diff options
| author | Erik Schnetter <schnetter@cct.lsu.edu> | 2011-01-03 20:52:14 -0500 |
|---|---|---|
| committer | Erik Schnetter <schnetter@cct.lsu.edu> | 2011-01-03 20:52:14 -0500 |
| commit | 2d3cc7e6ec5ee99362d0a2136794a86de1c530de (patch) | |
| tree | 0d7dac5ef112110feaf94610869137c2a65c4d41 /m/McLachlan_BSSN.m | |
| parent | d878d1165de32fb3bd3c66abfe9121af67ccca85 (diff) | |
Calculate the Ricci scalar for the BSSN constrains in the same way as for the time evolution; this simplifies the generated code significantly.
Diffstat (limited to 'm/McLachlan_BSSN.m')
| -rw-r--r-- | m/McLachlan_BSSN.m | 30 |
1 files changed, 18 insertions, 12 deletions
diff --git a/m/McLachlan_BSSN.m b/m/McLachlan_BSSN.m index 0550d4d..8cb0fdd 100644 --- a/m/McLachlan_BSSN.m +++ b/m/McLachlan_BSSN.m @@ -908,7 +908,9 @@ constraintsCalc = Name -> BSSN <> "_constraints", Schedule -> Automatic, Where -> Interior, - Shorthands -> {detgt, ddetgt[la], gtu[ua,ub], Gt[ua,lb,lc], e4phi, em4phi, + Shorthands -> {detgt, ddetgt[la], gtu[ua,ub], + Gt[ua,lb,lc], Gtl[la,lb,lc], Gtlu[la,lb,uc], Xtn[ua], + e4phi, em4phi, g[la,lb], detg, gu[ua,ub], ddetg[la], G[ua,lb,lc], Rt[la,lb], Rphi[la,lb], R[la,lb], trR, Atm[la,lb], gK[la,lb,lc], cdphi[la], cdphi2[la,lb], @@ -917,23 +919,27 @@ constraintsCalc = { detgt -> 1 (* detgtExpr *), ddetgt[la] -> 0 (* ddetgtExpr[la] *), + + (* This leads to simpler code... *) gtu[ua,ub] -> 1/detgt detgtExpr MatrixInverse [gt[ua,ub]], - Gt[ua,lb,lc] -> 1/2 gtu[ua,ud] - (PD[gt[lb,ld],lc] + PD[gt[lc,ld],lb] - PD[gt[lb,lc],ld]), + Gtl[la,lb,lc] -> 1/2 + (PD[gt[lb,la],lc] + PD[gt[lc,la],lb] - PD[gt[lb,lc],la]), + Gtlu[la,lb,uc] -> gtu[uc,ud] Gtl[la,lb,ld], + Gt[ua,lb,lc] -> gtu[ua,ud] Gtl[ld,lb,lc], + (* The conformal connection functions calculated from the conformal metric, + used instead of Xt where no derivatives of Xt are taken *) + Xtn[ui] -> gtu[uj,uk] Gt[ui,lj,lk], + (* PRD 62, 044034 (2000), eqn. (18) *) - (* Note: This differs from the Goddard formulation, - which is e.g. described in PRD 70 (2004) 124025, eqn. (6). - Goddard has a Gamma^k replaced by its definition in terms - of metric derivatives. *) Rt[li,lj] -> - (1/2) gtu[ul,um] PD[gt[li,lj],ll,lm] + (1/2) gt[lk,li] PD[Xt[uk],lj] + (1/2) gt[lk,lj] PD[Xt[uk],li] - + (1/2) Xt[uk] gt[li,ln] Gt[un,lj,lk] - + (1/2) Xt[uk] gt[lj,ln] Gt[un,li,lk] - + gtu[ul,um] (+ Gt[uk,ll,li] gt[lj,ln] Gt[un,lk,lm] - + Gt[uk,ll,lj] gt[li,ln] Gt[un,lk,lm] - + Gt[uk,li,lm] gt[lk,ln] Gt[un,ll,lj]), + + (1/2) Xtn[uk] Gtl[li,lj,lk] + + (1/2) Xtn[uk] Gtl[lj,li,lk] + + (+ Gt[uk,li,ll] Gtlu[lj,lk,ul] + + Gt[uk,lj,ll] Gtlu[li,lk,ul] + + Gt[uk,li,ll] Gtlu[lk,lj,ul]), (* From the long turducken paper. This expression seems to give the same result as the one from 044034. *) |