK_REAL PDstandard4th2At22 = INITVALUE; - CCTK_REAL PDstandard4th3At22 = INITVALUE; - CCTK_REAL PDstandard4th1At23 = INITVALUE; - CCTK_REAL PDstandard4th2At23 = INITVALUE; - CCTK_REAL PDstandard4th3At23 = INITVALUE; - CCTK_REAL PDstandard4th1At33 = INITVALUE; - CCTK_REAL PDstandard4th2At33 = INITVALUE; - CCTK_REAL PDstandard4th3At33 = INITVALUE; - CCTK_REAL PDstandard4th1beta1 = INITVALUE; - CCTK_REAL PDstandard4th2beta1 = INITVALUE; - CCTK_REAL PDstandard4th3beta1 = INITVALUE; - CCTK_REAL PDstandard4th11beta1 = INITVALUE; - CCTK_REAL PDstandard4th22beta1 = INITVALUE; - CCTK_REAL PDstandard4th33beta1 = INITVALUE; - CCTK_REAL PDstandard4th12beta1 = INITVALUE; - CCTK_REAL PDstandard4th13beta1 = INITVALUE; - CCTK_REAL PDstandard4th21beta1 = INITVALUE; - CCTK_REAL PDstandard4th23beta1 = INITVALUE; - CCTK_REAL PDstandard4th31beta1 = INITVALUE; - CCTK_REAL PDstandard4th32beta1 = INITVALUE; - CCTK_REAL PDstandard4th1beta2 = INITVALUE; - CCTK_REAL PDstandard4th2beta2 = INITVALUE; - CCTK_REAL PDstandard4th3beta2 = INITVALUE; - CCTK_REAL PDstandard4th11beta2 = INITVALUE; - CCTK_REAL PDstandard4th22beta2 = INITVALUE; - CCTK_REAL PDstandard4th33beta2 = INITVALUE; - CCTK_REAL PDstandard4th12beta2 = INITVALUE; - CCTK_REAL PDstandard4th13beta2 = INITVALUE; - CCTK_REAL PDstandard4th21beta2 = INITVALUE; - CCTK_REAL PDstandard4th23beta2 = INITVALUE; - CCTK_REAL PDstandard4th31beta2 = INITVALUE; - CCTK_REAL PDstandard4th32beta2 = INITVALUE; - CCTK_REAL PDstandard4th1beta3 = INITVALUE; - CCTK_REAL PDstandard4th2beta3 = INITVALUE; - CCTK_REAL PDstandard4th3beta3 = INITVALUE; - CCTK_REAL PDstandard4th11beta3 = INITVALUE; - CCTK_REAL PDstandard4th22beta3 = INITVALUE; - CCTK_REAL PDstandard4th33beta3 = INITVALUE; - CCTK_REAL PDstandard4th12beta3 = INITVALUE; - CCTK_REAL PDstandard4th13beta3 = INITVALUE; - CCTK_REAL PDstandard4th21beta3 = INITVALUE; - CCTK_REAL PDstandard4th23beta3 = INITVALUE; - CCTK_REAL PDstandard4th31beta3 = INITVALUE; - CCTK_REAL PDstandard4th32beta3 = INITVALUE; - CCTK_REAL PDstandard4th1gt11 = INITVALUE; - CCTK_REAL PDstandard4th2gt11 = INITVALUE; - CCTK_REAL PDstandard4th3gt11 = INITVALUE; - CCTK_REAL PDstandard4th11gt11 = INITVALUE; - CCTK_REAL PDstandard4th22gt11 = INITVALUE; - CCTK_REAL PDstandard4th33gt11 = INITVALUE; - CCTK_REAL PDstandard4th12gt11 = INITVALUE; - CCTK_REAL PDstandard4th13gt11 = INITVALUE; - CCTK_REAL PDstandard4th21gt11 = INITVALUE; - CCTK_REAL PDstandard4th23gt11 = INITVALUE; - CCTK_REAL PDstandard4th31gt11 = INITVALUE; - CCTK_REAL PDstandard4th32gt11 = INITVALUE; - CCTK_REAL PDstandard4th1gt12 = INITVALUE; - CCTK_REAL PDstandard4th2gt12 = INITVALUE; - CCTK_REAL PDstandard4th3gt12 = INITVALUE; - CCTK_REAL PDstandard4th11gt12 = INITVALUE; - CCTK_REAL PDstandard4th22gt12 = INITVALUE; - CCTK_REAL PDstandard4th33gt12 = INITVALUE; - CCTK_REAL PDstandard4th12gt12 = INITVALUE; - CCTK_REAL PDstandard4th13gt12 = INITVALUE; - CCTK_REAL PDstandard4th21gt12 = INITVALUE; - CCTK_REAL PDstandard4th23gt12 = INITVALUE; - CCTK_REAL PDstandard4th31gt12 = INITVALUE; - CCTK_REAL PDstandard4th32gt12 = INITVALUE; - CCTK_REAL PDstandard4th1gt13 = INITVALUE; - CCTK_REAL PDstandard4th2gt13 = INITVALUE; - CCTK_REAL PDstandard4th3gt13 = INITVALUE; - CCTK_REAL PDstandard4th11gt13 = INITVALUE; - CCTK_REAL PDstandard4th22gt13 = INITVALUE; - CCTK_REAL PDstandard4th33gt13 = INITVALUE; - CCTK_REAL PDstandard4th12gt13 = INITVALUE; - CCTK_REAL PDstandard4th13gt13 = INITVALUE; - CCTK_REAL PDstandard4th21gt13 = INITVALUE; - CCTK_REAL PDstandard4th23gt13 = INITVALUE; - CCTK_REAL PDstandard4th31gt13 = INITVALUE; - CCTK_REAL PDstandard4th32gt13 = INITVALUE; - CCTK_REAL PDstandard4th1gt22 = INITVALUE; - CCTK_REAL PDstandard4th2gt22 = INITVALUE; - CCTK_REAL PDstandard4th3gt22 = INITVALUE; - CCTK_REAL PDstandard4th11gt22 = INITVALUE; - CCTK_REAL PDstandard4th22gt22 = INITVALUE; - CCTK_REAL PDstandard4th33gt22 = INITVALUE; - CCTK_REAL PDstandard4th12gt22 = INITVALUE; - CCTK_REAL PDstandard4th13gt22 = INITVALUE; - CCTK_REAL PDstandard4th21gt22 = INITVALUE; - CCTK_REAL PDstandard4th23gt22 = INITVALUE; - CCTK_REAL PDstandard4th31gt22 = INITVALUE; - CCTK_REAL PDstandard4th32gt22 = INITVALUE; - CCTK_REAL PDstandard4th1gt23 = INITVALUE; - CCTK_REAL PDstandard4th2gt23 = INITVALUE; - CCTK_REAL PDstandard4th3gt23 = INITVALUE; - CCTK_REAL PDstandard4th11gt23 = INITVALUE; - CCTK_REAL PDstandard4th22gt23 = INITVALUE; - CCTK_REAL PDstandard4th33gt23 = INITVALUE; - CCTK_REAL PDstandard4th12gt23 = INITVALUE; - CCTK_REAL PDstandard4th13gt23 = INITVALUE; - CCTK_REAL PDstandard4th21gt23 = INITVALUE; - CCTK_REAL PDstandard4th23gt23 = INITVALUE; - CCTK_REAL PDstandard4th31gt23 = INITVALUE; - CCTK_REAL PDstandard4th32gt23 = INITVALUE; - CCTK_REAL PDstandard4th1gt33 = INITVALUE; - CCTK_REAL PDstandard4th2gt33 = INITVALUE; - CCTK_REAL PDstandard4th3gt33 = INITVALUE; - CCTK_REAL PDstandard4th11gt33 = INITVALUE; - CCTK_REAL PDstandard4th22gt33 = INITVALUE; - CCTK_REAL PDstandard4th33gt33 = INITVALUE; - CCTK_REAL PDstandard4th12gt33 = INITVALUE; - CCTK_REAL PDstandard4th13gt33 = INITVALUE; - CCTK_REAL PDstandard4th21gt33 = INITVALUE; - CCTK_REAL PDstandard4th23gt33 = INITVALUE; - CCTK_REAL PDstandard4th31gt33 = INITVALUE; - CCTK_REAL PDstandard4th32gt33 = INITVALUE; - CCTK_REAL PDstandard4th1phi = INITVALUE; - CCTK_REAL PDstandard4th2phi = INITVALUE; - CCTK_REAL PDstandard4th3phi = INITVALUE; - CCTK_REAL PDstandard4th11phi = INITVALUE; - CCTK_REAL PDstandard4th22phi = INITVALUE; - CCTK_REAL PDstandard4th33phi = INITVALUE; - CCTK_REAL PDstandard4th12phi = INITVALUE; - CCTK_REAL PDstandard4th13phi = INITVALUE; - CCTK_REAL PDstandard4th21phi = INITVALUE; - CCTK_REAL PDstandard4th23phi = INITVALUE; - CCTK_REAL PDstandard4th31phi = INITVALUE; - CCTK_REAL PDstandard4th32phi = INITVALUE; - CCTK_REAL PDstandard4th1trK = INITVALUE; - CCTK_REAL PDstandard4th2trK = INITVALUE; - CCTK_REAL PDstandard4th3trK = INITVALUE; - CCTK_REAL PDstandard4th1Xt1 = INITVALUE; - CCTK_REAL PDstandard4th2Xt1 = INITVALUE; - CCTK_REAL PDstandard4th3Xt1 = INITVALUE; - CCTK_REAL PDstandard4th1Xt2 = INITVALUE; - CCTK_REAL PDstandard4th2Xt2 = INITVALUE; - CCTK_REAL PDstandard4th3Xt2 = INITVALUE; - CCTK_REAL PDstandard4th1Xt3 = INITVALUE; - CCTK_REAL PDstandard4th2Xt3 = INITVALUE; - CCTK_REAL PDstandard4th3Xt3 = INITVALUE; + CCTK_REAL PDstandardNth1alpha = INITVALUE; + CCTK_REAL PDstandardNth2alpha = INITVALUE; + CCTK_REAL PDstandardNth3alpha = INITVALUE; + CCTK_REAL PDstandardNth11alpha = INITVALUE; + CCTK_REAL PDstandardNth22alpha = INITVALUE; + CCTK_REAL PDstandardNth33alpha = INITVALUE; + CCTK_REAL PDstandardNth12alpha = INITVALUE; + CCTK_REAL PDstandardNth13alpha = INITVALUE; + CCTK_REAL PDstandardNth21alpha = INITVALUE; + CCTK_REAL PDstandardNth23alpha = INITVALUE; + CCTK_REAL PDstandardNth31alpha = INITVALUE; + CCTK_REAL PDstandardNth32alpha = INITVALUE; + CCTK_REAL PDstandardNth1At11 = INITVALUE; + CCTK_REAL PDstandardNth2At11 = INITVALUE; + CCTK_REAL PDstandardNth3At11 = INITVALUE; + CCTK_REAL PDstandardNth1At12 = INITVALUE; + CCTK_REAL PDstandardNth2At12 = INITVALUE; + CCTK_REAL PDstandardNth3At12 = INITVALUE; + CCTK_REAL PDstandardNth1At13 = INITVALUE; + CCTK_REAL PDstandardNth2At13 = INITVALUE; + CCTK_REAL PDstandardNth3At13 = INITVALUE; + CCTK_REAL PDstandardNth1At22 = INITVALUE; + CCTK_REAL PDstandardNth2At22 = INITVALUE; + CCTK_REAL PDstandardNth3At22 = INITVALUE; + CCTK_REAL PDstandardNth1At23 = INITVALUE; + CCTK_REAL PDstandardNth2At23 = INITVALUE; + CCTK_REAL PDstandardNth3At23 = INITVALUE; + CCTK_REAL PDstandardNth1At33 = INITVALUE; + CCTK_REAL PDstandardNth2At33 = INITVALUE; + CCTK_REAL PDstandardNth3At33 = INITVALUE; + CCTK_REAL PDstandardNth1beta1 = INITVALUE; + CCTK_REAL PDstandardNth2beta1 = INITVALUE; + CCTK_REAL PDstandardNth3beta1 = INITVALUE; + CCTK_REAL PDstandardNth11beta1 = INITVALUE; + CCTK_REAL PDstandardNth22beta1 = INITVALUE; + CCTK_REAL PDstandardNth33beta1 = INITVALUE; + CCTK_REAL PDstandardNth12beta1 = INITVALUE; + CCTK_REAL PDstandardNth13beta1 = INITVALUE; + CCTK_REAL PDstandardNth21beta1 = INITVALUE; + CCTK_REAL PDstandardNth23beta1 = INITVALUE; + CCTK_REAL PDstandardNth31beta1 = INITVALUE; + CCTK_REAL PDstandardNth32beta1 = INITVALUE; + CCTK_REAL PDstandardNth1beta2 = INITVALUE; + CCTK_REAL PDstandardNth2beta2 = INITVALUE; + CCTK_REAL PDstandardNth3beta2 = INITVALUE; + CCTK_REAL PDstandardNth11beta2 = INITVALUE; + CCTK_REAL PDstandardNth22beta2 = INITVALUE; + CCTK_REAL PDstandardNth33beta2 = INITVALUE; + CCTK_REAL PDstandardNth12beta2 = INITVALUE; + CCTK_REAL PDstandardNth13beta2 = INITVALUE; + CCTK_REAL PDstandardNth21beta2 = INITVALUE; + CCTK_REAL PDstandardNth23beta2 = INITVALUE; + CCTK_REAL PDstandardNth31beta2 = INITVALUE; + CCTK_REAL PDstandardNth32beta2 = INITVALUE; + CCTK_REAL PDstandardNth1beta3 = INITVALUE; + CCTK_REAL PDstandardNth2beta3 = INITVALUE; + CCTK_REAL PDstandardNth3beta3 = INITVALUE; + CCTK_REAL PDstandardNth11beta3 = INITVALUE; + CCTK_REAL PDstandardNth22beta3 = INITVALUE; + CCTK_REAL PDstandardNth33beta3 = INITVALUE; + CCTK_REAL PDstandardNth12beta3 = INITVALUE; + CCTK_REAL PDstandardNth13beta3 = INITVALUE; + CCTK_REAL PDstandardNth21beta3 = INITVALUE; + CCTK_REAL PDstandardNth23beta3 = INITVALUE; + CCTK_REAL PDstandardNth31beta3 = INITVALUE; + CCTK_REAL PDstandardNth32beta3 = INITVALUE; + CCTK_REAL PDstandardNth1gt11 = INITVALUE; + CCTK_REAL PDstandardNth2gt11 = INITVALUE; + CCTK_REAL PDstandardNth3gt11 = INITVALUE; + CCTK_REAL PDstandardNth11gt11 = INITVALUE; + CCTK_REAL PDstandardNth22gt11 = INITVALUE; + CCTK_REAL PDstandardNth33gt11 = INITVALUE; + CCTK_REAL PDstandardNth12gt11 = INITVALUE; + CCTK_REAL PDstandardNth13gt11 = INITVALUE; + CCTK_REAL PDstandardNth21gt11 = INITVALUE; + CCTK_REAL PDstandardNth23gt11 = INITVALUE; + CCTK_REAL PDstandardNth31gt11 = INITVALUE; + CCTK_REAL PDstandardNth32gt11 = INITVALUE; + CCTK_REAL PDstandardNth1gt12 = INITVALUE; + CCTK_REAL PDstandardNth2gt12 = INITVALUE; + CCTK_REAL PDstandardNth3gt12 = INITVALUE; + CCTK_REAL PDstandardNth11gt12 = INITVALUE; + CCTK_REAL PDstandardNth22gt12 = INITVALUE; + CCTK_REAL PDstandardNth33gt12 = INITVALUE; + CCTK_REAL PDstandardNth12gt12 = INITVALUE; + CCTK_REAL PDstandardNth13gt12 = INITVALUE; + CCTK_REAL PDstandardNth21gt12 = INITVALUE; + CCTK_REAL PDstandardNth23gt12 = INITVALUE; + CCTK_REAL PDstandardNth31gt12 = INITVALUE; + CCTK_REAL PDstandardNth32gt12 = INITVALUE; + CCTK_REAL PDstandardNth1gt13 = INITVALUE; + CCTK_REAL PDstandardNth2gt13 = INITVALUE; + CCTK_REAL PDstandardNth3gt13 = INITVALUE; + CCTK_REAL PDstandardNth11gt13 = INITVALUE; + CCTK_REAL PDstandardNth22gt13 = INITVALUE; + CCTK_REAL PDstandardNth33gt13 = INITVALUE; + CCTK_REAL PDstandardNth12gt13 = INITVALUE; + CCTK_REAL PDstandardNth13gt13 = INITVALUE; + CCTK_REAL PDstandardNth21gt13 = INITVALUE; + CCTK_REAL PDstandardNth23gt13 = INITVALUE; + CCTK_REAL PDstandardNth31gt13 = INITVALUE; + CCTK_REAL PDstandardNth32gt13 = INITVALUE; + CCTK_REAL PDstandardNth1gt22 = INITVALUE; + CCTK_REAL PDstandardNth2gt22 = INITVALUE; + CCTK_REAL PDstandardNth3gt22 = INITVALUE; + CCTK_REAL PDstandardNth11gt22 = INITVALUE; + CCTK_REAL PDstandardNth22gt22 = INITVALUE; + CCTK_REAL PDstandardNth33gt22 = INITVALUE; + CCTK_REAL PDstandardNth12gt22 = INITVALUE; + CCTK_REAL PDstandardNth13gt22 = INITVALUE; + CCTK_REAL PDstandardNth21gt22 = INITVALUE; + CCTK_REAL PDstandardNth23gt22 = INITVALUE; + CCTK_REAL PDstandardNth31gt22 = INITVALUE; + CCTK_REAL PDstandardNth32gt22 = INITVALUE; + CCTK_REAL PDstandardNth1gt23 = INITVALUE; + CCTK_REAL PDstandardNth2gt23 = INITVALUE; + CCTK_REAL PDstandardNth3gt23 = INITVALUE; + CCTK_REAL PDstandardNth11gt23 = INITVALUE; + CCTK_REAL PDstandardNth22gt23 = INITVALUE; + CCTK_REAL PDstandardNth33gt23 = INITVALUE; + CCTK_REAL PDstandardNth12gt23 = INITVALUE; + CCTK_REAL PDstandardNth13gt23 = INITVALUE; + CCTK_REAL PDstandardNth21gt23 = INITVALUE; + CCTK_REAL PDstandardNth23gt23 = INITVALUE; + CCTK_REAL PDstandardNth31gt23 = INITVALUE; + CCTK_REAL PDstandardNth32gt23 = INITVALUE; + CCTK_REAL PDstandardNth1gt33 = INITVALUE; + CCTK_REAL PDstandardNth2gt33 = INITVALUE; + CCTK_REAL PDstandardNth3gt33 = INITVALUE; + CCTK_REAL PDstandardNth11gt33 = INITVALUE; + CCTK_REAL PDstandardNth22gt33 = INITVALUE; + CCTK_REAL PDstandardNth33gt33 = INITVALUE; + CCTK_REAL PDstandardNth12gt33 = INITVALUE; + CCTK_REAL PDstandardNth13gt33 = INITVALUE; + CCTK_REAL PDstandardNth21gt33 = INITVALUE; + CCTK_REAL PDstandardNth23gt33 = INITVALUE; + CCTK_REAL PDstandardNth31gt33 = INITVALUE; + CCTK_REAL PDstandardNth32gt33 = INITVALUE; + CCTK_REAL PDstandardNth1phi = INITVALUE; + CCTK_REAL PDstandardNth2phi = INITVALUE; + CCTK_REAL PDstandardNth3phi = INITVALUE; + CCTK_REAL PDstandardNth11phi = INITVALUE; + CCTK_REAL PDstandardNth22phi = INITVALUE; + CCTK_REAL PDstandardNth33phi = INITVALUE; + CCTK_REAL PDstandardNth12phi = INITVALUE; + CCTK_REAL PDstandardNth13phi = INITVALUE; + CCTK_REAL PDstandardNth21phi = INITVALUE; + CCTK_REAL PDstandardNth23phi = INITVALUE; + CCTK_REAL PDstandardNth31phi = INITVALUE; + CCTK_REAL PDstandardNth32phi = INITVALUE; + CCTK_REAL PDstandardNth1trK = INITVALUE; + CCTK_REAL PDstandardNth2trK = INITVALUE; + CCTK_REAL PDstandardNth3trK = INITVALUE; + CCTK_REAL PDstandardNth1Xt1 = INITVALUE; + CCTK_REAL PDstandardNth2Xt1 = INITVALUE; + CCTK_REAL PDstandardNth3Xt1 = INITVALUE; + CCTK_REAL PDstandardNth1Xt2 = INITVALUE; + CCTK_REAL PDstandardNth2Xt2 = INITVALUE; + CCTK_REAL PDstandardNth3Xt2 = INITVALUE; + CCTK_REAL PDstandardNth1Xt3 = INITVALUE; + CCTK_REAL PDstandardNth2Xt3 = INITVALUE; + CCTK_REAL PDstandardNth3Xt3 = INITVALUE; /* Assign local copies of grid functions */ AL = A[index]; @@ -346,135 +346,135 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal /* Include user supplied include files */ /* Precompute derivatives (new style) */ - PDstandard4th1alpha = PDstandard4th1(alpha, i, j, k); - PDstandard4th2alpha = PDstandard4th2(alpha, i, j, k); - PDstandard4th3alpha = PDstandard4th3(alpha, i, j, k); - PDstandard4th11alpha = PDstandard4th11(alpha, i, j, k); - PDstandard4th22alpha = PDstandard4th22(alpha, i, j, k); - PDstandard4th33alpha = PDstandard4th33(alpha, i, j, k); - PDstandard4th12alpha = PDstandard4th12(alpha, i, j, k); - PDstandard4th13alpha = PDstandard4th13(alpha, i, j, k); - PDstandard4th23alpha = PDstandard4th23(alpha, i, j, k); - PDstandard4th1At11 = PDstandard4th1(At11, i, j, k); - PDstandard4th2At11 = PDstandard4th2(At11, i, j, k); - PDstandard4th3At11 = PDstandard4th3(At11, i, j, k); - PDstandard4th1At12 = PDstandard4th1(At12, i, j, k); - PDstandard4th2At12 = PDstandard4th2(At12, i, j, k); - PDstandard4th3At12 = PDstandard4th3(At12, i, j, k); - PDstandard4th1At13 = PDstandard4th1(At13, i, j, k); - PDstandard4th2At13 = PDstandard4th2(At13, i, j, k); - PDstandard4th3At13 = PDstandard4th3(At13, i, j, k); - PDstandard4th1At22 = PDstandard4th1(At22, i, j, k); - PDstandard4th2At22 = PDstandard4th2(At22, i, j, k); - PDstandard4th3At22 = PDstandard4th3(At22, i, j, k); - PDstandard4th1At23 = PDstandard4th1(At23, i, j, k); - PDstandard4th2At23 = PDstandard4th2(At23, i, j, k); - PDstandard4th3At23 = PDstandard4th3(At23, i, j, k); - PDstandard4th1At33 = PDstandard4th1(At33, i, j, k); - PDstandard4th2At33 = PDstandard4th2(At33, i, j, k); - PDstandard4th3At33 = PDstandard4th3(At33, i, j, k); - PDstandard4th1beta1 = PDstandard4th1(beta1, i, j, k); - PDstandard4th2beta1 = PDstandard4th2(beta1, i, j, k); - PDstandard4th3beta1 = PDstandard4th3(beta1, i, j, k); - PDstandard4th11beta1 = PDstandard4th11(beta1, i, j, k); - PDstandard4th22beta1 = PDstandard4th22(beta1, i, j, k); - PDstandard4th33beta1 = PDstandard4th33(beta1, i, j, k); - PDstandard4th12beta1 = PDstandard4th12(beta1, i, j, k); - PDstandard4th13beta1 = PDstandard4th13(beta1, i, j, k); - PDstandard4th23beta1 = PDstandard4th23(beta1, i, j, k); - PDstandard4th1beta2 = PDstandard4th1(beta2, i, j, k); - PDstandard4th2beta2 = PDstandard4th2(beta2, i, j, k); - PDstandard4th3beta2 = PDstandard4th3(beta2, i, j, k); - PDstandard4th11beta2 = PDstandard4th11(beta2, i, j, k); - PDstandard4th22beta2 = PDstandard4th22(beta2, i, j, k); - PDstandard4th33beta2 = PDstandard4th33(beta2, i, j, k); - PDstandard4th12beta2 = PDstandard4th12(beta2, i, j, k); - PDstandard4th13beta2 = PDstandard4th13(beta2, i, j, k); - PDstandard4th23beta2 = PDstandard4th23(beta2, i, j, k); - PDstandard4th1beta3 = PDstandard4th1(beta3, i, j, k); - PDstandard4th2beta3 = PDstandard4th2(beta3, i, j, k); - PDstandard4th3beta3 = PDstandard4th3(beta3, i, j, k); - PDstandard4th11beta3 = PDstandard4th11(beta3, i, j, k); - PDstandard4th22beta3 = PDstandard4th22(beta3, i, j, k); - PDstandard4th33beta3 = PDstandard4th33(beta3, i, j, k); - PDstandard4th12beta3 = PDstandard4th12(beta3, i, j, k); - PDstandard4th13beta3 = PDstandard4th13(beta3, i, j, k); - PDstandard4th23beta3 = PDstandard4th23(beta3, i, j, k); - PDstandard4th1gt11 = PDstandard4th1(gt11, i, j, k); - PDstandard4th2gt11 = PDstandard4th2(gt11, i, j, k); - PDstandard4th3gt11 = PDstandard4th3(gt11, i, j, k); - PDstandard4th11gt11 = PDstandard4th11(gt11, i, j, k); - PDstandard4th22gt11 = PDstandard4th22(gt11, i, j, k); - PDstandard4th33gt11 = PDstandard4th33(gt11, i, j, k); - PDstandard4th12gt11 = PDstandard4th12(gt11, i, j, k); - PDstandard4th13gt11 = PDstandard4th13(gt11, i, j, k); - PDstandard4th23gt11 = PDstandard4th23(gt11, i, j, k); - PDstandard4th1gt12 = PDstandard4th1(gt12, i, j, k); - PDstandard4th2gt12 = PDstandard4th2(gt12, i, j, k); - PDstandard4th3gt12 = PDstandard4th3(gt12, i, j, k); - PDstandard4th11gt12 = PDstandard4th11(gt12, i, j, k); - PDstandard4th22gt12 = PDstandard4th22(gt12, i, j, k); - PDstandard4th33gt12 = PDstandard4th33(gt12, i, j, k); - PDstandard4th12gt12 = PDstandard4th12(gt12, i, j, k); - PDstandard4th13gt12 = PDstandard4th13(gt12, i, j, k); - PDstandard4th23gt12 = PDstandard4th23(gt12, i, j, k); - PDstandard4th1gt13 = PDstandard4th1(gt13, i, j, k); - PDstandard4th2gt13 = PDstandard4th2(gt13, i, j, k); - PDstandard4th3gt13 = PDstandard4th3(gt13, i, j, k); - PDstandard4th11gt13 = PDstandard4th11(gt13, i, j, k); - PDstandard4th22gt13 = PDstandard4th22(gt13, i, j, k); - PDstandard4th33gt13 = PDstandard4th33(gt13, i, j, k); - PDstandard4th12gt13 = PDstandard4th12(gt13, i, j, k); - PDstandard4th13gt13 = PDstandard4th13(gt13, i, j, k); - PDstandard4th23gt13 = PDstandard4th23(gt13, i, j, k); - PDstandard4th1gt22 = PDstandard4th1(gt22, i, j, k); - PDstandard4th2gt22 = PDstandard4th2(gt22, i, j, k); - PDstandard4th3gt22 = PDstandard4th3(gt22, i, j, k); - PDstandard4th11gt22 = PDstandard4th11(gt22, i, j, k); - PDstandard4th22gt22 = PDstandard4th22(gt22, i, j, k); - PDstandard4th33gt22 = PDstandard4th33(gt22, i, j, k); - PDstandard4th12gt22 = PDstandard4th12(gt22, i, j, k); - PDstandard4th13gt22 = PDstandard4th13(gt22, i, j, k); - PDstandard4th23gt22 = PDstandard4th23(gt22, i, j, k); - PDstandard4th1gt23 = PDstandard4th1(gt23, i, j, k); - PDstandard4th2gt23 = PDstandard4th2(gt23, i, j, k); - PDstandard4th3gt23 = PDstandard4th3(gt23, i, j, k); - PDstandard4th11gt23 = PDstandard4th11(gt23, i, j, k); - PDstandard4th22gt23 = PDstandard4th22(gt23, i, j, k); - PDstandard4th33gt23 = PDstandard4th33(gt23, i, j, k); - PDstandard4th12gt23 = PDstandard4th12(gt23, i, j, k); - PDstandard4th13gt23 = PDstandard4th13(gt23, i, j, k); - PDstandard4th23gt23 = PDstandard4th23(gt23, i, j, k); - PDstandard4th1gt33 = PDstandard4th1(gt33, i, j, k); - PDstandard4th2gt33 = PDstandard4th2(gt33, i, j, k); - PDstandard4th3gt33 = PDstandard4th3(gt33, i, j, k); - PDstandard4th11gt33 = PDstandard4th11(gt33, i, j, k); - PDstandard4th22gt33 = PDstandard4th22(gt33, i, j, k); - PDstandard4th33gt33 = PDstandard4th33(gt33, i, j, k); - PDstandard4th12gt33 = PDstandard4th12(gt33, i, j, k); - PDstandard4th13gt33 = PDstandard4th13(gt33, i, j, k); - PDstandard4th23gt33 = PDstandard4th23(gt33, i, j, k); - PDstandard4th1phi = PDstandard4th1(phi, i, j, k); - PDstandard4th2phi = PDstandard4th2(phi, i, j, k); - PDstandard4th3phi = PDstandard4th3(phi, i, j, k); - PDstandard4th11phi = PDstandard4th11(phi, i, j, k); - PDstandard4th22phi = PDstandard4th22(phi, i, j, k); - PDstandard4th33phi = PDstandard4th33(phi, i, j, k); - PDstandard4th12phi = PDstandard4th12(phi, i, j, k); - PDstandard4th13phi = PDstandard4th13(phi, i, j, k); - PDstandard4th23phi = PDstandard4th23(phi, i, j, k); - PDstandard4th1trK = PDstandard4th1(trK, i, j, k); - PDstandard4th2trK = PDstandard4th2(trK, i, j, k); - PDstandard4th3trK = PDstandard4th3(trK, i, j, k); - PDstandard4th1Xt1 = PDstandard4th1(Xt1, i, j, k); - PDstandard4th2Xt1 = PDstandard4th2(Xt1, i, j, k); - PDstandard4th3Xt1 = PDstandard4th3(Xt1, i, j, k); - PDstandard4th1Xt2 = PDstandard4th1(Xt2, i, j, k); - PDstandard4th2Xt2 = PDstandard4th2(Xt2, i, j, k); - PDstandard4th3Xt2 = PDstandard4th3(Xt2, i, j, k); - PDstandard4th1Xt3 = PDstandard4th1(Xt3, i, j, k); - PDstandard4th2Xt3 = PDstandard4th2(Xt3, i, j, k); - PDstandard4th3Xt3 = PDstandard4th3(Xt3, i, j, k); + PDstandardNth1alpha = PDstandardNth1(alpha, i, j, k); + PDstandardNth2alpha = PDstandardNth2(alpha, i, j, k); + PDstandardNth3alpha = PDstandardNth3(alpha, i, j, k); + PDstandardNth11alpha = PDstandardNth11(alpha, i, j, k); + PDstandardNth22alpha = PDstandardNth22(alpha, i, j, k); + PDstandardNth33alpha = PDstandardNth33(alpha, i, j, k); + PDstandardNth12alpha = PDstandardNth12(alpha, i, j, k); + PDstandardNth13alpha = PDstandardNth13(alpha, i, j, k); + PDstandardNth23alpha = PDstandardNth23(alpha, i, j, k); + PDstandardNth1At11 = PDstandardNth1(At11, i, j, k); + PDstandardNth2At11 = PDstandardNth2(At11, i, j, k); + PDstandardNth3At11 = PDstandardNth3(At11, i, j, k); + PDstandardNth1At12 = PDstandardNth1(At12, i, j, k); + PDstandardNth2At12 = PDstandardNth2(At12, i, j, k); + PDstandardNth3At12 = PDstandardNth3(At12, i, j, k); + PDstandardNth1At13 = PDstandardNth1(At13, i, j, k); + PDstandardNth2At13 = PDstandardNth2(At13, i, j, k); + PDstandardNth3At13 = PDstandardNth3(At13, i, j, k); + PDstandardNth1At22 = PDstandardNth1(At22, i, j, k); + PDstandardNth2At22 = PDstandardNth2(At22, i, j, k); + PDstandardNth3At22 = PDstandardNth3(At22, i, j, k); + PDstandardNth1At23 = PDstandardNth1(At23, i, j, k); + PDstandardNth2At23 = PDstandardNth2(At23, i, j, k); + PDstandardNth3At23 = PDstandardNth3(At23, i, j, k); + PDstandardNth1At33 = PDstandardNth1(At33, i, j, k); + PDstandardNth2At33 = PDstandardNth2(At33, i, j, k); + PDstandardNth3At33 = PDstandardNth3(At33, i, j, k); + PDstandardNth1beta1 = PDstandardNth1(beta1, i, j, k); + PDstandardNth2beta1 = PDstandardNth2(beta1, i, j, k); + PDstandardNth3beta1 = PDstandardNth3(beta1, i, j, k); + PDstandardNth11beta1 = PDstandardNth11(beta1, i, j, k); + PDstandardNth22beta1 = PDstandardNth22(beta1, i, j, k); + PDstandardNth33beta1 = PDstandardNth33(beta1, i, j, k); + PDstandardNth12beta1 = PDstandardNth12(beta1, i, j, k); + PDstandardNth13beta1 = PDstandardNth13(beta1, i, j, k); + PDstandardNth23beta1 = PDstandardNth23(beta1, i, j, k); + PDstandardNth1beta2 = PDstandardNth1(beta2, i, j, k); + PDstandardNth2beta2 = PDstandardNth2(beta2, i, j, k); + PDstandardNth3beta2 = PDstandardNth3(beta2, i, j, k); + PDstandardNth11beta2 = PDstandardNth11(beta2, i, j, k); + PDstandardNth22beta2 = PDstandardNth22(beta2, i, j, k); + PDstandardNth33beta2 = PDstandardNth33(beta2, i, j, k); + PDstandardNth12beta2 = PDstandardNth12(beta2, i, j, k); + PDstandardNth13beta2 = PDstandardNth13(beta2, i, j, k); + PDstandardNth23beta2 = PDstandardNth23(beta2, i, j, k); + PDstandardNth1beta3 = PDstandardNth1(beta3, i, j, k); + PDstandardNth2beta3 = PDstandardNth2(beta3, i, j, k); + PDstandardNth3beta3 = PDstandardNth3(beta3, i, j, k); + PDstandardNth11beta3 = PDstandardNth11(beta3, i, j, k); + PDstandardNth22beta3 = PDstandardNth22(beta3, i, j, k); + PDstandardNth33beta3 = PDstandardNth33(beta3, i, j, k); + PDstandardNth12beta3 = PDstandardNth12(beta3, i, j, k); + PDstandardNth13beta3 = PDstandardNth13(beta3, i, j, k); + PDstandardNth23beta3 = PDstandardNth23(beta3, i, j, k); + PDstandardNth1gt11 = PDstandardNth1(gt11, i, j, k); + PDstandardNth2gt11 = PDstandardNth2(gt11, i, j, k); + PDstandardNth3gt11 = PDstandardNth3(gt11, i, j, k); + PDstandardNth11gt11 = PDstandardNth11(gt11, i, j, k); + PDstandardNth22gt11 = PDstandardNth22(gt11, i, j, k); + PDstandardNth33gt11 = PDstandardNth33(gt11, i, j, k); + PDstandardNth12gt11 = PDstandardNth12(gt11, i, j, k); + PDstandardNth13gt11 = PDstandardNth13(gt11, i, j, k); + PDstandardNth23gt11 = PDstandardNth23(gt11, i, j, k); + PDstandardNth1gt12 = PDstandardNth1(gt12, i, j, k); + PDstandardNth2gt12 = PDstandardNth2(gt12, i, j, k); + PDstandardNth3gt12 = PDstandardNth3(gt12, i, j, k); + PDstandardNth11gt12 = PDstandardNth11(gt12, i, j, k); + PDstandardNth22gt12 = PDstandardNth22(gt12, i, j, k); + PDstandardNth33gt12 = PDstandardNth33(gt12, i, j, k); + PDstandardNth12gt12 = PDstandardNth12(gt12, i, j, k); + PDstandardNth13gt12 = PDstandardNth13(gt12, i, j, k); + PDstandardNth23gt12 = PDstandardNth23(gt12, i, j, k); + PDstandardNth1gt13 = PDstandardNth1(gt13, i, j, k); + PDstandardNth2gt13 = PDstandardNth2(gt13, i, j, k); + PDstandardNth3gt13 = PDstandardNth3(gt13, i, j, k); + PDstandardNth11gt13 = PDstandardNth11(gt13, i, j, k); + PDstandardNth22gt13 = PDstandardNth22(gt13, i, j, k); + PDstandardNth33gt13 = PDstandardNth33(gt13, i, j, k); + PDstandardNth12gt13 = PDstandardNth12(gt13, i, j, k); + PDstandardNth13gt13 = PDstandardNth13(gt13, i, j, k); + PDstandardNth23gt13 = PDstandardNth23(gt13, i, j, k); + PDstandardNth1gt22 = PDstandardNth1(gt22, i, j, k); + PDstandardNth2gt22 = PDstandardNth2(gt22, i, j, k); + PDstandardNth3gt22 = PDstandardNth3(gt22, i, j, k); + PDstandardNth11gt22 = PDstandardNth11(gt22, i, j, k); + PDstandardNth22gt22 = PDstandardNth22(gt22, i, j, k); + PDstandardNth33gt22 = PDstandardNth33(gt22, i, j, k); + PDstandardNth12gt22 = PDstandardNth12(gt22, i, j, k); + PDstandardNth13gt22 = PDstandardNth13(gt22, i, j, k); + PDstandardNth23gt22 = PDstandardNth23(gt22, i, j, k); + PDstandardNth1gt23 = PDstandardNth1(gt23, i, j, k); + PDstandardNth2gt23 = PDstandardNth2(gt23, i, j, k); + PDstandardNth3gt23 = PDstandardNth3(gt23, i, j, k); + PDstandardNth11gt23 = PDstandardNth11(gt23, i, j, k); + PDstandardNth22gt23 = PDstandardNth22(gt23, i, j, k); + PDstandardNth33gt23 = PDstandardNth33(gt23, i, j, k); + PDstandardNth12gt23 = PDstandardNth12(gt23, i, j, k); + PDstandardNth13gt23 = PDstandardNth13(gt23, i, j, k); + PDstandardNth23gt23 = PDstandardNth23(gt23, i, j, k); + PDstandardNth1gt33 = PDstandardNth1(gt33, i, j, k); + PDstandardNth2gt33 = PDstandardNth2(gt33, i, j, k); + PDstandardNth3gt33 = PDstandardNth3(gt33, i, j, k); + PDstandardNth11gt33 = PDstandardNth11(gt33, i, j, k); + PDstandardNth22gt33 = PDstandardNth22(gt33, i, j, k); + PDstandardNth33gt33 = PDstandardNth33(gt33, i, j, k); + PDstandardNth12gt33 = PDstandardNth12(gt33, i, j, k); + PDstandardNth13gt33 = PDstandardNth13(gt33, i, j, k); + PDstandardNth23gt33 = PDstandardNth23(gt33, i, j, k); + PDstandardNth1phi = PDstandardNth1(phi, i, j, k); + PDstandardNth2phi = PDstandardNth2(phi, i, j, k); + PDstandardNth3phi = PDstandardNth3(phi, i, j, k); + PDstandardNth11phi = PDstandardNth11(phi, i, j, k); + PDstandardNth22phi = PDstandardNth22(phi, i, j, k); + PDstandardNth33phi = PDstandardNth33(phi, i, j, k); + PDstandardNth12phi = PDstandardNth12(phi, i, j, k); + PDstandardNth13phi = PDstandardNth13(phi, i, j, k); + PDstandardNth23phi = PDstandardNth23(phi, i, j, k); + PDstandardNth1trK = PDstandardNth1(trK, i, j, k); + PDstandardNth2trK = PDstandardNth2(trK, i, j, k); + PDstandardNth3trK = PDstandardNth3(trK, i, j, k); + PDstandardNth1Xt1 = PDstandardNth1(Xt1, i, j, k); + PDstandardNth2Xt1 = PDstandardNth2(Xt1, i, j, k); + PDstandardNth3Xt1 = PDstandardNth3(Xt1, i, j, k); + PDstandardNth1Xt2 = PDstandardNth1(Xt2, i, j, k); + PDstandardNth2Xt2 = PDstandardNth2(Xt2, i, j, k); + PDstandardNth3Xt2 = PDstandardNth3(Xt2, i, j, k); + PDstandardNth1Xt3 = PDstandardNth1(Xt3, i, j, k); + PDstandardNth2Xt3 = PDstandardNth2(Xt3, i, j, k); + PDstandardNth3Xt3 = PDstandardNth3(Xt3, i, j, k); /* Precompute derivatives (old style) */ @@ -499,335 +499,335 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); - dgtu111 = -2*(gtu11*gtu21*PDstandard4th1gt12 + gtu11*gtu31*PDstandard4th1gt13 + gtu21*gtu31*PDstandard4th1gt23) - - PDstandard4th1gt11*SQR(gtu11) - PDstandard4th1gt22*SQR(gtu21) - PDstandard4th1gt33*SQR(gtu31); - - dgtu211 = -(gtu11*gtu21*PDstandard4th1gt11) - gtu11*gtu22*PDstandard4th1gt12 - gtu21*gtu31*PDstandard4th1gt13 - - gtu11*gtu32*PDstandard4th1gt13 - gtu21*gtu22*PDstandard4th1gt22 - gtu22*gtu31*PDstandard4th1gt23 - - gtu21*gtu32*PDstandard4th1gt23 - gtu31*gtu32*PDstandard4th1gt33 - PDstandard4th1gt12*SQR(gtu21); - - dgtu311 = -(gtu11*gtu31*PDstandard4th1gt11) - gtu21*gtu31*PDstandard4th1gt12 - gtu11*gtu32*PDstandard4th1gt12 - - gtu11*gtu33*PDstandard4th1gt13 - gtu21*gtu32*PDstandard4th1gt22 - gtu31*gtu32*PDstandard4th1gt23 - - gtu21*gtu33*PDstandard4th1gt23 - gtu31*gtu33*PDstandard4th1gt33 - PDstandard4th1gt13*SQR(gtu31); - - dgtu221 = -2*(gtu21*gtu22*PDstandard4th1gt12 + gtu21*gtu32*PDstandard4th1gt13 + gtu22*gtu32*PDstandard4th1gt23) - - PDstandard4th1gt11*SQR(gtu21) - PDstandard4th1gt22*SQR(gtu22) - PDstandard4th1gt33*SQR(gtu32); - - dgtu321 = -(gtu21*gtu31*PDstandard4th1gt11) - gtu22*gtu31*PDstandard4th1gt12 - gtu21*gtu32*PDstandard4th1gt12 - - gtu31*gtu32*PDstandard4th1gt13 - gtu21*gtu33*PDstandard4th1gt13 - gtu22*gtu32*PDstandard4th1gt22 - - gtu22*gtu33*PDstandard4th1gt23 - gtu32*gtu33*PDstandard4th1gt33 - PDstandard4th1gt23*SQR(gtu32); - - dgtu331 = -2*(gtu31*gtu32*PDstandard4th1gt12 + gtu31*gtu33*PDstandard4th1gt13 + gtu32*gtu33*PDstandard4th1gt23) - - PDstandard4th1gt11*SQR(gtu31) - PDstandard4th1gt22*SQR(gtu32) - PDstandard4th1gt33*SQR(gtu33); - - dgtu112 = -2*(gtu11*gtu21*PDstandard4th2gt12 + gtu11*gtu31*PDstandard4th2gt13 + gtu21*gtu31*PDstandard4th2gt23) - - PDstandard4th2gt11*SQR(gtu11) - PDstandard4th2gt22*SQR(gtu21) - PDstandard4th2gt33*SQR(gtu31); - - dgtu212 = -(gtu11*gtu21*PDstandard4th2gt11) - gtu11*gtu22*PDstandard4th2gt12 - gtu21*gtu31*PDstandard4th2gt13 - - gtu11*gtu32*PDstandard4th2gt13 - gtu21*gtu22*PDstandard4th2gt22 - gtu22*gtu31*PDstandard4th2gt23 - - gtu21*gtu32*PDstandard4th2gt23 - gtu31*gtu32*PDstandard4th2gt33 - PDstandard4th2gt12*SQR(gtu21); - - dgtu312 = -(gtu11*gtu31*PDstandard4th2gt11) - gtu21*gtu31*PDstandard4th2gt12 - gtu11*gtu32*PDstandard4th2gt12 - - gtu11*gtu33*PDstandard4th2gt13 - gtu21*gtu32*PDstandard4th2gt22 - gtu31*gtu32*PDstandard4th2gt23 - - gtu21*gtu33*PDstandard4th2gt23 - gtu31*gtu33*PDstandard4th2gt33 - PDstandard4th2gt13*SQR(gtu31); - - dgtu222 = -2*(gtu21*gtu22*PDstandard4th2gt12 + gtu21*gtu32*PDstandard4th2gt13 + gtu22*gtu32*PDstandard4th2gt23) - - PDstandard4th2gt11*SQR(gtu21) - PDstandard4th2gt22*SQR(gtu22) - PDstandard4th2gt33*SQR(gtu32); - - dgtu322 = -(gtu21*gtu31*PDstandard4th2gt11) - gtu22*gtu31*PDstandard4th2gt12 - gtu21*gtu32*PDstandard4th2gt12 - - gtu31*gtu32*PDstandard4th2gt13 - gtu21*gtu33*PDstandard4th2gt13 - gtu22*gtu32*PDstandard4th2gt22 - - gtu22*gtu33*PDstandard4th2gt23 - gtu32*gtu33*PDstandard4th2gt33 - PDstandard4th2gt23*SQR(gtu32); - - dgtu332 = -2*(gtu31*gtu32*PDstandard4th2gt12 + gtu31*gtu33*PDstandard4th2gt13 + gtu32*gtu33*PDstandard4th2gt23) - - PDstandard4th2gt11*SQR(gtu31) - PDstandard4th2gt22*SQR(gtu32) - PDstandard4th2gt33*SQR(gtu33); - - dgtu113 = -2*(gtu11*gtu21*PDstandard4th3gt12 + gtu11*gtu31*PDstandard4th3gt13 + gtu21*gtu31*PDstandard4th3gt23) - - PDstandard4th3gt11*SQR(gtu11) - PDstandard4th3gt22*SQR(gtu21) - PDstandard4th3gt33*SQR(gtu31); - - dgtu213 = -(gtu11*gtu21*PDstandard4th3gt11) - gtu11*gtu22*PDstandard4th3gt12 - gtu21*gtu31*PDstandard4th3gt13 - - gtu11*gtu32*PDstandard4th3gt13 - gtu21*gtu22*PDstandard4th3gt22 - gtu22*gtu31*PDstandard4th3gt23 - - gtu21*gtu32*PDstandard4th3gt23 - gtu31*gtu32*PDstandard4th3gt33 - PDstandard4th3gt12*SQR(gtu21); - - dgtu313 = -(gtu11*gtu31*PDstandard4th3gt11) - gtu21*gtu31*PDstandard4th3gt12 - gtu11*gtu32*PDstandard4th3gt12 - - gtu11*gtu33*PDstandard4th3gt13 - gtu21*gtu32*PDstandard4th3gt22 - gtu31*gtu32*PDstandard4th3gt23 - - gtu21*gtu33*PDstandard4th3gt23 - gtu31*gtu33*PDstandard4th3gt33 - PDstandard4th3gt13*SQR(gtu31); - - dgtu223 = -2*(gtu21*gtu22*PDstandard4th3gt12 + gtu21*gtu32*PDstandard4th3gt13 + gtu22*gtu32*PDstandard4th3gt23) - - PDstandard4th3gt11*SQR(gtu21) - PDstandard4th3gt22*SQR(gtu22) - PDstandard4th3gt33*SQR(gtu32); - - dgtu323 = -(gtu21*gtu31*PDstandard4th3gt11) - gtu22*gtu31*PDstandard4th3gt12 - gtu21*gtu32*PDstandard4th3gt12 - - gtu31*gtu32*PDstandard4th3gt13 - gtu21*gtu33*PDstandard4th3gt13 - gtu22*gtu32*PDstandard4th3gt22 - - gtu22*gtu33*PDstandard4th3gt23 - gtu32*gtu33*PDstandard4th3gt33 - PDstandard4th3gt23*SQR(gtu32); - - dgtu333 = -2*(gtu31*gtu32*PDstandard4th3gt12 + gtu31*gtu33*PDstandard4th3gt13 + gtu32*gtu33*PDstandard4th3gt23) - - PDstandard4th3gt11*SQR(gtu31) - PDstandard4th3gt22*SQR(gtu32) - PDstandard4th3gt33*SQR(gtu33); - - ddgtu1111 = -2*(gtu11*gtu21*PDstandard4th11gt12 + gtu11*gtu31*PDstandard4th11gt13 + gtu21*gtu31*PDstandard4th11gt23 + - dgtu111*gtu11*PDstandard4th1gt11 + dgtu211*gtu11*PDstandard4th1gt12 + dgtu111*gtu21*PDstandard4th1gt12 + - dgtu311*gtu11*PDstandard4th1gt13 + dgtu111*gtu31*PDstandard4th1gt13 + dgtu211*gtu21*PDstandard4th1gt22 + - dgtu311*gtu21*PDstandard4th1gt23 + dgtu211*gtu31*PDstandard4th1gt23 + dgtu311*gtu31*PDstandard4th1gt33) - - PDstandard4th11gt11*SQR(gtu11) - PDstandard4th11gt22*SQR(gtu21) - PDstandard4th11gt33*SQR(gtu31); - - ddgtu2111 = -(gtu11*gtu21*PDstandard4th11gt11) - gtu11*gtu22*PDstandard4th11gt12 - gtu21*gtu31*PDstandard4th11gt13 - - gtu11*gtu32*PDstandard4th11gt13 - gtu21*gtu22*PDstandard4th11gt22 - gtu22*gtu31*PDstandard4th11gt23 - - gtu21*gtu32*PDstandard4th11gt23 - gtu31*gtu32*PDstandard4th11gt33 - dgtu211*gtu11*PDstandard4th1gt11 - - dgtu111*gtu21*PDstandard4th1gt11 - dgtu221*gtu11*PDstandard4th1gt12 - 2*dgtu211*gtu21*PDstandard4th1gt12 - - dgtu111*gtu22*PDstandard4th1gt12 - dgtu321*gtu11*PDstandard4th1gt13 - dgtu311*gtu21*PDstandard4th1gt13 - - dgtu211*gtu31*PDstandard4th1gt13 - dgtu111*gtu32*PDstandard4th1gt13 - dgtu221*gtu21*PDstandard4th1gt22 - - dgtu211*gtu22*PDstandard4th1gt22 - dgtu321*gtu21*PDstandard4th1gt23 - dgtu311*gtu22*PDstandard4th1gt23 - - dgtu221*gtu31*PDstandard4th1gt23 - dgtu211*gtu32*PDstandard4th1gt23 - dgtu321*gtu31*PDstandard4th1gt33 - - dgtu311*gtu32*PDstandard4th1gt33 - PDstandard4th11gt12*SQR(gtu21); - - ddgtu3111 = -(gtu11*gtu31*PDstandard4th11gt11) - gtu21*gtu31*PDstandard4th11gt12 - gtu11*gtu32*PDstandard4th11gt12 - - gtu11*gtu33*PDstandard4th11gt13 - gtu21*gtu32*PDstandard4th11gt22 - gtu31*gtu32*PDstandard4th11gt23 - - gtu21*gtu33*PDstandard4th11gt23 - gtu31*gtu33*PDstandard4th11gt33 - dgtu311*gtu11*PDstandard4th1gt11 - - dgtu111*gtu31*PDstandard4th1gt11 - dgtu321*gtu11*PDstandard4th1gt12 - dgtu311*gtu21*PDstandard4th1gt12 - - dgtu211*gtu31*PDstandard4th1gt12 - dgtu111*gtu32*PDstandard4th1gt12 - dgtu331*gtu11*PDstandard4th1gt13 - - 2*dgtu311*gtu31*PDstandard4th1gt13 - dgtu111*gtu33*PDstandard4th1gt13 - dgtu321*gtu21*PDstandard4th1gt22 - - dgtu211*gtu32*PDstandard4th1gt22 - dgtu331*gtu21*PDstandard4th1gt23 - dgtu321*gtu31*PDstandard4th1gt23 - - dgtu311*gtu32*PDstandard4th1gt23 - dgtu211*gtu33*PDstandard4th1gt23 - dgtu331*gtu31*PDstandard4th1gt33 - - dgtu311*gtu33*PDstandard4th1gt33 - PDstandard4th11gt13*SQR(gtu31); - - ddgtu1112 = -2*(gtu11*gtu21*PDstandard4th12gt12 + gtu11*gtu31*PDstandard4th12gt13 + gtu21*gtu31*PDstandard4th12gt23 + - dgtu112*gtu11*PDstandard4th1gt11 + dgtu212*gtu11*PDstandard4th1gt12 + dgtu112*gtu21*PDstandard4th1gt12 + - dgtu312*gtu11*PDstandard4th1gt13 + dgtu112*gtu31*PDstandard4th1gt13 + dgtu212*gtu21*PDstandard4th1gt22 + - dgtu312*gtu21*PDstandard4th1gt23 + dgtu212*gtu31*PDstandard4th1gt23 + dgtu312*gtu31*PDstandard4th1gt33) - - PDstandard4th12gt11*SQR(gtu11) - PDstandard4th12gt22*SQR(gtu21) - PDstandard4th12gt33*SQR(gtu31); - - ddgtu2112 = -(gtu11*gtu21*PDstandard4th12gt11) - gtu11*gtu22*PDstandard4th12gt12 - gtu21*gtu31*PDstandard4th12gt13 - - gtu11*gtu32*PDstandard4th12gt13 - gtu21*gtu22*PDstandard4th12gt22 - gtu22*gtu31*PDstandard4th12gt23 - - gtu21*gtu32*PDstandard4th12gt23 - gtu31*gtu32*PDstandard4th12gt33 - dgtu212*gtu11*PDstandard4th1gt11 - - dgtu112*gtu21*PDstandard4th1gt11 - dgtu222*gtu11*PDstandard4th1gt12 - 2*dgtu212*gtu21*PDstandard4th1gt12 - - dgtu112*gtu22*PDstandard4th1gt12 - dgtu322*gtu11*PDstandard4th1gt13 - dgtu312*gtu21*PDstandard4th1gt13 - - dgtu212*gtu31*PDstandard4th1gt13 - dgtu112*gtu32*PDstandard4th1gt13 - dgtu222*gtu21*PDstandard4th1gt22 - - dgtu212*gtu22*PDstandard4th1gt22 - dgtu322*gtu21*PDstandard4th1gt23 - dgtu312*gtu22*PDstandard4th1gt23 - - dgtu222*gtu31*PDstandard4th1gt23 - dgtu212*gtu32*PDstandard4th1gt23 - dgtu322*gtu31*PDstandard4th1gt33 - - dgtu312*gtu32*PDstandard4th1gt33 - PDstandard4th12gt12*SQR(gtu21); - - ddgtu3112 = -(gtu11*gtu31*PDstandard4th12gt11) - gtu21*gtu31*PDstandard4th12gt12 - gtu11*gtu32*PDstandard4th12gt12 - - gtu11*gtu33*PDstandard4th12gt13 - gtu21*gtu32*PDstandard4th12gt22 - gtu31*gtu32*PDstandard4th12gt23 - - gtu21*gtu33*PDstandard4th12gt23 - gtu31*gtu33*PDstandard4th12gt33 - dgtu312*gtu11*PDstandard4th1gt11 - - dgtu112*gtu31*PDstandard4th1gt11 - dgtu322*gtu11*PDstandard4th1gt12 - dgtu312*gtu21*PDstandard4th1gt12 - - dgtu212*gtu31*PDstandard4th1gt12 - dgtu112*gtu32*PDstandard4th1gt12 - dgtu332*gtu11*PDstandard4th1gt13 - - 2*dgtu312*gtu31*PDstandard4th1gt13 - dgtu112*gtu33*PDstandard4th1gt13 - dgtu322*gtu21*PDstandard4th1gt22 - - dgtu212*gtu32*PDstandard4th1gt22 - dgtu332*gtu21*PDstandard4th1gt23 - dgtu322*gtu31*PDstandard4th1gt23 - - dgtu312*gtu32*PDstandard4th1gt23 - dgtu212*gtu33*PDstandard4th1gt23 - dgtu332*gtu31*PDstandard4th1gt33 - - dgtu312*gtu33*PDstandard4th1gt33 - PDstandard4th12gt13*SQR(gtu31); - - ddgtu2212 = -2*(gtu21*gtu22*PDstandard4th12gt12 + gtu21*gtu32*PDstandard4th12gt13 + gtu22*gtu32*PDstandard4th12gt23 + - dgtu212*gtu21*PDstandard4th1gt11 + dgtu222*gtu21*PDstandard4th1gt12 + dgtu212*gtu22*PDstandard4th1gt12 + - dgtu322*gtu21*PDstandard4th1gt13 + dgtu212*gtu32*PDstandard4th1gt13 + dgtu222*gtu22*PDstandard4th1gt22 + - dgtu322*gtu22*PDstandard4th1gt23 + dgtu222*gtu32*PDstandard4th1gt23 + dgtu322*gtu32*PDstandard4th1gt33) - - PDstandard4th12gt11*SQR(gtu21) - PDstandard4th12gt22*SQR(gtu22) - PDstandard4th12gt33*SQR(gtu32); - - ddgtu3212 = -(gtu21*gtu31*PDstandard4th12gt11) - gtu22*gtu31*PDstandard4th12gt12 - gtu21*gtu32*PDstandard4th12gt12 - - gtu31*gtu32*PDstandard4th12gt13 - gtu21*gtu33*PDstandard4th12gt13 - gtu22*gtu32*PDstandard4th12gt22 - - gtu22*gtu33*PDstandard4th12gt23 - gtu32*gtu33*PDstandard4th12gt33 - dgtu312*gtu21*PDstandard4th1gt11 - - dgtu212*gtu31*PDstandard4th1gt11 - dgtu322*gtu21*PDstandard4th1gt12 - dgtu312*gtu22*PDstandard4th1gt12 - - dgtu222*gtu31*PDstandard4th1gt12 - dgtu212*gtu32*PDstandard4th1gt12 - dgtu332*gtu21*PDstandard4th1gt13 - - dgtu322*gtu31*PDstandard4th1gt13 - dgtu312*gtu32*PDstandard4th1gt13 - dgtu212*gtu33*PDstandard4th1gt13 - - dgtu322*gtu22*PDstandard4th1gt22 - dgtu222*gtu32*PDstandard4th1gt22 - dgtu332*gtu22*PDstandard4th1gt23 - - 2*dgtu322*gtu32*PDstandard4th1gt23 - dgtu222*gtu33*PDstandard4th1gt23 - dgtu332*gtu32*PDstandard4th1gt33 - - dgtu322*gtu33*PDstandard4th1gt33 - PDstandard4th12gt23*SQR(gtu32); - - ddgtu1113 = -2*(gtu11*gtu21*PDstandard4th13gt12 + gtu11*gtu31*PDstandard4th13gt13 + gtu21*gtu31*PDstandard4th13gt23 + - dgtu113*gtu11*PDstandard4th1gt11 + dgtu213*gtu11*PDstandard4th1gt12 + dgtu113*gtu21*PDstandard4th1gt12 + - dgtu313*gtu11*PDstandard4th1gt13 + dgtu113*gtu31*PDstandard4th1gt13 + dgtu213*gtu21*PDstandard4th1gt22 + - dgtu313*gtu21*PDstandard4th1gt23 + dgtu213*gtu31*PDstandard4th1gt23 + dgtu313*gtu31*PDstandard4th1gt33) - - PDstandard4th13gt11*SQR(gtu11) - PDstandard4th13gt22*SQR(gtu21) - PDstandard4th13gt33*SQR(gtu31); - - ddgtu2113 = -(gtu11*gtu21*PDstandard4th13gt11) - gtu11*gtu22*PDstandard4th13gt12 - gtu21*gtu31*PDstandard4th13gt13 - - gtu11*gtu32*PDstandard4th13gt13 - gtu21*gtu22*PDstandard4th13gt22 - gtu22*gtu31*PDstandard4th13gt23 - - gtu21*gtu32*PDstandard4th13gt23 - gtu31*gtu32*PDstandard4th13gt33 - dgtu213*gtu11*PDstandard4th1gt11 - - dgtu113*gtu21*PDstandard4th1gt11 - dgtu223*gtu11*PDstandard4th1gt12 - 2*dgtu213*gtu21*PDstandard4th1gt12 - - dgtu113*gtu22*PDstandard4th1gt12 - dgtu323*gtu11*PDstandard4th1gt13 - dgtu313*gtu21*PDstandard4th1gt13 - - dgtu213*gtu31*PDstandard4th1gt13 - dgtu113*gtu32*PDstandard4th1gt13 - dgtu223*gtu21*PDstandard4th1gt22 - - dgtu213*gtu22*PDstandard4th1gt22 - dgtu323*gtu21*PDstandard4th1gt23 - dgtu313*gtu22*PDstandard4th1gt23 - - dgtu223*gtu31*PDstandard4th1gt23 - dgtu213*gtu32*PDstandard4th1gt23 - dgtu323*gtu31*PDstandard4th1gt33 - - dgtu313*gtu32*PDstandard4th1gt33 - PDstandard4th13gt12*SQR(gtu21); - - ddgtu3113 = -(gtu11*gtu31*PDstandard4th13gt11) - gtu21*gtu31*PDstandard4th13gt12 - gtu11*gtu32*PDstandard4th13gt12 - - gtu11*gtu33*PDstandard4th13gt13 - gtu21*gtu32*PDstandard4th13gt22 - gtu31*gtu32*PDstandard4th13gt23 - - gtu21*gtu33*PDstandard4th13gt23 - gtu31*gtu33*PDstandard4th13gt33 - dgtu313*gtu11*PDstandard4th1gt11 - - dgtu113*gtu31*PDstandard4th1gt11 - dgtu323*gtu11*PDstandard4th1gt12 - dgtu313*gtu21*PDstandard4th1gt12 - - dgtu213*gtu31*PDstandard4th1gt12 - dgtu113*gtu32*PDstandard4th1gt12 - dgtu333*gtu11*PDstandard4th1gt13 - - 2*dgtu313*gtu31*PDstandard4th1gt13 - dgtu113*gtu33*PDstandard4th1gt13 - dgtu323*gtu21*PDstandard4th1gt22 - - dgtu213*gtu32*PDstandard4th1gt22 - dgtu333*gtu21*PDstandard4th1gt23 - dgtu323*gtu31*PDstandard4th1gt23 - - dgtu313*gtu32*PDstandard4th1gt23 - dgtu213*gtu33*PDstandard4th1gt23 - dgtu333*gtu31*PDstandard4th1gt33 - - dgtu313*gtu33*PDstandard4th1gt33 - PDstandard4th13gt13*SQR(gtu31); - - ddgtu3213 = -(gtu21*gtu31*PDstandard4th13gt11) - gtu22*gtu31*PDstandard4th13gt12 - gtu21*gtu32*PDstandard4th13gt12 - - gtu31*gtu32*PDstandard4th13gt13 - gtu21*gtu33*PDstandard4th13gt13 - gtu22*gtu32*PDstandard4th13gt22 - - gtu22*gtu33*PDstandard4th13gt23 - gtu32*gtu33*PDstandard4th13gt33 - dgtu313*gtu21*PDstandard4th1gt11 - - dgtu213*gtu31*PDstandard4th1gt11 - dgtu323*gtu21*PDstandard4th1gt12 - dgtu313*gtu22*PDstandard4th1gt12 - - dgtu223*gtu31*PDstandard4th1gt12 - dgtu213*gtu32*PDstandard4th1gt12 - dgtu333*gtu21*PDstandard4th1gt13 - - dgtu323*gtu31*PDstandard4th1gt13 - dgtu313*gtu32*PDstandard4th1gt13 - dgtu213*gtu33*PDstandard4th1gt13 - - dgtu323*gtu22*PDstandard4th1gt22 - dgtu223*gtu32*PDstandard4th1gt22 - dgtu333*gtu22*PDstandard4th1gt23 - - 2*dgtu323*gtu32*PDstandard4th1gt23 - dgtu223*gtu33*PDstandard4th1gt23 - dgtu333*gtu32*PDstandard4th1gt33 - - dgtu323*gtu33*PDstandard4th1gt33 - PDstandard4th13gt23*SQR(gtu32); - - ddgtu3313 = -2*(gtu31*gtu32*PDstandard4th13gt12 + gtu31*gtu33*PDstandard4th13gt13 + gtu32*gtu33*PDstandard4th13gt23 + - dgtu313*gtu31*PDstandard4th1gt11 + dgtu323*gtu31*PDstandard4th1gt12 + dgtu313*gtu32*PDstandard4th1gt12 + - dgtu333*gtu31*PDstandard4th1gt13 + dgtu313*gtu33*PDstandard4th1gt13 + dgtu323*gtu32*PDstandard4th1gt22 + - dgtu333*gtu32*PDstandard4th1gt23 + dgtu323*gtu33*PDstandard4th1gt23 + dgtu333*gtu33*PDstandard4th1gt33) - - PDstandard4th13gt11*SQR(gtu31) - PDstandard4th13gt22*SQR(gtu32) - PDstandard4th13gt33*SQR(gtu33); - - ddgtu2122 = -(gtu11*gtu21*PDstandard4th22gt11) - gtu11*gtu22*PDstandard4th22gt12 - gtu21*gtu31*PDstandard4th22gt13 - - gtu11*gtu32*PDstandard4th22gt13 - gtu21*gtu22*PDstandard4th22gt22 - gtu22*gtu31*PDstandard4th22gt23 - - gtu21*gtu32*PDstandard4th22gt23 - gtu31*gtu32*PDstandard4th22gt33 - dgtu212*gtu11*PDstandard4th2gt11 - - dgtu112*gtu21*PDstandard4th2gt11 - dgtu222*gtu11*PDstandard4th2gt12 - 2*dgtu212*gtu21*PDstandard4th2gt12 - - dgtu112*gtu22*PDstandard4th2gt12 - dgtu322*gtu11*PDstandard4th2gt13 - dgtu312*gtu21*PDstandard4th2gt13 - - dgtu212*gtu31*PDstandard4th2gt13 - dgtu112*gtu32*PDstandard4th2gt13 - dgtu222*gtu21*PDstandard4th2gt22 - - dgtu212*gtu22*PDstandard4th2gt22 - dgtu322*gtu21*PDstandard4th2gt23 - dgtu312*gtu22*PDstandard4th2gt23 - - dgtu222*gtu31*PDstandard4th2gt23 - dgtu212*gtu32*PDstandard4th2gt23 - dgtu322*gtu31*PDstandard4th2gt33 - - dgtu312*gtu32*PDstandard4th2gt33 - PDstandard4th22gt12*SQR(gtu21); - - ddgtu2222 = -2*(gtu21*gtu22*PDstandard4th22gt12 + gtu21*gtu32*PDstandard4th22gt13 + gtu22*gtu32*PDstandard4th22gt23 + - dgtu212*gtu21*PDstandard4th2gt11 + dgtu222*gtu21*PDstandard4th2gt12 + dgtu212*gtu22*PDstandard4th2gt12 + - dgtu322*gtu21*PDstandard4th2gt13 + dgtu212*gtu32*PDstandard4th2gt13 + dgtu222*gtu22*PDstandard4th2gt22 + - dgtu322*gtu22*PDstandard4th2gt23 + dgtu222*gtu32*PDstandard4th2gt23 + dgtu322*gtu32*PDstandard4th2gt33) - - PDstandard4th22gt11*SQR(gtu21) - PDstandard4th22gt22*SQR(gtu22) - PDstandard4th22gt33*SQR(gtu32); - - ddgtu3222 = -(gtu21*gtu31*PDstandard4th22gt11) - gtu22*gtu31*PDstandard4th22gt12 - gtu21*gtu32*PDstandard4th22gt12 - - gtu31*gtu32*PDstandard4th22gt13 - gtu21*gtu33*PDstandard4th22gt13 - gtu22*gtu32*PDstandard4th22gt22 - - gtu22*gtu33*PDstandard4th22gt23 - gtu32*gtu33*PDstandard4th22gt33 - dgtu312*gtu21*PDstandard4th2gt11 - - dgtu212*gtu31*PDstandard4th2gt11 - dgtu322*gtu21*PDstandard4th2gt12 - dgtu312*gtu22*PDstandard4th2gt12 - - dgtu222*gtu31*PDstandard4th2gt12 - dgtu212*gtu32*PDstandard4th2gt12 - dgtu332*gtu21*PDstandard4th2gt13 - - dgtu322*gtu31*PDstandard4th2gt13 - dgtu312*gtu32*PDstandard4th2gt13 - dgtu212*gtu33*PDstandard4th2gt13 - - dgtu322*gtu22*PDstandard4th2gt22 - dgtu222*gtu32*PDstandard4th2gt22 - dgtu332*gtu22*PDstandard4th2gt23 - - 2*dgtu322*gtu32*PDstandard4th2gt23 - dgtu222*gtu33*PDstandard4th2gt23 - dgtu332*gtu32*PDstandard4th2gt33 - - dgtu322*gtu33*PDstandard4th2gt33 - PDstandard4th22gt23*SQR(gtu32); - - ddgtu2123 = -(gtu11*gtu21*PDstandard4th23gt11) - gtu11*gtu22*PDstandard4th23gt12 - gtu21*gtu31*PDstandard4th23gt13 - - gtu11*gtu32*PDstandard4th23gt13 - gtu21*gtu22*PDstandard4th23gt22 - gtu22*gtu31*PDstandard4th23gt23 - - gtu21*gtu32*PDstandard4th23gt23 - gtu31*gtu32*PDstandard4th23gt33 - dgtu213*gtu11*PDstandard4th2gt11 - - dgtu113*gtu21*PDstandard4th2gt11 - dgtu223*gtu11*PDstandard4th2gt12 - 2*dgtu213*gtu21*PDstandard4th2gt12 - - dgtu113*gtu22*PDstandard4th2gt12 - dgtu323*gtu11*PDstandard4th2gt13 - dgtu313*gtu21*PDstandard4th2gt13 - - dgtu213*gtu31*PDstandard4th2gt13 - dgtu113*gtu32*PDstandard4th2gt13 - dgtu223*gtu21*PDstandard4th2gt22 - - dgtu213*gtu22*PDstandard4th2gt22 - dgtu323*gtu21*PDstandard4th2gt23 - dgtu313*gtu22*PDstandard4th2gt23 - - dgtu223*gtu31*PDstandard4th2gt23 - dgtu213*gtu32*PDstandard4th2gt23 - dgtu323*gtu31*PDstandard4th2gt33 - - dgtu313*gtu32*PDstandard4th2gt33 - PDstandard4th23gt12*SQR(gtu21); - - ddgtu3123 = -(gtu11*gtu31*PDstandard4th23gt11) - gtu21*gtu31*PDstandard4th23gt12 - gtu11*gtu32*PDstandard4th23gt12 - - gtu11*gtu33*PDstandard4th23gt13 - gtu21*gtu32*PDstandard4th23gt22 - gtu31*gtu32*PDstandard4th23gt23 - - gtu21*gtu33*PDstandard4th23gt23 - gtu31*gtu33*PDstandard4th23gt33 - dgtu313*gtu11*PDstandard4th2gt11 - - dgtu113*gtu31*PDstandard4th2gt11 - dgtu323*gtu11*PDstandard4th2gt12 - dgtu313*gtu21*PDstandard4th2gt12 - - dgtu213*gtu31*PDstandard4th2gt12 - dgtu113*gtu32*PDstandard4th2gt12 - dgtu333*gtu11*PDstandard4th2gt13 - - 2*dgtu313*gtu31*PDstandard4th2gt13 - dgtu113*gtu33*PDstandard4th2gt13 - dgtu323*gtu21*PDstandard4th2gt22 - - dgtu213*gtu32*PDstandard4th2gt22 - dgtu333*gtu21*PDstandard4th2gt23 - dgtu323*gtu31*PDstandard4th2gt23 - - dgtu313*gtu32*PDstandard4th2gt23 - dgtu213*gtu33*PDstandard4th2gt23 - dgtu333*gtu31*PDstandard4th2gt33 - - dgtu313*gtu33*PDstandard4th2gt33 - PDstandard4th23gt13*SQR(gtu31); - - ddgtu2223 = -2*(gtu21*gtu22*PDstandard4th23gt12 + gtu21*gtu32*PDstandard4th23gt13 + gtu22*gtu32*PDstandard4th23gt23 + - dgtu213*gtu21*PDstandard4th2gt11 + dgtu223*gtu21*PDstandard4th2gt12 + dgtu213*gtu22*PDstandard4th2gt12 + - dgtu323*gtu21*PDstandard4th2gt13 + dgtu213*gtu32*PDstandard4th2gt13 + dgtu223*gtu22*PDstandard4th2gt22 + - dgtu323*gtu22*PDstandard4th2gt23 + dgtu223*gtu32*PDstandard4th2gt23 + dgtu323*gtu32*PDstandard4th2gt33) - - PDstandard4th23gt11*SQR(gtu21) - PDstandard4th23gt22*SQR(gtu22) - PDstandard4th23gt33*SQR(gtu32); - - ddgtu3223 = -(gtu21*gtu31*PDstandard4th23gt11) - gtu22*gtu31*PDstandard4th23gt12 - gtu21*gtu32*PDstandard4th23gt12 - - gtu31*gtu32*PDstandard4th23gt13 - gtu21*gtu33*PDstandard4th23gt13 - gtu22*gtu32*PDstandard4th23gt22 - - gtu22*gtu33*PDstandard4th23gt23 - gtu32*gtu33*PDstandard4th23gt33 - dgtu313*gtu21*PDstandard4th2gt11 - - dgtu213*gtu31*PDstandard4th2gt11 - dgtu323*gtu21*PDstandard4th2gt12 - dgtu313*gtu22*PDstandard4th2gt12 - - dgtu223*gtu31*PDstandard4th2gt12 - dgtu213*gtu32*PDstandard4th2gt12 - dgtu333*gtu21*PDstandard4th2gt13 - - dgtu323*gtu31*PDstandard4th2gt13 - dgtu313*gtu32*PDstandard4th2gt13 - dgtu213*gtu33*PDstandard4th2gt13 - - dgtu323*gtu22*PDstandard4th2gt22 - dgtu223*gtu32*PDstandard4th2gt22 - dgtu333*gtu22*PDstandard4th2gt23 - - 2*dgtu323*gtu32*PDstandard4th2gt23 - dgtu223*gtu33*PDstandard4th2gt23 - dgtu333*gtu32*PDstandard4th2gt33 - - dgtu323*gtu33*PDstandard4th2gt33 - PDstandard4th23gt23*SQR(gtu32); - - ddgtu3323 = -2*(gtu31*gtu32*PDstandard4th23gt12 + gtu31*gtu33*PDstandard4th23gt13 + gtu32*gtu33*PDstandard4th23gt23 + - dgtu313*gtu31*PDstandard4th2gt11 + dgtu323*gtu31*PDstandard4th2gt12 + dgtu313*gtu32*PDstandard4th2gt12 + - dgtu333*gtu31*PDstandard4th2gt13 + dgtu313*gtu33*PDstandard4th2gt13 + dgtu323*gtu32*PDstandard4th2gt22 + - dgtu333*gtu32*PDstandard4th2gt23 + dgtu323*gtu33*PDstandard4th2gt23 + dgtu333*gtu33*PDstandard4th2gt33) - - PDstandard4th23gt11*SQR(gtu31) - PDstandard4th23gt22*SQR(gtu32) - PDstandard4th23gt33*SQR(gtu33); - - ddgtu3133 = -(gtu11*gtu31*PDstandard4th33gt11) - gtu21*gtu31*PDstandard4th33gt12 - gtu11*gtu32*PDstandard4th33gt12 - - gtu11*gtu33*PDstandard4th33gt13 - gtu21*gtu32*PDstandard4th33gt22 - gtu31*gtu32*PDstandard4th33gt23 - - gtu21*gtu33*PDstandard4th33gt23 - gtu31*gtu33*PDstandard4th33gt33 - dgtu313*gtu11*PDstandard4th3gt11 - - dgtu113*gtu31*PDstandard4th3gt11 - dgtu323*gtu11*PDstandard4th3gt12 - dgtu313*gtu21*PDstandard4th3gt12 - - dgtu213*gtu31*PDstandard4th3gt12 - dgtu113*gtu32*PDstandard4th3gt12 - dgtu333*gtu11*PDstandard4th3gt13 - - 2*dgtu313*gtu31*PDstandard4th3gt13 - dgtu113*gtu33*PDstandard4th3gt13 - dgtu323*gtu21*PDstandard4th3gt22 - - dgtu213*gtu32*PDstandard4th3gt22 - dgtu333*gtu21*PDstandard4th3gt23 - dgtu323*gtu31*PDstandard4th3gt23 - - dgtu313*gtu32*PDstandard4th3gt23 - dgtu213*gtu33*PDstandard4th3gt23 - dgtu333*gtu31*PDstandard4th3gt33 - - dgtu313*gtu33*PDstandard4th3gt33 - PDstandard4th33gt13*SQR(gtu31); - - ddgtu3233 = -(gtu21*gtu31*PDstandard4th33gt11) - gtu22*gtu31*PDstandard4th33gt12 - gtu21*gtu32*PDstandard4th33gt12 - - gtu31*gtu32*PDstandard4th33gt13 - gtu21*gtu33*PDstandard4th33gt13 - gtu22*gtu32*PDstandard4th33gt22 - - gtu22*gtu33*PDstandard4th33gt23 - gtu32*gtu33*PDstandard4th33gt33 - dgtu313*gtu21*PDstandard4th3gt11 - - dgtu213*gtu31*PDstandard4th3gt11 - dgtu323*gtu21*PDstandard4th3gt12 - dgtu313*gtu22*PDstandard4th3gt12 - - dgtu223*gtu31*PDstandard4th3gt12 - dgtu213*gtu32*PDstandard4th3gt12 - dgtu333*gtu21*PDstandard4th3gt13 - - dgtu323*gtu31*PDstandard4th3gt13 - dgtu313*gtu32*PDstandard4th3gt13 - dgtu213*gtu33*PDstandard4th3gt13 - - dgtu323*gtu22*PDstandard4th3gt22 - dgtu223*gtu32*PDstandard4th3gt22 - dgtu333*gtu22*PDstandard4th3gt23 - - 2*dgtu323*gtu32*PDstandard4th3gt23 - dgtu223*gtu33*PDstandard4th3gt23 - dgtu333*gtu32*PDstandard4th3gt33 - - dgtu323*gtu33*PDstandard4th3gt33 - PDstandard4th33gt23*SQR(gtu32); - - ddgtu3333 = -2*(gtu31*gtu32*PDstandard4th33gt12 + gtu31*gtu33*PDstandard4th33gt13 + gtu32*gtu33*PDstandard4th33gt23 + - dgtu313*gtu31*PDstandard4th3gt11 + dgtu323*gtu31*PDstandard4th3gt12 + dgtu313*gtu32*PDstandard4th3gt12 + - dgtu333*gtu31*PDstandard4th3gt13 + dgtu313*gtu33*PDstandard4th3gt13 + dgtu323*gtu32*PDstandard4th3gt22 + - dgtu333*gtu32*PDstandard4th3gt23 + dgtu323*gtu33*PDstandard4th3gt23 + dgtu333*gtu33*PDstandard4th3gt33) - - PDstandard4th33gt11*SQR(gtu31) - PDstandard4th33gt22*SQR(gtu32) - PDstandard4th33gt33*SQR(gtu33); - - Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu21*PDstandard4th1gt12 + gtu31*PDstandard4th1gt13) - - gtu21*PDstandard4th2gt11 - gtu31*PDstandard4th3gt11); - - Gt211 = khalf*(gtu21*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt12 + gtu32*PDstandard4th1gt13) - - gtu22*PDstandard4th2gt11 - gtu32*PDstandard4th3gt11); - - Gt311 = khalf*(gtu31*PDstandard4th1gt11 + 2*(gtu32*PDstandard4th1gt12 + gtu33*PDstandard4th1gt13) - - gtu32*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); - - Gt112 = khalf*(gtu21*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + - gtu31*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - - Gt212 = khalf*(gtu22*PDstandard4th1gt22 + gtu21*PDstandard4th2gt11 + - gtu32*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - - Gt312 = khalf*(gtu32*PDstandard4th1gt22 + gtu31*PDstandard4th2gt11 + - gtu33*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - - Gt113 = khalf*(gtu31*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + - gtu21*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - - Gt213 = khalf*(gtu32*PDstandard4th1gt33 + gtu21*PDstandard4th3gt11 + - gtu22*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - - Gt313 = khalf*(gtu33*PDstandard4th1gt33 + gtu31*PDstandard4th3gt11 + - gtu32*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - - Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu21*PDstandard4th2gt22 + - gtu31*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - - Gt222 = khalf*(gtu21*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu22*PDstandard4th2gt22 + - gtu32*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - - Gt322 = khalf*(gtu31*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu32*PDstandard4th2gt22 + - gtu33*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - - Gt123 = khalf*(gtu31*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu21*PDstandard4th3gt22); - - Gt223 = khalf*(gtu32*PDstandard4th2gt33 + gtu21*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu22*PDstandard4th3gt22); - - Gt323 = khalf*(gtu33*PDstandard4th2gt33 + gtu31*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu32*PDstandard4th3gt22); - - Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu21*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt13 + - 2*gtu21*PDstandard4th3gt23 + gtu31*PDstandard4th3gt33); - - Gt233 = khalf*(-(gtu21*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu21*PDstandard4th3gt13 + - 2*gtu22*PDstandard4th3gt23 + gtu32*PDstandard4th3gt33); - - Gt333 = khalf*(-(gtu31*PDstandard4th1gt33) - gtu32*PDstandard4th2gt33 + 2*gtu31*PDstandard4th3gt13 + - 2*gtu32*PDstandard4th3gt23 + gtu33*PDstandard4th3gt33); - - Rt11 = -(gtu11*khalf*PDstandard4th11gt11) + gtu21* + dgtu111 = -2*(gtu11*gtu21*PDstandardNth1gt12 + gtu11*gtu31*PDstandardNth1gt13 + gtu21*gtu31*PDstandardNth1gt23) - + PDstandardNth1gt11*SQR(gtu11) - PDstandardNth1gt22*SQR(gtu21) - PDstandardNth1gt33*SQR(gtu31); + + dgtu211 = -(gtu11*gtu21*PDstandardNth1gt11) - gtu11*gtu22*PDstandardNth1gt12 - gtu21*gtu31*PDstandardNth1gt13 - + gtu11*gtu32*PDstandardNth1gt13 - gtu21*gtu22*PDstandardNth1gt22 - gtu22*gtu31*PDstandardNth1gt23 - + gtu21*gtu32*PDstandardNth1gt23 - gtu31*gtu32*PDstandardNth1gt33 - PDstandardNth1gt12*SQR(gtu21); + + dgtu311 = -(gtu11*gtu31*PDstandardNth1gt11) - gtu21*gtu31*PDstandardNth1gt12 - gtu11*gtu32*PDstandardNth1gt12 - + gtu11*gtu33*PDstandardNth1gt13 - gtu21*gtu32*PDstandardNth1gt22 - gtu31*gtu32*PDstandardNth1gt23 - + gtu21*gtu33*PDstandardNth1gt23 - gtu31*gtu33*PDstandardNth1gt33 - PDstandardNth1gt13*SQR(gtu31); + + dgtu221 = -2*(gtu21*gtu22*PDstandardNth1gt12 + gtu21*gtu32*PDstandardNth1gt13 + gtu22*gtu32*PDstandardNth1gt23) - + PDstandardNth1gt11*SQR(gtu21) - PDstandardNth1gt22*SQR(gtu22) - PDstandardNth1gt33*SQR(gtu32); + + dgtu321 = -(gtu21*gtu31*PDstandardNth1gt11) - gtu22*gtu31*PDstandardNth1gt12 - gtu21*gtu32*PDstandardNth1gt12 - + gtu31*gtu32*PDstandardNth1gt13 - gtu21*gtu33*PDstandardNth1gt13 - gtu22*gtu32*PDstandardNth1gt22 - + gtu22*gtu33*PDstandardNth1gt23 - gtu32*gtu33*PDstandardNth1gt33 - PDstandardNth1gt23*SQR(gtu32); + + dgtu331 = -2*(gtu31*gtu32*PDstandardNth1gt12 + gtu31*gtu33*PDstandardNth1gt13 + gtu32*gtu33*PDstandardNth1gt23) - + PDstandardNth1gt11*SQR(gtu31) - PDstandardNth1gt22*SQR(gtu32) - PDstandardNth1gt33*SQR(gtu33); + + dgtu112 = -2*(gtu11*gtu21*PDstandardNth2gt12 + gtu11*gtu31*PDstandardNth2gt13 + gtu21*gtu31*PDstandardNth2gt23) - + PDstandardNth2gt11*SQR(gtu11) - PDstandardNth2gt22*SQR(gtu21) - PDstandardNth2gt33*SQR(gtu31); + + dgtu212 = -(gtu11*gtu21*PDstandardNth2gt11) - gtu11*gtu22*PDstandardNth2gt12 - gtu21*gtu31*PDstandardNth2gt13 - + gtu11*gtu32*PDstandardNth2gt13 - gtu21*gtu22*PDstandardNth2gt22 - gtu22*gtu31*PDstandardNth2gt23 - + gtu21*gtu32*PDstandardNth2gt23 - gtu31*gtu32*PDstandardNth2gt33 - PDstandardNth2gt12*SQR(gtu21); + + dgtu312 = -(gtu11*gtu31*PDstandardNth2gt11) - gtu21*gtu31*PDstandardNth2gt12 - gtu11*gtu32*PDstandardNth2gt12 - + gtu11*gtu33*PDstandardNth2gt13 - gtu21*gtu32*PDstandardNth2gt22 - gtu31*gtu32*PDstandardNth2gt23 - + gtu21*gtu33*PDstandardNth2gt23 - gtu31*gtu33*PDstandardNth2gt33 - PDstandardNth2gt13*SQR(gtu31); + + dgtu222 = -2*(gtu21*gtu22*PDstandardNth2gt12 + gtu21*gtu32*PDstandardNth2gt13 + gtu22*gtu32*PDstandardNth2gt23) - + PDstandardNth2gt11*SQR(gtu21) - PDstandardNth2gt22*SQR(gtu22) - PDstandardNth2gt33*SQR(gtu32); + + dgtu322 = -(gtu21*gtu31*PDstandardNth2gt11) - gtu22*gtu31*PDstandardNth2gt12 - gtu21*gtu32*PDstandardNth2gt12 - + gtu31*gtu32*PDstandardNth2gt13 - gtu21*gtu33*PDstandardNth2gt13 - gtu22*gtu32*PDstandardNth2gt22 - + gtu22*gtu33*PDstandardNth2gt23 - gtu32*gtu33*PDstandardNth2gt33 - PDstandardNth2gt23*SQR(gtu32); + + dgtu332 = -2*(gtu31*gtu32*PDstandardNth2gt12 + gtu31*gtu33*PDstandardNth2gt13 + gtu32*gtu33*PDstandardNth2gt23) - + PDstandardNth2gt11*SQR(gtu31) - PDstandardNth2gt22*SQR(gtu32) - PDstandardNth2gt33*SQR(gtu33); + + dgtu113 = -2*(gtu11*gtu21*PDstandardNth3gt12 + gtu11*gtu31*PDstandardNth3gt13 + gtu21*gtu31*PDstandardNth3gt23) - + PDstandardNth3gt11*SQR(gtu11) - PDstandardNth3gt22*SQR(gtu21) - PDstandardNth3gt33*SQR(gtu31); + + dgtu213 = -(gtu11*gtu21*PDstandardNth3gt11) - gtu11*gtu22*PDstandardNth3gt12 - gtu21*gtu31*PDstandardNth3gt13 - + gtu11*gtu32*PDstandardNth3gt13 - gtu21*gtu22*PDstandardNth3gt22 - gtu22*gtu31*PDstandardNth3gt23 - + gtu21*gtu32*PDstandardNth3gt23 - gtu31*gtu32*PDstandardNth3gt33 - PDstandardNth3gt12*SQR(gtu21); + + dgtu313 = -(gtu11*gtu31*PDstandardNth3gt11) - gtu21*gtu31*PDstandardNth3gt12 - gtu11*gtu32*PDstandardNth3gt12 - + gtu11*gtu33*PDstandardNth3gt13 - gtu21*gtu32*PDstandardNth3gt22 - gtu31*gtu32*PDstandardNth3gt23 - + gtu21*gtu33*PDstandardNth3gt23 - gtu31*gtu33*PDstandardNth3gt33 - PDstandardNth3gt13*SQR(gtu31); + + dgtu223 = -2*(gtu21*gtu22*PDstandardNth3gt12 + gtu21*gtu32*PDstandardNth3gt13 + gtu22*gtu32*PDstandardNth3gt23) - + PDstandardNth3gt11*SQR(gtu21) - PDstandardNth3gt22*SQR(gtu22) - PDstandardNth3gt33*SQR(gtu32); + + dgtu323 = -(gtu21*gtu31*PDstandardNth3gt11) - gtu22*gtu31*PDstandardNth3gt12 - gtu21*gtu32*PDstandardNth3gt12 - + gtu31*gtu32*PDstandardNth3gt13 - gtu21*gtu33*PDstandardNth3gt13 - gtu22*gtu32*PDstandardNth3gt22 - + gtu22*gtu33*PDstandardNth3gt23 - gtu32*gtu33*PDstandardNth3gt33 - PDstandardNth3gt23*SQR(gtu32); + + dgtu333 = -2*(gtu31*gtu32*PDstandardNth3gt12 + gtu31*gtu33*PDstandardNth3gt13 + gtu32*gtu33*PDstandardNth3gt23) - + PDstandardNth3gt11*SQR(gtu31) - PDstandardNth3gt22*SQR(gtu32) - PDstandardNth3gt33*SQR(gtu33); + + ddgtu1111 = -2*(gtu11*gtu21*PDstandardNth11gt12 + gtu11*gtu31*PDstandardNth11gt13 + gtu21*gtu31*PDstandardNth11gt23 + + dgtu111*gtu11*PDstandardNth1gt11 + dgtu211*gtu11*PDstandardNth1gt12 + dgtu111*gtu21*PDstandardNth1gt12 + + dgtu311*gtu11*PDstandardNth1gt13 + dgtu111*gtu31*PDstandardNth1gt13 + dgtu211*gtu21*PDstandardNth1gt22 + + dgtu311*gtu21*PDstandardNth1gt23 + dgtu211*gtu31*PDstandardNth1gt23 + dgtu311*gtu31*PDstandardNth1gt33) - + PDstandardNth11gt11*SQR(gtu11) - PDstandardNth11gt22*SQR(gtu21) - PDstandardNth11gt33*SQR(gtu31); + + ddgtu2111 = -(gtu11*gtu21*PDstandardNth11gt11) - gtu11*gtu22*PDstandardNth11gt12 - gtu21*gtu31*PDstandardNth11gt13 - + gtu11*gtu32*PDstandardNth11gt13 - gtu21*gtu22*PDstandardNth11gt22 - gtu22*gtu31*PDstandardNth11gt23 - + gtu21*gtu32*PDstandardNth11gt23 - gtu31*gtu32*PDstandardNth11gt33 - dgtu211*gtu11*PDstandardNth1gt11 - + dgtu111*gtu21*PDstandardNth1gt11 - dgtu221*gtu11*PDstandardNth1gt12 - 2*dgtu211*gtu21*PDstandardNth1gt12 - + dgtu111*gtu22*PDstandardNth1gt12 - dgtu321*gtu11*PDstandardNth1gt13 - dgtu311*gtu21*PDstandardNth1gt13 - + dgtu211*gtu31*PDstandardNth1gt13 - dgtu111*gtu32*PDstandardNth1gt13 - dgtu221*gtu21*PDstandardNth1gt22 - + dgtu211*gtu22*PDstandardNth1gt22 - dgtu321*gtu21*PDstandardNth1gt23 - dgtu311*gtu22*PDstandardNth1gt23 - + dgtu221*gtu31*PDstandardNth1gt23 - dgtu211*gtu32*PDstandardNth1gt23 - dgtu321*gtu31*PDstandardNth1gt33 - + dgtu311*gtu32*PDstandardNth1gt33 - PDstandardNth11gt12*SQR(gtu21); + + ddgtu3111 = -(gtu11*gtu31*PDstandardNth11gt11) - gtu21*gtu31*PDstandardNth11gt12 - gtu11*gtu32*PDstandardNth11gt12 - + gtu11*gtu33*PDstandardNth11gt13 - gtu21*gtu32*PDstandardNth11gt22 - gtu31*gtu32*PDstandardNth11gt23 - + gtu21*gtu33*PDstandardNth11gt23 - gtu31*gtu33*PDstandardNth11gt33 - dgtu311*gtu11*PDstandardNth1gt11 - + dgtu111*gtu31*PDstandardNth1gt11 - dgtu321*gtu11*PDstandardNth1gt12 - dgtu311*gtu21*PDstandardNth1gt12 - + dgtu211*gtu31*PDstandardNth1gt12 - dgtu111*gtu32*PDstandardNth1gt12 - dgtu331*gtu11*PDstandardNth1gt13 - + 2*dgtu311*gtu31*PDstandardNth1gt13 - dgtu111*gtu33*PDstandardNth1gt13 - dgtu321*gtu21*PDstandardNth1gt22 - + dgtu211*gtu32*PDstandardNth1gt22 - dgtu331*gtu21*PDstandardNth1gt23 - dgtu321*gtu31*PDstandardNth1gt23 - + dgtu311*gtu32*PDstandardNth1gt23 - dgtu211*gtu33*PDstandardNth1gt23 - dgtu331*gtu31*PDstandardNth1gt33 - + dgtu311*gtu33*PDstandardNth1gt33 - PDstandardNth11gt13*SQR(gtu31); + + ddgtu1112 = -2*(gtu11*gtu21*PDstandardNth12gt12 + gtu11*gtu31*PDstandardNth12gt13 + gtu21*gtu31*PDstandardNth12gt23 + + dgtu112*gtu11*PDstandardNth1gt11 + dgtu212*gtu11*PDstandardNth1gt12 + dgtu112*gtu21*PDstandardNth1gt12 + + dgtu312*gtu11*PDstandardNth1gt13 + dgtu112*gtu31*PDstandardNth1gt13 + dgtu212*gtu21*PDstandardNth1gt22 + + dgtu312*gtu21*PDstandardNth1gt23 + dgtu212*gtu31*PDstandardNth1gt23 + dgtu312*gtu31*PDstandardNth1gt33) - + PDstandardNth12gt11*SQR(gtu11) - PDstandardNth12gt22*SQR(gtu21) - PDstandardNth12gt33*SQR(gtu31); + + ddgtu2112 = -(gtu11*gtu21*PDstandardNth12gt11) - gtu11*gtu22*PDstandardNth12gt12 - gtu21*gtu31*PDstandardNth12gt13 - + gtu11*gtu32*PDstandardNth12gt13 - gtu21*gtu22*PDstandardNth12gt22 - gtu22*gtu31*PDstandardNth12gt23 - + gtu21*gtu32*PDstandardNth12gt23 - gtu31*gtu32*PDstandardNth12gt33 - dgtu212*gtu11*PDstandardNth1gt11 - + dgtu112*gtu21*PDstandardNth1gt11 - dgtu222*gtu11*PDstandardNth1gt12 - 2*dgtu212*gtu21*PDstandardNth1gt12 - + dgtu112*gtu22*PDstandardNth1gt12 - dgtu322*gtu11*PDstandardNth1gt13 - dgtu312*gtu21*PDstandardNth1gt13 - + dgtu212*gtu31*PDstandardNth1gt13 - dgtu112*gtu32*PDstandardNth1gt13 - dgtu222*gtu21*PDstandardNth1gt22 - + dgtu212*gtu22*PDstandardNth1gt22 - dgtu322*gtu21*PDstandardNth1gt23 - dgtu312*gtu22*PDstandardNth1gt23 - + dgtu222*gtu31*PDstandardNth1gt23 - dgtu212*gtu32*PDstandardNth1gt23 - dgtu322*gtu31*PDstandardNth1gt33 - + dgtu312*gtu32*PDstandardNth1gt33 - PDstandardNth12gt12*SQR(gtu21); + + ddgtu3112 = -(gtu11*gtu31*PDstandardNth12gt11) - gtu21*gtu31*PDstandardNth12gt12 - gtu11*gtu32*PDstandardNth12gt12 - + gtu11*gtu33*PDstandardNth12gt13 - gtu21*gtu32*PDstandardNth12gt22 - gtu31*gtu32*PDstandardNth12gt23 - + gtu21*gtu33*PDstandardNth12gt23 - gtu31*gtu33*PDstandardNth12gt33 - dgtu312*gtu11*PDstandardNth1gt11 - + dgtu112*gtu31*PDstandardNth1gt11 - dgtu322*gtu11*PDstandardNth1gt12 - dgtu312*gtu21*PDstandardNth1gt12 - + dgtu212*gtu31*PDstandardNth1gt12 - dgtu112*gtu32*PDstandardNth1gt12 - dgtu332*gtu11*PDstandardNth1gt13 - + 2*dgtu312*gtu31*PDstandardNth1gt13 - dgtu112*gtu33*PDstandardNth1gt13 - dgtu322*gtu21*PDstandardNth1gt22 - + dgtu212*gtu32*PDstandardNth1gt22 - dgtu332*gtu21*PDstandardNth1gt23 - dgtu322*gtu31*PDstandardNth1gt23 - + dgtu312*gtu32*PDstandardNth1gt23 - dgtu212*gtu33*PDstandardNth1gt23 - dgtu332*gtu31*PDstandardNth1gt33 - + dgtu312*gtu33*PDstandardNth1gt33 - PDstandardNth12gt13*SQR(gtu31); + + ddgtu2212 = -2*(gtu21*gtu22*PDstandardNth12gt12 + gtu21*gtu32*PDstandardNth12gt13 + gtu22*gtu32*PDstandardNth12gt23 + + dgtu212*gtu21*PDstandardNth1gt11 + dgtu222*gtu21*PDstandardNth1gt12 + dgtu212*gtu22*PDstandardNth1gt12 + + dgtu322*gtu21*PDstandardNth1gt13 + dgtu212*gtu32*PDstandardNth1gt13 + dgtu222*gtu22*PDstandardNth1gt22 + + dgtu322*gtu22*PDstandardNth1gt23 + dgtu222*gtu32*PDstandardNth1gt23 + dgtu322*gtu32*PDstandardNth1gt33) - + PDstandardNth12gt11*SQR(gtu21) - PDstandardNth12gt22*SQR(gtu22) - PDstandardNth12gt33*SQR(gtu32); + + ddgtu3212 = -(gtu21*gtu31*PDstandardNth12gt11) - gtu22*gtu31*PDstandardNth12gt12 - gtu21*gtu32*PDstandardNth12gt12 - + gtu31*gtu32*PDstandardNth12gt13 - gtu21*gtu33*PDstandardNth12gt13 - gtu22*gtu32*PDstandardNth12gt22 - + gtu22*gtu33*PDstandardNth12gt23 - gtu32*gtu33*PDstandardNth12gt33 - dgtu312*gtu21*PDstandardNth1gt11 - + dgtu212*gtu31*PDstandardNth1gt11 - dgtu322*gtu21*PDstandardNth1gt12 - dgtu312*gtu22*PDstandardNth1gt12 - + dgtu222*gtu31*PDstandardNth1gt12 - dgtu212*gtu32*PDstandardNth1gt12 - dgtu332*gtu21*PDstandardNth1gt13 - + dgtu322*gtu31*PDstandardNth1gt13 - dgtu312*gtu32*PDstandardNth1gt13 - dgtu212*gtu33*PDstandardNth1gt13 - + dgtu322*gtu22*PDstandardNth1gt22 - dgtu222*gtu32*PDstandardNth1gt22 - dgtu332*gtu22*PDstandardNth1gt23 - + 2*dgtu322*gtu32*PDstandardNth1gt23 - dgtu222*gtu33*PDstandardNth1gt23 - dgtu332*gtu32*PDstandardNth1gt33 - + dgtu322*gtu33*PDstandardNth1gt33 - PDstandardNth12gt23*SQR(gtu32); + + ddgtu1113 = -2*(gtu11*gtu21*PDstandardNth13gt12 + gtu11*gtu31*PDstandardNth13gt13 + gtu21*gtu31*PDstandardNth13gt23 + + dgtu113*gtu11*PDstandardNth1gt11 + dgtu213*gtu11*PDstandardNth1gt12 + dgtu113*gtu21*PDstandardNth1gt12 + + dgtu313*gtu11*PDstandardNth1gt13 + dgtu113*gtu31*PDstandardNth1gt13 + dgtu213*gtu21*PDstandardNth1gt22 + + dgtu313*gtu21*PDstandardNth1gt23 + dgtu213*gtu31*PDstandardNth1gt23 + dgtu313*gtu31*PDstandardNth1gt33) - + PDstandardNth13gt11*SQR(gtu11) - PDstandardNth13gt22*SQR(gtu21) - PDstandardNth13gt33*SQR(gtu31); + + ddgtu2113 = -(gtu11*gtu21*PDstandardNth13gt11) - gtu11*gtu22*PDstandardNth13gt12 - gtu21*gtu31*PDstandardNth13gt13 - + gtu11*gtu32*PDstandardNth13gt13 - gtu21*gtu22*PDstandardNth13gt22 - gtu22*gtu31*PDstandardNth13gt23 - + gtu21*gtu32*PDstandardNth13gt23 - gtu31*gtu32*PDstandardNth13gt33 - dgtu213*gtu11*PDstandardNth1gt11 - + dgtu113*gtu21*PDstandardNth1gt11 - dgtu223*gtu11*PDstandardNth1gt12 - 2*dgtu213*gtu21*PDstandardNth1gt12 - + dgtu113*gtu22*PDstandardNth1gt12 - dgtu323*gtu11*PDstandardNth1gt13 - dgtu313*gtu21*PDstandardNth1gt13 - + dgtu213*gtu31*PDstandardNth1gt13 - dgtu113*gtu32*PDstandardNth1gt13 - dgtu223*gtu21*PDstandardNth1gt22 - + dgtu213*gtu22*PDstandardNth1gt22 - dgtu323*gtu21*PDstandardNth1gt23 - dgtu313*gtu22*PDstandardNth1gt23 - + dgtu223*gtu31*PDstandardNth1gt23 - dgtu213*gtu32*PDstandardNth1gt23 - dgtu323*gtu31*PDstandardNth1gt33 - + dgtu313*gtu32*PDstandardNth1gt33 - PDstandardNth13gt12*SQR(gtu21); + + ddgtu3113 = -(gtu11*gtu31*PDstandardNth13gt11) - gtu21*gtu31*PDstandardNth13gt12 - gtu11*gtu32*PDstandardNth13gt12 - + gtu11*gtu33*PDstandardNth13gt13 - gtu21*gtu32*PDstandardNth13gt22 - gtu31*gtu32*PDstandardNth13gt23 - + gtu21*gtu33*PDstandardNth13gt23 - gtu31*gtu33*PDstandardNth13gt33 - dgtu313*gtu11*PDstandardNth1gt11 - + dgtu113*gtu31*PDstandardNth1gt11 - dgtu323*gtu11*PDstandardNth1gt12 - dgtu313*gtu21*PDstandardNth1gt12 - + dgtu213*gtu31*PDstandardNth1gt12 - dgtu113*gtu32*PDstandardNth1gt12 - dgtu333*gtu11*PDstandardNth1gt13 - + 2*dgtu313*gtu31*PDstandardNth1gt13 - dgtu113*gtu33*PDstandardNth1gt13 - dgtu323*gtu21*PDstandardNth1gt22 - + dgtu213*gtu32*PDstandardNth1gt22 - dgtu333*gtu21*PDstandardNth1gt23 - dgtu323*gtu31*PDstandardNth1gt23 - + dgtu313*gtu32*PDstandardNth1gt23 - dgtu213*gtu33*PDstandardNth1gt23 - dgtu333*gtu31*PDstandardNth1gt33 - + dgtu313*gtu33*PDstandardNth1gt33 - PDstandardNth13gt13*SQR(gtu31); + + ddgtu3213 = -(gtu21*gtu31*PDstandardNth13gt11) - gtu22*gtu31*PDstandardNth13gt12 - gtu21*gtu32*PDstandardNth13gt12 - + gtu31*gtu32*PDstandardNth13gt13 - gtu21*gtu33*PDstandardNth13gt13 - gtu22*gtu32*PDstandardNth13gt22 - + gtu22*gtu33*PDstandardNth13gt23 - gtu32*gtu33*PDstandardNth13gt33 - dgtu313*gtu21*PDstandardNth1gt11 - + dgtu213*gtu31*PDstandardNth1gt11 - dgtu323*gtu21*PDstandardNth1gt12 - dgtu313*gtu22*PDstandardNth1gt12 - + dgtu223*gtu31*PDstandardNth1gt12 - dgtu213*gtu32*PDstandardNth1gt12 - dgtu333*gtu21*PDstandardNth1gt13 - + dgtu323*gtu31*PDstandardNth1gt13 - dgtu313*gtu32*PDstandardNth1gt13 - dgtu213*gtu33*PDstandardNth1gt13 - + dgtu323*gtu22*PDstandardNth1gt22 - dgtu223*gtu32*PDstandardNth1gt22 - dgtu333*gtu22*PDstandardNth1gt23 - + 2*dgtu323*gtu32*PDstandardNth1gt23 - dgtu223*gtu33*PDstandardNth1gt23 - dgtu333*gtu32*PDstandardNth1gt33 - + dgtu323*gtu33*PDstandardNth1gt33 - PDstandardNth13gt23*SQR(gtu32); + + ddgtu3313 = -2*(gtu31*gtu32*PDstandardNth13gt12 + gtu31*gtu33*PDstandardNth13gt13 + gtu32*gtu33*PDstandardNth13gt23 + + dgtu313*gtu31*PDstandardNth1gt11 + dgtu323*gtu31*PDstandardNth1gt12 + dgtu313*gtu32*PDstandardNth1gt12 + + dgtu333*gtu31*PDstandardNth1gt13 + dgtu313*gtu33*PDstandardNth1gt13 + dgtu323*gtu32*PDstandardNth1gt22 + + dgtu333*gtu32*PDstandardNth1gt23 + dgtu323*gtu33*PDstandardNth1gt23 + dgtu333*gtu33*PDstandardNth1gt33) - + PDstandardNth13gt11*SQR(gtu31) - PDstandardNth13gt22*SQR(gtu32) - PDstandardNth13gt33*SQR(gtu33); + + ddgtu2122 = -(gtu11*gtu21*PDstandardNth22gt11) - gtu11*gtu22*PDstandardNth22gt12 - gtu21*gtu31*PDstandardNth22gt13 - + gtu11*gtu32*PDstandardNth22gt13 - gtu21*gtu22*PDstandardNth22gt22 - gtu22*gtu31*PDstandardNth22gt23 - + gtu21*gtu32*PDstandardNth22gt23 - gtu31*gtu32*PDstandardNth22gt33 - dgtu212*gtu11*PDstandardNth2gt11 - + dgtu112*gtu21*PDstandardNth2gt11 - dgtu222*gtu11*PDstandardNth2gt12 - 2*dgtu212*gtu21*PDstandardNth2gt12 - + dgtu112*gtu22*PDstandardNth2gt12 - dgtu322*gtu11*PDstandardNth2gt13 - dgtu312*gtu21*PDstandardNth2gt13 - + dgtu212*gtu31*PDstandardNth2gt13 - dgtu112*gtu32*PDstandardNth2gt13 - dgtu222*gtu21*PDstandardNth2gt22 - + dgtu212*gtu22*PDstandardNth2gt22 - dgtu322*gtu21*PDstandardNth2gt23 - dgtu312*gtu22*PDstandardNth2gt23 - + dgtu222*gtu31*PDstandardNth2gt23 - dgtu212*gtu32*PDstandardNth2gt23 - dgtu322*gtu31*PDstandardNth2gt33 - + dgtu312*gtu32*PDstandardNth2gt33 - PDstandardNth22gt12*SQR(gtu21); + + ddgtu2222 = -2*(gtu21*gtu22*PDstandardNth22gt12 + gtu21*gtu32*PDstandardNth22gt13 + gtu22*gtu32*PDstandardNth22gt23 + + dgtu212*gtu21*PDstandardNth2gt11 + dgtu222*gtu21*PDstandardNth2gt12 + dgtu212*gtu22*PDstandardNth2gt12 + + dgtu322*gtu21*PDstandardNth2gt13 + dgtu212*gtu32*PDstandardNth2gt13 + dgtu222*gtu22*PDstandardNth2gt22 + + dgtu322*gtu22*PDstandardNth2gt23 + dgtu222*gtu32*PDstandardNth2gt23 + dgtu322*gtu32*PDstandardNth2gt33) - + PDstandardNth22gt11*SQR(gtu21) - PDstandardNth22gt22*SQR(gtu22) - PDstandardNth22gt33*SQR(gtu32); + + ddgtu3222 = -(gtu21*gtu31*PDstandardNth22gt11) - gtu22*gtu31*PDstandardNth22gt12 - gtu21*gtu32*PDstandardNth22gt12 - + gtu31*gtu32*PDstandardNth22gt13 - gtu21*gtu33*PDstandardNth22gt13 - gtu22*gtu32*PDstandardNth22gt22 - + gtu22*gtu33*PDstandardNth22gt23 - gtu32*gtu33*PDstandardNth22gt33 - dgtu312*gtu21*PDstandardNth2gt11 - + dgtu212*gtu31*PDstandardNth2gt11 - dgtu322*gtu21*PDstandardNth2gt12 - dgtu312*gtu22*PDstandardNth2gt12 - + dgtu222*gtu31*PDstandardNth2gt12 - dgtu212*gtu32*PDstandardNth2gt12 - dgtu332*gtu21*PDstandardNth2gt13 - + dgtu322*gtu31*PDstandardNth2gt13 - dgtu312*gtu32*PDstandardNth2gt13 - dgtu212*gtu33*PDstandardNth2gt13 - + dgtu322*gtu22*PDstandardNth2gt22 - dgtu222*gtu32*PDstandardNth2gt22 - dgtu332*gtu22*PDstandardNth2gt23 - + 2*dgtu322*gtu32*PDstandardNth2gt23 - dgtu222*gtu33*PDstandardNth2gt23 - dgtu332*gtu32*PDstandardNth2gt33 - + dgtu322*gtu33*PDstandardNth2gt33 - PDstandardNth22gt23*SQR(gtu32); + + ddgtu2123 = -(gtu11*gtu21*PDstandardNth23gt11) - gtu11*gtu22*PDstandardNth23gt12 - gtu21*gtu31*PDstandardNth23gt13 - + gtu11*gtu32*PDstandardNth23gt13 - gtu21*gtu22*PDstandardNth23gt22 - gtu22*gtu31*PDstandardNth23gt23 - + gtu21*gtu32*PDstandardNth23gt23 - gtu31*gtu32*PDstandardNth23gt33 - dgtu213*gtu11*PDstandardNth2gt11 - + dgtu113*gtu21*PDstandardNth2gt11 - dgtu223*gtu11*PDstandardNth2gt12 - 2*dgtu213*gtu21*PDstandardNth2gt12 - + dgtu113*gtu22*PDstandardNth2gt12 - dgtu323*gtu11*PDstandardNth2gt13 - dgtu313*gtu21*PDstandardNth2gt13 - + dgtu213*gtu31*PDstandardNth2gt13 - dgtu113*gtu32*PDstandardNth2gt13 - dgtu223*gtu21*PDstandardNth2gt22 - + dgtu213*gtu22*PDstandardNth2gt22 - dgtu323*gtu21*PDstandardNth2gt23 - dgtu313*gtu22*PDstandardNth2gt23 - + dgtu223*gtu31*PDstandardNth2gt23 - dgtu213*gtu32*PDstandardNth2gt23 - dgtu323*gtu31*PDstandardNth2gt33 - + dgtu313*gtu32*PDstandardNth2gt33 - PDstandardNth23gt12*SQR(gtu21); + + ddgtu3123 = -(gtu11*gtu31*PDstandardNth23gt11) - gtu21*gtu31*PDstandardNth23gt12 - gtu11*gtu32*PDstandardNth23gt12 - + gtu11*gtu33*PDstandardNth23gt13 - gtu21*gtu32*PDstandardNth23gt22 - gtu31*gtu32*PDstandardNth23gt23 - + gtu21*gtu33*PDstandardNth23gt23 - gtu31*gtu33*PDstandardNth23gt33 - dgtu313*gtu11*PDstandardNth2gt11 - + dgtu113*gtu31*PDstandardNth2gt11 - dgtu323*gtu11*PDstandardNth2gt12 - dgtu313*gtu21*PDstandardNth2gt12 - + dgtu213*gtu31*PDstandardNth2gt12 - dgtu113*gtu32*PDstandardNth2gt12 - dgtu333*gtu11*PDstandardNth2gt13 - + 2*dgtu313*gtu31*PDstandardNth2gt13 - dgtu113*gtu33*PDstandardNth2gt13 - dgtu323*gtu21*PDstandardNth2gt22 - + dgtu213*gtu32*PDstandardNth2gt22 - dgtu333*gtu21*PDstandardNth2gt23 - dgtu323*gtu31*PDstandardNth2gt23 - + dgtu313*gtu32*PDstandardNth2gt23 - dgtu213*gtu33*PDstandardNth2gt23 - dgtu333*gtu31*PDstandardNth2gt33 - + dgtu313*gtu33*PDstandardNth2gt33 - PDstandardNth23gt13*SQR(gtu31); + + ddgtu2223 = -2*(gtu21*gtu22*PDstandardNth23gt12 + gtu21*gtu32*PDstandardNth23gt13 + gtu22*gtu32*PDstandardNth23gt23 + + dgtu213*gtu21*PDstandardNth2gt11 + dgtu223*gtu21*PDstandardNth2gt12 + dgtu213*gtu22*PDstandardNth2gt12 + + dgtu323*gtu21*PDstandardNth2gt13 + dgtu213*gtu32*PDstandardNth2gt13 + dgtu223*gtu22*PDstandardNth2gt22 + + dgtu323*gtu22*PDstandardNth2gt23 + dgtu223*gtu32*PDstandardNth2gt23 + dgtu323*gtu32*PDstandardNth2gt33) - + PDstandardNth23gt11*SQR(gtu21) - PDstandardNth23gt22*SQR(gtu22) - PDstandardNth23gt33*SQR(gtu32); + + ddgtu3223 = -(gtu21*gtu31*PDstandardNth23gt11) - gtu22*gtu31*PDstandardNth23gt12 - gtu21*gtu32*PDstandardNth23gt12 - + gtu31*gtu32*PDstandardNth23gt13 - gtu21*gtu33*PDstandardNth23gt13 - gtu22*gtu32*PDstandardNth23gt22 - + gtu22*gtu33*PDstandardNth23gt23 - gtu32*gtu33*PDstandardNth23gt33 - dgtu313*gtu21*PDstandardNth2gt11 - + dgtu213*gtu31*PDstandardNth2gt11 - dgtu323*gtu21*PDstandardNth2gt12 - dgtu313*gtu22*PDstandardNth2gt12 - + dgtu223*gtu31*PDstandardNth2gt12 - dgtu213*gtu32*PDstandardNth2gt12 - dgtu333*gtu21*PDstandardNth2gt13 - + dgtu323*gtu31*PDstandardNth2gt13 - dgtu313*gtu32*PDstandardNth2gt13 - dgtu213*gtu33*PDstandardNth2gt13 - + dgtu323*gtu22*PDstandardNth2gt22 - dgtu223*gtu32*PDstandardNth2gt22 - dgtu333*gtu22*PDstandardNth2gt23 - + 2*dgtu323*gtu32*PDstandardNth2gt23 - dgtu223*gtu33*PDstandardNth2gt23 - dgtu333*gtu32*PDstandardNth2gt33 - + dgtu323*gtu33*PDstandardNth2gt33 - PDstandardNth23gt23*SQR(gtu32); + + ddgtu3323 = -2*(gtu31*gtu32*PDstandardNth23gt12 + gtu31*gtu33*PDstandardNth23gt13 + gtu32*gtu33*PDstandardNth23gt23 + + dgtu313*gtu31*PDstandardNth2gt11 + dgtu323*gtu31*PDstandardNth2gt12 + dgtu313*gtu32*PDstandardNth2gt12 + + dgtu333*gtu31*PDstandardNth2gt13 + dgtu313*gtu33*PDstandardNth2gt13 + dgtu323*gtu32*PDstandardNth2gt22 + + dgtu333*gtu32*PDstandardNth2gt23 + dgtu323*gtu33*PDstandardNth2gt23 + dgtu333*gtu33*PDstandardNth2gt33) - + PDstandardNth23gt11*SQR(gtu31) - PDstandardNth23gt22*SQR(gtu32) - PDstandardNth23gt33*SQR(gtu33); + + ddgtu3133 = -(gtu11*gtu31*PDstandardNth33gt11) - gtu21*gtu31*PDstandardNth33gt12 - gtu11*gtu32*PDstandardNth33gt12 - + gtu11*gtu33*PDstandardNth33gt13 - gtu21*gtu32*PDstandardNth33gt22 - gtu31*gtu32*PDstandardNth33gt23 - + gtu21*gtu33*PDstandardNth33gt23 - gtu31*gtu33*PDstandardNth33gt33 - dgtu313*gtu11*PDstandardNth3gt11 - + dgtu113*gtu31*PDstandardNth3gt11 - dgtu323*gtu11*PDstandardNth3gt12 - dgtu313*gtu21*PDstandardNth3gt12 - + dgtu213*gtu31*PDstandardNth3gt12 - dgtu113*gtu32*PDstandardNth3gt12 - dgtu333*gtu11*PDstandardNth3gt13 - + 2*dgtu313*gtu31*PDstandardNth3gt13 - dgtu113*gtu33*PDstandardNth3gt13 - dgtu323*gtu21*PDstandardNth3gt22 - + dgtu213*gtu32*PDstandardNth3gt22 - dgtu333*gtu21*PDstandardNth3gt23 - dgtu323*gtu31*PDstandardNth3gt23 - + dgtu313*gtu32*PDstandardNth3gt23 - dgtu213*gtu33*PDstandardNth3gt23 - dgtu333*gtu31*PDstandardNth3gt33 - + dgtu313*gtu33*PDstandardNth3gt33 - PDstandardNth33gt13*SQR(gtu31); + + ddgtu3233 = -(gtu21*gtu31*PDstandardNth33gt11) - gtu22*gtu31*PDstandardNth33gt12 - gtu21*gtu32*PDstandardNth33gt12 - + gtu31*gtu32*PDstandardNth33gt13 - gtu21*gtu33*PDstandardNth33gt13 - gtu22*gtu32*PDstandardNth33gt22 - + gtu22*gtu33*PDstandardNth33gt23 - gtu32*gtu33*PDstandardNth33gt33 - dgtu313*gtu21*PDstandardNth3gt11 - + dgtu213*gtu31*PDstandardNth3gt11 - dgtu323*gtu21*PDstandardNth3gt12 - dgtu313*gtu22*PDstandardNth3gt12 - + dgtu223*gtu31*PDstandardNth3gt12 - dgtu213*gtu32*PDstandardNth3gt12 - dgtu333*gtu21*PDstandardNth3gt13 - + dgtu323*gtu31*PDstandardNth3gt13 - dgtu313*gtu32*PDstandardNth3gt13 - dgtu213*gtu33*PDstandardNth3gt13 - + dgtu323*gtu22*PDstandardNth3gt22 - dgtu223*gtu32*PDstandardNth3gt22 - dgtu333*gtu22*PDstandardNth3gt23 - + 2*dgtu323*gtu32*PDstandardNth3gt23 - dgtu223*gtu33*PDstandardNth3gt23 - dgtu333*gtu32*PDstandardNth3gt33 - + dgtu323*gtu33*PDstandardNth3gt33 - PDstandardNth33gt23*SQR(gtu32); + + ddgtu3333 = -2*(gtu31*gtu32*PDstandardNth33gt12 + gtu31*gtu33*PDstandardNth33gt13 + gtu32*gtu33*PDstandardNth33gt23 + + dgtu313*gtu31*PDstandardNth3gt11 + dgtu323*gtu31*PDstandardNth3gt12 + dgtu313*gtu32*PDstandardNth3gt12 + + dgtu333*gtu31*PDstandardNth3gt13 + dgtu313*gtu33*PDstandardNth3gt13 + dgtu323*gtu32*PDstandardNth3gt22 + + dgtu333*gtu32*PDstandardNth3gt23 + dgtu323*gtu33*PDstandardNth3gt23 + dgtu333*gtu33*PDstandardNth3gt33) - + PDstandardNth33gt11*SQR(gtu31) - PDstandardNth33gt22*SQR(gtu32) - PDstandardNth33gt33*SQR(gtu33); + + Gt111 = khalf*(gtu11*PDstandardNth1gt11 + 2*(gtu21*PDstandardNth1gt12 + gtu31*PDstandardNth1gt13) - + gtu21*PDstandardNth2gt11 - gtu31*PDstandardNth3gt11); + + Gt211 = khalf*(gtu21*PDstandardNth1gt11 + 2*(gtu22*PDstandardNth1gt12 + gtu32*PDstandardNth1gt13) - + gtu22*PDstandardNth2gt11 - gtu32*PDstandardNth3gt11); + + Gt311 = khalf*(gtu31*PDstandardNth1gt11 + 2*(gtu32*PDstandardNth1gt12 + gtu33*PDstandardNth1gt13) - + gtu32*PDstandardNth2gt11 - gtu33*PDstandardNth3gt11); + + Gt112 = khalf*(gtu21*PDstandardNth1gt22 + gtu11*PDstandardNth2gt11 + + gtu31*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); + + Gt212 = khalf*(gtu22*PDstandardNth1gt22 + gtu21*PDstandardNth2gt11 + + gtu32*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); + + Gt312 = khalf*(gtu32*PDstandardNth1gt22 + gtu31*PDstandardNth2gt11 + + gtu33*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); + + Gt113 = khalf*(gtu31*PDstandardNth1gt33 + gtu11*PDstandardNth3gt11 + + gtu21*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); + + Gt213 = khalf*(gtu32*PDstandardNth1gt33 + gtu21*PDstandardNth3gt11 + + gtu22*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); + + Gt313 = khalf*(gtu33*PDstandardNth1gt33 + gtu31*PDstandardNth3gt11 + + gtu32*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); + + Gt122 = khalf*(gtu11*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu21*PDstandardNth2gt22 + + gtu31*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); + + Gt222 = khalf*(gtu21*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu22*PDstandardNth2gt22 + + gtu32*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); + + Gt322 = khalf*(gtu31*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu32*PDstandardNth2gt22 + + gtu33*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); + + Gt123 = khalf*(gtu31*PDstandardNth2gt33 + gtu11*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu21*PDstandardNth3gt22); + + Gt223 = khalf*(gtu32*PDstandardNth2gt33 + gtu21*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu22*PDstandardNth3gt22); + + Gt323 = khalf*(gtu33*PDstandardNth2gt33 + gtu31*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu32*PDstandardNth3gt22); + + Gt133 = khalf*(-(gtu11*PDstandardNth1gt33) - gtu21*PDstandardNth2gt33 + 2*gtu11*PDstandardNth3gt13 + + 2*gtu21*PDstandardNth3gt23 + gtu31*PDstandardNth3gt33); + + Gt233 = khalf*(-(gtu21*PDstandardNth1gt33) - gtu22*PDstandardNth2gt33 + 2*gtu21*PDstandardNth3gt13 + + 2*gtu22*PDstandardNth3gt23 + gtu32*PDstandardNth3gt33); + + Gt333 = khalf*(-(gtu31*PDstandardNth1gt33) - gtu32*PDstandardNth2gt33 + 2*gtu31*PDstandardNth3gt13 + + 2*gtu32*PDstandardNth3gt23 + gtu33*PDstandardNth3gt33); + + Rt11 = -(gtu11*khalf*PDstandardNth11gt11) + gtu21* (2*Gt211*Gt212*gt22L + 4*Gt112*gt13L*Gt311 + 2*Gt113*gt11L*Gt312 + 2*gt13L*Gt312*Gt313 + 2*gt13L*Gt211*Gt322 + - 2*gt13L*Gt311*Gt323 + 2*Gt311*Gt312*gt33L - PDstandard4th12gt11) - gtu31*PDstandard4th13gt11 + - gt11L*PDstandard4th1Xt1 + gt12L*(4*Gt111*Gt212*gtu21 + 2*Gt211*Gt222*gtu21 + 2*Gt212*Gt222*gtu22 + - 4*Gt113*Gt211*gtu31 + 4*Gt113*Gt212*gtu32 + 4*Gt113*Gt213*gtu33 + PDstandard4th1Xt2) + + 2*gt13L*Gt311*Gt323 + 2*Gt311*Gt312*gt33L - PDstandardNth12gt11) - gtu31*PDstandardNth13gt11 + + gt11L*PDstandardNth1Xt1 + gt12L*(4*Gt111*Gt212*gtu21 + 2*Gt211*Gt222*gtu21 + 2*Gt212*Gt222*gtu22 + + 4*Gt113*Gt211*gtu31 + 4*Gt113*Gt212*gtu32 + 4*Gt113*Gt213*gtu33 + PDstandardNth1Xt2) + gt13L*(4*Gt111*Gt312*gtu21 + 2*Gt212*Gt312*gtu21 + 4*Gt112*Gt312*gtu22 + 4*Gt113*Gt311*gtu31 + - 4*Gt113*Gt312*gtu32 + 4*Gt113*Gt313*gtu33 + PDstandard4th1Xt3) - gtu22*khalf*PDstandard4th22gt11 - - gtu32*PDstandard4th23gt11 - gtu33*khalf*PDstandard4th33gt11 + + 4*Gt113*Gt312*gtu32 + 4*Gt113*Gt313*gtu33 + PDstandardNth1Xt3) - gtu22*khalf*PDstandardNth22gt11 - + gtu32*PDstandardNth23gt11 - gtu33*khalf*PDstandardNth33gt11 + Gt111*(6*Gt113*gt11L*gtu31 + 4*gt12L*Gt213*gtu31 + gt11L*Xt1L) + Gt211*(2*Gt112*gt11L*gtu11 + 4*Gt111*gt12L*gtu11 + 2*gt11L*Gt122*gtu21 + 2*gt11L*Gt123*gtu31 + gt12L*Xt1L) + Gt311*(4*Gt111*gt13L*gtu11 + 2*gt12L*Gt213*gtu11 + 2*gt13L*Gt313*gtu11 + 2*gt11L*Gt123*gtu21 + @@ -852,10 +852,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gt12L*gtu21*SQR(Gt212)) + gt22L*gtu33*SQR(Gt213) + gt33L*gtu11*SQR(Gt311) + gt33L*gtu22*SQR(Gt312) + 2*gt13L*gtu31*SQR(Gt313) + gt33L*gtu33*SQR(Gt313); - Rt12 = khalf*(-(gtu11*PDstandard4th11gt12) - 2*gtu21*PDstandard4th12gt12 - 2*gtu31*PDstandard4th13gt12 + - gt12L*PDstandard4th1Xt1 + gt22L*PDstandard4th1Xt2 + gt23L*PDstandard4th1Xt3 - gtu22*PDstandard4th22gt12 - - 2*gtu32*PDstandard4th23gt12 + gt11L*PDstandard4th2Xt1 + gt12L*PDstandard4th2Xt2 + gt13L*PDstandard4th2Xt3 - - gtu33*PDstandard4th33gt12 + (Gt111*gt12L + Gt211*gt22L + gt23L*Gt311)*Xt1L + + Rt12 = khalf*(-(gtu11*PDstandardNth11gt12) - 2*gtu21*PDstandardNth12gt12 - 2*gtu31*PDstandardNth13gt12 + + gt12L*PDstandardNth1Xt1 + gt22L*PDstandardNth1Xt2 + gt23L*PDstandardNth1Xt3 - gtu22*PDstandardNth22gt12 - + 2*gtu32*PDstandardNth23gt12 + gt11L*PDstandardNth2Xt1 + gt12L*PDstandardNth2Xt2 + gt13L*PDstandardNth2Xt3 - + gtu33*PDstandardNth33gt12 + (Gt111*gt12L + Gt211*gt22L + gt23L*Gt311)*Xt1L + (Gt112*gt11L + gt12L*Gt212 + gt13L*Gt312)*Xt1L + (Gt112*gt12L + Gt212*gt22L + gt23L*Gt312)*Xt2L + (gt11L*Gt122 + gt12L*Gt222 + gt13L*Gt322)*Xt2L + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt3L + (gt11L*Gt123 + gt12L*Gt223 + gt13L*Gt323)*Xt3L + @@ -904,10 +904,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal Gt112*(2*gt11L*Gt123 + Gt113*gt12L + gt12L*Gt223 + gt13L*Gt323) + gt12L*(Gt122*Gt213 + Gt123*(2*Gt212 + Gt313) + Gt223*(Gt222 + Gt323)) + Gt312*Gt323*gt33L + gt13L*SQR(Gt323))); - Rt13 = khalf*(-(gtu11*PDstandard4th11gt13) - 2*gtu21*PDstandard4th12gt13 - 2*gtu31*PDstandard4th13gt13 + - gt13L*PDstandard4th1Xt1 + gt23L*PDstandard4th1Xt2 + gt33L*PDstandard4th1Xt3 - gtu22*PDstandard4th22gt13 - - 2*gtu32*PDstandard4th23gt13 - gtu33*PDstandard4th33gt13 + gt11L*PDstandard4th3Xt1 + gt12L*PDstandard4th3Xt2 + - gt13L*PDstandard4th3Xt3 + (Gt113*gt11L + gt12L*Gt213 + gt13L*Gt313)*Xt1L + + Rt13 = khalf*(-(gtu11*PDstandardNth11gt13) - 2*gtu21*PDstandardNth12gt13 - 2*gtu31*PDstandardNth13gt13 + + gt13L*PDstandardNth1Xt1 + gt23L*PDstandardNth1Xt2 + gt33L*PDstandardNth1Xt3 - gtu22*PDstandardNth22gt13 - + 2*gtu32*PDstandardNth23gt13 - gtu33*PDstandardNth33gt13 + gt11L*PDstandardNth3Xt1 + gt12L*PDstandardNth3Xt2 + + gt13L*PDstandardNth3Xt3 + (Gt113*gt11L + gt12L*Gt213 + gt13L*Gt313)*Xt1L + (Gt111*gt13L + Gt211*gt23L + Gt311*gt33L)*Xt1L + (gt11L*Gt123 + gt12L*Gt223 + gt13L*Gt323)*Xt2L + (Gt112*gt13L + Gt212*gt23L + Gt312*gt33L)*Xt2L + (gt11L*Gt133 + gt12L*Gt233 + gt13L*Gt333)*Xt3L + (Gt113*gt13L + Gt213*gt23L + Gt313*gt33L)*Xt3L + @@ -957,18 +957,18 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gt13L*SQR(Gt333))); Rt22 = 4*(Gt122*gt12L*Gt212*gtu21 + Gt112*gt12L*Gt222*gtu21 + Gt122*gt12L*Gt222*gtu22 + Gt123*gt12L*Gt212*gtu31 + - Gt123*gt12L*Gt222*gtu32 + Gt123*gt12L*Gt223*gtu33) - gtu11*khalf*PDstandard4th11gt22 + + Gt123*gt12L*Gt222*gtu32 + Gt123*gt12L*Gt223*gtu33) - gtu11*khalf*PDstandardNth11gt22 + gtu21*(6*Gt212*Gt222*gt22L + 2*Gt122*gt23L*Gt311 + 2*Gt122*gt13L*Gt312 + 4*Gt222*gt23L*Gt312 + - 2*Gt113*gt12L*Gt322 + 2*gt23L*Gt312*Gt323 + 2*Gt312*Gt322*gt33L - PDstandard4th12gt22) + + 2*Gt113*gt12L*Gt322 + 2*gt23L*Gt312*Gt323 + 2*Gt312*Gt322*gt33L - PDstandardNth12gt22) + gtu31*(6*Gt212*Gt223*gt22L + 2*Gt123*gt13L*Gt312 + 2*Gt112*gt23L*Gt313 + 2*Gt113*gt12L*Gt323 + - 2*gt23L*Gt312*Gt333 + 2*Gt312*Gt323*gt33L - PDstandard4th13gt22) - gtu22*khalf*PDstandard4th22gt22 + + 2*gt23L*Gt312*Gt333 + 2*Gt312*Gt323*gt33L - PDstandardNth13gt22) - gtu22*khalf*PDstandardNth22gt22 + gtu32*(4*Gt122*gt12L*Gt223 + 2*Gt123*Gt212*gt22L + 2*gt12L*Gt133*Gt322 + 4*Gt223*gt23L*Gt322 + - 2*Gt123*gt12L*Gt323 + 4*Gt222*gt23L*Gt323 + 2*gt23L*Gt322*Gt333 + 2*Gt322*Gt323*gt33L - PDstandard4th23gt22) + - gt12L*(2*Gt111*Gt123*gtu31 + 4*Gt112*Gt223*gtu31 + 2*Gt113*Gt122*gtu32 + 2*Gt113*Gt123*gtu33 + PDstandard4th2Xt1) + - gt22L*(2*Gt122*Gt213*gtu32 + 6*Gt222*Gt223*gtu32 + 2*Gt123*Gt213*gtu33 + PDstandard4th2Xt2) + + 2*Gt123*gt12L*Gt323 + 4*Gt222*gt23L*Gt323 + 2*gt23L*Gt322*Gt333 + 2*Gt322*Gt323*gt33L - PDstandardNth23gt22) + + gt12L*(2*Gt111*Gt123*gtu31 + 4*Gt112*Gt223*gtu31 + 2*Gt113*Gt122*gtu32 + 2*Gt113*Gt123*gtu33 + PDstandardNth2Xt1) + + gt22L*(2*Gt122*Gt213*gtu32 + 6*Gt222*Gt223*gtu32 + 2*Gt123*Gt213*gtu33 + PDstandardNth2Xt2) + gt23L*(4*Gt212*Gt322*gtu21 + 2*Gt313*Gt322*gtu21 + 4*Gt222*Gt322*gtu22 + 2*Gt123*Gt311*gtu31 + 4*Gt212*Gt323*gtu31 + 2*Gt313*Gt323*gtu31 + 2*Gt122*Gt313*gtu32 + 2*Gt123*Gt313*gtu33 + 4*Gt223*Gt323*gtu33 + - 2*Gt323*Gt333*gtu33 + PDstandard4th2Xt3) - gtu33*khalf*PDstandard4th33gt22 + Gt212*gt22L*Xt1L + + 2*Gt323*Gt333*gtu33 + PDstandardNth2Xt3) - gtu33*khalf*PDstandardNth33gt22 + Gt212*gt22L*Xt1L + Gt112*(2*Gt111*gt12L*gtu11 + 4*gt12L*Gt212*gtu11 + 2*gt11L*Gt122*gtu21 + 2*Gt122*gt12L*gtu22 + 2*gt11L*Gt123*gtu31 + 2*Gt123*gt12L*gtu32 + gt12L*Xt1L) + Gt312*(2*Gt213*gt22L*gtu11 + 4*Gt212*gt23L*gtu11 + 2*gt23L*Gt313*gtu11 + 2*Gt123*gt12L*gtu21 + @@ -986,10 +986,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal 3*gt22L*gtu11*SQR(Gt212) + 3*gt22L*gtu22*SQR(Gt222) + 3*gt22L*gtu33*SQR(Gt223) + gt33L*gtu11*SQR(Gt312) + gt33L*gtu22*SQR(Gt322) + 2*gt23L*gtu32*SQR(Gt323) + gt33L*gtu33*SQR(Gt323); - Rt23 = khalf*(-(gtu11*PDstandard4th11gt23) - 2*gtu21*PDstandard4th12gt23 - 2*gtu31*PDstandard4th13gt23 - - gtu22*PDstandard4th22gt23 - 2*gtu32*PDstandard4th23gt23 + gt13L*PDstandard4th2Xt1 + gt23L*PDstandard4th2Xt2 + - gt33L*PDstandard4th2Xt3 - gtu33*PDstandard4th33gt23 + gt12L*PDstandard4th3Xt1 + gt22L*PDstandard4th3Xt2 + - gt23L*PDstandard4th3Xt3 + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt1L + + Rt23 = khalf*(-(gtu11*PDstandardNth11gt23) - 2*gtu21*PDstandardNth12gt23 - 2*gtu31*PDstandardNth13gt23 - + gtu22*PDstandardNth22gt23 - 2*gtu32*PDstandardNth23gt23 + gt13L*PDstandardNth2Xt1 + gt23L*PDstandardNth2Xt2 + + gt33L*PDstandardNth2Xt3 - gtu33*PDstandardNth33gt23 + gt12L*PDstandardNth3Xt1 + gt22L*PDstandardNth3Xt2 + + gt23L*PDstandardNth3Xt3 + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt1L + (Gt112*gt13L + Gt212*gt23L + Gt312*gt33L)*Xt1L + (Gt123*gt12L + Gt223*gt22L + gt23L*Gt323)*Xt2L + (Gt122*gt13L + Gt222*gt23L + Gt322*gt33L)*Xt2L + (gt12L*Gt133 + gt22L*Gt233 + gt23L*Gt333)*Xt3L + (Gt123*gt13L + Gt223*gt23L + Gt323*gt33L)*Xt3L + @@ -1040,16 +1040,16 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal Rt33 = 4*(Gt123*gt13L*Gt323*gtu22 + Gt223*gt23L*Gt323*gtu22 + Gt133*gt13L*Gt313*gtu31 + Gt233*gt23L*Gt313*gtu31 + Gt113*gt13L*Gt333*gtu31 + Gt133*gt13L*Gt323*gtu32 + Gt233*gt23L*Gt323*gtu32 + Gt123*gt13L*Gt333*gtu32 + Gt133*gt13L*Gt333*gtu33) + gtu21*(2*Gt212*Gt223*gt23L + 4*Gt123*gt13L*Gt313 + 4*Gt223*gt23L*Gt313 + - 4*Gt113*gt13L*Gt323 + 4*Gt213*gt23L*Gt323 + 2*Gt123*Gt311*gt33L - PDstandard4th12gt33) + - gtu31*(4*Gt213*gt23L*Gt333 + 2*Gt233*Gt312*gt33L + 6*Gt313*Gt333*gt33L - PDstandard4th13gt33) - - gtu22*khalf*PDstandard4th22gt33 + gtu32*(4*Gt223*gt23L*Gt333 + 2*Gt123*Gt313*gt33L + 6*Gt323*Gt333*gt33L - - PDstandard4th23gt33) - gtu33*khalf*PDstandard4th33gt33 + gt13L*PDstandard4th3Xt1 + gt23L*PDstandard4th3Xt2 + + 4*Gt113*gt13L*Gt323 + 4*Gt213*gt23L*Gt323 + 2*Gt123*Gt311*gt33L - PDstandardNth12gt33) + + gtu31*(4*Gt213*gt23L*Gt333 + 2*Gt233*Gt312*gt33L + 6*Gt313*Gt333*gt33L - PDstandardNth13gt33) - + gtu22*khalf*PDstandardNth22gt33 + gtu32*(4*Gt223*gt23L*Gt333 + 2*Gt123*Gt313*gt33L + 6*Gt323*Gt333*gt33L - + PDstandardNth23gt33) - gtu33*khalf*PDstandardNth33gt33 + gt13L*PDstandardNth3Xt1 + gt23L*PDstandardNth3Xt2 + gt33L*(2*Gt213*Gt322*gtu21 + 6*Gt313*Gt323*gtu21 + 2*Gt123*Gt312*gtu22 + 2*Gt133*Gt311*gtu31 + - 2*Gt133*Gt312*gtu32 + 2*Gt133*Gt313*gtu33 + PDstandard4th3Xt3) + Gt113*gt13L*Xt1L + Gt213*gt23L*Xt1L + + 2*Gt133*Gt312*gtu32 + 2*Gt133*Gt313*gtu33 + PDstandardNth3Xt3) + Gt113*gt13L*Xt1L + Gt213*gt23L*Xt1L + Gt313*gt33L*Xt1L + Gt123*gt13L*Xt2L + Gt223*gt23L*Xt2L + Gt323*gt33L*Xt2L + Gt133*gt13L*Xt3L + Gt333*gt33L*Xt3L + Gt233*(4*gt23L*Gt333*gtu33 + 2*Gt323*gt33L*gtu33 + gt23L*Xt3L) + gtu11*(2*Gt212*Gt213*gt23L + 4*Gt113*gt13L*Gt313 + 4*Gt213*gt23L*Gt313 + 2*Gt113*Gt311*gt33L + - 2*Gt213*Gt312*gt33L - khalf*PDstandard4th11gt33 + gt11L*SQR(Gt113)) + + 2*Gt213*Gt312*gt33L - khalf*PDstandardNth11gt33 + gt11L*SQR(Gt113)) + 2*(Gt111*Gt113*gt13L*gtu11 + Gt113*gt12L*Gt213*gtu11 + Gt112*gt13L*Gt213*gtu11 + Gt113*Gt211*gt23L*gtu11 + Gt113*gt11L*Gt123*gtu21 + Gt112*Gt113*gt13L*gtu21 + Gt111*Gt123*gt13L*gtu21 + Gt123*gt12L*Gt213*gtu21 + Gt122*gt13L*Gt213*gtu21 + Gt113*gt12L*Gt223*gtu21 + Gt112*gt13L*Gt223*gtu21 + Gt213*Gt223*gt22L*gtu21 + @@ -1067,82 +1067,82 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gt11L*gtu33*SQR(Gt133) + gt22L*gtu11*SQR(Gt213) + gt22L*gtu22*SQR(Gt223) + 2*gt23L*gtu32*SQR(Gt223) + gt22L*gtu33*SQR(Gt233) + 3*gt33L*gtu11*SQR(Gt313) + 3*gt33L*gtu22*SQR(Gt323) + 3*gt33L*gtu33*SQR(Gt333); - Rphi11 = 2*(-PDstandard4th11phi - gt11L*gtu11*PDstandard4th11phi - 2*gt11L*gtu21*PDstandard4th12phi - - 2*gt11L*gtu31*PDstandard4th13phi - gt11L*gtu22*PDstandard4th22phi - 2*gt11L*gtu32*PDstandard4th23phi - - gt11L*gtu33*PDstandard4th33phi + Gt311*PDstandard4th3phi + gt11L*Gt311*gtu11*PDstandard4th3phi + - 2*gt11L*Gt312*gtu21*PDstandard4th3phi + gt11L*Gt322*gtu22*PDstandard4th3phi + - 2*gt11L*Gt313*gtu31*PDstandard4th3phi + 2*gt11L*Gt323*gtu32*PDstandard4th3phi + - gt11L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + Rphi11 = 2*(-PDstandardNth11phi - gt11L*gtu11*PDstandardNth11phi - 2*gt11L*gtu21*PDstandardNth12phi - + 2*gt11L*gtu31*PDstandardNth13phi - gt11L*gtu22*PDstandardNth22phi - 2*gt11L*gtu32*PDstandardNth23phi - + gt11L*gtu33*PDstandardNth33phi + Gt311*PDstandardNth3phi + gt11L*Gt311*gtu11*PDstandardNth3phi + + 2*gt11L*Gt312*gtu21*PDstandardNth3phi + gt11L*Gt322*gtu22*PDstandardNth3phi + + 2*gt11L*Gt313*gtu31*PDstandardNth3phi + 2*gt11L*Gt323*gtu32*PDstandardNth3phi + + gt11L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt111 + Gt111*gt11L*gtu11 + 2*Gt112*gt11L*gtu21 + gt11L*Gt122*gtu22 + 2*Gt113*gt11L*gtu31 + - 2*gt11L*Gt123*gtu32 + gt11L*Gt133*gtu33 - 4*gt11L*gtu21*PDstandard4th2phi - 4*gt11L*gtu31*PDstandard4th3phi) + - PDstandard4th2phi*(Gt211 + gt11L*Gt211*gtu11 + + 2*gt11L*Gt123*gtu32 + gt11L*Gt133*gtu33 - 4*gt11L*gtu21*PDstandardNth2phi - 4*gt11L*gtu31*PDstandardNth3phi) + + PDstandardNth2phi*(Gt211 + gt11L*Gt211*gtu11 + gt11L*(2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt11L*gtu32*PDstandard4th3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandard4th1phi) - - 2*gt11L*gtu22*SQR(PDstandard4th2phi) - 2*gt11L*gtu33*SQR(PDstandard4th3phi)); - - Rphi12 = 2*(-(gt12L*gtu11*PDstandard4th11phi) - PDstandard4th12phi - 2*gt12L*gtu21*PDstandard4th12phi - - 2*gt12L*gtu31*PDstandard4th13phi - gt12L*gtu22*PDstandard4th22phi - 2*gt12L*gtu32*PDstandard4th23phi - - gt12L*gtu33*PDstandard4th33phi + Gt312*PDstandard4th3phi + gt12L*Gt311*gtu11*PDstandard4th3phi + - 2*gt12L*Gt312*gtu21*PDstandard4th3phi + gt12L*Gt322*gtu22*PDstandard4th3phi + - 2*gt12L*Gt313*gtu31*PDstandard4th3phi + 2*gt12L*Gt323*gtu32*PDstandard4th3phi + - gt12L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt11L*gtu32*PDstandardNth3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandardNth1phi) - + 2*gt11L*gtu22*SQR(PDstandardNth2phi) - 2*gt11L*gtu33*SQR(PDstandardNth3phi)); + + Rphi12 = 2*(-(gt12L*gtu11*PDstandardNth11phi) - PDstandardNth12phi - 2*gt12L*gtu21*PDstandardNth12phi - + 2*gt12L*gtu31*PDstandardNth13phi - gt12L*gtu22*PDstandardNth22phi - 2*gt12L*gtu32*PDstandardNth23phi - + gt12L*gtu33*PDstandardNth33phi + Gt312*PDstandardNth3phi + gt12L*Gt311*gtu11*PDstandardNth3phi + + 2*gt12L*Gt312*gtu21*PDstandardNth3phi + gt12L*Gt322*gtu22*PDstandardNth3phi + + 2*gt12L*Gt313*gtu31*PDstandardNth3phi + 2*gt12L*Gt323*gtu32*PDstandardNth3phi + + gt12L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt112 + Gt111*gt12L*gtu11 + 2*Gt112*gt12L*gtu21 + Gt122*gt12L*gtu22 + 2*Gt113*gt12L*gtu31 + - 2*Gt123*gt12L*gtu32 + gt12L*Gt133*gtu33 + (2 - 4*gt12L*gtu21)*PDstandard4th2phi - - 4*gt12L*gtu31*PDstandard4th3phi) + PDstandard4th2phi* + 2*Gt123*gt12L*gtu32 + gt12L*Gt133*gtu33 + (2 - 4*gt12L*gtu21)*PDstandardNth2phi - + 4*gt12L*gtu31*PDstandardNth3phi) + PDstandardNth2phi* (Gt212 + 2*gt12L*Gt212*gtu21 + gt12L*(Gt211*gtu11 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt12L*gtu32*PDstandard4th3phi) - 2*gt12L*gtu11*SQR(PDstandard4th1phi) - - 2*gt12L*gtu22*SQR(PDstandard4th2phi) - 2*gt12L*gtu33*SQR(PDstandard4th3phi)); - - Rphi13 = 2*(-PDstandard4th13phi + gt13L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - - 2*gtu31*PDstandard4th13phi) - gt13L*gtu22*PDstandard4th22phi - 2*gt13L*gtu32*PDstandard4th23phi - - gt13L*gtu33*PDstandard4th33phi + Gt313*PDstandard4th3phi + gt13L*Gt311*gtu11*PDstandard4th3phi + - 2*gt13L*Gt312*gtu21*PDstandard4th3phi + gt13L*Gt322*gtu22*PDstandard4th3phi + - 2*gt13L*Gt313*gtu31*PDstandard4th3phi + 2*gt13L*Gt323*gtu32*PDstandard4th3phi + - gt13L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt12L*gtu32*PDstandardNth3phi) - 2*gt12L*gtu11*SQR(PDstandardNth1phi) - + 2*gt12L*gtu22*SQR(PDstandardNth2phi) - 2*gt12L*gtu33*SQR(PDstandardNth3phi)); + + Rphi13 = 2*(-PDstandardNth13phi + gt13L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - + 2*gtu31*PDstandardNth13phi) - gt13L*gtu22*PDstandardNth22phi - 2*gt13L*gtu32*PDstandardNth23phi - + gt13L*gtu33*PDstandardNth33phi + Gt313*PDstandardNth3phi + gt13L*Gt311*gtu11*PDstandardNth3phi + + 2*gt13L*Gt312*gtu21*PDstandardNth3phi + gt13L*Gt322*gtu22*PDstandardNth3phi + + 2*gt13L*Gt313*gtu31*PDstandardNth3phi + 2*gt13L*Gt323*gtu32*PDstandardNth3phi + + gt13L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt113 + Gt111*gt13L*gtu11 + 2*Gt112*gt13L*gtu21 + Gt122*gt13L*gtu22 + 2*Gt113*gt13L*gtu31 + - 2*Gt123*gt13L*gtu32 + Gt133*gt13L*gtu33 - 4*gt13L*gtu21*PDstandard4th2phi + - (2 - 4*gt13L*gtu31)*PDstandard4th3phi) + - PDstandard4th2phi*(Gt213 + 2*gt13L*Gt213*gtu31 + + 2*Gt123*gt13L*gtu32 + Gt133*gt13L*gtu33 - 4*gt13L*gtu21*PDstandardNth2phi + + (2 - 4*gt13L*gtu31)*PDstandardNth3phi) + + PDstandardNth2phi*(Gt213 + 2*gt13L*Gt213*gtu31 + gt13L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt13L*gtu32*PDstandard4th3phi) - 2*gt13L*gtu11*SQR(PDstandard4th1phi) - - 2*gt13L*gtu22*SQR(PDstandard4th2phi) - 2*gt13L*gtu33*SQR(PDstandard4th3phi)); - - Rphi22 = 2*(-PDstandard4th22phi + gt22L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - - 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi) - 2*gt22L*gtu32*PDstandard4th23phi - - gt22L*gtu33*PDstandard4th33phi + Gt322*PDstandard4th3phi + gt22L*Gt311*gtu11*PDstandard4th3phi + - 2*gt22L*Gt312*gtu21*PDstandard4th3phi + gt22L*Gt322*gtu22*PDstandard4th3phi + - 2*gt22L*Gt313*gtu31*PDstandard4th3phi + 2*gt22L*Gt323*gtu32*PDstandard4th3phi + - gt22L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt13L*gtu32*PDstandardNth3phi) - 2*gt13L*gtu11*SQR(PDstandardNth1phi) - + 2*gt13L*gtu22*SQR(PDstandardNth2phi) - 2*gt13L*gtu33*SQR(PDstandardNth3phi)); + + Rphi22 = 2*(-PDstandardNth22phi + gt22L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - + 2*gtu31*PDstandardNth13phi - gtu22*PDstandardNth22phi) - 2*gt22L*gtu32*PDstandardNth23phi - + gt22L*gtu33*PDstandardNth33phi + Gt322*PDstandardNth3phi + gt22L*Gt311*gtu11*PDstandardNth3phi + + 2*gt22L*Gt312*gtu21*PDstandardNth3phi + gt22L*Gt322*gtu22*PDstandardNth3phi + + 2*gt22L*Gt313*gtu31*PDstandardNth3phi + 2*gt22L*Gt323*gtu32*PDstandardNth3phi + + gt22L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt122 + Gt111*gt22L*gtu11 + 2*Gt112*gt22L*gtu21 + Gt122*gt22L*gtu22 + 2*Gt113*gt22L*gtu31 + - 2*Gt123*gt22L*gtu32 + Gt133*gt22L*gtu33 - 4*gt22L*gtu21*PDstandard4th2phi - 4*gt22L*gtu31*PDstandard4th3phi) + - PDstandard4th2phi*(Gt222 + Gt222*gt22L*gtu22 + + 2*Gt123*gt22L*gtu32 + Gt133*gt22L*gtu33 - 4*gt22L*gtu21*PDstandardNth2phi - 4*gt22L*gtu31*PDstandardNth3phi) + + PDstandardNth2phi*(Gt222 + Gt222*gt22L*gtu22 + gt22L*(Gt211*gtu11 + 2*Gt212*gtu21 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt22L*gtu32*PDstandard4th3phi) - 2*gt22L*gtu11*SQR(PDstandard4th1phi) + - (2 - 2*gt22L*gtu22)*SQR(PDstandard4th2phi) - 2*gt22L*gtu33*SQR(PDstandard4th3phi)); - - Rphi23 = 2*(-PDstandard4th23phi + gt23L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - - 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi) - - gt23L*gtu33*PDstandard4th33phi + Gt323*PDstandard4th3phi + gt23L*Gt311*gtu11*PDstandard4th3phi + - 2*gt23L*Gt312*gtu21*PDstandard4th3phi + gt23L*Gt322*gtu22*PDstandard4th3phi + - 2*gt23L*Gt313*gtu31*PDstandard4th3phi + 2*gt23L*Gt323*gtu32*PDstandard4th3phi + - gt23L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt22L*gtu32*PDstandardNth3phi) - 2*gt22L*gtu11*SQR(PDstandardNth1phi) + + (2 - 2*gt22L*gtu22)*SQR(PDstandardNth2phi) - 2*gt22L*gtu33*SQR(PDstandardNth3phi)); + + Rphi23 = 2*(-PDstandardNth23phi + gt23L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - + 2*gtu31*PDstandardNth13phi - gtu22*PDstandardNth22phi - 2*gtu32*PDstandardNth23phi) - + gt23L*gtu33*PDstandardNth33phi + Gt323*PDstandardNth3phi + gt23L*Gt311*gtu11*PDstandardNth3phi + + 2*gt23L*Gt312*gtu21*PDstandardNth3phi + gt23L*Gt322*gtu22*PDstandardNth3phi + + 2*gt23L*Gt313*gtu31*PDstandardNth3phi + 2*gt23L*Gt323*gtu32*PDstandardNth3phi + + gt23L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt123 + Gt111*gt23L*gtu11 + 2*Gt112*gt23L*gtu21 + Gt122*gt23L*gtu22 + 2*Gt113*gt23L*gtu31 + - 2*Gt123*gt23L*gtu32 + Gt133*gt23L*gtu33 - 4*gt23L*gtu21*PDstandard4th2phi - 4*gt23L*gtu31*PDstandard4th3phi) + - PDstandard4th2phi*(Gt223 + 2*Gt223*gt23L*gtu32 + + 2*Gt123*gt23L*gtu32 + Gt133*gt23L*gtu33 - 4*gt23L*gtu21*PDstandardNth2phi - 4*gt23L*gtu31*PDstandardNth3phi) + + PDstandardNth2phi*(Gt223 + 2*Gt223*gt23L*gtu32 + gt23L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + Gt233*gtu33) + - (2 - 4*gt23L*gtu32)*PDstandard4th3phi) - 2*gt23L*gtu11*SQR(PDstandard4th1phi) - - 2*gt23L*gtu22*SQR(PDstandard4th2phi) - 2*gt23L*gtu33*SQR(PDstandard4th3phi)); - - Rphi33 = 2*(-PDstandard4th33phi + (Gt333 + gt33L* - (Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33))*PDstandard4th3phi + - PDstandard4th2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + - Gt233*gtu33 - 4*gtu32*PDstandard4th3phi)) + - PDstandard4th1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + - Gt133*gtu33 - 4*(gtu21*PDstandard4th2phi + gtu31*PDstandard4th3phi))) + 2*SQR(PDstandard4th3phi) + - gt33L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 2*gtu31*PDstandard4th13phi - - gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi - gtu33*PDstandard4th33phi + - Gt311*gtu11*PDstandard4th3phi - 2*gtu11*SQR(PDstandard4th1phi) - 2*gtu22*SQR(PDstandard4th2phi) - - 2*gtu33*SQR(PDstandard4th3phi))); + (2 - 4*gt23L*gtu32)*PDstandardNth3phi) - 2*gt23L*gtu11*SQR(PDstandardNth1phi) - + 2*gt23L*gtu22*SQR(PDstandardNth2phi) - 2*gt23L*gtu33*SQR(PDstandardNth3phi)); + + Rphi33 = 2*(-PDstandardNth33phi + (Gt333 + gt33L* + (Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33))*PDstandardNth3phi + + PDstandardNth2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + + Gt233*gtu33 - 4*gtu32*PDstandardNth3phi)) + + PDstandardNth1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + + Gt133*gtu33 - 4*(gtu21*PDstandardNth2phi + gtu31*PDstandardNth3phi))) + 2*SQR(PDstandardNth3phi) + + gt33L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - 2*gtu31*PDstandardNth13phi - + gtu22*PDstandardNth22phi - 2*gtu32*PDstandardNth23phi - gtu33*PDstandardNth33phi + + Gt311*gtu11*PDstandardNth3phi - 2*gtu11*SQR(PDstandardNth1phi) - 2*gtu22*SQR(PDstandardNth2phi) - + 2*gtu33*SQR(PDstandardNth3phi))); Atm11 = At11L*gtu11 + At12L*gtu21 + At13L*gtu31; @@ -1204,11 +1204,11 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gu33 = em4phi*gtu33; - ddetg1 = e4phi*(ddetgt1 + 4*detgt*PDstandard4th1phi); + ddetg1 = e4phi*(ddetgt1 + 4*detgt*PDstandardNth1phi); - ddetg2 = e4phi*(ddetgt2 + 4*detgt*PDstandard4th2phi); + ddetg2 = e4phi*(ddetgt2 + 4*detgt*PDstandardNth2phi); - ddetg3 = e4phi*(ddetgt3 + 4*detgt*PDstandard4th3phi); + ddetg3 = e4phi*(ddetgt3 + 4*detgt*PDstandardNth3phi); G111 = -((-6*detg*Gt111 + ddetg1*(-6 + g11*gu11) + g11*(ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; @@ -1258,182 +1258,182 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal R33 = Rphi33 + Rt33; - phirhsL = beta1L*PDstandard4th1phi + beta2L*PDstandard4th2phi + beta3L*PDstandard4th3phi + - ((PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)*phiL)/6. - (alphaL*trKL)/6.; + phirhsL = beta1L*PDstandardNth1phi + beta2L*PDstandardNth2phi + beta3L*PDstandardNth3phi + + ((PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3)*phiL)/6. - (alphaL*trKL)/6.; - gt11rhsL = -2*alphaL*At11L + 2*(gt11L*PDstandard4th1beta1 + gt12L*PDstandard4th1beta2 + gt13L*PDstandard4th1beta3) + - beta1L*PDstandard4th1gt11 + beta2L*PDstandard4th2gt11 - - gt11L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + beta3L*PDstandard4th3gt11; + gt11rhsL = -2*alphaL*At11L + 2*(gt11L*PDstandardNth1beta1 + gt12L*PDstandardNth1beta2 + gt13L*PDstandardNth1beta3) + + beta1L*PDstandardNth1gt11 + beta2L*PDstandardNth2gt11 - + gt11L*ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3) + beta3L*PDstandardNth3gt11; - gt12rhsL = -2*alphaL*At12L + gt22L*PDstandard4th1beta2 + gt23L*PDstandard4th1beta3 + beta1L*PDstandard4th1gt12 + - gt11L*PDstandard4th2beta1 + gt13L*PDstandard4th2beta3 + beta2L*PDstandard4th2gt12 + - gt12L*(kthird*(PDstandard4th1beta1 + PDstandard4th2beta2) - ktwothird*PDstandard4th3beta3) + - beta3L*PDstandard4th3gt12; + gt12rhsL = -2*alphaL*At12L + gt22L*PDstandardNth1beta2 + gt23L*PDstandardNth1beta3 + beta1L*PDstandardNth1gt12 + + gt11L*PDstandardNth2beta1 + gt13L*PDstandardNth2beta3 + beta2L*PDstandardNth2gt12 + + gt12L*(kthird*(PDstandardNth1beta1 + PDstandardNth2beta2) - ktwothird*PDstandardNth3beta3) + + beta3L*PDstandardNth3gt12; - gt13rhsL = -2*alphaL*At13L + gt23L*PDstandard4th1beta2 + gt33L*PDstandard4th1beta3 + beta1L*PDstandard4th1gt13 + - beta2L*PDstandard4th2gt13 + gt11L*PDstandard4th3beta1 + gt12L*PDstandard4th3beta2 + - gt13L*(-(ktwothird*PDstandard4th2beta2) + kthird*(PDstandard4th1beta1 + PDstandard4th3beta3)) + - beta3L*PDstandard4th3gt13; + gt13rhsL = -2*alphaL*At13L + gt23L*PDstandardNth1beta2 + gt33L*PDstandardNth1beta3 + beta1L*PDstandardNth1gt13 + + beta2L*PDstandardNth2gt13 + gt11L*PDstandardNth3beta1 + gt12L*PDstandardNth3beta2 + + gt13L*(-(ktwothird*PDstandardNth2beta2) + kthird*(PDstandardNth1beta1 + PDstandardNth3beta3)) + + beta3L*PDstandardNth3gt13; - gt22rhsL = -2*alphaL*At22L + beta1L*PDstandard4th1gt22 + - 2*(gt12L*PDstandard4th2beta1 + gt22L*PDstandard4th2beta2 + gt23L*PDstandard4th2beta3) + beta2L*PDstandard4th2gt22 - - gt22L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + beta3L*PDstandard4th3gt22; + gt22rhsL = -2*alphaL*At22L + beta1L*PDstandardNth1gt22 + + 2*(gt12L*PDstandardNth2beta1 + gt22L*PDstandardNth2beta2 + gt23L*PDstandardNth2beta3) + beta2L*PDstandardNth2gt22 - + gt22L*ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3) + beta3L*PDstandardNth3gt22; - gt23rhsL = -2*alphaL*At23L + beta1L*PDstandard4th1gt23 + gt13L*PDstandard4th2beta1 + gt33L*PDstandard4th2beta3 + - beta2L*PDstandard4th2gt23 + gt12L*PDstandard4th3beta1 + gt22L*PDstandard4th3beta2 + - gt23L*(-(ktwothird*PDstandard4th1beta1) + kthird*(PDstandard4th2beta2 + PDstandard4th3beta3)) + - beta3L*PDstandard4th3gt23; + gt23rhsL = -2*alphaL*At23L + beta1L*PDstandardNth1gt23 + gt13L*PDstandardNth2beta1 + gt33L*PDstandardNth2beta3 + + beta2L*PDstandardNth2gt23 + gt12L*PDstandardNth3beta1 + gt22L*PDstandardNth3beta2 + + gt23L*(-(ktwothird*PDstandardNth1beta1) + kthird*(PDstandardNth2beta2 + PDstandardNth3beta3)) + + beta3L*PDstandardNth3gt23; - gt33rhsL = -2*alphaL*At33L + beta1L*PDstandard4th1gt33 + beta2L*PDstandard4th2gt33 - - gt33L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + - 2*(gt13L*PDstandard4th3beta1 + gt23L*PDstandard4th3beta2 + gt33L*PDstandard4th3beta3) + beta3L*PDstandard4th3gt33; + gt33rhsL = -2*alphaL*At33L + beta1L*PDstandardNth1gt33 + beta2L*PDstandardNth2gt33 - + gt33L*ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3) + + 2*(gt13L*PDstandardNth3beta1 + gt23L*PDstandardNth3beta2 + gt33L*PDstandardNth3beta3) + beta3L*PDstandardNth3gt33; Xt1rhsL = kthird*(-3*(beta1L*(ddgtu1111 + ddgtu2112 + ddgtu3113) + beta2L*(ddgtu1112 + ddgtu2122 + ddgtu3123) + - beta3L*(ddgtu1113 + ddgtu2123 + ddgtu3133)) + 16*(gtu21*PDstandard4th12beta1 + gtu31*PDstandard4th13beta1) + - (7*dgtu111 + 4*(dgtu212 + dgtu313))*PDstandard4th1beta1 + - gtu11*(10*PDstandard4th11beta1 + 4*(PDstandard4th12beta2 + PDstandard4th13beta3) - 4*alphaL*PDstandard4th1trK) + - 12*gtu32*PDstandard4th23beta1 + (9*dgtu211 + 6*dgtu323)*PDstandard4th2beta1 + - (dgtu212 - 2*(dgtu111 + dgtu313))*PDstandard4th2beta2 + - 4*(gtu21*(PDstandard4th22beta2 + PDstandard4th23beta3) + gtu31*(PDstandard4th23beta2 + PDstandard4th33beta3)) - - 6*(Atu11*PDstandard4th1alpha + Atu21*PDstandard4th2alpha + Atu31*PDstandard4th3alpha) + - (9*dgtu311 + 6*dgtu333)*PDstandard4th3beta1 + - 6*(gtu22*PDstandard4th22beta1 + dgtu222*PDstandard4th2beta1 + gtu33*PDstandard4th33beta1 + - dgtu322*PDstandard4th3beta1) + 3*(dgtu112*PDstandard4th1beta2 + dgtu113*PDstandard4th1beta3 + - dgtu213*PDstandard4th2beta3 + dgtu312*PDstandard4th3beta2) + - (-2*(dgtu111 + dgtu212) + dgtu313)*PDstandard4th3beta3 + + beta3L*(ddgtu1113 + ddgtu2123 + ddgtu3133)) + 16*(gtu21*PDstandardNth12beta1 + gtu31*PDstandardNth13beta1) + + (7*dgtu111 + 4*(dgtu212 + dgtu313))*PDstandardNth1beta1 + + gtu11*(10*PDstandardNth11beta1 + 4*(PDstandardNth12beta2 + PDstandardNth13beta3) - 4*alphaL*PDstandardNth1trK) + + 12*gtu32*PDstandardNth23beta1 + (9*dgtu211 + 6*dgtu323)*PDstandardNth2beta1 + + (dgtu212 - 2*(dgtu111 + dgtu313))*PDstandardNth2beta2 + + 4*(gtu21*(PDstandardNth22beta2 + PDstandardNth23beta3) + gtu31*(PDstandardNth23beta2 + PDstandardNth33beta3)) - + 6*(Atu11*PDstandardNth1alpha + Atu21*PDstandardNth2alpha + Atu31*PDstandardNth3alpha) + + (9*dgtu311 + 6*dgtu333)*PDstandardNth3beta1 + + 6*(gtu22*PDstandardNth22beta1 + dgtu222*PDstandardNth2beta1 + gtu33*PDstandardNth33beta1 + + dgtu322*PDstandardNth3beta1) + 3*(dgtu112*PDstandardNth1beta2 + dgtu113*PDstandardNth1beta3 + + dgtu213*PDstandardNth2beta3 + dgtu312*PDstandardNth3beta2) + + (-2*(dgtu111 + dgtu212) + dgtu313)*PDstandardNth3beta3 + alphaL*(12*(Atu21*Gt112 + Atu31*Gt113 + Atu32*Gt123) + 6*(Atu11*Gt111 + Atu22*Gt122 + Atu33*Gt133) + - 36*(Atu11*PDstandard4th1phi + Atu21*PDstandard4th2phi + Atu31*PDstandard4th3phi) - - 4*(gtu21*PDstandard4th2trK + gtu31*PDstandard4th3trK))); + 36*(Atu11*PDstandardNth1phi + Atu21*PDstandardNth2phi + Atu31*PDstandardNth3phi) - + 4*(gtu21*PDstandardNth2trK + gtu31*PDstandardNth3trK))); Xt2rhsL = kthird*(-3*(beta1L*(ddgtu2111 + ddgtu2212 + ddgtu3213) + beta2L*(ddgtu2112 + ddgtu2222 + ddgtu3223) + - beta3L*(ddgtu2113 + ddgtu2223 + ddgtu3233)) + 12*gtu31*PDstandard4th13beta2 + - (dgtu211 - 2*(dgtu222 + dgtu323))*PDstandard4th1beta1 + (9*dgtu212 + 6*dgtu313)*PDstandard4th1beta2 + - gtu21*(16*PDstandard4th12beta2 + 4*PDstandard4th13beta3 - 4*alphaL*PDstandard4th1trK) + - (7*dgtu222 + 4*dgtu323)*PDstandard4th2beta2 + - 4*(gtu21*PDstandard4th11beta1 + gtu32*PDstandard4th13beta1 + - gtu22*(PDstandard4th12beta1 + PDstandard4th23beta3) + dgtu211*PDstandard4th2beta2) + - gtu22*(10*PDstandard4th22beta2 - 4*alphaL*PDstandard4th2trK) - - 6*(Atu21*PDstandard4th1alpha + Atu22*PDstandard4th2alpha + Atu32*PDstandard4th3alpha) + - 3*(dgtu213*PDstandard4th1beta3 + dgtu221*PDstandard4th2beta1 + dgtu223*PDstandard4th2beta3 + - dgtu321*PDstandard4th3beta1) + (9*dgtu322 + 6*dgtu333)*PDstandard4th3beta2 + - 6*(gtu11*PDstandard4th11beta2 + dgtu111*PDstandard4th1beta2 + gtu33*PDstandard4th33beta2 + - dgtu311*PDstandard4th3beta2) + (-2*(dgtu211 + dgtu222) + dgtu323)*PDstandard4th3beta3 + + beta3L*(ddgtu2113 + ddgtu2223 + ddgtu3233)) + 12*gtu31*PDstandardNth13beta2 + + (dgtu211 - 2*(dgtu222 + dgtu323))*PDstandardNth1beta1 + (9*dgtu212 + 6*dgtu313)*PDstandardNth1beta2 + + gtu21*(16*PDstandardNth12beta2 + 4*PDstandardNth13beta3 - 4*alphaL*PDstandardNth1trK) + + (7*dgtu222 + 4*dgtu323)*PDstandardNth2beta2 + + 4*(gtu21*PDstandardNth11beta1 + gtu32*PDstandardNth13beta1 + + gtu22*(PDstandardNth12beta1 + PDstandardNth23beta3) + dgtu211*PDstandardNth2beta2) + + gtu22*(10*PDstandardNth22beta2 - 4*alphaL*PDstandardNth2trK) - + 6*(Atu21*PDstandardNth1alpha + Atu22*PDstandardNth2alpha + Atu32*PDstandardNth3alpha) + + 3*(dgtu213*PDstandardNth1beta3 + dgtu221*PDstandardNth2beta1 + dgtu223*PDstandardNth2beta3 + + dgtu321*PDstandardNth3beta1) + (9*dgtu322 + 6*dgtu333)*PDstandardNth3beta2 + + 6*(gtu11*PDstandardNth11beta2 + dgtu111*PDstandardNth1beta2 + gtu33*PDstandardNth33beta2 + + dgtu311*PDstandardNth3beta2) + (-2*(dgtu211 + dgtu222) + dgtu323)*PDstandardNth3beta3 + alphaL*(12*(Atu21*Gt212 + Atu31*Gt213 + Atu32*Gt223) + 6*(Atu11*Gt211 + Atu22*Gt222 + Atu33*Gt233) + - 36*(Atu21*PDstandard4th1phi + Atu22*PDstandard4th2phi + Atu32*PDstandard4th3phi)) + - gtu32*(16*PDstandard4th23beta2 + 4*PDstandard4th33beta3 - 4*alphaL*PDstandard4th3trK)); + 36*(Atu21*PDstandardNth1phi + Atu22*PDstandardNth2phi + Atu32*PDstandardNth3phi)) + + gtu32*(16*PDstandardNth23beta2 + 4*PDstandardNth33beta3 - 4*alphaL*PDstandardNth3trK)); Xt3rhsL = kthird*(-3*(beta1L*(ddgtu3111 + ddgtu3212 + ddgtu3313) + beta2L*(ddgtu3112 + ddgtu3222 + ddgtu3323) + - beta3L*(ddgtu3113 + ddgtu3223 + ddgtu3333)) + 12*gtu21*PDstandard4th12beta3 + - (dgtu311 - 2*(dgtu322 + dgtu333))*PDstandard4th1beta1 + (6*dgtu212 + 9*dgtu313)*PDstandard4th1beta3 + - gtu31*(16*PDstandard4th13beta3 - 4*alphaL*PDstandard4th1trK) + - (dgtu322 - 2*(dgtu311 + dgtu333))*PDstandard4th2beta2 + (6*dgtu222 + 9*dgtu323)*PDstandard4th2beta3 + - 6*(gtu11*PDstandard4th11beta3 + dgtu111*PDstandard4th1beta3 + gtu22*PDstandard4th22beta3 + - dgtu211*PDstandard4th2beta3) + gtu32*(16*PDstandard4th23beta3 - 4*alphaL*PDstandard4th2trK) - - 6*(Atu31*PDstandard4th1alpha + Atu32*PDstandard4th2alpha + Atu33*PDstandard4th3alpha) + - 3*(dgtu312*PDstandard4th1beta2 + dgtu321*PDstandard4th2beta1 + dgtu331*PDstandard4th3beta1 + - dgtu332*PDstandard4th3beta2) + (4*dgtu322 + 7*dgtu333)*PDstandard4th3beta3 + - 4*(gtu31*(PDstandard4th11beta1 + PDstandard4th12beta2) + gtu32*(PDstandard4th12beta1 + PDstandard4th22beta2) + - gtu33*(PDstandard4th13beta1 + PDstandard4th23beta2) + dgtu311*PDstandard4th3beta3) + + beta3L*(ddgtu3113 + ddgtu3223 + ddgtu3333)) + 12*gtu21*PDstandardNth12beta3 + + (dgtu311 - 2*(dgtu322 + dgtu333))*PDstandardNth1beta1 + (6*dgtu212 + 9*dgtu313)*PDstandardNth1beta3 + + gtu31*(16*PDstandardNth13beta3 - 4*alphaL*PDstandardNth1trK) + + (dgtu322 - 2*(dgtu311 + dgtu333))*PDstandardNth2beta2 + (6*dgtu222 + 9*dgtu323)*PDstandardNth2beta3 + + 6*(gtu11*PDstandardNth11beta3 + dgtu111*PDstandardNth1beta3 + gtu22*PDstandardNth22beta3 + + dgtu211*PDstandardNth2beta3) + gtu32*(16*PDstandardNth23beta3 - 4*alphaL*PDstandardNth2trK) - + 6*(Atu31*PDstandardNth1alpha + Atu32*PDstandardNth2alpha + Atu33*PDstandardNth3alpha) + + 3*(dgtu312*PDstandardNth1beta2 + dgtu321*PDstandardNth2beta1 + dgtu331*PDstandardNth3beta1 + + dgtu332*PDstandardNth3beta2) + (4*dgtu322 + 7*dgtu333)*PDstandardNth3beta3 + + 4*(gtu31*(PDstandardNth11beta1 + PDstandardNth12beta2) + gtu32*(PDstandardNth12beta1 + PDstandardNth22beta2) + + gtu33*(PDstandardNth13beta1 + PDstandardNth23beta2) + dgtu311*PDstandardNth3beta3) + alphaL*(12*(Atu21*Gt312 + Atu31*Gt313 + Atu32*Gt323) + 6*(Atu11*Gt311 + Atu22*Gt322 + Atu33*Gt333) + - 36*(Atu31*PDstandard4th1phi + Atu32*PDstandard4th2phi + Atu33*PDstandard4th3phi)) + - gtu33*(10*PDstandard4th33beta3 - 4*alphaL*PDstandard4th3trK)); - - trKrhsL = -(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - 2*gu31*PDstandard4th13alpha + - (G111*gu11 + 2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33)*PDstandard4th1alpha + - beta1L*PDstandard4th1trK - gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha + - (G211*gu11 + 2*G212*gu21 + G222*gu22 + 2*G213*gu31 + 2*G223*gu32 + G233*gu33)*PDstandard4th2alpha + - beta2L*PDstandard4th2trK - gu33*PDstandard4th33alpha + G311*gu11*PDstandard4th3alpha + - G322*gu22*PDstandard4th3alpha + 2*G313*gu31*PDstandard4th3alpha + 2*G323*gu32*PDstandard4th3alpha + - G333*gu33*PDstandard4th3alpha + 2*(alphaL*Atm12*Atm21 + alphaL*Atm13*Atm31 + alphaL*Atm23*Atm32 + - G312*gu21*PDstandard4th3alpha) + beta3L*PDstandard4th3trK + alphaL*SQR(Atm11) + alphaL*SQR(Atm22) + + 36*(Atu31*PDstandardNth1phi + Atu32*PDstandardNth2phi + Atu33*PDstandardNth3phi)) + + gtu33*(10*PDstandardNth33beta3 - 4*alphaL*PDstandardNth3trK)); + + trKrhsL = -(gu11*PDstandardNth11alpha) - 2*gu21*PDstandardNth12alpha - 2*gu31*PDstandardNth13alpha + + (G111*gu11 + 2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33)*PDstandardNth1alpha + + beta1L*PDstandardNth1trK - gu22*PDstandardNth22alpha - 2*gu32*PDstandardNth23alpha + + (G211*gu11 + 2*G212*gu21 + G222*gu22 + 2*G213*gu31 + 2*G223*gu32 + G233*gu33)*PDstandardNth2alpha + + beta2L*PDstandardNth2trK - gu33*PDstandardNth33alpha + G311*gu11*PDstandardNth3alpha + + G322*gu22*PDstandardNth3alpha + 2*G313*gu31*PDstandardNth3alpha + 2*G323*gu32*PDstandardNth3alpha + + G333*gu33*PDstandardNth3alpha + 2*(alphaL*Atm12*Atm21 + alphaL*Atm13*Atm31 + alphaL*Atm23*Atm32 + + G312*gu21*PDstandardNth3alpha) + beta3L*PDstandardNth3trK + alphaL*SQR(Atm11) + alphaL*SQR(Atm22) + alphaL*SQR(Atm33) + alphaL*kthird*SQR(trKL); - At11rhsL = beta1L*PDstandard4th1At11 + 2*(At11L*PDstandard4th1beta1 + At12L*PDstandard4th1beta2 + - At13L*PDstandard4th1beta3) + beta2L*PDstandard4th2At11 + beta3L*PDstandard4th3At11 - - At11L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) - - em4phi*kthird*(3*PDstandard4th11alpha - g11*gu11*PDstandard4th11alpha - 2*g11*gu21*PDstandard4th12alpha - - 2*g11*gu31*PDstandard4th13alpha + (G111*(-3 + g11*gu11) + - g11*(2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33))*PDstandard4th1alpha - - g11*gu22*PDstandard4th22alpha - 2*g11*gu32*PDstandard4th23alpha + + At11rhsL = beta1L*PDstandardNth1At11 + 2*(At11L*PDstandardNth1beta1 + At12L*PDstandardNth1beta2 + + At13L*PDstandardNth1beta3) + beta2L*PDstandardNth2At11 + beta3L*PDstandardNth3At11 - + At11L*ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3) - + em4phi*kthird*(3*PDstandardNth11alpha - g11*gu11*PDstandardNth11alpha - 2*g11*gu21*PDstandardNth12alpha - + 2*g11*gu31*PDstandardNth13alpha + (G111*(-3 + g11*gu11) + + g11*(2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33))*PDstandardNth1alpha - + g11*gu22*PDstandardNth22alpha - 2*g11*gu32*PDstandardNth23alpha + (G211*(-3 + g11*gu11) + g11*(2*G212*gu21 + G222*gu22 + 2*G213*gu31 + 2*G223*gu32 + G233*gu33))* - PDstandard4th2alpha - g11*gu33*PDstandard4th33alpha - 3*G311*PDstandard4th3alpha + - g11*G311*gu11*PDstandard4th3alpha + 2*g11*G312*gu21*PDstandard4th3alpha + g11*G322*gu22*PDstandard4th3alpha + - 2*g11*G313*gu31*PDstandard4th3alpha + 2*g11*G323*gu32*PDstandard4th3alpha + g11*G333*gu33*PDstandard4th3alpha - + PDstandardNth2alpha - g11*gu33*PDstandardNth33alpha - 3*G311*PDstandardNth3alpha + + g11*G311*gu11*PDstandardNth3alpha + 2*g11*G312*gu21*PDstandardNth3alpha + g11*G322*gu22*PDstandardNth3alpha + + 2*g11*G313*gu31*PDstandardNth3alpha + 2*g11*G323*gu32*PDstandardNth3alpha + g11*G333*gu33*PDstandardNth3alpha - 3*alphaL*R11 + alphaL*g11*gu11*R11 + 2*alphaL*g11*gu21*R12 + 2*alphaL*g11*gu31*R13 + alphaL*g11*gu22*R22 + 2*alphaL*g11*gu32*R23 + alphaL*g11*gu33*R33) + alphaL*(-2*(At11L*Atm11 + At12L*Atm21 + At13L*Atm31) + At11L*trKL); - At12rhsL = beta1L*PDstandard4th1At12 + At22L*PDstandard4th1beta2 + At23L*PDstandard4th1beta3 + - beta2L*PDstandard4th2At12 + At11L*PDstandard4th2beta1 + At13L*PDstandard4th2beta3 + beta3L*PDstandard4th3At12 + - At12L*(PDstandard4th1beta1 + PDstandard4th2beta2 - - ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)) - - em4phi*kthird*(3*PDstandard4th12alpha + (G112*(-3 + 2*g12*gu21) + - g12*(G111*gu11 + G122*gu22 + 2*(G113*gu31 + G123*gu32) + G133*gu33))*PDstandard4th1alpha + + At12rhsL = beta1L*PDstandardNth1At12 + At22L*PDstandardNth1beta2 + At23L*PDstandardNth1beta3 + + beta2L*PDstandardNth2At12 + At11L*PDstandardNth2beta1 + At13L*PDstandardNth2beta3 + beta3L*PDstandardNth3At12 + + At12L*(PDstandardNth1beta1 + PDstandardNth2beta2 - + ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3)) - + em4phi*kthird*(3*PDstandardNth12alpha + (G112*(-3 + 2*g12*gu21) + + g12*(G111*gu11 + G122*gu22 + 2*(G113*gu31 + G123*gu32) + G133*gu33))*PDstandardNth1alpha + (G212*(-3 + 2*g12*gu21) + g12*(G211*gu11 + G222*gu22 + 2*(G213*gu31 + G223*gu32) + G233*gu33))* - PDstandard4th2alpha + G312*(-3 + 2*g12*gu21)*PDstandard4th3alpha + + PDstandardNth2alpha + G312*(-3 + 2*g12*gu21)*PDstandardNth3alpha + alphaL*(-3*R12 + 2*g12*(gu31*R13 + gu32*R23)) + - g12*(-(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - 2*gu31*PDstandard4th13alpha - - gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha - gu33*PDstandard4th33alpha + - G311*gu11*PDstandard4th3alpha + G322*gu22*PDstandard4th3alpha + 2*G313*gu31*PDstandard4th3alpha + - 2*G323*gu32*PDstandard4th3alpha + G333*gu33*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + + g12*(-(gu11*PDstandardNth11alpha) - 2*gu21*PDstandardNth12alpha - 2*gu31*PDstandardNth13alpha - + gu22*PDstandardNth22alpha - 2*gu32*PDstandardNth23alpha - gu33*PDstandardNth33alpha + + G311*gu11*PDstandardNth3alpha + G322*gu22*PDstandardNth3alpha + 2*G313*gu31*PDstandardNth3alpha + + 2*G323*gu32*PDstandardNth3alpha + G333*gu33*PDstandardNth3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + alphaL*gu22*R22 + alphaL*gu33*R33)) + alphaL*(-2*(At11L*Atm12 + At12L*Atm22 + At13L*Atm32) + At12L*trKL); - At13rhsL = beta1L*PDstandard4th1At13 + At23L*PDstandard4th1beta2 + At33L*PDstandard4th1beta3 + - beta2L*PDstandard4th2At13 + beta3L*PDstandard4th3At13 + At11L*PDstandard4th3beta1 + At12L*PDstandard4th3beta2 + - At13L*(PDstandard4th1beta1 + PDstandard4th3beta3 - - ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)) - - em4phi*kthird*(3*PDstandard4th13alpha + (G113*(-3 + 2*g13*gu31) + - g13*(G111*gu11 + G122*gu22 + 2*(G112*gu21 + G123*gu32) + G133*gu33))*PDstandard4th1alpha + + At13rhsL = beta1L*PDstandardNth1At13 + At23L*PDstandardNth1beta2 + At33L*PDstandardNth1beta3 + + beta2L*PDstandardNth2At13 + beta3L*PDstandardNth3At13 + At11L*PDstandardNth3beta1 + At12L*PDstandardNth3beta2 + + At13L*(PDstandardNth1beta1 + PDstandardNth3beta3 - + ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3)) - + em4phi*kthird*(3*PDstandardNth13alpha + (G113*(-3 + 2*g13*gu31) + + g13*(G111*gu11 + G122*gu22 + 2*(G112*gu21 + G123*gu32) + G133*gu33))*PDstandardNth1alpha + (G213*(-3 + 2*g13*gu31) + g13*(G211*gu11 + G222*gu22 + 2*(G212*gu21 + G223*gu32) + G233*gu33))* - PDstandard4th2alpha + (G313*(-3 + 2*g13*gu31) + g13*(G322*gu22 + 2*(G312*gu21 + G323*gu32) + G333*gu33))* - PDstandard4th3alpha + g13*(-(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - - 2*gu31*PDstandard4th13alpha - gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha - - gu33*PDstandard4th33alpha + G311*gu11*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + + PDstandardNth2alpha + (G313*(-3 + 2*g13*gu31) + g13*(G322*gu22 + 2*(G312*gu21 + G323*gu32) + G333*gu33))* + PDstandardNth3alpha + g13*(-(gu11*PDstandardNth11alpha) - 2*gu21*PDstandardNth12alpha - + 2*gu31*PDstandardNth13alpha - gu22*PDstandardNth22alpha - 2*gu32*PDstandardNth23alpha - + gu33*PDstandardNth33alpha + G311*gu11*PDstandardNth3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + 2*alphaL*gu31*R13 + 2*alphaL*gu32*R23) + alphaL*(-3*R13 + g13*(gu22*R22 + gu33*R33))) + alphaL*(-2*(At11L*Atm13 + At12L*Atm23 + At13L*Atm33) + At13L*trKL); - At22rhsL = beta1L*PDstandard4th1At22 + beta2L*PDstandard4th2At22 + - 2*(At12L*PDstandard4th2beta1 + At22L*PDstandard4th2beta2 + At23L*PDstandard4th2beta3) + beta3L*PDstandard4th3At22 - - At22L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) - - em4phi*kthird*(-(g22*gu11*PDstandard4th11alpha) - 2*g22*gu21*PDstandard4th12alpha - - 2*g22*gu31*PDstandard4th13alpha + (G122*(-3 + g22*gu22) + - g22*(G111*gu11 + 2*G112*gu21 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33))*PDstandard4th1alpha + - 3*PDstandard4th22alpha - g22*gu22*PDstandard4th22alpha - 2*g22*gu32*PDstandard4th23alpha + + At22rhsL = beta1L*PDstandardNth1At22 + beta2L*PDstandardNth2At22 + + 2*(At12L*PDstandardNth2beta1 + At22L*PDstandardNth2beta2 + At23L*PDstandardNth2beta3) + beta3L*PDstandardNth3At22 - + At22L*ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3) - + em4phi*kthird*(-(g22*gu11*PDstandardNth11alpha) - 2*g22*gu21*PDstandardNth12alpha - + 2*g22*gu31*PDstandardNth13alpha + (G122*(-3 + g22*gu22) + + g22*(G111*gu11 + 2*G112*gu21 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33))*PDstandardNth1alpha + + 3*PDstandardNth22alpha - g22*gu22*PDstandardNth22alpha - 2*g22*gu32*PDstandardNth23alpha + (G222*(-3 + g22*gu22) + g22*(G211*gu11 + 2*G212*gu21 + 2*G213*gu31 + 2*G223*gu32 + G233*gu33))* - PDstandard4th2alpha - g22*gu33*PDstandard4th33alpha - 3*G322*PDstandard4th3alpha + - g22*G311*gu11*PDstandard4th3alpha + 2*g22*G312*gu21*PDstandard4th3alpha + g22*G322*gu22*PDstandard4th3alpha + - 2*g22*G313*gu31*PDstandard4th3alpha + 2*g22*G323*gu32*PDstandard4th3alpha + g22*G333*gu33*PDstandard4th3alpha + + PDstandardNth2alpha - g22*gu33*PDstandardNth33alpha - 3*G322*PDstandardNth3alpha + + g22*G311*gu11*PDstandardNth3alpha + 2*g22*G312*gu21*PDstandardNth3alpha + g22*G322*gu22*PDstandardNth3alpha + + 2*g22*G313*gu31*PDstandardNth3alpha + 2*g22*G323*gu32*PDstandardNth3alpha + g22*G333*gu33*PDstandardNth3alpha + alphaL*g22*gu11*R11 + 2*alphaL*g22*gu21*R12 + 2*alphaL*g22*gu31*R13 - 3*alphaL*R22 + alphaL*g22*gu22*R22 + 2*alphaL*g22*gu32*R23 + alphaL*g22*gu33*R33) + alphaL*(-2*(At12L*Atm12 + At22L*Atm22 + At23L*Atm32) + At22L*trKL); - At23rhsL = beta1L*PDstandard4th1At23 + beta2L*PDstandard4th2At23 + At13L*PDstandard4th2beta1 + - At33L*PDstandard4th2beta3 + beta3L*PDstandard4th3At23 + At12L*PDstandard4th3beta1 + At22L*PDstandard4th3beta2 + - At23L*(PDstandard4th2beta2 + PDstandard4th3beta3 - - ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)) - + At23rhsL = beta1L*PDstandardNth1At23 + beta2L*PDstandardNth2At23 + At13L*PDstandardNth2beta1 + + At33L*PDstandardNth2beta3 + beta3L*PDstandardNth3At23 + At12L*PDstandardNth3beta1 + At22L*PDstandardNth3beta2 + + At23L*(PDstandardNth2beta2 + PDstandardNth3beta3 - + ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3)) - em4phi*kthird*((G123*(-3 + 2*g23*gu32) + g23*(G111*gu11 + G122*gu22 + 2*(G112*gu21 + G113*gu31) + G133*gu33))* - PDstandard4th1alpha + 3*PDstandard4th23alpha + + PDstandardNth1alpha + 3*PDstandardNth23alpha + (G223*(-3 + 2*g23*gu32) + g23*(G211*gu11 + G222*gu22 + 2*(G212*gu21 + G213*gu31) + G233*gu33))* - PDstandard4th2alpha + (G323*(-3 + 2*g23*gu32) + g23*(G322*gu22 + 2*(G312*gu21 + G313*gu31) + G333*gu33))* - PDstandard4th3alpha + g23*(-(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - - 2*gu31*PDstandard4th13alpha - gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha - - gu33*PDstandard4th33alpha + G311*gu11*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + + PDstandardNth2alpha + (G323*(-3 + 2*g23*gu32) + g23*(G322*gu22 + 2*(G312*gu21 + G313*gu31) + G333*gu33))* + PDstandardNth3alpha + g23*(-(gu11*PDstandardNth11alpha) - 2*gu21*PDstandardNth12alpha - + 2*gu31*PDstandardNth13alpha - gu22*PDstandardNth22alpha - 2*gu32*PDstandardNth23alpha - + gu33*PDstandardNth33alpha + G311*gu11*PDstandardNth3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + 2*alphaL*gu31*R13 + alphaL*gu22*R22 + 2*alphaL*gu32*R23) + alphaL*(-3*R23 + g23*gu33*R33)) + alphaL*(-2*(At12L*Atm13 + At22L*Atm23 + At23L*Atm33) + At23L*trKL); - At33rhsL = beta1L*PDstandard4th1At33 + beta2L*PDstandard4th2At33 + beta3L*PDstandard4th3At33 - - At33L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + - 2*(At13L*PDstandard4th3beta1 + At23L*PDstandard4th3beta2 + At33L*PDstandard4th3beta3) - - em4phi*kthird*(-(g33*gu11*PDstandard4th11alpha) - 2*g33*gu21*PDstandard4th12alpha - - 2*g33*gu31*PDstandard4th13alpha + (g33*(G111*gu11 + 2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32) + - G133*(-3 + g33*gu33))*PDstandard4th1alpha - g33*gu22*PDstandard4th22alpha - 2*g33*gu32*PDstandard4th23alpha + + At33rhsL = beta1L*PDstandardNth1At33 + beta2L*PDstandardNth2At33 + beta3L*PDstandardNth3At33 - + At33L*ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3) + + 2*(At13L*PDstandardNth3beta1 + At23L*PDstandardNth3beta2 + At33L*PDstandardNth3beta3) - + em4phi*kthird*(-(g33*gu11*PDstandardNth11alpha) - 2*g33*gu21*PDstandardNth12alpha - + 2*g33*gu31*PDstandardNth13alpha + (g33*(G111*gu11 + 2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32) + + G133*(-3 + g33*gu33))*PDstandardNth1alpha - g33*gu22*PDstandardNth22alpha - 2*g33*gu32*PDstandardNth23alpha + (g33*(G211*gu11 + 2*G212*gu21 + G222*gu22 + 2*G213*gu31 + 2*G223*gu32) + G233*(-3 + g33*gu33))* - PDstandard4th2alpha + 3*PDstandard4th33alpha - g33*gu33*PDstandard4th33alpha - 3*G333*PDstandard4th3alpha + - G311*g33*gu11*PDstandard4th3alpha + 2*G312*g33*gu21*PDstandard4th3alpha + G322*g33*gu22*PDstandard4th3alpha + - 2*G313*g33*gu31*PDstandard4th3alpha + 2*G323*g33*gu32*PDstandard4th3alpha + g33*G333*gu33*PDstandard4th3alpha + + PDstandardNth2alpha + 3*PDstandardNth33alpha - g33*gu33*PDstandardNth33alpha - 3*G333*PDstandardNth3alpha + + G311*g33*gu11*PDstandardNth3alpha + 2*G312*g33*gu21*PDstandardNth3alpha + G322*g33*gu22*PDstandardNth3alpha + + 2*G313*g33*gu31*PDstandardNth3alpha + 2*G323*g33*gu32*PDstandardNth3alpha + g33*G333*gu33*PDstandardNth3alpha + alphaL*g33*gu11*R11 + 2*alphaL*g33*gu21*R12 + 2*alphaL*g33*gu31*R13 + alphaL*g33*gu22*R22 + 2*alphaL*g33*gu32*R23 - 3*alphaL*R33 + alphaL*g33*gu33*R33) + alphaL*(-2*(At13L*Atm13 + At23L*Atm23 + At33L*Atm33) + At33L*trKL); - alpharhsL = beta1L*PDstandard4th1alpha + beta2L*PDstandard4th2alpha + beta3L*PDstandard4th3alpha - + alpharhsL = beta1L*PDstandardNth1alpha + beta2L*PDstandardNth2alpha + beta3L*PDstandardNth3alpha - AL*harmonicF*pow(alphaL,harmonicN); ArhsL = -(AL*AlphaDriver) + trKrhsL; diff --git a/ML_BSSN/src/ML_BSSN_constraints.c b/ML_BSSN/src/ML_BSSN_constraints.c index 9d8b388..23af4fa 100644 --- a/ML_BSSN/src/ML_BSSN_constraints.c +++ b/ML_BSSN/src/ML_BSSN_constraints.c @@ -123,120 +123,120 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Declare precomputed derivatives*/ /* Declare derivatives */ - CCTK_REAL PDstandard4th1At11 = INITVALUE; - CCTK_REAL PDstandard4th2At11 = INITVALUE; - CCTK_REAL PDstandard4th3At11 = INITVALUE; - CCTK_REAL PDstandard4th1At12 = INITVALUE; - CCTK_REAL PDstandard4th2At12 = INITVALUE; - CCTK_REAL PDstandard4th3At12 = INITVALUE; - CCTK_REAL PDstandard4th1At13 = INITVALUE; - CCTK_REAL PDstandard4th2At13 = INITVALUE; - CCTK_REAL PDstandard4th3At13 = INITVALUE; - CCTK_REAL PDstandard4th1At22 = INITVALUE; - CCTK_REAL PDstandard4th2At22 = INITVALUE; - CCTK_REAL PDstandard4th3At22 = INITVALUE; - CCTK_REAL PDstandard4th1At23 = INITVALUE; - CCTK_REAL PDstandard4th2At23 = INITVALUE; - CCTK_REAL PDstandard4th3At23 = INITVALUE; - CCTK_REAL PDstandard4th1At33 = INITVALUE; - CCTK_REAL PDstandard4th2At33 = INITVALUE; - CCTK_REAL PDstandard4th3At33 = INITVALUE; - CCTK_REAL PDstandard4th1gt11 = INITVALUE; - CCTK_REAL PDstandard4th2gt11 = INITVALUE; - CCTK_REAL PDstandard4th3gt11 = INITVALUE; - CCTK_REAL PDstandard4th11gt11 = INITVALUE; - CCTK_REAL PDstandard4th22gt11 = INITVALUE; - CCTK_REAL PDstandard4th33gt11 = INITVALUE; - CCTK_REAL PDstandard4th12gt11 = INITVALUE; - CCTK_REAL PDstandard4th13gt11 = INITVALUE; - CCTK_REAL PDstandard4th21gt11 = INITVALUE; - CCTK_REAL PDstandard4th23gt11 = INITVALUE; - CCTK_REAL PDstandard4th31gt11 = INITVALUE; - CCTK_REAL PDstandard4th32gt11 = INITVALUE; - CCTK_REAL PDstandard4th1gt12 = INITVALUE; - CCTK_REAL PDstandard4th2gt12 = INITVALUE; - CCTK_REAL PDstandard4th3gt12 = INITVALUE; - CCTK_REAL PDstandard4th11gt12 = INITVALUE; - CCTK_REAL PDstandard4th22gt12 = INITVALUE; - CCTK_REAL PDstandard4th33gt12 = INITVALUE; - CCTK_REAL PDstandard4th12gt12 = INITVALUE; - CCTK_REAL PDstandard4th13gt12 = INITVALUE; - CCTK_REAL PDstandard4th21gt12 = INITVALUE; - CCTK_REAL PDstandard4th23gt12 = INITVALUE; - CCTK_REAL PDstandard4th31gt12 = INITVALUE; - CCTK_REAL PDstandard4th32gt12 = INITVALUE; - CCTK_REAL PDstandard4th1gt13 = INITVALUE; - CCTK_REAL PDstandard4th2gt13 = INITVALUE; - CCTK_REAL PDstandard4th3gt13 = INITVALUE; - CCTK_REAL PDstandard4th11gt13 = INITVALUE; - CCTK_REAL PDstandard4th22gt13 = INITVALUE; - CCTK_REAL PDstandard4th33gt13 = INITVALUE; - CCTK_REAL PDstandard4th12gt13 = INITVALUE; - CCTK_REAL PDstandard4th13gt13 = INITVALUE; - CCTK_REAL PDstandard4th21gt13 = INITVALUE; - CCTK_REAL PDstandard4th23gt13 = INITVALUE; - CCTK_REAL PDstandard4th31gt13 = INITVALUE; - CCTK_REAL PDstandard4th32gt13 = INITVALUE; - CCTK_REAL PDstandard4th1gt22 = INITVALUE; - CCTK_REAL PDstandard4th2gt22 = INITVALUE; - CCTK_REAL PDstandard4th3gt22 = INITVALUE; - CCTK_REAL PDstandard4th11gt22 = INITVALUE; - CCTK_REAL PDstandard4th22gt22 = INITVALUE; - CCTK_REAL PDstandard4th33gt22 = INITVALUE; - CCTK_REAL PDstandard4th12gt22 = INITVALUE; - CCTK_REAL PDstandard4th13gt22 = INITVALUE; - CCTK_REAL PDstandard4th21gt22 = INITVALUE; - CCTK_REAL PDstandard4th23gt22 = INITVALUE; - CCTK_REAL PDstandard4th31gt22 = INITVALUE; - CCTK_REAL PDstandard4th32gt22 = INITVALUE; - CCTK_REAL PDstandard4th1gt23 = INITVALUE; - CCTK_REAL PDstandard4th2gt23 = INITVALUE; - CCTK_REAL PDstandard4th3gt23 = INITVALUE; - CCTK_REAL PDstandard4th11gt23 = INITVALUE; - CCTK_REAL PDstandard4th22gt23 = INITVALUE; - CCTK_REAL PDstandard4th33gt23 = INITVALUE; - CCTK_REAL PDstandard4th12gt23 = INITVALUE; - CCTK_REAL PDstandard4th13gt23 = INITVALUE; - CCTK_REAL PDstandard4th21gt23 = INITVALUE; - CCTK_REAL PDstandard4th23gt23 = INITVALUE; - CCTK_REAL PDstandard4th31gt23 = INITVALUE; - CCTK_REAL PDstandard4th32gt23 = INITVALUE; - CCTK_REAL PDstandard4th1gt33 = INITVALUE; - CCTK_REAL PDstandard4th2gt33 = INITVALUE; - CCTK_REAL PDstandard4th3gt33 = INITVALUE; - CCTK_REAL PDstandard4th11gt33 = INITVALUE; - CCTK_REAL PDstandard4th22gt33 = INITVALUE; - CCTK_REAL PDstandard4th33gt33 = INITVALUE; - CCTK_REAL PDstandard4th12gt33 = INITVALUE; - CCTK_REAL PDstandard4th13gt33 = INITVALUE; - CCTK_REAL PDstandard4th21gt33 = INITVALUE; - CCTK_REAL PDstandard4th23gt33 = INITVALUE; - CCTK_REAL PDstandard4th31gt33 = INITVALUE; - CCTK_REAL PDstandard4th32gt33 = INITVALUE; - CCTK_REAL PDstandard4th1phi = INITVALUE; - CCTK_REAL PDstandard4th2phi = INITVALUE; - CCTK_REAL PDstandard4th3phi = INITVALUE; - CCTK_REAL PDstandard4th11phi = INITVALUE; - CCTK_REAL PDstandard4th22phi = INITVALUE; - CCTK_REAL PDstandard4th33phi = INITVALUE; - CCTK_REAL PDstandard4th12phi = INITVALUE; - CCTK_REAL PDstandard4th13phi = INITVALUE; - CCTK_REAL PDstandard4th21phi = INITVALUE; - CCTK_REAL PDstandard4th23phi = INITVALUE; - CCTK_REAL PDstandard4th31phi = INITVALUE; - CCTK_REAL PDstandard4th32phi = INITVALUE; - CCTK_REAL PDstandard4th1trK = INITVALUE; - CCTK_REAL PDstandard4th2trK = INITVALUE; - CCTK_REAL PDstandard4th3trK = INITVALUE; - CCTK_REAL PDstandard4th1Xt1 = INITVALUE; - CCTK_REAL PDstandard4th2Xt1 = INITVALUE; - CCTK_REAL PDstandard4th3Xt1 = INITVALUE; - CCTK_REAL PDstandard4th1Xt2 = INITVALUE; - CCTK_REAL PDstandard4th2Xt2 = INITVALUE; - CCTK_REAL PDstandard4th3Xt2 = INITVALUE; - CCTK_REAL PDstandard4th1Xt3 = INITVALUE; - CCTK_REAL PDstandard4th2Xt3 = INITVALUE; - CCTK_REAL PDstandard4th3Xt3 = INITVALUE; + CCTK_REAL PDstandardNth1At11 = INITVALUE; + CCTK_REAL PDstandardNth2At11 = INITVALUE; + CCTK_REAL PDstandardNth3At11 = INITVALUE; + CCTK_REAL PDstandardNth1At12 = INITVALUE; + CCTK_REAL PDstandardNth2At12 = INITVALUE; + CCTK_REAL PDstandardNth3At12 = INITVALUE; + CCTK_REAL PDstandardNth1At13 = INITVALUE; + CCTK_REAL PDstandardNth2At13 = INITVALUE; + CCTK_REAL PDstandardNth3At13 = INITVALUE; + CCTK_REAL PDstandardNth1At22 = INITVALUE; + CCTK_REAL PDstandardNth2At22 = INITVALUE; + CCTK_REAL PDstandardNth3At22 = INITVALUE; + CCTK_REAL PDstandardNth1At23 = INITVALUE; + CCTK_REAL PDstandardNth2At23 = INITVALUE; + CCTK_REAL PDstandardNth3At23 = INITVALUE; + CCTK_REAL PDstandardNth1At33 = INITVALUE; + CCTK_REAL PDstandardNth2At33 = INITVALUE; + CCTK_REAL PDstandardNth3At33 = INITVALUE; + CCTK_REAL PDstandardNth1gt11 = INITVALUE; + CCTK_REAL PDstandardNth2gt11 = INITVALUE; + CCTK_REAL PDstandardNth3gt11 = INITVALUE; + CCTK_REAL PDstandardNth11gt11 = INITVALUE; + CCTK_REAL PDstandardNth22gt11 = INITVALUE; + CCTK_REAL PDstandardNth33gt11 = INITVALUE; + CCTK_REAL PDstandardNth12gt11 = INITVALUE; + CCTK_REAL PDstandardNth13gt11 = INITVALUE; + CCTK_REAL PDstandardNth21gt11 = INITVALUE; + CCTK_REAL PDstandardNth23gt11 = INITVALUE; + CCTK_REAL PDstandardNth31gt11 = INITVALUE; + CCTK_REAL PDstandardNth32gt11 = INITVALUE; + CCTK_REAL PDstandardNth1gt12 = INITVALUE; + CCTK_REAL PDstandardNth2gt12 = INITVALUE; + CCTK_REAL PDstandardNth3gt12 = INITVALUE; + CCTK_REAL PDstandardNth11gt12 = INITVALUE; + CCTK_REAL PDstandardNth22gt12 = INITVALUE; + CCTK_REAL PDstandardNth33gt12 = INITVALUE; + CCTK_REAL PDstandardNth12gt12 = INITVALUE; + CCTK_REAL PDstandardNth13gt12 = INITVALUE; + CCTK_REAL PDstandardNth21gt12 = INITVALUE; + CCTK_REAL PDstandardNth23gt12 = INITVALUE; + CCTK_REAL PDstandardNth31gt12 = INITVALUE; + CCTK_REAL PDstandardNth32gt12 = INITVALUE; + CCTK_REAL PDstandardNth1gt13 = INITVALUE; + CCTK_REAL PDstandardNth2gt13 = INITVALUE; + CCTK_REAL PDstandardNth3gt13 = INITVALUE; + CCTK_REAL PDstandardNth11gt13 = INITVALUE; + CCTK_REAL PDstandardNth22gt13 = INITVALUE; + CCTK_REAL PDstandardNth33gt13 = INITVALUE; + CCTK_REAL PDstandardNth12gt13 = INITVALUE; + CCTK_REAL PDstandardNth13gt13 = INITVALUE; + CCTK_REAL PDstandardNth21gt13 = INITVALUE; + CCTK_REAL PDstandardNth23gt13 = INITVALUE; + CCTK_REAL PDstandardNth31gt13 = INITVALUE; + CCTK_REAL PDstandardNth32gt13 = INITVALUE; + CCTK_REAL PDstandardNth1gt22 = INITVALUE; + CCTK_REAL PDstandardNth2gt22 = INITVALUE; + CCTK_REAL PDstandardNth3gt22 = INITVALUE; + CCTK_REAL PDstandardNth11gt22 = INITVALUE; + CCTK_REAL PDstandardNth22gt22 = INITVALUE; + CCTK_REAL PDstandardNth33gt22 = INITVALUE; + CCTK_REAL PDstandardNth12gt22 = INITVALUE; + CCTK_REAL PDstandardNth13gt22 = INITVALUE; + CCTK_REAL PDstandardNth21gt22 = INITVALUE; + CCTK_REAL PDstandardNth23gt22 = INITVALUE; + CCTK_REAL PDstandardNth31gt22 = INITVALUE; + CCTK_REAL PDstandardNth32gt22 = INITVALUE; + CCTK_REAL PDstandardNth1gt23 = INITVALUE; + CCTK_REAL PDstandardNth2gt23 = INITVALUE; + CCTK_REAL PDstandardNth3gt23 = INITVALUE; + CCTK_REAL PDstandardNth11gt23 = INITVALUE; + CCTK_REAL PDstandardNth22gt23 = INITVALUE; + CCTK_REAL PDstandardNth33gt23 = INITVALUE; + CCTK_REAL PDstandardNth12gt23 = INITVALUE; + CCTK_REAL PDstandardNth13gt23 = INITVALUE; + CCTK_REAL PDstandardNth21gt23 = INITVALUE; + CCTK_REAL PDstandardNth23gt23 = INITVALUE; + CCTK_REAL PDstandardNth31gt23 = INITVALUE; + CCTK_REAL PDstandardNth32gt23 = INITVALUE; + CCTK_REAL PDstandardNth1gt33 = INITVALUE; + CCTK_REAL PDstandardNth2gt33 = INITVALUE; + CCTK_REAL PDstandardNth3gt33 = INITVALUE; + CCTK_REAL PDstandardNth11gt33 = INITVALUE; + CCTK_REAL PDstandardNth22gt33 = INITVALUE; + CCTK_REAL PDstandardNth33gt33 = INITVALUE; + CCTK_REAL PDstandardNth12gt33 = INITVALUE; + CCTK_REAL PDstandardNth13gt33 = INITVALUE; + CCTK_REAL PDstandardNth21gt33 = INITVALUE; + CCTK_REAL PDstandardNth23gt33 = INITVALUE; + CCTK_REAL PDstandardNth31gt33 = INITVALUE; + CCTK_REAL PDstandardNth32gt33 = INITVALUE; + CCTK_REAL PDstandardNth1phi = INITVALUE; + CCTK_REAL PDstandardNth2phi = INITVALUE; + CCTK_REAL PDstandardNth3phi = INITVALUE; + CCTK_REAL PDstandardNth11phi = INITVALUE; + CCTK_REAL PDstandardNth22phi = INITVALUE; + CCTK_REAL PDstandardNth33phi = INITVALUE; + CCTK_REAL PDstandardNth12phi = INITVALUE; + CCTK_REAL PDstandardNth13phi = INITVALUE; + CCTK_REAL PDstandardNth21phi = INITVALUE; + CCTK_REAL PDstandardNth23phi = INITVALUE; + CCTK_REAL PDstandardNth31phi = INITVALUE; + CCTK_REAL PDstandardNth32phi = INITVALUE; + CCTK_REAL PDstandardNth1trK = INITVALUE; + CCTK_REAL PDstandardNth2trK = INITVALUE; + CCTK_REAL PDstandardNth3trK = INITVALUE; + CCTK_REAL PDstandardNth1Xt1 = INITVALUE; + CCTK_REAL PDstandardNth2Xt1 = INITVALUE; + CCTK_REAL PDstandardNth3Xt1 = INITVALUE; + CCTK_REAL PDstandardNth1Xt2 = INITVALUE; + CCTK_REAL PDstandardNth2Xt2 = INITVALUE; + CCTK_REAL PDstandardNth3Xt2 = INITVALUE; + CCTK_REAL PDstandardNth1Xt3 = INITVALUE; + CCTK_REAL PDstandardNth2Xt3 = INITVALUE; + CCTK_REAL PDstandardNth3Xt3 = INITVALUE; /* Assign local copies of grid functions */ At11L = At11[index]; @@ -262,99 +262,99 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Include user supplied include files */ /* Precompute derivatives (new style) */ - PDstandard4th1At11 = PDstandard4th1(At11, i, j, k); - PDstandard4th2At11 = PDstandard4th2(At11, i, j, k); - PDstandard4th3At11 = PDstandard4th3(At11, i, j, k); - PDstandard4th1At12 = PDstandard4th1(At12, i, j, k); - PDstandard4th2At12 = PDstandard4th2(At12, i, j, k); - PDstandard4th3At12 = PDstandard4th3(At12, i, j, k); - PDstandard4th1At13 = PDstandard4th1(At13, i, j, k); - PDstandard4th2At13 = PDstandard4th2(At13, i, j, k); - PDstandard4th3At13 = PDstandard4th3(At13, i, j, k); - PDstandard4th1At22 = PDstandard4th1(At22, i, j, k); - PDstandard4th2At22 = PDstandard4th2(At22, i, j, k); - PDstandard4th3At22 = PDstandard4th3(At22, i, j, k); - PDstandard4th1At23 = PDstandard4th1(At23, i, j, k); - PDstandard4th2At23 = PDstandard4th2(At23, i, j, k); - PDstandard4th3At23 = PDstandard4th3(At23, i, j, k); - PDstandard4th1At33 = PDstandard4th1(At33, i, j, k); - PDstandard4th2At33 = PDstandard4th2(At33, i, j, k); - PDstandard4th3At33 = PDstandard4th3(At33, i, j, k); - PDstandard4th1gt11 = PDstandard4th1(gt11, i, j, k); - PDstandard4th2gt11 = PDstandard4th2(gt11, i, j, k); - PDstandard4th3gt11 = PDstandard4th3(gt11, i, j, k); - PDstandard4th11gt11 = PDstandard4th11(gt11, i, j, k); - PDstandard4th22gt11 = PDstandard4th22(gt11, i, j, k); - PDstandard4th33gt11 = PDstandard4th33(gt11, i, j, k); - PDstandard4th12gt11 = PDstandard4th12(gt11, i, j, k); - PDstandard4th13gt11 = PDstandard4th13(gt11, i, j, k); - PDstandard4th23gt11 = PDstandard4th23(gt11, i, j, k); - PDstandard4th1gt12 = PDstandard4th1(gt12, i, j, k); - PDstandard4th2gt12 = PDstandard4th2(gt12, i, j, k); - PDstandard4th3gt12 = PDstandard4th3(gt12, i, j, k); - PDstandard4th11gt12 = PDstandard4th11(gt12, i, j, k); - PDstandard4th22gt12 = PDstandard4th22(gt12, i, j, k); - PDstandard4th33gt12 = PDstandard4th33(gt12, i, j, k); - PDstandard4th12gt12 = PDstandard4th12(gt12, i, j, k); - PDstandard4th13gt12 = PDstandard4th13(gt12, i, j, k); - PDstandard4th23gt12 = PDstandard4th23(gt12, i, j, k); - PDstandard4th1gt13 = PDstandard4th1(gt13, i, j, k); - PDstandard4th2gt13 = PDstandard4th2(gt13, i, j, k); - PDstandard4th3gt13 = PDstandard4th3(gt13, i, j, k); - PDstandard4th11gt13 = PDstandard4th11(gt13, i, j, k); - PDstandard4th22gt13 = PDstandard4th22(gt13, i, j, k); - PDstandard4th33gt13 = PDstandard4th33(gt13, i, j, k); - PDstandard4th12gt13 = PDstandard4th12(gt13, i, j, k); - PDstandard4th13gt13 = PDstandard4th13(gt13, i, j, k); - PDstandard4th23gt13 = PDstandard4th23(gt13, i, j, k); - PDstandard4th1gt22 = PDstandard4th1(gt22, i, j, k); - PDstandard4th2gt22 = PDstandard4th2(gt22, i, j, k); - PDstandard4th3gt22 = PDstandard4th3(gt22, i, j, k); - PDstandard4th11gt22 = PDstandard4th11(gt22, i, j, k); - PDstandard4th22gt22 = PDstandard4th22(gt22, i, j, k); - PDstandard4th33gt22 = PDstandard4th33(gt22, i, j, k); - PDstandard4th12gt22 = PDstandard4th12(gt22, i, j, k); - PDstandard4th13gt22 = PDstandard4th13(gt22, i, j, k); - PDstandard4th23gt22 = PDstandard4th23(gt22, i, j, k); - PDstandard4th1gt23 = PDstandard4th1(gt23, i, j, k); - PDstandard4th2gt23 = PDstandard4th2(gt23, i, j, k); - PDstandard4th3gt23 = PDstandard4th3(gt23, i, j, k); - PDstandard4th11gt23 = PDstandard4th11(gt23, i, j, k); - PDstandard4th22gt23 = PDstandard4th22(gt23, i, j, k); - PDstandard4th33gt23 = PDstandard4th33(gt23, i, j, k); - PDstandard4th12gt23 = PDstandard4th12(gt23, i, j, k); - PDstandard4th13gt23 = PDstandard4th13(gt23, i, j, k); - PDstandard4th23gt23 = PDstandard4th23(gt23, i, j, k); - PDstandard4th1gt33 = PDstandard4th1(gt33, i, j, k); - PDstandard4th2gt33 = PDstandard4th2(gt33, i, j, k); - PDstandard4th3gt33 = PDstandard4th3(gt33, i, j, k); - PDstandard4th11gt33 = PDstandard4th11(gt33, i, j, k); - PDstandard4th22gt33 = PDstandard4th22(gt33, i, j, k); - PDstandard4th33gt33 = PDstandard4th33(gt33, i, j, k); - PDstandard4th12gt33 = PDstandard4th12(gt33, i, j, k); - PDstandard4th13gt33 = PDstandard4th13(gt33, i, j, k); - PDstandard4th23gt33 = PDstandard4th23(gt33, i, j, k); - PDstandard4th1phi = PDstandard4th1(phi, i, j, k); - PDstandard4th2phi = PDstandard4th2(phi, i, j, k); - PDstandard4th3phi = PDstandard4th3(phi, i, j, k); - PDstandard4th11phi = PDstandard4th11(phi, i, j, k); - PDstandard4th22phi = PDstandard4th22(phi, i, j, k); - PDstandard4th33phi = PDstandard4th33(phi, i, j, k); - PDstandard4th12phi = PDstandard4th12(phi, i, j, k); - PDstandard4th13phi = PDstandard4th13(phi, i, j, k); - PDstandard4th23phi = PDstandard4th23(phi, i, j, k); - PDstandard4th1trK = PDstandard4th1(trK, i, j, k); - PDstandard4th2trK = PDstandard4th2(trK, i, j, k); - PDstandard4th3trK = PDstandard4th3(trK, i, j, k); - PDstandard4th1Xt1 = PDstandard4th1(Xt1, i, j, k); - PDstandard4th2Xt1 = PDstandard4th2(Xt1, i, j, k); - PDstandard4th3Xt1 = PDstandard4th3(Xt1, i, j, k); - PDstandard4th1Xt2 = PDstandard4th1(Xt2, i, j, k); - PDstandard4th2Xt2 = PDstandard4th2(Xt2, i, j, k); - PDstandard4th3Xt2 = PDstandard4th3(Xt2, i, j, k); - PDstandard4th1Xt3 = PDstandard4th1(Xt3, i, j, k); - PDstandard4th2Xt3 = PDstandard4th2(Xt3, i, j, k); - PDstandard4th3Xt3 = PDstandard4th3(Xt3, i, j, k); + PDstandardNth1At11 = PDstandardNth1(At11, i, j, k); + PDstandardNth2At11 = PDstandardNth2(At11, i, j, k); + PDstandardNth3At11 = PDstandardNth3(At11, i, j, k); + PDstandardNth1At12 = PDstandardNth1(At12, i, j, k); + PDstandardNth2At12 = PDstandardNth2(At12, i, j, k); + PDstandardNth3At12 = PDstandardNth3(At12, i, j, k); + PDstandardNth1At13 = PDstandardNth1(At13, i, j, k); + PDstandardNth2At13 = PDstandardNth2(At13, i, j, k); + PDstandardNth3At13 = PDstandardNth3(At13, i, j, k); + PDstandardNth1At22 = PDstandardNth1(At22, i, j, k); + PDstandardNth2At22 = PDstandardNth2(At22, i, j, k); + PDstandardNth3At22 = PDstandardNth3(At22, i, j, k); + PDstandardNth1At23 = PDstandardNth1(At23, i, j, k); + PDstandardNth2At23 = PDstandardNth2(At23, i, j, k); + PDstandardNth3At23 = PDstandardNth3(At23, i, j, k); + PDstandardNth1At33 = PDstandardNth1(At33, i, j, k); + PDstandardNth2At33 = PDstandardNth2(At33, i, j, k); + PDstandardNth3At33 = PDstandardNth3(At33, i, j, k); + PDstandardNth1gt11 = PDstandardNth1(gt11, i, j, k); + PDstandardNth2gt11 = PDstandardNth2(gt11, i, j, k); + PDstandardNth3gt11 = PDstandardNth3(gt11, i, j, k); + PDstandardNth11gt11 = PDstandardNth11(gt11, i, j, k); + PDstandardNth22gt11 = PDstandardNth22(gt11, i, j, k); + PDstandardNth33gt11 = PDstandardNth33(gt11, i, j, k); + PDstandardNth12gt11 = PDstandardNth12(gt11, i, j, k); + PDstandardNth13gt11 = PDstandardNth13(gt11, i, j, k); + PDstandardNth23gt11 = PDstandardNth23(gt11, i, j, k); + PDstandardNth1gt12 = PDstandardNth1(gt12, i, j, k); + PDstandardNth2gt12 = PDstandardNth2(gt12, i, j, k); + PDstandardNth3gt12 = PDstandardNth3(gt12, i, j, k); + PDstandardNth11gt12 = PDstandardNth11(gt12, i, j, k); + PDstandardNth22gt12 = PDstandardNth22(gt12, i, j, k); + PDstandardNth33gt12 = PDstandardNth33(gt12, i, j, k); + PDstandardNth12gt12 = PDstandardNth12(gt12, i, j, k); + PDstandardNth13gt12 = PDstandardNth13(gt12, i, j, k); + PDstandardNth23gt12 = PDstandardNth23(gt12, i, j, k); + PDstandardNth1gt13 = PDstandardNth1(gt13, i, j, k); + PDstandardNth2gt13 = PDstandardNth2(gt13, i, j, k); + PDstandardNth3gt13 = PDstandardNth3(gt13, i, j, k); + PDstandardNth11gt13 = PDstandardNth11(gt13, i, j, k); + PDstandardNth22gt13 = PDstandardNth22(gt13, i, j, k); + PDstandardNth33gt13 = PDstandardNth33(gt13, i, j, k); + PDstandardNth12gt13 = PDstandardNth12(gt13, i, j, k); + PDstandardNth13gt13 = PDstandardNth13(gt13, i, j, k); + PDstandardNth23gt13 = PDstandardNth23(gt13, i, j, k); + PDstandardNth1gt22 = PDstandardNth1(gt22, i, j, k); + PDstandardNth2gt22 = PDstandardNth2(gt22, i, j, k); + PDstandardNth3gt22 = PDstandardNth3(gt22, i, j, k); + PDstandardNth11gt22 = PDstandardNth11(gt22, i, j, k); + PDstandardNth22gt22 = PDstandardNth22(gt22, i, j, k); + PDstandardNth33gt22 = PDstandardNth33(gt22, i, j, k); + PDstandardNth12gt22 = PDstandardNth12(gt22, i, j, k); + PDstandardNth13gt22 = PDstandardNth13(gt22, i, j, k); + PDstandardNth23gt22 = PDstandardNth23(gt22, i, j, k); + PDstandardNth1gt23 = PDstandardNth1(gt23, i, j, k); + PDstandardNth2gt23 = PDstandardNth2(gt23, i, j, k); + PDstandardNth3gt23 = PDstandardNth3(gt23, i, j, k); + PDstandardNth11gt23 = PDstandardNth11(gt23, i, j, k); + PDstandardNth22gt23 = PDstandardNth22(gt23, i, j, k); + PDstandardNth33gt23 = PDstandardNth33(gt23, i, j, k); + PDstandardNth12gt23 = PDstandardNth12(gt23, i, j, k); + PDstandardNth13gt23 = PDstandardNth13(gt23, i, j, k); + PDstandardNth23gt23 = PDstandardNth23(gt23, i, j, k); + PDstandardNth1gt33 = PDstandardNth1(gt33, i, j, k); + PDstandardNth2gt33 = PDstandardNth2(gt33, i, j, k); + PDstandardNth3gt33 = PDstandardNth3(gt33, i, j, k); + PDstandardNth11gt33 = PDstandardNth11(gt33, i, j, k); + PDstandardNth22gt33 = PDstandardNth22(gt33, i, j, k); + PDstandardNth33gt33 = PDstandardNth33(gt33, i, j, k); + PDstandardNth12gt33 = PDstandardNth12(gt33, i, j, k); + PDstandardNth13gt33 = PDstandardNth13(gt33, i, j, k); + PDstandardNth23gt33 = PDstandardNth23(gt33, i, j, k); + PDstandardNth1phi = PDstandardNth1(phi, i, j, k); + PDstandardNth2phi = PDstandardNth2(phi, i, j, k); + PDstandardNth3phi = PDstandardNth3(phi, i, j, k); + PDstandardNth11phi = PDstandardNth11(phi, i, j, k); + PDstandardNth22phi = PDstandardNth22(phi, i, j, k); + PDstandardNth33phi = PDstandardNth33(phi, i, j, k); + PDstandardNth12phi = PDstandardNth12(phi, i, j, k); + PDstandardNth13phi = PDstandardNth13(phi, i, j, k); + PDstandardNth23phi = PDstandardNth23(phi, i, j, k); + PDstandardNth1trK = PDstandardNth1(trK, i, j, k); + PDstandardNth2trK = PDstandardNth2(trK, i, j, k); + PDstandardNth3trK = PDstandardNth3(trK, i, j, k); + PDstandardNth1Xt1 = PDstandardNth1(Xt1, i, j, k); + PDstandardNth2Xt1 = PDstandardNth2(Xt1, i, j, k); + PDstandardNth3Xt1 = PDstandardNth3(Xt1, i, j, k); + PDstandardNth1Xt2 = PDstandardNth1(Xt2, i, j, k); + PDstandardNth2Xt2 = PDstandardNth2(Xt2, i, j, k); + PDstandardNth3Xt2 = PDstandardNth3(Xt2, i, j, k); + PDstandardNth1Xt3 = PDstandardNth1(Xt3, i, j, k); + PDstandardNth2Xt3 = PDstandardNth2(Xt3, i, j, k); + PDstandardNth3Xt3 = PDstandardNth3(Xt3, i, j, k); /* Precompute derivatives (old style) */ @@ -373,68 +373,68 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); - Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu21*PDstandard4th1gt12 + gtu31*PDstandard4th1gt13) - - gtu21*PDstandard4th2gt11 - gtu31*PDstandard4th3gt11); + Gt111 = khalf*(gtu11*PDstandardNth1gt11 + 2*(gtu21*PDstandardNth1gt12 + gtu31*PDstandardNth1gt13) - + gtu21*PDstandardNth2gt11 - gtu31*PDstandardNth3gt11); - Gt211 = khalf*(gtu21*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt12 + gtu32*PDstandard4th1gt13) - - gtu22*PDstandard4th2gt11 - gtu32*PDstandard4th3gt11); + Gt211 = khalf*(gtu21*PDstandardNth1gt11 + 2*(gtu22*PDstandardNth1gt12 + gtu32*PDstandardNth1gt13) - + gtu22*PDstandardNth2gt11 - gtu32*PDstandardNth3gt11); - Gt311 = khalf*(gtu31*PDstandard4th1gt11 + 2*(gtu32*PDstandard4th1gt12 + gtu33*PDstandard4th1gt13) - - gtu32*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); + Gt311 = khalf*(gtu31*PDstandardNth1gt11 + 2*(gtu32*PDstandardNth1gt12 + gtu33*PDstandardNth1gt13) - + gtu32*PDstandardNth2gt11 - gtu33*PDstandardNth3gt11); - Gt112 = khalf*(gtu21*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + - gtu31*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + Gt112 = khalf*(gtu21*PDstandardNth1gt22 + gtu11*PDstandardNth2gt11 + + gtu31*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); - Gt212 = khalf*(gtu22*PDstandard4th1gt22 + gtu21*PDstandard4th2gt11 + - gtu32*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + Gt212 = khalf*(gtu22*PDstandardNth1gt22 + gtu21*PDstandardNth2gt11 + + gtu32*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); - Gt312 = khalf*(gtu32*PDstandard4th1gt22 + gtu31*PDstandard4th2gt11 + - gtu33*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + Gt312 = khalf*(gtu32*PDstandardNth1gt22 + gtu31*PDstandardNth2gt11 + + gtu33*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); - Gt113 = khalf*(gtu31*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + - gtu21*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + Gt113 = khalf*(gtu31*PDstandardNth1gt33 + gtu11*PDstandardNth3gt11 + + gtu21*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); - Gt213 = khalf*(gtu32*PDstandard4th1gt33 + gtu21*PDstandard4th3gt11 + - gtu22*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + Gt213 = khalf*(gtu32*PDstandardNth1gt33 + gtu21*PDstandardNth3gt11 + + gtu22*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); - Gt313 = khalf*(gtu33*PDstandard4th1gt33 + gtu31*PDstandard4th3gt11 + - gtu32*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + Gt313 = khalf*(gtu33*PDstandardNth1gt33 + gtu31*PDstandardNth3gt11 + + gtu32*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); - Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu21*PDstandard4th2gt22 + - gtu31*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + Gt122 = khalf*(gtu11*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu21*PDstandardNth2gt22 + + gtu31*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); - Gt222 = khalf*(gtu21*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu22*PDstandard4th2gt22 + - gtu32*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + Gt222 = khalf*(gtu21*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu22*PDstandardNth2gt22 + + gtu32*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); - Gt322 = khalf*(gtu31*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu32*PDstandard4th2gt22 + - gtu33*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + Gt322 = khalf*(gtu31*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu32*PDstandardNth2gt22 + + gtu33*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); - Gt123 = khalf*(gtu31*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu21*PDstandard4th3gt22); + Gt123 = khalf*(gtu31*PDstandardNth2gt33 + gtu11*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu21*PDstandardNth3gt22); - Gt223 = khalf*(gtu32*PDstandard4th2gt33 + gtu21*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu22*PDstandard4th3gt22); + Gt223 = khalf*(gtu32*PDstandardNth2gt33 + gtu21*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu22*PDstandardNth3gt22); - Gt323 = khalf*(gtu33*PDstandard4th2gt33 + gtu31*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu32*PDstandard4th3gt22); + Gt323 = khalf*(gtu33*PDstandardNth2gt33 + gtu31*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu32*PDstandardNth3gt22); - Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu21*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt13 + - 2*gtu21*PDstandard4th3gt23 + gtu31*PDstandard4th3gt33); + Gt133 = khalf*(-(gtu11*PDstandardNth1gt33) - gtu21*PDstandardNth2gt33 + 2*gtu11*PDstandardNth3gt13 + + 2*gtu21*PDstandardNth3gt23 + gtu31*PDstandardNth3gt33); - Gt233 = khalf*(-(gtu21*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu21*PDstandard4th3gt13 + - 2*gtu22*PDstandard4th3gt23 + gtu32*PDstandard4th3gt33); + Gt233 = khalf*(-(gtu21*PDstandardNth1gt33) - gtu22*PDstandardNth2gt33 + 2*gtu21*PDstandardNth3gt13 + + 2*gtu22*PDstandardNth3gt23 + gtu32*PDstandardNth3gt33); - Gt333 = khalf*(-(gtu31*PDstandard4th1gt33) - gtu32*PDstandard4th2gt33 + 2*gtu31*PDstandard4th3gt13 + - 2*gtu32*PDstandard4th3gt23 + gtu33*PDstandard4th3gt33); + Gt333 = khalf*(-(gtu31*PDstandardNth1gt33) - gtu32*PDstandardNth2gt33 + 2*gtu31*PDstandardNth3gt13 + + 2*gtu32*PDstandardNth3gt23 + gtu33*PDstandardNth3gt33); - Rt11 = -(gtu11*khalf*PDstandard4th11gt11) + gtu21* + Rt11 = -(gtu11*khalf*PDstandardNth11gt11) + gtu21* (2*Gt211*Gt212*gt22L + 4*Gt112*gt13L*Gt311 + 2*Gt113*gt11L*Gt312 + 2*gt13L*Gt312*Gt313 + 2*gt13L*Gt211*Gt322 + - 2*gt13L*Gt311*Gt323 + 2*Gt311*Gt312*gt33L - PDstandard4th12gt11) - gtu31*PDstandard4th13gt11 + - gt11L*PDstandard4th1Xt1 + gt12L*(4*Gt111*Gt212*gtu21 + 2*Gt211*Gt222*gtu21 + 2*Gt212*Gt222*gtu22 + - 4*Gt113*Gt211*gtu31 + 4*Gt113*Gt212*gtu32 + 4*Gt113*Gt213*gtu33 + PDstandard4th1Xt2) + + 2*gt13L*Gt311*Gt323 + 2*Gt311*Gt312*gt33L - PDstandardNth12gt11) - gtu31*PDstandardNth13gt11 + + gt11L*PDstandardNth1Xt1 + gt12L*(4*Gt111*Gt212*gtu21 + 2*Gt211*Gt222*gtu21 + 2*Gt212*Gt222*gtu22 + + 4*Gt113*Gt211*gtu31 + 4*Gt113*Gt212*gtu32 + 4*Gt113*Gt213*gtu33 + PDstandardNth1Xt2) + gt13L*(4*Gt111*Gt312*gtu21 + 2*Gt212*Gt312*gtu21 + 4*Gt112*Gt312*gtu22 + 4*Gt113*Gt311*gtu31 + - 4*Gt113*Gt312*gtu32 + 4*Gt113*Gt313*gtu33 + PDstandard4th1Xt3) - gtu22*khalf*PDstandard4th22gt11 - - gtu32*PDstandard4th23gt11 - gtu33*khalf*PDstandard4th33gt11 + + 4*Gt113*Gt312*gtu32 + 4*Gt113*Gt313*gtu33 + PDstandardNth1Xt3) - gtu22*khalf*PDstandardNth22gt11 - + gtu32*PDstandardNth23gt11 - gtu33*khalf*PDstandardNth33gt11 + Gt111*(6*Gt113*gt11L*gtu31 + 4*gt12L*Gt213*gtu31 + gt11L*Xt1L) + Gt211*(2*Gt112*gt11L*gtu11 + 4*Gt111*gt12L*gtu11 + 2*gt11L*Gt122*gtu21 + 2*gt11L*Gt123*gtu31 + gt12L*Xt1L) + Gt311*(4*Gt111*gt13L*gtu11 + 2*gt12L*Gt213*gtu11 + 2*gt13L*Gt313*gtu11 + 2*gt11L*Gt123*gtu21 + @@ -459,10 +459,10 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA gt12L*gtu21*SQR(Gt212)) + gt22L*gtu33*SQR(Gt213) + gt33L*gtu11*SQR(Gt311) + gt33L*gtu22*SQR(Gt312) + 2*gt13L*gtu31*SQR(Gt313) + gt33L*gtu33*SQR(Gt313); - Rt12 = khalf*(-(gtu11*PDstandard4th11gt12) - 2*gtu21*PDstandard4th12gt12 - 2*gtu31*PDstandard4th13gt12 + - gt12L*PDstandard4th1Xt1 + gt22L*PDstandard4th1Xt2 + gt23L*PDstandard4th1Xt3 - gtu22*PDstandard4th22gt12 - - 2*gtu32*PDstandard4th23gt12 + gt11L*PDstandard4th2Xt1 + gt12L*PDstandard4th2Xt2 + gt13L*PDstandard4th2Xt3 - - gtu33*PDstandard4th33gt12 + (Gt111*gt12L + Gt211*gt22L + gt23L*Gt311)*Xt1L + + Rt12 = khalf*(-(gtu11*PDstandardNth11gt12) - 2*gtu21*PDstandardNth12gt12 - 2*gtu31*PDstandardNth13gt12 + + gt12L*PDstandardNth1Xt1 + gt22L*PDstandardNth1Xt2 + gt23L*PDstandardNth1Xt3 - gtu22*PDstandardNth22gt12 - + 2*gtu32*PDstandardNth23gt12 + gt11L*PDstandardNth2Xt1 + gt12L*PDstandardNth2Xt2 + gt13L*PDstandardNth2Xt3 - + gtu33*PDstandardNth33gt12 + (Gt111*gt12L + Gt211*gt22L + gt23L*Gt311)*Xt1L + (Gt112*gt11L + gt12L*Gt212 + gt13L*Gt312)*Xt1L + (Gt112*gt12L + Gt212*gt22L + gt23L*Gt312)*Xt2L + (gt11L*Gt122 + gt12L*Gt222 + gt13L*Gt322)*Xt2L + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt3L + (gt11L*Gt123 + gt12L*Gt223 + gt13L*Gt323)*Xt3L + @@ -511,10 +511,10 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA Gt112*(2*gt11L*Gt123 + Gt113*gt12L + gt12L*Gt223 + gt13L*Gt323) + gt12L*(Gt122*Gt213 + Gt123*(2*Gt212 + Gt313) + Gt223*(Gt222 + Gt323)) + Gt312*Gt323*gt33L + gt13L*SQR(Gt323))); - Rt13 = khalf*(-(gtu11*PDstandard4th11gt13) - 2*gtu21*PDstandard4th12gt13 - 2*gtu31*PDstandard4th13gt13 + - gt13L*PDstandard4th1Xt1 + gt23L*PDstandard4th1Xt2 + gt33L*PDstandard4th1Xt3 - gtu22*PDstandard4th22gt13 - - 2*gtu32*PDstandard4th23gt13 - gtu33*PDstandard4th33gt13 + gt11L*PDstandard4th3Xt1 + gt12L*PDstandard4th3Xt2 + - gt13L*PDstandard4th3Xt3 + (Gt113*gt11L + gt12L*Gt213 + gt13L*Gt313)*Xt1L + + Rt13 = khalf*(-(gtu11*PDstandardNth11gt13) - 2*gtu21*PDstandardNth12gt13 - 2*gtu31*PDstandardNth13gt13 + + gt13L*PDstandardNth1Xt1 + gt23L*PDstandardNth1Xt2 + gt33L*PDstandardNth1Xt3 - gtu22*PDstandardNth22gt13 - + 2*gtu32*PDstandardNth23gt13 - gtu33*PDstandardNth33gt13 + gt11L*PDstandardNth3Xt1 + gt12L*PDstandardNth3Xt2 + + gt13L*PDstandardNth3Xt3 + (Gt113*gt11L + gt12L*Gt213 + gt13L*Gt313)*Xt1L + (Gt111*gt13L + Gt211*gt23L + Gt311*gt33L)*Xt1L + (gt11L*Gt123 + gt12L*Gt223 + gt13L*Gt323)*Xt2L + (Gt112*gt13L + Gt212*gt23L + Gt312*gt33L)*Xt2L + (gt11L*Gt133 + gt12L*Gt233 + gt13L*Gt333)*Xt3L + (Gt113*gt13L + Gt213*gt23L + Gt313*gt33L)*Xt3L + @@ -564,18 +564,18 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA gt13L*SQR(Gt333))); Rt22 = 4*(Gt122*gt12L*Gt212*gtu21 + Gt112*gt12L*Gt222*gtu21 + Gt122*gt12L*Gt222*gtu22 + Gt123*gt12L*Gt212*gtu31 + - Gt123*gt12L*Gt222*gtu32 + Gt123*gt12L*Gt223*gtu33) - gtu11*khalf*PDstandard4th11gt22 + + Gt123*gt12L*Gt222*gtu32 + Gt123*gt12L*Gt223*gtu33) - gtu11*khalf*PDstandardNth11gt22 + gtu21*(6*Gt212*Gt222*gt22L + 2*Gt122*gt23L*Gt311 + 2*Gt122*gt13L*Gt312 + 4*Gt222*gt23L*Gt312 + - 2*Gt113*gt12L*Gt322 + 2*gt23L*Gt312*Gt323 + 2*Gt312*Gt322*gt33L - PDstandard4th12gt22) + + 2*Gt113*gt12L*Gt322 + 2*gt23L*Gt312*Gt323 + 2*Gt312*Gt322*gt33L - PDstandardNth12gt22) + gtu31*(6*Gt212*Gt223*gt22L + 2*Gt123*gt13L*Gt312 + 2*Gt112*gt23L*Gt313 + 2*Gt113*gt12L*Gt323 + - 2*gt23L*Gt312*Gt333 + 2*Gt312*Gt323*gt33L - PDstandard4th13gt22) - gtu22*khalf*PDstandard4th22gt22 + + 2*gt23L*Gt312*Gt333 + 2*Gt312*Gt323*gt33L - PDstandardNth13gt22) - gtu22*khalf*PDstandardNth22gt22 + gtu32*(4*Gt122*gt12L*Gt223 + 2*Gt123*Gt212*gt22L + 2*gt12L*Gt133*Gt322 + 4*Gt223*gt23L*Gt322 + - 2*Gt123*gt12L*Gt323 + 4*Gt222*gt23L*Gt323 + 2*gt23L*Gt322*Gt333 + 2*Gt322*Gt323*gt33L - PDstandard4th23gt22) + - gt12L*(2*Gt111*Gt123*gtu31 + 4*Gt112*Gt223*gtu31 + 2*Gt113*Gt122*gtu32 + 2*Gt113*Gt123*gtu33 + PDstandard4th2Xt1) + - gt22L*(2*Gt122*Gt213*gtu32 + 6*Gt222*Gt223*gtu32 + 2*Gt123*Gt213*gtu33 + PDstandard4th2Xt2) + + 2*Gt123*gt12L*Gt323 + 4*Gt222*gt23L*Gt323 + 2*gt23L*Gt322*Gt333 + 2*Gt322*Gt323*gt33L - PDstandardNth23gt22) + + gt12L*(2*Gt111*Gt123*gtu31 + 4*Gt112*Gt223*gtu31 + 2*Gt113*Gt122*gtu32 + 2*Gt113*Gt123*gtu33 + PDstandardNth2Xt1) + + gt22L*(2*Gt122*Gt213*gtu32 + 6*Gt222*Gt223*gtu32 + 2*Gt123*Gt213*gtu33 + PDstandardNth2Xt2) + gt23L*(4*Gt212*Gt322*gtu21 + 2*Gt313*Gt322*gtu21 + 4*Gt222*Gt322*gtu22 + 2*Gt123*Gt311*gtu31 + 4*Gt212*Gt323*gtu31 + 2*Gt313*Gt323*gtu31 + 2*Gt122*Gt313*gtu32 + 2*Gt123*Gt313*gtu33 + 4*Gt223*Gt323*gtu33 + - 2*Gt323*Gt333*gtu33 + PDstandard4th2Xt3) - gtu33*khalf*PDstandard4th33gt22 + Gt212*gt22L*Xt1L + + 2*Gt323*Gt333*gtu33 + PDstandardNth2Xt3) - gtu33*khalf*PDstandardNth33gt22 + Gt212*gt22L*Xt1L + Gt112*(2*Gt111*gt12L*gtu11 + 4*gt12L*Gt212*gtu11 + 2*gt11L*Gt122*gtu21 + 2*Gt122*gt12L*gtu22 + 2*gt11L*Gt123*gtu31 + 2*Gt123*gt12L*gtu32 + gt12L*Xt1L) + Gt312*(2*Gt213*gt22L*gtu11 + 4*Gt212*gt23L*gtu11 + 2*gt23L*Gt313*gtu11 + 2*Gt123*gt12L*gtu21 + @@ -593,10 +593,10 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA 3*gt22L*gtu11*SQR(Gt212) + 3*gt22L*gtu22*SQR(Gt222) + 3*gt22L*gtu33*SQR(Gt223) + gt33L*gtu11*SQR(Gt312) + gt33L*gtu22*SQR(Gt322) + 2*gt23L*gtu32*SQR(Gt323) + gt33L*gtu33*SQR(Gt323); - Rt23 = khalf*(-(gtu11*PDstandard4th11gt23) - 2*gtu21*PDstandard4th12gt23 - 2*gtu31*PDstandard4th13gt23 - - gtu22*PDstandard4th22gt23 - 2*gtu32*PDstandard4th23gt23 + gt13L*PDstandard4th2Xt1 + gt23L*PDstandard4th2Xt2 + - gt33L*PDstandard4th2Xt3 - gtu33*PDstandard4th33gt23 + gt12L*PDstandard4th3Xt1 + gt22L*PDstandard4th3Xt2 + - gt23L*PDstandard4th3Xt3 + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt1L + + Rt23 = khalf*(-(gtu11*PDstandardNth11gt23) - 2*gtu21*PDstandardNth12gt23 - 2*gtu31*PDstandardNth13gt23 - + gtu22*PDstandardNth22gt23 - 2*gtu32*PDstandardNth23gt23 + gt13L*PDstandardNth2Xt1 + gt23L*PDstandardNth2Xt2 + + gt33L*PDstandardNth2Xt3 - gtu33*PDstandardNth33gt23 + gt12L*PDstandardNth3Xt1 + gt22L*PDstandardNth3Xt2 + + gt23L*PDstandardNth3Xt3 + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt1L + (Gt112*gt13L + Gt212*gt23L + Gt312*gt33L)*Xt1L + (Gt123*gt12L + Gt223*gt22L + gt23L*Gt323)*Xt2L + (Gt122*gt13L + Gt222*gt23L + Gt322*gt33L)*Xt2L + (gt12L*Gt133 + gt22L*Gt233 + gt23L*Gt333)*Xt3L + (Gt123*gt13L + Gt223*gt23L + Gt323*gt33L)*Xt3L + @@ -647,16 +647,16 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA Rt33 = 4*(Gt123*gt13L*Gt323*gtu22 + Gt223*gt23L*Gt323*gtu22 + Gt133*gt13L*Gt313*gtu31 + Gt233*gt23L*Gt313*gtu31 + Gt113*gt13L*Gt333*gtu31 + Gt133*gt13L*Gt323*gtu32 + Gt233*gt23L*Gt323*gtu32 + Gt123*gt13L*Gt333*gtu32 + Gt133*gt13L*Gt333*gtu33) + gtu21*(2*Gt212*Gt223*gt23L + 4*Gt123*gt13L*Gt313 + 4*Gt223*gt23L*Gt313 + - 4*Gt113*gt13L*Gt323 + 4*Gt213*gt23L*Gt323 + 2*Gt123*Gt311*gt33L - PDstandard4th12gt33) + - gtu31*(4*Gt213*gt23L*Gt333 + 2*Gt233*Gt312*gt33L + 6*Gt313*Gt333*gt33L - PDstandard4th13gt33) - - gtu22*khalf*PDstandard4th22gt33 + gtu32*(4*Gt223*gt23L*Gt333 + 2*Gt123*Gt313*gt33L + 6*Gt323*Gt333*gt33L - - PDstandard4th23gt33) - gtu33*khalf*PDstandard4th33gt33 + gt13L*PDstandard4th3Xt1 + gt23L*PDstandard4th3Xt2 + + 4*Gt113*gt13L*Gt323 + 4*Gt213*gt23L*Gt323 + 2*Gt123*Gt311*gt33L - PDstandardNth12gt33) + + gtu31*(4*Gt213*gt23L*Gt333 + 2*Gt233*Gt312*gt33L + 6*Gt313*Gt333*gt33L - PDstandardNth13gt33) - + gtu22*khalf*PDstandardNth22gt33 + gtu32*(4*Gt223*gt23L*Gt333 + 2*Gt123*Gt313*gt33L + 6*Gt323*Gt333*gt33L - + PDstandardNth23gt33) - gtu33*khalf*PDstandardNth33gt33 + gt13L*PDstandardNth3Xt1 + gt23L*PDstandardNth3Xt2 + gt33L*(2*Gt213*Gt322*gtu21 + 6*Gt313*Gt323*gtu21 + 2*Gt123*Gt312*gtu22 + 2*Gt133*Gt311*gtu31 + - 2*Gt133*Gt312*gtu32 + 2*Gt133*Gt313*gtu33 + PDstandard4th3Xt3) + Gt113*gt13L*Xt1L + Gt213*gt23L*Xt1L + + 2*Gt133*Gt312*gtu32 + 2*Gt133*Gt313*gtu33 + PDstandardNth3Xt3) + Gt113*gt13L*Xt1L + Gt213*gt23L*Xt1L + Gt313*gt33L*Xt1L + Gt123*gt13L*Xt2L + Gt223*gt23L*Xt2L + Gt323*gt33L*Xt2L + Gt133*gt13L*Xt3L + Gt333*gt33L*Xt3L + Gt233*(4*gt23L*Gt333*gtu33 + 2*Gt323*gt33L*gtu33 + gt23L*Xt3L) + gtu11*(2*Gt212*Gt213*gt23L + 4*Gt113*gt13L*Gt313 + 4*Gt213*gt23L*Gt313 + 2*Gt113*Gt311*gt33L + - 2*Gt213*Gt312*gt33L - khalf*PDstandard4th11gt33 + gt11L*SQR(Gt113)) + + 2*Gt213*Gt312*gt33L - khalf*PDstandardNth11gt33 + gt11L*SQR(Gt113)) + 2*(Gt111*Gt113*gt13L*gtu11 + Gt113*gt12L*Gt213*gtu11 + Gt112*gt13L*Gt213*gtu11 + Gt113*Gt211*gt23L*gtu11 + Gt113*gt11L*Gt123*gtu21 + Gt112*Gt113*gt13L*gtu21 + Gt111*Gt123*gt13L*gtu21 + Gt123*gt12L*Gt213*gtu21 + Gt122*gt13L*Gt213*gtu21 + Gt113*gt12L*Gt223*gtu21 + Gt112*gt13L*Gt223*gtu21 + Gt213*Gt223*gt22L*gtu21 + @@ -674,82 +674,82 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA gt11L*gtu33*SQR(Gt133) + gt22L*gtu11*SQR(Gt213) + gt22L*gtu22*SQR(Gt223) + 2*gt23L*gtu32*SQR(Gt223) + gt22L*gtu33*SQR(Gt233) + 3*gt33L*gtu11*SQR(Gt313) + 3*gt33L*gtu22*SQR(Gt323) + 3*gt33L*gtu33*SQR(Gt333); - Rphi11 = 2*(-PDstandard4th11phi - gt11L*gtu11*PDstandard4th11phi - 2*gt11L*gtu21*PDstandard4th12phi - - 2*gt11L*gtu31*PDstandard4th13phi - gt11L*gtu22*PDstandard4th22phi - 2*gt11L*gtu32*PDstandard4th23phi - - gt11L*gtu33*PDstandard4th33phi + Gt311*PDstandard4th3phi + gt11L*Gt311*gtu11*PDstandard4th3phi + - 2*gt11L*Gt312*gtu21*PDstandard4th3phi + gt11L*Gt322*gtu22*PDstandard4th3phi + - 2*gt11L*Gt313*gtu31*PDstandard4th3phi + 2*gt11L*Gt323*gtu32*PDstandard4th3phi + - gt11L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + Rphi11 = 2*(-PDstandardNth11phi - gt11L*gtu11*PDstandardNth11phi - 2*gt11L*gtu21*PDstandardNth12phi - + 2*gt11L*gtu31*PDstandardNth13phi - gt11L*gtu22*PDstandardNth22phi - 2*gt11L*gtu32*PDstandardNth23phi - + gt11L*gtu33*PDstandardNth33phi + Gt311*PDstandardNth3phi + gt11L*Gt311*gtu11*PDstandardNth3phi + + 2*gt11L*Gt312*gtu21*PDstandardNth3phi + gt11L*Gt322*gtu22*PDstandardNth3phi + + 2*gt11L*Gt313*gtu31*PDstandardNth3phi + 2*gt11L*Gt323*gtu32*PDstandardNth3phi + + gt11L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt111 + Gt111*gt11L*gtu11 + 2*Gt112*gt11L*gtu21 + gt11L*Gt122*gtu22 + 2*Gt113*gt11L*gtu31 + - 2*gt11L*Gt123*gtu32 + gt11L*Gt133*gtu33 - 4*gt11L*gtu21*PDstandard4th2phi - 4*gt11L*gtu31*PDstandard4th3phi) + - PDstandard4th2phi*(Gt211 + gt11L*Gt211*gtu11 + + 2*gt11L*Gt123*gtu32 + gt11L*Gt133*gtu33 - 4*gt11L*gtu21*PDstandardNth2phi - 4*gt11L*gtu31*PDstandardNth3phi) + + PDstandardNth2phi*(Gt211 + gt11L*Gt211*gtu11 + gt11L*(2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt11L*gtu32*PDstandard4th3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandard4th1phi) - - 2*gt11L*gtu22*SQR(PDstandard4th2phi) - 2*gt11L*gtu33*SQR(PDstandard4th3phi)); - - Rphi12 = 2*(-(gt12L*gtu11*PDstandard4th11phi) - PDstandard4th12phi - 2*gt12L*gtu21*PDstandard4th12phi - - 2*gt12L*gtu31*PDstandard4th13phi - gt12L*gtu22*PDstandard4th22phi - 2*gt12L*gtu32*PDstandard4th23phi - - gt12L*gtu33*PDstandard4th33phi + Gt312*PDstandard4th3phi + gt12L*Gt311*gtu11*PDstandard4th3phi + - 2*gt12L*Gt312*gtu21*PDstandard4th3phi + gt12L*Gt322*gtu22*PDstandard4th3phi + - 2*gt12L*Gt313*gtu31*PDstandard4th3phi + 2*gt12L*Gt323*gtu32*PDstandard4th3phi + - gt12L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt11L*gtu32*PDstandardNth3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandardNth1phi) - + 2*gt11L*gtu22*SQR(PDstandardNth2phi) - 2*gt11L*gtu33*SQR(PDstandardNth3phi)); + + Rphi12 = 2*(-(gt12L*gtu11*PDstandardNth11phi) - PDstandardNth12phi - 2*gt12L*gtu21*PDstandardNth12phi - + 2*gt12L*gtu31*PDstandardNth13phi - gt12L*gtu22*PDstandardNth22phi - 2*gt12L*gtu32*PDstandardNth23phi - + gt12L*gtu33*PDstandardNth33phi + Gt312*PDstandardNth3phi + gt12L*Gt311*gtu11*PDstandardNth3phi + + 2*gt12L*Gt312*gtu21*PDstandardNth3phi + gt12L*Gt322*gtu22*PDstandardNth3phi + + 2*gt12L*Gt313*gtu31*PDstandardNth3phi + 2*gt12L*Gt323*gtu32*PDstandardNth3phi + + gt12L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt112 + Gt111*gt12L*gtu11 + 2*Gt112*gt12L*gtu21 + Gt122*gt12L*gtu22 + 2*Gt113*gt12L*gtu31 + - 2*Gt123*gt12L*gtu32 + gt12L*Gt133*gtu33 + (2 - 4*gt12L*gtu21)*PDstandard4th2phi - - 4*gt12L*gtu31*PDstandard4th3phi) + PDstandard4th2phi* + 2*Gt123*gt12L*gtu32 + gt12L*Gt133*gtu33 + (2 - 4*gt12L*gtu21)*PDstandardNth2phi - + 4*gt12L*gtu31*PDstandardNth3phi) + PDstandardNth2phi* (Gt212 + 2*gt12L*Gt212*gtu21 + gt12L*(Gt211*gtu11 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt12L*gtu32*PDstandard4th3phi) - 2*gt12L*gtu11*SQR(PDstandard4th1phi) - - 2*gt12L*gtu22*SQR(PDstandard4th2phi) - 2*gt12L*gtu33*SQR(PDstandard4th3phi)); - - Rphi13 = 2*(-PDstandard4th13phi + gt13L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - - 2*gtu31*PDstandard4th13phi) - gt13L*gtu22*PDstandard4th22phi - 2*gt13L*gtu32*PDstandard4th23phi - - gt13L*gtu33*PDstandard4th33phi + Gt313*PDstandard4th3phi + gt13L*Gt311*gtu11*PDstandard4th3phi + - 2*gt13L*Gt312*gtu21*PDstandard4th3phi + gt13L*Gt322*gtu22*PDstandard4th3phi + - 2*gt13L*Gt313*gtu31*PDstandard4th3phi + 2*gt13L*Gt323*gtu32*PDstandard4th3phi + - gt13L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt12L*gtu32*PDstandardNth3phi) - 2*gt12L*gtu11*SQR(PDstandardNth1phi) - + 2*gt12L*gtu22*SQR(PDstandardNth2phi) - 2*gt12L*gtu33*SQR(PDstandardNth3phi)); + + Rphi13 = 2*(-PDstandardNth13phi + gt13L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - + 2*gtu31*PDstandardNth13phi) - gt13L*gtu22*PDstandardNth22phi - 2*gt13L*gtu32*PDstandardNth23phi - + gt13L*gtu33*PDstandardNth33phi + Gt313*PDstandardNth3phi + gt13L*Gt311*gtu11*PDstandardNth3phi + + 2*gt13L*Gt312*gtu21*PDstandardNth3phi + gt13L*Gt322*gtu22*PDstandardNth3phi + + 2*gt13L*Gt313*gtu31*PDstandardNth3phi + 2*gt13L*Gt323*gtu32*PDstandardNth3phi + + gt13L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt113 + Gt111*gt13L*gtu11 + 2*Gt112*gt13L*gtu21 + Gt122*gt13L*gtu22 + 2*Gt113*gt13L*gtu31 + - 2*Gt123*gt13L*gtu32 + Gt133*gt13L*gtu33 - 4*gt13L*gtu21*PDstandard4th2phi + - (2 - 4*gt13L*gtu31)*PDstandard4th3phi) + - PDstandard4th2phi*(Gt213 + 2*gt13L*Gt213*gtu31 + + 2*Gt123*gt13L*gtu32 + Gt133*gt13L*gtu33 - 4*gt13L*gtu21*PDstandardNth2phi + + (2 - 4*gt13L*gtu31)*PDstandardNth3phi) + + PDstandardNth2phi*(Gt213 + 2*gt13L*Gt213*gtu31 + gt13L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt13L*gtu32*PDstandard4th3phi) - 2*gt13L*gtu11*SQR(PDstandard4th1phi) - - 2*gt13L*gtu22*SQR(PDstandard4th2phi) - 2*gt13L*gtu33*SQR(PDstandard4th3phi)); - - Rphi22 = 2*(-PDstandard4th22phi + gt22L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - - 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi) - 2*gt22L*gtu32*PDstandard4th23phi - - gt22L*gtu33*PDstandard4th33phi + Gt322*PDstandard4th3phi + gt22L*Gt311*gtu11*PDstandard4th3phi + - 2*gt22L*Gt312*gtu21*PDstandard4th3phi + gt22L*Gt322*gtu22*PDstandard4th3phi + - 2*gt22L*Gt313*gtu31*PDstandard4th3phi + 2*gt22L*Gt323*gtu32*PDstandard4th3phi + - gt22L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt13L*gtu32*PDstandardNth3phi) - 2*gt13L*gtu11*SQR(PDstandardNth1phi) - + 2*gt13L*gtu22*SQR(PDstandardNth2phi) - 2*gt13L*gtu33*SQR(PDstandardNth3phi)); + + Rphi22 = 2*(-PDstandardNth22phi + gt22L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - + 2*gtu31*PDstandardNth13phi - gtu22*PDstandardNth22phi) - 2*gt22L*gtu32*PDstandardNth23phi - + gt22L*gtu33*PDstandardNth33phi + Gt322*PDstandardNth3phi + gt22L*Gt311*gtu11*PDstandardNth3phi + + 2*gt22L*Gt312*gtu21*PDstandardNth3phi + gt22L*Gt322*gtu22*PDstandardNth3phi + + 2*gt22L*Gt313*gtu31*PDstandardNth3phi + 2*gt22L*Gt323*gtu32*PDstandardNth3phi + + gt22L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt122 + Gt111*gt22L*gtu11 + 2*Gt112*gt22L*gtu21 + Gt122*gt22L*gtu22 + 2*Gt113*gt22L*gtu31 + - 2*Gt123*gt22L*gtu32 + Gt133*gt22L*gtu33 - 4*gt22L*gtu21*PDstandard4th2phi - 4*gt22L*gtu31*PDstandard4th3phi) + - PDstandard4th2phi*(Gt222 + Gt222*gt22L*gtu22 + + 2*Gt123*gt22L*gtu32 + Gt133*gt22L*gtu33 - 4*gt22L*gtu21*PDstandardNth2phi - 4*gt22L*gtu31*PDstandardNth3phi) + + PDstandardNth2phi*(Gt222 + Gt222*gt22L*gtu22 + gt22L*(Gt211*gtu11 + 2*Gt212*gtu21 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - - 4*gt22L*gtu32*PDstandard4th3phi) - 2*gt22L*gtu11*SQR(PDstandard4th1phi) + - (2 - 2*gt22L*gtu22)*SQR(PDstandard4th2phi) - 2*gt22L*gtu33*SQR(PDstandard4th3phi)); - - Rphi23 = 2*(-PDstandard4th23phi + gt23L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - - 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi) - - gt23L*gtu33*PDstandard4th33phi + Gt323*PDstandard4th3phi + gt23L*Gt311*gtu11*PDstandard4th3phi + - 2*gt23L*Gt312*gtu21*PDstandard4th3phi + gt23L*Gt322*gtu22*PDstandard4th3phi + - 2*gt23L*Gt313*gtu31*PDstandard4th3phi + 2*gt23L*Gt323*gtu32*PDstandard4th3phi + - gt23L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + 4*gt22L*gtu32*PDstandardNth3phi) - 2*gt22L*gtu11*SQR(PDstandardNth1phi) + + (2 - 2*gt22L*gtu22)*SQR(PDstandardNth2phi) - 2*gt22L*gtu33*SQR(PDstandardNth3phi)); + + Rphi23 = 2*(-PDstandardNth23phi + gt23L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - + 2*gtu31*PDstandardNth13phi - gtu22*PDstandardNth22phi - 2*gtu32*PDstandardNth23phi) - + gt23L*gtu33*PDstandardNth33phi + Gt323*PDstandardNth3phi + gt23L*Gt311*gtu11*PDstandardNth3phi + + 2*gt23L*Gt312*gtu21*PDstandardNth3phi + gt23L*Gt322*gtu22*PDstandardNth3phi + + 2*gt23L*Gt313*gtu31*PDstandardNth3phi + 2*gt23L*Gt323*gtu32*PDstandardNth3phi + + gt23L*Gt333*gtu33*PDstandardNth3phi + PDstandardNth1phi* (Gt123 + Gt111*gt23L*gtu11 + 2*Gt112*gt23L*gtu21 + Gt122*gt23L*gtu22 + 2*Gt113*gt23L*gtu31 + - 2*Gt123*gt23L*gtu32 + Gt133*gt23L*gtu33 - 4*gt23L*gtu21*PDstandard4th2phi - 4*gt23L*gtu31*PDstandard4th3phi) + - PDstandard4th2phi*(Gt223 + 2*Gt223*gt23L*gtu32 + + 2*Gt123*gt23L*gtu32 + Gt133*gt23L*gtu33 - 4*gt23L*gtu21*PDstandardNth2phi - 4*gt23L*gtu31*PDstandardNth3phi) + + PDstandardNth2phi*(Gt223 + 2*Gt223*gt23L*gtu32 + gt23L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + Gt233*gtu33) + - (2 - 4*gt23L*gtu32)*PDstandard4th3phi) - 2*gt23L*gtu11*SQR(PDstandard4th1phi) - - 2*gt23L*gtu22*SQR(PDstandard4th2phi) - 2*gt23L*gtu33*SQR(PDstandard4th3phi)); - - Rphi33 = 2*(-PDstandard4th33phi + (Gt333 + gt33L* - (Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33))*PDstandard4th3phi + - PDstandard4th2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + - Gt233*gtu33 - 4*gtu32*PDstandard4th3phi)) + - PDstandard4th1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + - Gt133*gtu33 - 4*(gtu21*PDstandard4th2phi + gtu31*PDstandard4th3phi))) + 2*SQR(PDstandard4th3phi) + - gt33L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 2*gtu31*PDstandard4th13phi - - gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi - gtu33*PDstandard4th33phi + - Gt311*gtu11*PDstandard4th3phi - 2*gtu11*SQR(PDstandard4th1phi) - 2*gtu22*SQR(PDstandard4th2phi) - - 2*gtu33*SQR(PDstandard4th3phi))); + (2 - 4*gt23L*gtu32)*PDstandardNth3phi) - 2*gt23L*gtu11*SQR(PDstandardNth1phi) - + 2*gt23L*gtu22*SQR(PDstandardNth2phi) - 2*gt23L*gtu33*SQR(PDstandardNth3phi)); + + Rphi33 = 2*(-PDstandardNth33phi + (Gt333 + gt33L* + (Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33))*PDstandardNth3phi + + PDstandardNth2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + + Gt233*gtu33 - 4*gtu32*PDstandardNth3phi)) + + PDstandardNth1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + + Gt133*gtu33 - 4*(gtu21*PDstandardNth2phi + gtu31*PDstandardNth3phi))) + 2*SQR(PDstandardNth3phi) + + gt33L*(-(gtu11*PDstandardNth11phi) - 2*gtu21*PDstandardNth12phi - 2*gtu31*PDstandardNth13phi - + gtu22*PDstandardNth22phi - 2*gtu32*PDstandardNth23phi - gtu33*PDstandardNth33phi + + Gt311*gtu11*PDstandardNth3phi - 2*gtu11*SQR(PDstandardNth1phi) - 2*gtu22*SQR(PDstandardNth2phi) - + 2*gtu33*SQR(PDstandardNth3phi))); e4phi = exp(4*phiL); @@ -807,13 +807,13 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA At22L*Gt213*gtu32 - 2*At12L*Gt223*gtu32 - At33L*Gt312*gtu32 - At23L*Gt313*gtu32 - 2*At13L*Gt323*gtu32 - 2*(At11L*Gt111*gtu11 + At12L*Gt211*gtu11 + At13L*Gt311*gtu11 + At11L*Gt123*gtu32) - At13L*Gt113*gtu33 - At11L*Gt133*gtu33 - At23L*Gt213*gtu33 - At12L*Gt233*gtu33 - At33L*Gt313*gtu33 - At13L*Gt333*gtu33 + - gtu11*PDstandard4th1At11 + gtu21*(-(At12L*Gt111) - 3*At11L*Gt112 - At22L*Gt211 - 3*At12L*Gt212 - At23L*Gt311 - - 3*At13L*Gt312 + PDstandard4th1At12) + gtu31*PDstandard4th1At13 + 6*At11L*gtu11*PDstandard4th1phi + - 6*At12L*gtu21*PDstandard4th1phi + 6*At13L*gtu31*PDstandard4th1phi - ktwothird*PDstandard4th1trK + - gtu21*PDstandard4th2At11 + gtu22*PDstandard4th2At12 + gtu32*PDstandard4th2At13 + 6*At11L*gtu21*PDstandard4th2phi + - 6*At12L*gtu22*PDstandard4th2phi + 6*At13L*gtu32*PDstandard4th2phi + gtu31*PDstandard4th3At11 + - gtu32*PDstandard4th3At12 + gtu33*PDstandard4th3At13 + 6*At11L*gtu31*PDstandard4th3phi + - 6*At12L*gtu32*PDstandard4th3phi + 6*At13L*gtu33*PDstandard4th3phi; + gtu11*PDstandardNth1At11 + gtu21*(-(At12L*Gt111) - 3*At11L*Gt112 - At22L*Gt211 - 3*At12L*Gt212 - At23L*Gt311 - + 3*At13L*Gt312 + PDstandardNth1At12) + gtu31*PDstandardNth1At13 + 6*At11L*gtu11*PDstandardNth1phi + + 6*At12L*gtu21*PDstandardNth1phi + 6*At13L*gtu31*PDstandardNth1phi - ktwothird*PDstandardNth1trK + + gtu21*PDstandardNth2At11 + gtu22*PDstandardNth2At12 + gtu32*PDstandardNth2At13 + 6*At11L*gtu21*PDstandardNth2phi + + 6*At12L*gtu22*PDstandardNth2phi + 6*At13L*gtu32*PDstandardNth2phi + gtu31*PDstandardNth3At11 + + gtu32*PDstandardNth3At12 + gtu33*PDstandardNth3At13 + 6*At11L*gtu31*PDstandardNth3phi + + 6*At12L*gtu32*PDstandardNth3phi + 6*At13L*gtu33*PDstandardNth3phi; M2L = -(At12L*Gt111*gtu11) - At11L*Gt112*gtu11 - At22L*Gt211*gtu11 - At12L*Gt212*gtu11 - At23L*Gt311*gtu11 - At13L*Gt312*gtu11 - 3*At12L*Gt112*gtu21 - At11L*Gt122*gtu21 - 3*At22L*Gt212*gtu21 - At12L*Gt222*gtu21 - @@ -822,12 +822,12 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA At12L*Gt223*gtu31 - At33L*Gt312*gtu31 - 2*At23L*Gt313*gtu31 - At13L*Gt323*gtu31 - At13L*Gt122*gtu32 - 3*At12L*Gt123*gtu32 - At23L*Gt222*gtu32 - 3*At22L*Gt223*gtu32 - At33L*Gt322*gtu32 - 3*At23L*Gt323*gtu32 - At13L*Gt123*gtu33 - At12L*Gt133*gtu33 - At23L*Gt223*gtu33 - At22L*Gt233*gtu33 - At33L*Gt323*gtu33 - - At23L*Gt333*gtu33 + gtu11*PDstandard4th1At12 + gtu21*PDstandard4th1At22 + gtu31*PDstandard4th1At23 + - 6*At12L*gtu11*PDstandard4th1phi + 6*At22L*gtu21*PDstandard4th1phi + 6*At23L*gtu31*PDstandard4th1phi + - gtu21*PDstandard4th2At12 + gtu22*PDstandard4th2At22 + gtu32*PDstandard4th2At23 + 6*At12L*gtu21*PDstandard4th2phi + - 6*At22L*gtu22*PDstandard4th2phi + 6*At23L*gtu32*PDstandard4th2phi - ktwothird*PDstandard4th2trK + - gtu31*PDstandard4th3At12 + gtu32*PDstandard4th3At22 + gtu33*PDstandard4th3At23 + 6*At12L*gtu31*PDstandard4th3phi + - 6*At22L*gtu32*PDstandard4th3phi + 6*At23L*gtu33*PDstandard4th3phi; + At23L*Gt333*gtu33 + gtu11*PDstandardNth1At12 + gtu21*PDstandardNth1At22 + gtu31*PDstandardNth1At23 + + 6*At12L*gtu11*PDstandardNth1phi + 6*At22L*gtu21*PDstandardNth1phi + 6*At23L*gtu31*PDstandardNth1phi + + gtu21*PDstandardNth2At12 + gtu22*PDstandardNth2At22 + gtu32*PDstandardNth2At23 + 6*At12L*gtu21*PDstandardNth2phi + + 6*At22L*gtu22*PDstandardNth2phi + 6*At23L*gtu32*PDstandardNth2phi - ktwothird*PDstandardNth2trK + + gtu31*PDstandardNth3At12 + gtu32*PDstandardNth3At22 + gtu33*PDstandardNth3At23 + 6*At12L*gtu31*PDstandardNth3phi + + 6*At22L*gtu32*PDstandardNth3phi + 6*At23L*gtu33*PDstandardNth3phi; M3L = -(At13L*Gt111*gtu11) - At11L*Gt113*gtu11 - At23L*Gt211*gtu11 - At12L*Gt213*gtu11 - At33L*Gt311*gtu11 - At13L*Gt313*gtu11 - 2*At13L*Gt112*gtu21 - At12L*Gt113*gtu21 - At11L*Gt123*gtu21 - 2*At23L*Gt212*gtu21 - @@ -836,14 +836,14 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA At23L*Gt323*gtu22 - 3*At13L*Gt113*gtu31 - At11L*Gt133*gtu31 - 3*At23L*Gt213*gtu31 - At12L*Gt233*gtu31 - 3*At33L*Gt313*gtu31 - At13L*Gt333*gtu31 - 3*At13L*Gt123*gtu32 - At12L*Gt133*gtu32 - 3*At23L*Gt223*gtu32 - At22L*Gt233*gtu32 - 3*At33L*Gt323*gtu32 - At23L*Gt333*gtu32 - 2*At13L*Gt133*gtu33 - 2*At23L*Gt233*gtu33 - - 2*At33L*Gt333*gtu33 + gtu11*PDstandard4th1At13 + gtu21*PDstandard4th1At23 + gtu31*PDstandard4th1At33 + - 6*At13L*gtu11*PDstandard4th1phi + 6*At23L*gtu21*PDstandard4th1phi + 6*At33L*gtu31*PDstandard4th1phi + - gtu21*PDstandard4th2At13 + gtu22*PDstandard4th2At23 + gtu32*PDstandard4th2At33 + 6*At13L*gtu21*PDstandard4th2phi + - 6*At23L*gtu22*PDstandard4th2phi + 6*At33L*gtu32*PDstandard4th2phi + gtu31*PDstandard4th3At13 + - gtu32*PDstandard4th3At23 + gtu33*PDstandard4th3At33 + 6*At13L*gtu31*PDstandard4th3phi + - 6*At23L*gtu32*PDstandard4th3phi + 6*At33L*gtu33*PDstandard4th3phi - ktwothird*PDstandard4th3trK; - - cSL = trR; + 2*At33L*Gt333*gtu33 + gtu11*PDstandardNth1At13 + gtu21*PDstandardNth1At23 + gtu31*PDstandardNth1At33 + + 6*At13L*gtu11*PDstandardNth1phi + 6*At23L*gtu21*PDstandardNth1phi + 6*At33L*gtu31*PDstandardNth1phi + + gtu21*PDstandardNth2At13 + gtu22*PDstandardNth2At23 + gtu32*PDstandardNth2At33 + 6*At13L*gtu21*PDstandardNth2phi + + 6*At23L*gtu22*PDstandardNth2phi + 6*At33L*gtu32*PDstandardNth2phi + gtu31*PDstandardNth3At13 + + gtu32*PDstandardNth3At23 + gtu33*PDstandardNth3At33 + 6*At13L*gtu31*PDstandardNth3phi + + 6*At23L*gtu32*PDstandardNth3phi + 6*At33L*gtu33*PDstandardNth3phi - ktwothird*PDstandardNth3trK; + + cSL = Log(detgt); cXt1L = Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + Gt133*gtu33 - Xt1L; diff --git a/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c b/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c index 9f36ec8..3465b8f 100644 --- a/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c +++ b/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c @@ -106,24 +106,24 @@ void ML_BSSN_convertFromADMBaseGamma_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT fa /* Declare precomputed derivatives*/ /* Declare derivatives */ - CCTK_REAL PDstandard4th1gt11 = INITVALUE; - CCTK_REAL PDstandard4th2gt11 = INITVALUE; - CCTK_REAL PDstandard4th3gt11 = INITVALUE; - CCTK_REAL PDstandard4th1gt12 = INITVALUE; - CCTK_REAL PDstandard4th2gt12 = INITVALUE; - CCTK_REAL PDstandard4th3gt12 = INITVALUE; - CCTK_REAL PDstandard4th1gt13 = INITVALUE; - CCTK_REAL PDstandard4th2gt13 = INITVALUE; - CCTK_REAL PDstandard4th3gt13 = INITVALUE; - CCTK_REAL PDstandard4th1gt22 = INITVALUE; - CCTK_REAL PDstandard4th2gt22 = INITVALUE; - CCTK_REAL PDstandard4th3gt22 = INITVALUE; - CCTK_REAL PDstandard4th1gt23 = INITVALUE; - CCTK_REAL PDstandard4th2gt23 = INITVALUE; - CCTK_REAL PDstandard4th3gt23 = INITVALUE; - CCTK_REAL PDstandard4th1gt33 = INITVALUE; - CCTK_REAL PDstandard4th2gt33 = INITVALUE; - CCTK_REAL PDstandard4th3gt33 = INITVALUE; + CCTK_REAL PDstandardNth1gt11 = INITVALUE; + CCTK_REAL PDstandardNth2gt11 = INITVALUE; + CCTK_REAL PDstandardNth3gt11 = INITVALUE; + CCTK_REAL PDstandardNth1gt12 = INITVALUE; + CCTK_REAL PDstandardNth2gt12 = INITVALUE; + CCTK_REAL PDstandardNth3gt12 = INITVALUE; + CCTK_REAL PDstandardNth1gt13 = INITVALUE; + CCTK_REAL PDstandardNth2gt13 = INITVALUE; + CCTK_REAL PDstandardNth3gt13 = INITVALUE; + CCTK_REAL PDstandardNth1gt22 = INITVALUE; + CCTK_REAL PDstandardNth2gt22 = INITVALUE; + CCTK_REAL PDstandardNth3gt22 = INITVALUE; + CCTK_REAL PDstandardNth1gt23 = INITVALUE; + CCTK_REAL PDstandardNth2gt23 = INITVALUE; + CCTK_REAL PDstandardNth3gt23 = INITVALUE; + CCTK_REAL PDstandardNth1gt33 = INITVALUE; + CCTK_REAL PDstandardNth2gt33 = INITVALUE; + CCTK_REAL PDstandardNth3gt33 = INITVALUE; /* Assign local copies of grid functions */ gt11L = gt11[index]; @@ -138,24 +138,24 @@ void ML_BSSN_convertFromADMBaseGamma_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT fa /* Include user supplied include files */ /* Precompute derivatives (new style) */ - PDstandard4th1gt11 = PDstandard4th1(gt11, i, j, k); - PDstandard4th2gt11 = PDstandard4th2(gt11, i, j, k); - PDstandard4th3gt11 = PDstandard4th3(gt11, i, j, k); - PDstandard4th1gt12 = PDstandard4th1(gt12, i, j, k); - PDstandard4th2gt12 = PDstandard4th2(gt12, i, j, k); - PDstandard4th3gt12 = PDstandard4th3(gt12, i, j, k); - PDstandard4th1gt13 = PDstandard4th1(gt13, i, j, k); - PDstandard4th2gt13 = PDstandard4th2(gt13, i, j, k); - PDstandard4th3gt13 = PDstandard4th3(gt13, i, j, k); - PDstandard4th1gt22 = PDstandard4th1(gt22, i, j, k); - PDstandard4th2gt22 = PDstandard4th2(gt22, i, j, k); - PDstandard4th3gt22 = PDstandard4th3(gt22, i, j, k); - PDstandard4th1gt23 = PDstandard4th1(gt23, i, j, k); - PDstandard4th2gt23 = PDstandard4th2(gt23, i, j, k); - PDstandard4th3gt23 = PDstandard4th3(gt23, i, j, k); - PDstandard4th1gt33 = PDstandard4th1(gt33, i, j, k); - PDstandard4th2gt33 = PDstandard4th2(gt33, i, j, k); - PDstandard4th3gt33 = PDstandard4th3(gt33, i, j, k); + PDstandardNth1gt11 = PDstandardNth1(gt11, i, j, k); + PDstandardNth2gt11 = PDstandardNth2(gt11, i, j, k); + PDstandardNth3gt11 = PDstandardNth3(gt11, i, j, k); + PDstandardNth1gt12 = PDstandardNth1(gt12, i, j, k); + PDstandardNth2gt12 = PDstandardNth2(gt12, i, j, k); + PDstandardNth3gt12 = PDstandardNth3(gt12, i, j, k); + PDstandardNth1gt13 = PDstandardNth1(gt13, i, j, k); + PDstandardNth2gt13 = PDstandardNth2(gt13, i, j, k); + PDstandardNth3gt13 = PDstandardNth3(gt13, i, j, k); + PDstandardNth1gt22 = PDstandardNth1(gt22, i, j, k); + PDstandardNth2gt22 = PDstandardNth2(gt22, i, j, k); + PDstandardNth3gt22 = PDstandardNth3(gt22, i, j, k); + PDstandardNth1gt23 = PDstandardNth1(gt23, i, j, k); + PDstandardNth2gt23 = PDstandardNth2(gt23, i, j, k); + PDstandardNth3gt23 = PDstandardNth3(gt23, i, j, k); + PDstandardNth1gt33 = PDstandardNth1(gt33, i, j, k); + PDstandardNth2gt33 = PDstandardNth2(gt33, i, j, k); + PDstandardNth3gt33 = PDstandardNth3(gt33, i, j, k); /* Precompute derivatives (old style) */ @@ -174,59 +174,59 @@ void ML_BSSN_convertFromADMBaseGamma_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT fa gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); - Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu21*PDstandard4th1gt12 + gtu31*PDstandard4th1gt13) - - gtu21*PDstandard4th2gt11 - gtu31*PDstandard4th3gt11); + Gt111 = khalf*(gtu11*PDstandardNth1gt11 + 2*(gtu21*PDstandardNth1gt12 + gtu31*PDstandardNth1gt13) - + gtu21*PDstandardNth2gt11 - gtu31*PDstandardNth3gt11); - Gt211 = khalf*(gtu21*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt12 + gtu32*PDstandard4th1gt13) - - gtu22*PDstandard4th2gt11 - gtu32*PDstandard4th3gt11); + Gt211 = khalf*(gtu21*PDstandardNth1gt11 + 2*(gtu22*PDstandardNth1gt12 + gtu32*PDstandardNth1gt13) - + gtu22*PDstandardNth2gt11 - gtu32*PDstandardNth3gt11); - Gt311 = khalf*(gtu31*PDstandard4th1gt11 + 2*(gtu32*PDstandard4th1gt12 + gtu33*PDstandard4th1gt13) - - gtu32*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); + Gt311 = khalf*(gtu31*PDstandardNth1gt11 + 2*(gtu32*PDstandardNth1gt12 + gtu33*PDstandardNth1gt13) - + gtu32*PDstandardNth2gt11 - gtu33*PDstandardNth3gt11); - Gt112 = khalf*(gtu21*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + - gtu31*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + Gt112 = khalf*(gtu21*PDstandardNth1gt22 + gtu11*PDstandardNth2gt11 + + gtu31*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); - Gt212 = khalf*(gtu22*PDstandard4th1gt22 + gtu21*PDstandard4th2gt11 + - gtu32*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + Gt212 = khalf*(gtu22*PDstandardNth1gt22 + gtu21*PDstandardNth2gt11 + + gtu32*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); - Gt312 = khalf*(gtu32*PDstandard4th1gt22 + gtu31*PDstandard4th2gt11 + - gtu33*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + Gt312 = khalf*(gtu32*PDstandardNth1gt22 + gtu31*PDstandardNth2gt11 + + gtu33*(PDstandardNth1gt23 + PDstandardNth2gt13 - PDstandardNth3gt12)); - Gt113 = khalf*(gtu31*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + - gtu21*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + Gt113 = khalf*(gtu31*PDstandardNth1gt33 + gtu11*PDstandardNth3gt11 + + gtu21*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); - Gt213 = khalf*(gtu32*PDstandard4th1gt33 + gtu21*PDstandard4th3gt11 + - gtu22*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + Gt213 = khalf*(gtu32*PDstandardNth1gt33 + gtu21*PDstandardNth3gt11 + + gtu22*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); - Gt313 = khalf*(gtu33*PDstandard4th1gt33 + gtu31*PDstandard4th3gt11 + - gtu32*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + Gt313 = khalf*(gtu33*PDstandardNth1gt33 + gtu31*PDstandardNth3gt11 + + gtu32*(PDstandardNth1gt23 - PDstandardNth2gt13 + PDstandardNth3gt12)); - Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu21*PDstandard4th2gt22 + - gtu31*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + Gt122 = khalf*(gtu11*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu21*PDstandardNth2gt22 + + gtu31*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); - Gt222 = khalf*(gtu21*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu22*PDstandard4th2gt22 + - gtu32*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + Gt222 = khalf*(gtu21*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu22*PDstandardNth2gt22 + + gtu32*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); - Gt322 = khalf*(gtu31*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu32*PDstandard4th2gt22 + - gtu33*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + Gt322 = khalf*(gtu31*(-PDstandardNth1gt22 + 2*PDstandardNth2gt12) + gtu32*PDstandardNth2gt22 + + gtu33*(2*PDstandardNth2gt23 - PDstandardNth3gt22)); - Gt123 = khalf*(gtu31*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu21*PDstandard4th3gt22); + Gt123 = khalf*(gtu31*PDstandardNth2gt33 + gtu11*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu21*PDstandardNth3gt22); - Gt223 = khalf*(gtu32*PDstandard4th2gt33 + gtu21*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu22*PDstandard4th3gt22); + Gt223 = khalf*(gtu32*PDstandardNth2gt33 + gtu21*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu22*PDstandardNth3gt22); - Gt323 = khalf*(gtu33*PDstandard4th2gt33 + gtu31*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + - gtu32*PDstandard4th3gt22); + Gt323 = khalf*(gtu33*PDstandardNth2gt33 + gtu31*(-PDstandardNth1gt23 + PDstandardNth2gt13 + PDstandardNth3gt12) + + gtu32*PDstandardNth3gt22); - Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu21*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt13 + - 2*gtu21*PDstandard4th3gt23 + gtu31*PDstandard4th3gt33); + Gt133 = khalf*(-(gtu11*PDstandardNth1gt33) - gtu21*PDstandardNth2gt33 + 2*gtu11*PDstandardNth3gt13 + + 2*gtu21*PDstandardNth3gt23 + gtu31*PDstandardNth3gt33); - Gt233 = khalf*(-(gtu21*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu21*PDstandard4th3gt13 + - 2*gtu22*PDstandard4th3gt23 + gtu32*PDstandard4th3gt33); + Gt233 = khalf*(-(gtu21*PDstandardNth1gt33) - gtu22*PDstandardNth2gt33 + 2*gtu21*PDstandardNth3gt13 + + 2*gtu22*PDstandardNth3gt23 + gtu32*PDstandardNth3gt33); - Gt333 = khalf*(-(gtu31*PDstandard4th1gt33) - gtu32*PDstandard4th2gt33 + 2*gtu31*PDstandard4th3gt13 + - 2*gtu32*PDstandard4th3gt23 + gtu33*PDstandard4th3gt33); + Gt333 = khalf*(-(gtu31*PDstandardNth1gt33) - gtu32*PDstandardNth2gt33 + 2*gtu31*PDstandardNth3gt13 + + 2*gtu32*PDstandardNth3gt23 + gtu33*PDstandardNth3gt33); Xt1L = Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + Gt133*gtu33; diff --git a/m/McLachlan.m b/m/McLachlan.m index 67cf90a..010d503 100644 --- a/m/McLachlan.m +++ b/m/McLachlan.m @@ -10,29 +10,31 @@ SetSourceLanguage["C"]; (* Derivatives *) (******************************************************************************) +derivOrder = 4; + derivatives = { (* PDstandard2nd[i_] -> StandardCenteredDifferenceOperator[1,1,i], PDstandard2nd[i_, i_] -> StandardCenteredDifferenceOperator[2,1,i], PDstandard2nd[i_, j_] -> StandardCenteredDifferenceOperator[1,1,i] - StandardCenteredDifferenceOperator[1,1,j], + StandardCenteredDifferenceOperator[1,1,j] *) + (* PDstandard4th[i_] -> StandardCenteredDifferenceOperator[1,2,i], PDstandard4th[i_, i_] -> StandardCenteredDifferenceOperator[2,2,i], PDstandard4th[i_, j_] -> StandardCenteredDifferenceOperator[1,2,i] StandardCenteredDifferenceOperator[1,2,j] - - (* - PDstandard6th[i_] -> StandardCenteredDifferenceOperator[1,3,i], - PDstandard6th[i_, i_] -> StandardCenteredDifferenceOperator[2,3,i], - PDstandard6th[i_, j_] -> StandardCenteredDifferenceOperator[1,3,i] - StandardCenteredDifferenceOperator[1,3,j] *) + + PDstandardNth[i_] -> StandardCenteredDifferenceOperator[1,derivOrder/2,i], + PDstandardNth[i_, i_] -> StandardCenteredDifferenceOperator[2,derivOrder/2,i], + PDstandardNth[i_, j_] -> StandardCenteredDifferenceOperator[1,derivOrder/2,i] + StandardCenteredDifferenceOperator[1,derivOrder/2,j] }; -PD = PDstandard4th; +PD = PDstandardNth; KD = KroneckerDelta; @@ -621,18 +623,21 @@ constraintsCalcBSSN = Atm[ua,lb] -> gtu[ua,uc] At[lc,lb], (* H -> trR - Km[ua,lb] Km[ub,la] + trK^2, *) + (* PRD 67, 084023 (2003), eqn. (19) *) H -> trR - Atm[ua,lb] Atm[ub,la] + (2/3) trK^2, (* (* gK[la,lb,lc] -> CD[K[la,lb],lc], *) gK[la,lb,lc] -> + 4 e4phi PD[phi,lc] At[la,lb] + e4phi CD[At[la,lb],lc] + (1/3) g[la,lb] PD[trK,lc], + M[la] -> gu[ub,uc] (gK[lc,la,lb] - gK[lc,lb,la]), *) M[li] -> + gtu[uj,uk] ( CDt[At[li,lj],lk] + 6 At[li,lj] PD[phi,lk] ) - (2/3) PD[trK,li], + (* TODO: use PRD 67, 084023 (2003), eqn. (20) *) + (* det gamma-tilde *) - (* TODO cS -> Log [detgt], *) - cS -> trR, + cS -> Log [detgt], (* Gamma constraint *) cXt[ua] -> gtu[ub,uc] Gt[ua,lb,lc] - Xt[ua], diff --git a/m/McLachlan.sh b/m/McLachlan.sh index d305eaa..b4f74f3 100755 --- a/m/McLachlan.sh +++ b/m/McLachlan.sh @@ -7,6 +7,9 @@ #MATHEMATICA="/Applications/Mathematica.app/Contents/MacOS/MathKernel" MATHEMATICA="math" +# Abort on errors +set -e + # Remove old output rm -rf ML_ADM ML_BSSN @@ -28,5 +31,5 @@ fi ./copy-if-changed.sh ML_BSSN ../ML_BSSN echo -echo "The Cactus thorns have been successfully regenerated." +echo "The Cactus thorns have been regenerated successfully." echo diff --git a/par/ks_bssn_0_8th.par b/par/ks_bssn_0_8th.par new file mode 100644 index 0000000..fa8b6c6 --- /dev/null +++ b/par/ks_bssn_0_8th.par @@ -0,0 +1,172 @@ +ActiveThorns = " + Boundary + CartGrid3D + CoordBase + IOUtil + InitBase + MoL + SymBase + + ADMAnalysis + ADMBase + ADMConstraints + ADMCoupling + ADMMacros + CoordGauge + SpaceMask + StaticConformal + + NaNChecker + + Carpet + CarpetIOASCII + CarpetIOBasic + CarpetIOScalar + CarpetLib + CarpetReduce + LoopControl + + ReflectionSymmetry + + Exact + Formaline + GSL + + Slab + + GenericFD + + ML_BSSN +" + + + +Cactus::cctk_itlast = 0 + +grid::type = "CoordBase" + +CoordBase::domainsize = "minmax" + +CoordBase::xmax = 4.0 +CoordBase::ymax = 4.0 +CoordBase::zmax = 4.0 +CoordBase::dx = 0.4 +CoordBase::dy = 0.4 +CoordBase::dz = 0.4 + +ReflectionSymmetry::reflection_x = yes +ReflectionSymmetry::reflection_y = yes +ReflectionSymmetry::reflection_z = yes +ReflectionSymmetry::avoid_origin_x = no +ReflectionSymmetry::avoid_origin_y = no +ReflectionSymmetry::avoid_origin_z = no + +CoordBase::boundary_shiftout_x_lower = 1 +CoordBase::boundary_shiftout_y_lower = 1 +CoordBase::boundary_shiftout_z_lower = 1 + +Carpet::domain_from_coordbase = yes +driver::ghost_size = 4 +Carpet::use_buffer_zones = yes + +CoordBase::boundary_size_x_lower = 4 +CoordBase::boundary_size_y_lower = 4 +CoordBase::boundary_size_z_lower = 4 +CoordBase::boundary_size_x_upper = 4 +CoordBase::boundary_size_y_upper = 4 +CoordBase::boundary_size_z_upper = 4 + + + +ADMBase::initial_data = "exact" +ADMBase::initial_lapse = "exact" +ADMBase::initial_shift = "exact" +ADMBase::initial_dtlapse = "zero" +ADMBase::initial_dtshift = "zero" + +Exact::exact_model = "Kerr/Kerr-Schild" +Exact::Kerr_KerrSchild__mass = 1.0 +Exact::Kerr_KerrSchild__spin = 0.0 + +ML_BSSN::harmonicN = 0 # 1+log +ML_BSSN::harmonicF = 2.0 # 1+log +ML_BSSN::ShiftGammaCoeff = 0.75 +ML_BSSN::BetaDriver = 0.5 + +ML_BSSN::log_confac_bound = "none" +ML_BSSN::metric_bound = "none" +ML_BSSN::Gamma_bound = "none" +ML_BSSN::trace_curv_bound = "none" +ML_BSSN::curv_bound = "none" +ML_BSSN::lapse_bound = "none" +ML_BSSN::dtlapse_bound = "none" +ML_BSSN::shift_bound = "none" +ML_BSSN::dtshift_bound = "none" + +ADMMacros::spatial_order = 4 + + + +IO::out_dir = $parfile + +IOBasic::outInfo_every = 1 +IOBasic::outInfo_vars = " + ML_BSSN::H + ML_BSSN::trKrhs +" + +IOScalar::one_file_per_group = yes +IOScalar::outScalar_every = 1 +IOScalar::outScalar_vars = " + ADMBase::metric + ADMBase::curv + ADMBase::lapse + ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma + ML_BSSN::Ham + ML_BSSN::mom + ML_BSSN::cons_detg + ML_BSSN::cons_Gamma + ML_BSSN::cons_traceA + ML_BSSN::log_confacrhs + ML_BSSN::metricrhs + ML_BSSN::Gammarhs + ML_BSSN::trace_curvrhs + ML_BSSN::curvrhs +" + +IOASCII::one_file_per_group = yes +IOASCII::out1D_every = 1 +IOASCII::out1D_vars = " + ADMBase::metric + ADMBase::curv + ADMBase::lapse + ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma + ML_BSSN::Ham + ML_BSSN::mom + ML_BSSN::cons_detg + ML_BSSN::cons_Gamma + ML_BSSN::cons_traceA + ML_BSSN::log_confacrhs + ML_BSSN::metricrhs + ML_BSSN::Gammarhs + ML_BSSN::trace_curvrhs + ML_BSSN::curvrhs +" diff --git a/par/ks_bssn_1_8th.par b/par/ks_bssn_1_8th.par new file mode 100644 index 0000000..64b0497 --- /dev/null +++ b/par/ks_bssn_1_8th.par @@ -0,0 +1,172 @@ +ActiveThorns = " + Boundary + CartGrid3D + CoordBase + IOUtil + InitBase + MoL + SymBase + + ADMAnalysis + ADMBase + ADMConstraints + ADMCoupling + ADMMacros + CoordGauge + SpaceMask + StaticConformal + + NaNChecker + + Carpet + CarpetIOASCII + CarpetIOBasic + CarpetIOScalar + CarpetLib + CarpetReduce + LoopControl + + ReflectionSymmetry + + Exact + Formaline + GSL + + Slab + + GenericFD + + ML_BSSN +" + + + +Cactus::cctk_itlast = 0 + +grid::type = "CoordBase" + +CoordBase::domainsize = "minmax" + +CoordBase::xmax = 4.0 +CoordBase::ymax = 4.0 +CoordBase::zmax = 4.0 +CoordBase::dx = 0.2 +CoordBase::dy = 0.2 +CoordBase::dz = 0.2 + +ReflectionSymmetry::reflection_x = yes +ReflectionSymmetry::reflection_y = yes +ReflectionSymmetry::reflection_z = yes +ReflectionSymmetry::avoid_origin_x = no +ReflectionSymmetry::avoid_origin_y = no +ReflectionSymmetry::avoid_origin_z = no + +CoordBase::boundary_shiftout_x_lower = 1 +CoordBase::boundary_shiftout_y_lower = 1 +CoordBase::boundary_shiftout_z_lower = 1 + +Carpet::domain_from_coordbase = yes +driver::ghost_size = 4 +Carpet::use_buffer_zones = yes + +CoordBase::boundary_size_x_lower = 4 +CoordBase::boundary_size_y_lower = 4 +CoordBase::boundary_size_z_lower = 4 +CoordBase::boundary_size_x_upper = 4 +CoordBase::boundary_size_y_upper = 4 +CoordBase::boundary_size_z_upper = 4 + + + +ADMBase::initial_data = "exact" +ADMBase::initial_lapse = "exact" +ADMBase::initial_shift = "exact" +ADMBase::initial_dtlapse = "zero" +ADMBase::initial_dtshift = "zero" + +Exact::exact_model = "Kerr/Kerr-Schild" +Exact::Kerr_KerrSchild__mass = 1.0 +Exact::Kerr_KerrSchild__spin = 0.0 + +ML_BSSN::harmonicN = 0 # 1+log +ML_BSSN::harmonicF = 2.0 # 1+log +ML_BSSN::ShiftGammaCoeff = 0.75 +ML_BSSN::BetaDriver = 0.5 + +ML_BSSN::log_confac_bound = "none" +ML_BSSN::metric_bound = "none" +ML_BSSN::Gamma_bound = "none" +ML_BSSN::trace_curv_bound = "none" +ML_BSSN::curv_bound = "none" +ML_BSSN::lapse_bound = "none" +ML_BSSN::dtlapse_bound = "none" +ML_BSSN::shift_bound = "none" +ML_BSSN::dtshift_bound = "none" + +ADMMacros::spatial_order = 4 + + + +IO::out_dir = $parfile + +IOBasic::outInfo_every = 1 +IOBasic::outInfo_vars = " + ML_BSSN::H + ML_BSSN::trKrhs +" + +IOScalar::one_file_per_group = yes +IOScalar::outScalar_every = 1 +IOScalar::outScalar_vars = " + ADMBase::metric + ADMBase::curv + ADMBase::lapse + ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma + ML_BSSN::Ham + ML_BSSN::mom + ML_BSSN::cons_detg + ML_BSSN::cons_Gamma + ML_BSSN::cons_traceA + ML_BSSN::log_confacrhs + ML_BSSN::metricrhs + ML_BSSN::Gammarhs + ML_BSSN::trace_curvrhs + ML_BSSN::curvrhs +" + +IOASCII::one_file_per_group = yes +IOASCII::out1D_every = 1 +IOASCII::out1D_vars = " + ADMBase::metric + ADMBase::curv + ADMBase::lapse + ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma + ML_BSSN::Ham + ML_BSSN::mom + ML_BSSN::cons_detg + ML_BSSN::cons_Gamma + ML_BSSN::cons_traceA + ML_BSSN::log_confacrhs + ML_BSSN::metricrhs + ML_BSSN::Gammarhs + ML_BSSN::trace_curvrhs + ML_BSSN::curvrhs +" diff --git a/par/ks_bssn_2_8th.par b/par/ks_bssn_2_8th.par new file mode 100644 index 0000000..4c757d8 --- /dev/null +++ b/par/ks_bssn_2_8th.par @@ -0,0 +1,172 @@ +ActiveThorns = " + Boundary + CartGrid3D + CoordBase + IOUtil + InitBase + MoL + SymBase + + ADMAnalysis + ADMBase + ADMConstraints + ADMCoupling + ADMMacros + CoordGauge + SpaceMask + StaticConformal + + NaNChecker + + Carpet + CarpetIOASCII + CarpetIOBasic + CarpetIOScalar + CarpetLib + CarpetReduce + LoopControl + + ReflectionSymmetry + + Exact + Formaline + GSL + + Slab + + GenericFD + + ML_BSSN +" + + + +Cactus::cctk_itlast = 0 + +grid::type = "CoordBase" + +CoordBase::domainsize = "minmax" + +CoordBase::xmax = 4.0 +CoordBase::ymax = 4.0 +CoordBase::zmax = 4.0 +CoordBase::dx = 0.1 +CoordBase::dy = 0.1 +CoordBase::dz = 0.1 + +ReflectionSymmetry::reflection_x = yes +ReflectionSymmetry::reflection_y = yes +ReflectionSymmetry::reflection_z = yes +ReflectionSymmetry::avoid_origin_x = no +ReflectionSymmetry::avoid_origin_y = no +ReflectionSymmetry::avoid_origin_z = no + +CoordBase::boundary_shiftout_x_lower = 1 +CoordBase::boundary_shiftout_y_lower = 1 +CoordBase::boundary_shiftout_z_lower = 1 + +Carpet::domain_from_coordbase = yes +driver::ghost_size = 4 +Carpet::use_buffer_zones = yes + +CoordBase::boundary_size_x_lower = 4 +CoordBase::boundary_size_y_lower = 4 +CoordBase::boundary_size_z_lower = 4 +CoordBase::boundary_size_x_upper = 4 +CoordBase::boundary_size_y_upper = 4 +CoordBase::boundary_size_z_upper = 4 + + + +ADMBase::initial_data = "exact" +ADMBase::initial_lapse = "exact" +ADMBase::initial_shift = "exact" +ADMBase::initial_dtlapse = "zero" +ADMBase::initial_dtshift = "zero" + +Exact::exact_model = "Kerr/Kerr-Schild" +Exact::Kerr_KerrSchild__mass = 1.0 +Exact::Kerr_KerrSchild__spin = 0.0 + +ML_BSSN::harmonicN = 0 # 1+log +ML_BSSN::harmonicF = 2.0 # 1+log +ML_BSSN::ShiftGammaCoeff = 0.75 +ML_BSSN::BetaDriver = 0.5 + +ML_BSSN::log_confac_bound = "none" +ML_BSSN::metric_bound = "none" +ML_BSSN::Gamma_bound = "none" +ML_BSSN::trace_curv_bound = "none" +ML_BSSN::curv_bound = "none" +ML_BSSN::lapse_bound = "none" +ML_BSSN::dtlapse_bound = "none" +ML_BSSN::shift_bound = "none" +ML_BSSN::dtshift_bound = "none" + +ADMMacros::spatial_order = 4 + + + +IO::out_dir = $parfile + +IOBasic::outInfo_every = 1 +IOBasic::outInfo_vars = " + ML_BSSN::H + ML_BSSN::trKrhs +" + +IOScalar::one_file_per_group = yes +IOScalar::outScalar_every = 1 +IOScalar::outScalar_vars = " + ADMBase::metric + ADMBase::curv + ADMBase::lapse + ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma + ML_BSSN::Ham + ML_BSSN::mom + ML_BSSN::cons_detg + ML_BSSN::cons_Gamma + ML_BSSN::cons_traceA + ML_BSSN::log_confacrhs + ML_BSSN::metricrhs + ML_BSSN::Gammarhs + ML_BSSN::trace_curvrhs + ML_BSSN::curvrhs +" + +IOASCII::one_file_per_group = yes +IOASCII::out1D_every = 1 +IOASCII::out1D_vars = " + ADMBase::metric + ADMBase::curv + ADMBase::lapse + ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma + ML_BSSN::Ham + ML_BSSN::mom + ML_BSSN::cons_detg + ML_BSSN::cons_Gamma + ML_BSSN::cons_traceA + ML_BSSN::log_confacrhs + ML_BSSN::metricrhs + ML_BSSN::Gammarhs + ML_BSSN::trace_curvrhs + ML_BSSN::curvrhs +" |