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greens_function_bulk.py
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from packages import *
import calculate
from numerical_param import*
def Gcap_free(grid_points,s,domain,epsilon):#\hat{Go}
bounds = (0,domain)
Lz = bounds[1]
# Bases
coords = d3.CartesianCoordinates('z')
dist = d3.Distributor(coords,dtype = np.float64)
zbasis = d3.Chebyshev(coords['z'],size = grid_points,bounds = bounds,dealias = dealias)
# General fields
z = dist.local_grids(zbasis)
dz = lambda A: d3.Differentiate(A,coords['z'])
lift_basis = zbasis.derivative_basis(2)
lift = lambda A,n: d3.Lift(A,lift_basis,n)
# Fields for G(Pz or dzlog(U))
Pz = dist.Field(name = 'Pz',bases = zbasis)
tau_1 = dist.Field(name = 'tau_1')
# Differential equation for Pz (U)
problem = d3.NLBVP([Pz,tau_1],namespace = locals())
problem.add_equation("-dz(Pz) + s*s + lift(tau_1,-1) = Pz**2")
# Boundary conditions for Pz/U
problem.add_equation("Pz(z=0) = s")
# Initial guess
Pz['g'] = s
# Solver
solver0 = problem.build_solver(ncc_cutoff = ncc_cutoff_greens)
pert_norm0 = np.inf
Pz.change_scales(dealias)
while pert_norm0 > tolerance_greens:
solver0.newton_iteration()
pert_norm0 = sum(pert0.allreduce_data_norm('c',2) for pert0 in solver0.perturbations)
Pz.change_scales(1)
Pz = Pz['g']
Qz = -Pz
## Sturm-Liouville for G
G = (-1 / epsilon) * np.true_divide(1,Qz - Pz)
del z,Pz,Qz,tau_1,dz,lift_basis,lift,problem,solver0,pert_norm0
gc.collect()
return G
def Gcap_full(n_bulk_profile, n_bulk, valency, s, domain,epsilon): # \hat{G}
grid_points = len(n_bulk_profile)
bounds = (0,domain)
Lz = bounds[1]
# Bases
coords = d3.CartesianCoordinates('z')
dist = d3.Distributor(coords,dtype = np.float64)
zbasis = d3.Chebyshev(coords['z'],size = grid_points,bounds = bounds,dealias = dealias)
# General fields
z = dist.local_grids(zbasis)
dz = lambda A: d3.Differentiate(A,coords['z'])
lift_basis = zbasis.derivative_basis(2)
lift = lambda A,n: d3.Lift(A,lift_basis,n)
omega_sqr = dist.Field(bases = zbasis)
omega_sqr['g'] = s * s + calculate.kappa_sqr_profile(n_bulk_profile,valency,epsilon)
omega_b = np.sqrt(s * s + calculate.kappa_sqr(n_bulk,valency,epsilon))
# Fields for G(Pz or log(U))
Pz = dist.Field(name = 'Pz',bases = zbasis)
tau_1 = dist.Field(name = 'tau_1')
# Differential equation for Pz/U
problem = d3.NLBVP([Pz,tau_1],namespace = locals())
problem.add_equation("-dz(Pz) + omega_sqr + lift(tau_1,-1) = Pz**2")
# Boundary conditions for Pz
problem.add_equation("Pz(z=0) = omega_b")
# Initial guess for Pz
Pz['g'] = omega_b
# Solver
solver1 = problem.build_solver(ncc_cutoff = ncc_cutoff_greens)
pert_norm1 = np.inf
Pz.change_scales(dealias)
p = 0
while pert_norm1 > tolerance_greens:
p = p + 1
solver1.newton_iteration()
pert_norm1 = sum(pert1.allreduce_data_norm('c',2) for pert1 in solver1.perturbations)
Pz.change_scales(1)
Pz = Pz.allgather_data('g')[0]
# Fields for G(Qz or log(V))
Qz = dist.Field(name = 'Qz',bases = zbasis)
tau_1 = dist.Field(name = 'tau_1')
# Differential equation for Qz/V
problem1 = d3.NLBVP([Qz,tau_1],namespace = locals())
problem1.add_equation("-dz(Qz) + omega_sqr + lift(tau_1,-1) = Qz**2")
# Boundary conditions for Qz
problem1.add_equation("Qz(z=Lz) = -omega_b")
# Initial guess for Qz
Qz['g'] = -omega_b
# Solver
solver2 = problem1.build_solver(ncc_cutoff = ncc_cutoff_greens)
pert_norm2 = np.inf
Qz.change_scales(dealias)
q = 1
while pert_norm2 > tolerance_greens:
q = q + 1
solver2.newton_iteration()
pert_norm2 = sum(pert2.allreduce_data_norm('c',2) for pert2 in solver2.perturbations)
Qz.change_scales(1)
Qz = Qz.allgather_data('g')[0]
## Sturm-Liouville for G
G = (-1 / epsilon) * np.true_divide(1,Qz - Pz)
del z,Pz,Qz,tau_1,dz,lift_basis,lift,problem,solver1,solver2,pert_norm2,pert_norm1
gc.collect()
return G