def BSSN_constraints__generate_symbolic_expressions(
enable_stress_energy_source_terms=False,
leave_Ricci_symbolic=True,
output_H_only=False):
######################################
# START: GENERATE SYMBOLIC EXPRESSIONS
starttime = print_msg_with_timing("BSSN constraints",
msg="Symbolic",
startstop="start")
# Define the Hamiltonian constraint and output the optimized C code.
par.set_parval_from_str("BSSN.BSSN_quantities::LeaveRicciSymbolic",
str(leave_Ricci_symbolic))
import BSSN.BSSN_constraints as bssncon
# Returns None if enable_stress_energy_source_terms==False; otherwise returns symb expressions for T4UU
T4UU = register_stress_energy_source_terms_return_T4UU(
enable_stress_energy_source_terms)
bssncon.BSSN_constraints(
add_T4UUmunu_source_terms=False,
output_H_only=output_H_only) # We'll add them below if desired.
if enable_stress_energy_source_terms:
import BSSN.BSSN_stress_energy_source_terms as Bsest
Bsest.BSSN_source_terms_for_BSSN_constraints(T4UU)
bssncon.H += Bsest.sourceterm_H
for i in range(3):
bssncon.MU[i] += Bsest.sourceterm_MU[i]
BSSN_constraints_SymbExpressions = [
lhrh(lhs=gri.gfaccess("aux_gfs", "H"), rhs=bssncon.H)
]
if not output_H_only:
BSSN_constraints_SymbExpressions += [
lhrh(lhs=gri.gfaccess("aux_gfs", "MU0"), rhs=bssncon.MU[0]),
lhrh(lhs=gri.gfaccess("aux_gfs", "MU1"), rhs=bssncon.MU[1]),
lhrh(lhs=gri.gfaccess("aux_gfs", "MU2"), rhs=bssncon.MU[2])
]
par.set_parval_from_str("BSSN.BSSN_quantities::LeaveRicciSymbolic",
"False")
print_msg_with_timing("BSSN constraints",
msg="Symbolic",
startstop="stop",
starttime=starttime)
# END: GENERATE SYMBOLIC EXPRESSIONS
######################################
return BSSN_constraints_SymbExpressions
def BSSN_constraints__generate_symbolic_expressions_and_C_code():
######################################
# START: GENERATE SYMBOLIC EXPRESSIONS
# Define the Hamiltonian constraint and output the optimized C code.
import BSSN.BSSN_constraints as bssncon
bssncon.BSSN_constraints(add_T4UUmunu_source_terms=False)
if T4UU != None:
import BSSN.BSSN_stress_energy_source_terms as Bsest
Bsest.BSSN_source_terms_for_BSSN_RHSs(T4UU)
Bsest.BSSN_source_terms_for_BSSN_constraints(T4UU)
bssncon.H += Bsest.sourceterm_H
for i in range(3):
bssncon.MU[i] += Bsest.sourceterm_MU[i]
# END: GENERATE SYMBOLIC EXPRESSIONS
######################################
# Store original finite-differencing order:
FD_order_orig = par.parval_from_str("finite_difference::FD_CENTDERIVS_ORDER")
# Set new finite-differencing order:
par.set_parval_from_str("finite_difference::FD_CENTDERIVS_ORDER", FD_order)
start = time.time()
print("Generating optimized C code for Ham. & mom. constraints. May take a while, depending on CoordSystem.")
Ham_mom_string = fin.FD_outputC("returnstring",
[lhrh(lhs=gri.gfaccess("aux_gfs", "H"), rhs=bssncon.H),
lhrh(lhs=gri.gfaccess("aux_gfs", "MU0"), rhs=bssncon.MU[0]),
lhrh(lhs=gri.gfaccess("aux_gfs", "MU1"), rhs=bssncon.MU[1]),
lhrh(lhs=gri.gfaccess("aux_gfs", "MU2"), rhs=bssncon.MU[2])],
params="outCverbose=False")
with open(os.path.join(outdir,"BSSN_constraints_enable_Tmunu_"+str(enable_stress_energy_source_terms)+"_FD_order_"+str(FD_order)+".h"), "w") as file:
file.write(lp.loop(["i2","i1","i0"],["cctk_nghostzones[2]","cctk_nghostzones[1]","cctk_nghostzones[0]"],
["cctk_lsh[2]-cctk_nghostzones[2]","cctk_lsh[1]-cctk_nghostzones[1]","cctk_lsh[0]-cctk_nghostzones[0]"],
["1","1","1"],["#pragma omp parallel for","",""], "", Ham_mom_string))
# Restore original finite-differencing order:
par.set_parval_from_str("finite_difference::FD_CENTDERIVS_ORDER", FD_order_orig)
end = time.time()
print("(BENCH) Finished Hamiltonian & momentum constraint C codegen (FD_order="+str(FD_order)+",Tmunu="+str(enable_stress_energy_source_terms)+") in " + str(end - start) + " seconds.")
def test_example_BSSN():
parse_latex(r"""
\begin{align}
% keydef basis [x, y, z]
% ignore "\\%", "\qquad"
% vardef -kron 'deltaDD'
% parse \hat{\gamma}_{ij} = \delta_{ij}
% assign -diff_type=symbolic -metric 'gammahatDD'
% vardef -diff_type=dD -symmetry=sym01 'hDD'
% parse \bar{\gamma}_{ij} = h_{ij} + \hat{\gamma}_{ij}
% assign -diff_type=dD -metric 'gammabarDD'
% srepl "\beta" -> "\text{vet}"
% vardef -diff_type=dD 'vetU'
%% upwind pattern inside Lie derivative expansion
% srepl -persist "\text{vet}^{<1>} \partial_{<1>}" -> "\text{vet}^{<1>} \vphantom{dupD} \partial_{<1>}"
%% substitute tensor identity (see appropriate BSSN notebook)
% srepl "\bar{D}_k \text{vet}^k" -> "(\partial_k \text{vet}^k + \frac{\partial_k \text{gammahatdet} \text{vet}^k}{2 \text{gammahatdet}})"
% srepl "\bar{A}" -> "\text{a}"
% vardef -diff_type=dD -symmetry=sym01 'aDD'
% assign -metric='gammabar' 'aDD'
% srepl "\partial_t \bar{\gamma}" -> "\text{h_rhs}"
\partial_t \bar{\gamma}_{ij} &= \mathcal{L}_\beta \bar{\gamma}_{ij}
+ \frac{2}{3} \bar{\gamma}_{ij} \left(\alpha \bar{A}^k{}_k - \bar{D}_k \beta^k\right) - 2 \alpha \bar{A}_{ij} \\
% srepl "K" -> "\text{trK}"
% vardef -diff_type=dD 'cf', 'trK'
%% replace 'phi' with conformal factor cf = W = e^{-2\phi}
% srepl "e^{-4\phi}" -> "\text{cf}^2"
% srepl "\partial_t \phi = <1..> \\" -> "\text{cf_rhs} = -2 \text{cf} (<1..>) \\"
% srepl -persist "\partial_{<1>} \phi" -> "\partial_{<1>} \text{cf} \frac{-1}{2 \text{cf}}"
% srepl "\partial_<1> \phi" -> "\partial_<1> \text{cf} \frac{-1}{2 \text{cf}}"
\partial_t \phi &= \mathcal{L}_\beta \phi + \frac{1}{6} \left(\bar{D}_k \beta^k - \alpha K \right) \\
% vardef -diff_type=dD 'alpha'
% srepl "\partial_t \text{trK}" -> "\text{trK_rhs}"
\partial_t K &= \mathcal{L}_\beta K + \frac{1}{3} \alpha K^2 + \alpha \bar{A}_{ij} \bar{A}^{ij}
- e^{-4\phi} \left(\bar{D}_i \bar{D}^i \alpha + 2 \bar{D}^i \alpha \bar{D}_i \phi\right) \\
% srepl "\bar{\Lambda}" -> "\text{lambda}"
% vardef -diff_type=dD 'lambdaU'
% parse \Delta^k_{ij} = \bar{\Gamma}^k_{ij} - \hat{\Gamma}^k_{ij}
% assign -metric='gammabar' 'DeltaUDD'
% parse \Delta^k = \bar{\gamma}^{ij} \Delta^k_{ij}
% srepl "\partial_t \text{lambda}" -> "\text{Lambdabar_rhs}"
\partial_t \bar{\Lambda}^i &= \mathcal{L}_\beta \bar{\Lambda}^i + \bar{\gamma}^{jk} \hat{D}_j \hat{D}_k \beta^i
+ \frac{2}{3} \Delta^i \bar{D}_k \beta^k + \frac{1}{3} \bar{D}^i \bar{D}_k \beta^k \\%
&\qquad- 2 \bar{A}^{ij} \left(\partial_j \alpha - 6 \alpha \partial_j \phi\right)
+ 2 \alpha \bar{A}^{jk} \Delta^i_{jk} - \frac{4}{3} \alpha \bar{\gamma}^{ij} \partial_j K \\
% vardef -diff_type=dD -symmetry=sym01 'RbarDD'
X_{ij} &= -2 \alpha \bar{D}_i \bar{D}_j \phi + 4 \alpha \bar{D}_i \phi \bar{D}_j \phi
+ 2 \bar{D}_i \alpha \bar{D}_j \phi + 2 \bar{D}_j \alpha \bar{D}_i \phi
- \bar{D}_i \bar{D}_j \alpha + \alpha \bar{R}_{ij} \\
\hat{X}_{ij} &= X_{ij} - \frac{1}{3} \bar{\gamma}_{ij} \bar{\gamma}^{kl} X_{kl} \\
% srepl "\partial_t \text{a}" -> "\text{a_rhs}"
\partial_t \bar{A}_{ij} &= \mathcal{L}_\beta \bar{A}_{ij} - \frac{2}{3} \bar{A}_{ij} \bar{D}_k \beta^k
- 2 \alpha \bar{A}_{ik} \bar{A}^k_j + \alpha \bar{A}_{ij} K + e^{-4\phi} \hat{X}_{ij} \\
% srepl "\partial_t \alpha" -> "\text{alpha_rhs}"
\partial_t \alpha &= \mathcal{L}_\beta \alpha - 2 \alpha K \\
% srepl "B" -> "\text{bet}"
% vardef -diff_type=dD 'betU'
% srepl "\partial_t \text{vet}" -> "\text{vet_rhs}"
\partial_t \beta^i &= \left[\beta^j \vphantom{dupD} \bar{D}_j \beta^i\right] + B^i \\
% vardef -const 'eta'
% srepl "\partial_t \text{bet}" -> "\text{bet_rhs}"
\partial_t B^i &= \left[\beta^j \vphantom{dupD} \bar{D}_j B^i\right]
+ \frac{3}{4} \left(\partial_t \bar{\Lambda}^i - \left[\beta^j \vphantom{dupD} \bar{D}_j \bar{\Lambda}^i\right]\right) - \eta B^i \\
% parse \bar{R} = \bar{\gamma}^{ij} \bar{R}_{ij}
% srepl "\bar{D}^2" -> "\bar{D}^i \bar{D}_i", "\mathcal{<1>}" -> "<1>"
\mathcal{H} &= \frac{2}{3} K^2 - \bar{A}_{ij} \bar{A}^{ij}
+ e^{-4\phi} \left(\bar{R} - 8 \bar{D}^i \phi \bar{D}_i \phi - 8 \bar{D}^2 \phi\right) \\
\mathcal{M}^i &= e^{-4\phi} \left(\bar{D}_j \bar{A}^{ij} + 6 \bar{A}^{ij} \partial_j \phi
- \frac{2}{3} \bar{\gamma}^{ij} \partial_j K\right) \\
\bar{R}_{ij} &= -\frac{1}{2} \bar{\gamma}^{kl} \hat{D}_k \hat{D}_l \bar{\gamma}_{ij}
+ \frac{1}{2} \left(\bar{\gamma}_{ki} \hat{D}_j \bar{\Lambda}^k + \bar{\gamma}_{kj} \hat{D}_i \bar{\Lambda}^k\right)
+ \frac{1}{2} \Delta^k \left(\Delta_{ijk} + \Delta_{jik}\right) \\%
&\qquad+ \bar{\gamma}^{kl} \left(\Delta^m_{ki} \Delta_{jml} + \Delta^m_{kj} \Delta_{iml} + \Delta^m_{ik} \Delta_{mjl}\right)
\end{align}
""",
ignore_warning=True)
par.set_parval_from_str('reference_metric::CoordSystem', 'Cartesian')
par.set_parval_from_str('BSSN.BSSN_quantities::LeaveRicciSymbolic',
'True')
rfm.reference_metric()
Brhs.BSSN_RHSs()
gaugerhs.BSSN_gauge_RHSs()
bssncon.BSSN_constraints()
par.set_parval_from_str('BSSN.BSSN_quantities::LeaveRicciSymbolic',
'False')
Bq.RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU()
assert_equal(
{
'h_rhsDD': h_rhsDD,
'cf_rhs': cf_rhs,
'trK_rhs': trK_rhs,
'Lambdabar_rhsU': Lambdabar_rhsU,
'a_rhsDD': a_rhsDD,
'alpha_rhs': alpha_rhs,
'vet_rhsU': vet_rhsU,
'bet_rhsU': bet_rhsU,
'H': H,
'MU': MU,
'RbarDD': RbarDD
}, {
'h_rhsDD': Brhs.h_rhsDD,
'cf_rhs': Brhs.cf_rhs,
'trK_rhs': Brhs.trK_rhs,
'Lambdabar_rhsU': Brhs.Lambdabar_rhsU,
'a_rhsDD': Brhs.a_rhsDD,
'alpha_rhs': gaugerhs.alpha_rhs,
'vet_rhsU': gaugerhs.vet_rhsU,
'bet_rhsU': gaugerhs.bet_rhsU,
'H': bssncon.H,
'MU': bssncon.MU,
'RbarDD': Bq.RbarDD
},
suppress_message=True)