I-Front Test

We first consider the simplest example, HII region expansion around a single source of ionizing radiation and constant density field.

This test is known as the ionization front (I-front) test and is a standard test in reionization (Mellema+ 2006).

[2]:

import pyc2ray as pc2r
import numpy as np, matplotlib.pyplot as plt

from matplotlib.colors import LogNorm

import astropy.units as u

Analytical Solution

Here, we consider a source emitting \(\dot{N}_\gamma\) ionizing photons per unit of time igniting in a medium of neutral hydrogen with number density \(n_\mathrm{H}\).

The ionizing photons propagate, resulting in an I-front with a radius, \(r_I\), that ionizes the surrounding neutral gas. The I-front propagation speed, \(v_I\), is determined by the balance between the flux of ionizing photons and the number of neutral atoms.

\[n_\mathrm{H} \frac{dV_I}{dt} = \dot{N}_\gamma - \int_{V_I} n^2_\mathrm{H}\,C\alpha_B\,dV\]

where \(V_I = \frac{4\pi}{3}r^3_I\), and in this case, an analytical solution exist.

[3]:

# Analytical Solution
Ngamma = 1e54 / u.s
nH = 1.87e-4 / u.cm**3
alpha_B = 2.59e-13 * u.cm**3 / u.s
clump = 5

r_S = ((3*Ngamma/(4*np.pi*clump*alpha_B*nH**2))**(1./3)).to('kpc')
t_rec = (1.0 / (clump*alpha_B*nH)).to('Myr')

print("r_S = ", r_S)
print("t_rec = ", t_rec)

def r_I(t):
    return r_S * (1.0 - np.exp(-t/t_rec))**(1./3)

def v_I(t):
    return (r_S/(3*t_rec) * (np.exp(-t/t_rec))/(1.0 - np.exp(-t/t_rec))**(2./3)).to('km/s')

r_S =  564.0300697516011 kpc
t_rec =  130.85329347357774 Myr

Calculate analytical solution and plot results.

[4]:

t_evol = 5e8 # years

t_analytical = np.linspace(0, t_evol*u.yr, 200, endpoint=True).to('Myr')

r_analytical = r_I(t_analytical)
v_analytical = v_I(t_analytical[1:])

[5]:

fig, axs = plt.subplots(figsize=(12,5), ncols=2, nrows=1)

axs[0].plot(t_analytical, r_analytical, color='black', ls='-', label="Analytical", lw=2)
axs[0].set_ylabel("$r_I(t)$ [kpc]")

axs[1].semilogy(t_analytical[1:],v_analytical,color='black',label="Analytical",lw=2)
axs[1].set_ylabel("$v_I(t)$ [km s$^{-1}$]")

for ax in axs:
    ax.set_xlabel("$t$ [Myr]")
    ax.grid()
    ax.legend()
../_images/examples_ifront_6_0.png

Numerical Solution

Here, we use pyC\(^2\)Ray to compute the I-front and test whether it provides the correct solution.

The coarseness of the numerical solution depends on the number of time steps. Here, we define the number of redshift steps we want to output. Increasing the value of numzred will refine the numerical solution and increase the computing time (numzred=10 takes approximately 15 minutes).

[6]:

numzred = 10

Define some global parameters and instance the test simulation class.

[7]:

# Global parameters
num_steps_between_slices = 1

# Create C2Ray object
sim = pc2r.C2Ray_Test(paramfile='parameters_ifront.yml')

                 _________   ____
    ____  __  __/ ____/__ \ / __ \____ ___  __
   / __ \/ / / / /    __/ // /_/ / __ `/ / / /
  / /_/ / /_/ / /___ / __// _, _/ /_/ / /_/ /
 / .___/\__, /\____//____/_/ |_|\__,_/\__, /
/_/    /____/                        /____/

Welcome! Mesh size is N = 256.
Simulation Box size (comoving Mpc): 1.620e+00
Cosmology is off.
Warning: Using grey opacity
Using Black-Body sources with effective temperature T = 5.0e+04 K and Radius  1.437e-11 rsun
Spectrum Frequency Range: 3.288e+15 to 1.316e+17 Hz
This is Energy:           1.360e+01 to 5.442e+02 eV
Integrating photoionization rates tables...
INFO: No heating rates

---- Calculated Clumping Factor (constant model):
 min, mean and max clumping : 5.000e+00  5.000e+00  5.000e+00

---- Calculated Mean-Free Path (constant model):
Maximum comoving distance for photons from source mfp = 15.00 cMpc (constant model).
 This corresponds to 2370.048 grid cells.

Using CPU Raytracing (subboxsize = 128, max_subbox = 1000)
Running in non-MPI (single-GPU/CPU) mode
Starting simulation...


Running: "C2Ray Test"

Read the source file and define some redshift step.

[8]:

# Generate redshift list (test case)
t_evol = 5e8 # years
zred_array = sim.generate_redshift_array(numzred+1,t_evol/numzred)

# Read sources
numsrc = 1
srcpos, srcflux = sim.read_sources("src_ifront.txt", numsrc)

show_plot = True
xc = np.linspace(0, sim.boxsize*1000, sim.N)

[9]:

# Start the timer ot measure the wall clock time
timer = pc2r.Timer()
timer.start()

# Loop over redshifts
for k in range(len(zred_array)-1):
    # Compute timestep of current redshift slice
    zi = zred_array[k]
    zf = zred_array[k+1]

    sim.printlog("\n==============\nDoing redshift %.3f to %.3f\n==============\n" %(zi, zf), sim.logfile)

    # Compute timestep of current redshift slice
    dt = sim.set_timestep(zi,zf,num_steps_between_slices)

    # Write output
    sim.write_output(zi)

    # Set density (when cosmological is false, zi has no effect)
    sim.density_init(zi)

    # Set redshift to current slice redshift
    sim.zred = zi

    # Do num_steps_between_slices timesteps
    for t in range(num_steps_between_slices):
        sim.printlog("\n --- Timestep %d. Redshift: z = %.3f --- \n" %(t+1, sim.zred), sim.logfile)

        # Evolve Cosmology: increment redshift and scale physical quantities (density, proper cell size, etc.). If cosmology is disabled in parameter, this step does nothing (checked internally by the class)
        sim.cosmo_evolve(dt)

        # Evolve the simulation: raytrace -> photoionization rates -> chemistry -> until convergence
        sim.evolve3D(dt, srcflux, srcpos)

        # Register elapsed Wall clock time
        tnow = timer.lap('k=%d, t=%d' %(k,t))

    # Show results at each redshift step
    if show_plot:
        fig, ax = plt.subplots(figsize=(8, 6), ncols=1, nrows=1)
        ax.set_title('z = %.3f' %sim.zred)
        im = ax.pcolormesh(xc, xc, sim.xh[:,:,sim.N//2], vmin=0, vmax=1, cmap='jet')
        plt.colorbar(im, ax=ax, label=r'$x_\mathrm{HII}$')
        ax.set_xlabel('$x$ [kpc]'), ax.set_ylabel('$y$ [kpc]')
        plt.show(), plt.clf()

# Write final output
sim.write_output(zf)

# stop the timer and print the summary
timer.stop()
sim.printlog(timer.summary, sim.logfile)

Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.200e-03
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.38s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 19 of 16777216 ( 0.000 % ), Relative change in ionfrac:  1.67e+03
Rank=0 is doing Raytracing... took 1.39s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 32 of 16777216 ( 0.000 % ), Relative change in ionfrac:  1.12e-03
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 98 of 16777216 ( 0.001 % ), Relative change in ionfrac:  4.83e-03
Rank=0 is doing Raytracing... took 1.39s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 218 of 16777216 ( 0.001 % ), Relative change in ionfrac:  1.06e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 386 of 16777216 ( 0.002 % ), Relative change in ionfrac:  1.85e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 610 of 16777216 ( 0.004 % ), Relative change in ionfrac:  2.80e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 1054 of 16777216 ( 0.006 % ), Relative change in ionfrac:  3.87e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 1678 of 16777216 ( 0.010 % ), Relative change in ionfrac:  5.01e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 2494 of 16777216 ( 0.015 % ), Relative change in ionfrac:  6.13e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 3454 of 16777216 ( 0.021 % ), Relative change in ionfrac:  7.20e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 4348 of 16777216 ( 0.026 % ), Relative change in ionfrac:  8.16e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 5308 of 16777216 ( 0.032 % ), Relative change in ionfrac:  8.99e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 6364 of 16777216 ( 0.038 % ), Relative change in ionfrac:  9.66e-02
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 7516 of 16777216 ( 0.045 % ), Relative change in ionfrac:  1.02e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 8764 of 16777216 ( 0.052 % ), Relative change in ionfrac:  1.06e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 10108 of 16777216 ( 0.060 % ), Relative change in ionfrac:  1.08e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 11548 of 16777216 ( 0.069 % ), Relative change in ionfrac:  1.09e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 13084 of 16777216 ( 0.078 % ), Relative change in ionfrac:  1.09e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 14716 of 16777216 ( 0.088 % ), Relative change in ionfrac:  1.07e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 16420 of 16777216 ( 0.098 % ), Relative change in ionfrac:  1.06e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 18196 of 16777216 ( 0.108 % ), Relative change in ionfrac:  1.03e-01
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 19996 of 16777216 ( 0.119 % ), Relative change in ionfrac:  9.94e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 22096 of 16777216 ( 0.132 % ), Relative change in ionfrac:  9.50e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 23892 of 16777216 ( 0.142 % ), Relative change in ionfrac:  9.18e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 25996 of 16777216 ( 0.155 % ), Relative change in ionfrac:  8.92e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 28156 of 16777216 ( 0.168 % ), Relative change in ionfrac:  8.63e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 30472 of 16777216 ( 0.182 % ), Relative change in ionfrac:  8.23e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 32644 of 16777216 ( 0.195 % ), Relative change in ionfrac:  7.92e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 35020 of 16777216 ( 0.209 % ), Relative change in ionfrac:  7.67e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 37228 of 16777216 ( 0.222 % ), Relative change in ionfrac:  7.36e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 40012 of 16777216 ( 0.238 % ), Relative change in ionfrac:  7.03e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 41956 of 16777216 ( 0.250 % ), Relative change in ionfrac:  6.81e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 44860 of 16777216 ( 0.267 % ), Relative change in ionfrac:  6.54e-02
Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 47524 of 16777216 ( 0.283 % ), Relative change in ionfrac:  6.25e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 49828 of 16777216 ( 0.297 % ), Relative change in ionfrac:  6.04e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 52456 of 16777216 ( 0.313 % ), Relative change in ionfrac:  5.79e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 54868 of 16777216 ( 0.327 % ), Relative change in ionfrac:  5.53e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 56530 of 16777216 ( 0.337 % ), Relative change in ionfrac:  5.34e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 58756 of 16777216 ( 0.350 % ), Relative change in ionfrac:  5.26e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 61444 of 16777216 ( 0.366 % ), Relative change in ionfrac:  5.11e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 63292 of 16777216 ( 0.377 % ), Relative change in ionfrac:  4.87e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 66124 of 16777216 ( 0.394 % ), Relative change in ionfrac:  4.65e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 67594 of 16777216 ( 0.403 % ), Relative change in ionfrac:  4.48e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 69628 of 16777216 ( 0.415 % ), Relative change in ionfrac:  4.43e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 72076 of 16777216 ( 0.430 % ), Relative change in ionfrac:  4.22e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 74308 of 16777216 ( 0.443 % ), Relative change in ionfrac:  4.01e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 75922 of 16777216 ( 0.453 % ), Relative change in ionfrac:  3.88e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 77748 of 16777216 ( 0.463 % ), Relative change in ionfrac:  3.80e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 79684 of 16777216 ( 0.475 % ), Relative change in ionfrac:  3.59e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 81322 of 16777216 ( 0.485 % ), Relative change in ionfrac:  3.41e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 82708 of 16777216 ( 0.493 % ), Relative change in ionfrac:  3.34e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 84772 of 16777216 ( 0.505 % ), Relative change in ionfrac:  3.12e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 86482 of 16777216 ( 0.515 % ), Relative change in ionfrac:  2.97e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 87292 of 16777216 ( 0.520 % ), Relative change in ionfrac:  2.88e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 88668 of 16777216 ( 0.529 % ), Relative change in ionfrac:  2.66e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 89636 of 16777216 ( 0.534 % ), Relative change in ionfrac:  2.56e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 91148 of 16777216 ( 0.543 % ), Relative change in ionfrac:  2.39e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 92378 of 16777216 ( 0.551 % ), Relative change in ionfrac:  2.23e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 92852 of 16777216 ( 0.553 % ), Relative change in ionfrac:  2.12e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 93104 of 16777216 ( 0.555 % ), Relative change in ionfrac:  1.92e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 92980 of 16777216 ( 0.554 % ), Relative change in ionfrac:  1.83e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 92564 of 16777216 ( 0.552 % ), Relative change in ionfrac:  1.63e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 92908 of 16777216 ( 0.554 % ), Relative change in ionfrac:  1.54e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 93220 of 16777216 ( 0.556 % ), Relative change in ionfrac:  1.36e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 91684 of 16777216 ( 0.546 % ), Relative change in ionfrac:  1.26e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 91210 of 16777216 ( 0.544 % ), Relative change in ionfrac:  1.11e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 89264 of 16777216 ( 0.532 % ), Relative change in ionfrac:  9.89e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 88504 of 16777216 ( 0.528 % ), Relative change in ionfrac:  8.79e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 87144 of 16777216 ( 0.519 % ), Relative change in ionfrac:  7.47e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 85264 of 16777216 ( 0.508 % ), Relative change in ionfrac:  6.72e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 83608 of 16777216 ( 0.498 % ), Relative change in ionfrac:  5.69e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 81800 of 16777216 ( 0.488 % ), Relative change in ionfrac:  4.69e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 78824 of 16777216 ( 0.470 % ), Relative change in ionfrac:  4.03e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 75492 of 16777216 ( 0.450 % ), Relative change in ionfrac:  3.40e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 72388 of 16777216 ( 0.431 % ), Relative change in ionfrac:  2.71e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 68964 of 16777216 ( 0.411 % ), Relative change in ionfrac:  2.11e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 65220 of 16777216 ( 0.389 % ), Relative change in ionfrac:  1.65e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 62196 of 16777216 ( 0.371 % ), Relative change in ionfrac:  1.29e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 57204 of 16777216 ( 0.341 % ), Relative change in ionfrac:  1.01e-03
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 52820 of 16777216 ( 0.315 % ), Relative change in ionfrac:  7.58e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 47310 of 16777216 ( 0.282 % ), Relative change in ionfrac:  5.55e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 40790 of 16777216 ( 0.243 % ), Relative change in ionfrac:  3.99e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 35286 of 16777216 ( 0.210 % ), Relative change in ionfrac:  2.83e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 30294 of 16777216 ( 0.181 % ), Relative change in ionfrac:  2.00e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 26118 of 16777216 ( 0.156 % ), Relative change in ionfrac:  1.41e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 21438 of 16777216 ( 0.128 % ), Relative change in ionfrac:  1.01e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 17358 of 16777216 ( 0.103 % ), Relative change in ionfrac:  7.23e-05
Multiple source convergence reached after 87 ray-tracing iterations.
../_images/examples_ifront_13_1.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 5.024e-02
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.39s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 291880 of 16777216 ( 1.740 % ), Relative change in ionfrac:  3.73e+01
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 112420 of 16777216 ( 0.670 % ), Relative change in ionfrac:  3.45e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 118444 of 16777216 ( 0.706 % ), Relative change in ionfrac:  3.34e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 123580 of 16777216 ( 0.737 % ), Relative change in ionfrac:  3.16e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 126292 of 16777216 ( 0.753 % ), Relative change in ionfrac:  3.11e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 128362 of 16777216 ( 0.765 % ), Relative change in ionfrac:  2.89e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 130168 of 16777216 ( 0.776 % ), Relative change in ionfrac:  2.88e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 133612 of 16777216 ( 0.796 % ), Relative change in ionfrac:  2.65e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 134452 of 16777216 ( 0.801 % ), Relative change in ionfrac:  2.58e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 136372 of 16777216 ( 0.813 % ), Relative change in ionfrac:  2.39e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 136852 of 16777216 ( 0.816 % ), Relative change in ionfrac:  2.31e-02
Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 138556 of 16777216 ( 0.826 % ), Relative change in ionfrac:  2.17e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 139564 of 16777216 ( 0.832 % ), Relative change in ionfrac:  2.06e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 141484 of 16777216 ( 0.843 % ), Relative change in ionfrac:  1.90e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 141064 of 16777216 ( 0.841 % ), Relative change in ionfrac:  1.82e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 142498 of 16777216 ( 0.849 % ), Relative change in ionfrac:  1.64e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 141164 of 16777216 ( 0.841 % ), Relative change in ionfrac:  1.53e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 141596 of 16777216 ( 0.844 % ), Relative change in ionfrac:  1.39e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 140824 of 16777216 ( 0.839 % ), Relative change in ionfrac:  1.25e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 140052 of 16777216 ( 0.835 % ), Relative change in ionfrac:  1.13e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 138532 of 16777216 ( 0.826 % ), Relative change in ionfrac:  9.97e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 136468 of 16777216 ( 0.813 % ), Relative change in ionfrac:  8.59e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 134444 of 16777216 ( 0.801 % ), Relative change in ionfrac:  7.35e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 131996 of 16777216 ( 0.787 % ), Relative change in ionfrac:  6.27e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 129416 of 16777216 ( 0.771 % ), Relative change in ionfrac:  5.20e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 125586 of 16777216 ( 0.749 % ), Relative change in ionfrac:  4.19e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 122288 of 16777216 ( 0.729 % ), Relative change in ionfrac:  3.31e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 119216 of 16777216 ( 0.711 % ), Relative change in ionfrac:  2.57e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 115448 of 16777216 ( 0.688 % ), Relative change in ionfrac:  1.97e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 112112 of 16777216 ( 0.668 % ), Relative change in ionfrac:  1.49e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 108128 of 16777216 ( 0.644 % ), Relative change in ionfrac:  1.11e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 104960 of 16777216 ( 0.626 % ), Relative change in ionfrac:  8.14e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 101792 of 16777216 ( 0.607 % ), Relative change in ionfrac:  5.93e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 98024 of 16777216 ( 0.584 % ), Relative change in ionfrac:  4.29e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 92666 of 16777216 ( 0.552 % ), Relative change in ionfrac:  3.10e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 86570 of 16777216 ( 0.516 % ), Relative change in ionfrac:  2.25e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 76290 of 16777216 ( 0.455 % ), Relative change in ionfrac:  1.64e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 58506 of 16777216 ( 0.349 % ), Relative change in ionfrac:  1.21e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 44500 of 16777216 ( 0.265 % ), Relative change in ionfrac:  8.94e-05
Multiple source convergence reached after 39 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_4.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 8.591e-02
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 348818 of 16777216 ( 2.079 % ), Relative change in ionfrac:  2.16e+01
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 160180 of 16777216 ( 0.955 % ), Relative change in ionfrac:  2.34e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 158612 of 16777216 ( 0.945 % ), Relative change in ionfrac:  2.18e-02
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 165220 of 16777216 ( 0.985 % ), Relative change in ionfrac:  2.04e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 169780 of 16777216 ( 1.012 % ), Relative change in ionfrac:  1.87e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 170332 of 16777216 ( 1.015 % ), Relative change in ionfrac:  1.76e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 171268 of 16777216 ( 1.021 % ), Relative change in ionfrac:  1.66e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 170986 of 16777216 ( 1.019 % ), Relative change in ionfrac:  1.51e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 171276 of 16777216 ( 1.021 % ), Relative change in ionfrac:  1.40e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 171844 of 16777216 ( 1.024 % ), Relative change in ionfrac:  1.28e-02
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 170282 of 16777216 ( 1.015 % ), Relative change in ionfrac:  1.15e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 168820 of 16777216 ( 1.006 % ), Relative change in ionfrac:  1.03e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 167440 of 16777216 ( 0.998 % ), Relative change in ionfrac:  9.09e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 164380 of 16777216 ( 0.980 % ), Relative change in ionfrac:  7.89e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 162028 of 16777216 ( 0.966 % ), Relative change in ionfrac:  6.74e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 158692 of 16777216 ( 0.946 % ), Relative change in ionfrac:  5.64e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 155572 of 16777216 ( 0.927 % ), Relative change in ionfrac:  4.66e-03
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 151316 of 16777216 ( 0.902 % ), Relative change in ionfrac:  3.78e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 146684 of 16777216 ( 0.874 % ), Relative change in ionfrac:  2.99e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 142766 of 16777216 ( 0.851 % ), Relative change in ionfrac:  2.32e-03
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 138194 of 16777216 ( 0.824 % ), Relative change in ionfrac:  1.77e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 133730 of 16777216 ( 0.797 % ), Relative change in ionfrac:  1.32e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 128914 of 16777216 ( 0.768 % ), Relative change in ionfrac:  9.70e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 124370 of 16777216 ( 0.741 % ), Relative change in ionfrac:  7.06e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 119634 of 16777216 ( 0.713 % ), Relative change in ionfrac:  5.10e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 115670 of 16777216 ( 0.689 % ), Relative change in ionfrac:  3.68e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 110454 of 16777216 ( 0.658 % ), Relative change in ionfrac:  2.66e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 103182 of 16777216 ( 0.615 % ), Relative change in ionfrac:  1.93e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 88194 of 16777216 ( 0.526 % ), Relative change in ionfrac:  1.42e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 68814 of 16777216 ( 0.410 % ), Relative change in ionfrac:  1.05e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 53358 of 16777216 ( 0.318 % ), Relative change in ionfrac:  7.81e-05
Multiple source convergence reached after 31 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_7.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.118e-01
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.40s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 340242 of 16777216 ( 2.028 % ), Relative change in ionfrac:  1.64e+01
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 186292 of 16777216 ( 1.110 % ), Relative change in ionfrac:  1.80e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 179044 of 16777216 ( 1.067 % ), Relative change in ionfrac:  1.56e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 184316 of 16777216 ( 1.099 % ), Relative change in ionfrac:  1.36e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 188876 of 16777216 ( 1.126 % ), Relative change in ionfrac:  1.28e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 191092 of 16777216 ( 1.139 % ), Relative change in ionfrac:  1.13e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 187324 of 16777216 ( 1.117 % ), Relative change in ionfrac:  9.90e-03
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.1 s.
Number of non-converged points: 186100 of 16777216 ( 1.109 % ), Relative change in ionfrac:  8.84e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 183784 of 16777216 ( 1.095 % ), Relative change in ionfrac:  7.69e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 181456 of 16777216 ( 1.082 % ), Relative change in ionfrac:  6.57e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 178004 of 16777216 ( 1.061 % ), Relative change in ionfrac:  5.55e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 174708 of 16777216 ( 1.041 % ), Relative change in ionfrac:  4.64e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 169772 of 16777216 ( 1.012 % ), Relative change in ionfrac:  3.77e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 164204 of 16777216 ( 0.979 % ), Relative change in ionfrac:  2.98e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 158966 of 16777216 ( 0.948 % ), Relative change in ionfrac:  2.30e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 153566 of 16777216 ( 0.915 % ), Relative change in ionfrac:  1.74e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 148226 of 16777216 ( 0.883 % ), Relative change in ionfrac:  1.30e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 143650 of 16777216 ( 0.856 % ), Relative change in ionfrac:  9.51e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 138338 of 16777216 ( 0.825 % ), Relative change in ionfrac:  6.91e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 133722 of 16777216 ( 0.797 % ), Relative change in ionfrac:  4.99e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 129410 of 16777216 ( 0.771 % ), Relative change in ionfrac:  3.60e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 124174 of 16777216 ( 0.740 % ), Relative change in ionfrac:  2.61e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.1 s.
Number of non-converged points: 115958 of 16777216 ( 0.691 % ), Relative change in ionfrac:  1.90e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 100630 of 16777216 ( 0.600 % ), Relative change in ionfrac:  1.39e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 81766 of 16777216 ( 0.487 % ), Relative change in ionfrac:  1.03e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 62270 of 16777216 ( 0.371 % ), Relative change in ionfrac:  7.70e-05
Multiple source convergence reached after 26 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_10.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.306e-01
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 308868 of 16777216 ( 1.841 % ), Relative change in ionfrac:  1.40e+01
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  0.9 s.
Number of non-converged points: 198724 of 16777216 ( 1.184 % ), Relative change in ionfrac:  1.45e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 187892 of 16777216 ( 1.120 % ), Relative change in ionfrac:  1.15e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 188556 of 16777216 ( 1.124 % ), Relative change in ionfrac:  9.17e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 192604 of 16777216 ( 1.148 % ), Relative change in ionfrac:  8.03e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 194968 of 16777216 ( 1.162 % ), Relative change in ionfrac:  7.11e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 193948 of 16777216 ( 1.156 % ), Relative change in ionfrac:  6.01e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 188980 of 16777216 ( 1.126 % ), Relative change in ionfrac:  4.90e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 183364 of 16777216 ( 1.093 % ), Relative change in ionfrac:  3.95e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 177052 of 16777216 ( 1.055 % ), Relative change in ionfrac:  3.17e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.1 s.
Number of non-converged points: 172172 of 16777216 ( 1.026 % ), Relative change in ionfrac:  2.49e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 166604 of 16777216 ( 0.993 % ), Relative change in ionfrac:  1.91e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 162254 of 16777216 ( 0.967 % ), Relative change in ionfrac:  1.44e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 156398 of 16777216 ( 0.932 % ), Relative change in ionfrac:  1.07e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 150986 of 16777216 ( 0.900 % ), Relative change in ionfrac:  7.78e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 145706 of 16777216 ( 0.868 % ), Relative change in ionfrac:  5.64e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 140802 of 16777216 ( 0.839 % ), Relative change in ionfrac:  4.07e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 135954 of 16777216 ( 0.810 % ), Relative change in ionfrac:  2.94e-04
Rank=0 is doing Raytracing... took 1.44s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 129058 of 16777216 ( 0.769 % ), Relative change in ionfrac:  2.13e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 114296 of 16777216 ( 0.681 % ), Relative change in ionfrac:  1.55e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 96760 of 16777216 ( 0.577 % ), Relative change in ionfrac:  1.14e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 75920 of 16777216 ( 0.453 % ), Relative change in ionfrac:  8.46e-05
Multiple source convergence reached after 22 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_13.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.442e-01
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 279586 of 16777216 ( 1.666 % ), Relative change in ionfrac:  1.26e+01
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 203256 of 16777216 ( 1.212 % ), Relative change in ionfrac:  1.14e-02
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 190588 of 16777216 ( 1.136 % ), Relative change in ionfrac:  8.90e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 187078 of 16777216 ( 1.115 % ), Relative change in ionfrac:  6.47e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 184732 of 16777216 ( 1.101 % ), Relative change in ionfrac:  4.81e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 185052 of 16777216 ( 1.103 % ), Relative change in ionfrac:  3.78e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 182984 of 16777216 ( 1.091 % ), Relative change in ionfrac:  3.07e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 181784 of 16777216 ( 1.084 % ), Relative change in ionfrac:  2.47e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 178096 of 16777216 ( 1.062 % ), Relative change in ionfrac:  1.94e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 173536 of 16777216 ( 1.034 % ), Relative change in ionfrac:  1.47e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 168506 of 16777216 ( 1.004 % ), Relative change in ionfrac:  1.10e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 162242 of 16777216 ( 0.967 % ), Relative change in ionfrac:  8.03e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 155570 of 16777216 ( 0.927 % ), Relative change in ionfrac:  5.81e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 150098 of 16777216 ( 0.895 % ), Relative change in ionfrac:  4.18e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 143774 of 16777216 ( 0.857 % ), Relative change in ionfrac:  3.00e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 136782 of 16777216 ( 0.815 % ), Relative change in ionfrac:  2.17e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 123368 of 16777216 ( 0.735 % ), Relative change in ionfrac:  1.57e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 102824 of 16777216 ( 0.613 % ), Relative change in ionfrac:  1.15e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 80280 of 16777216 ( 0.479 % ), Relative change in ionfrac:  8.49e-05
Multiple source convergence reached after 19 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_16.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.540e-01
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 254792 of 16777216 ( 1.519 % ), Relative change in ionfrac:  1.18e+01
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.1 s.
Number of non-converged points: 201100 of 16777216 ( 1.199 % ), Relative change in ionfrac:  8.68e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 187684 of 16777216 ( 1.119 % ), Relative change in ionfrac:  6.27e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 183340 of 16777216 ( 1.093 % ), Relative change in ionfrac:  4.45e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 178882 of 16777216 ( 1.066 % ), Relative change in ionfrac:  3.07e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 173162 of 16777216 ( 1.032 % ), Relative change in ionfrac:  2.11e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 167866 of 16777216 ( 1.001 % ), Relative change in ionfrac:  1.47e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 163586 of 16777216 ( 0.975 % ), Relative change in ionfrac:  1.05e-03
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 160010 of 16777216 ( 0.954 % ), Relative change in ionfrac:  7.55e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 156050 of 16777216 ( 0.930 % ), Relative change in ionfrac:  5.49e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 152058 of 16777216 ( 0.906 % ), Relative change in ionfrac:  4.01e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 146670 of 16777216 ( 0.874 % ), Relative change in ionfrac:  2.94e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 139062 of 16777216 ( 0.829 % ), Relative change in ionfrac:  2.16e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 126174 of 16777216 ( 0.752 % ), Relative change in ionfrac:  1.59e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 108718 of 16777216 ( 0.648 % ), Relative change in ionfrac:  1.18e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 86534 of 16777216 ( 0.516 % ), Relative change in ionfrac:  8.78e-05
Multiple source convergence reached after 16 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_19.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.611e-01
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 234688 of 16777216 ( 1.399 % ), Relative change in ionfrac:  1.13e+01
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 205972 of 16777216 ( 1.228 % ), Relative change in ionfrac:  6.86e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 187844 of 16777216 ( 1.120 % ), Relative change in ionfrac:  4.48e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 178334 of 16777216 ( 1.063 % ), Relative change in ionfrac:  2.86e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 169862 of 16777216 ( 1.012 % ), Relative change in ionfrac:  1.80e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 163654 of 16777216 ( 0.975 % ), Relative change in ionfrac:  1.13e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 157138 of 16777216 ( 0.937 % ), Relative change in ionfrac:  7.13e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 151474 of 16777216 ( 0.903 % ), Relative change in ionfrac:  4.56e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 144426 of 16777216 ( 0.861 % ), Relative change in ionfrac:  2.96e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 131862 of 16777216 ( 0.786 % ), Relative change in ionfrac:  1.95e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 108806 of 16777216 ( 0.649 % ), Relative change in ionfrac:  1.31e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 78078 of 16777216 ( 0.465 % ), Relative change in ionfrac:  8.97e-05
Multiple source convergence reached after 12 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_22.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.662e-01
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 209404 of 16777216 ( 1.248 % ), Relative change in ionfrac:  1.09e+01
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 197368 of 16777216 ( 1.176 % ), Relative change in ionfrac:  4.76e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 187840 of 16777216 ( 1.120 % ), Relative change in ionfrac:  2.99e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 180252 of 16777216 ( 1.074 % ), Relative change in ionfrac:  1.84e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 170730 of 16777216 ( 1.018 % ), Relative change in ionfrac:  1.09e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 161498 of 16777216 ( 0.963 % ), Relative change in ionfrac:  6.33e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 152538 of 16777216 ( 0.909 % ), Relative change in ionfrac:  3.68e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 141522 of 16777216 ( 0.844 % ), Relative change in ionfrac:  2.17e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 108400 of 16777216 ( 0.646 % ), Relative change in ionfrac:  1.31e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 67872 of 16777216 ( 0.405 % ), Relative change in ionfrac:  8.09e-05
Multiple source convergence reached after 10 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_25.png 
Calling evolve3D...
dr [Mpc]: 6.328e-03
dt [years]: 5.000e+07
Running on 1 source(s), total normalized ionizing flux: 1.00e+06
Mean density (cgs): 1.870e-04, Mean ionized fraction: 1.699e-01
Convergence Criterion (Number of points):  0

Rank=0 is doing Raytracing... took 1.41s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 202574 of 16777216 ( 1.207 % ), Relative change in ionfrac:  1.07e+01
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 189206 of 16777216 ( 1.128 % ), Relative change in ionfrac:  3.20e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 176348 of 16777216 ( 1.051 % ), Relative change in ionfrac:  1.72e-03
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 168412 of 16777216 ( 1.004 % ), Relative change in ionfrac:  9.73e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 161324 of 16777216 ( 0.962 % ), Relative change in ionfrac:  5.49e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 152100 of 16777216 ( 0.907 % ), Relative change in ionfrac:  3.10e-04
Rank=0 is doing Raytracing... took 1.43s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 125576 of 16777216 ( 0.748 % ), Relative change in ionfrac:  1.77e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 83592 of 16777216 ( 0.498 % ), Relative change in ionfrac:  1.03e-04
Rank=0 is doing Raytracing... took 1.42s.
Average number of subboxes: 1, Total photon loss: 0.000e+00
Doing Chemistry... took  1.0 s.
Number of non-converged points: 53114 of 16777216 ( 0.317 % ), Relative change in ionfrac:  6.12e-05
Multiple source convergence reached after 9 ray-tracing iterations.

<Figure size 640x480 with 0 Axes>
../_images/examples_ifront_13_28.png 
<Figure size 640x480 with 0 Axes>

Let’s have a look the wall clock time for this run.

[10]:

print(timer.summary)


--- TIMER SUMMARY ---
 step 1: 3m 24.72s - k=0, t=0
 step 2: 1m 33.54s - k=1, t=0
 step 3: 1m 15.23s - k=2, t=0
 step 4: 1m 3.69s - k=3, t=0
 step 5: 54.01s - k=4, t=0
 step 6: 46.63s - k=5, t=0
 step 7: 39.41s - k=6, t=0
 step 8: 29.47s - k=7, t=0
 step 9: 24.83s - k=8, t=0
 step 10: 22.27s - k=9, t=0
Elapsed time: 10m 54.04s

Here, we calculate the numerical solution for \(r_I\). We define the I-front position as the point where the gas is 50% ionized. Here, we use a simple interpolation for a line of sight starting at the center of the box.

The I-front velocity, \(v_I\), was obtained by simple finite-differencing of its position based on the current and previous time steps.

[11]:

# get half box length for interpolation in kpc
xc = np.linspace(0, sim.boxsize*1000/2, sim.N//2)

# get time of the corresponding redshift step
t_num = (sim.cosmology.age(zred_array) - sim.cosmology.age(sim.zred_0)).to('Myr')
t_aveg = 0.5*(t_num[1:]+t_num[:-1])

# get numerical radius and velocity
r_num = np.zeros_like(zred_array)
v_num = np.zeros(zred_array.size-1)

for k, z in enumerate(zred_array):
    # load ionized fraction
    xh = np.load('%sxfrac_%.3f.npy' %(sim.results_basename, z))

    # line of sight from the center to the box side
    los_xh = xh[sim.N//2:,sim.N//2,sim.N//2]

    # Compute the I-front radius at 50% ionized
    r_num[k] = np.interp(0.5, np.flip(los_xh), np.flip(xc))

    # Compute the I-front velocity
    if(k > 0):
        v_num[k-1] = ((r_num[k] - r_num[k-1])/(t_num[k]-t_num[k-1]) * u.kpc).to('km/s').value

        # plt the xHII profile
        plt.plot(xc, los_xh, label='z = %.1f' %z, color=plt.cm.jet(k/zred_array.size))
        plt.legend()

plt.xlabel('x [kpc]'), plt.ylabel(r'$x_\mathrm{HII}$')
plt.show(), plt.clf()
../_images/examples_ifront_17_0.png 
[11]:

(None, None)

<Figure size 640x480 with 0 Axes>

We plot the final result and compare the numerical and the analytical solutions. Despite employing only a few redshift steps (numzred = 10), the numerical solution agrees well with the analytical solution.

Increasing the value of numzred, for instance to 100, will have a less coarse numerical solution however, it will increase the computing time substantially.

[12]:

fig, axs = plt.subplots(figsize=(12,5), ncols=2, nrows=1)

axs[0].plot(t_analytical, r_analytical, color='black', ls='-', label="Analytical", lw=2)
axs[0].plot(t_num, r_num, color='tab:blue', marker='o', ls='--', label="Numerical", lw=2)
axs[0].set_ylabel("$r_I(t)$ [kpc]")

axs[1].semilogy(t_analytical[1:],v_analytical,color='black',label="Analytical",lw=2)
axs[1].plot(t_aveg, v_num, color='tab:blue', marker='o', ls='--', label="Numerical", lw=2)
axs[1].set_ylabel("$v_I(t)$ [km s$^{-1}$]")

for ax in axs:
    ax.set_xlabel("$t$ [Myr]")
    ax.grid()
    ax.legend()
../_images/examples_ifront_19_0.png