def BSSN_source_terms_for_BSSN_constraints(custom_T4UU=None):
global sourceterm_H, sourceterm_MU
# Step 4.a: Call BSSN_source_terms_ito_T4UU to get SDD, SD, S, & rho
if custom_T4UU == "unrescaled BSSN source terms already given":
SDD = ixp.declarerank2("SDD", "sym01")
SD = ixp.declarerank1("SD")
S = sp.symbols("S", real=True)
rho = sp.symbols("rho", real=True)
else:
SDD, SD, S, rho = stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(
"BSSN", custom_T4UU)
PI = par.Cparameters("REAL", thismodule, ["PI"],
"3.14159265358979323846264338327950288")
# Step 4.b: Add source term to the Hamiltonian constraint H
sourceterm_H = -16 * PI * rho
# Step 4.c: Add source term to the momentum constraint M^i
# Step 4.c.i: Compute gammaUU in terms of BSSN quantities
import BSSN.ADM_in_terms_of_BSSN as AitoB
AitoB.ADM_in_terms_of_BSSN() # Provides gammaUU
# Step 4.c.ii: Raise S_i
SU = ixp.zerorank1()
for i in range(3):
for j in range(3):
SU[i] += AitoB.gammaUU[i][j] * SD[j]
# Step 4.c.iii: Add source term to momentum constraint & rescale:
sourceterm_MU = ixp.zerorank1()
for i in range(3):
sourceterm_MU[i] = -8 * PI * SU[i] / rfm.ReU[i]
def ScalarField_Tmunu():
global T4UU
# Step 1.c: Set spatial dimension (must be 3 for BSSN, as BSSN is
# a 3+1-dimensional decomposition of the general
# relativistic field equations)
DIM = 3
# Step 1.d: Given the chosen coordinate system, set up
# corresponding reference metric and needed
# reference metric quantities
# The following function call sets up the reference metric
# and related quantities, including rescaling matrices ReDD,
# ReU, and hatted quantities.
rfm.reference_metric()
# Step 1.e: Import all basic (unrescaled) BSSN scalars & tensors
Bq.BSSN_basic_tensors()
alpha = Bq.alpha
betaU = Bq.betaU
# Step 1.g: Define ADM quantities in terms of BSSN quantities
BtoA.ADM_in_terms_of_BSSN()
gammaDD = BtoA.gammaDD
gammaUU = BtoA.gammaUU
# Step 1.h: Define scalar field quantitites
sf_dD = ixp.declarerank1("sf_dD")
Pi = sp.Symbol("sfM", real=True)
# Step 2a: Set up \partial^{t}\varphi = Pi/alpha
sf4dU = ixp.zerorank1(DIM=4)
sf4dU[0] = Pi / alpha
# Step 2b: Set up \partial^{i}\varphi = -Pi*beta^{i}/alpha + gamma^{ij}\partial_{j}\varphi
for i in range(DIM):
sf4dU[i + 1] = -Pi * betaU[i] / alpha
for j in range(DIM):
sf4dU[i + 1] += gammaUU[i][j] * sf_dD[j]
# Step 2c: Set up \partial^{i}\varphi\partial_{i}\varphi = -Pi**2 + gamma^{ij}\partial_{i}\varphi\partial_{j}\varphi
sf4d2 = -Pi**2
for i in range(DIM):
for j in range(DIM):
sf4d2 += gammaUU[i][j] * sf_dD[i] * sf_dD[j]
# Step 3a: Setting up g^{\mu\nu}
ADMg.g4UU_ito_BSSN_or_ADM("ADM",
gammaDD=gammaDD,
betaU=betaU,
alpha=alpha,
gammaUU=gammaUU)
g4UU = ADMg.g4UU
# Step 3b: Setting up T^{\mu\nu} for a massless scalar field
T4UU = ixp.zerorank2(DIM=4)
for mu in range(4):
for nu in range(4):
T4UU[mu][nu] = sf4dU[mu] * sf4dU[nu] - g4UU[mu][nu] * sf4d2 / 2
def setup_ADM_quantities(inputvars):
if inputvars == "ADM":
gammaDD = ixp.declarerank2("gammaDD", "sym01")
betaU = ixp.declarerank1("betaU")
alpha = sp.symbols("alpha", real=True)
elif inputvars == "BSSN":
import BSSN.ADM_in_terms_of_BSSN as AitoB
# Construct gamma_{ij} in terms of cf & gammabar_{ij}
AitoB.ADM_in_terms_of_BSSN()
gammaDD = AitoB.gammaDD
# Next construct beta^i in terms of vet^i and reference metric quantities
import BSSN.BSSN_quantities as Bq
Bq.BSSN_basic_tensors()
betaU = Bq.betaU
alpha = sp.symbols("alpha", real=True)
else:
print("inputvars = " + str(inputvars) + " not supported. Please choose ADM or BSSN.")
sys.exit(1)
return gammaDD,betaU,alpha
def Psi4(specify_tetrad=True):
global psi4_im_pt, psi4_re_pt
# Step 1.b: Given the chosen coordinate system, set up
# corresponding reference metric and needed
# reference metric quantities
# The following function call sets up the reference metric
# and related quantities, including rescaling matrices ReDD,
# ReU, and hatted quantities.
rfm.reference_metric()
# Step 1.c: Set spatial dimension (must be 3 for BSSN, as BSSN is
# a 3+1-dimensional decomposition of the general
# relativistic field equations)
DIM = 3
# Step 1.d: Import all ADM quantities as written in terms of BSSN quantities
import BSSN.ADM_in_terms_of_BSSN as AB
AB.ADM_in_terms_of_BSSN()
# Step 1.e: Set up tetrad vectors
if specify_tetrad == True:
import BSSN.Psi4_tetrads as BP4t
BP4t.Psi4_tetrads()
mre4U = BP4t.mre4U
mim4U = BP4t.mim4U
n4U = BP4t.n4U
else:
# For code validation against NRPy+ psi_4 tutorial module (Tutorial-Psi4.ipynb);
# ensures a more complete code validation.
mre4U = ixp.declarerank1("mre4U", DIM=4)
mim4U = ixp.declarerank1("mim4U", DIM=4)
n4U = ixp.declarerank1("n4U", DIM=4)
# Step 2: Construct the (rank-4) Riemann curvature tensor associated with the ADM 3-metric:
RDDDD = ixp.zerorank4()
gammaDDdDD = AB.gammaDDdDD
for i in range(DIM):
for k in range(DIM):
for l in range(DIM):
for m in range(DIM):
RDDDD[i][k][l][m] = sp.Rational(1, 2) * \
(gammaDDdDD[i][m][k][l] + gammaDDdDD[k][l][i][m] - gammaDDdDD[i][l][k][m] -
gammaDDdDD[k][m][i][l])
# ... then we add the term on the right:
gammaDD = AB.gammaDD
GammaUDD = AB.GammaUDD
for i in range(DIM):
for k in range(DIM):
for l in range(DIM):
for m in range(DIM):
for n in range(DIM):
for p in range(DIM):
RDDDD[i][k][l][m] += gammaDD[n][p] * \
(GammaUDD[n][k][l] * GammaUDD[p][i][m] - GammaUDD[n][k][m] * GammaUDD[p][i][l])
# Step 3: Construct the (rank-4) tensor in term 1 of psi_4 (referring to Eq 5.1 in
# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf
rank4term1DDDD = ixp.zerorank4()
KDD = AB.KDD
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
rank4term1DDDD[i][j][k][l] = RDDDD[i][j][k][
l] + KDD[i][k] * KDD[l][j] - KDD[i][l] * KDD[k][j]
# Step 4: Construct the (rank-3) tensor in term 2 of psi_4 (referring to Eq 5.1 in
# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf
rank3term2DDD = ixp.zerorank3()
KDDdD = AB.KDDdD
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
rank3term2DDD[j][k][l] = sp.Rational(
1, 2) * (KDDdD[j][k][l] - KDDdD[j][l][k])
# ... then we construct the second term in this sum:
# \Gamma^{p}_{j[k} K_{l]p} = \frac{1}{2} (\Gamma^{p}_{jk} K_{lp}-\Gamma^{p}_{jl} K_{kp}):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
for p in range(DIM):
rank3term2DDD[j][k][l] += sp.Rational(
1, 2) * (GammaUDD[p][j][k] * KDD[l][p] -
GammaUDD[p][j][l] * KDD[k][p])
# Finally, we multiply the term by $-8$:
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
rank3term2DDD[j][k][l] *= sp.sympify(-8)
# Step 5: Construct the (rank-2) tensor in term 3 of psi_4 (referring to Eq 5.1 in
# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf
# Step 5.1: Construct 3-Ricci tensor R_{ij} = gamma^{im} R_{ijml}
RDD = ixp.zerorank2()
gammaUU = AB.gammaUU
for j in range(DIM):
for l in range(DIM):
for i in range(DIM):
for m in range(DIM):
RDD[j][l] += gammaUU[i][m] * RDDDD[i][j][m][l]
# Step 5.2: Construct K^p_l = gamma^{pi} K_{il}
KUD = ixp.zerorank2()
for p in range(DIM):
for l in range(DIM):
for i in range(DIM):
KUD[p][l] += gammaUU[p][i] * KDD[i][l]
# Step 5.3: Construct trK = gamma^{ij} K_{ij}
trK = sp.sympify(0)
for i in range(DIM):
for j in range(DIM):
trK += gammaUU[i][j] * KDD[i][j]
# Next we put these terms together to construct the entire term in parentheses:
# +4 \left(R_{jl} - K_{jp} K^p_l + K K_{jl} \right),
rank2term3DD = ixp.zerorank2()
for j in range(DIM):
for l in range(DIM):
rank2term3DD[j][l] = RDD[j][l] + trK * KDD[j][l]
for p in range(DIM):
rank2term3DD[j][l] += -KDD[j][p] * KUD[p][l]
# Finally we multiply by +4:
for j in range(DIM):
for l in range(DIM):
rank2term3DD[j][l] *= sp.sympify(4)
# Step 6: Construct real & imaginary parts of psi_4
# by contracting constituent rank 2, 3, and 4
# tensors with input tetrads mre4U, mim4U, & n4U.
def tetrad_product__Real_psi4(n, Mre, Mim, mu, nu, eta, delta):
return +n[mu] * Mre[nu] * n[eta] * Mre[delta] - n[mu] * Mim[nu] * n[
eta] * Mim[delta]
def tetrad_product__Imag_psi4(n, Mre, Mim, mu, nu, eta, delta):
return -n[mu] * Mre[nu] * n[eta] * Mim[delta] - n[mu] * Mim[nu] * n[
eta] * Mre[delta]
# We split psi_4 into three pieces, to expedite & possibly parallelize C code generation.
psi4_re_pt = [sp.sympify(0), sp.sympify(0), sp.sympify(0)]
psi4_im_pt = [sp.sympify(0), sp.sympify(0), sp.sympify(0)]
# First term:
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
psi4_re_pt[0] += rank4term1DDDD[i][j][
k][l] * tetrad_product__Real_psi4(
n4U, mre4U, mim4U, i + 1, j + 1, k + 1, l + 1)
psi4_im_pt[0] += rank4term1DDDD[i][j][
k][l] * tetrad_product__Imag_psi4(
n4U, mre4U, mim4U, i + 1, j + 1, k + 1, l + 1)
# Second term:
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
psi4_re_pt[1] += rank3term2DDD[j][k][l] * \
sp.Rational(1, 2) * (+tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, k + 1, l + 1)
- tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, k + 1, l + 1))
psi4_im_pt[1] += rank3term2DDD[j][k][l] * \
sp.Rational(1, 2) * (+tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, k + 1, l + 1)
- tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, k + 1, l + 1))
# Third term:
for j in range(DIM):
for l in range(DIM):
psi4_re_pt[2] += rank2term3DD[j][l] * \
(sp.Rational(1, 4) * (+tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, 0, l + 1)
- tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, 0, l + 1)
- tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, l + 1, 0)
+ tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, l + 1, 0)))
psi4_im_pt[2] += rank2term3DD[j][l] * \
(sp.Rational(1, 4) * (+tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, 0, l + 1)
- tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, 0, l + 1)
- tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, l + 1, 0)
+ tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, l + 1, 0)))
def driver_C_codes(Csrcdict,
ThornName,
rhs_list,
evol_gfs_list,
aux_gfs_list,
auxevol_gfs_list,
LapseCondition="OnePlusLog",
enable_stress_energy_source_terms=False):
# First the ETK banner code, proudly showing the NRPy+ banner
import NRPy_logo as logo
outstr = """
#include <stdio.h>
void BaikalETK_Banner()
{
"""
logostr = logo.print_logo(print_to_stdout=False)
outstr += "printf(\"BaikalETK: another Einstein Toolkit thorn generated by\\n\");\n"
for line in logostr.splitlines():
outstr += " printf(\"" + line + "\\n\");\n"
outstr += "}\n"
# Finally add C code string to dictionaries (Python dictionaries are immutable)
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list("Banner.c")] = outstr.replace(
"BaikalETK", ThornName)
# Then the RegisterSlicing() function, needed for other ETK thorns
outstr = """
#include "cctk.h"
#include "Slicing.h"
int BaikalETK_RegisterSlicing (void)
{
Einstein_RegisterSlicing ("BaikalETK");
return 0;
}"""
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"RegisterSlicing.c")] = outstr.replace("BaikalETK", ThornName)
# Next BaikalETK_Symmetry_registration(): Register symmetries
full_gfs_list = []
full_gfs_list.extend(evol_gfs_list)
full_gfs_list.extend(auxevol_gfs_list)
full_gfs_list.extend(aux_gfs_list)
outstr = """
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Symmetry.h"
void BaikalETK_Symmetry_registration(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
// Stores gridfunction parity across x=0, y=0, and z=0 planes, respectively
int sym[3];
// Next register parities for each gridfunction based on its name
// (to ensure this algorithm is robust, gridfunctions with integers
// in their base names are forbidden in NRPy+).
"""
outstr += ""
for gf in full_gfs_list:
# Do not add T4UU gridfunctions if enable_stress_energy_source_terms==False:
if not (enable_stress_energy_source_terms == False and "T4UU" in gf):
outstr += """
// Default to scalar symmetry:
sym[0] = 1; sym[1] = 1; sym[2] = 1;
// Now modify sym[0], sym[1], and/or sym[2] as needed
// to account for gridfunction parity across
// x=0, y=0, and/or z=0 planes, respectively
"""
# If gridfunction name does not end in a digit, by NRPy+ syntax, it must be a scalar
if gf[len(gf) - 1].isdigit() == False:
pass # Scalar = default
elif len(gf) > 2:
# Rank-1 indexed expression (e.g., vector)
if gf[len(gf) - 2].isdigit() == False:
if int(gf[-1]) > 2:
print("Error: Found invalid gridfunction name: " + gf)
sys.exit(1)
symidx = gf[-1]
outstr += " sym[" + symidx + "] = -1;\n"
# Rank-2 indexed expression
elif gf[len(gf) - 2].isdigit() == True:
if len(gf) > 3 and gf[len(gf) - 3].isdigit() == True:
print("Error: Found a Rank-3 or above gridfunction: " +
gf + ", which is at the moment unsupported.")
print("It should be easy to support this if desired.")
sys.exit(1)
symidx0 = gf[-2]
outstr += " sym[" + symidx0 + "] *= -1;\n"
symidx1 = gf[-1]
outstr += " sym[" + symidx1 + "] *= -1;\n"
else:
print(
"Don't know how you got this far with a gridfunction named "
+ gf + ", but I'll take no more of this nonsense.")
print(
" Please follow best-practices and rename your gridfunction to be more descriptive"
)
sys.exit(1)
outstr += " SetCartSymVN(cctkGH, sym, \"BaikalETK::" + gf + "\");\n"
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list("Symmetry_registration_oldCartGrid3D.c")] = \
outstr.replace("BaikalETK",ThornName)
# Next set RHSs to zero
outstr = """
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Symmetry.h"
void BaikalETK_zero_rhss(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
"""
set_rhss_to_zero = ""
for gf in rhs_list:
set_rhss_to_zero += gf + "[CCTK_GFINDEX3D(cctkGH,i0,i1,i2)] = 0.0;\n"
outstr += lp.loop(["i2", "i1", "i0"], ["0", "0", "0"],
["cctk_lsh[2]", "cctk_lsh[1]", "cctk_lsh[0]"],
["1", "1", "1"], [
"#pragma omp parallel for",
"",
"",
], "", set_rhss_to_zero)
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list("zero_rhss.c")] = outstr.replace(
"BaikalETK", ThornName)
# Next registration with the Method of Lines thorn
outstr = """
//--------------------------------------------------------------------------
// Register with the Method of Lines time stepper
// (MoL thorn, found in arrangements/CactusBase/MoL)
// MoL documentation located in arrangements/CactusBase/MoL/doc
//--------------------------------------------------------------------------
#include <stdio.h>
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "Symmetry.h"
void BaikalETK_MoL_registration(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_INT ierr = 0, group, rhs;
// Register evolution & RHS gridfunction groups with MoL, so it knows
group = CCTK_GroupIndex("BaikalETK::evol_variables");
rhs = CCTK_GroupIndex("BaikalETK::evol_variables_rhs");
ierr += MoLRegisterEvolvedGroup(group, rhs);
if (ierr) CCTK_ERROR("Problems registering with MoL");
}
"""
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"MoL_registration.c")] = outstr.replace("BaikalETK", ThornName)
# Next register with the boundary conditions thorns.
# PART 1: Set BC type to "none" for all variables
# Since we choose NewRad boundary conditions, we must register all
# gridfunctions to have boundary type "none". This is because
# NewRad is seen by the rest of the Toolkit as a modification to the
# RHSs.
# This code is based on Kranc's McLachlan/ML_BSSN/src/Boundaries.cc code.
outstr = """
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "cctk_Faces.h"
#include "util_Table.h"
#include "Symmetry.h"
// Set `none` boundary conditions on BSSN RHSs, as these are set via NewRad.
void BaikalETK_BoundaryConditions_evolved_gfs(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
"""
for gf in evol_gfs_list:
outstr += """
ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, "BaikalETK::""" + gf + """", "none");
if (ierr < 0) CCTK_ERROR("Failed to register BC for BaikalETK::""" + gf + """!");
"""
outstr += """
}
// Set `flat` boundary conditions on BSSN constraints, similar to what Lean does.
void BaikalETK_BoundaryConditions_aux_gfs(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
"""
for gf in aux_gfs_list:
outstr += """
ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, cctk_nghostzones[0], -1, "BaikalETK::""" + gf + """", "flat");
if (ierr < 0) CCTK_ERROR("Failed to register BC for BaikalETK::""" + gf + """!");
"""
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"BoundaryConditions.c")] = outstr.replace("BaikalETK", ThornName)
# PART 2: Set C code for calling NewRad BCs
# As explained in lean_public/LeanBSSNMoL/src/calc_bssn_rhs.F90,
# the function NewRad_Apply takes the following arguments:
# NewRad_Apply(cctkGH, var, rhs, var0, v0, radpower),
# which implement the boundary condition:
# var = var_at_infinite_r + u(r-var_char_speed*t)/r^var_radpower
# Obviously for var_radpower>0, var_at_infinite_r is the value of
# the variable at r->infinity. var_char_speed is the propagation
# speed at the outer boundary, and var_radpower is the radial
# falloff rate.
outstr = """
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
void BaikalETK_NewRad(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
"""
for gf in evol_gfs_list:
var_at_infinite_r = "0.0"
var_char_speed = "1.0"
var_radpower = "1.0"
if gf == "alpha":
var_at_infinite_r = "1.0"
if LapseCondition == "OnePlusLog":
var_char_speed = "sqrt(2.0)"
else:
pass # 1.0 (default) is fine
if "aDD" in gf or "trK" in gf: # consistent with Lean code.
var_radpower = "2.0"
outstr += " NewRad_Apply(cctkGH, " + gf + ", " + gf.replace(
"GF", ""
) + "_rhsGF, " + var_at_infinite_r + ", " + var_char_speed + ", " + var_radpower + ");\n"
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"BoundaryCondition_NewRad.c")] = outstr.replace(
"BaikalETK", ThornName)
# First we convert from ADM to BSSN, as is required to convert initial data
# (given using) ADM quantities, to the BSSN evolved variables
import BSSN.ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear as atob
IDhDD,IDaDD,IDtrK,IDvetU,IDbetU,IDalpha,IDcf,IDlambdaU = \
atob.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear("Cartesian","DoNotOutputADMInputFunction",os.path.join(ThornName,"src"))
# Store the original list of registered gridfunctions; we'll want to unregister
# all the *SphorCart* gridfunctions after we're finished with them below.
orig_glb_gridfcs_list = []
for gf in gri.glb_gridfcs_list:
orig_glb_gridfcs_list.append(gf)
alphaSphorCart = gri.register_gridfunctions("AUXEVOL", "alphaSphorCart")
betaSphorCartU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "betaSphorCartU")
BSphorCartU = ixp.register_gridfunctions_for_single_rank1(
"AUXEVOL", "BSphorCartU")
gammaSphorCartDD = ixp.register_gridfunctions_for_single_rank2(
"AUXEVOL", "gammaSphorCartDD", "sym01")
KSphorCartDD = ixp.register_gridfunctions_for_single_rank2(
"AUXEVOL", "KSphorCartDD", "sym01")
# ADM to BSSN conversion, used for converting ADM initial data into a form readable by this thorn.
# ADM to BSSN, Part 1: Set up function call and pointers to ADM gridfunctions
outstr = """
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
void BaikalETK_ADM_to_BSSN(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_REAL *alphaSphorCartGF = alp;
"""
# It's ugly if we output code in the following ordering, so we'll first
# output to a string and then sort the string to beautify the code a bit.
outstrtmp = []
for i in range(3):
outstrtmp.append(" CCTK_REAL *betaSphorCartU" + str(i) +
"GF = beta" + chr(ord('x') + i) + ";\n")
outstrtmp.append(" CCTK_REAL *BSphorCartU" + str(i) +
"GF = dtbeta" + chr(ord('x') + i) + ";\n")
for j in range(i, 3):
outstrtmp.append(" CCTK_REAL *gammaSphorCartDD" + str(i) +
str(j) + "GF = g" + chr(ord('x') + i) +
chr(ord('x') + j) + ";\n")
outstrtmp.append(" CCTK_REAL *KSphorCartDD" + str(i) + str(j) +
"GF = k" + chr(ord('x') + i) + chr(ord('x') + j) +
";\n")
outstrtmp.sort()
for line in outstrtmp:
outstr += line
# ADM to BSSN, Part 2: Set up ADM to BSSN conversions for BSSN gridfunctions that do not require
# finite-difference derivatives (i.e., all gridfunctions except lambda^i (=Gamma^i
# in non-covariant BSSN)):
# h_{ij}, a_{ij}, trK, vet^i=beta^i,bet^i=B^i, cf (conformal factor), and alpha
all_but_lambdaU_expressions = [
lhrh(lhs=gri.gfaccess("in_gfs", "hDD00"), rhs=IDhDD[0][0]),
lhrh(lhs=gri.gfaccess("in_gfs", "hDD01"), rhs=IDhDD[0][1]),
lhrh(lhs=gri.gfaccess("in_gfs", "hDD02"), rhs=IDhDD[0][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "hDD11"), rhs=IDhDD[1][1]),
lhrh(lhs=gri.gfaccess("in_gfs", "hDD12"), rhs=IDhDD[1][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "hDD22"), rhs=IDhDD[2][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "aDD00"), rhs=IDaDD[0][0]),
lhrh(lhs=gri.gfaccess("in_gfs", "aDD01"), rhs=IDaDD[0][1]),
lhrh(lhs=gri.gfaccess("in_gfs", "aDD02"), rhs=IDaDD[0][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "aDD11"), rhs=IDaDD[1][1]),
lhrh(lhs=gri.gfaccess("in_gfs", "aDD12"), rhs=IDaDD[1][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "aDD22"), rhs=IDaDD[2][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "trK"), rhs=IDtrK),
lhrh(lhs=gri.gfaccess("in_gfs", "vetU0"), rhs=IDvetU[0]),
lhrh(lhs=gri.gfaccess("in_gfs", "vetU1"), rhs=IDvetU[1]),
lhrh(lhs=gri.gfaccess("in_gfs", "vetU2"), rhs=IDvetU[2]),
lhrh(lhs=gri.gfaccess("in_gfs", "betU0"), rhs=IDbetU[0]),
lhrh(lhs=gri.gfaccess("in_gfs", "betU1"), rhs=IDbetU[1]),
lhrh(lhs=gri.gfaccess("in_gfs", "betU2"), rhs=IDbetU[2]),
lhrh(lhs=gri.gfaccess("in_gfs", "alpha"), rhs=IDalpha),
lhrh(lhs=gri.gfaccess("in_gfs", "cf"), rhs=IDcf)
]
outCparams = "preindent=1,outCfileaccess=a,outCverbose=False,includebraces=False"
all_but_lambdaU_outC = fin.FD_outputC("returnstring",
all_but_lambdaU_expressions,
outCparams)
outstr += lp.loop(["i2", "i1", "i0"], ["0", "0", "0"],
["cctk_lsh[2]", "cctk_lsh[1]", "cctk_lsh[0]"],
["1", "1", "1"], ["#pragma omp parallel for", "", ""],
" ", all_but_lambdaU_outC)
# ADM to BSSN, Part 3: Set up ADM to BSSN conversions for BSSN gridfunctions defined from
# finite-difference derivatives: lambda^i, which is Gamma^i in non-covariant BSSN):
outstr += """
const CCTK_REAL invdx0 = 1.0/CCTK_DELTA_SPACE(0);
const CCTK_REAL invdx1 = 1.0/CCTK_DELTA_SPACE(1);
const CCTK_REAL invdx2 = 1.0/CCTK_DELTA_SPACE(2);
"""
path = os.path.join(ThornName, "src")
BSSN_RHS_FD_orders_output = []
for root, dirs, files in os.walk(path):
for file in files:
if "BSSN_RHSs_FD_order" in file:
array = file.replace(".", "_").split("_")
BSSN_RHS_FD_orders_output.append(int(array[4]))
for current_FD_order in BSSN_RHS_FD_orders_output:
# Store original finite-differencing order:
orig_FD_order = par.parval_from_str(
"finite_difference::FD_CENTDERIVS_ORDER")
# Set new finite-differencing order:
par.set_parval_from_str("finite_difference::FD_CENTDERIVS_ORDER",
current_FD_order)
outCparams = "preindent=1,outCfileaccess=a,outCverbose=False,includebraces=False"
lambdaU_expressions = [
lhrh(lhs=gri.gfaccess("in_gfs", "lambdaU0"), rhs=IDlambdaU[0]),
lhrh(lhs=gri.gfaccess("in_gfs", "lambdaU1"), rhs=IDlambdaU[1]),
lhrh(lhs=gri.gfaccess("in_gfs", "lambdaU2"), rhs=IDlambdaU[2])
]
lambdaU_expressions_FDout = fin.FD_outputC("returnstring",
lambdaU_expressions,
outCparams)
lambdafile = "ADM_to_BSSN__compute_lambdaU_FD_order_" + str(
current_FD_order) + ".h"
with open(os.path.join(ThornName, "src", lambdafile), "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", "", ""], "",
lambdaU_expressions_FDout))
outstr += " if(FD_order == " + str(current_FD_order) + ") {\n"
outstr += " #include \"" + lambdafile + "\"\n"
outstr += " }\n"
# Restore original FD order
par.set_parval_from_str("finite_difference::FD_CENTDERIVS_ORDER",
orig_FD_order)
outstr += """
ExtrapolateGammas(cctkGH,lambdaU0GF);
ExtrapolateGammas(cctkGH,lambdaU1GF);
ExtrapolateGammas(cctkGH,lambdaU2GF);
}
"""
# Unregister the *SphorCartGF's.
gri.glb_gridfcs_list = orig_glb_gridfcs_list
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list("ADM_to_BSSN.c")] = outstr.replace(
"BaikalETK", ThornName)
import BSSN.ADM_in_terms_of_BSSN as btoa
import BSSN.BSSN_quantities as Bq
btoa.ADM_in_terms_of_BSSN()
Bq.BSSN_basic_tensors() # Gives us betaU & BU
outstr = """
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
void BaikalETK_BSSN_to_ADM(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
"""
btoa_lhrh = []
for i in range(3):
for j in range(i, 3):
btoa_lhrh.append(
lhrh(lhs="g" + chr(ord('x') + i) + chr(ord('x') + j) +
"[CCTK_GFINDEX3D(cctkGH,i0,i1,i2)]",
rhs=btoa.gammaDD[i][j]))
for i in range(3):
for j in range(i, 3):
btoa_lhrh.append(
lhrh(lhs="k" + chr(ord('x') + i) + chr(ord('x') + j) +
"[CCTK_GFINDEX3D(cctkGH,i0,i1,i2)]",
rhs=btoa.KDD[i][j]))
btoa_lhrh.append(
lhrh(lhs="alp[CCTK_GFINDEX3D(cctkGH,i0,i1,i2)]", rhs=Bq.alpha))
for i in range(3):
btoa_lhrh.append(
lhrh(lhs="beta" + chr(ord('x') + i) +
"[CCTK_GFINDEX3D(cctkGH,i0,i1,i2)]",
rhs=Bq.betaU[i]))
for i in range(3):
btoa_lhrh.append(
lhrh(lhs="dtbeta" + chr(ord('x') + i) +
"[CCTK_GFINDEX3D(cctkGH,i0,i1,i2)]",
rhs=Bq.BU[i]))
outCparams = "preindent=1,outCfileaccess=a,outCverbose=False,includebraces=False"
bssn_to_adm_Ccode = fin.FD_outputC("returnstring", btoa_lhrh, outCparams)
outstr += lp.loop(["i2", "i1", "i0"], ["0", "0", "0"],
["cctk_lsh[2]", "cctk_lsh[1]", "cctk_lsh[0]"],
["1", "1", "1"], ["#pragma omp parallel for", "", ""],
"", bssn_to_adm_Ccode)
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list("BSSN_to_ADM.c")] = outstr.replace(
"BaikalETK", ThornName)
# Next, the driver for computing the Ricci tensor:
outstr = """
#include <math.h>
#include "SIMD/SIMD_intrinsics.h"
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
void BaikalETK_driver_pt1_BSSN_Ricci(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
const CCTK_INT *FD_order = CCTK_ParameterGet("FD_order","BaikalETK",NULL);
const CCTK_REAL NOSIMDinvdx0 = 1.0/CCTK_DELTA_SPACE(0);
const REAL_SIMD_ARRAY invdx0 = ConstSIMD(NOSIMDinvdx0);
const CCTK_REAL NOSIMDinvdx1 = 1.0/CCTK_DELTA_SPACE(1);
const REAL_SIMD_ARRAY invdx1 = ConstSIMD(NOSIMDinvdx1);
const CCTK_REAL NOSIMDinvdx2 = 1.0/CCTK_DELTA_SPACE(2);
const REAL_SIMD_ARRAY invdx2 = ConstSIMD(NOSIMDinvdx2);
"""
path = os.path.join(ThornName, "src")
for root, dirs, files in os.walk(path):
for file in files:
if "BSSN_Ricci_FD_order" in file:
array = file.replace(".", "_").split("_")
outstr += " if(*FD_order == " + str(array[4]) + ") {\n"
outstr += " #include \"" + file + "\"\n"
outstr += " }\n"
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"driver_pt1_BSSN_Ricci.c")] = outstr.replace("BaikalETK", ThornName)
def SIMD_declare_C_params():
SIMD_declare_C_params_str = ""
for i in range(len(par.glb_Cparams_list)):
# keep_param is a boolean indicating whether we should accept or reject
# the parameter. singleparstring will contain the string indicating
# the variable type.
keep_param, singleparstring = ccl.keep_param__return_type(
par.glb_Cparams_list[i])
if (keep_param) and ("CCTK_REAL" in singleparstring):
parname = par.glb_Cparams_list[i].parname
SIMD_declare_C_params_str += " const "+singleparstring + "*NOSIMD"+parname+\
" = CCTK_ParameterGet(\""+parname+"\",\"BaikalETK\",NULL);\n"
SIMD_declare_C_params_str += " const REAL_SIMD_ARRAY " + parname + " = ConstSIMD(*NOSIMD" + parname + ");\n"
return SIMD_declare_C_params_str
# Next, the driver for computing the BSSN RHSs:
outstr = """
#include <math.h>
#include "SIMD/SIMD_intrinsics.h"
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
void BaikalETK_driver_pt2_BSSN_RHSs(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
const CCTK_INT *FD_order = CCTK_ParameterGet("FD_order","BaikalETK",NULL);
const CCTK_REAL NOSIMDinvdx0 = 1.0/CCTK_DELTA_SPACE(0);
const REAL_SIMD_ARRAY invdx0 = ConstSIMD(NOSIMDinvdx0);
const CCTK_REAL NOSIMDinvdx1 = 1.0/CCTK_DELTA_SPACE(1);
const REAL_SIMD_ARRAY invdx1 = ConstSIMD(NOSIMDinvdx1);
const CCTK_REAL NOSIMDinvdx2 = 1.0/CCTK_DELTA_SPACE(2);
const REAL_SIMD_ARRAY invdx2 = ConstSIMD(NOSIMDinvdx2);
""" + SIMD_declare_C_params()
path = os.path.join(ThornName, "src")
for root, dirs, files in os.walk(path):
for file in files:
if "BSSN_RHSs_FD_order" in file:
array = file.replace(".", "_").split("_")
outstr += " if(*FD_order == " + str(array[4]) + ") {\n"
outstr += " #include \"" + file + "\"\n"
outstr += " }\n"
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"driver_pt2_BSSN_RHSs.c")] = outstr.replace("BaikalETK", ThornName)
# Next, the driver for enforcing detgammabar = detgammahat constraint:
outstr = """
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
void BaikalETK_enforce_detgammabar_constraint(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
"""
path = os.path.join(ThornName, "src")
for root, dirs, files in os.walk(path):
for file in files:
if "enforcedetgammabar_constraint_FD_order" in file:
array = file.replace(".", "_").split("_")
outstr += " if(FD_order == " + str(array[4]) + ") {\n"
outstr += " #include \"" + file + "\"\n"
outstr += " }\n"
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list("driver_enforcedetgammabar_constraint.c")] = \
outstr.replace("BaikalETK",ThornName)
# Next, the driver for computing the BSSN Hamiltonian & momentum constraints
outstr = """
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
void BaikalETK_BSSN_constraints(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
const CCTK_REAL invdx0 = 1.0/CCTK_DELTA_SPACE(0);
const CCTK_REAL invdx1 = 1.0/CCTK_DELTA_SPACE(1);
const CCTK_REAL invdx2 = 1.0/CCTK_DELTA_SPACE(2);
"""
path = os.path.join(ThornName, "src")
for root, dirs, files in os.walk(path):
for file in files:
if "BSSN_constraints_FD_order" in file:
array = file.replace(".", "_").split("_")
outstr += " if(FD_order == " + str(array[4]) + ") {\n"
outstr += " #include \"" + file + "\"\n"
outstr += " }\n"
outstr += "}\n"
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"driver_BSSN_constraints.c")] = outstr.replace("BaikalETK", ThornName)
if enable_stress_energy_source_terms == True:
# Declare T4DD as a set of gridfunctions. These won't
# actually appear in interface.ccl, as interface.ccl
# was set above. Thus before calling the code output
# by FD_outputC(), we'll have to set pointers
# to the actual gridfunctions they reference.
# (In this case the eTab's.)
T4DD = ixp.register_gridfunctions_for_single_rank2("AUXEVOL",
"T4DD",
"sym01",
DIM=4)
import BSSN.ADMBSSN_tofrom_4metric as AB4m
AB4m.g4UU_ito_BSSN_or_ADM("BSSN")
T4UUraised = ixp.zerorank2(DIM=4)
for mu in range(4):
for nu in range(4):
for delta in range(4):
for gamma in range(4):
T4UUraised[mu][nu] += AB4m.g4UU[mu][delta] * AB4m.g4UU[
nu][gamma] * T4DD[delta][gamma]
T4UU_expressions = [
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU00"), rhs=T4UUraised[0][0]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU01"), rhs=T4UUraised[0][1]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU02"), rhs=T4UUraised[0][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU03"), rhs=T4UUraised[0][3]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU11"), rhs=T4UUraised[1][1]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU12"), rhs=T4UUraised[1][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU13"), rhs=T4UUraised[1][3]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU22"), rhs=T4UUraised[2][2]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU23"), rhs=T4UUraised[2][3]),
lhrh(lhs=gri.gfaccess("in_gfs", "T4UU33"), rhs=T4UUraised[3][3])
]
outCparams = "outCverbose=False,includebraces=False,preindent=2,SIMD_enable=True"
T4UUstr = fin.FD_outputC("returnstring", T4UU_expressions, outCparams)
T4UUstr_loop = lp.loop(["i2", "i1", "i0"], ["0", "0", "0"],
["cctk_lsh[2]", "cctk_lsh[1]", "cctk_lsh[0]"],
["1", "1", "SIMD_width"],
["#pragma omp parallel for", "", ""], "",
T4UUstr)
outstr = """
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "SIMD/SIMD_intrinsics.h"
void BaikalETK_driver_BSSN_T4UU(CCTK_ARGUMENTS) {
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
const CCTK_REAL *restrict T4DD00GF = eTtt;
const CCTK_REAL *restrict T4DD01GF = eTtx;
const CCTK_REAL *restrict T4DD02GF = eTty;
const CCTK_REAL *restrict T4DD03GF = eTtz;
const CCTK_REAL *restrict T4DD11GF = eTxx;
const CCTK_REAL *restrict T4DD12GF = eTxy;
const CCTK_REAL *restrict T4DD13GF = eTxz;
const CCTK_REAL *restrict T4DD22GF = eTyy;
const CCTK_REAL *restrict T4DD23GF = eTyz;
const CCTK_REAL *restrict T4DD33GF = eTzz;
""" + T4UUstr_loop + """
}\n"""
# Add C code string to dictionary (Python dictionaries are immutable)
Csrcdict[append_to_make_code_defn_list(
"driver_BSSN_T4UU.c")] = outstr.replace("BaikalETK", ThornName)
def Psi4_tetradsv2():
global l4U, n4U, mre4U, mim4U
# Step 1.c: Check if tetrad choice is implemented:
if par.parval_from_str(thismodule + "::TetradChoice") != "QuasiKinnersley":
print("ERROR: " + thismodule + "::TetradChoice = " +
par.parval_from_str("TetradChoice") + " currently unsupported!")
exit(1)
# Step 1.d: Given the chosen coordinate system, set up
# corresponding reference metric and needed
# reference metric quantities
# The following function call sets up the reference metric
# and related quantities, including rescaling matrices ReDD,
# ReU, and hatted quantities.
rfm.reference_metric()
# Step 1.e: Set spatial dimension (must be 3 for BSSN, as BSSN is
# a 3+1-dimensional decomposition of the general
# relativistic field equations)
DIM = 3
# Step 1.f: Import all ADM quantities as written in terms of BSSN quantities
import BSSN.ADM_in_terms_of_BSSN as AB
AB.ADM_in_terms_of_BSSN()
# Step 2.a: Declare the Cartesian x,y,z as input parameters
# and v_1^a, v_2^a, and v_3^a tetrads,
# as well as detgamma and gammaUU from
# BSSN.ADM_in_terms_of_BSSN
x, y, z = par.Cparameters("REAL", thismodule, ["x", "y", "z"])
v1UCart = ixp.zerorank1()
v2UCart = ixp.zerorank1()
# detgamma = AB.detgamma
# gammaUU = AB.gammaUU
# Step 2.b: Define v1U and v2U
v1UCart = [-y, x, sp.sympify(0)]
v2UCart = [x, y, z]
# Step 2.c: Construct the Jacobian d x_Cart^i / d xx^j
Jac_dUCart_dDrfmUD = ixp.zerorank2()
for i in range(DIM):
for j in range(DIM):
Jac_dUCart_dDrfmUD[i][j] = sp.diff(rfm.xxCart[i], rfm.xx[j])
# Step 2.d: Invert above Jacobian to get needed d xx^j / d x_Cart^i
Jac_dUrfm_dDCartUD, dummyDET = ixp.generic_matrix_inverter3x3(
Jac_dUCart_dDrfmUD)
# Step 2.e: Transform gammaDD to Cartesian basis:
gammaCartDD = ixp.zerorank2()
gammaDD = AB.gammaDD
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
gammaCartDD[i][j] += Jac_dUrfm_dDCartUD[k][
i] * Jac_dUrfm_dDCartUD[l][j] * gammaDD[k][l]
gammaCartUU, detgammaCart = ixp.symm_matrix_inverter3x3(gammaCartDD)
# Step 2.e: Transform v1U and v2U from the Cartesian to the xx^i basis
v1U = ixp.zerorank1()
v2U = ixp.zerorank1()
for i in range(DIM):
v1U[i] = v1UCart[i]
v2U[i] = v2UCart[i]
# for i in range(DIM):
# for j in range(DIM):
# v1U[i] += Jac_dUrfm_dDCartUD[i][j]*v1UCart[j]
# v2U[i] += Jac_dUrfm_dDCartUD[i][j]*v2UCart[j]
# Step 2.f: Define the rank-3 version of the Levi-Civita symbol. Amongst
# other uses, this is needed for the construction of the approximate
# quasi-Kinnersley tetrad.
def define_LeviCivitaSymbol_rank3(DIM=-1):
if DIM == -1:
DIM = par.parval_from_str("DIM")
LeviCivitaSymbol = ixp.zerorank3()
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
# From https://codegolf.stackexchange.com/questions/160359/levi-civita-symbol :
LeviCivitaSymbol[i][j][k] = (i - j) * (j - k) * (k - i) / 2
return LeviCivitaSymbol
# Step 2.g: Define v3U
v3U = ixp.zerorank1()
LeviCivitaSymbolDDD = define_LeviCivitaSymbol_rank3(DIM=3)
for a in range(DIM):
for b in range(DIM):
for c in range(DIM):
for d in range(DIM):
v3U[a] += sp.sqrt(detgammaCart) * gammaCartUU[a][
d] * LeviCivitaSymbolDDD[d][b][c] * v1U[b] * v2U[c]
# Step 2.h: Define omega_{ij}
omegaDD = ixp.zerorank2()
# Step 2.i: Define e^a_i. Note that:
# omegaDD[0][0] = \omega_{11} above;
# omegaDD[1][1] = \omega_{22} above, etc.
e1U = ixp.zerorank1()
e2U = ixp.zerorank1()
e3U = ixp.zerorank1()
update_omega(omegaDD, v1U, v2U, v3U, gammaCartDD)
for a in range(DIM):
e1U[a] = v1U[a] / sp.sqrt(omegaDD[0][0])
update_omega(omegaDD, e1U, v2U, v3U, gammaCartDD)
for a in range(DIM):
e2U[a] = (v2U[a] - omegaDD[0][1] * e1U[a]) / sp.sqrt(omegaDD[1][1])
update_omega(omegaDD, e1U, e2U, v3U, gammaCartDD)
for a in range(DIM):
e3U[a] = (v3U[a] - omegaDD[0][2] * e1U[a] -
omegaDD[1][2] * e2U[a]) / sp.sqrt(omegaDD[2][2])
# Step 2.j: Construct l^mu, n^mu, and m^mu, based on r^mu, theta^mu, phi^mu, and u^mu:
rCart4U = ixp.zerorank1(DIM=4)
thetaCart4U = ixp.zerorank1(DIM=4)
phiCart4U = ixp.zerorank1(DIM=4)
for a in range(DIM):
rCart4U[a + 1] = e2U[a]
thetaCart4U[a + 1] = e3U[a]
phiCart4U[a + 1] = e1U[a]
r4U = ixp.zerorank1(DIM=4)
theta4U = ixp.zerorank1(DIM=4)
phi4U = ixp.zerorank1(DIM=4)
for a in range(DIM):
for b in range(DIM):
r4U[a + 1] += Jac_dUrfm_dDCartUD[a][b] * rCart4U[b + 1]
theta4U[a + 1] += Jac_dUrfm_dDCartUD[a][b] * thetaCart4U[b + 1]
phi4U[a + 1] += Jac_dUrfm_dDCartUD[a][b] * phiCart4U[b + 1]
u4U = ixp.zerorank1(DIM=4)
# FIXME? assumes alpha=1, beta^i = 0
u4U[0] = 1
l4U = ixp.zerorank1(DIM=4)
n4U = ixp.zerorank1(DIM=4)
mre4U = ixp.zerorank1(DIM=4)
mim4U = ixp.zerorank1(DIM=4)
isqrt2 = 1 / sp.sqrt(2)
for mu in range(4):
l4U[mu] = isqrt2 * (u4U[mu] + r4U[mu])
n4U[mu] = isqrt2 * (u4U[mu] - r4U[mu])
mre4U[mu] = isqrt2 * theta4U[mu]
mim4U[mu] = isqrt2 * phi4U[mu]
def Psi4_tetrads():
global l4U, n4U, mre4U, mim4U
# Step 1.c: Check if tetrad choice is implemented:
if par.parval_from_str(thismodule + "::TetradChoice") != "QuasiKinnersley":
print("ERROR: " + thismodule + "::TetradChoice = " +
par.parval_from_str("TetradChoice") + " currently unsupported!")
sys.exit(1)
# Step 1.d: Given the chosen coordinate system, set up
# corresponding reference metric and needed
# reference metric quantities
# The following function call sets up the reference metric
# and related quantities, including rescaling matrices ReDD,
# ReU, and hatted quantities.
rfm.reference_metric()
# Step 1.e: Set spatial dimension (must be 3 for BSSN, as BSSN is
# a 3+1-dimensional decomposition of the general
# relativistic field equations)
DIM = 3
# Step 1.f: Import all ADM quantities as written in terms of BSSN quantities
import BSSN.ADM_in_terms_of_BSSN as AB
AB.ADM_in_terms_of_BSSN()
# Step 2.a: Declare the Cartesian x,y,z in terms of
# xx0,xx1,xx2.
x = rfm.xxCart[0]
y = rfm.xxCart[1]
z = rfm.xxCart[2]
# Step 2.b: Declare detgamma and gammaUU from
# BSSN.ADM_in_terms_of_BSSN;
# simplify detgamma & gammaUU expressions,
# which expedites Psi4 codegen.
detgamma = sp.simplify(AB.detgamma)
gammaUU = ixp.zerorank2()
for i in range(DIM):
for j in range(DIM):
gammaUU[i][j] = sp.simplify(AB.gammaUU[i][j])
# Step 2.c: Define v1U and v2U
v1UCart = [-y, x, sp.sympify(0)]
v2UCart = [x, y, z]
# Step 2.d: Construct the Jacobian d x_Cart^i / d xx^j
Jac_dUCart_dDrfmUD = ixp.zerorank2()
for i in range(DIM):
for j in range(DIM):
Jac_dUCart_dDrfmUD[i][j] = sp.simplify(
sp.diff(rfm.xxCart[i], rfm.xx[j]))
# Step 2.e: Invert above Jacobian to get needed d xx^j / d x_Cart^i
Jac_dUrfm_dDCartUD, dummyDET = ixp.generic_matrix_inverter3x3(
Jac_dUCart_dDrfmUD)
# Step 2.e.i: Simplify expressions for d xx^j / d x_Cart^i:
for i in range(DIM):
for j in range(DIM):
Jac_dUrfm_dDCartUD[i][j] = sp.simplify(Jac_dUrfm_dDCartUD[i][j])
# Step 2.f: Transform v1U and v2U from the Cartesian to the xx^i basis
v1U = ixp.zerorank1()
v2U = ixp.zerorank1()
for i in range(DIM):
for j in range(DIM):
v1U[i] += Jac_dUrfm_dDCartUD[i][j] * v1UCart[j]
v2U[i] += Jac_dUrfm_dDCartUD[i][j] * v2UCart[j]
# Step 2.g: Define v3U
v3U = ixp.zerorank1()
LeviCivitaSymbolDDD = ixp.LeviCivitaSymbol_dim3_rank3()
for a in range(DIM):
for b in range(DIM):
for c in range(DIM):
for d in range(DIM):
v3U[a] += sp.sqrt(detgamma) * gammaUU[a][
d] * LeviCivitaSymbolDDD[d][b][c] * v1U[b] * v2U[c]
# Step 2.g.i: Simplify expressions for v1U,v2U,v3U. This greatly expedites the C code generation (~10x faster)
# Drat. Simplification with certain versions of SymPy & coord systems results in a hang. Let's just
# evaluate the expressions so the most trivial optimizations can be performed.
for a in range(DIM):
v1U[a] = v1U[a].doit() # sp.simplify(v1U[a])
v2U[a] = v2U[a].doit() # sp.simplify(v2U[a])
v3U[a] = v3U[a].doit() # sp.simplify(v3U[a])
# Step 2.h: Define omega_{ij}
omegaDD = ixp.zerorank2()
gammaDD = AB.gammaDD
def v_vectorDU(v1U, v2U, v3U, i, a):
if i == 0:
return v1U[a]
if i == 1:
return v2U[a]
if i == 2:
return v3U[a]
print("ERROR: unknown vector!")
sys.exit(1)
def update_omega(omegaDD, i, j, v1U, v2U, v3U, gammaDD):
omegaDD[i][j] = sp.sympify(0)
for a in range(DIM):
for b in range(DIM):
omegaDD[i][j] += v_vectorDU(v1U, v2U, v3U, i, a) * v_vectorDU(
v1U, v2U, v3U, j, b) * gammaDD[a][b]
# Step 2.i: Define e^a_i. Note that:
# omegaDD[0][0] = \omega_{11} above;
# omegaDD[1][1] = \omega_{22} above, etc.
# First e_1^a: Orthogonalize & normalize:
e1U = ixp.zerorank1()
update_omega(omegaDD, 0, 0, v1U, v2U, v3U, gammaDD)
for a in range(DIM):
e1U[a] = v1U[a] / sp.sqrt(omegaDD[0][0])
# Next e_2^a: First orthogonalize:
e2U = ixp.zerorank1()
update_omega(omegaDD, 0, 1, e1U, v2U, v3U, gammaDD)
for a in range(DIM):
e2U[a] = (v2U[a] - omegaDD[0][1] * e1U[a])
# Then normalize:
update_omega(omegaDD, 1, 1, e1U, e2U, v3U, gammaDD)
for a in range(DIM):
e2U[a] /= sp.sqrt(omegaDD[1][1])
# Next e_3^a: First orthogonalize:
e3U = ixp.zerorank1()
update_omega(omegaDD, 0, 2, e1U, e2U, v3U, gammaDD)
update_omega(omegaDD, 1, 2, e1U, e2U, v3U, gammaDD)
for a in range(DIM):
e3U[a] = (v3U[a] - omegaDD[0][2] * e1U[a] - omegaDD[1][2] * e2U[a])
# Then normalize:
update_omega(omegaDD, 2, 2, e1U, e2U, e3U, gammaDD)
for a in range(DIM):
e3U[a] /= sp.sqrt(omegaDD[2][2])
# Step 2.j: Construct l^mu, n^mu, and m^mu, based on r^mu, theta^mu, phi^mu, and u^mu:
r4U = ixp.zerorank1(DIM=4)
u4U = ixp.zerorank1(DIM=4)
theta4U = ixp.zerorank1(DIM=4)
phi4U = ixp.zerorank1(DIM=4)
for a in range(DIM):
r4U[a + 1] = e2U[a]
theta4U[a + 1] = e3U[a]
phi4U[a + 1] = e1U[a]
# FIXME? assumes alpha=1, beta^i = 0
if par.parval_from_str(thismodule + "::UseCorrectUnitNormal") == "False":
u4U[0] = 1
else:
# Eq. 2.116 in Baumgarte & Shapiro:
# n^mu = {1/alpha, -beta^i/alpha}. Note that n_mu = {alpha,0}, so n^mu n_mu = -1.
import BSSN.BSSN_quantities as Bq
Bq.declare_BSSN_gridfunctions_if_not_declared_already()
Bq.BSSN_basic_tensors()
u4U[0] = 1 / Bq.alpha
for i in range(DIM):
u4U[i + 1] = -Bq.betaU[i] / Bq.alpha
l4U = ixp.zerorank1(DIM=4)
n4U = ixp.zerorank1(DIM=4)
mre4U = ixp.zerorank1(DIM=4)
mim4U = ixp.zerorank1(DIM=4)
# M_SQRT1_2 = 1 / sqrt(2) (defined in math.h on Linux)
M_SQRT1_2 = par.Cparameters("#define", thismodule, "M_SQRT1_2", "")
isqrt2 = M_SQRT1_2 #1/sp.sqrt(2) <- SymPy drops precision to 15 sig. digits in unit tests
for mu in range(4):
l4U[mu] = isqrt2 * (u4U[mu] + r4U[mu])
n4U[mu] = isqrt2 * (u4U[mu] - r4U[mu])
mre4U[mu] = isqrt2 * theta4U[mu]
mim4U[mu] = isqrt2 * phi4U[mu]
def stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(
inputvars, custom_T4UU=None):
# Step 1: Check if rfm.reference_metric() already called. If not, BSSN
# quantities are not yet defined, so cannot proceed!
if rfm.have_already_called_reference_metric_function == False:
print(
"BSSN_source_terms_ito_T4UU(): Must call reference_metric() first!"
)
sys.exit(1)
# Step 2.a: Define gamma4DD[mu][nu] = g_{mu nu} + n_{mu} n_{nu}
alpha = sp.symbols("alpha", real=True)
zero = sp.sympify(0)
n4D = [-alpha, zero, zero, zero]
AB4m.g4DD_ito_BSSN_or_ADM(inputvars)
gamma4DD = ixp.zerorank2(DIM=4)
for mu in range(4):
for nu in range(4):
gamma4DD[mu][nu] = AB4m.g4DD[mu][nu] + n4D[mu] * n4D[nu]
# Step 2.b: If expression for components of T4UU not given, declare T4UU here
if custom_T4UU == None:
T4UU = ixp.declarerank2("T4UU", "sym01", DIM=4)
else:
T4UU = custom_T4UU
# Step 2.c: Define BSSN source terms
global SDD, SD, S, rho
# Step 2.c.i: S_{ij} = gamma_{i mu} gamma_{j nu} T^{mu nu}
SDD = ixp.zerorank2()
for i in range(3):
for j in range(3):
for mu in range(4):
for nu in range(4):
SDD[i][j] += gamma4DD[i + 1][mu] * gamma4DD[
j + 1][nu] * T4UU[mu][nu]
# Step 2.c.ii: S_{i} = -gamma_{i mu} n_{nu} T^{mu nu}
SD = ixp.zerorank1()
for i in range(3):
for mu in range(4):
for nu in range(4):
SD[i] += -gamma4DD[i + 1][mu] * n4D[nu] * T4UU[mu][nu]
# Step 2.c.iii: S = gamma^{ij} S_{ij}
if inputvars == "ADM":
gammaDD = ixp.declarerank2("gammaDD", "sym01")
gammaUU, dummydet = ixp.symm_matrix_inverter3x3(gammaDD) # Set gammaUU
elif inputvars == "BSSN":
import BSSN.ADM_in_terms_of_BSSN as AitoB # NRPy+: ADM quantities in terms of BSSN quantities
AitoB.ADM_in_terms_of_BSSN()
gammaUU = AitoB.gammaUU
S = zero
for i in range(3):
for j in range(3):
S += gammaUU[i][j] * SDD[i][j]
# Step 2.c.iv: rho = n_{mu} n_{nu} T^{mu nu}
rho = zero
for mu in range(4):
for nu in range(4):
rho += n4D[mu] * n4D[nu] * T4UU[mu][nu]
return SDD, SD, S, rho
def Psi4():
global psi4_im, psi4_re
# Step 1.b: Given the chosen coordinate system, set up
# corresponding reference metric and needed
# reference metric quantities
# The following function call sets up the reference metric
# and related quantities, including rescaling matrices ReDD,
# ReU, and hatted quantities.
rfm.reference_metric()
# Step 1.c: Set spatial dimension (must be 3 for BSSN, as BSSN is
# a 3+1-dimensional decomposition of the general
# relativistic field equations)
DIM = 3
# Step 1.d: Import all ADM quantities as written in terms of BSSN quantities
import BSSN.ADM_in_terms_of_BSSN as AB
AB.ADM_in_terms_of_BSSN()
# Step 2: Construct the (rank-4) Riemann curvature tensor associated with the ADM 3-metric:
RDDDD = ixp.zerorank4()
gammaDDdDD = AB.gammaDDdDD
for i in range(DIM):
for k in range(DIM):
for l in range(DIM):
for m in range(DIM):
RDDDD[i][k][l][m] = sp.Rational(1, 2) * \
(gammaDDdDD[i][m][k][l] + gammaDDdDD[k][l][i][m] - gammaDDdDD[i][l][k][m] -
gammaDDdDD[k][m][i][l])
# ... then we add the term on the right:
gammaDD = AB.gammaDD
GammaUDD = AB.GammaUDD
for i in range(DIM):
for k in range(DIM):
for l in range(DIM):
for m in range(DIM):
for n in range(DIM):
for p in range(DIM):
RDDDD[i][k][l][m] += gammaDD[n][p] * \
(GammaUDD[n][k][l] * GammaUDD[p][i][m] - GammaUDD[n][k][m] * GammaUDD[p][i][l])
# Step 3: Construct the (rank-4) tensor in term 1 of psi_4 (referring to Eq 5.1 in
# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf
rank4term1 = ixp.zerorank4()
KDD = AB.KDD
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
rank4term1[i][j][k][l] = RDDDD[i][j][k][
l] + KDD[i][k] * KDD[l][j] - KDD[i][l] * KDD[k][j]
# Step 4: Construct the (rank-3) tensor in term 2 of psi_4 (referring to Eq 5.1 in
# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf
rank3term2 = ixp.zerorank3()
KDDdD = AB.KDDdD
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
rank3term2[j][k][l] = sp.Rational(
1, 2) * (KDDdD[j][k][l] - KDDdD[j][l][k])
# ... then we construct the second term in this sum:
# \Gamma^{p}_{j[k} K_{l]p} = \frac{1}{2} (\Gamma^{p}_{jk} K_{lp}-\Gamma^{p}_{jl} K_{kp}):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
for p in range(DIM):
rank3term2[j][k][l] += sp.Rational(
1, 2) * (GammaUDD[p][j][k] * KDD[l][p] -
GammaUDD[p][j][l] * KDD[k][p])
# Finally, we multiply the term by $-8$:
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
rank3term2[j][k][l] *= sp.sympify(-8)
# Step 5: Construct the (rank-2) tensor in term 3 of psi_4 (referring to Eq 5.1 in
# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf
rank2term3 = ixp.zerorank2()
gammaUU = AB.gammaUU
for j in range(DIM):
for l in range(DIM):
for i in range(DIM):
for m in range(DIM):
rank2term3[j][l] += gammaUU[i][m] * RDDDD[i][j][m][l]
# ... then we add on the second term in parentheses, where $K^p_l = \gamma^{mp} K_{ml}$
for j in range(DIM):
for l in range(DIM):
for m in range(DIM):
for p in range(DIM):
rank2term3[j][l] += -KDD[j][p] * gammaUU[p][m] * KDD[m][l]
# Finally we add the third term in parentheses, and multiply all terms by $+4$:
for j in range(DIM):
for l in range(DIM):
for i in range(DIM):
for m in range(DIM):
rank2term3[j][l] += gammaUU[i][m] * KDD[i][m] * KDD[j][l]
for j in range(DIM):
for l in range(DIM):
rank2term3[j][l] *= sp.sympify(4)
mre4U = ixp.declarerank1("mre4U", DIM=4)
mim4U = ixp.declarerank1("mim4U", DIM=4)
n4U = ixp.declarerank1("n4U", DIM=4)
def tetrad_product__Real_psi4(n, Mre, Mim, mu, nu, eta, delta):
return +n[mu] * Mre[nu] * n[eta] * Mre[delta] - n[mu] * Mim[nu] * n[
eta] * Mim[delta]
def tetrad_product__Imag_psi4(n, Mre, Mim, mu, nu, eta, delta):
return -n[mu] * Mre[nu] * n[eta] * Mim[delta] - n[mu] * Mim[nu] * n[
eta] * Mre[delta]
psi4_re = sp.sympify(0)
psi4_im = sp.sympify(0)
# First term:
for i in range(DIM):
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
psi4_re += rank4term1[i][j][
k][l] * tetrad_product__Real_psi4(
n4U, mre4U, mim4U, i + 1, j + 1, k + 1, l + 1)
psi4_im += rank4term1[i][j][
k][l] * tetrad_product__Imag_psi4(
n4U, mre4U, mim4U, i + 1, j + 1, k + 1, l + 1)
# Second term:
for j in range(DIM):
for k in range(DIM):
for l in range(DIM):
psi4_re += rank3term2[j][k][l] * \
sp.Rational(1, 2) * (+tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, k + 1, l + 1)
- tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, k + 1, l + 1))
psi4_im += rank3term2[j][k][l] * \
sp.Rational(1, 2) * (+tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, k + 1, l + 1)
- tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, k + 1, l + 1))
# Third term:
for j in range(DIM):
for l in range(DIM):
psi4_re += rank2term3[j][l] * \
(sp.Rational(1, 4) * (+tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, 0, l + 1)
- tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, 0, l + 1)
- tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, l + 1, 0)
+ tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, l + 1, 0)))
psi4_im += rank2term3[j][l] * \
(sp.Rational(1, 4) * (+tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, 0, l + 1)
- tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, 0, l + 1)
- tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, l + 1, 0)
+ tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, l + 1, 0)))
