Radioactive decay 1D#
This example is a radioactive decay (RadioactiveDecay) problem on simple unit interval with a uniform mobile concentration and no boundary condition.
In this problem, for simplicity, we don’t set any traps and we model an isolated domain (no flux boundary conditions) to mimick a simple 0D case. Diffusion can therefore be neglected and the problem is:
(20)#\[\begin{split}
\begin{align}
\frac{\partial c}{\partial t} = - \lambda \ c & \quad \text{on } \Omega \\
\end{align}
\end{split}\]
The exact solution for mobile concentration is:
(21)#\[
\begin{equation}
c_\mathrm{exact} = c_0 e^{-\lambda t}
\end{equation}
\]
Here, \(c_0\) is the initial concentration and \(\lambda\) is the decay constant (in \(s^{-1}\)). We can then run a FESTIM model with these conditions and compare the numerical solution with \(c_\mathrm{exact}\).
We can then run a FESTIM model with these conditions and compare the numerical solution with \(c_\mathrm{exact}\).
FESTIM Code#
Show code cell content
import festim as F
import numpy as np
import matplotlib.pyplot as plt
initial_concentration = 3
def run_model(half_life):
my_model = F.Simulation()
my_model.initial_conditions = [
F.InitialCondition(value=initial_concentration, field="solute")
]
my_model.dt = F.Stepsize(
initial_value=0.05,
stepsize_change_ratio=1.01,
dt_min=1e-05,
)
my_model.materials = F.Material(id=1, D_0=1, E_D=0)
my_model.T = F.Temperature(value=300)
my_model.boundary_conditions = [] # no BCs to have 0D case
my_model.mesh = F.MeshFromVertices(np.linspace(0, 1, 1001))
my_model.sources = [
F.RadioactiveDecay(decay_constant=np.log(2) / half_life, volume=1)
]
derived_quantities = F.DerivedQuantities([F.AverageVolume("solute", volume=1)])
my_model.exports = [derived_quantities]
my_model.settings = F.Settings(
absolute_tolerance=1e-10,
relative_tolerance=1e-10,
final_time=5 * half_life, # s
)
my_model.initialise()
my_model.run()
time = derived_quantities.t
concentration = derived_quantities[0].data
return time, concentration
tests = []
for half_life in np.linspace(1, 100, 5):
tests.append((*run_model(half_life), half_life))
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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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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41.5 % 5.3e+01 s Elapsed time so far: 3.0 s
41.9 % 5.4e+01 s Elapsed time so far: 3.0 s
42.4 % 5.5e+01 s Elapsed time so far: 3.0 s
42.8 % 5.5e+01 s Elapsed time so far: 3.0 s
43.3 % 5.6e+01 s Elapsed time so far: 3.0 s
43.8 % 5.6e+01 s Elapsed time so far: 3.1 s
44.3 % 5.7e+01 s Elapsed time so far: 3.1 s
44.7 % 5.8e+01 s Elapsed time so far: 3.1 s
45.2 % 5.8e+01 s Elapsed time so far: 3.1 s
45.7 % 5.9e+01 s Elapsed time so far: 3.1 s
46.2 % 6.0e+01 s Elapsed time so far: 3.1 s
46.7 % 6.0e+01 s Elapsed time so far: 3.1 s
47.2 % 6.1e+01 s Elapsed time so far: 3.1 s
47.7 % 6.1e+01 s Elapsed time so far: 3.1 s
48.2 % 6.2e+01 s Elapsed time so far: 3.1 s
48.8 % 6.3e+01 s Elapsed time so far: 3.1 s
49.3 % 6.3e+01 s Elapsed time so far: 3.1 s
49.8 % 6.4e+01 s Elapsed time so far: 3.1 s
50.4 % 6.5e+01 s Elapsed time so far: 3.1 s
50.9 % 6.6e+01 s Elapsed time so far: 3.1 s
51.5 % 6.6e+01 s Elapsed time so far: 3.2 s
52.0 % 6.7e+01 s Elapsed time so far: 3.2 s
52.6 % 6.8e+01 s Elapsed time so far: 3.2 s
53.1 % 6.8e+01 s Elapsed time so far: 3.2 s
53.7 % 6.9e+01 s Elapsed time so far: 3.2 s
54.3 % 7.0e+01 s Elapsed time so far: 3.2 s
54.9 % 7.1e+01 s Elapsed time so far: 3.2 s
55.5 % 7.1e+01 s Elapsed time so far: 3.2 s
56.0 % 7.2e+01 s Elapsed time so far: 3.2 s
56.6 % 7.3e+01 s Elapsed time so far: 3.2 s
57.2 % 7.4e+01 s Elapsed time so far: 3.2 s
57.9 % 7.4e+01 s Elapsed time so far: 3.2 s
58.5 % 7.5e+01 s Elapsed time so far: 3.2 s
59.1 % 7.6e+01 s Elapsed time so far: 3.2 s
59.7 % 7.7e+01 s Elapsed time so far: 3.2 s
60.4 % 7.8e+01 s Elapsed time so far: 3.2 s
61.0 % 7.9e+01 s Elapsed time so far: 3.3 s
61.6 % 7.9e+01 s Elapsed time so far: 3.3 s
62.3 % 8.0e+01 s Elapsed time so far: 3.3 s
63.0 % 8.1e+01 s Elapsed time so far: 3.3 s
63.6 % 8.2e+01 s Elapsed time so far: 3.3 s
64.3 % 8.3e+01 s Elapsed time so far: 3.3 s
65.0 % 8.4e+01 s Elapsed time so far: 3.3 s
65.7 % 8.5e+01 s Elapsed time so far: 3.3 s
66.4 % 8.5e+01 s Elapsed time so far: 3.3 s
67.1 % 8.6e+01 s Elapsed time so far: 3.3 s
67.8 % 8.7e+01 s Elapsed time so far: 3.3 s
68.5 % 8.8e+01 s Elapsed time so far: 3.3 s
69.2 % 8.9e+01 s Elapsed time so far: 3.3 s
70.0 % 9.0e+01 s Elapsed time so far: 3.3 s
70.7 % 9.1e+01 s Elapsed time so far: 3.4 s
71.5 % 9.2e+01 s Elapsed time so far: 3.4 s
72.2 % 9.3e+01 s Elapsed time so far: 3.4 s
73.0 % 9.4e+01 s Elapsed time so far: 3.4 s
73.7 % 9.5e+01 s Elapsed time so far: 3.4 s
74.5 % 9.6e+01 s Elapsed time so far: 3.4 s
75.3 % 9.7e+01 s Elapsed time so far: 3.4 s
76.1 % 9.8e+01 s Elapsed time so far: 3.4 s
76.9 % 9.9e+01 s Elapsed time so far: 3.4 s
77.7 % 1.0e+02 s Elapsed time so far: 3.4 s
78.5 % 1.0e+02 s Elapsed time so far: 3.4 s
79.3 % 1.0e+02 s Elapsed time so far: 3.4 s
80.2 % 1.0e+02 s Elapsed time so far: 3.4 s
81.0 % 1.0e+02 s Elapsed time so far: 3.4 s
81.8 % 1.1e+02 s Elapsed time so far: 3.4 s
82.7 % 1.1e+02 s Elapsed time so far: 3.5 s
83.6 % 1.1e+02 s Elapsed time so far: 3.5 s
84.5 % 1.1e+02 s Elapsed time so far: 3.5 s
85.3 % 1.1e+02 s Elapsed time so far: 3.5 s
86.2 % 1.1e+02 s Elapsed time so far: 3.5 s
87.1 % 1.1e+02 s Elapsed time so far: 3.5 s
88.0 % 1.1e+02 s Elapsed time so far: 3.5 s
89.0 % 1.1e+02 s Elapsed time so far: 3.5 s
89.9 % 1.2e+02 s Elapsed time so far: 3.5 s
90.8 % 1.2e+02 s Elapsed time so far: 3.5 s
91.8 % 1.2e+02 s Elapsed time so far: 3.5 s
92.7 % 1.2e+02 s Elapsed time so far: 3.5 s
93.7 % 1.2e+02 s Elapsed time so far: 3.5 s
94.7 % 1.2e+02 s Elapsed time so far: 3.5 s
95.7 % 1.2e+02 s Elapsed time so far: 3.5 s
96.7 % 1.2e+02 s Elapsed time so far: 3.6 s
97.7 % 1.3e+02 s Elapsed time so far: 3.6 s
98.7 % 1.3e+02 s Elapsed time so far: 3.6 s
99.7 % 1.3e+02 s Elapsed time so far: 3.6 s
100.0 % 1.3e+02 s Elapsed time so far: 3.6 s
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.
0.0 % 5.0e-02 s Elapsed time so far: 1.4 s
0.0 % 1.0e-01 s Elapsed time so far: 1.4 s
0.1 % 1.5e-01 s Elapsed time so far: 1.4 s
0.1 % 2.0e-01 s Elapsed time so far: 1.4 s
0.1 % 2.6e-01 s Elapsed time so far: 1.5 s
0.1 % 3.1e-01 s Elapsed time so far: 1.5 s
0.1 % 3.6e-01 s Elapsed time so far: 1.5 s
0.2 % 4.1e-01 s Elapsed time so far: 1.5 s
0.2 % 4.7e-01 s Elapsed time so far: 1.5 s
0.2 % 5.2e-01 s Elapsed time so far: 1.5 s
0.2 % 5.8e-01 s Elapsed time so far: 1.5 s
0.2 % 6.3e-01 s Elapsed time so far: 1.5 s
0.3 % 6.9e-01 s Elapsed time so far: 1.5 s
0.3 % 7.5e-01 s Elapsed time so far: 1.5 s
0.3 % 8.0e-01 s Elapsed time so far: 1.5 s
0.3 % 8.6e-01 s Elapsed time so far: 1.5 s
0.4 % 9.2e-01 s Elapsed time so far: 1.5 s
0.4 % 9.8e-01 s Elapsed time so far: 1.5 s
0.4 % 1.0e+00 s Elapsed time so far: 1.5 s
0.4 % 1.1e+00 s Elapsed time so far: 1.6 s
0.5 % 1.2e+00 s Elapsed time so far: 1.6 s
0.5 % 1.2e+00 s Elapsed time so far: 1.6 s
0.5 % 1.3e+00 s Elapsed time so far: 1.6 s
0.5 % 1.3e+00 s Elapsed time so far: 1.6 s
0.6 % 1.4e+00 s Elapsed time so far: 1.6 s
0.6 % 1.5e+00 s Elapsed time so far: 1.6 s
0.6 % 1.5e+00 s Elapsed time so far: 1.6 s
0.6 % 1.6e+00 s Elapsed time so far: 1.6 s
0.7 % 1.7e+00 s Elapsed time so far: 1.6 s
0.7 % 1.7e+00 s Elapsed time so far: 1.6 s
0.7 % 1.8e+00 s Elapsed time so far: 1.6 s
0.7 % 1.9e+00 s Elapsed time so far: 1.6 s
0.8 % 1.9e+00 s Elapsed time so far: 1.6 s
0.8 % 2.0e+00 s Elapsed time so far: 1.6 s
0.8 % 2.1e+00 s Elapsed time so far: 1.7 s
0.8 % 2.2e+00 s Elapsed time so far: 1.7 s
0.9 % 2.2e+00 s Elapsed time so far: 1.7 s
0.9 % 2.3e+00 s Elapsed time so far: 1.7 s
0.9 % 2.4e+00 s Elapsed time so far: 1.7 s
1.0 % 2.4e+00 s Elapsed time so far: 1.7 s
1.0 % 2.5e+00 s Elapsed time so far: 1.7 s
1.0 % 2.6e+00 s Elapsed time so far: 1.7 s
1.1 % 2.7e+00 s Elapsed time so far: 1.7 s
1.1 % 2.7e+00 s Elapsed time so far: 1.7 s
1.1 % 2.8e+00 s Elapsed time so far: 1.7 s
1.1 % 2.9e+00 s Elapsed time so far: 1.7 s
1.2 % 3.0e+00 s Elapsed time so far: 1.7 s
1.2 % 3.1e+00 s Elapsed time so far: 1.7 s
1.2 % 3.1e+00 s Elapsed time so far: 1.7 s
1.3 % 3.2e+00 s Elapsed time so far: 1.8 s
1.3 % 3.3e+00 s Elapsed time so far: 1.8 s
1.3 % 3.4e+00 s Elapsed time so far: 1.8 s
1.4 % 3.5e+00 s Elapsed time so far: 1.8 s
1.4 % 3.6e+00 s Elapsed time so far: 1.8 s
1.4 % 3.6e+00 s Elapsed time so far: 1.8 s
1.5 % 3.7e+00 s Elapsed time so far: 1.8 s
1.5 % 3.8e+00 s Elapsed time so far: 1.8 s
1.6 % 3.9e+00 s Elapsed time so far: 1.8 s
1.6 % 4.0e+00 s Elapsed time so far: 1.8 s
1.6 % 4.1e+00 s Elapsed time so far: 1.8 s
1.6 % 4.2e+00 s Elapsed time so far: 1.8 s
1.7 % 4.3e+00 s Elapsed time so far: 1.8 s
1.7 % 4.4e+00 s Elapsed time so far: 1.8 s
1.8 % 4.5e+00 s Elapsed time so far: 1.8 s
1.8 % 4.5e+00 s Elapsed time so far: 1.9 s
1.8 % 4.6e+00 s Elapsed time so far: 1.9 s
1.9 % 4.7e+00 s Elapsed time so far: 1.9 s
1.9 % 4.8e+00 s Elapsed time so far: 1.9 s
1.9 % 4.9e+00 s Elapsed time so far: 1.9 s
2.0 % 5.0e+00 s Elapsed time so far: 1.9 s
2.0 % 5.1e+00 s Elapsed time so far: 1.9 s
2.1 % 5.2e+00 s Elapsed time so far: 1.9 s
2.1 % 5.3e+00 s Elapsed time so far: 1.9 s
2.1 % 5.4e+00 s Elapsed time so far: 1.9 s
2.2 % 5.5e+00 s Elapsed time so far: 1.9 s
2.2 % 5.7e+00 s Elapsed time so far: 1.9 s
2.3 % 5.8e+00 s Elapsed time so far: 1.9 s
2.3 % 5.9e+00 s Elapsed time so far: 1.9 s
2.4 % 6.0e+00 s Elapsed time so far: 1.9 s
2.4 % 6.1e+00 s Elapsed time so far: 2.0 s
2.5 % 6.2e+00 s Elapsed time so far: 2.0 s
2.5 % 6.3e+00 s Elapsed time so far: 2.0 s
2.5 % 6.4e+00 s Elapsed time so far: 2.0 s
2.6 % 6.5e+00 s Elapsed time so far: 2.0 s
2.6 % 6.6e+00 s Elapsed time so far: 2.0 s
2.7 % 6.8e+00 s Elapsed time so far: 2.0 s
2.7 % 6.9e+00 s Elapsed time so far: 2.0 s
2.8 % 7.0e+00 s Elapsed time so far: 2.0 s
2.8 % 7.1e+00 s Elapsed time so far: 2.0 s
2.9 % 7.2e+00 s Elapsed time so far: 2.0 s
2.9 % 7.4e+00 s Elapsed time so far: 2.0 s
3.0 % 7.5e+00 s Elapsed time so far: 2.0 s
3.0 % 7.6e+00 s Elapsed time so far: 2.0 s
3.1 % 7.7e+00 s Elapsed time so far: 2.0 s
3.1 % 7.9e+00 s Elapsed time so far: 2.1 s
3.2 % 8.0e+00 s Elapsed time so far: 2.1 s
3.2 % 8.1e+00 s Elapsed time so far: 2.1 s
3.3 % 8.3e+00 s Elapsed time so far: 2.1 s
3.3 % 8.4e+00 s Elapsed time so far: 2.1 s
3.4 % 8.5e+00 s Elapsed time so far: 2.1 s
3.4 % 8.7e+00 s Elapsed time so far: 2.1 s
3.5 % 8.8e+00 s Elapsed time so far: 2.1 s
3.5 % 8.9e+00 s Elapsed time so far: 2.1 s
3.6 % 9.1e+00 s Elapsed time so far: 2.1 s
3.6 % 9.2e+00 s Elapsed time so far: 2.1 s
3.7 % 9.4e+00 s Elapsed time so far: 2.1 s
3.8 % 9.5e+00 s Elapsed time so far: 2.1 s
3.8 % 9.6e+00 s Elapsed time so far: 2.1 s
3.9 % 9.8e+00 s Elapsed time so far: 2.1 s
3.9 % 9.9e+00 s Elapsed time so far: 2.2 s
4.0 % 1.0e+01 s Elapsed time so far: 2.2 s
4.1 % 1.0e+01 s Elapsed time so far: 2.2 s
4.1 % 1.0e+01 s Elapsed time so far: 2.2 s
4.2 % 1.1e+01 s Elapsed time so far: 2.2 s
4.2 % 1.1e+01 s Elapsed time so far: 2.2 s
4.3 % 1.1e+01 s Elapsed time so far: 2.2 s
4.4 % 1.1e+01 s Elapsed time so far: 2.2 s
4.4 % 1.1e+01 s Elapsed time so far: 2.2 s
4.5 % 1.1e+01 s Elapsed time so far: 2.2 s
4.6 % 1.2e+01 s Elapsed time so far: 2.2 s
4.6 % 1.2e+01 s Elapsed time so far: 2.2 s
4.7 % 1.2e+01 s Elapsed time so far: 2.2 s
4.8 % 1.2e+01 s Elapsed time so far: 2.2 s
4.8 % 1.2e+01 s Elapsed time so far: 2.2 s
4.9 % 1.2e+01 s Elapsed time so far: 2.2 s
5.0 % 1.3e+01 s Elapsed time so far: 2.3 s
5.0 % 1.3e+01 s Elapsed time so far: 2.3 s
5.1 % 1.3e+01 s Elapsed time so far: 2.3 s
5.2 % 1.3e+01 s Elapsed time so far: 2.3 s
5.2 % 1.3e+01 s Elapsed time so far: 2.3 s
5.3 % 1.3e+01 s Elapsed time so far: 2.3 s
5.4 % 1.4e+01 s Elapsed time so far: 2.3 s
5.5 % 1.4e+01 s Elapsed time so far: 2.3 s
5.5 % 1.4e+01 s Elapsed time so far: 2.3 s
5.6 % 1.4e+01 s Elapsed time so far: 2.3 s
5.7 % 1.4e+01 s Elapsed time so far: 2.3 s
5.8 % 1.5e+01 s Elapsed time so far: 2.3 s
5.8 % 1.5e+01 s Elapsed time so far: 2.3 s
5.9 % 1.5e+01 s Elapsed time so far: 2.3 s
6.0 % 1.5e+01 s Elapsed time so far: 2.4 s
6.1 % 1.5e+01 s Elapsed time so far: 2.4 s
6.2 % 1.6e+01 s Elapsed time so far: 2.4 s
6.2 % 1.6e+01 s Elapsed time so far: 2.4 s
6.3 % 1.6e+01 s Elapsed time so far: 2.4 s
6.4 % 1.6e+01 s Elapsed time so far: 2.4 s
6.5 % 1.6e+01 s Elapsed time so far: 2.4 s
6.6 % 1.7e+01 s Elapsed time so far: 2.4 s
6.7 % 1.7e+01 s Elapsed time so far: 2.4 s
6.7 % 1.7e+01 s Elapsed time so far: 2.4 s
6.8 % 1.7e+01 s Elapsed time so far: 2.4 s
6.9 % 1.7e+01 s Elapsed time so far: 2.4 s
7.0 % 1.8e+01 s Elapsed time so far: 2.4 s
7.1 % 1.8e+01 s Elapsed time so far: 2.4 s
7.2 % 1.8e+01 s Elapsed time so far: 2.4 s
7.3 % 1.8e+01 s Elapsed time so far: 2.5 s
7.4 % 1.9e+01 s Elapsed time so far: 2.5 s
7.5 % 1.9e+01 s Elapsed time so far: 2.5 s
7.6 % 1.9e+01 s Elapsed time so far: 2.5 s
7.7 % 1.9e+01 s Elapsed time so far: 2.5 s
7.8 % 2.0e+01 s Elapsed time so far: 2.5 s
7.8 % 2.0e+01 s Elapsed time so far: 2.5 s
8.0 % 2.0e+01 s Elapsed time so far: 2.5 s
8.0 % 2.0e+01 s Elapsed time so far: 2.5 s
8.2 % 2.1e+01 s Elapsed time so far: 2.5 s
8.2 % 2.1e+01 s Elapsed time so far: 2.5 s
8.3 % 2.1e+01 s Elapsed time so far: 2.5 s
8.4 % 2.1e+01 s Elapsed time so far: 2.5 s
8.6 % 2.2e+01 s Elapsed time so far: 2.5 s
8.7 % 2.2e+01 s Elapsed time so far: 2.5 s
8.8 % 2.2e+01 s Elapsed time so far: 2.6 s
8.9 % 2.2e+01 s Elapsed time so far: 2.6 s
9.0 % 2.3e+01 s Elapsed time so far: 2.6 s
9.1 % 2.3e+01 s Elapsed time so far: 2.6 s
9.2 % 2.3e+01 s Elapsed time so far: 2.6 s
9.3 % 2.4e+01 s Elapsed time so far: 2.6 s
9.4 % 2.4e+01 s Elapsed time so far: 2.6 s
9.5 % 2.4e+01 s Elapsed time so far: 2.6 s
9.7 % 2.4e+01 s Elapsed time so far: 2.6 s
9.8 % 2.5e+01 s Elapsed time so far: 2.6 s
9.9 % 2.5e+01 s Elapsed time so far: 2.6 s
10.0 % 2.5e+01 s Elapsed time so far: 2.6 s
10.1 % 2.6e+01 s Elapsed time so far: 2.6 s
10.2 % 2.6e+01 s Elapsed time so far: 2.6 s
10.4 % 2.6e+01 s Elapsed time so far: 2.6 s
10.5 % 2.7e+01 s Elapsed time so far: 2.7 s
10.6 % 2.7e+01 s Elapsed time so far: 2.7 s
10.8 % 2.7e+01 s Elapsed time so far: 2.7 s
10.9 % 2.7e+01 s Elapsed time so far: 2.7 s
11.0 % 2.8e+01 s Elapsed time so far: 2.7 s
11.1 % 2.8e+01 s Elapsed time so far: 2.7 s
11.3 % 2.8e+01 s Elapsed time so far: 2.7 s
11.4 % 2.9e+01 s Elapsed time so far: 2.7 s
11.5 % 2.9e+01 s Elapsed time so far: 2.7 s
11.7 % 2.9e+01 s Elapsed time so far: 2.7 s
11.8 % 3.0e+01 s Elapsed time so far: 2.7 s
11.9 % 3.0e+01 s Elapsed time so far: 2.7 s
12.1 % 3.1e+01 s Elapsed time so far: 2.7 s
12.2 % 3.1e+01 s Elapsed time so far: 2.7 s
12.4 % 3.1e+01 s Elapsed time so far: 2.7 s
12.5 % 3.2e+01 s Elapsed time so far: 2.8 s
12.7 % 3.2e+01 s Elapsed time so far: 2.8 s
12.8 % 3.2e+01 s Elapsed time so far: 2.8 s
12.9 % 3.3e+01 s Elapsed time so far: 2.8 s
13.1 % 3.3e+01 s Elapsed time so far: 2.8 s
13.2 % 3.3e+01 s Elapsed time so far: 2.8 s
13.4 % 3.4e+01 s Elapsed time so far: 2.8 s
13.6 % 3.4e+01 s Elapsed time so far: 2.8 s
13.7 % 3.5e+01 s Elapsed time so far: 2.8 s
13.9 % 3.5e+01 s Elapsed time so far: 2.8 s
14.0 % 3.5e+01 s Elapsed time so far: 2.8 s
14.2 % 3.6e+01 s Elapsed time so far: 2.8 s
14.3 % 3.6e+01 s Elapsed time so far: 2.8 s
14.5 % 3.7e+01 s Elapsed time so far: 2.8 s
14.7 % 3.7e+01 s Elapsed time so far: 2.8 s
14.8 % 3.7e+01 s Elapsed time so far: 2.9 s
15.0 % 3.8e+01 s Elapsed time so far: 2.9 s
15.2 % 3.8e+01 s Elapsed time so far: 2.9 s
15.3 % 3.9e+01 s Elapsed time so far: 2.9 s
15.5 % 3.9e+01 s Elapsed time so far: 2.9 s
15.7 % 4.0e+01 s Elapsed time so far: 2.9 s
15.9 % 4.0e+01 s Elapsed time so far: 2.9 s
16.1 % 4.1e+01 s Elapsed time so far: 2.9 s
16.2 % 4.1e+01 s Elapsed time so far: 2.9 s
16.4 % 4.1e+01 s Elapsed time so far: 2.9 s
16.6 % 4.2e+01 s Elapsed time so far: 2.9 s
16.8 % 4.2e+01 s Elapsed time so far: 2.9 s
17.0 % 4.3e+01 s Elapsed time so far: 2.9 s
17.2 % 4.3e+01 s Elapsed time so far: 2.9 s
17.4 % 4.4e+01 s Elapsed time so far: 2.9 s
17.6 % 4.4e+01 s Elapsed time so far: 3.0 s
17.7 % 4.5e+01 s Elapsed time so far: 3.0 s
17.9 % 4.5e+01 s Elapsed time so far: 3.0 s
18.1 % 4.6e+01 s Elapsed time so far: 3.0 s
18.3 % 4.6e+01 s Elapsed time so far: 3.0 s
18.5 % 4.7e+01 s Elapsed time so far: 3.0 s
18.8 % 4.7e+01 s Elapsed time so far: 3.0 s
18.9 % 4.8e+01 s Elapsed time so far: 3.0 s
19.2 % 4.8e+01 s Elapsed time so far: 3.0 s
19.4 % 4.9e+01 s Elapsed time so far: 3.0 s
19.6 % 4.9e+01 s Elapsed time so far: 3.0 s
19.8 % 5.0e+01 s Elapsed time so far: 3.0 s
20.0 % 5.1e+01 s Elapsed time so far: 3.0 s
20.2 % 5.1e+01 s Elapsed time so far: 3.0 s
20.5 % 5.2e+01 s Elapsed time so far: 3.0 s
20.7 % 5.2e+01 s Elapsed time so far: 3.1 s
20.9 % 5.3e+01 s Elapsed time so far: 3.1 s
21.1 % 5.3e+01 s Elapsed time so far: 3.1 s
21.4 % 5.4e+01 s Elapsed time so far: 3.1 s
21.6 % 5.5e+01 s Elapsed time so far: 3.1 s
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22.1 % 5.6e+01 s Elapsed time so far: 3.1 s
22.3 % 5.6e+01 s Elapsed time so far: 3.1 s
22.6 % 5.7e+01 s Elapsed time so far: 3.1 s
22.8 % 5.8e+01 s Elapsed time so far: 3.1 s
23.1 % 5.8e+01 s Elapsed time so far: 3.1 s
23.3 % 5.9e+01 s Elapsed time so far: 3.1 s
23.6 % 6.0e+01 s Elapsed time so far: 3.1 s
23.8 % 6.0e+01 s Elapsed time so far: 3.1 s
24.1 % 6.1e+01 s Elapsed time so far: 3.1 s
24.3 % 6.1e+01 s Elapsed time so far: 3.2 s
24.6 % 6.2e+01 s Elapsed time so far: 3.2 s
24.9 % 6.3e+01 s Elapsed time so far: 3.2 s
25.1 % 6.3e+01 s Elapsed time so far: 3.2 s
25.4 % 6.4e+01 s Elapsed time so far: 3.2 s
25.7 % 6.5e+01 s Elapsed time so far: 3.2 s
26.0 % 6.6e+01 s Elapsed time so far: 3.2 s
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27.1 % 6.8e+01 s Elapsed time so far: 3.2 s
27.4 % 6.9e+01 s Elapsed time so far: 3.2 s
27.7 % 7.0e+01 s Elapsed time so far: 3.2 s
28.0 % 7.1e+01 s Elapsed time so far: 3.2 s
28.3 % 7.1e+01 s Elapsed time so far: 3.2 s
28.6 % 7.2e+01 s Elapsed time so far: 3.2 s
28.9 % 7.3e+01 s Elapsed time so far: 3.3 s
29.2 % 7.4e+01 s Elapsed time so far: 3.3 s
29.5 % 7.4e+01 s Elapsed time so far: 3.3 s
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30.1 % 7.6e+01 s Elapsed time so far: 3.3 s
30.4 % 7.7e+01 s Elapsed time so far: 3.3 s
30.8 % 7.8e+01 s Elapsed time so far: 3.3 s
31.1 % 7.9e+01 s Elapsed time so far: 3.3 s
31.4 % 7.9e+01 s Elapsed time so far: 3.3 s
31.8 % 8.0e+01 s Elapsed time so far: 3.3 s
32.1 % 8.1e+01 s Elapsed time so far: 3.3 s
32.5 % 8.2e+01 s Elapsed time so far: 3.3 s
32.8 % 8.3e+01 s Elapsed time so far: 3.3 s
33.1 % 8.4e+01 s Elapsed time so far: 3.3 s
33.5 % 8.5e+01 s Elapsed time so far: 3.4 s
33.9 % 8.5e+01 s Elapsed time so far: 3.4 s
34.2 % 8.6e+01 s Elapsed time so far: 3.4 s
34.6 % 8.7e+01 s Elapsed time so far: 3.4 s
34.9 % 8.8e+01 s Elapsed time so far: 3.4 s
35.3 % 8.9e+01 s Elapsed time so far: 3.4 s
35.7 % 9.0e+01 s Elapsed time so far: 3.4 s
36.0 % 9.1e+01 s Elapsed time so far: 3.4 s
36.4 % 9.2e+01 s Elapsed time so far: 3.4 s
36.8 % 9.3e+01 s Elapsed time so far: 3.4 s
37.2 % 9.4e+01 s Elapsed time so far: 3.4 s
37.6 % 9.5e+01 s Elapsed time so far: 3.4 s
38.0 % 9.6e+01 s Elapsed time so far: 3.4 s
38.4 % 9.7e+01 s Elapsed time so far: 3.4 s
38.8 % 9.8e+01 s Elapsed time so far: 3.4 s
39.2 % 9.9e+01 s Elapsed time so far: 3.5 s
39.6 % 1.0e+02 s Elapsed time so far: 3.5 s
40.0 % 1.0e+02 s Elapsed time so far: 3.5 s
40.5 % 1.0e+02 s Elapsed time so far: 3.5 s
40.9 % 1.0e+02 s Elapsed time so far: 3.5 s
41.3 % 1.0e+02 s Elapsed time so far: 3.5 s
41.7 % 1.1e+02 s Elapsed time so far: 3.5 s
42.2 % 1.1e+02 s Elapsed time so far: 3.5 s
42.6 % 1.1e+02 s Elapsed time so far: 3.5 s
43.1 % 1.1e+02 s Elapsed time so far: 3.5 s
43.5 % 1.1e+02 s Elapsed time so far: 3.5 s
44.0 % 1.1e+02 s Elapsed time so far: 3.5 s
44.4 % 1.1e+02 s Elapsed time so far: 3.5 s
44.9 % 1.1e+02 s Elapsed time so far: 3.5 s
45.4 % 1.1e+02 s Elapsed time so far: 3.5 s
45.8 % 1.2e+02 s Elapsed time so far: 3.6 s
46.3 % 1.2e+02 s Elapsed time so far: 3.6 s
46.8 % 1.2e+02 s Elapsed time so far: 3.6 s
47.3 % 1.2e+02 s Elapsed time so far: 3.6 s
47.8 % 1.2e+02 s Elapsed time so far: 3.6 s
48.3 % 1.2e+02 s Elapsed time so far: 3.6 s
48.8 % 1.2e+02 s Elapsed time so far: 3.6 s
49.3 % 1.2e+02 s Elapsed time so far: 3.6 s
49.8 % 1.3e+02 s Elapsed time so far: 3.6 s
50.3 % 1.3e+02 s Elapsed time so far: 3.6 s
50.8 % 1.3e+02 s Elapsed time so far: 3.6 s
51.4 % 1.3e+02 s Elapsed time so far: 3.6 s
51.9 % 1.3e+02 s Elapsed time so far: 3.6 s
52.4 % 1.3e+02 s Elapsed time so far: 3.6 s
53.0 % 1.3e+02 s Elapsed time so far: 3.6 s
53.5 % 1.4e+02 s Elapsed time so far: 3.7 s
54.1 % 1.4e+02 s Elapsed time so far: 3.7 s
54.6 % 1.4e+02 s Elapsed time so far: 3.7 s
55.2 % 1.4e+02 s Elapsed time so far: 3.7 s
55.8 % 1.4e+02 s Elapsed time so far: 3.7 s
56.4 % 1.4e+02 s Elapsed time so far: 3.7 s
56.9 % 1.4e+02 s Elapsed time so far: 3.7 s
57.5 % 1.5e+02 s Elapsed time so far: 3.7 s
58.1 % 1.5e+02 s Elapsed time so far: 3.7 s
58.7 % 1.5e+02 s Elapsed time so far: 3.7 s
59.3 % 1.5e+02 s Elapsed time so far: 3.7 s
60.0 % 1.5e+02 s Elapsed time so far: 3.7 s
60.6 % 1.5e+02 s Elapsed time so far: 3.7 s
61.2 % 1.5e+02 s Elapsed time so far: 3.7 s
61.8 % 1.6e+02 s Elapsed time so far: 3.7 s
62.5 % 1.6e+02 s Elapsed time so far: 3.8 s
63.1 % 1.6e+02 s Elapsed time so far: 3.8 s
63.8 % 1.6e+02 s Elapsed time so far: 3.8 s
64.4 % 1.6e+02 s Elapsed time so far: 3.8 s
65.1 % 1.6e+02 s Elapsed time so far: 3.8 s
65.8 % 1.7e+02 s Elapsed time so far: 3.8 s
66.4 % 1.7e+02 s Elapsed time so far: 3.8 s
67.1 % 1.7e+02 s Elapsed time so far: 3.8 s
67.8 % 1.7e+02 s Elapsed time so far: 3.8 s
68.5 % 1.7e+02 s Elapsed time so far: 3.8 s
69.2 % 1.7e+02 s Elapsed time so far: 3.8 s
69.9 % 1.8e+02 s Elapsed time so far: 3.8 s
70.6 % 1.8e+02 s Elapsed time so far: 3.8 s
71.4 % 1.8e+02 s Elapsed time so far: 3.8 s
72.1 % 1.8e+02 s Elapsed time so far: 3.8 s
72.8 % 1.8e+02 s Elapsed time so far: 3.9 s
73.6 % 1.9e+02 s Elapsed time so far: 3.9 s
74.3 % 1.9e+02 s Elapsed time so far: 3.9 s
75.1 % 1.9e+02 s Elapsed time so far: 3.9 s
75.9 % 1.9e+02 s Elapsed time so far: 3.9 s
76.7 % 1.9e+02 s Elapsed time so far: 3.9 s
77.4 % 2.0e+02 s Elapsed time so far: 3.9 s
78.2 % 2.0e+02 s Elapsed time so far: 3.9 s
79.0 % 2.0e+02 s Elapsed time so far: 3.9 s
79.8 % 2.0e+02 s Elapsed time so far: 3.9 s
80.7 % 2.0e+02 s Elapsed time so far: 3.9 s
81.5 % 2.1e+02 s Elapsed time so far: 3.9 s
82.3 % 2.1e+02 s Elapsed time so far: 3.9 s
83.2 % 2.1e+02 s Elapsed time so far: 3.9 s
84.0 % 2.1e+02 s Elapsed time so far: 3.9 s
84.9 % 2.1e+02 s Elapsed time so far: 4.0 s
85.8 % 2.2e+02 s Elapsed time so far: 4.0 s
86.6 % 2.2e+02 s Elapsed time so far: 4.0 s
87.5 % 2.2e+02 s Elapsed time so far: 4.0 s
88.4 % 2.2e+02 s Elapsed time so far: 4.0 s
89.3 % 2.3e+02 s Elapsed time so far: 4.0 s
90.2 % 2.3e+02 s Elapsed time so far: 4.0 s
91.2 % 2.3e+02 s Elapsed time so far: 4.0 s
92.1 % 2.3e+02 s Elapsed time so far: 4.0 s
93.0 % 2.3e+02 s Elapsed time so far: 4.0 s
94.0 % 2.4e+02 s Elapsed time so far: 4.0 s
94.9 % 2.4e+02 s Elapsed time so far: 4.0 s
95.9 % 2.4e+02 s Elapsed time so far: 4.0 s
96.9 % 2.4e+02 s Elapsed time so far: 4.0 s
97.9 % 2.5e+02 s Elapsed time so far: 4.0 s
98.9 % 2.5e+02 s Elapsed time so far: 4.0 s
99.9 % 2.5e+02 s Elapsed time so far: 4.1 s
100.0 % 2.5e+02 s Elapsed time so far: 4.1 s
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.
0.0 % 5.0e-02 s Elapsed time so far: 1.4 s
0.0 % 1.0e-01 s Elapsed time so far: 1.4 s
0.0 % 1.5e-01 s Elapsed time so far: 1.4 s
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0.3 % 9.8e-01 s Elapsed time so far: 1.5 s
0.3 % 1.0e+00 s Elapsed time so far: 1.5 s
0.3 % 1.1e+00 s Elapsed time so far: 1.5 s
0.3 % 1.2e+00 s Elapsed time so far: 1.5 s
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0.6 % 2.3e+00 s Elapsed time so far: 1.6 s
0.6 % 2.4e+00 s Elapsed time so far: 1.6 s
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0.8 % 2.8e+00 s Elapsed time so far: 1.7 s
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0.8 % 3.0e+00 s Elapsed time so far: 1.7 s
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0.8 % 3.1e+00 s Elapsed time so far: 1.7 s
0.9 % 3.2e+00 s Elapsed time so far: 1.7 s
0.9 % 3.3e+00 s Elapsed time so far: 1.7 s
0.9 % 3.4e+00 s Elapsed time so far: 1.7 s
0.9 % 3.5e+00 s Elapsed time so far: 1.7 s
0.9 % 3.6e+00 s Elapsed time so far: 1.7 s
1.0 % 3.6e+00 s Elapsed time so far: 1.7 s
1.0 % 3.7e+00 s Elapsed time so far: 1.7 s
1.0 % 3.8e+00 s Elapsed time so far: 1.7 s
1.0 % 3.9e+00 s Elapsed time so far: 1.7 s
1.1 % 4.0e+00 s Elapsed time so far: 1.8 s
1.1 % 4.1e+00 s Elapsed time so far: 1.8 s
1.1 % 4.2e+00 s Elapsed time so far: 1.8 s
1.1 % 4.3e+00 s Elapsed time so far: 1.8 s
1.2 % 4.4e+00 s Elapsed time so far: 1.8 s
1.2 % 4.5e+00 s Elapsed time so far: 1.8 s
1.2 % 4.5e+00 s Elapsed time so far: 1.8 s
1.2 % 4.6e+00 s Elapsed time so far: 1.8 s
1.3 % 4.7e+00 s Elapsed time so far: 1.8 s
1.3 % 4.8e+00 s Elapsed time so far: 1.8 s
1.3 % 4.9e+00 s Elapsed time so far: 1.8 s
1.3 % 5.0e+00 s Elapsed time so far: 1.8 s
1.4 % 5.1e+00 s Elapsed time so far: 1.8 s
1.4 % 5.2e+00 s Elapsed time so far: 1.8 s
1.4 % 5.3e+00 s Elapsed time so far: 1.8 s
1.4 % 5.4e+00 s Elapsed time so far: 1.9 s
1.5 % 5.5e+00 s Elapsed time so far: 1.9 s
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1.6 % 5.9e+00 s Elapsed time so far: 1.9 s
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1.7 % 6.3e+00 s Elapsed time so far: 1.9 s
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1.8 % 6.6e+00 s Elapsed time so far: 1.9 s
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1.8 % 6.9e+00 s Elapsed time so far: 1.9 s
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1.9 % 7.1e+00 s Elapsed time so far: 2.0 s
1.9 % 7.2e+00 s Elapsed time so far: 2.0 s
2.0 % 7.4e+00 s Elapsed time so far: 2.0 s
2.0 % 7.5e+00 s Elapsed time so far: 2.0 s
2.0 % 7.6e+00 s Elapsed time so far: 2.0 s
2.1 % 7.7e+00 s Elapsed time so far: 2.0 s
2.1 % 7.9e+00 s Elapsed time so far: 2.0 s
2.1 % 8.0e+00 s Elapsed time so far: 2.0 s
2.2 % 8.1e+00 s Elapsed time so far: 2.0 s
2.2 % 8.3e+00 s Elapsed time so far: 2.0 s
2.2 % 8.4e+00 s Elapsed time so far: 2.0 s
2.3 % 8.5e+00 s Elapsed time so far: 2.0 s
2.3 % 8.7e+00 s Elapsed time so far: 2.0 s
2.3 % 8.8e+00 s Elapsed time so far: 2.0 s
2.4 % 8.9e+00 s Elapsed time so far: 2.0 s
2.4 % 9.1e+00 s Elapsed time so far: 2.1 s
2.5 % 9.2e+00 s Elapsed time so far: 2.1 s
2.5 % 9.4e+00 s Elapsed time so far: 2.1 s
2.5 % 9.5e+00 s Elapsed time so far: 2.1 s
2.6 % 9.6e+00 s Elapsed time so far: 2.1 s
2.6 % 9.8e+00 s Elapsed time so far: 2.1 s
2.6 % 9.9e+00 s Elapsed time so far: 2.1 s
2.7 % 1.0e+01 s Elapsed time so far: 2.1 s
2.7 % 1.0e+01 s Elapsed time so far: 2.1 s
2.8 % 1.0e+01 s Elapsed time so far: 2.1 s
2.8 % 1.1e+01 s Elapsed time so far: 2.1 s
2.8 % 1.1e+01 s Elapsed time so far: 2.1 s
2.9 % 1.1e+01 s Elapsed time so far: 2.1 s
2.9 % 1.1e+01 s Elapsed time so far: 2.1 s
3.0 % 1.1e+01 s Elapsed time so far: 2.1 s
3.0 % 1.1e+01 s Elapsed time so far: 2.2 s
3.1 % 1.2e+01 s Elapsed time so far: 2.2 s
3.1 % 1.2e+01 s Elapsed time so far: 2.2 s
3.1 % 1.2e+01 s Elapsed time so far: 2.2 s
3.2 % 1.2e+01 s Elapsed time so far: 2.2 s
3.2 % 1.2e+01 s Elapsed time so far: 2.2 s
3.3 % 1.2e+01 s Elapsed time so far: 2.2 s
3.3 % 1.3e+01 s Elapsed time so far: 2.2 s
3.4 % 1.3e+01 s Elapsed time so far: 2.2 s
3.4 % 1.3e+01 s Elapsed time so far: 2.2 s
3.5 % 1.3e+01 s Elapsed time so far: 2.2 s
3.5 % 1.3e+01 s Elapsed time so far: 2.2 s
3.6 % 1.3e+01 s Elapsed time so far: 2.2 s
3.6 % 1.4e+01 s Elapsed time so far: 2.2 s
3.7 % 1.4e+01 s Elapsed time so far: 2.2 s
3.7 % 1.4e+01 s Elapsed time so far: 2.2 s
3.8 % 1.4e+01 s Elapsed time so far: 2.3 s
3.8 % 1.4e+01 s Elapsed time so far: 2.3 s
3.9 % 1.5e+01 s Elapsed time so far: 2.3 s
3.9 % 1.5e+01 s Elapsed time so far: 2.3 s
4.0 % 1.5e+01 s Elapsed time so far: 2.3 s
4.0 % 1.5e+01 s Elapsed time so far: 2.3 s
4.1 % 1.5e+01 s Elapsed time so far: 2.3 s
4.1 % 1.6e+01 s Elapsed time so far: 2.3 s
4.2 % 1.6e+01 s Elapsed time so far: 2.3 s
4.2 % 1.6e+01 s Elapsed time so far: 2.3 s
4.3 % 1.6e+01 s Elapsed time so far: 2.3 s
4.3 % 1.6e+01 s Elapsed time so far: 2.3 s
4.4 % 1.7e+01 s Elapsed time so far: 2.3 s
4.5 % 1.7e+01 s Elapsed time so far: 2.3 s
4.5 % 1.7e+01 s Elapsed time so far: 2.4 s
4.6 % 1.7e+01 s Elapsed time so far: 2.4 s
4.6 % 1.7e+01 s Elapsed time so far: 2.4 s
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5.0 % 1.9e+01 s Elapsed time so far: 2.4 s
5.0 % 1.9e+01 s Elapsed time so far: 2.4 s
5.1 % 1.9e+01 s Elapsed time so far: 2.4 s
5.1 % 1.9e+01 s Elapsed time so far: 2.4 s
5.2 % 2.0e+01 s Elapsed time so far: 2.4 s
5.3 % 2.0e+01 s Elapsed time so far: 2.4 s
5.3 % 2.0e+01 s Elapsed time so far: 2.4 s
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6.0 % 2.2e+01 s Elapsed time so far: 2.5 s
6.0 % 2.3e+01 s Elapsed time so far: 2.5 s
6.1 % 2.3e+01 s Elapsed time so far: 2.5 s
6.2 % 2.3e+01 s Elapsed time so far: 2.5 s
6.2 % 2.4e+01 s Elapsed time so far: 2.5 s
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7.0 % 2.6e+01 s Elapsed time so far: 2.6 s
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7.1 % 2.7e+01 s Elapsed time so far: 2.6 s
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7.3 % 2.7e+01 s Elapsed time so far: 2.6 s
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7.7 % 2.9e+01 s Elapsed time so far: 2.7 s
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8.0 % 3.0e+01 s Elapsed time so far: 2.7 s
8.1 % 3.1e+01 s Elapsed time so far: 2.7 s
8.2 % 3.1e+01 s Elapsed time so far: 2.7 s
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8.5 % 3.2e+01 s Elapsed time so far: 2.7 s
8.6 % 3.2e+01 s Elapsed time so far: 2.7 s
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8.9 % 3.3e+01 s Elapsed time so far: 2.7 s
9.0 % 3.4e+01 s Elapsed time so far: 2.7 s
9.1 % 3.4e+01 s Elapsed time so far: 2.7 s
9.2 % 3.5e+01 s Elapsed time so far: 2.7 s
9.3 % 3.5e+01 s Elapsed time so far: 2.8 s
9.4 % 3.5e+01 s Elapsed time so far: 2.8 s
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9.6 % 3.6e+01 s Elapsed time so far: 2.8 s
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9.8 % 3.7e+01 s Elapsed time so far: 2.8 s
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10.1 % 3.8e+01 s Elapsed time so far: 2.8 s
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10.7 % 4.0e+01 s Elapsed time so far: 2.8 s
10.8 % 4.1e+01 s Elapsed time so far: 2.8 s
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11.0 % 4.1e+01 s Elapsed time so far: 2.9 s
11.1 % 4.2e+01 s Elapsed time so far: 2.9 s
11.3 % 4.2e+01 s Elapsed time so far: 2.9 s
11.4 % 4.3e+01 s Elapsed time so far: 2.9 s
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11.7 % 4.4e+01 s Elapsed time so far: 2.9 s
11.8 % 4.4e+01 s Elapsed time so far: 2.9 s
11.9 % 4.5e+01 s Elapsed time so far: 2.9 s
12.0 % 4.5e+01 s Elapsed time so far: 2.9 s
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12.3 % 4.6e+01 s Elapsed time so far: 2.9 s
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13.0 % 4.9e+01 s Elapsed time so far: 3.0 s
13.2 % 4.9e+01 s Elapsed time so far: 3.0 s
13.3 % 5.0e+01 s Elapsed time so far: 3.0 s
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13.6 % 5.1e+01 s Elapsed time so far: 3.0 s
13.7 % 5.2e+01 s Elapsed time so far: 3.0 s
13.9 % 5.2e+01 s Elapsed time so far: 3.0 s
14.0 % 5.3e+01 s Elapsed time so far: 3.0 s
14.2 % 5.3e+01 s Elapsed time so far: 3.0 s
14.3 % 5.4e+01 s Elapsed time so far: 3.0 s
14.5 % 5.5e+01 s Elapsed time so far: 3.0 s
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14.8 % 5.6e+01 s Elapsed time so far: 3.0 s
15.0 % 5.6e+01 s Elapsed time so far: 3.0 s
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15.3 % 5.8e+01 s Elapsed time so far: 3.1 s
15.5 % 5.8e+01 s Elapsed time so far: 3.1 s
15.6 % 5.9e+01 s Elapsed time so far: 3.1 s
15.8 % 6.0e+01 s Elapsed time so far: 3.1 s
16.0 % 6.0e+01 s Elapsed time so far: 3.1 s
16.2 % 6.1e+01 s Elapsed time so far: 3.1 s
16.3 % 6.1e+01 s Elapsed time so far: 3.1 s
16.5 % 6.2e+01 s Elapsed time so far: 3.1 s
16.7 % 6.3e+01 s Elapsed time so far: 3.1 s
16.9 % 6.3e+01 s Elapsed time so far: 3.1 s
17.1 % 6.4e+01 s Elapsed time so far: 3.1 s
17.2 % 6.5e+01 s Elapsed time so far: 3.1 s
17.4 % 6.6e+01 s Elapsed time so far: 3.1 s
17.6 % 6.6e+01 s Elapsed time so far: 3.1 s
17.8 % 6.7e+01 s Elapsed time so far: 3.1 s
18.0 % 6.8e+01 s Elapsed time so far: 3.2 s
18.2 % 6.8e+01 s Elapsed time so far: 3.2 s
18.4 % 6.9e+01 s Elapsed time so far: 3.2 s
18.6 % 7.0e+01 s Elapsed time so far: 3.2 s
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19.0 % 7.1e+01 s Elapsed time so far: 3.2 s
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20.4 % 7.7e+01 s Elapsed time so far: 3.2 s
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21.1 % 7.9e+01 s Elapsed time so far: 3.2 s
21.3 % 8.0e+01 s Elapsed time so far: 3.3 s
21.6 % 8.1e+01 s Elapsed time so far: 3.3 s
21.8 % 8.2e+01 s Elapsed time so far: 3.3 s
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22.2 % 8.4e+01 s Elapsed time so far: 3.3 s
22.5 % 8.5e+01 s Elapsed time so far: 3.3 s
22.7 % 8.5e+01 s Elapsed time so far: 3.3 s
23.0 % 8.6e+01 s Elapsed time so far: 3.3 s
23.2 % 8.7e+01 s Elapsed time so far: 3.3 s
23.4 % 8.8e+01 s Elapsed time so far: 3.3 s
23.7 % 8.9e+01 s Elapsed time so far: 3.3 s
23.9 % 9.0e+01 s Elapsed time so far: 3.3 s
24.2 % 9.1e+01 s Elapsed time so far: 3.3 s
24.4 % 9.2e+01 s Elapsed time so far: 3.3 s
24.7 % 9.3e+01 s Elapsed time so far: 3.4 s
25.0 % 9.4e+01 s Elapsed time so far: 3.4 s
25.2 % 9.5e+01 s Elapsed time so far: 3.4 s
25.5 % 9.6e+01 s Elapsed time so far: 3.4 s
25.8 % 9.7e+01 s Elapsed time so far: 3.4 s
26.0 % 9.8e+01 s Elapsed time so far: 3.4 s
26.3 % 9.9e+01 s Elapsed time so far: 3.4 s
26.6 % 1.0e+02 s Elapsed time so far: 3.4 s
26.9 % 1.0e+02 s Elapsed time so far: 3.4 s
27.1 % 1.0e+02 s Elapsed time so far: 3.4 s
27.4 % 1.0e+02 s Elapsed time so far: 3.4 s
27.7 % 1.0e+02 s Elapsed time so far: 3.4 s
28.0 % 1.1e+02 s Elapsed time so far: 3.4 s
28.3 % 1.1e+02 s Elapsed time so far: 3.4 s
28.6 % 1.1e+02 s Elapsed time so far: 3.4 s
28.9 % 1.1e+02 s Elapsed time so far: 3.5 s
29.2 % 1.1e+02 s Elapsed time so far: 3.5 s
29.5 % 1.1e+02 s Elapsed time so far: 3.5 s
29.8 % 1.1e+02 s Elapsed time so far: 3.5 s
30.1 % 1.1e+02 s Elapsed time so far: 3.5 s
30.4 % 1.1e+02 s Elapsed time so far: 3.5 s
30.8 % 1.2e+02 s Elapsed time so far: 3.5 s
31.1 % 1.2e+02 s Elapsed time so far: 3.5 s
31.4 % 1.2e+02 s Elapsed time so far: 3.5 s
31.7 % 1.2e+02 s Elapsed time so far: 3.5 s
32.1 % 1.2e+02 s Elapsed time so far: 3.5 s
32.4 % 1.2e+02 s Elapsed time so far: 3.5 s
32.7 % 1.2e+02 s Elapsed time so far: 3.5 s
33.1 % 1.2e+02 s Elapsed time so far: 3.5 s
33.4 % 1.3e+02 s Elapsed time so far: 3.5 s
33.8 % 1.3e+02 s Elapsed time so far: 3.6 s
34.1 % 1.3e+02 s Elapsed time so far: 3.6 s
34.5 % 1.3e+02 s Elapsed time so far: 3.6 s
34.8 % 1.3e+02 s Elapsed time so far: 3.6 s
35.2 % 1.3e+02 s Elapsed time so far: 3.6 s
35.5 % 1.3e+02 s Elapsed time so far: 3.6 s
35.9 % 1.4e+02 s Elapsed time so far: 3.6 s
36.3 % 1.4e+02 s Elapsed time so far: 3.6 s
36.7 % 1.4e+02 s Elapsed time so far: 3.6 s
37.0 % 1.4e+02 s Elapsed time so far: 3.6 s
37.4 % 1.4e+02 s Elapsed time so far: 3.6 s
37.8 % 1.4e+02 s Elapsed time so far: 3.6 s
38.2 % 1.4e+02 s Elapsed time so far: 3.6 s
38.6 % 1.5e+02 s Elapsed time so far: 3.6 s
39.0 % 1.5e+02 s Elapsed time so far: 3.6 s
39.4 % 1.5e+02 s Elapsed time so far: 3.7 s
39.8 % 1.5e+02 s Elapsed time so far: 3.7 s
40.2 % 1.5e+02 s Elapsed time so far: 3.7 s
40.6 % 1.5e+02 s Elapsed time so far: 3.7 s
41.1 % 1.5e+02 s Elapsed time so far: 3.7 s
41.5 % 1.6e+02 s Elapsed time so far: 3.7 s
41.9 % 1.6e+02 s Elapsed time so far: 3.7 s
42.4 % 1.6e+02 s Elapsed time so far: 3.7 s
42.8 % 1.6e+02 s Elapsed time so far: 3.7 s
43.2 % 1.6e+02 s Elapsed time so far: 3.7 s
43.7 % 1.6e+02 s Elapsed time so far: 3.7 s
44.1 % 1.7e+02 s Elapsed time so far: 3.7 s
44.6 % 1.7e+02 s Elapsed time so far: 3.7 s
45.0 % 1.7e+02 s Elapsed time so far: 3.7 s
45.5 % 1.7e+02 s Elapsed time so far: 3.7 s
46.0 % 1.7e+02 s Elapsed time so far: 3.8 s
46.4 % 1.7e+02 s Elapsed time so far: 3.8 s
46.9 % 1.8e+02 s Elapsed time so far: 3.8 s
47.4 % 1.8e+02 s Elapsed time so far: 3.8 s
47.9 % 1.8e+02 s Elapsed time so far: 3.8 s
48.4 % 1.8e+02 s Elapsed time so far: 3.8 s
48.9 % 1.8e+02 s Elapsed time so far: 3.8 s
49.4 % 1.9e+02 s Elapsed time so far: 3.8 s
49.9 % 1.9e+02 s Elapsed time so far: 3.8 s
50.4 % 1.9e+02 s Elapsed time so far: 3.8 s
50.9 % 1.9e+02 s Elapsed time so far: 3.8 s
51.4 % 1.9e+02 s Elapsed time so far: 3.8 s
52.0 % 2.0e+02 s Elapsed time so far: 3.8 s
52.5 % 2.0e+02 s Elapsed time so far: 3.8 s
53.0 % 2.0e+02 s Elapsed time so far: 3.8 s
53.6 % 2.0e+02 s Elapsed time so far: 3.9 s
54.1 % 2.0e+02 s Elapsed time so far: 3.9 s
54.7 % 2.1e+02 s Elapsed time so far: 3.9 s
55.2 % 2.1e+02 s Elapsed time so far: 3.9 s
55.8 % 2.1e+02 s Elapsed time so far: 3.9 s
56.4 % 2.1e+02 s Elapsed time so far: 3.9 s
57.0 % 2.1e+02 s Elapsed time so far: 3.9 s
57.5 % 2.2e+02 s Elapsed time so far: 3.9 s
58.1 % 2.2e+02 s Elapsed time so far: 3.9 s
58.7 % 2.2e+02 s Elapsed time so far: 3.9 s
59.3 % 2.2e+02 s Elapsed time so far: 3.9 s
59.9 % 2.3e+02 s Elapsed time so far: 3.9 s
60.5 % 2.3e+02 s Elapsed time so far: 3.9 s
61.2 % 2.3e+02 s Elapsed time so far: 3.9 s
61.8 % 2.3e+02 s Elapsed time so far: 3.9 s
62.4 % 2.3e+02 s Elapsed time so far: 4.0 s
63.1 % 2.4e+02 s Elapsed time so far: 4.0 s
63.7 % 2.4e+02 s Elapsed time so far: 4.0 s
64.4 % 2.4e+02 s Elapsed time so far: 4.0 s
65.0 % 2.4e+02 s Elapsed time so far: 4.0 s
65.7 % 2.5e+02 s Elapsed time so far: 4.0 s
66.3 % 2.5e+02 s Elapsed time so far: 4.0 s
67.0 % 2.5e+02 s Elapsed time so far: 4.0 s
67.7 % 2.5e+02 s Elapsed time so far: 4.0 s
68.4 % 2.6e+02 s Elapsed time so far: 4.0 s
69.1 % 2.6e+02 s Elapsed time so far: 4.0 s
69.8 % 2.6e+02 s Elapsed time so far: 4.0 s
70.5 % 2.7e+02 s Elapsed time so far: 4.0 s
71.2 % 2.7e+02 s Elapsed time so far: 4.0 s
72.0 % 2.7e+02 s Elapsed time so far: 4.0 s
72.7 % 2.7e+02 s Elapsed time so far: 4.0 s
73.4 % 2.8e+02 s Elapsed time so far: 4.0 s
74.2 % 2.8e+02 s Elapsed time so far: 4.1 s
74.9 % 2.8e+02 s Elapsed time so far: 4.1 s
75.7 % 2.8e+02 s Elapsed time so far: 4.1 s
76.5 % 2.9e+02 s Elapsed time so far: 4.1 s
77.2 % 2.9e+02 s Elapsed time so far: 4.1 s
78.0 % 2.9e+02 s Elapsed time so far: 4.1 s
78.8 % 3.0e+02 s Elapsed time so far: 4.1 s
79.6 % 3.0e+02 s Elapsed time so far: 4.1 s
80.4 % 3.0e+02 s Elapsed time so far: 4.1 s
81.2 % 3.1e+02 s Elapsed time so far: 4.1 s
82.1 % 3.1e+02 s Elapsed time so far: 4.1 s
82.9 % 3.1e+02 s Elapsed time so far: 4.1 s
83.8 % 3.2e+02 s Elapsed time so far: 4.1 s
84.6 % 3.2e+02 s Elapsed time so far: 4.2 s
85.5 % 3.2e+02 s Elapsed time so far: 4.2 s
86.3 % 3.2e+02 s Elapsed time so far: 4.2 s
87.2 % 3.3e+02 s Elapsed time so far: 4.2 s
88.1 % 3.3e+02 s Elapsed time so far: 4.2 s
89.0 % 3.3e+02 s Elapsed time so far: 4.2 s
89.9 % 3.4e+02 s Elapsed time so far: 4.2 s
90.8 % 3.4e+02 s Elapsed time so far: 4.2 s
91.7 % 3.5e+02 s Elapsed time so far: 4.2 s
92.7 % 3.5e+02 s Elapsed time so far: 4.2 s
93.6 % 3.5e+02 s Elapsed time so far: 4.2 s
94.5 % 3.6e+02 s Elapsed time so far: 4.2 s
95.5 % 3.6e+02 s Elapsed time so far: 4.2 s
96.5 % 3.6e+02 s Elapsed time so far: 4.2 s
97.5 % 3.7e+02 s Elapsed time so far: 4.2 s
98.4 % 3.7e+02 s Elapsed time so far: 4.2 s
99.4 % 3.7e+02 s Elapsed time so far: 4.2 s
100.0 % 3.8e+02 s Elapsed time so far: 4.3 s
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.
0.0 % 5.0e-02 s Elapsed time so far: 1.4 s
0.0 % 1.0e-01 s Elapsed time so far: 1.4 s
0.0 % 1.5e-01 s Elapsed time so far: 1.4 s
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1.8 % 9.1e+00 s Elapsed time so far: 2.1 s
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2.0 % 9.8e+00 s Elapsed time so far: 2.1 s
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2.0 % 1.0e+01 s Elapsed time so far: 2.1 s
2.0 % 1.0e+01 s Elapsed time so far: 2.1 s
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2.3 % 1.1e+01 s Elapsed time so far: 2.2 s
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2.7 % 1.3e+01 s Elapsed time so far: 2.2 s
2.7 % 1.4e+01 s Elapsed time so far: 2.2 s
2.8 % 1.4e+01 s Elapsed time so far: 2.2 s
2.8 % 1.4e+01 s Elapsed time so far: 2.2 s
2.8 % 1.4e+01 s Elapsed time so far: 2.2 s
2.9 % 1.4e+01 s Elapsed time so far: 2.3 s
2.9 % 1.5e+01 s Elapsed time so far: 2.3 s
3.0 % 1.5e+01 s Elapsed time so far: 2.3 s
3.0 % 1.5e+01 s Elapsed time so far: 2.3 s
3.0 % 1.5e+01 s Elapsed time so far: 2.3 s
3.1 % 1.5e+01 s Elapsed time so far: 2.3 s
3.1 % 1.6e+01 s Elapsed time so far: 2.3 s
3.1 % 1.6e+01 s Elapsed time so far: 2.3 s
3.2 % 1.6e+01 s Elapsed time so far: 2.3 s
3.2 % 1.6e+01 s Elapsed time so far: 2.3 s
3.3 % 1.6e+01 s Elapsed time so far: 2.3 s
3.3 % 1.7e+01 s Elapsed time so far: 2.3 s
3.4 % 1.7e+01 s Elapsed time so far: 2.3 s
3.4 % 1.7e+01 s Elapsed time so far: 2.4 s
3.5 % 1.7e+01 s Elapsed time so far: 2.4 s
3.5 % 1.7e+01 s Elapsed time so far: 2.4 s
3.5 % 1.8e+01 s Elapsed time so far: 2.4 s
3.6 % 1.8e+01 s Elapsed time so far: 2.4 s
3.6 % 1.8e+01 s Elapsed time so far: 2.4 s
3.7 % 1.8e+01 s Elapsed time so far: 2.4 s
3.7 % 1.9e+01 s Elapsed time so far: 2.4 s
3.8 % 1.9e+01 s Elapsed time so far: 2.4 s
3.8 % 1.9e+01 s Elapsed time so far: 2.4 s
3.9 % 1.9e+01 s Elapsed time so far: 2.4 s
3.9 % 2.0e+01 s Elapsed time so far: 2.4 s
4.0 % 2.0e+01 s Elapsed time so far: 2.4 s
4.0 % 2.0e+01 s Elapsed time so far: 2.4 s
4.1 % 2.0e+01 s Elapsed time so far: 2.4 s
4.1 % 2.1e+01 s Elapsed time so far: 2.5 s
4.2 % 2.1e+01 s Elapsed time so far: 2.5 s
4.2 % 2.1e+01 s Elapsed time so far: 2.5 s
4.3 % 2.1e+01 s Elapsed time so far: 2.5 s
4.3 % 2.2e+01 s Elapsed time so far: 2.5 s
4.4 % 2.2e+01 s Elapsed time so far: 2.5 s
4.4 % 2.2e+01 s Elapsed time so far: 2.5 s
4.5 % 2.2e+01 s Elapsed time so far: 2.5 s
4.5 % 2.3e+01 s Elapsed time so far: 2.5 s
4.6 % 2.3e+01 s Elapsed time so far: 2.5 s
4.7 % 2.3e+01 s Elapsed time so far: 2.5 s
4.7 % 2.4e+01 s Elapsed time so far: 2.5 s
4.8 % 2.4e+01 s Elapsed time so far: 2.5 s
4.8 % 2.4e+01 s Elapsed time so far: 2.5 s
4.9 % 2.4e+01 s Elapsed time so far: 2.5 s
4.9 % 2.5e+01 s Elapsed time so far: 2.6 s
5.0 % 2.5e+01 s Elapsed time so far: 2.6 s
5.1 % 2.5e+01 s Elapsed time so far: 2.6 s
5.1 % 2.6e+01 s Elapsed time so far: 2.6 s
5.2 % 2.6e+01 s Elapsed time so far: 2.6 s
5.2 % 2.6e+01 s Elapsed time so far: 2.6 s
5.3 % 2.7e+01 s Elapsed time so far: 2.6 s
5.4 % 2.7e+01 s Elapsed time so far: 2.6 s
5.4 % 2.7e+01 s Elapsed time so far: 2.6 s
5.5 % 2.7e+01 s Elapsed time so far: 2.6 s
5.6 % 2.8e+01 s Elapsed time so far: 2.6 s
5.6 % 2.8e+01 s Elapsed time so far: 2.6 s
5.7 % 2.8e+01 s Elapsed time so far: 2.6 s
5.8 % 2.9e+01 s Elapsed time so far: 2.6 s
5.8 % 2.9e+01 s Elapsed time so far: 2.6 s
5.9 % 2.9e+01 s Elapsed time so far: 2.7 s
6.0 % 3.0e+01 s Elapsed time so far: 2.7 s
6.0 % 3.0e+01 s Elapsed time so far: 2.7 s
6.1 % 3.1e+01 s Elapsed time so far: 2.7 s
6.2 % 3.1e+01 s Elapsed time so far: 2.7 s
6.2 % 3.1e+01 s Elapsed time so far: 2.7 s
6.3 % 3.2e+01 s Elapsed time so far: 2.7 s
6.4 % 3.2e+01 s Elapsed time so far: 2.7 s
6.5 % 3.2e+01 s Elapsed time so far: 2.7 s
6.5 % 3.3e+01 s Elapsed time so far: 2.7 s
6.6 % 3.3e+01 s Elapsed time so far: 2.7 s
6.7 % 3.3e+01 s Elapsed time so far: 2.7 s
6.8 % 3.4e+01 s Elapsed time so far: 2.7 s
6.8 % 3.4e+01 s Elapsed time so far: 2.7 s
6.9 % 3.5e+01 s Elapsed time so far: 2.7 s
7.0 % 3.5e+01 s Elapsed time so far: 2.8 s
7.1 % 3.5e+01 s Elapsed time so far: 2.8 s
7.2 % 3.6e+01 s Elapsed time so far: 2.8 s
7.2 % 3.6e+01 s Elapsed time so far: 2.8 s
7.3 % 3.7e+01 s Elapsed time so far: 2.8 s
7.4 % 3.7e+01 s Elapsed time so far: 2.8 s
7.5 % 3.7e+01 s Elapsed time so far: 2.8 s
7.6 % 3.8e+01 s Elapsed time so far: 2.8 s
7.7 % 3.8e+01 s Elapsed time so far: 2.8 s
7.8 % 3.9e+01 s Elapsed time so far: 2.8 s
7.8 % 3.9e+01 s Elapsed time so far: 2.8 s
7.9 % 4.0e+01 s Elapsed time so far: 2.8 s
8.0 % 4.0e+01 s Elapsed time so far: 2.8 s
8.1 % 4.1e+01 s Elapsed time so far: 2.8 s
8.2 % 4.1e+01 s Elapsed time so far: 2.8 s
8.3 % 4.1e+01 s Elapsed time so far: 2.9 s
8.4 % 4.2e+01 s Elapsed time so far: 2.9 s
8.5 % 4.2e+01 s Elapsed time so far: 2.9 s
8.6 % 4.3e+01 s Elapsed time so far: 2.9 s
8.7 % 4.3e+01 s Elapsed time so far: 2.9 s
8.8 % 4.4e+01 s Elapsed time so far: 2.9 s
8.9 % 4.4e+01 s Elapsed time so far: 2.9 s
9.0 % 4.5e+01 s Elapsed time so far: 2.9 s
9.1 % 4.5e+01 s Elapsed time so far: 2.9 s
9.2 % 4.6e+01 s Elapsed time so far: 2.9 s
9.3 % 4.6e+01 s Elapsed time so far: 2.9 s
9.4 % 4.7e+01 s Elapsed time so far: 2.9 s
9.5 % 4.7e+01 s Elapsed time so far: 2.9 s
9.6 % 4.8e+01 s Elapsed time so far: 2.9 s
9.7 % 4.8e+01 s Elapsed time so far: 2.9 s
9.8 % 4.9e+01 s Elapsed time so far: 3.0 s
9.9 % 4.9e+01 s Elapsed time so far: 3.0 s
10.0 % 5.0e+01 s Elapsed time so far: 3.0 s
10.1 % 5.1e+01 s Elapsed time so far: 3.0 s
10.2 % 5.1e+01 s Elapsed time so far: 3.0 s
10.3 % 5.2e+01 s Elapsed time so far: 3.0 s
10.4 % 5.2e+01 s Elapsed time so far: 3.0 s
10.6 % 5.3e+01 s Elapsed time so far: 3.0 s
10.7 % 5.3e+01 s Elapsed time so far: 3.0 s
10.8 % 5.4e+01 s Elapsed time so far: 3.0 s
10.9 % 5.5e+01 s Elapsed time so far: 3.0 s
11.0 % 5.5e+01 s Elapsed time so far: 3.0 s
11.2 % 5.6e+01 s Elapsed time so far: 3.0 s
11.3 % 5.6e+01 s Elapsed time so far: 3.0 s
11.4 % 5.7e+01 s Elapsed time so far: 3.0 s
11.5 % 5.8e+01 s Elapsed time so far: 3.1 s
11.7 % 5.8e+01 s Elapsed time so far: 3.1 s
11.8 % 5.9e+01 s Elapsed time so far: 3.1 s
11.9 % 6.0e+01 s Elapsed time so far: 3.1 s
12.0 % 6.0e+01 s Elapsed time so far: 3.1 s
12.2 % 6.1e+01 s Elapsed time so far: 3.1 s
12.3 % 6.1e+01 s Elapsed time so far: 3.1 s
12.4 % 6.2e+01 s Elapsed time so far: 3.1 s
12.6 % 6.3e+01 s Elapsed time so far: 3.1 s
12.7 % 6.3e+01 s Elapsed time so far: 3.1 s
12.8 % 6.4e+01 s Elapsed time so far: 3.1 s
13.0 % 6.5e+01 s Elapsed time so far: 3.1 s
13.1 % 6.6e+01 s Elapsed time so far: 3.1 s
13.2 % 6.6e+01 s Elapsed time so far: 3.1 s
13.4 % 6.7e+01 s Elapsed time so far: 3.1 s
13.5 % 6.8e+01 s Elapsed time so far: 3.2 s
13.7 % 6.8e+01 s Elapsed time so far: 3.2 s
13.8 % 6.9e+01 s Elapsed time so far: 3.2 s
14.0 % 7.0e+01 s Elapsed time so far: 3.2 s
14.1 % 7.1e+01 s Elapsed time so far: 3.2 s
14.3 % 7.1e+01 s Elapsed time so far: 3.2 s
14.4 % 7.2e+01 s Elapsed time so far: 3.2 s
14.6 % 7.3e+01 s Elapsed time so far: 3.2 s
14.7 % 7.4e+01 s Elapsed time so far: 3.2 s
14.9 % 7.4e+01 s Elapsed time so far: 3.2 s
15.1 % 7.5e+01 s Elapsed time so far: 3.2 s
15.2 % 7.6e+01 s Elapsed time so far: 3.2 s
15.4 % 7.7e+01 s Elapsed time so far: 3.2 s
15.5 % 7.8e+01 s Elapsed time so far: 3.2 s
15.7 % 7.9e+01 s Elapsed time so far: 3.2 s
15.9 % 7.9e+01 s Elapsed time so far: 3.2 s
16.0 % 8.0e+01 s Elapsed time so far: 3.2 s
16.2 % 8.1e+01 s Elapsed time so far: 3.3 s
16.4 % 8.2e+01 s Elapsed time so far: 3.3 s
16.6 % 8.3e+01 s Elapsed time so far: 3.3 s
16.7 % 8.4e+01 s Elapsed time so far: 3.3 s
16.9 % 8.5e+01 s Elapsed time so far: 3.3 s
17.1 % 8.5e+01 s Elapsed time so far: 3.3 s
17.3 % 8.6e+01 s Elapsed time so far: 3.3 s
17.5 % 8.7e+01 s Elapsed time so far: 3.3 s
17.6 % 8.8e+01 s Elapsed time so far: 3.3 s
17.8 % 8.9e+01 s Elapsed time so far: 3.3 s
18.0 % 9.0e+01 s Elapsed time so far: 3.3 s
18.2 % 9.1e+01 s Elapsed time so far: 3.3 s
18.4 % 9.2e+01 s Elapsed time so far: 3.3 s
18.6 % 9.3e+01 s Elapsed time so far: 3.4 s
18.8 % 9.4e+01 s Elapsed time so far: 3.4 s
19.0 % 9.5e+01 s Elapsed time so far: 3.4 s
19.2 % 9.6e+01 s Elapsed time so far: 3.4 s
19.4 % 9.7e+01 s Elapsed time so far: 3.4 s
19.6 % 9.8e+01 s Elapsed time so far: 3.4 s
19.8 % 9.9e+01 s Elapsed time so far: 3.4 s
20.0 % 1.0e+02 s Elapsed time so far: 3.4 s
20.2 % 1.0e+02 s Elapsed time so far: 3.4 s
20.4 % 1.0e+02 s Elapsed time so far: 3.4 s
20.6 % 1.0e+02 s Elapsed time so far: 3.4 s
20.9 % 1.0e+02 s Elapsed time so far: 3.4 s
21.1 % 1.1e+02 s Elapsed time so far: 3.4 s
21.3 % 1.1e+02 s Elapsed time so far: 3.4 s
21.5 % 1.1e+02 s Elapsed time so far: 3.4 s
21.8 % 1.1e+02 s Elapsed time so far: 3.5 s
22.0 % 1.1e+02 s Elapsed time so far: 3.5 s
22.2 % 1.1e+02 s Elapsed time so far: 3.5 s
22.4 % 1.1e+02 s Elapsed time so far: 3.5 s
22.7 % 1.1e+02 s Elapsed time so far: 3.5 s
22.9 % 1.1e+02 s Elapsed time so far: 3.5 s
23.1 % 1.2e+02 s Elapsed time so far: 3.5 s
23.4 % 1.2e+02 s Elapsed time so far: 3.5 s
23.6 % 1.2e+02 s Elapsed time so far: 3.5 s
23.9 % 1.2e+02 s Elapsed time so far: 3.5 s
24.1 % 1.2e+02 s Elapsed time so far: 3.5 s
24.4 % 1.2e+02 s Elapsed time so far: 3.5 s
24.6 % 1.2e+02 s Elapsed time so far: 3.5 s
24.9 % 1.2e+02 s Elapsed time so far: 3.5 s
25.1 % 1.3e+02 s Elapsed time so far: 3.5 s
25.4 % 1.3e+02 s Elapsed time so far: 3.6 s
25.7 % 1.3e+02 s Elapsed time so far: 3.6 s
25.9 % 1.3e+02 s Elapsed time so far: 3.6 s
26.2 % 1.3e+02 s Elapsed time so far: 3.6 s
26.5 % 1.3e+02 s Elapsed time so far: 3.6 s
26.8 % 1.3e+02 s Elapsed time so far: 3.6 s
27.0 % 1.4e+02 s Elapsed time so far: 3.6 s
27.3 % 1.4e+02 s Elapsed time so far: 3.6 s
27.6 % 1.4e+02 s Elapsed time so far: 3.6 s
27.9 % 1.4e+02 s Elapsed time so far: 3.6 s
28.2 % 1.4e+02 s Elapsed time so far: 3.6 s
28.5 % 1.4e+02 s Elapsed time so far: 3.6 s
28.8 % 1.4e+02 s Elapsed time so far: 3.6 s
29.1 % 1.5e+02 s Elapsed time so far: 3.6 s
29.4 % 1.5e+02 s Elapsed time so far: 3.6 s
29.7 % 1.5e+02 s Elapsed time so far: 3.7 s
30.0 % 1.5e+02 s Elapsed time so far: 3.7 s
30.3 % 1.5e+02 s Elapsed time so far: 3.7 s
30.6 % 1.5e+02 s Elapsed time so far: 3.7 s
30.9 % 1.5e+02 s Elapsed time so far: 3.7 s
31.2 % 1.6e+02 s Elapsed time so far: 3.7 s
31.5 % 1.6e+02 s Elapsed time so far: 3.7 s
31.9 % 1.6e+02 s Elapsed time so far: 3.7 s
32.2 % 1.6e+02 s Elapsed time so far: 3.7 s
32.5 % 1.6e+02 s Elapsed time so far: 3.7 s
32.9 % 1.6e+02 s Elapsed time so far: 3.7 s
33.2 % 1.7e+02 s Elapsed time so far: 3.7 s
33.5 % 1.7e+02 s Elapsed time so far: 3.7 s
33.9 % 1.7e+02 s Elapsed time so far: 3.7 s
34.2 % 1.7e+02 s Elapsed time so far: 3.7 s
34.6 % 1.7e+02 s Elapsed time so far: 3.8 s
35.0 % 1.7e+02 s Elapsed time so far: 3.8 s
35.3 % 1.8e+02 s Elapsed time so far: 3.8 s
35.7 % 1.8e+02 s Elapsed time so far: 3.8 s
36.0 % 1.8e+02 s Elapsed time so far: 3.8 s
36.4 % 1.8e+02 s Elapsed time so far: 3.8 s
36.8 % 1.8e+02 s Elapsed time so far: 3.8 s
37.2 % 1.9e+02 s Elapsed time so far: 3.8 s
37.5 % 1.9e+02 s Elapsed time so far: 3.8 s
37.9 % 1.9e+02 s Elapsed time so far: 3.8 s
38.3 % 1.9e+02 s Elapsed time so far: 3.8 s
38.7 % 1.9e+02 s Elapsed time so far: 3.8 s
39.1 % 2.0e+02 s Elapsed time so far: 3.8 s
39.5 % 2.0e+02 s Elapsed time so far: 3.8 s
39.9 % 2.0e+02 s Elapsed time so far: 3.8 s
40.3 % 2.0e+02 s Elapsed time so far: 3.9 s
40.7 % 2.0e+02 s Elapsed time so far: 3.9 s
41.1 % 2.1e+02 s Elapsed time so far: 3.9 s
41.6 % 2.1e+02 s Elapsed time so far: 3.9 s
42.0 % 2.1e+02 s Elapsed time so far: 3.9 s
42.4 % 2.1e+02 s Elapsed time so far: 3.9 s
42.9 % 2.1e+02 s Elapsed time so far: 3.9 s
43.3 % 2.2e+02 s Elapsed time so far: 3.9 s
43.8 % 2.2e+02 s Elapsed time so far: 3.9 s
44.2 % 2.2e+02 s Elapsed time so far: 3.9 s
44.6 % 2.2e+02 s Elapsed time so far: 3.9 s
45.1 % 2.3e+02 s Elapsed time so far: 3.9 s
45.6 % 2.3e+02 s Elapsed time so far: 3.9 s
46.0 % 2.3e+02 s Elapsed time so far: 3.9 s
46.5 % 2.3e+02 s Elapsed time so far: 3.9 s
47.0 % 2.3e+02 s Elapsed time so far: 4.0 s
47.5 % 2.4e+02 s Elapsed time so far: 4.0 s
47.9 % 2.4e+02 s Elapsed time so far: 4.0 s
48.4 % 2.4e+02 s Elapsed time so far: 4.0 s
48.9 % 2.4e+02 s Elapsed time so far: 4.0 s
49.4 % 2.5e+02 s Elapsed time so far: 4.0 s
49.9 % 2.5e+02 s Elapsed time so far: 4.0 s
50.4 % 2.5e+02 s Elapsed time so far: 4.0 s
51.0 % 2.5e+02 s Elapsed time so far: 4.0 s
51.5 % 2.6e+02 s Elapsed time so far: 4.0 s
52.0 % 2.6e+02 s Elapsed time so far: 4.0 s
52.5 % 2.6e+02 s Elapsed time so far: 4.0 s
53.1 % 2.7e+02 s Elapsed time so far: 4.0 s
53.6 % 2.7e+02 s Elapsed time so far: 4.0 s
54.1 % 2.7e+02 s Elapsed time so far: 4.0 s
54.7 % 2.7e+02 s Elapsed time so far: 4.0 s
55.2 % 2.8e+02 s Elapsed time so far: 4.0 s
55.8 % 2.8e+02 s Elapsed time so far: 4.0 s
56.4 % 2.8e+02 s Elapsed time so far: 4.1 s
57.0 % 2.8e+02 s Elapsed time so far: 4.1 s
57.5 % 2.9e+02 s Elapsed time so far: 4.1 s
58.1 % 2.9e+02 s Elapsed time so far: 4.1 s
58.7 % 2.9e+02 s Elapsed time so far: 4.1 s
59.3 % 3.0e+02 s Elapsed time so far: 4.1 s
59.9 % 3.0e+02 s Elapsed time so far: 4.1 s
60.5 % 3.0e+02 s Elapsed time so far: 4.1 s
61.1 % 3.1e+02 s Elapsed time so far: 4.1 s
61.8 % 3.1e+02 s Elapsed time so far: 4.1 s
62.4 % 3.1e+02 s Elapsed time so far: 4.1 s
63.0 % 3.2e+02 s Elapsed time so far: 4.1 s
63.7 % 3.2e+02 s Elapsed time so far: 4.1 s
64.3 % 3.2e+02 s Elapsed time so far: 4.1 s
65.0 % 3.2e+02 s Elapsed time so far: 4.2 s
65.6 % 3.3e+02 s Elapsed time so far: 4.2 s
66.3 % 3.3e+02 s Elapsed time so far: 4.2 s
67.0 % 3.3e+02 s Elapsed time so far: 4.2 s
67.6 % 3.4e+02 s Elapsed time so far: 4.2 s
68.3 % 3.4e+02 s Elapsed time so far: 4.2 s
69.0 % 3.5e+02 s Elapsed time so far: 4.2 s
69.7 % 3.5e+02 s Elapsed time so far: 4.2 s
70.4 % 3.5e+02 s Elapsed time so far: 4.2 s
71.1 % 3.6e+02 s Elapsed time so far: 4.2 s
71.9 % 3.6e+02 s Elapsed time so far: 4.2 s
72.6 % 3.6e+02 s Elapsed time so far: 4.2 s
73.3 % 3.7e+02 s Elapsed time so far: 4.2 s
74.1 % 3.7e+02 s Elapsed time so far: 4.2 s
74.8 % 3.7e+02 s Elapsed time so far: 4.2 s
75.6 % 3.8e+02 s Elapsed time so far: 4.2 s
76.3 % 3.8e+02 s Elapsed time so far: 4.3 s
77.1 % 3.9e+02 s Elapsed time so far: 4.3 s
77.9 % 3.9e+02 s Elapsed time so far: 4.3 s
78.7 % 3.9e+02 s Elapsed time so far: 4.3 s
79.5 % 4.0e+02 s Elapsed time so far: 4.3 s
80.3 % 4.0e+02 s Elapsed time so far: 4.3 s
81.1 % 4.1e+02 s Elapsed time so far: 4.3 s
81.9 % 4.1e+02 s Elapsed time so far: 4.3 s
82.8 % 4.1e+02 s Elapsed time so far: 4.3 s
83.6 % 4.2e+02 s Elapsed time so far: 4.3 s
84.4 % 4.2e+02 s Elapsed time so far: 4.3 s
85.3 % 4.3e+02 s Elapsed time so far: 4.3 s
86.2 % 4.3e+02 s Elapsed time so far: 4.3 s
87.0 % 4.4e+02 s Elapsed time so far: 4.3 s
87.9 % 4.4e+02 s Elapsed time so far: 4.4 s
88.8 % 4.4e+02 s Elapsed time so far: 4.4 s
89.7 % 4.5e+02 s Elapsed time so far: 4.4 s
90.6 % 4.5e+02 s Elapsed time so far: 4.4 s
91.5 % 4.6e+02 s Elapsed time so far: 4.4 s
92.4 % 4.6e+02 s Elapsed time so far: 4.4 s
93.4 % 4.7e+02 s Elapsed time so far: 4.4 s
94.3 % 4.7e+02 s Elapsed time so far: 4.4 s
95.3 % 4.8e+02 s Elapsed time so far: 4.4 s
96.2 % 4.8e+02 s Elapsed time so far: 4.4 s
97.2 % 4.9e+02 s Elapsed time so far: 4.4 s
98.2 % 4.9e+02 s Elapsed time so far: 4.4 s
99.2 % 5.0e+02 s Elapsed time so far: 4.4 s
100.0 % 5.0e+02 s Elapsed time so far: 4.4 s
Comparison with exact solution#
The evolution of the hydrogen concentration is computed with FESTIM and compared with the exact solution (shown in dashed lines).
Show code cell source
from matplotlib import cm
from matplotlib.colors import LogNorm
norm = LogNorm(vmin=1e-2, vmax=100)
for time, concentration, half_life in tests:
plt.plot(
time,
concentration,
label=f"half-life = {half_life:.2f} s",
color=cm.Blues(norm(half_life)),
linewidth=3,
)
exact = initial_concentration * np.exp(-np.log(2) / half_life * np.array(time))
plt.plot(time, exact, "--", color="tab:grey")
plt.legend()
plt.ylim(bottom=0)
plt.xlabel("Time (s)")
plt.ylabel("Concentration (H/m3)")
plt.show()
