l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta')
lf0, lf1 = symbols('lambda_f[0] lambda_f[1]')
# Additional parameters for damping term
R0 = symbols('BSSN_ETA_R0')
ep1, ep2 = symbols('BSSN_ETA_POWER[0] BSSN_ETA_POWER[1]')
xi1, xi2, xi3 = symbols('BSSN_XI[0] BSSN_XI[1] BSSN_XI[2] ')
# declare variables
a = dendro.scalar("alpha", "[pp]")
chi = dendro.scalar("chi", "[pp]")
K = dendro.scalar("K", "[pp]")
Gt = dendro.vec3("Gt", "[pp]")
b = dendro.vec3("beta", "[pp]")
B = dendro.vec3("B", "[pp]")
gt = dendro.sym_3x3("gt", "[pp]")
At = dendro.sym_3x3("At", "[pp]")
Gt_rhs = dendro.vec3("Gt_rhs", "[pp]")
# Lie derivative weight
weight = -Rational(2, 3)
weight_Gt = Rational(2, 3)
# specify the functions for computing first and second derivatives
d = dendro.set_first_derivative('grad') # first argument is direction
def bssn_puncture_gauge(eta_damp, isStaged=False, prefix=""):
if (not isStaged):
C1 = dendro.get_first_christoffel()
C2 = dendro.get_second_christoffel()
C2_spatial = dendro.get_complete_christoffel(chi)
[R, Rt, Rphi, CalGt] = dendro.compute_ricci(Gt, chi)
a_rhs = l1 * dendro.lie(b, a) - 2 * a * K
b_rhs = [(Rational(3, 4) * (lf0 + lf1 * a) * B[i] +
l2 * dendro.vec_j_ad_j(b, b[i])) for i in dendro.e_i]
gt_rhs = dendro.lie(b, gt, weight) - 2 * a * At
chi_rhs = dendro.lie(b, chi, weight) + Rational(2, 3) * (chi * a * K)
AikAkj = Matrix([
sum([
At[i, k] *
sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i])
for k in dendro.e_i
]) for i, j in dendro.e_ij
])
At_rhs = dendro.lie(b, At, weight) + chi * dendro.trace_free(
a * R - dendro.DiDj(a)) + a * (K * At - 2 * AikAkj.reshape(3, 3))
K_rhs = dendro.lie(b, K) - dendro.laplacian(
a, chi) + a * (K * K / 3 + dendro.sqr(At))
At_UU = dendro.up_up(At)
Gt_rhs = Matrix([sum(b[j]*ad(j,Gt[i]) for j in dendro.e_i) for i in dendro.e_i]) - \
Matrix([sum(CalGt[j]*d(j,b[i]) for j in dendro.e_i) for i in dendro.e_i]) + \
Rational(2,3)*Matrix([ CalGt[i] * sum(d(j,b[j]) for j in dendro.e_i) for i in dendro.e_i ]) + \
Matrix([sum([igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k])/3 for j, k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([2*At_UU[i, j]*d(j, a) for j in dendro.e_i]) for i in dendro.e_i]) + \
Matrix([sum([2*a*dendro.C2[i, j, k]*At_UU[j, k] for j,k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([a*(3/chi*At_UU[i,j]*d(j, chi) + Rational(4,3)*dendro.inv_metric[i, j]*d(j, K)) for j in dendro.e_i]) for i in dendro.e_i])
Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist]
B_rhs = [
(Gt_rhs[i] - eta_damp * B[i] + l3 * dendro.vec_j_ad_j(b, B[i]) -
l4 * dendro.vec_j_ad_j(b, Gt[i])) for i in dendro.e_i
]
###################################################################
# generate code
###################################################################
outs = [a_rhs, b_rhs, gt_rhs, chi_rhs, At_rhs, K_rhs, Gt_rhs, B_rhs]
vnames = [
'a_rhs', 'b_rhs', 'gt_rhs', 'chi_rhs', 'At_rhs', 'K_rhs', 'Gt_rhs',
'B_rhs'
]
dendro.generate_cpu(outs, vnames, '[pp]')
else:
# note: these are just the symbolic vars that is being used to generate the
# Gt_rhs by satges
_Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]")
_Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]")
_Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]")
_Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]")
_Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]")
_Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]")
_Gt_rhs_s7 = dendro.vec3("Gt_rhs_s7_", "[pp]")
_CalGt = dendro.vec3("CalGt", "[pp]")
_Gt_rhs = dendro.vec3("Gt_rhs", "[pp]")
# Gt_rhs staged vars that is being used to generate the code.
At_UU = dendro.sym_3x3("At_UU", "[pp]")
CalGt = dendro.vec3("CalGt", "[pp]")
Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]")
Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]")
Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]")
Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]")
Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]")
Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]")
Gt_rhs_s7 = dendro.vec3("Gt_rhs_s7_", "[pp]")
C1 = dendro.get_first_christoffel()
C2 = dendro.get_second_christoffel()
C2_spatial = dendro.get_complete_christoffel(chi)
[R, Rt, Rphi, CalGt] = dendro.compute_ricci(Gt, chi)
a_rhs = l1 * dendro.lie(b, a) - 2 * a * K
b_rhs = [(Rational(3, 4) * (lf0 + lf1 * a) * B[i] +
l2 * dendro.vec_j_ad_j(b, b[i])) for i in dendro.e_i]
gt_rhs = dendro.lie(b, gt, weight) - 2 * a * At
chi_rhs = dendro.lie(b, chi, weight) + Rational(2, 3) * (chi * a * K)
AikAkj = Matrix([
sum([
At[i, k] *
sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i])
for k in dendro.e_i
]) for i, j in dendro.e_ij
])
At_rhs = dendro.lie(b, At, weight) + chi * dendro.trace_free(
a * R - dendro.DiDj(a)) + a * (K * At - 2 * AikAkj.reshape(3, 3))
K_rhs = dendro.lie(b, K) - dendro.laplacian(
a, chi) + a * (K * K / 3 + dendro.sqr(At))
At_UU = dendro.up_up(At)
Gt_rhs_s1 = ([
sum(b[j] * ad(j, Gt[i]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s2 = ([
sum(_CalGt[j] * d(j, b[i]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s3 = ([
_CalGt[i] * sum(d(j, b[j]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s4 = ([
sum([
igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k]) / 3
for j, k in dendro.e_ij
]) for i in dendro.e_i
])
Gt_rhs_s5 = ([
sum([2 * At_UU[i, j] * d(j, a) for j in dendro.e_i])
for i in dendro.e_i
])
Gt_rhs_s6 = ([
sum([
2 * a * dendro.C2[i, j, k] * At_UU[j, k]
for j, k in dendro.e_ij
]) for i in dendro.e_i
])
Gt_rhs_s7 = ([
sum([
a * (3 / chi * At_UU[i, j] * d(j, chi) +
Rational(4, 3) * dendro.inv_metric[i, j] * d(j, K))
for j in dendro.e_i
]) for i in dendro.e_i
])
Gt_rhs = Matrix(_Gt_rhs_s1) - \
Matrix(_Gt_rhs_s2) + \
Rational(2,3)*Matrix(_Gt_rhs_s3) + \
Matrix(_Gt_rhs_s4) - \
Matrix(_Gt_rhs_s5) + \
Matrix(_Gt_rhs_s6) - \
Matrix(_Gt_rhs_s7)
Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist]
B_rhs = [
(Gt_rhs[i] - eta_damp * B[i] + l3 * dendro.vec_j_ad_j(b, B[i]) -
l4 * dendro.vec_j_ad_j(b, Gt[i])) for i in dendro.e_i
]
outs = [
a_rhs, b_rhs, gt_rhs, chi_rhs, At_rhs, K_rhs, CalGt, Gt_rhs_s1,
Gt_rhs_s2, Gt_rhs_s3, Gt_rhs_s4, Gt_rhs_s5, Gt_rhs_s6, Gt_rhs_s7,
Gt_rhs, B_rhs
]
vnames = [
'a_rhs', 'b_rhs', 'gt_rhs', 'chi_rhs', 'At_rhs', 'K_rhs', 'CalGt',
'Gt_rhs_s1_', 'Gt_rhs_s2_', 'Gt_rhs_s3_', 'Gt_rhs_s4_',
'Gt_rhs_s5_', 'Gt_rhs_s6_', 'Gt_rhs_s7_', 'Gt_rhs', 'B_rhs'
]
###################################################################
# generate code
###################################################################
numVars = len(outs)
for i in range(0, numVars):
dendro.generate_separate([outs[i]], [vnames[i]], '[pp]')
#!/usr/bin/env/ python3
import dendro
from sympy import *
###################################################################
# initialize
###################################################################
# Declare variables.
# These include the BSSN variables that we need for the Psi4
# calculation.
chi = dendro.scalar("chi", "[pp]")
K = dendro.scalar("K", "[pp]")
Gt = dendro.vec3("Gt", "[pp]")
gt = dendro.sym_3x3("gt", "[pp]")
At = dendro.sym_3x3("At", "[pp]")
# Specify the operators needed for computing first and second derivatives
d = dendro.set_first_derivative('grad') # first argument is direction
d2 = dendro.set_second_derivative('grad2') # first 2 arguments are directions
ad = dendro.set_advective_derivative('agrad') # first argument is direction
# Metric related quantities, i.e. the metric and its inverse
dendro.set_metric(gt)
igt = dendro.get_inverse_metric()
# Christoffels, Ricci, et al
C1 = dendro.get_first_christoffel()
C2 = dendro.get_second_christoffel()
from sympy import *
from sympy.physics.vector.vector import Vector
from sympy.printing.dot import dotprint
###################################################################
# initialize
###################################################################
l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta')
lf0, lf1 = symbols('lambda_f[0] lambda_f[1]')
# declare variables
a = dendro.scalar("alpha", "[pp]")
chi = dendro.scalar("chi", "[pp]")
K = dendro.scalar("K", "[pp]")
Gt = dendro.vec3("Gt", "[pp]")
b = dendro.vec3("beta", "[pp]")
B = dendro.vec3("B", "[pp]")
gt = dendro.sym_3x3("gt", "[pp]")
At = dendro.sym_3x3("At", "[pp]")
# note: these are just the symbolic vars that is being used to generate the
# Gt_rhs by satges
_Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]")
_Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]")
_Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]")
_Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]")
_Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]")
_Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]")
import dendro
from sympy import *
###################################################################
# initialize
###################################################################
l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta')
lf0, lf1 = symbols('lambda_f[0] lambda_f[1]')
# declare variables
a = dendro.scalar("alpha")
chi = dendro.scalar("chi")
K = dendro.scalar("K")
Gt = dendro.vec3("Gt")
b = dendro.vec3("beta")
B = dendro.vec3("B")
gt = dendro.sym_3x3("gt")
At = dendro.sym_3x3("At")
Gt_rhs = dendro.vec3("Gt_rhs")
# Lie derivative weight
weight = -2 / 3
weight_Gt = 2 / 3
# specify the functions for computing first and second derivatives
d = dendro.set_first_derivative('grad') # first argument is direction
d2 = dendro.set_second_derivative('grad2') # first 2 arguments are directions
import dendro
from sympy import *
###################################################################
# initialize
###################################################################
l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta')
lf0, lf1 = symbols('lambda_f[0] lambda_f[1]')
# declare variables
a = dendro.scalar("alpha")
chi = dendro.scalar("chi")
K = dendro.scalar("K")
Gt = dendro.vec3("Gt")
b = dendro.vec3("beta")
B = dendro.vec3("B")
gt = dendro.sym_3x3("gt")
At = dendro.sym_3x3("At")
Gt_rhs = dendro.vec3("Gt_rhs")
# Lie derivative weight
weight = -2 / 3
weight_Gt = 2 / 3
# specify the functions for computing first and second derivatives
d = dendro.set_first_derivative('grad') # first argument is direction
d2 = dendro.set_second_derivative('grad2') # first 2 arguments are directions
#!/usr/bin/env/ python3
import dendro
from sympy import *
###################################################################
# initialize
###################################################################
# Declare variables.
# These include the BSSN variables that we need for the Psi4
# calculation.
chi = dendro.scalar("chi", "[pp]")
K = dendro.scalar("K", "[pp]")
Gt = dendro.vec3("Gt", "[pp]")
gt = dendro.sym_3x3("gt", "[pp]")
At = dendro.sym_3x3("At", "[pp]")
# Define some symbolic variables that will be used to stage the
# calculation of the constraints.
_ham_s1 = dendro.scalar("ham_s1_", "[pp]")
_ham_s2 = dendro.scalar("ham_s2_", "[pp]")
_mom_s1 = dendro.vec3("mom_s1_", "[pp]")
_mom_s2 = dendro.vec3("mom_s2_", "[pp]")
_mom_s3 = dendro.vec3("mom_s3_", "[pp]")
# Now for the same variables that will be used to generate the code
ham_s1 = dendro.scalar("ham_s1_", "[pp]")
ham_s2 = dendro.scalar("ham_s2_", "[pp]")
mom_s1 = dendro.scalar("mom_s1_", "[pp]")
#!/usr/bin/env/ python3
import dendro
from sympy import *
###################################################################
# initialize
###################################################################
# Declare variables.
# These include the BSSN variables that we need for the Psi4
# calculation.
chi = dendro.scalar("chi", "[pp]")
K = dendro.scalar("K", "[pp]")
Gt = dendro.vec3("Gt", "[pp]")
gt = dendro.sym_3x3("gt", "[pp]")
At = dendro.sym_3x3("At", "[pp]")
b = dendro.vec3("beta", "[pp]")
a = dendro.scalar("alpha", "[pp]")
# declare reference metric related vars
# TODO : this is not really evolution variables... but somewhat need to be defined
#a_ref = dendro.scalar("alpha_ref", "[pp]")
#b_ref = dendro.vec3("beta_ref", "[pp]")
#f_ref = dendro.sym_3x3("f_ref", "[pp]")
# Alternative way (same as in evolution eqs part)
a_ref = 1
b_ref = Matrix([[0, 0, 0]])
f_ref = eye(3)
###############################################################################
import dendro
from sympy import *
from sympy.physics.vector.vector import Vector
from sympy.printing.dot import dotprint
###################################################################
# initialize
###################################################################
l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta')
lf0, lf1 = symbols('lambda_f[0] lambda_f[1]')
# declare variables
RccSc = dendro.scalar("RccSc", "[pp]")
Vaux = dendro.vec3("Vaux", "[pp]")
gm = dendro.sym_3x3("gm", "[pp]")
Rcct = dendro.sym_3x3("Rcct", "[pp]")
# Lie derivative weight
weight = -Rational(2,3)
weight_Gt = Rational(2,3)
# specify the functions for computing first and second derivatives
d = dendro.set_first_derivative('grad') # first argument is direction
d2s = dendro.set_second_derivative('grad2') # first 2 arguments are directions
ad = dendro.set_advective_derivative('agrad') # first argument is direction
kod = dendro.set_kreiss_oliger_dissipation('kograd')
d2 = dendro.d2
