Kinetic surface model#
This MMS case verifies the implementation of the SurfaceKinetics boundary condition in FESTIM. We will consider a time-dependent case of hydrogen diffusion on domain \(\Omega: x\in[0,1] \cup t\in[0, 5]\) with a homogeneous diffusion coefficient \(D\), and a Dirichlet boundary condition on the rear domain side.
The problem is:
(27)#\[\begin{align}
&\dfrac{\partial c_\mathrm{m}}{\partial t} = \nabla\cdot\left(D\nabla c_\mathrm{m} \right) + S \quad \textrm{ on } \Omega, \\
&-D \nabla c_\mathrm{m} \cdot \mathbf{n} = \lambda_{\mathrm{IS}} \dfrac{\partial c_{\mathrm{m}}}{\partial t} + J_{\mathrm{bs}} - J_{\mathrm{sb}} \quad \textrm{ at } x=0, \\
&c_\mathrm{m} = c_\mathrm{m, 0} \quad \textrm{ at } x=1, \\
&c_\mathrm{m} = c_\mathrm{m, 0} \quad \textrm{ at } t=0, \\
&\dfrac{d c_\mathrm{s}}{d t} = J_{\mathrm{bs}} - J_{\mathrm{sb}} + J_{\mathrm{vs}} \quad \textrm{ at } x=0, \\
&c_\mathrm{s}= c_\mathrm{s, 0}\quad \textrm{ at } t=0, \\
\end{align}\]
with \(J_{\mathrm{bs}} = k_{\mathrm{bs}} c_{\mathrm{m}} \lambda_{\mathrm{abs}} \left(1 - \dfrac{c_\mathrm{s}}{n_{\mathrm{surf}}}\right)\), \(J_{\mathrm{sb}} = k_{\mathrm{sb}} c_{\mathrm{s}} \left(1 - \dfrac{c_{\mathrm{m}}}{n_\mathrm{IS}}\right)\), \(\lambda_{\mathrm{abs}}=n_\mathrm{surf}/n_\mathrm{IS}\).
The manufactured exact solution for mobile concentration is:
(28)#\[\begin{equation}
c_\mathrm{m, exact}=1+2x^2+x+2t.
\end{equation}\]
For this problem, we choose:
\[\begin{align*}
& k_{\mathrm{bs}}=1/\lambda_{\mathrm{abs}} \\
& k_{\mathrm{sb}}=2/\lambda_{\mathrm{abs}} \\
& n_{\mathrm{IS}} = 20 \\
& n_{\mathrm{surf}} = 5 \\
& D = 5 \\
& \lambda_\mathrm{IS} = 2
\end{align*}\]
Injecting these parameters and the exact solution for solute H, we obtain:
(29)#\[\begin{align}
& S = 2(1-2D) \\
& J_{\mathrm{vs}}=2n_\mathrm{surf}\dfrac{2n_\mathrm{IS}+2\lambda_\mathrm{IS}-D}{(2n_\mathrm{IS}-1-2t)^2}+2\lambda_\mathrm{IS}-D \\
& c_\mathrm{s, exact}=n_\mathrm{surf}\dfrac{1+2t+2\lambda_\mathrm{IS}-D}{2n_\mathrm{IS}-1-2t} \\
& c_\mathrm{s,0}=c_\mathrm{s, exact} \\
& c_\mathrm{m,0}=c_\mathrm{m, exact}
\end{align}\]
We can then run a FESTIM model with these values and compare the numerical solutions with \(c_\mathrm{m, exact}\) and \(c_\mathrm{s, exact}\).
FESTIM code#
Show code cell source
import festim as F
import matplotlib.pyplot as plt
import numpy as np
n_IS = 20
n_surf = 5
D = 5
lambda_IS = 2
k_bs = n_IS / n_surf
k_sb = 2 * n_IS / n_surf
solute_source = 2 * (1 - 2 * D)
exact_solution_cm = lambda x, t: 1 + 2 * x**2 + x + 2 * t
exact_solution_cs = (
lambda t: n_surf * (1 + 2 * t + 2 * lambda_IS - D) / (2 * n_IS - 1 - 2 * t)
)
solute_source = 2 * (1 - 2 * D)
def run_sim(export_times=None):
# Create the FESTIM model
my_model = F.Simulation()
my_model.mesh = F.MeshFromVertices(np.linspace(0, 1, 1000))
my_model.sources = [F.Source(solute_source, volume=1, field="solute")]
def J_vs(T, surf_conc, t):
return (
2 * n_surf * (2 * n_IS + 2 * lambda_IS - D) / (2 * n_IS - 1 - 2 * t) ** 2
+ 2 * lambda_IS
- D
)
my_model.boundary_conditions = [
F.DirichletBC(
surfaces=[2], value=exact_solution_cm(x=F.x, t=F.t), field="solute"
),
F.SurfaceKinetics(
k_sb=k_sb,
k_bs=k_bs,
lambda_IS=lambda_IS,
n_surf=n_surf,
n_IS=n_IS,
J_vs=J_vs,
surfaces=1,
initial_condition=exact_solution_cs(t=0),
t=F.t,
),
]
my_model.initial_conditions = [
F.InitialCondition(field="solute", value=exact_solution_cm(x=F.x, t=F.t))
]
my_model.materials = F.Material(id=1, D_0=D, E_D=0)
my_model.T = 300 # this is ignored since no parameter is T-dependent
my_model.settings = F.Settings(
absolute_tolerance=1e-10, relative_tolerance=1e-10, transient=True, final_time=5
)
my_model.dt = F.Stepsize(initial_value=5e-3, milestones=export_times)
derived_quantities = F.DerivedQuantities(
[F.AdsorbedHydrogen(surface=1)], show_units=True
)
my_model.exports = [
F.TXTExport("solute", filename="./mobile_conc.txt", times=export_times),
derived_quantities,
]
my_model.initialise()
my_model.run()
return derived_quantities
Comparison with exact solution#
Show code cell source
def norm(x, c_comp, c_ex):
return np.sqrt(np.trapz(y=(c_comp - c_ex) ** 2, x=x))
export_times = [1, 2, 3, 4, 5]
adsorbed_data = run_sim(export_times)
solute_data = np.genfromtxt("mobile_conc.txt", names=True, delimiter=",")
Show code cell output
Defining initial values
Defining variational problem
Defining source terms
Defining boundary conditions
Time stepping...
Calling FFC just-in-time (JIT) compiler, this may take some time.
Calling FFC just-in-time (JIT) compiler, this may take some time.
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27.5 % 1.4e+00 s Elapsed time so far: 2.9 s
27.6 % 1.4e+00 s Elapsed time so far: 2.9 s
27.7 % 1.4e+00 s Elapsed time so far: 2.9 s
27.8 % 1.4e+00 s Elapsed time so far: 2.9 s
27.9 % 1.4e+00 s Elapsed time so far: 2.9 s
28.0 % 1.4e+00 s Elapsed time so far: 2.9 s
28.1 % 1.4e+00 s Elapsed time so far: 2.9 s
28.2 % 1.4e+00 s Elapsed time so far: 2.9 s
28.3 % 1.4e+00 s Elapsed time so far: 2.9 s
28.4 % 1.4e+00 s Elapsed time so far: 2.9 s
28.5 % 1.4e+00 s Elapsed time so far: 2.9 s
28.6 % 1.4e+00 s Elapsed time so far: 2.9 s
28.7 % 1.4e+00 s Elapsed time so far: 2.9 s
28.8 % 1.4e+00 s Elapsed time so far: 2.9 s
28.9 % 1.4e+00 s Elapsed time so far: 3.0 s
29.0 % 1.4e+00 s Elapsed time so far: 3.0 s
29.1 % 1.5e+00 s Elapsed time so far: 3.0 s
29.2 % 1.5e+00 s Elapsed time so far: 3.0 s
29.3 % 1.5e+00 s Elapsed time so far: 3.0 s
29.4 % 1.5e+00 s Elapsed time so far: 3.0 s
29.5 % 1.5e+00 s Elapsed time so far: 3.0 s
29.6 % 1.5e+00 s Elapsed time so far: 3.0 s
29.7 % 1.5e+00 s Elapsed time so far: 3.0 s
29.8 % 1.5e+00 s Elapsed time so far: 3.0 s
29.9 % 1.5e+00 s Elapsed time so far: 3.0 s
30.0 % 1.5e+00 s Elapsed time so far: 3.0 s
30.1 % 1.5e+00 s Elapsed time so far: 3.0 s
30.2 % 1.5e+00 s Elapsed time so far: 3.0 s
30.3 % 1.5e+00 s Elapsed time so far: 3.1 s
30.4 % 1.5e+00 s Elapsed time so far: 3.1 s
30.5 % 1.5e+00 s Elapsed time so far: 3.1 s
30.6 % 1.5e+00 s Elapsed time so far: 3.1 s
30.7 % 1.5e+00 s Elapsed time so far: 3.1 s
30.8 % 1.5e+00 s Elapsed time so far: 3.1 s
30.9 % 1.5e+00 s Elapsed time so far: 3.1 s
31.0 % 1.5e+00 s Elapsed time so far: 3.1 s
31.1 % 1.6e+00 s Elapsed time so far: 3.1 s
31.2 % 1.6e+00 s Elapsed time so far: 3.1 s
31.3 % 1.6e+00 s Elapsed time so far: 3.1 s
31.4 % 1.6e+00 s Elapsed time so far: 3.1 s
31.5 % 1.6e+00 s Elapsed time so far: 3.1 s
31.6 % 1.6e+00 s Elapsed time so far: 3.1 s
31.7 % 1.6e+00 s Elapsed time so far: 3.1 s
31.8 % 1.6e+00 s Elapsed time so far: 3.1 s
31.9 % 1.6e+00 s Elapsed time so far: 3.2 s
32.0 % 1.6e+00 s Elapsed time so far: 3.2 s
32.1 % 1.6e+00 s Elapsed time so far: 3.2 s
32.2 % 1.6e+00 s Elapsed time so far: 3.2 s
32.3 % 1.6e+00 s Elapsed time so far: 3.2 s
32.4 % 1.6e+00 s Elapsed time so far: 3.2 s
32.5 % 1.6e+00 s Elapsed time so far: 3.2 s
32.6 % 1.6e+00 s Elapsed time so far: 3.2 s
32.7 % 1.6e+00 s Elapsed time so far: 3.2 s
32.8 % 1.6e+00 s Elapsed time so far: 3.2 s
32.9 % 1.6e+00 s Elapsed time so far: 3.2 s
33.0 % 1.6e+00 s Elapsed time so far: 3.2 s
33.1 % 1.7e+00 s Elapsed time so far: 3.2 s
33.2 % 1.7e+00 s Elapsed time so far: 3.2 s
33.3 % 1.7e+00 s Elapsed time so far: 3.2 s
33.4 % 1.7e+00 s Elapsed time so far: 3.2 s
33.5 % 1.7e+00 s Elapsed time so far: 3.3 s
33.6 % 1.7e+00 s Elapsed time so far: 3.3 s
33.7 % 1.7e+00 s Elapsed time so far: 3.3 s
33.8 % 1.7e+00 s Elapsed time so far: 3.3 s
33.9 % 1.7e+00 s Elapsed time so far: 3.3 s
34.0 % 1.7e+00 s Elapsed time so far: 3.3 s
34.1 % 1.7e+00 s Elapsed time so far: 3.3 s
34.2 % 1.7e+00 s Elapsed time so far: 3.3 s
34.3 % 1.7e+00 s Elapsed time so far: 3.3 s
34.4 % 1.7e+00 s Elapsed time so far: 3.3 s
34.5 % 1.7e+00 s Elapsed time so far: 3.3 s
34.6 % 1.7e+00 s Elapsed time so far: 3.3 s
34.7 % 1.7e+00 s Elapsed time so far: 3.3 s
34.8 % 1.7e+00 s Elapsed time so far: 3.4 s
34.9 % 1.7e+00 s Elapsed time so far: 3.4 s
35.0 % 1.7e+00 s Elapsed time so far: 3.4 s
35.1 % 1.8e+00 s Elapsed time so far: 3.4 s
35.2 % 1.8e+00 s Elapsed time so far: 3.4 s
35.3 % 1.8e+00 s Elapsed time so far: 3.4 s
35.4 % 1.8e+00 s Elapsed time so far: 3.4 s
35.5 % 1.8e+00 s Elapsed time so far: 3.4 s
35.6 % 1.8e+00 s Elapsed time so far: 3.4 s
35.7 % 1.8e+00 s Elapsed time so far: 3.4 s
35.8 % 1.8e+00 s Elapsed time so far: 3.4 s
35.9 % 1.8e+00 s Elapsed time so far: 3.4 s
36.0 % 1.8e+00 s Elapsed time so far: 3.4 s
36.1 % 1.8e+00 s Elapsed time so far: 3.4 s
36.2 % 1.8e+00 s Elapsed time so far: 3.4 s
36.3 % 1.8e+00 s Elapsed time so far: 3.5 s
36.4 % 1.8e+00 s Elapsed time so far: 3.5 s
36.5 % 1.8e+00 s Elapsed time so far: 3.5 s
36.6 % 1.8e+00 s Elapsed time so far: 3.5 s
36.7 % 1.8e+00 s Elapsed time so far: 3.5 s
36.8 % 1.8e+00 s Elapsed time so far: 3.5 s
36.9 % 1.8e+00 s Elapsed time so far: 3.5 s
37.0 % 1.8e+00 s Elapsed time so far: 3.5 s
37.1 % 1.9e+00 s Elapsed time so far: 3.5 s
37.2 % 1.9e+00 s Elapsed time so far: 3.5 s
37.3 % 1.9e+00 s Elapsed time so far: 3.5 s
37.4 % 1.9e+00 s Elapsed time so far: 3.5 s
37.5 % 1.9e+00 s Elapsed time so far: 3.5 s
37.6 % 1.9e+00 s Elapsed time so far: 3.5 s
37.7 % 1.9e+00 s Elapsed time so far: 3.6 s
37.8 % 1.9e+00 s Elapsed time so far: 3.6 s
37.9 % 1.9e+00 s Elapsed time so far: 3.6 s
38.0 % 1.9e+00 s Elapsed time so far: 3.6 s
38.1 % 1.9e+00 s Elapsed time so far: 3.6 s
38.2 % 1.9e+00 s Elapsed time so far: 3.6 s
38.3 % 1.9e+00 s Elapsed time so far: 3.6 s
38.4 % 1.9e+00 s Elapsed time so far: 3.6 s
38.5 % 1.9e+00 s Elapsed time so far: 3.6 s
38.6 % 1.9e+00 s Elapsed time so far: 3.6 s
38.7 % 1.9e+00 s Elapsed time so far: 3.6 s
38.8 % 1.9e+00 s Elapsed time so far: 3.6 s
38.9 % 1.9e+00 s Elapsed time so far: 3.6 s
39.0 % 1.9e+00 s Elapsed time so far: 3.6 s
39.1 % 2.0e+00 s Elapsed time so far: 3.7 s
39.2 % 2.0e+00 s Elapsed time so far: 3.7 s
39.3 % 2.0e+00 s Elapsed time so far: 3.7 s
39.4 % 2.0e+00 s Elapsed time so far: 3.7 s
39.5 % 2.0e+00 s Elapsed time so far: 3.7 s
39.6 % 2.0e+00 s Elapsed time so far: 3.7 s
39.7 % 2.0e+00 s Elapsed time so far: 3.7 s
39.8 % 2.0e+00 s Elapsed time so far: 3.7 s
39.9 % 2.0e+00 s Elapsed time so far: 3.7 s
40.0 % 2.0e+00 s Elapsed time so far: 3.7 s
40.1 % 2.0e+00 s Elapsed time so far: 3.7 s
40.2 % 2.0e+00 s Elapsed time so far: 3.7 s
40.3 % 2.0e+00 s Elapsed time so far: 3.7 s
40.4 % 2.0e+00 s Elapsed time so far: 3.7 s
40.5 % 2.0e+00 s Elapsed time so far: 3.8 s
40.6 % 2.0e+00 s Elapsed time so far: 3.8 s
40.7 % 2.0e+00 s Elapsed time so far: 3.8 s
40.8 % 2.0e+00 s Elapsed time so far: 3.8 s
40.9 % 2.0e+00 s Elapsed time so far: 3.8 s
41.0 % 2.0e+00 s Elapsed time so far: 3.8 s
41.1 % 2.1e+00 s Elapsed time so far: 3.8 s
41.2 % 2.1e+00 s Elapsed time so far: 3.8 s
41.3 % 2.1e+00 s Elapsed time so far: 3.8 s
41.4 % 2.1e+00 s Elapsed time so far: 3.8 s
41.5 % 2.1e+00 s Elapsed time so far: 3.8 s
41.6 % 2.1e+00 s Elapsed time so far: 3.8 s
41.7 % 2.1e+00 s Elapsed time so far: 3.8 s
41.8 % 2.1e+00 s Elapsed time so far: 3.8 s
41.9 % 2.1e+00 s Elapsed time so far: 3.9 s
42.0 % 2.1e+00 s Elapsed time so far: 3.9 s
42.1 % 2.1e+00 s Elapsed time so far: 3.9 s
42.2 % 2.1e+00 s Elapsed time so far: 3.9 s
42.3 % 2.1e+00 s Elapsed time so far: 3.9 s
42.4 % 2.1e+00 s Elapsed time so far: 3.9 s
42.5 % 2.1e+00 s Elapsed time so far: 3.9 s
42.6 % 2.1e+00 s Elapsed time so far: 3.9 s
42.7 % 2.1e+00 s Elapsed time so far: 3.9 s
42.8 % 2.1e+00 s Elapsed time so far: 3.9 s
42.9 % 2.1e+00 s Elapsed time so far: 3.9 s
43.0 % 2.1e+00 s Elapsed time so far: 3.9 s
43.1 % 2.2e+00 s Elapsed time so far: 3.9 s
43.2 % 2.2e+00 s Elapsed time so far: 3.9 s
43.3 % 2.2e+00 s Elapsed time so far: 4.0 s
43.4 % 2.2e+00 s Elapsed time so far: 4.0 s
43.5 % 2.2e+00 s Elapsed time so far: 4.0 s
43.6 % 2.2e+00 s Elapsed time so far: 4.0 s
43.7 % 2.2e+00 s Elapsed time so far: 4.0 s
43.8 % 2.2e+00 s Elapsed time so far: 4.0 s
43.9 % 2.2e+00 s Elapsed time so far: 4.0 s
44.0 % 2.2e+00 s Elapsed time so far: 4.0 s
44.1 % 2.2e+00 s Elapsed time so far: 4.0 s
44.2 % 2.2e+00 s Elapsed time so far: 4.0 s
44.3 % 2.2e+00 s Elapsed time so far: 4.0 s
44.4 % 2.2e+00 s Elapsed time so far: 4.0 s
44.5 % 2.2e+00 s Elapsed time so far: 4.0 s
44.6 % 2.2e+00 s Elapsed time so far: 4.0 s
44.7 % 2.2e+00 s Elapsed time so far: 4.0 s
44.8 % 2.2e+00 s Elapsed time so far: 4.0 s
44.9 % 2.2e+00 s Elapsed time so far: 4.1 s
45.0 % 2.2e+00 s Elapsed time so far: 4.1 s
45.1 % 2.3e+00 s Elapsed time so far: 4.1 s
45.2 % 2.3e+00 s Elapsed time so far: 4.1 s
45.3 % 2.3e+00 s Elapsed time so far: 4.1 s
45.4 % 2.3e+00 s Elapsed time so far: 4.1 s
45.5 % 2.3e+00 s Elapsed time so far: 4.1 s
45.6 % 2.3e+00 s Elapsed time so far: 4.1 s
45.7 % 2.3e+00 s Elapsed time so far: 4.1 s
45.8 % 2.3e+00 s Elapsed time so far: 4.1 s
45.9 % 2.3e+00 s Elapsed time so far: 4.1 s
46.0 % 2.3e+00 s Elapsed time so far: 4.1 s
46.1 % 2.3e+00 s Elapsed time so far: 4.1 s
46.2 % 2.3e+00 s Elapsed time so far: 4.2 s
46.3 % 2.3e+00 s Elapsed time so far: 4.2 s
46.4 % 2.3e+00 s Elapsed time so far: 4.2 s
46.5 % 2.3e+00 s Elapsed time so far: 4.2 s
46.6 % 2.3e+00 s Elapsed time so far: 4.2 s
46.7 % 2.3e+00 s Elapsed time so far: 4.2 s
46.8 % 2.3e+00 s Elapsed time so far: 4.2 s
46.9 % 2.3e+00 s Elapsed time so far: 4.2 s
47.0 % 2.3e+00 s Elapsed time so far: 4.2 s
47.1 % 2.4e+00 s Elapsed time so far: 4.2 s
47.2 % 2.4e+00 s Elapsed time so far: 4.2 s
47.3 % 2.4e+00 s Elapsed time so far: 4.2 s
47.4 % 2.4e+00 s Elapsed time so far: 4.2 s
47.5 % 2.4e+00 s Elapsed time so far: 4.2 s
47.6 % 2.4e+00 s Elapsed time so far: 4.2 s
47.7 % 2.4e+00 s Elapsed time so far: 4.2 s
47.8 % 2.4e+00 s Elapsed time so far: 4.3 s
47.9 % 2.4e+00 s Elapsed time so far: 4.3 s
48.0 % 2.4e+00 s Elapsed time so far: 4.3 s
48.1 % 2.4e+00 s Elapsed time so far: 4.3 s
48.2 % 2.4e+00 s Elapsed time so far: 4.3 s
48.3 % 2.4e+00 s Elapsed time so far: 4.3 s
48.4 % 2.4e+00 s Elapsed time so far: 4.3 s
48.5 % 2.4e+00 s Elapsed time so far: 4.3 s
48.6 % 2.4e+00 s Elapsed time so far: 4.3 s
48.7 % 2.4e+00 s Elapsed time so far: 4.3 s
48.8 % 2.4e+00 s Elapsed time so far: 4.3 s
48.9 % 2.4e+00 s Elapsed time so far: 4.3 s
49.0 % 2.4e+00 s Elapsed time so far: 4.3 s
49.1 % 2.5e+00 s Elapsed time so far: 4.4 s
49.2 % 2.5e+00 s Elapsed time so far: 4.4 s
49.3 % 2.5e+00 s Elapsed time so far: 4.4 s
49.4 % 2.5e+00 s Elapsed time so far: 4.4 s
49.5 % 2.5e+00 s Elapsed time so far: 4.4 s
49.6 % 2.5e+00 s Elapsed time so far: 4.4 s
49.7 % 2.5e+00 s Elapsed time so far: 4.4 s
49.8 % 2.5e+00 s Elapsed time so far: 4.4 s
49.9 % 2.5e+00 s Elapsed time so far: 4.4 s
50.0 % 2.5e+00 s Elapsed time so far: 4.4 s
50.1 % 2.5e+00 s Elapsed time so far: 4.4 s
50.2 % 2.5e+00 s Elapsed time so far: 4.4 s
50.3 % 2.5e+00 s Elapsed time so far: 4.4 s
50.4 % 2.5e+00 s Elapsed time so far: 4.4 s
50.5 % 2.5e+00 s Elapsed time so far: 4.5 s
50.6 % 2.5e+00 s Elapsed time so far: 4.5 s
50.7 % 2.5e+00 s Elapsed time so far: 4.5 s
50.8 % 2.5e+00 s Elapsed time so far: 4.5 s
50.9 % 2.5e+00 s Elapsed time so far: 4.5 s
51.0 % 2.5e+00 s Elapsed time so far: 4.5 s
51.1 % 2.6e+00 s Elapsed time so far: 4.5 s
51.2 % 2.6e+00 s Elapsed time so far: 4.5 s
51.3 % 2.6e+00 s Elapsed time so far: 4.5 s
51.4 % 2.6e+00 s Elapsed time so far: 4.5 s
51.5 % 2.6e+00 s Elapsed time so far: 4.5 s
51.6 % 2.6e+00 s Elapsed time so far: 4.5 s
51.7 % 2.6e+00 s Elapsed time so far: 4.5 s
51.8 % 2.6e+00 s Elapsed time so far: 4.5 s
51.9 % 2.6e+00 s Elapsed time so far: 4.6 s
52.0 % 2.6e+00 s Elapsed time so far: 4.6 s
52.1 % 2.6e+00 s Elapsed time so far: 4.6 s
52.2 % 2.6e+00 s Elapsed time so far: 4.6 s
52.3 % 2.6e+00 s Elapsed time so far: 4.6 s
52.4 % 2.6e+00 s Elapsed time so far: 4.6 s
52.5 % 2.6e+00 s Elapsed time so far: 4.6 s
52.6 % 2.6e+00 s Elapsed time so far: 4.6 s
52.7 % 2.6e+00 s Elapsed time so far: 4.6 s
52.8 % 2.6e+00 s Elapsed time so far: 4.6 s
52.9 % 2.6e+00 s Elapsed time so far: 4.6 s
53.0 % 2.6e+00 s Elapsed time so far: 4.6 s
53.1 % 2.7e+00 s Elapsed time so far: 4.6 s
53.2 % 2.7e+00 s Elapsed time so far: 4.6 s
53.3 % 2.7e+00 s Elapsed time so far: 4.6 s
53.4 % 2.7e+00 s Elapsed time so far: 4.7 s
53.5 % 2.7e+00 s Elapsed time so far: 4.7 s
53.6 % 2.7e+00 s Elapsed time so far: 4.7 s
53.7 % 2.7e+00 s Elapsed time so far: 4.7 s
53.8 % 2.7e+00 s Elapsed time so far: 4.7 s
53.9 % 2.7e+00 s Elapsed time so far: 4.7 s
54.0 % 2.7e+00 s Elapsed time so far: 4.7 s
54.1 % 2.7e+00 s Elapsed time so far: 4.7 s
54.2 % 2.7e+00 s Elapsed time so far: 4.7 s
54.3 % 2.7e+00 s Elapsed time so far: 4.7 s
54.4 % 2.7e+00 s Elapsed time so far: 4.7 s
54.5 % 2.7e+00 s Elapsed time so far: 4.7 s
54.6 % 2.7e+00 s Elapsed time so far: 4.7 s
54.7 % 2.7e+00 s Elapsed time so far: 4.7 s
54.8 % 2.7e+00 s Elapsed time so far: 4.8 s
54.9 % 2.7e+00 s Elapsed time so far: 4.8 s
55.0 % 2.7e+00 s Elapsed time so far: 4.8 s
55.1 % 2.8e+00 s Elapsed time so far: 4.8 s
55.2 % 2.8e+00 s Elapsed time so far: 4.8 s
55.3 % 2.8e+00 s Elapsed time so far: 4.8 s
55.4 % 2.8e+00 s Elapsed time so far: 4.8 s
55.5 % 2.8e+00 s Elapsed time so far: 4.8 s
55.6 % 2.8e+00 s Elapsed time so far: 4.8 s
55.7 % 2.8e+00 s Elapsed time so far: 4.8 s
55.8 % 2.8e+00 s Elapsed time so far: 4.8 s
55.9 % 2.8e+00 s Elapsed time so far: 4.8 s
56.0 % 2.8e+00 s Elapsed time so far: 4.8 s
56.1 % 2.8e+00 s Elapsed time so far: 4.8 s
56.2 % 2.8e+00 s Elapsed time so far: 4.8 s
56.3 % 2.8e+00 s Elapsed time so far: 4.9 s
56.4 % 2.8e+00 s Elapsed time so far: 4.9 s
56.5 % 2.8e+00 s Elapsed time so far: 4.9 s
56.6 % 2.8e+00 s Elapsed time so far: 4.9 s
56.7 % 2.8e+00 s Elapsed time so far: 4.9 s
56.8 % 2.8e+00 s Elapsed time so far: 4.9 s
56.9 % 2.8e+00 s Elapsed time so far: 4.9 s
57.0 % 2.8e+00 s Elapsed time so far: 4.9 s
57.1 % 2.9e+00 s Elapsed time so far: 4.9 s
57.2 % 2.9e+00 s Elapsed time so far: 4.9 s
57.3 % 2.9e+00 s Elapsed time so far: 4.9 s
57.4 % 2.9e+00 s Elapsed time so far: 4.9 s
57.5 % 2.9e+00 s Elapsed time so far: 4.9 s
57.6 % 2.9e+00 s Elapsed time so far: 4.9 s
57.7 % 2.9e+00 s Elapsed time so far: 4.9 s
57.8 % 2.9e+00 s Elapsed time so far: 5.0 s
57.9 % 2.9e+00 s Elapsed time so far: 5.0 s
58.0 % 2.9e+00 s Elapsed time so far: 5.0 s
58.1 % 2.9e+00 s Elapsed time so far: 5.0 s
58.2 % 2.9e+00 s Elapsed time so far: 5.0 s
58.3 % 2.9e+00 s Elapsed time so far: 5.0 s
58.4 % 2.9e+00 s Elapsed time so far: 5.0 s
58.5 % 2.9e+00 s Elapsed time so far: 5.0 s
58.6 % 2.9e+00 s Elapsed time so far: 5.0 s
58.7 % 2.9e+00 s Elapsed time so far: 5.0 s
58.8 % 2.9e+00 s Elapsed time so far: 5.0 s
58.9 % 2.9e+00 s Elapsed time so far: 5.0 s
59.0 % 2.9e+00 s Elapsed time so far: 5.0 s
59.1 % 3.0e+00 s Elapsed time so far: 5.0 s
59.2 % 3.0e+00 s Elapsed time so far: 5.0 s
59.3 % 3.0e+00 s Elapsed time so far: 5.1 s
59.4 % 3.0e+00 s Elapsed time so far: 5.1 s
59.5 % 3.0e+00 s Elapsed time so far: 5.1 s
59.6 % 3.0e+00 s Elapsed time so far: 5.1 s
59.7 % 3.0e+00 s Elapsed time so far: 5.1 s
59.8 % 3.0e+00 s Elapsed time so far: 5.1 s
59.9 % 3.0e+00 s Elapsed time so far: 5.1 s
60.0 % 3.0e+00 s Elapsed time so far: 5.1 s
60.1 % 3.0e+00 s Elapsed time so far: 5.1 s
60.2 % 3.0e+00 s Elapsed time so far: 5.1 s
60.3 % 3.0e+00 s Elapsed time so far: 5.1 s
60.4 % 3.0e+00 s Elapsed time so far: 5.1 s
60.5 % 3.0e+00 s Elapsed time so far: 5.1 s
60.6 % 3.0e+00 s Elapsed time so far: 5.1 s
60.7 % 3.0e+00 s Elapsed time so far: 5.2 s
60.8 % 3.0e+00 s Elapsed time so far: 5.2 s
60.9 % 3.0e+00 s Elapsed time so far: 5.2 s
61.0 % 3.0e+00 s Elapsed time so far: 5.2 s
61.1 % 3.1e+00 s Elapsed time so far: 5.2 s
61.2 % 3.1e+00 s Elapsed time so far: 5.2 s
61.3 % 3.1e+00 s Elapsed time so far: 5.2 s
61.4 % 3.1e+00 s Elapsed time so far: 5.2 s
61.5 % 3.1e+00 s Elapsed time so far: 5.2 s
61.6 % 3.1e+00 s Elapsed time so far: 5.2 s
61.7 % 3.1e+00 s Elapsed time so far: 5.2 s
61.8 % 3.1e+00 s Elapsed time so far: 5.2 s
61.9 % 3.1e+00 s Elapsed time so far: 5.2 s
62.0 % 3.1e+00 s Elapsed time so far: 5.2 s
62.1 % 3.1e+00 s Elapsed time so far: 5.2 s
62.2 % 3.1e+00 s Elapsed time so far: 5.2 s
62.3 % 3.1e+00 s Elapsed time so far: 5.2 s
62.4 % 3.1e+00 s Elapsed time so far: 5.3 s
62.5 % 3.1e+00 s Elapsed time so far: 5.3 s
62.6 % 3.1e+00 s Elapsed time so far: 5.3 s
62.7 % 3.1e+00 s Elapsed time so far: 5.3 s
62.8 % 3.1e+00 s Elapsed time so far: 5.3 s
62.9 % 3.1e+00 s Elapsed time so far: 5.3 s
63.0 % 3.1e+00 s Elapsed time so far: 5.3 s
63.1 % 3.2e+00 s Elapsed time so far: 5.3 s
63.2 % 3.2e+00 s Elapsed time so far: 5.3 s
63.3 % 3.2e+00 s Elapsed time so far: 5.3 s
63.4 % 3.2e+00 s Elapsed time so far: 5.3 s
63.5 % 3.2e+00 s Elapsed time so far: 5.3 s
63.6 % 3.2e+00 s Elapsed time so far: 5.3 s
63.7 % 3.2e+00 s Elapsed time so far: 5.4 s
63.8 % 3.2e+00 s Elapsed time so far: 5.4 s
63.9 % 3.2e+00 s Elapsed time so far: 5.4 s
64.0 % 3.2e+00 s Elapsed time so far: 5.4 s
64.1 % 3.2e+00 s Elapsed time so far: 5.4 s
64.2 % 3.2e+00 s Elapsed time so far: 5.4 s
64.3 % 3.2e+00 s Elapsed time so far: 5.4 s
64.4 % 3.2e+00 s Elapsed time so far: 5.4 s
64.5 % 3.2e+00 s Elapsed time so far: 5.4 s
64.6 % 3.2e+00 s Elapsed time so far: 5.4 s
64.7 % 3.2e+00 s Elapsed time so far: 5.4 s
64.8 % 3.2e+00 s Elapsed time so far: 5.4 s
64.9 % 3.2e+00 s Elapsed time so far: 5.4 s
65.0 % 3.2e+00 s Elapsed time so far: 5.4 s
65.1 % 3.3e+00 s Elapsed time so far: 5.4 s
65.2 % 3.3e+00 s Elapsed time so far: 5.5 s
65.3 % 3.3e+00 s Elapsed time so far: 5.5 s
65.4 % 3.3e+00 s Elapsed time so far: 5.5 s
65.5 % 3.3e+00 s Elapsed time so far: 5.5 s
65.6 % 3.3e+00 s Elapsed time so far: 5.5 s
65.7 % 3.3e+00 s Elapsed time so far: 5.5 s
65.8 % 3.3e+00 s Elapsed time so far: 5.5 s
65.9 % 3.3e+00 s Elapsed time so far: 5.5 s
66.0 % 3.3e+00 s Elapsed time so far: 5.5 s
66.1 % 3.3e+00 s Elapsed time so far: 5.5 s
66.2 % 3.3e+00 s Elapsed time so far: 5.5 s
66.3 % 3.3e+00 s Elapsed time so far: 5.5 s
66.4 % 3.3e+00 s Elapsed time so far: 5.5 s
66.5 % 3.3e+00 s Elapsed time so far: 5.5 s
66.6 % 3.3e+00 s Elapsed time so far: 5.5 s
66.7 % 3.3e+00 s Elapsed time so far: 5.6 s
66.8 % 3.3e+00 s Elapsed time so far: 5.6 s
66.9 % 3.3e+00 s Elapsed time so far: 5.6 s
67.0 % 3.3e+00 s Elapsed time so far: 5.6 s
67.1 % 3.4e+00 s Elapsed time so far: 5.6 s
67.2 % 3.4e+00 s Elapsed time so far: 5.6 s
67.3 % 3.4e+00 s Elapsed time so far: 5.6 s
67.4 % 3.4e+00 s Elapsed time so far: 5.6 s
67.5 % 3.4e+00 s Elapsed time so far: 5.6 s
67.6 % 3.4e+00 s Elapsed time so far: 5.6 s
67.7 % 3.4e+00 s Elapsed time so far: 5.6 s
67.8 % 3.4e+00 s Elapsed time so far: 5.6 s
67.9 % 3.4e+00 s Elapsed time so far: 5.6 s
68.0 % 3.4e+00 s Elapsed time so far: 5.6 s
68.1 % 3.4e+00 s Elapsed time so far: 5.6 s
68.2 % 3.4e+00 s Elapsed time so far: 5.7 s
68.3 % 3.4e+00 s Elapsed time so far: 5.7 s
68.4 % 3.4e+00 s Elapsed time so far: 5.7 s
68.5 % 3.4e+00 s Elapsed time so far: 5.7 s
68.6 % 3.4e+00 s Elapsed time so far: 5.7 s
68.7 % 3.4e+00 s Elapsed time so far: 5.7 s
68.8 % 3.4e+00 s Elapsed time so far: 5.7 s
68.9 % 3.4e+00 s Elapsed time so far: 5.7 s
69.0 % 3.4e+00 s Elapsed time so far: 5.7 s
69.1 % 3.5e+00 s Elapsed time so far: 5.7 s
69.2 % 3.5e+00 s Elapsed time so far: 5.7 s
69.3 % 3.5e+00 s Elapsed time so far: 5.7 s
69.4 % 3.5e+00 s Elapsed time so far: 5.7 s
69.5 % 3.5e+00 s Elapsed time so far: 5.7 s
69.6 % 3.5e+00 s Elapsed time so far: 5.7 s
69.7 % 3.5e+00 s Elapsed time so far: 5.8 s
69.8 % 3.5e+00 s Elapsed time so far: 5.8 s
69.9 % 3.5e+00 s Elapsed time so far: 5.8 s
70.0 % 3.5e+00 s Elapsed time so far: 5.8 s
70.1 % 3.5e+00 s Elapsed time so far: 5.8 s
70.2 % 3.5e+00 s Elapsed time so far: 5.8 s
70.3 % 3.5e+00 s Elapsed time so far: 5.8 s
70.4 % 3.5e+00 s Elapsed time so far: 5.8 s
70.5 % 3.5e+00 s Elapsed time so far: 5.8 s
70.6 % 3.5e+00 s Elapsed time so far: 5.8 s
70.7 % 3.5e+00 s Elapsed time so far: 5.8 s
70.8 % 3.5e+00 s Elapsed time so far: 5.8 s
70.9 % 3.5e+00 s Elapsed time so far: 5.8 s
71.0 % 3.5e+00 s Elapsed time so far: 5.8 s
71.1 % 3.6e+00 s Elapsed time so far: 5.9 s
71.2 % 3.6e+00 s Elapsed time so far: 5.9 s
71.3 % 3.6e+00 s Elapsed time so far: 5.9 s
71.4 % 3.6e+00 s Elapsed time so far: 5.9 s
71.5 % 3.6e+00 s Elapsed time so far: 5.9 s
71.6 % 3.6e+00 s Elapsed time so far: 5.9 s
71.7 % 3.6e+00 s Elapsed time so far: 5.9 s
71.8 % 3.6e+00 s Elapsed time so far: 5.9 s
71.9 % 3.6e+00 s Elapsed time so far: 5.9 s
72.0 % 3.6e+00 s Elapsed time so far: 5.9 s
72.1 % 3.6e+00 s Elapsed time so far: 5.9 s
72.2 % 3.6e+00 s Elapsed time so far: 5.9 s
72.3 % 3.6e+00 s Elapsed time so far: 5.9 s
72.4 % 3.6e+00 s Elapsed time so far: 5.9 s
72.5 % 3.6e+00 s Elapsed time so far: 5.9 s
72.6 % 3.6e+00 s Elapsed time so far: 6.0 s
72.7 % 3.6e+00 s Elapsed time so far: 6.0 s
72.8 % 3.6e+00 s Elapsed time so far: 6.0 s
72.9 % 3.6e+00 s Elapsed time so far: 6.0 s
73.0 % 3.6e+00 s Elapsed time so far: 6.0 s
73.1 % 3.7e+00 s Elapsed time so far: 6.0 s
73.2 % 3.7e+00 s Elapsed time so far: 6.0 s
73.3 % 3.7e+00 s Elapsed time so far: 6.0 s
73.4 % 3.7e+00 s Elapsed time so far: 6.0 s
73.5 % 3.7e+00 s Elapsed time so far: 6.0 s
73.6 % 3.7e+00 s Elapsed time so far: 6.0 s
73.7 % 3.7e+00 s Elapsed time so far: 6.0 s
73.8 % 3.7e+00 s Elapsed time so far: 6.0 s
73.9 % 3.7e+00 s Elapsed time so far: 6.0 s
74.0 % 3.7e+00 s Elapsed time so far: 6.1 s
74.1 % 3.7e+00 s Elapsed time so far: 6.1 s
74.2 % 3.7e+00 s Elapsed time so far: 6.1 s
74.3 % 3.7e+00 s Elapsed time so far: 6.1 s
74.4 % 3.7e+00 s Elapsed time so far: 6.1 s
74.5 % 3.7e+00 s Elapsed time so far: 6.1 s
74.6 % 3.7e+00 s Elapsed time so far: 6.1 s
74.7 % 3.7e+00 s Elapsed time so far: 6.1 s
74.8 % 3.7e+00 s Elapsed time so far: 6.1 s
74.9 % 3.7e+00 s Elapsed time so far: 6.1 s
75.0 % 3.7e+00 s Elapsed time so far: 6.1 s
75.1 % 3.8e+00 s Elapsed time so far: 6.1 s
75.2 % 3.8e+00 s Elapsed time so far: 6.1 s
75.3 % 3.8e+00 s Elapsed time so far: 6.1 s
75.4 % 3.8e+00 s Elapsed time so far: 6.1 s
75.5 % 3.8e+00 s Elapsed time so far: 6.2 s
75.6 % 3.8e+00 s Elapsed time so far: 6.2 s
75.7 % 3.8e+00 s Elapsed time so far: 6.2 s
75.8 % 3.8e+00 s Elapsed time so far: 6.2 s
75.9 % 3.8e+00 s Elapsed time so far: 6.2 s
76.0 % 3.8e+00 s Elapsed time so far: 6.2 s
76.1 % 3.8e+00 s Elapsed time so far: 6.2 s
76.2 % 3.8e+00 s Elapsed time so far: 6.2 s
76.3 % 3.8e+00 s Elapsed time so far: 6.2 s
76.4 % 3.8e+00 s Elapsed time so far: 6.2 s
76.5 % 3.8e+00 s Elapsed time so far: 6.2 s
76.6 % 3.8e+00 s Elapsed time so far: 6.2 s
76.7 % 3.8e+00 s Elapsed time so far: 6.2 s
76.8 % 3.8e+00 s Elapsed time so far: 6.2 s
76.9 % 3.8e+00 s Elapsed time so far: 6.2 s
77.0 % 3.8e+00 s Elapsed time so far: 6.2 s
77.1 % 3.9e+00 s Elapsed time so far: 6.2 s
77.2 % 3.9e+00 s Elapsed time so far: 6.3 s
77.3 % 3.9e+00 s Elapsed time so far: 6.3 s
77.4 % 3.9e+00 s Elapsed time so far: 6.3 s
77.5 % 3.9e+00 s Elapsed time so far: 6.3 s
77.6 % 3.9e+00 s Elapsed time so far: 6.3 s
77.7 % 3.9e+00 s Elapsed time so far: 6.3 s
77.8 % 3.9e+00 s Elapsed time so far: 6.3 s
77.9 % 3.9e+00 s Elapsed time so far: 6.3 s
78.0 % 3.9e+00 s Elapsed time so far: 6.3 s
78.1 % 3.9e+00 s Elapsed time so far: 6.3 s
78.2 % 3.9e+00 s Elapsed time so far: 6.3 s
78.3 % 3.9e+00 s Elapsed time so far: 6.3 s
78.4 % 3.9e+00 s Elapsed time so far: 6.3 s
78.5 % 3.9e+00 s Elapsed time so far: 6.4 s
78.6 % 3.9e+00 s Elapsed time so far: 6.4 s
78.7 % 3.9e+00 s Elapsed time so far: 6.4 s
78.8 % 3.9e+00 s Elapsed time so far: 6.4 s
78.9 % 3.9e+00 s Elapsed time so far: 6.4 s
79.0 % 3.9e+00 s Elapsed time so far: 6.4 s
79.1 % 4.0e+00 s Elapsed time so far: 6.4 s
79.2 % 4.0e+00 s Elapsed time so far: 6.4 s
79.3 % 4.0e+00 s Elapsed time so far: 6.4 s
79.4 % 4.0e+00 s Elapsed time so far: 6.4 s
79.5 % 4.0e+00 s Elapsed time so far: 6.4 s
79.6 % 4.0e+00 s Elapsed time so far: 6.4 s
79.7 % 4.0e+00 s Elapsed time so far: 6.4 s
79.8 % 4.0e+00 s Elapsed time so far: 6.4 s
79.9 % 4.0e+00 s Elapsed time so far: 6.4 s
80.0 % 4.0e+00 s Elapsed time so far: 6.5 s
80.1 % 4.0e+00 s Elapsed time so far: 6.5 s
80.2 % 4.0e+00 s Elapsed time so far: 6.5 s
80.3 % 4.0e+00 s Elapsed time so far: 6.5 s
80.4 % 4.0e+00 s Elapsed time so far: 6.5 s
80.5 % 4.0e+00 s Elapsed time so far: 6.5 s
80.6 % 4.0e+00 s Elapsed time so far: 6.5 s
80.7 % 4.0e+00 s Elapsed time so far: 6.5 s
80.8 % 4.0e+00 s Elapsed time so far: 6.5 s
80.9 % 4.0e+00 s Elapsed time so far: 6.5 s
81.0 % 4.0e+00 s Elapsed time so far: 6.5 s
81.1 % 4.1e+00 s Elapsed time so far: 6.5 s
81.2 % 4.1e+00 s Elapsed time so far: 6.5 s
81.3 % 4.1e+00 s Elapsed time so far: 6.5 s
81.4 % 4.1e+00 s Elapsed time so far: 6.6 s
81.5 % 4.1e+00 s Elapsed time so far: 6.6 s
81.6 % 4.1e+00 s Elapsed time so far: 6.6 s
81.7 % 4.1e+00 s Elapsed time so far: 6.6 s
81.8 % 4.1e+00 s Elapsed time so far: 6.6 s
81.9 % 4.1e+00 s Elapsed time so far: 6.6 s
82.0 % 4.1e+00 s Elapsed time so far: 6.6 s
82.1 % 4.1e+00 s Elapsed time so far: 6.6 s
82.2 % 4.1e+00 s Elapsed time so far: 6.6 s
82.3 % 4.1e+00 s Elapsed time so far: 6.6 s
82.4 % 4.1e+00 s Elapsed time so far: 6.6 s
82.5 % 4.1e+00 s Elapsed time so far: 6.6 s
82.6 % 4.1e+00 s Elapsed time so far: 6.6 s
82.7 % 4.1e+00 s Elapsed time so far: 6.6 s
82.8 % 4.1e+00 s Elapsed time so far: 6.6 s
82.9 % 4.1e+00 s Elapsed time so far: 6.6 s
83.0 % 4.1e+00 s Elapsed time so far: 6.7 s
83.1 % 4.2e+00 s Elapsed time so far: 6.7 s
83.2 % 4.2e+00 s Elapsed time so far: 6.7 s
83.3 % 4.2e+00 s Elapsed time so far: 6.7 s
83.4 % 4.2e+00 s Elapsed time so far: 6.7 s
83.5 % 4.2e+00 s Elapsed time so far: 6.7 s
83.6 % 4.2e+00 s Elapsed time so far: 6.7 s
83.7 % 4.2e+00 s Elapsed time so far: 6.7 s
83.8 % 4.2e+00 s Elapsed time so far: 6.7 s
83.9 % 4.2e+00 s Elapsed time so far: 6.7 s
84.0 % 4.2e+00 s Elapsed time so far: 6.7 s
84.1 % 4.2e+00 s Elapsed time so far: 6.7 s
84.2 % 4.2e+00 s Elapsed time so far: 6.7 s
84.3 % 4.2e+00 s Elapsed time so far: 6.7 s
84.4 % 4.2e+00 s Elapsed time so far: 6.8 s
84.5 % 4.2e+00 s Elapsed time so far: 6.8 s
84.6 % 4.2e+00 s Elapsed time so far: 6.8 s
84.7 % 4.2e+00 s Elapsed time so far: 6.8 s
84.8 % 4.2e+00 s Elapsed time so far: 6.8 s
84.9 % 4.2e+00 s Elapsed time so far: 6.8 s
85.0 % 4.2e+00 s Elapsed time so far: 6.8 s
85.1 % 4.3e+00 s Elapsed time so far: 6.8 s
85.2 % 4.3e+00 s Elapsed time so far: 6.8 s
85.3 % 4.3e+00 s Elapsed time so far: 6.8 s
85.4 % 4.3e+00 s Elapsed time so far: 6.8 s
85.5 % 4.3e+00 s Elapsed time so far: 6.8 s
85.6 % 4.3e+00 s Elapsed time so far: 6.8 s
85.7 % 4.3e+00 s Elapsed time so far: 6.8 s
85.8 % 4.3e+00 s Elapsed time so far: 6.8 s
85.9 % 4.3e+00 s Elapsed time so far: 6.8 s
86.0 % 4.3e+00 s Elapsed time so far: 6.9 s
86.1 % 4.3e+00 s Elapsed time so far: 6.9 s
86.2 % 4.3e+00 s Elapsed time so far: 6.9 s
86.3 % 4.3e+00 s Elapsed time so far: 6.9 s
86.4 % 4.3e+00 s Elapsed time so far: 6.9 s
86.5 % 4.3e+00 s Elapsed time so far: 6.9 s
86.6 % 4.3e+00 s Elapsed time so far: 6.9 s
86.7 % 4.3e+00 s Elapsed time so far: 6.9 s
86.8 % 4.3e+00 s Elapsed time so far: 6.9 s
86.9 % 4.3e+00 s Elapsed time so far: 6.9 s
87.0 % 4.3e+00 s Elapsed time so far: 6.9 s
87.1 % 4.4e+00 s Elapsed time so far: 6.9 s
87.2 % 4.4e+00 s Elapsed time so far: 6.9 s
87.3 % 4.4e+00 s Elapsed time so far: 6.9 s
87.4 % 4.4e+00 s Elapsed time so far: 6.9 s
87.5 % 4.4e+00 s Elapsed time so far: 7.0 s
87.6 % 4.4e+00 s Elapsed time so far: 7.0 s
87.7 % 4.4e+00 s Elapsed time so far: 7.0 s
87.8 % 4.4e+00 s Elapsed time so far: 7.0 s
87.9 % 4.4e+00 s Elapsed time so far: 7.0 s
88.0 % 4.4e+00 s Elapsed time so far: 7.0 s
88.1 % 4.4e+00 s Elapsed time so far: 7.0 s
88.2 % 4.4e+00 s Elapsed time so far: 7.0 s
88.3 % 4.4e+00 s Elapsed time so far: 7.0 s
88.4 % 4.4e+00 s Elapsed time so far: 7.0 s
88.5 % 4.4e+00 s Elapsed time so far: 7.0 s
88.6 % 4.4e+00 s Elapsed time so far: 7.0 s
88.7 % 4.4e+00 s Elapsed time so far: 7.0 s
88.8 % 4.4e+00 s Elapsed time so far: 7.0 s
88.9 % 4.4e+00 s Elapsed time so far: 7.0 s
89.0 % 4.4e+00 s Elapsed time so far: 7.1 s
89.1 % 4.5e+00 s Elapsed time so far: 7.1 s
89.2 % 4.5e+00 s Elapsed time so far: 7.1 s
89.3 % 4.5e+00 s Elapsed time so far: 7.1 s
89.4 % 4.5e+00 s Elapsed time so far: 7.1 s
89.5 % 4.5e+00 s Elapsed time so far: 7.1 s
89.6 % 4.5e+00 s Elapsed time so far: 7.1 s
89.7 % 4.5e+00 s Elapsed time so far: 7.1 s
89.8 % 4.5e+00 s Elapsed time so far: 7.1 s
89.9 % 4.5e+00 s Elapsed time so far: 7.1 s
90.0 % 4.5e+00 s Elapsed time so far: 7.1 s
90.1 % 4.5e+00 s Elapsed time so far: 7.1 s
90.2 % 4.5e+00 s Elapsed time so far: 7.1 s
90.3 % 4.5e+00 s Elapsed time so far: 7.1 s
90.4 % 4.5e+00 s Elapsed time so far: 7.1 s
90.5 % 4.5e+00 s Elapsed time so far: 7.2 s
90.6 % 4.5e+00 s Elapsed time so far: 7.2 s
90.7 % 4.5e+00 s Elapsed time so far: 7.2 s
90.8 % 4.5e+00 s Elapsed time so far: 7.2 s
90.9 % 4.5e+00 s Elapsed time so far: 7.2 s
91.0 % 4.5e+00 s Elapsed time so far: 7.2 s
91.1 % 4.6e+00 s Elapsed time so far: 7.2 s
91.2 % 4.6e+00 s Elapsed time so far: 7.2 s
91.3 % 4.6e+00 s Elapsed time so far: 7.2 s
91.4 % 4.6e+00 s Elapsed time so far: 7.2 s
91.5 % 4.6e+00 s Elapsed time so far: 7.2 s
91.6 % 4.6e+00 s Elapsed time so far: 7.2 s
91.7 % 4.6e+00 s Elapsed time so far: 7.2 s
91.8 % 4.6e+00 s Elapsed time so far: 7.2 s
91.9 % 4.6e+00 s Elapsed time so far: 7.2 s
92.0 % 4.6e+00 s Elapsed time so far: 7.3 s
92.1 % 4.6e+00 s Elapsed time so far: 7.3 s
92.2 % 4.6e+00 s Elapsed time so far: 7.3 s
92.3 % 4.6e+00 s Elapsed time so far: 7.3 s
92.4 % 4.6e+00 s Elapsed time so far: 7.3 s
92.5 % 4.6e+00 s Elapsed time so far: 7.3 s
92.6 % 4.6e+00 s Elapsed time so far: 7.3 s
92.7 % 4.6e+00 s Elapsed time so far: 7.3 s
92.8 % 4.6e+00 s Elapsed time so far: 7.3 s
92.9 % 4.6e+00 s Elapsed time so far: 7.3 s
93.0 % 4.6e+00 s Elapsed time so far: 7.3 s
93.1 % 4.7e+00 s Elapsed time so far: 7.3 s
93.2 % 4.7e+00 s Elapsed time so far: 7.3 s
93.3 % 4.7e+00 s Elapsed time so far: 7.3 s
93.4 % 4.7e+00 s Elapsed time so far: 7.4 s
93.5 % 4.7e+00 s Elapsed time so far: 7.4 s
93.6 % 4.7e+00 s Elapsed time so far: 7.4 s
93.7 % 4.7e+00 s Elapsed time so far: 7.4 s
93.8 % 4.7e+00 s Elapsed time so far: 7.4 s
93.9 % 4.7e+00 s Elapsed time so far: 7.4 s
94.0 % 4.7e+00 s Elapsed time so far: 7.4 s
94.1 % 4.7e+00 s Elapsed time so far: 7.4 s
94.2 % 4.7e+00 s Elapsed time so far: 7.4 s
94.3 % 4.7e+00 s Elapsed time so far: 7.4 s
94.4 % 4.7e+00 s Elapsed time so far: 7.4 s
94.5 % 4.7e+00 s Elapsed time so far: 7.4 s
94.6 % 4.7e+00 s Elapsed time so far: 7.4 s
94.7 % 4.7e+00 s Elapsed time so far: 7.4 s
94.8 % 4.7e+00 s Elapsed time so far: 7.4 s
94.9 % 4.7e+00 s Elapsed time so far: 7.5 s
95.0 % 4.7e+00 s Elapsed time so far: 7.5 s
95.1 % 4.8e+00 s Elapsed time so far: 7.5 s
95.2 % 4.8e+00 s Elapsed time so far: 7.5 s
95.3 % 4.8e+00 s Elapsed time so far: 7.5 s
95.4 % 4.8e+00 s Elapsed time so far: 7.5 s
95.5 % 4.8e+00 s Elapsed time so far: 7.5 s
95.6 % 4.8e+00 s Elapsed time so far: 7.5 s
95.7 % 4.8e+00 s Elapsed time so far: 7.5 s
95.8 % 4.8e+00 s Elapsed time so far: 7.5 s
95.9 % 4.8e+00 s Elapsed time so far: 7.5 s
96.0 % 4.8e+00 s Elapsed time so far: 7.5 s
96.1 % 4.8e+00 s Elapsed time so far: 7.5 s
96.2 % 4.8e+00 s Elapsed time so far: 7.5 s
96.3 % 4.8e+00 s Elapsed time so far: 7.5 s
96.4 % 4.8e+00 s Elapsed time so far: 7.6 s
96.5 % 4.8e+00 s Elapsed time so far: 7.6 s
96.6 % 4.8e+00 s Elapsed time so far: 7.6 s
96.7 % 4.8e+00 s Elapsed time so far: 7.6 s
96.8 % 4.8e+00 s Elapsed time so far: 7.6 s
96.9 % 4.8e+00 s Elapsed time so far: 7.6 s
97.0 % 4.8e+00 s Elapsed time so far: 7.6 s
97.1 % 4.9e+00 s Elapsed time so far: 7.6 s
97.2 % 4.9e+00 s Elapsed time so far: 7.6 s
97.3 % 4.9e+00 s Elapsed time so far: 7.6 s
97.4 % 4.9e+00 s Elapsed time so far: 7.6 s
97.5 % 4.9e+00 s Elapsed time so far: 7.6 s
97.6 % 4.9e+00 s Elapsed time so far: 7.6 s
97.7 % 4.9e+00 s Elapsed time so far: 7.6 s
97.8 % 4.9e+00 s Elapsed time so far: 7.6 s
97.9 % 4.9e+00 s Elapsed time so far: 7.7 s
98.0 % 4.9e+00 s Elapsed time so far: 7.7 s
98.1 % 4.9e+00 s Elapsed time so far: 7.7 s
98.2 % 4.9e+00 s Elapsed time so far: 7.7 s
98.3 % 4.9e+00 s Elapsed time so far: 7.7 s
98.4 % 4.9e+00 s Elapsed time so far: 7.7 s
98.5 % 4.9e+00 s Elapsed time so far: 7.7 s
98.6 % 4.9e+00 s Elapsed time so far: 7.7 s
98.7 % 4.9e+00 s Elapsed time so far: 7.7 s
98.8 % 4.9e+00 s Elapsed time so far: 7.7 s
98.9 % 4.9e+00 s Elapsed time so far: 7.7 s
99.0 % 4.9e+00 s Elapsed time so far: 7.7 s
99.1 % 5.0e+00 s Elapsed time so far: 7.7 s
99.2 % 5.0e+00 s Elapsed time so far: 7.7 s
99.3 % 5.0e+00 s Elapsed time so far: 7.8 s
99.4 % 5.0e+00 s Elapsed time so far: 7.8 s
99.5 % 5.0e+00 s Elapsed time so far: 7.8 s
99.6 % 5.0e+00 s Elapsed time so far: 7.8 s
99.7 % 5.0e+00 s Elapsed time so far: 7.8 s
99.8 % 5.0e+00 s Elapsed time so far: 7.8 s
99.9 % 5.0e+00 s Elapsed time so far: 7.8 s
100.0 % 5.0e+00 s Elapsed time so far: 7.8 s
Mobile H#
Show code cell source
plot_times = [1, 3, 5]
for t in plot_times:
x = solute_data["x"]
y = solute_data[f"t{t:.2e}s".replace(".", "").replace("+", "")]
# order y by x
x, y = zip(*sorted(zip(x, y)))
(l1,) = plt.plot(
x,
exact_solution_cm(np.array(x), t),
label=f"exact t = {t}",
)
plt.scatter(
x[::100],
y[::100],
label=f"t = {t}",
color=l1.get_color(),
alpha=0.6,
)
print(
f"L2 error for mobile H at t = {t}: {norm(np.array(x), np.array(y), exact_solution_cm(x=np.array(x), t=t))}"
)
plt.legend(reverse=True, ncols=3, loc=9, frameon=False)
plt.ylabel("$c_m$")
plt.xlabel("$x$")
plt.ylim(2, 16)
plt.show()
L2 error for mobile H at t = 1: 6.6901461844272124e-06
L2 error for mobile H at t = 3: 1.1040758395056417e-05
L2 error for mobile H at t = 5: 1.59299833608968e-05
Adsorbed H#
Show code cell source
c_s_computed = adsorbed_data[0].data
t = adsorbed_data[0].t
print(
f"L2 error for adsorbed H: {norm(t, c_s_computed, exact_solution_cs(t=np.array(t)))}"
)
plt.figure()
plt.scatter(t[::50], c_s_computed[::50], label="computed", alpha=0.6)
plt.plot(t, exact_solution_cs(np.array(t)), label="exact")
plt.ylabel("$c_s$")
plt.xlabel("$t$")
plt.legend()
plt.ylim(-0.05, 1.8)
plt.show()
L2 error for adsorbed H: 4.285475874092749e-05
