Isothermal absorption of protium in titanium#
This validation case reproduces H absorption curves for Ti at different temperatures obtained by Hirooka et al. [18].
Absorption experiments were performed in the vacuum chamber at the base pressure of \(1.3 \times 10^{4} \ \mathrm{Pa}\) with \(10 \times 13 \times 1 \ \mathrm{mm}^{3}\) cold rolled Ti strips. Absorption curves were acquired at the fixed sample temperature ranging from \(450 \ ^{\circ}\mathrm{C}\) to \(650 \ ^{\circ}\mathrm{C}\).
The FESTIM model is based on the work of Shimohata et al. [19]. By following the approach, evolution of the surface H concentration is assumed to be driven by adsorption from the gas phase and recombination. Only a half of the sample is simulated for simplicity.
The H diffusivity in Ti is taken from the report of Wille and Davis [20]. Rates of H desorption, absorption and re-absorption were fitted by Kulagin et al. [21].
The FESTIM results are compared to the experimental data from [19], extracted with PlotDigitizer.
FESTIM model#
Show code cell source
import festim as F
import fenics as f
import numpy as np
import h_transport_materials as htm
################### PARAMETERS ###################
N_A_const = 6.022e23 # Avogadro, mol^-1
e = 1.602e-19 # elementary charge, C
M_H2 = 2.016e-3 / N_A_const # the H2 mass, kg mol^-1
# Sample size
A = 1e-2 * 1.3e-2 # Ti surface area (1cm x 1.3cm), m^2
L = 1e-3 / 2 # Ti thickness, m
V = A * L # Ti volume (1cm x 1.3cm x 1mm), m^-3
# Ti properties
X_max = 3 # maximum number of H atoms per a Ti atom in the bulk
n_b = 9.4e4 * N_A_const # the number of atomic sites per unit of volume of Ti, m^-3
n_surf = (
X_max * 2.16e-5 * N_A_const
) # the number of atomic sites per unit of surface area of Ti, m^-2
N_Ti = n_b * V # the number of moles of Ti
n_IS = X_max * n_b
lambda_Ti = n_surf / n_IS
D = htm.diffusivities.filter(material=htm.TITANIUM, author="wille")[0]
D0 = D.pre_exp.magnitude # diffusivity pre-factor, m^2 s^-1
E_diff = D.act_energy.magnitude # diffusion activation energy, eV
k_sb = 5.1413505e9 # frequency factor of surface-to-bulk transition, s^-1
E_sb = 1.0087995 # activation energy for surface-to-bulk transition, eV
k_bs = 1.0012013e10 # # frequency factor of bulk-to-surface transition, s^-1
E_bs = 1.0518870 # activation energy for bulk-to-surface transition, eV
k_des = 3.4115671e-11 # desorption rate, m^2 s^-1
E_des = 5.6197034e-01 # desorption activation energy, eV
# Chamber
V_ch = 2.95e-3 # the chamber volume, m^3
P0 = 1.3e4 # the initial pressure, Pa
T_list = [
450 + 273,
500 + 273,
550 + 273,
600 + 273,
650 + 273,
] # list of considered temperatures, reference data is given in deg C
################### FUNCTIONS ###################
def S0(T):
# the capturing coefficient
return 0.0143 * f.exp(F.kJmol_to_eV(1.99) / F.k_B / T)
def P_H2(T, X):
# partial pressure of hydrogen, Pa
X0 = 0
return F.k_B * T * e / V_ch * (P0 * V_ch / (F.k_B * T * e) + (X0 - X) / 2)
def J_vs(T, surf_conc, X):
J_ads = (
2
* S0(T)
* (1 - surf_conc / n_surf) ** 2
* P_H2(T, X)
/ (2 * np.pi * M_H2 * F.k_B * T * e) ** 0.5
)
J_des = 2 * k_des * surf_conc**2 * f.exp(-E_des / F.k_B / T)
return J_ads - J_des
def K_sb(T, surf_conc, X):
return k_sb * f.exp(-E_sb / F.k_B / T)
def K_bs(T, surf_conc, X):
return k_bs * f.exp(-E_bs / F.k_B / T)
################### CUSTOM MODEL CLASS ###################
class CustomSimulation(F.Simulation):
def iterate(self):
super().iterate()
# Compute Content
surf = f.assemble(
self.h_transport_problem.boundary_conditions[0].solutions[0]
* self.mesh.ds(1)
)
X = 2 * (f.assemble(self.mobile.solution * self.mesh.dx) + surf) * A
# Normalised content parameter
self.h_transport_problem.boundary_conditions[0].prms["X"].assign(X)
def run_sim(T0):
Ti_model_impl = CustomSimulation()
# Mesh
vertices = np.linspace(0, L, num=1000)
Ti_model_impl.mesh = F.MeshFromVertices(vertices)
# Materials
Ti_model_impl.materials = F.Material(id=1, D_0=D0, E_D=E_diff)
surf_conc = F.SurfaceKinetics(
k_bs=K_bs,
k_sb=K_sb,
lambda_IS=lambda_Ti,
n_surf=n_surf,
n_IS=n_IS,
J_vs=J_vs,
surfaces=1,
initial_condition=0,
X=0,
)
# Boundary conditions
Ti_model_impl.boundary_conditions = [surf_conc]
# Homogenous temperature
Ti_model_impl.T = F.Temperature(value=T0)
# Exports
derived_quantities = F.DerivedQuantities(
[F.AdsorbedHydrogen(surface=1), F.TotalVolume(field="solute", volume=1)],
show_units=True,
)
Ti_model_impl.exports = [derived_quantities]
Ti_model_impl.dt = F.Stepsize(
initial_value=1e-3, stepsize_change_ratio=1.1, max_stepsize=5, dt_min=1e-5
)
Ti_model_impl.settings = F.Settings(
absolute_tolerance=1e6,
relative_tolerance=1e-4,
maximum_iterations=50,
final_time=25 * 60,
)
Ti_model_impl.initialise()
Ti_model_impl.run()
return derived_quantities
results = {}
for T0 in T_list:
results[T0] = run_sim(T0)
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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Calling FFC just-in-time (JIT) compiler, this may take some time.
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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62.5 % 9.4e+02 s Elapsed time so far: 7.0 s
62.9 % 9.4e+02 s Elapsed time so far: 7.0 s
63.2 % 9.5e+02 s Elapsed time so far: 7.0 s
63.5 % 9.5e+02 s Elapsed time so far: 7.0 s
63.9 % 9.6e+02 s Elapsed time so far: 7.1 s
64.2 % 9.6e+02 s Elapsed time so far: 7.1 s
64.5 % 9.7e+02 s Elapsed time so far: 7.1 s
64.9 % 9.7e+02 s Elapsed time so far: 7.1 s
65.2 % 9.8e+02 s Elapsed time so far: 7.1 s
65.5 % 9.8e+02 s Elapsed time so far: 7.1 s
65.9 % 9.9e+02 s Elapsed time so far: 7.1 s
66.2 % 9.9e+02 s Elapsed time so far: 7.1 s
66.5 % 1.0e+03 s Elapsed time so far: 7.2 s
66.9 % 1.0e+03 s Elapsed time so far: 7.2 s
67.2 % 1.0e+03 s Elapsed time so far: 7.2 s
67.5 % 1.0e+03 s Elapsed time so far: 7.2 s
67.9 % 1.0e+03 s Elapsed time so far: 7.2 s
68.2 % 1.0e+03 s Elapsed time so far: 7.2 s
68.5 % 1.0e+03 s Elapsed time so far: 7.2 s
68.9 % 1.0e+03 s Elapsed time so far: 7.2 s
69.2 % 1.0e+03 s Elapsed time so far: 7.2 s
69.5 % 1.0e+03 s Elapsed time so far: 7.3 s
69.9 % 1.0e+03 s Elapsed time so far: 7.3 s
70.2 % 1.1e+03 s Elapsed time so far: 7.3 s
70.5 % 1.1e+03 s Elapsed time so far: 7.3 s
70.9 % 1.1e+03 s Elapsed time so far: 7.3 s
71.2 % 1.1e+03 s Elapsed time so far: 7.3 s
71.5 % 1.1e+03 s Elapsed time so far: 7.3 s
71.9 % 1.1e+03 s Elapsed time so far: 7.3 s
72.2 % 1.1e+03 s Elapsed time so far: 7.4 s
72.5 % 1.1e+03 s Elapsed time so far: 7.4 s
72.9 % 1.1e+03 s Elapsed time so far: 7.4 s
73.2 % 1.1e+03 s Elapsed time so far: 7.4 s
73.5 % 1.1e+03 s Elapsed time so far: 7.4 s
73.9 % 1.1e+03 s Elapsed time so far: 7.4 s
74.2 % 1.1e+03 s Elapsed time so far: 7.4 s
74.5 % 1.1e+03 s Elapsed time so far: 7.4 s
74.9 % 1.1e+03 s Elapsed time so far: 7.4 s
75.2 % 1.1e+03 s Elapsed time so far: 7.5 s
75.5 % 1.1e+03 s Elapsed time so far: 7.5 s
75.9 % 1.1e+03 s Elapsed time so far: 7.5 s
76.2 % 1.1e+03 s Elapsed time so far: 7.5 s
76.5 % 1.1e+03 s Elapsed time so far: 7.5 s
76.9 % 1.2e+03 s Elapsed time so far: 7.5 s
77.2 % 1.2e+03 s Elapsed time so far: 7.5 s
77.5 % 1.2e+03 s Elapsed time so far: 7.5 s
77.9 % 1.2e+03 s Elapsed time so far: 7.5 s
78.2 % 1.2e+03 s Elapsed time so far: 7.6 s
78.5 % 1.2e+03 s Elapsed time so far: 7.6 s
78.9 % 1.2e+03 s Elapsed time so far: 7.6 s
79.2 % 1.2e+03 s Elapsed time so far: 7.6 s
79.5 % 1.2e+03 s Elapsed time so far: 7.6 s
79.9 % 1.2e+03 s Elapsed time so far: 7.6 s
80.2 % 1.2e+03 s Elapsed time so far: 7.6 s
80.5 % 1.2e+03 s Elapsed time so far: 7.6 s
80.9 % 1.2e+03 s Elapsed time so far: 7.7 s
81.2 % 1.2e+03 s Elapsed time so far: 7.7 s
81.5 % 1.2e+03 s Elapsed time so far: 7.7 s
81.9 % 1.2e+03 s Elapsed time so far: 7.7 s
82.2 % 1.2e+03 s Elapsed time so far: 7.7 s
82.5 % 1.2e+03 s Elapsed time so far: 7.7 s
82.9 % 1.2e+03 s Elapsed time so far: 7.7 s
83.2 % 1.2e+03 s Elapsed time so far: 7.7 s
83.5 % 1.3e+03 s Elapsed time so far: 7.7 s
83.9 % 1.3e+03 s Elapsed time so far: 7.8 s
84.2 % 1.3e+03 s Elapsed time so far: 7.8 s
84.5 % 1.3e+03 s Elapsed time so far: 7.8 s
84.9 % 1.3e+03 s Elapsed time so far: 7.8 s
85.2 % 1.3e+03 s Elapsed time so far: 7.8 s
85.5 % 1.3e+03 s Elapsed time so far: 7.8 s
85.9 % 1.3e+03 s Elapsed time so far: 7.8 s
86.2 % 1.3e+03 s Elapsed time so far: 7.8 s
86.5 % 1.3e+03 s Elapsed time so far: 7.9 s
86.9 % 1.3e+03 s Elapsed time so far: 7.9 s
87.2 % 1.3e+03 s Elapsed time so far: 7.9 s
87.5 % 1.3e+03 s Elapsed time so far: 7.9 s
87.9 % 1.3e+03 s Elapsed time so far: 7.9 s
88.2 % 1.3e+03 s Elapsed time so far: 7.9 s
88.5 % 1.3e+03 s Elapsed time so far: 7.9 s
88.9 % 1.3e+03 s Elapsed time so far: 7.9 s
89.2 % 1.3e+03 s Elapsed time so far: 7.9 s
89.5 % 1.3e+03 s Elapsed time so far: 8.0 s
89.9 % 1.3e+03 s Elapsed time so far: 8.0 s
90.2 % 1.4e+03 s Elapsed time so far: 8.0 s
90.5 % 1.4e+03 s Elapsed time so far: 8.0 s
90.9 % 1.4e+03 s Elapsed time so far: 8.0 s
91.2 % 1.4e+03 s Elapsed time so far: 8.0 s
91.5 % 1.4e+03 s Elapsed time so far: 8.0 s
91.9 % 1.4e+03 s Elapsed time so far: 8.0 s
92.2 % 1.4e+03 s Elapsed time so far: 8.0 s
92.5 % 1.4e+03 s Elapsed time so far: 8.1 s
92.9 % 1.4e+03 s Elapsed time so far: 8.1 s
93.2 % 1.4e+03 s Elapsed time so far: 8.1 s
93.5 % 1.4e+03 s Elapsed time so far: 8.1 s
93.9 % 1.4e+03 s Elapsed time so far: 8.1 s
94.2 % 1.4e+03 s Elapsed time so far: 8.1 s
94.5 % 1.4e+03 s Elapsed time so far: 8.1 s
94.9 % 1.4e+03 s Elapsed time so far: 8.1 s
95.2 % 1.4e+03 s Elapsed time so far: 8.2 s
95.5 % 1.4e+03 s Elapsed time so far: 8.2 s
95.9 % 1.4e+03 s Elapsed time so far: 8.2 s
96.2 % 1.4e+03 s Elapsed time so far: 8.2 s
96.5 % 1.4e+03 s Elapsed time so far: 8.2 s
96.9 % 1.5e+03 s Elapsed time so far: 8.2 s
97.2 % 1.5e+03 s Elapsed time so far: 8.2 s
97.5 % 1.5e+03 s Elapsed time so far: 8.2 s
97.9 % 1.5e+03 s Elapsed time so far: 8.2 s
98.2 % 1.5e+03 s Elapsed time so far: 8.2 s
98.5 % 1.5e+03 s Elapsed time so far: 8.3 s
98.9 % 1.5e+03 s Elapsed time so far: 8.3 s
99.2 % 1.5e+03 s Elapsed time so far: 8.3 s
99.5 % 1.5e+03 s Elapsed time so far: 8.3 s
99.9 % 1.5e+03 s Elapsed time so far: 8.3 s
100.0 % 1.5e+03 s Elapsed time so far: 8.3 s
Defining initial values
Defining variational problem
Defining source terms
Defining boundary conditions
Time stepping...
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0.0 % 1.6e-02 s Elapsed time so far: 0.1 s
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0.0 % 2.1e-02 s Elapsed time so far: 0.2 s
0.0 % 2.5e-02 s Elapsed time so far: 0.2 s
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0.0 % 3.2e-02 s Elapsed time so far: 0.2 s
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0.0 % 4.1e-02 s Elapsed time so far: 0.2 s
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0.0 % 5.1e-02 s Elapsed time so far: 0.2 s
0.0 % 5.7e-02 s Elapsed time so far: 0.2 s
0.0 % 6.4e-02 s Elapsed time so far: 0.2 s
0.0 % 7.1e-02 s Elapsed time so far: 0.3 s
0.0 % 8.0e-02 s Elapsed time so far: 0.3 s
0.0 % 8.8e-02 s Elapsed time so far: 0.3 s
0.0 % 9.8e-02 s Elapsed time so far: 0.3 s
0.0 % 1.1e-01 s Elapsed time so far: 0.3 s
0.0 % 1.2e-01 s Elapsed time so far: 0.3 s
0.0 % 1.3e-01 s Elapsed time so far: 0.3 s
0.0 % 1.5e-01 s Elapsed time so far: 0.3 s
0.0 % 1.6e-01 s Elapsed time so far: 0.4 s
0.0 % 1.8e-01 s Elapsed time so far: 0.4 s
0.0 % 2.0e-01 s Elapsed time so far: 0.4 s
0.0 % 2.2e-01 s Elapsed time so far: 0.4 s
0.0 % 2.5e-01 s Elapsed time so far: 0.4 s
0.0 % 2.7e-01 s Elapsed time so far: 0.4 s
0.0 % 3.0e-01 s Elapsed time so far: 0.4 s
0.0 % 3.3e-01 s Elapsed time so far: 0.4 s
0.0 % 3.6e-01 s Elapsed time so far: 0.5 s
0.0 % 4.0e-01 s Elapsed time so far: 0.5 s
0.0 % 4.4e-01 s Elapsed time so far: 0.5 s
0.0 % 4.9e-01 s Elapsed time so far: 0.5 s
0.0 % 5.4e-01 s Elapsed time so far: 0.5 s
0.0 % 5.9e-01 s Elapsed time so far: 0.5 s
0.0 % 6.5e-01 s Elapsed time so far: 0.5 s
0.1 % 7.2e-01 s Elapsed time so far: 0.5 s
0.1 % 7.9e-01 s Elapsed time so far: 0.5 s
0.1 % 8.7e-01 s Elapsed time so far: 0.6 s
0.1 % 9.6e-01 s Elapsed time so far: 0.6 s
0.1 % 1.1e+00 s Elapsed time so far: 0.6 s
0.1 % 1.2e+00 s Elapsed time so far: 0.6 s
0.1 % 1.3e+00 s Elapsed time so far: 0.6 s
0.1 % 1.4e+00 s Elapsed time so far: 0.6 s
0.1 % 1.6e+00 s Elapsed time so far: 0.6 s
0.1 % 1.7e+00 s Elapsed time so far: 0.6 s
0.1 % 1.9e+00 s Elapsed time so far: 0.7 s
0.1 % 2.1e+00 s Elapsed time so far: 0.7 s
0.1 % 2.3e+00 s Elapsed time so far: 0.7 s
0.2 % 2.5e+00 s Elapsed time so far: 0.7 s
0.2 % 2.8e+00 s Elapsed time so far: 0.7 s
0.2 % 3.0e+00 s Elapsed time so far: 0.7 s
0.2 % 3.3e+00 s Elapsed time so far: 0.7 s
0.2 % 3.7e+00 s Elapsed time so far: 0.7 s
0.3 % 4.0e+00 s Elapsed time so far: 0.7 s
0.3 % 4.4e+00 s Elapsed time so far: 0.8 s
0.3 % 4.9e+00 s Elapsed time so far: 0.8 s
0.4 % 5.4e+00 s Elapsed time so far: 0.8 s
0.4 % 5.9e+00 s Elapsed time so far: 0.8 s
0.4 % 6.5e+00 s Elapsed time so far: 0.8 s
0.5 % 7.2e+00 s Elapsed time so far: 0.8 s
0.5 % 7.9e+00 s Elapsed time so far: 0.8 s
0.6 % 8.7e+00 s Elapsed time so far: 0.8 s
0.6 % 9.5e+00 s Elapsed time so far: 0.8 s
0.7 % 1.1e+01 s Elapsed time so far: 0.9 s
0.8 % 1.2e+01 s Elapsed time so far: 0.9 s
0.8 % 1.3e+01 s Elapsed time so far: 0.9 s
0.9 % 1.4e+01 s Elapsed time so far: 0.9 s
1.0 % 1.5e+01 s Elapsed time so far: 0.9 s
1.1 % 1.7e+01 s Elapsed time so far: 0.9 s
1.2 % 1.9e+01 s Elapsed time so far: 0.9 s
1.4 % 2.0e+01 s Elapsed time so far: 0.9 s
1.5 % 2.3e+01 s Elapsed time so far: 1.0 s
1.6 % 2.5e+01 s Elapsed time so far: 1.0 s
1.8 % 2.7e+01 s Elapsed time so far: 1.0 s
2.0 % 3.0e+01 s Elapsed time so far: 1.0 s
2.2 % 3.3e+01 s Elapsed time so far: 1.0 s
2.4 % 3.6e+01 s Elapsed time so far: 1.0 s
2.7 % 4.0e+01 s Elapsed time so far: 1.0 s
2.9 % 4.4e+01 s Elapsed time so far: 1.0 s
3.2 % 4.8e+01 s Elapsed time so far: 1.0 s
3.5 % 5.3e+01 s Elapsed time so far: 1.1 s
3.9 % 5.8e+01 s Elapsed time so far: 1.1 s
4.2 % 6.3e+01 s Elapsed time so far: 1.1 s
4.5 % 6.8e+01 s Elapsed time so far: 1.1 s
4.9 % 7.3e+01 s Elapsed time so far: 1.1 s
5.2 % 7.8e+01 s Elapsed time so far: 1.1 s
5.5 % 8.3e+01 s Elapsed time so far: 1.1 s
5.9 % 8.8e+01 s Elapsed time so far: 1.1 s
6.2 % 9.3e+01 s Elapsed time so far: 1.2 s
6.5 % 9.8e+01 s Elapsed time so far: 1.2 s
6.9 % 1.0e+02 s Elapsed time so far: 1.2 s
7.2 % 1.1e+02 s Elapsed time so far: 1.2 s
7.5 % 1.1e+02 s Elapsed time so far: 1.2 s
7.9 % 1.2e+02 s Elapsed time so far: 1.2 s
8.2 % 1.2e+02 s Elapsed time so far: 1.2 s
8.5 % 1.3e+02 s Elapsed time so far: 1.2 s
8.9 % 1.3e+02 s Elapsed time so far: 1.2 s
9.2 % 1.4e+02 s Elapsed time so far: 1.2 s
9.5 % 1.4e+02 s Elapsed time so far: 1.3 s
9.9 % 1.5e+02 s Elapsed time so far: 1.3 s
10.2 % 1.5e+02 s Elapsed time so far: 1.3 s
10.5 % 1.6e+02 s Elapsed time so far: 1.3 s
10.9 % 1.6e+02 s Elapsed time so far: 1.3 s
11.2 % 1.7e+02 s Elapsed time so far: 1.3 s
11.5 % 1.7e+02 s Elapsed time so far: 1.3 s
11.9 % 1.8e+02 s Elapsed time so far: 1.4 s
12.2 % 1.8e+02 s Elapsed time so far: 1.4 s
12.5 % 1.9e+02 s Elapsed time so far: 1.4 s
12.9 % 1.9e+02 s Elapsed time so far: 1.4 s
13.2 % 2.0e+02 s Elapsed time so far: 1.4 s
13.5 % 2.0e+02 s Elapsed time so far: 1.4 s
13.9 % 2.1e+02 s Elapsed time so far: 1.4 s
14.2 % 2.1e+02 s Elapsed time so far: 1.4 s
14.5 % 2.2e+02 s Elapsed time so far: 1.4 s
14.9 % 2.2e+02 s Elapsed time so far: 1.5 s
15.2 % 2.3e+02 s Elapsed time so far: 1.5 s
15.5 % 2.3e+02 s Elapsed time so far: 1.5 s
15.9 % 2.4e+02 s Elapsed time so far: 1.5 s
16.2 % 2.4e+02 s Elapsed time so far: 1.5 s
16.5 % 2.5e+02 s Elapsed time so far: 1.5 s
16.9 % 2.5e+02 s Elapsed time so far: 1.5 s
17.2 % 2.6e+02 s Elapsed time so far: 1.5 s
17.5 % 2.6e+02 s Elapsed time so far: 1.5 s
17.9 % 2.7e+02 s Elapsed time so far: 1.6 s
18.2 % 2.7e+02 s Elapsed time so far: 1.6 s
18.5 % 2.8e+02 s Elapsed time so far: 1.6 s
18.9 % 2.8e+02 s Elapsed time so far: 1.6 s
19.2 % 2.9e+02 s Elapsed time so far: 1.6 s
19.5 % 2.9e+02 s Elapsed time so far: 1.6 s
19.9 % 3.0e+02 s Elapsed time so far: 1.6 s
20.2 % 3.0e+02 s Elapsed time so far: 1.6 s
20.5 % 3.1e+02 s Elapsed time so far: 1.7 s
20.9 % 3.1e+02 s Elapsed time so far: 1.7 s
21.2 % 3.2e+02 s Elapsed time so far: 1.7 s
21.5 % 3.2e+02 s Elapsed time so far: 1.7 s
21.9 % 3.3e+02 s Elapsed time so far: 1.7 s
22.2 % 3.3e+02 s Elapsed time so far: 1.7 s
22.5 % 3.4e+02 s Elapsed time so far: 1.7 s
22.9 % 3.4e+02 s Elapsed time so far: 1.7 s
23.2 % 3.5e+02 s Elapsed time so far: 1.7 s
23.5 % 3.5e+02 s Elapsed time so far: 1.8 s
23.9 % 3.6e+02 s Elapsed time so far: 1.8 s
24.2 % 3.6e+02 s Elapsed time so far: 1.8 s
24.5 % 3.7e+02 s Elapsed time so far: 1.8 s
24.9 % 3.7e+02 s Elapsed time so far: 1.8 s
25.2 % 3.8e+02 s Elapsed time so far: 1.8 s
25.5 % 3.8e+02 s Elapsed time so far: 1.8 s
25.9 % 3.9e+02 s Elapsed time so far: 1.8 s
26.2 % 3.9e+02 s Elapsed time so far: 1.8 s
26.5 % 4.0e+02 s Elapsed time so far: 1.9 s
26.9 % 4.0e+02 s Elapsed time so far: 1.9 s
27.2 % 4.1e+02 s Elapsed time so far: 1.9 s
27.5 % 4.1e+02 s Elapsed time so far: 1.9 s
27.9 % 4.2e+02 s Elapsed time so far: 1.9 s
28.2 % 4.2e+02 s Elapsed time so far: 1.9 s
28.5 % 4.3e+02 s Elapsed time so far: 1.9 s
28.9 % 4.3e+02 s Elapsed time so far: 1.9 s
29.2 % 4.4e+02 s Elapsed time so far: 2.0 s
29.5 % 4.4e+02 s Elapsed time so far: 2.0 s
29.9 % 4.5e+02 s Elapsed time so far: 2.0 s
30.2 % 4.5e+02 s Elapsed time so far: 2.0 s
30.5 % 4.6e+02 s Elapsed time so far: 2.0 s
30.9 % 4.6e+02 s Elapsed time so far: 2.0 s
31.2 % 4.7e+02 s Elapsed time so far: 2.0 s
31.5 % 4.7e+02 s Elapsed time so far: 2.0 s
31.9 % 4.8e+02 s Elapsed time so far: 2.0 s
32.2 % 4.8e+02 s Elapsed time so far: 2.1 s
32.5 % 4.9e+02 s Elapsed time so far: 2.1 s
32.9 % 4.9e+02 s Elapsed time so far: 2.1 s
33.2 % 5.0e+02 s Elapsed time so far: 2.1 s
33.5 % 5.0e+02 s Elapsed time so far: 2.1 s
33.9 % 5.1e+02 s Elapsed time so far: 2.1 s
34.2 % 5.1e+02 s Elapsed time so far: 2.1 s
34.5 % 5.2e+02 s Elapsed time so far: 2.1 s
34.9 % 5.2e+02 s Elapsed time so far: 2.2 s
35.2 % 5.3e+02 s Elapsed time so far: 2.2 s
35.5 % 5.3e+02 s Elapsed time so far: 2.2 s
35.9 % 5.4e+02 s Elapsed time so far: 2.2 s
36.2 % 5.4e+02 s Elapsed time so far: 2.2 s
36.5 % 5.5e+02 s Elapsed time so far: 2.2 s
36.9 % 5.5e+02 s Elapsed time so far: 2.2 s
37.2 % 5.6e+02 s Elapsed time so far: 2.2 s
37.5 % 5.6e+02 s Elapsed time so far: 2.2 s
37.9 % 5.7e+02 s Elapsed time so far: 2.2 s
38.2 % 5.7e+02 s Elapsed time so far: 2.3 s
38.5 % 5.8e+02 s Elapsed time so far: 2.3 s
38.9 % 5.8e+02 s Elapsed time so far: 2.3 s
39.2 % 5.9e+02 s Elapsed time so far: 2.3 s
39.5 % 5.9e+02 s Elapsed time so far: 2.3 s
39.9 % 6.0e+02 s Elapsed time so far: 2.3 s
40.2 % 6.0e+02 s Elapsed time so far: 2.3 s
40.5 % 6.1e+02 s Elapsed time so far: 2.3 s
40.9 % 6.1e+02 s Elapsed time so far: 2.4 s
41.2 % 6.2e+02 s Elapsed time so far: 2.4 s
41.5 % 6.2e+02 s Elapsed time so far: 2.4 s
41.9 % 6.3e+02 s Elapsed time so far: 2.4 s
42.2 % 6.3e+02 s Elapsed time so far: 2.4 s
42.5 % 6.4e+02 s Elapsed time so far: 2.4 s
42.9 % 6.4e+02 s Elapsed time so far: 2.4 s
43.2 % 6.5e+02 s Elapsed time so far: 2.4 s
43.5 % 6.5e+02 s Elapsed time so far: 2.5 s
43.9 % 6.6e+02 s Elapsed time so far: 2.5 s
44.2 % 6.6e+02 s Elapsed time so far: 2.5 s
44.5 % 6.7e+02 s Elapsed time so far: 2.5 s
44.9 % 6.7e+02 s Elapsed time so far: 2.5 s
45.2 % 6.8e+02 s Elapsed time so far: 2.5 s
45.5 % 6.8e+02 s Elapsed time so far: 2.5 s
45.9 % 6.9e+02 s Elapsed time so far: 2.5 s
46.2 % 6.9e+02 s Elapsed time so far: 2.5 s
46.5 % 7.0e+02 s Elapsed time so far: 2.6 s
46.9 % 7.0e+02 s Elapsed time so far: 2.6 s
47.2 % 7.1e+02 s Elapsed time so far: 2.6 s
47.5 % 7.1e+02 s Elapsed time so far: 2.6 s
47.9 % 7.2e+02 s Elapsed time so far: 2.6 s
48.2 % 7.2e+02 s Elapsed time so far: 2.6 s
48.5 % 7.3e+02 s Elapsed time so far: 2.6 s
48.9 % 7.3e+02 s Elapsed time so far: 2.6 s
49.2 % 7.4e+02 s Elapsed time so far: 2.6 s
49.5 % 7.4e+02 s Elapsed time so far: 2.7 s
49.9 % 7.5e+02 s Elapsed time so far: 2.7 s
50.2 % 7.5e+02 s Elapsed time so far: 2.7 s
50.5 % 7.6e+02 s Elapsed time so far: 2.7 s
50.9 % 7.6e+02 s Elapsed time so far: 2.7 s
51.2 % 7.7e+02 s Elapsed time so far: 2.7 s
51.5 % 7.7e+02 s Elapsed time so far: 2.7 s
51.9 % 7.8e+02 s Elapsed time so far: 2.7 s
52.2 % 7.8e+02 s Elapsed time so far: 2.8 s
52.5 % 7.9e+02 s Elapsed time so far: 2.8 s
52.9 % 7.9e+02 s Elapsed time so far: 2.8 s
53.2 % 8.0e+02 s Elapsed time so far: 2.8 s
53.5 % 8.0e+02 s Elapsed time so far: 2.8 s
53.9 % 8.1e+02 s Elapsed time so far: 2.8 s
54.2 % 8.1e+02 s Elapsed time so far: 2.8 s
54.5 % 8.2e+02 s Elapsed time so far: 2.8 s
54.9 % 8.2e+02 s Elapsed time so far: 2.9 s
55.2 % 8.3e+02 s Elapsed time so far: 2.9 s
55.5 % 8.3e+02 s Elapsed time so far: 2.9 s
55.9 % 8.4e+02 s Elapsed time so far: 2.9 s
56.2 % 8.4e+02 s Elapsed time so far: 2.9 s
56.5 % 8.5e+02 s Elapsed time so far: 2.9 s
56.9 % 8.5e+02 s Elapsed time so far: 2.9 s
57.2 % 8.6e+02 s Elapsed time so far: 3.0 s
57.5 % 8.6e+02 s Elapsed time so far: 3.0 s
57.9 % 8.7e+02 s Elapsed time so far: 3.0 s
58.2 % 8.7e+02 s Elapsed time so far: 3.0 s
58.5 % 8.8e+02 s Elapsed time so far: 3.0 s
58.9 % 8.8e+02 s Elapsed time so far: 3.0 s
59.2 % 8.9e+02 s Elapsed time so far: 3.1 s
59.5 % 8.9e+02 s Elapsed time so far: 3.1 s
59.9 % 9.0e+02 s Elapsed time so far: 3.1 s
60.2 % 9.0e+02 s Elapsed time so far: 3.1 s
60.5 % 9.1e+02 s Elapsed time so far: 3.1 s
60.9 % 9.1e+02 s Elapsed time so far: 3.1 s
61.2 % 9.2e+02 s Elapsed time so far: 3.1 s
61.5 % 9.2e+02 s Elapsed time so far: 3.2 s
61.9 % 9.3e+02 s Elapsed time so far: 3.2 s
62.2 % 9.3e+02 s Elapsed time so far: 3.2 s
62.5 % 9.4e+02 s Elapsed time so far: 3.2 s
62.9 % 9.4e+02 s Elapsed time so far: 3.2 s
63.2 % 9.5e+02 s Elapsed time so far: 3.2 s
63.5 % 9.5e+02 s Elapsed time so far: 3.2 s
63.9 % 9.6e+02 s Elapsed time so far: 3.2 s
64.2 % 9.6e+02 s Elapsed time so far: 3.3 s
64.5 % 9.7e+02 s Elapsed time so far: 3.3 s
64.9 % 9.7e+02 s Elapsed time so far: 3.3 s
65.2 % 9.8e+02 s Elapsed time so far: 3.3 s
65.5 % 9.8e+02 s Elapsed time so far: 3.3 s
65.9 % 9.9e+02 s Elapsed time so far: 3.3 s
66.2 % 9.9e+02 s Elapsed time so far: 3.4 s
66.5 % 1.0e+03 s Elapsed time so far: 3.4 s
66.9 % 1.0e+03 s Elapsed time so far: 3.4 s
67.2 % 1.0e+03 s Elapsed time so far: 3.4 s
67.5 % 1.0e+03 s Elapsed time so far: 3.4 s
67.9 % 1.0e+03 s Elapsed time so far: 3.4 s
68.2 % 1.0e+03 s Elapsed time so far: 3.4 s
68.5 % 1.0e+03 s Elapsed time so far: 3.5 s
68.9 % 1.0e+03 s Elapsed time so far: 3.5 s
69.2 % 1.0e+03 s Elapsed time so far: 3.5 s
69.5 % 1.0e+03 s Elapsed time so far: 3.5 s
69.9 % 1.0e+03 s Elapsed time so far: 3.5 s
70.2 % 1.1e+03 s Elapsed time so far: 3.5 s
70.5 % 1.1e+03 s Elapsed time so far: 3.5 s
70.9 % 1.1e+03 s Elapsed time so far: 3.6 s
71.2 % 1.1e+03 s Elapsed time so far: 3.6 s
71.5 % 1.1e+03 s Elapsed time so far: 3.6 s
71.9 % 1.1e+03 s Elapsed time so far: 3.6 s
72.2 % 1.1e+03 s Elapsed time so far: 3.6 s
72.5 % 1.1e+03 s Elapsed time so far: 3.6 s
72.9 % 1.1e+03 s Elapsed time so far: 3.6 s
73.2 % 1.1e+03 s Elapsed time so far: 3.7 s
73.5 % 1.1e+03 s Elapsed time so far: 3.7 s
73.9 % 1.1e+03 s Elapsed time so far: 3.7 s
74.2 % 1.1e+03 s Elapsed time so far: 3.7 s
74.5 % 1.1e+03 s Elapsed time so far: 3.7 s
74.9 % 1.1e+03 s Elapsed time so far: 3.7 s
75.2 % 1.1e+03 s Elapsed time so far: 3.7 s
75.5 % 1.1e+03 s Elapsed time so far: 3.7 s
75.9 % 1.1e+03 s Elapsed time so far: 3.7 s
76.2 % 1.1e+03 s Elapsed time so far: 3.7 s
76.5 % 1.1e+03 s Elapsed time so far: 3.8 s
76.9 % 1.2e+03 s Elapsed time so far: 3.8 s
77.2 % 1.2e+03 s Elapsed time so far: 3.8 s
77.5 % 1.2e+03 s Elapsed time so far: 3.8 s
77.9 % 1.2e+03 s Elapsed time so far: 3.8 s
78.2 % 1.2e+03 s Elapsed time so far: 3.8 s
78.5 % 1.2e+03 s Elapsed time so far: 3.9 s
78.9 % 1.2e+03 s Elapsed time so far: 3.9 s
79.2 % 1.2e+03 s Elapsed time so far: 3.9 s
79.5 % 1.2e+03 s Elapsed time so far: 3.9 s
79.9 % 1.2e+03 s Elapsed time so far: 3.9 s
80.2 % 1.2e+03 s Elapsed time so far: 3.9 s
80.5 % 1.2e+03 s Elapsed time so far: 3.9 s
80.9 % 1.2e+03 s Elapsed time so far: 4.0 s
81.2 % 1.2e+03 s Elapsed time so far: 4.0 s
81.5 % 1.2e+03 s Elapsed time so far: 4.0 s
81.9 % 1.2e+03 s Elapsed time so far: 4.0 s
82.2 % 1.2e+03 s Elapsed time so far: 4.0 s
82.5 % 1.2e+03 s Elapsed time so far: 4.0 s
82.9 % 1.2e+03 s Elapsed time so far: 4.0 s
83.2 % 1.2e+03 s Elapsed time so far: 4.0 s
83.5 % 1.3e+03 s Elapsed time so far: 4.1 s
83.9 % 1.3e+03 s Elapsed time so far: 4.1 s
84.2 % 1.3e+03 s Elapsed time so far: 4.1 s
84.5 % 1.3e+03 s Elapsed time so far: 4.1 s
84.9 % 1.3e+03 s Elapsed time so far: 4.1 s
85.2 % 1.3e+03 s Elapsed time so far: 4.1 s
85.5 % 1.3e+03 s Elapsed time so far: 4.2 s
85.9 % 1.3e+03 s Elapsed time so far: 4.2 s
86.2 % 1.3e+03 s Elapsed time so far: 4.2 s
86.5 % 1.3e+03 s Elapsed time so far: 4.2 s
86.9 % 1.3e+03 s Elapsed time so far: 4.2 s
87.2 % 1.3e+03 s Elapsed time so far: 4.2 s
87.5 % 1.3e+03 s Elapsed time so far: 4.2 s
87.9 % 1.3e+03 s Elapsed time so far: 4.2 s
88.2 % 1.3e+03 s Elapsed time so far: 4.3 s
88.5 % 1.3e+03 s Elapsed time so far: 4.3 s
88.9 % 1.3e+03 s Elapsed time so far: 4.3 s
89.2 % 1.3e+03 s Elapsed time so far: 4.3 s
89.5 % 1.3e+03 s Elapsed time so far: 4.3 s
89.9 % 1.3e+03 s Elapsed time so far: 4.3 s
90.2 % 1.4e+03 s Elapsed time so far: 4.4 s
90.5 % 1.4e+03 s Elapsed time so far: 4.4 s
90.9 % 1.4e+03 s Elapsed time so far: 4.4 s
91.2 % 1.4e+03 s Elapsed time so far: 4.4 s
91.5 % 1.4e+03 s Elapsed time so far: 4.4 s
91.9 % 1.4e+03 s Elapsed time so far: 4.4 s
92.2 % 1.4e+03 s Elapsed time so far: 4.4 s
92.5 % 1.4e+03 s Elapsed time so far: 4.5 s
92.9 % 1.4e+03 s Elapsed time so far: 4.5 s
93.2 % 1.4e+03 s Elapsed time so far: 4.5 s
93.5 % 1.4e+03 s Elapsed time so far: 4.5 s
93.9 % 1.4e+03 s Elapsed time so far: 4.5 s
94.2 % 1.4e+03 s Elapsed time so far: 4.5 s
94.5 % 1.4e+03 s Elapsed time so far: 4.5 s
94.9 % 1.4e+03 s Elapsed time so far: 4.6 s
95.2 % 1.4e+03 s Elapsed time so far: 4.6 s
95.5 % 1.4e+03 s Elapsed time so far: 4.6 s
95.9 % 1.4e+03 s Elapsed time so far: 4.6 s
96.2 % 1.4e+03 s Elapsed time so far: 4.6 s
96.5 % 1.4e+03 s Elapsed time so far: 4.6 s
96.9 % 1.5e+03 s Elapsed time so far: 4.6 s
97.2 % 1.5e+03 s Elapsed time so far: 4.7 s
97.5 % 1.5e+03 s Elapsed time so far: 4.7 s
97.9 % 1.5e+03 s Elapsed time so far: 4.7 s
98.2 % 1.5e+03 s Elapsed time so far: 4.7 s
98.5 % 1.5e+03 s Elapsed time so far: 4.7 s
98.9 % 1.5e+03 s Elapsed time so far: 4.7 s
99.2 % 1.5e+03 s Elapsed time so far: 4.7 s
99.5 % 1.5e+03 s Elapsed time so far: 4.8 s
99.9 % 1.5e+03 s Elapsed time so far: 4.8 s
100.0 % 1.5e+03 s Elapsed time so far: 4.8 s
Defining initial values
Defining variational problem
Defining source terms
Defining boundary conditions
Time stepping...
0.0 % 1.0e-03 s Elapsed time so far: 0.0 s
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0.0 % 4.6e-03 s Elapsed time so far: 0.1 s
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0.0 % 1.6e-02 s Elapsed time so far: 0.1 s
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0.0 % 2.1e-02 s Elapsed time so far: 0.1 s
0.0 % 2.5e-02 s Elapsed time so far: 0.2 s
0.0 % 2.8e-02 s Elapsed time so far: 0.2 s
0.0 % 3.2e-02 s Elapsed time so far: 0.2 s
0.0 % 3.6e-02 s Elapsed time so far: 0.2 s
0.0 % 4.1e-02 s Elapsed time so far: 0.2 s
0.0 % 4.6e-02 s Elapsed time so far: 0.2 s
0.0 % 5.1e-02 s Elapsed time so far: 0.2 s
0.0 % 5.7e-02 s Elapsed time so far: 0.2 s
0.0 % 6.4e-02 s Elapsed time so far: 0.2 s
0.0 % 7.1e-02 s Elapsed time so far: 0.3 s
0.0 % 8.0e-02 s Elapsed time so far: 0.3 s
0.0 % 8.8e-02 s Elapsed time so far: 0.3 s
0.0 % 9.8e-02 s Elapsed time so far: 0.3 s
0.0 % 1.1e-01 s Elapsed time so far: 0.3 s
0.0 % 1.2e-01 s Elapsed time so far: 0.3 s
0.0 % 1.3e-01 s Elapsed time so far: 0.3 s
0.0 % 1.5e-01 s Elapsed time so far: 0.3 s
0.0 % 1.6e-01 s Elapsed time so far: 0.4 s
0.0 % 1.8e-01 s Elapsed time so far: 0.4 s
0.0 % 2.0e-01 s Elapsed time so far: 0.4 s
0.0 % 2.2e-01 s Elapsed time so far: 0.4 s
0.0 % 2.5e-01 s Elapsed time so far: 0.4 s
0.0 % 2.7e-01 s Elapsed time so far: 0.4 s
0.0 % 3.0e-01 s Elapsed time so far: 0.4 s
0.0 % 3.3e-01 s Elapsed time so far: 0.4 s
0.0 % 3.6e-01 s Elapsed time so far: 0.4 s
0.0 % 4.0e-01 s Elapsed time so far: 0.5 s
0.0 % 4.4e-01 s Elapsed time so far: 0.5 s
0.0 % 4.9e-01 s Elapsed time so far: 0.5 s
0.0 % 5.4e-01 s Elapsed time so far: 0.5 s
0.0 % 5.9e-01 s Elapsed time so far: 0.5 s
0.0 % 6.5e-01 s Elapsed time so far: 0.5 s
0.1 % 7.2e-01 s Elapsed time so far: 0.5 s
0.1 % 7.9e-01 s Elapsed time so far: 0.5 s
0.1 % 8.7e-01 s Elapsed time so far: 0.5 s
0.1 % 9.6e-01 s Elapsed time so far: 0.6 s
0.1 % 1.1e+00 s Elapsed time so far: 0.6 s
0.1 % 1.2e+00 s Elapsed time so far: 0.6 s
0.1 % 1.3e+00 s Elapsed time so far: 0.6 s
0.1 % 1.4e+00 s Elapsed time so far: 0.6 s
0.1 % 1.6e+00 s Elapsed time so far: 0.6 s
0.1 % 1.7e+00 s Elapsed time so far: 0.6 s
0.1 % 1.9e+00 s Elapsed time so far: 0.6 s
0.1 % 2.1e+00 s Elapsed time so far: 0.7 s
0.1 % 2.3e+00 s Elapsed time so far: 0.7 s
0.2 % 2.5e+00 s Elapsed time so far: 0.7 s
0.2 % 2.8e+00 s Elapsed time so far: 0.7 s
0.2 % 3.0e+00 s Elapsed time so far: 0.7 s
0.2 % 3.3e+00 s Elapsed time so far: 0.7 s
0.2 % 3.7e+00 s Elapsed time so far: 0.7 s
0.3 % 4.0e+00 s Elapsed time so far: 0.7 s
0.3 % 4.4e+00 s Elapsed time so far: 0.7 s
0.3 % 4.9e+00 s Elapsed time so far: 0.8 s
0.4 % 5.4e+00 s Elapsed time so far: 0.8 s
0.4 % 5.9e+00 s Elapsed time so far: 0.8 s
0.4 % 6.5e+00 s Elapsed time so far: 0.8 s
0.5 % 7.2e+00 s Elapsed time so far: 0.8 s
0.5 % 7.9e+00 s Elapsed time so far: 0.8 s
0.6 % 8.7e+00 s Elapsed time so far: 0.8 s
0.6 % 9.5e+00 s Elapsed time so far: 0.8 s
0.7 % 1.1e+01 s Elapsed time so far: 0.9 s
0.8 % 1.2e+01 s Elapsed time so far: 0.9 s
0.8 % 1.3e+01 s Elapsed time so far: 0.9 s
0.9 % 1.4e+01 s Elapsed time so far: 0.9 s
1.0 % 1.5e+01 s Elapsed time so far: 0.9 s
1.1 % 1.7e+01 s Elapsed time so far: 0.9 s
1.2 % 1.9e+01 s Elapsed time so far: 0.9 s
1.4 % 2.0e+01 s Elapsed time so far: 0.9 s
1.5 % 2.3e+01 s Elapsed time so far: 0.9 s
1.6 % 2.5e+01 s Elapsed time so far: 1.0 s
1.8 % 2.7e+01 s Elapsed time so far: 1.0 s
2.0 % 3.0e+01 s Elapsed time so far: 1.0 s
2.2 % 3.3e+01 s Elapsed time so far: 1.0 s
2.4 % 3.6e+01 s Elapsed time so far: 1.0 s
2.7 % 4.0e+01 s Elapsed time so far: 1.0 s
2.9 % 4.4e+01 s Elapsed time so far: 1.0 s
3.2 % 4.8e+01 s Elapsed time so far: 1.0 s
3.5 % 5.3e+01 s Elapsed time so far: 1.1 s
3.9 % 5.8e+01 s Elapsed time so far: 1.1 s
4.2 % 6.3e+01 s Elapsed time so far: 1.1 s
4.5 % 6.8e+01 s Elapsed time so far: 1.1 s
4.9 % 7.3e+01 s Elapsed time so far: 1.1 s
5.2 % 7.8e+01 s Elapsed time so far: 1.1 s
5.5 % 8.3e+01 s Elapsed time so far: 1.1 s
5.9 % 8.8e+01 s Elapsed time so far: 1.2 s
6.2 % 9.3e+01 s Elapsed time so far: 1.2 s
6.5 % 9.8e+01 s Elapsed time so far: 1.2 s
6.9 % 1.0e+02 s Elapsed time so far: 1.2 s
7.2 % 1.1e+02 s Elapsed time so far: 1.2 s
7.5 % 1.1e+02 s Elapsed time so far: 1.2 s
7.9 % 1.2e+02 s Elapsed time so far: 1.2 s
8.2 % 1.2e+02 s Elapsed time so far: 1.2 s
8.5 % 1.3e+02 s Elapsed time so far: 1.3 s
8.9 % 1.3e+02 s Elapsed time so far: 1.3 s
9.2 % 1.4e+02 s Elapsed time so far: 1.3 s
9.5 % 1.4e+02 s Elapsed time so far: 1.3 s
9.9 % 1.5e+02 s Elapsed time so far: 1.3 s
10.2 % 1.5e+02 s Elapsed time so far: 1.3 s
10.5 % 1.6e+02 s Elapsed time so far: 1.4 s
10.9 % 1.6e+02 s Elapsed time so far: 1.4 s
11.2 % 1.7e+02 s Elapsed time so far: 1.4 s
11.5 % 1.7e+02 s Elapsed time so far: 1.4 s
11.9 % 1.8e+02 s Elapsed time so far: 1.4 s
12.2 % 1.8e+02 s Elapsed time so far: 1.4 s
12.5 % 1.9e+02 s Elapsed time so far: 1.4 s
12.9 % 1.9e+02 s Elapsed time so far: 1.5 s
13.2 % 2.0e+02 s Elapsed time so far: 1.5 s
13.5 % 2.0e+02 s Elapsed time so far: 1.5 s
13.9 % 2.1e+02 s Elapsed time so far: 1.5 s
14.2 % 2.1e+02 s Elapsed time so far: 1.5 s
14.5 % 2.2e+02 s Elapsed time so far: 1.5 s
14.9 % 2.2e+02 s Elapsed time so far: 1.5 s
15.2 % 2.3e+02 s Elapsed time so far: 1.6 s
15.5 % 2.3e+02 s Elapsed time so far: 1.6 s
15.9 % 2.4e+02 s Elapsed time so far: 1.6 s
16.2 % 2.4e+02 s Elapsed time so far: 1.6 s
16.5 % 2.5e+02 s Elapsed time so far: 1.6 s
16.9 % 2.5e+02 s Elapsed time so far: 1.6 s
17.2 % 2.6e+02 s Elapsed time so far: 1.6 s
17.5 % 2.6e+02 s Elapsed time so far: 1.7 s
17.9 % 2.7e+02 s Elapsed time so far: 1.7 s
18.2 % 2.7e+02 s Elapsed time so far: 1.7 s
18.5 % 2.8e+02 s Elapsed time so far: 1.7 s
18.9 % 2.8e+02 s Elapsed time so far: 1.7 s
19.2 % 2.9e+02 s Elapsed time so far: 1.7 s
19.5 % 2.9e+02 s Elapsed time so far: 1.8 s
19.9 % 3.0e+02 s Elapsed time so far: 1.8 s
20.2 % 3.0e+02 s Elapsed time so far: 1.8 s
20.5 % 3.1e+02 s Elapsed time so far: 1.8 s
20.9 % 3.1e+02 s Elapsed time so far: 1.8 s
21.2 % 3.2e+02 s Elapsed time so far: 1.8 s
21.5 % 3.2e+02 s Elapsed time so far: 1.8 s
21.9 % 3.3e+02 s Elapsed time so far: 1.9 s
22.2 % 3.3e+02 s Elapsed time so far: 1.9 s
22.5 % 3.4e+02 s Elapsed time so far: 1.9 s
22.9 % 3.4e+02 s Elapsed time so far: 1.9 s
23.2 % 3.5e+02 s Elapsed time so far: 1.9 s
23.5 % 3.5e+02 s Elapsed time so far: 1.9 s
23.9 % 3.6e+02 s Elapsed time so far: 1.9 s
24.2 % 3.6e+02 s Elapsed time so far: 2.0 s
24.5 % 3.7e+02 s Elapsed time so far: 2.0 s
24.9 % 3.7e+02 s Elapsed time so far: 2.0 s
25.2 % 3.8e+02 s Elapsed time so far: 2.0 s
25.5 % 3.8e+02 s Elapsed time so far: 2.0 s
25.9 % 3.9e+02 s Elapsed time so far: 2.0 s
26.2 % 3.9e+02 s Elapsed time so far: 2.0 s
26.5 % 4.0e+02 s Elapsed time so far: 2.1 s
26.9 % 4.0e+02 s Elapsed time so far: 2.1 s
27.2 % 4.1e+02 s Elapsed time so far: 2.1 s
27.5 % 4.1e+02 s Elapsed time so far: 2.1 s
27.9 % 4.2e+02 s Elapsed time so far: 2.1 s
28.2 % 4.2e+02 s Elapsed time so far: 2.1 s
28.5 % 4.3e+02 s Elapsed time so far: 2.1 s
28.9 % 4.3e+02 s Elapsed time so far: 2.2 s
29.2 % 4.4e+02 s Elapsed time so far: 2.2 s
29.5 % 4.4e+02 s Elapsed time so far: 2.2 s
29.9 % 4.5e+02 s Elapsed time so far: 2.2 s
30.2 % 4.5e+02 s Elapsed time so far: 2.2 s
30.5 % 4.6e+02 s Elapsed time so far: 2.2 s
30.9 % 4.6e+02 s Elapsed time so far: 2.2 s
31.2 % 4.7e+02 s Elapsed time so far: 2.3 s
31.5 % 4.7e+02 s Elapsed time so far: 2.3 s
31.9 % 4.8e+02 s Elapsed time so far: 2.3 s
32.2 % 4.8e+02 s Elapsed time so far: 2.3 s
32.5 % 4.9e+02 s Elapsed time so far: 2.3 s
32.9 % 4.9e+02 s Elapsed time so far: 2.3 s
33.2 % 5.0e+02 s Elapsed time so far: 2.3 s
33.5 % 5.0e+02 s Elapsed time so far: 2.4 s
33.9 % 5.1e+02 s Elapsed time so far: 2.4 s
34.2 % 5.1e+02 s Elapsed time so far: 2.4 s
34.5 % 5.2e+02 s Elapsed time so far: 2.4 s
34.9 % 5.2e+02 s Elapsed time so far: 2.4 s
35.2 % 5.3e+02 s Elapsed time so far: 2.4 s
35.5 % 5.3e+02 s Elapsed time so far: 2.4 s
35.9 % 5.4e+02 s Elapsed time so far: 2.5 s
36.2 % 5.4e+02 s Elapsed time so far: 2.5 s
36.5 % 5.5e+02 s Elapsed time so far: 2.5 s
36.9 % 5.5e+02 s Elapsed time so far: 2.5 s
37.2 % 5.6e+02 s Elapsed time so far: 2.5 s
37.5 % 5.6e+02 s Elapsed time so far: 2.5 s
37.9 % 5.7e+02 s Elapsed time so far: 2.6 s
38.2 % 5.7e+02 s Elapsed time so far: 2.6 s
38.5 % 5.8e+02 s Elapsed time so far: 2.6 s
38.9 % 5.8e+02 s Elapsed time so far: 2.6 s
39.2 % 5.9e+02 s Elapsed time so far: 2.6 s
39.5 % 5.9e+02 s Elapsed time so far: 2.6 s
39.9 % 6.0e+02 s Elapsed time so far: 2.6 s
40.2 % 6.0e+02 s Elapsed time so far: 2.7 s
40.5 % 6.1e+02 s Elapsed time so far: 2.7 s
40.9 % 6.1e+02 s Elapsed time so far: 2.7 s
41.2 % 6.2e+02 s Elapsed time so far: 2.7 s
41.5 % 6.2e+02 s Elapsed time so far: 2.7 s
41.9 % 6.3e+02 s Elapsed time so far: 2.7 s
42.2 % 6.3e+02 s Elapsed time so far: 2.7 s
42.5 % 6.4e+02 s Elapsed time so far: 2.8 s
42.9 % 6.4e+02 s Elapsed time so far: 2.8 s
43.2 % 6.5e+02 s Elapsed time so far: 2.8 s
43.5 % 6.5e+02 s Elapsed time so far: 2.8 s
43.9 % 6.6e+02 s Elapsed time so far: 2.8 s
44.2 % 6.6e+02 s Elapsed time so far: 2.8 s
44.5 % 6.7e+02 s Elapsed time so far: 2.8 s
44.9 % 6.7e+02 s Elapsed time so far: 2.9 s
45.2 % 6.8e+02 s Elapsed time so far: 2.9 s
45.5 % 6.8e+02 s Elapsed time so far: 2.9 s
45.9 % 6.9e+02 s Elapsed time so far: 2.9 s
46.2 % 6.9e+02 s Elapsed time so far: 2.9 s
46.5 % 7.0e+02 s Elapsed time so far: 2.9 s
46.9 % 7.0e+02 s Elapsed time so far: 2.9 s
47.2 % 7.1e+02 s Elapsed time so far: 3.0 s
47.5 % 7.1e+02 s Elapsed time so far: 3.0 s
47.9 % 7.2e+02 s Elapsed time so far: 3.0 s
48.2 % 7.2e+02 s Elapsed time so far: 3.0 s
48.5 % 7.3e+02 s Elapsed time so far: 3.0 s
48.9 % 7.3e+02 s Elapsed time so far: 3.0 s
49.2 % 7.4e+02 s Elapsed time so far: 3.0 s
49.5 % 7.4e+02 s Elapsed time so far: 3.1 s
49.9 % 7.5e+02 s Elapsed time so far: 3.1 s
50.2 % 7.5e+02 s Elapsed time so far: 3.1 s
50.5 % 7.6e+02 s Elapsed time so far: 3.1 s
50.9 % 7.6e+02 s Elapsed time so far: 3.1 s
51.2 % 7.7e+02 s Elapsed time so far: 3.1 s
51.5 % 7.7e+02 s Elapsed time so far: 3.1 s
51.9 % 7.8e+02 s Elapsed time so far: 3.2 s
52.2 % 7.8e+02 s Elapsed time so far: 3.2 s
52.5 % 7.9e+02 s Elapsed time so far: 3.2 s
52.9 % 7.9e+02 s Elapsed time so far: 3.2 s
53.2 % 8.0e+02 s Elapsed time so far: 3.2 s
53.5 % 8.0e+02 s Elapsed time so far: 3.2 s
53.9 % 8.1e+02 s Elapsed time so far: 3.2 s
54.2 % 8.1e+02 s Elapsed time so far: 3.3 s
54.5 % 8.2e+02 s Elapsed time so far: 3.3 s
54.9 % 8.2e+02 s Elapsed time so far: 3.3 s
55.2 % 8.3e+02 s Elapsed time so far: 3.3 s
55.5 % 8.3e+02 s Elapsed time so far: 3.3 s
55.9 % 8.4e+02 s Elapsed time so far: 3.3 s
56.2 % 8.4e+02 s Elapsed time so far: 3.3 s
56.5 % 8.5e+02 s Elapsed time so far: 3.4 s
56.9 % 8.5e+02 s Elapsed time so far: 3.4 s
57.2 % 8.6e+02 s Elapsed time so far: 3.4 s
57.5 % 8.6e+02 s Elapsed time so far: 3.4 s
57.9 % 8.7e+02 s Elapsed time so far: 3.4 s
58.2 % 8.7e+02 s Elapsed time so far: 3.4 s
58.5 % 8.8e+02 s Elapsed time so far: 3.4 s
58.9 % 8.8e+02 s Elapsed time so far: 3.5 s
59.2 % 8.9e+02 s Elapsed time so far: 3.5 s
59.5 % 8.9e+02 s Elapsed time so far: 3.5 s
59.9 % 9.0e+02 s Elapsed time so far: 3.5 s
60.2 % 9.0e+02 s Elapsed time so far: 3.5 s
60.5 % 9.1e+02 s Elapsed time so far: 3.5 s
60.9 % 9.1e+02 s Elapsed time so far: 3.6 s
61.2 % 9.2e+02 s Elapsed time so far: 3.6 s
61.5 % 9.2e+02 s Elapsed time so far: 3.6 s
61.9 % 9.3e+02 s Elapsed time so far: 3.6 s
62.2 % 9.3e+02 s Elapsed time so far: 3.6 s
62.5 % 9.4e+02 s Elapsed time so far: 3.6 s
62.9 % 9.4e+02 s Elapsed time so far: 3.6 s
63.2 % 9.5e+02 s Elapsed time so far: 3.7 s
63.5 % 9.5e+02 s Elapsed time so far: 3.7 s
63.9 % 9.6e+02 s Elapsed time so far: 3.7 s
64.2 % 9.6e+02 s Elapsed time so far: 3.7 s
64.5 % 9.7e+02 s Elapsed time so far: 3.7 s
64.9 % 9.7e+02 s Elapsed time so far: 3.7 s
65.2 % 9.8e+02 s Elapsed time so far: 3.7 s
65.5 % 9.8e+02 s Elapsed time so far: 3.8 s
65.9 % 9.9e+02 s Elapsed time so far: 3.8 s
66.2 % 9.9e+02 s Elapsed time so far: 3.8 s
66.5 % 1.0e+03 s Elapsed time so far: 3.8 s
66.9 % 1.0e+03 s Elapsed time so far: 3.8 s
67.2 % 1.0e+03 s Elapsed time so far: 3.8 s
67.5 % 1.0e+03 s Elapsed time so far: 3.8 s
67.9 % 1.0e+03 s Elapsed time so far: 3.9 s
68.2 % 1.0e+03 s Elapsed time so far: 3.9 s
68.5 % 1.0e+03 s Elapsed time so far: 3.9 s
68.9 % 1.0e+03 s Elapsed time so far: 3.9 s
69.2 % 1.0e+03 s Elapsed time so far: 3.9 s
69.5 % 1.0e+03 s Elapsed time so far: 3.9 s
69.9 % 1.0e+03 s Elapsed time so far: 3.9 s
70.2 % 1.1e+03 s Elapsed time so far: 4.0 s
70.5 % 1.1e+03 s Elapsed time so far: 4.0 s
70.9 % 1.1e+03 s Elapsed time so far: 4.0 s
71.2 % 1.1e+03 s Elapsed time so far: 4.0 s
71.5 % 1.1e+03 s Elapsed time so far: 4.0 s
71.9 % 1.1e+03 s Elapsed time so far: 4.0 s
72.2 % 1.1e+03 s Elapsed time so far: 4.0 s
72.5 % 1.1e+03 s Elapsed time so far: 4.1 s
72.9 % 1.1e+03 s Elapsed time so far: 4.1 s
73.2 % 1.1e+03 s Elapsed time so far: 4.1 s
73.5 % 1.1e+03 s Elapsed time so far: 4.1 s
73.9 % 1.1e+03 s Elapsed time so far: 4.1 s
74.2 % 1.1e+03 s Elapsed time so far: 4.1 s
74.5 % 1.1e+03 s Elapsed time so far: 4.2 s
74.9 % 1.1e+03 s Elapsed time so far: 4.2 s
75.2 % 1.1e+03 s Elapsed time so far: 4.2 s
75.5 % 1.1e+03 s Elapsed time so far: 4.2 s
75.9 % 1.1e+03 s Elapsed time so far: 4.2 s
76.2 % 1.1e+03 s Elapsed time so far: 4.2 s
76.5 % 1.1e+03 s Elapsed time so far: 4.2 s
76.9 % 1.2e+03 s Elapsed time so far: 4.2 s
77.2 % 1.2e+03 s Elapsed time so far: 4.3 s
77.5 % 1.2e+03 s Elapsed time so far: 4.3 s
77.9 % 1.2e+03 s Elapsed time so far: 4.3 s
78.2 % 1.2e+03 s Elapsed time so far: 4.3 s
78.5 % 1.2e+03 s Elapsed time so far: 4.3 s
78.9 % 1.2e+03 s Elapsed time so far: 4.3 s
79.2 % 1.2e+03 s Elapsed time so far: 4.4 s
79.5 % 1.2e+03 s Elapsed time so far: 4.4 s
79.9 % 1.2e+03 s Elapsed time so far: 4.4 s
80.2 % 1.2e+03 s Elapsed time so far: 4.4 s
80.5 % 1.2e+03 s Elapsed time so far: 4.4 s
80.9 % 1.2e+03 s Elapsed time so far: 4.4 s
81.2 % 1.2e+03 s Elapsed time so far: 4.4 s
81.5 % 1.2e+03 s Elapsed time so far: 4.5 s
81.9 % 1.2e+03 s Elapsed time so far: 4.5 s
82.2 % 1.2e+03 s Elapsed time so far: 4.5 s
82.5 % 1.2e+03 s Elapsed time so far: 4.5 s
82.9 % 1.2e+03 s Elapsed time so far: 4.5 s
83.2 % 1.2e+03 s Elapsed time so far: 4.5 s
83.5 % 1.3e+03 s Elapsed time so far: 4.5 s
83.9 % 1.3e+03 s Elapsed time so far: 4.6 s
84.2 % 1.3e+03 s Elapsed time so far: 4.6 s
84.5 % 1.3e+03 s Elapsed time so far: 4.6 s
84.9 % 1.3e+03 s Elapsed time so far: 4.6 s
85.2 % 1.3e+03 s Elapsed time so far: 4.6 s
85.5 % 1.3e+03 s Elapsed time so far: 4.6 s
85.9 % 1.3e+03 s Elapsed time so far: 4.6 s
86.2 % 1.3e+03 s Elapsed time so far: 4.7 s
86.5 % 1.3e+03 s Elapsed time so far: 4.7 s
86.9 % 1.3e+03 s Elapsed time so far: 4.7 s
87.2 % 1.3e+03 s Elapsed time so far: 4.7 s
87.5 % 1.3e+03 s Elapsed time so far: 4.7 s
87.9 % 1.3e+03 s Elapsed time so far: 4.7 s
88.2 % 1.3e+03 s Elapsed time so far: 4.7 s
88.5 % 1.3e+03 s Elapsed time so far: 4.8 s
88.9 % 1.3e+03 s Elapsed time so far: 4.8 s
89.2 % 1.3e+03 s Elapsed time so far: 4.8 s
89.5 % 1.3e+03 s Elapsed time so far: 4.8 s
89.9 % 1.3e+03 s Elapsed time so far: 4.8 s
90.2 % 1.4e+03 s Elapsed time so far: 4.8 s
90.5 % 1.4e+03 s Elapsed time so far: 4.9 s
90.9 % 1.4e+03 s Elapsed time so far: 4.9 s
91.2 % 1.4e+03 s Elapsed time so far: 4.9 s
91.5 % 1.4e+03 s Elapsed time so far: 4.9 s
91.9 % 1.4e+03 s Elapsed time so far: 4.9 s
92.2 % 1.4e+03 s Elapsed time so far: 4.9 s
92.5 % 1.4e+03 s Elapsed time so far: 4.9 s
92.9 % 1.4e+03 s Elapsed time so far: 5.0 s
93.2 % 1.4e+03 s Elapsed time so far: 5.0 s
93.5 % 1.4e+03 s Elapsed time so far: 5.0 s
93.9 % 1.4e+03 s Elapsed time so far: 5.0 s
94.2 % 1.4e+03 s Elapsed time so far: 5.0 s
94.5 % 1.4e+03 s Elapsed time so far: 5.0 s
94.9 % 1.4e+03 s Elapsed time so far: 5.0 s
95.2 % 1.4e+03 s Elapsed time so far: 5.1 s
95.5 % 1.4e+03 s Elapsed time so far: 5.1 s
95.9 % 1.4e+03 s Elapsed time so far: 5.1 s
96.2 % 1.4e+03 s Elapsed time so far: 5.1 s
96.5 % 1.4e+03 s Elapsed time so far: 5.1 s
96.9 % 1.5e+03 s Elapsed time so far: 5.1 s
97.2 % 1.5e+03 s Elapsed time so far: 5.1 s
97.5 % 1.5e+03 s Elapsed time so far: 5.2 s
97.9 % 1.5e+03 s Elapsed time so far: 5.2 s
98.2 % 1.5e+03 s Elapsed time so far: 5.2 s
98.5 % 1.5e+03 s Elapsed time so far: 5.2 s
98.9 % 1.5e+03 s Elapsed time so far: 5.2 s
99.2 % 1.5e+03 s Elapsed time so far: 5.2 s
99.5 % 1.5e+03 s Elapsed time so far: 5.2 s
99.9 % 1.5e+03 s Elapsed time so far: 5.2 s
100.0 % 1.5e+03 s Elapsed time so far: 5.3 s
Defining initial values
Defining variational problem
Defining source terms
Defining boundary conditions
Time stepping...
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0.0 % 2.1e-02 s Elapsed time so far: 0.1 s
0.0 % 2.5e-02 s Elapsed time so far: 0.2 s
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0.0 % 3.2e-02 s Elapsed time so far: 0.2 s
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0.0 % 4.1e-02 s Elapsed time so far: 0.2 s
0.0 % 4.6e-02 s Elapsed time so far: 0.2 s
0.0 % 5.1e-02 s Elapsed time so far: 0.2 s
0.0 % 5.7e-02 s Elapsed time so far: 0.2 s
0.0 % 6.4e-02 s Elapsed time so far: 0.2 s
0.0 % 7.1e-02 s Elapsed time so far: 0.3 s
0.0 % 8.0e-02 s Elapsed time so far: 0.3 s
0.0 % 8.8e-02 s Elapsed time so far: 0.3 s
0.0 % 9.8e-02 s Elapsed time so far: 0.3 s
0.0 % 1.1e-01 s Elapsed time so far: 0.3 s
0.0 % 1.2e-01 s Elapsed time so far: 0.3 s
0.0 % 1.3e-01 s Elapsed time so far: 0.3 s
0.0 % 1.5e-01 s Elapsed time so far: 0.3 s
0.0 % 1.6e-01 s Elapsed time so far: 0.4 s
0.0 % 1.8e-01 s Elapsed time so far: 0.4 s
0.0 % 2.0e-01 s Elapsed time so far: 0.4 s
0.0 % 2.2e-01 s Elapsed time so far: 0.4 s
0.0 % 2.5e-01 s Elapsed time so far: 0.4 s
0.0 % 2.7e-01 s Elapsed time so far: 0.4 s
0.0 % 3.0e-01 s Elapsed time so far: 0.4 s
0.0 % 3.3e-01 s Elapsed time so far: 0.4 s
0.0 % 3.6e-01 s Elapsed time so far: 0.5 s
0.0 % 4.0e-01 s Elapsed time so far: 0.5 s
0.0 % 4.4e-01 s Elapsed time so far: 0.5 s
0.0 % 4.9e-01 s Elapsed time so far: 0.5 s
0.0 % 5.4e-01 s Elapsed time so far: 0.5 s
0.0 % 5.9e-01 s Elapsed time so far: 0.5 s
0.0 % 6.5e-01 s Elapsed time so far: 0.5 s
0.1 % 7.2e-01 s Elapsed time so far: 0.5 s
0.1 % 7.9e-01 s Elapsed time so far: 0.5 s
0.1 % 8.7e-01 s Elapsed time so far: 0.6 s
0.1 % 9.6e-01 s Elapsed time so far: 0.6 s
0.1 % 1.1e+00 s Elapsed time so far: 0.6 s
0.1 % 1.2e+00 s Elapsed time so far: 0.6 s
0.1 % 1.3e+00 s Elapsed time so far: 0.6 s
0.1 % 1.4e+00 s Elapsed time so far: 0.6 s
0.1 % 1.6e+00 s Elapsed time so far: 0.6 s
0.1 % 1.7e+00 s Elapsed time so far: 0.6 s
0.1 % 1.9e+00 s Elapsed time so far: 0.6 s
0.1 % 2.1e+00 s Elapsed time so far: 0.7 s
0.1 % 2.3e+00 s Elapsed time so far: 0.7 s
0.2 % 2.5e+00 s Elapsed time so far: 0.7 s
0.2 % 2.8e+00 s Elapsed time so far: 0.7 s
0.2 % 3.0e+00 s Elapsed time so far: 0.7 s
0.2 % 3.3e+00 s Elapsed time so far: 0.7 s
0.2 % 3.7e+00 s Elapsed time so far: 0.7 s
0.3 % 4.0e+00 s Elapsed time so far: 0.7 s
0.3 % 4.4e+00 s Elapsed time so far: 0.8 s
0.3 % 4.9e+00 s Elapsed time so far: 0.8 s
0.4 % 5.4e+00 s Elapsed time so far: 0.8 s
0.4 % 5.9e+00 s Elapsed time so far: 0.8 s
0.4 % 6.5e+00 s Elapsed time so far: 0.8 s
0.5 % 7.2e+00 s Elapsed time so far: 0.8 s
0.5 % 7.9e+00 s Elapsed time so far: 0.8 s
0.6 % 8.7e+00 s Elapsed time so far: 0.8 s
0.6 % 9.5e+00 s Elapsed time so far: 0.9 s
0.7 % 1.1e+01 s Elapsed time so far: 0.9 s
0.8 % 1.2e+01 s Elapsed time so far: 0.9 s
0.8 % 1.3e+01 s Elapsed time so far: 0.9 s
0.9 % 1.4e+01 s Elapsed time so far: 0.9 s
1.0 % 1.5e+01 s Elapsed time so far: 0.9 s
1.1 % 1.7e+01 s Elapsed time so far: 0.9 s
1.2 % 1.9e+01 s Elapsed time so far: 1.0 s
1.4 % 2.0e+01 s Elapsed time so far: 1.0 s
1.5 % 2.3e+01 s Elapsed time so far: 1.0 s
1.6 % 2.5e+01 s Elapsed time so far: 1.0 s
1.8 % 2.7e+01 s Elapsed time so far: 1.0 s
2.0 % 3.0e+01 s Elapsed time so far: 1.0 s
2.2 % 3.3e+01 s Elapsed time so far: 1.0 s
2.4 % 3.6e+01 s Elapsed time so far: 1.1 s
2.7 % 4.0e+01 s Elapsed time so far: 1.1 s
2.9 % 4.4e+01 s Elapsed time so far: 1.1 s
3.2 % 4.8e+01 s Elapsed time so far: 1.1 s
3.5 % 5.3e+01 s Elapsed time so far: 1.1 s
3.9 % 5.8e+01 s Elapsed time so far: 1.1 s
4.2 % 6.3e+01 s Elapsed time so far: 1.1 s
4.5 % 6.8e+01 s Elapsed time so far: 1.2 s
4.9 % 7.3e+01 s Elapsed time so far: 1.2 s
5.2 % 7.8e+01 s Elapsed time so far: 1.2 s
5.5 % 8.3e+01 s Elapsed time so far: 1.2 s
5.9 % 8.8e+01 s Elapsed time so far: 1.2 s
6.2 % 9.3e+01 s Elapsed time so far: 1.2 s
6.5 % 9.8e+01 s Elapsed time so far: 1.2 s
6.9 % 1.0e+02 s Elapsed time so far: 1.2 s
7.2 % 1.1e+02 s Elapsed time so far: 1.3 s
7.5 % 1.1e+02 s Elapsed time so far: 1.3 s
7.9 % 1.2e+02 s Elapsed time so far: 1.3 s
8.2 % 1.2e+02 s Elapsed time so far: 1.3 s
8.5 % 1.3e+02 s Elapsed time so far: 1.3 s
8.9 % 1.3e+02 s Elapsed time so far: 1.3 s
9.2 % 1.4e+02 s Elapsed time so far: 1.4 s
9.5 % 1.4e+02 s Elapsed time so far: 1.4 s
9.9 % 1.5e+02 s Elapsed time so far: 1.4 s
10.2 % 1.5e+02 s Elapsed time so far: 1.4 s
10.5 % 1.6e+02 s Elapsed time so far: 1.4 s
10.9 % 1.6e+02 s Elapsed time so far: 1.4 s
11.2 % 1.7e+02 s Elapsed time so far: 1.4 s
11.5 % 1.7e+02 s Elapsed time so far: 1.5 s
11.9 % 1.8e+02 s Elapsed time so far: 1.5 s
12.2 % 1.8e+02 s Elapsed time so far: 1.5 s
12.5 % 1.9e+02 s Elapsed time so far: 1.5 s
12.9 % 1.9e+02 s Elapsed time so far: 1.5 s
13.2 % 2.0e+02 s Elapsed time so far: 1.5 s
13.5 % 2.0e+02 s Elapsed time so far: 1.5 s
13.9 % 2.1e+02 s Elapsed time so far: 1.6 s
14.2 % 2.1e+02 s Elapsed time so far: 1.6 s
14.5 % 2.2e+02 s Elapsed time so far: 1.6 s
14.9 % 2.2e+02 s Elapsed time so far: 1.6 s
15.2 % 2.3e+02 s Elapsed time so far: 1.6 s
15.5 % 2.3e+02 s Elapsed time so far: 1.6 s
15.9 % 2.4e+02 s Elapsed time so far: 1.6 s
16.2 % 2.4e+02 s Elapsed time so far: 1.7 s
16.5 % 2.5e+02 s Elapsed time so far: 1.7 s
16.9 % 2.5e+02 s Elapsed time so far: 1.7 s
17.2 % 2.6e+02 s Elapsed time so far: 1.7 s
17.5 % 2.6e+02 s Elapsed time so far: 1.7 s
17.9 % 2.7e+02 s Elapsed time so far: 1.7 s
18.2 % 2.7e+02 s Elapsed time so far: 1.7 s
18.5 % 2.8e+02 s Elapsed time so far: 1.8 s
18.9 % 2.8e+02 s Elapsed time so far: 1.8 s
19.2 % 2.9e+02 s Elapsed time so far: 1.8 s
19.5 % 2.9e+02 s Elapsed time so far: 1.8 s
19.9 % 3.0e+02 s Elapsed time so far: 1.8 s
20.2 % 3.0e+02 s Elapsed time so far: 1.8 s
20.5 % 3.1e+02 s Elapsed time so far: 1.8 s
20.9 % 3.1e+02 s Elapsed time so far: 1.9 s
21.2 % 3.2e+02 s Elapsed time so far: 1.9 s
21.5 % 3.2e+02 s Elapsed time so far: 1.9 s
21.9 % 3.3e+02 s Elapsed time so far: 1.9 s
22.2 % 3.3e+02 s Elapsed time so far: 1.9 s
22.5 % 3.4e+02 s Elapsed time so far: 1.9 s
22.9 % 3.4e+02 s Elapsed time so far: 1.9 s
23.2 % 3.5e+02 s Elapsed time so far: 2.0 s
23.5 % 3.5e+02 s Elapsed time so far: 2.0 s
23.9 % 3.6e+02 s Elapsed time so far: 2.0 s
24.2 % 3.6e+02 s Elapsed time so far: 2.0 s
24.5 % 3.7e+02 s Elapsed time so far: 2.0 s
24.9 % 3.7e+02 s Elapsed time so far: 2.0 s
25.2 % 3.8e+02 s Elapsed time so far: 2.1 s
25.5 % 3.8e+02 s Elapsed time so far: 2.1 s
25.9 % 3.9e+02 s Elapsed time so far: 2.1 s
26.2 % 3.9e+02 s Elapsed time so far: 2.1 s
26.5 % 4.0e+02 s Elapsed time so far: 2.1 s
26.9 % 4.0e+02 s Elapsed time so far: 2.1 s
27.2 % 4.1e+02 s Elapsed time so far: 2.1 s
27.5 % 4.1e+02 s Elapsed time so far: 2.2 s
27.9 % 4.2e+02 s Elapsed time so far: 2.2 s
28.2 % 4.2e+02 s Elapsed time so far: 2.2 s
28.5 % 4.3e+02 s Elapsed time so far: 2.2 s
28.9 % 4.3e+02 s Elapsed time so far: 2.2 s
29.2 % 4.4e+02 s Elapsed time so far: 2.2 s
29.5 % 4.4e+02 s Elapsed time so far: 2.2 s
29.9 % 4.5e+02 s Elapsed time so far: 2.2 s
30.2 % 4.5e+02 s Elapsed time so far: 2.3 s
30.5 % 4.6e+02 s Elapsed time so far: 2.3 s
30.9 % 4.6e+02 s Elapsed time so far: 2.3 s
31.2 % 4.7e+02 s Elapsed time so far: 2.3 s
31.5 % 4.7e+02 s Elapsed time so far: 2.3 s
31.9 % 4.8e+02 s Elapsed time so far: 2.3 s
32.2 % 4.8e+02 s Elapsed time so far: 2.4 s
32.5 % 4.9e+02 s Elapsed time so far: 2.4 s
32.9 % 4.9e+02 s Elapsed time so far: 2.4 s
33.2 % 5.0e+02 s Elapsed time so far: 2.4 s
33.5 % 5.0e+02 s Elapsed time so far: 2.4 s
33.9 % 5.1e+02 s Elapsed time so far: 2.4 s
34.2 % 5.1e+02 s Elapsed time so far: 2.4 s
34.5 % 5.2e+02 s Elapsed time so far: 2.5 s
34.9 % 5.2e+02 s Elapsed time so far: 2.5 s
35.2 % 5.3e+02 s Elapsed time so far: 2.5 s
35.5 % 5.3e+02 s Elapsed time so far: 2.5 s
35.9 % 5.4e+02 s Elapsed time so far: 2.5 s
36.2 % 5.4e+02 s Elapsed time so far: 2.5 s
36.5 % 5.5e+02 s Elapsed time so far: 2.5 s
36.9 % 5.5e+02 s Elapsed time so far: 2.6 s
37.2 % 5.6e+02 s Elapsed time so far: 2.6 s
37.5 % 5.6e+02 s Elapsed time so far: 2.6 s
37.9 % 5.7e+02 s Elapsed time so far: 2.6 s
38.2 % 5.7e+02 s Elapsed time so far: 2.6 s
38.5 % 5.8e+02 s Elapsed time so far: 2.6 s
38.9 % 5.8e+02 s Elapsed time so far: 2.6 s
39.2 % 5.9e+02 s Elapsed time so far: 2.7 s
39.5 % 5.9e+02 s Elapsed time so far: 2.7 s
39.9 % 6.0e+02 s Elapsed time so far: 2.7 s
40.2 % 6.0e+02 s Elapsed time so far: 2.7 s
40.5 % 6.1e+02 s Elapsed time so far: 2.7 s
40.9 % 6.1e+02 s Elapsed time so far: 2.7 s
41.2 % 6.2e+02 s Elapsed time so far: 2.7 s
41.5 % 6.2e+02 s Elapsed time so far: 2.8 s
41.9 % 6.3e+02 s Elapsed time so far: 2.8 s
42.2 % 6.3e+02 s Elapsed time so far: 2.8 s
42.5 % 6.4e+02 s Elapsed time so far: 2.8 s
42.9 % 6.4e+02 s Elapsed time so far: 2.8 s
43.2 % 6.5e+02 s Elapsed time so far: 2.8 s
43.5 % 6.5e+02 s Elapsed time so far: 2.8 s
43.9 % 6.6e+02 s Elapsed time so far: 2.9 s
44.2 % 6.6e+02 s Elapsed time so far: 2.9 s
44.5 % 6.7e+02 s Elapsed time so far: 2.9 s
44.9 % 6.7e+02 s Elapsed time so far: 2.9 s
45.2 % 6.8e+02 s Elapsed time so far: 2.9 s
45.5 % 6.8e+02 s Elapsed time so far: 2.9 s
45.9 % 6.9e+02 s Elapsed time so far: 2.9 s
46.2 % 6.9e+02 s Elapsed time so far: 3.0 s
46.5 % 7.0e+02 s Elapsed time so far: 3.0 s
46.9 % 7.0e+02 s Elapsed time so far: 3.0 s
47.2 % 7.1e+02 s Elapsed time so far: 3.0 s
47.5 % 7.1e+02 s Elapsed time so far: 3.0 s
47.9 % 7.2e+02 s Elapsed time so far: 3.0 s
48.2 % 7.2e+02 s Elapsed time so far: 3.0 s
48.5 % 7.3e+02 s Elapsed time so far: 3.1 s
48.9 % 7.3e+02 s Elapsed time so far: 3.1 s
49.2 % 7.4e+02 s Elapsed time so far: 3.1 s
49.5 % 7.4e+02 s Elapsed time so far: 3.1 s
49.9 % 7.5e+02 s Elapsed time so far: 3.1 s
50.2 % 7.5e+02 s Elapsed time so far: 3.1 s
50.5 % 7.6e+02 s Elapsed time so far: 3.1 s
50.9 % 7.6e+02 s Elapsed time so far: 3.2 s
51.2 % 7.7e+02 s Elapsed time so far: 3.2 s
51.5 % 7.7e+02 s Elapsed time so far: 3.2 s
51.9 % 7.8e+02 s Elapsed time so far: 3.2 s
52.2 % 7.8e+02 s Elapsed time so far: 3.2 s
52.5 % 7.9e+02 s Elapsed time so far: 3.2 s
52.9 % 7.9e+02 s Elapsed time so far: 3.2 s
53.2 % 8.0e+02 s Elapsed time so far: 3.3 s
53.5 % 8.0e+02 s Elapsed time so far: 3.3 s
53.9 % 8.1e+02 s Elapsed time so far: 3.3 s
54.2 % 8.1e+02 s Elapsed time so far: 3.3 s
54.5 % 8.2e+02 s Elapsed time so far: 3.3 s
54.9 % 8.2e+02 s Elapsed time so far: 3.3 s
55.2 % 8.3e+02 s Elapsed time so far: 3.4 s
55.5 % 8.3e+02 s Elapsed time so far: 3.4 s
55.9 % 8.4e+02 s Elapsed time so far: 3.4 s
56.2 % 8.4e+02 s Elapsed time so far: 3.4 s
56.5 % 8.5e+02 s Elapsed time so far: 3.4 s
56.9 % 8.5e+02 s Elapsed time so far: 3.4 s
57.2 % 8.6e+02 s Elapsed time so far: 3.4 s
57.5 % 8.6e+02 s Elapsed time so far: 3.5 s
57.9 % 8.7e+02 s Elapsed time so far: 3.5 s
58.2 % 8.7e+02 s Elapsed time so far: 3.5 s
58.5 % 8.8e+02 s Elapsed time so far: 3.5 s
58.9 % 8.8e+02 s Elapsed time so far: 3.5 s
59.2 % 8.9e+02 s Elapsed time so far: 3.5 s
59.5 % 8.9e+02 s Elapsed time so far: 3.5 s
59.9 % 9.0e+02 s Elapsed time so far: 3.5 s
60.2 % 9.0e+02 s Elapsed time so far: 3.6 s
60.5 % 9.1e+02 s Elapsed time so far: 3.6 s
60.9 % 9.1e+02 s Elapsed time so far: 3.6 s
61.2 % 9.2e+02 s Elapsed time so far: 3.6 s
61.5 % 9.2e+02 s Elapsed time so far: 3.6 s
61.9 % 9.3e+02 s Elapsed time so far: 3.6 s
62.2 % 9.3e+02 s Elapsed time so far: 3.6 s
62.5 % 9.4e+02 s Elapsed time so far: 3.6 s
62.9 % 9.4e+02 s Elapsed time so far: 3.7 s
63.2 % 9.5e+02 s Elapsed time so far: 3.7 s
63.5 % 9.5e+02 s Elapsed time so far: 3.7 s
63.9 % 9.6e+02 s Elapsed time so far: 3.7 s
64.2 % 9.6e+02 s Elapsed time so far: 3.7 s
64.5 % 9.7e+02 s Elapsed time so far: 3.7 s
64.9 % 9.7e+02 s Elapsed time so far: 3.7 s
65.2 % 9.8e+02 s Elapsed time so far: 3.7 s
65.5 % 9.8e+02 s Elapsed time so far: 3.7 s
65.9 % 9.9e+02 s Elapsed time so far: 3.8 s
66.2 % 9.9e+02 s Elapsed time so far: 3.8 s
66.5 % 1.0e+03 s Elapsed time so far: 3.8 s
66.9 % 1.0e+03 s Elapsed time so far: 3.8 s
67.2 % 1.0e+03 s Elapsed time so far: 3.8 s
67.5 % 1.0e+03 s Elapsed time so far: 3.8 s
67.9 % 1.0e+03 s Elapsed time so far: 3.8 s
68.2 % 1.0e+03 s Elapsed time so far: 3.8 s
68.5 % 1.0e+03 s Elapsed time so far: 3.8 s
68.9 % 1.0e+03 s Elapsed time so far: 3.9 s
69.2 % 1.0e+03 s Elapsed time so far: 3.9 s
69.5 % 1.0e+03 s Elapsed time so far: 3.9 s
69.9 % 1.0e+03 s Elapsed time so far: 3.9 s
70.2 % 1.1e+03 s Elapsed time so far: 3.9 s
70.5 % 1.1e+03 s Elapsed time so far: 3.9 s
70.9 % 1.1e+03 s Elapsed time so far: 3.9 s
71.2 % 1.1e+03 s Elapsed time so far: 3.9 s
71.5 % 1.1e+03 s Elapsed time so far: 4.0 s
71.9 % 1.1e+03 s Elapsed time so far: 4.0 s
72.2 % 1.1e+03 s Elapsed time so far: 4.0 s
72.5 % 1.1e+03 s Elapsed time so far: 4.0 s
72.9 % 1.1e+03 s Elapsed time so far: 4.0 s
73.2 % 1.1e+03 s Elapsed time so far: 4.0 s
73.5 % 1.1e+03 s Elapsed time so far: 4.0 s
73.9 % 1.1e+03 s Elapsed time so far: 4.0 s
74.2 % 1.1e+03 s Elapsed time so far: 4.0 s
74.5 % 1.1e+03 s Elapsed time so far: 4.0 s
74.9 % 1.1e+03 s Elapsed time so far: 4.1 s
75.2 % 1.1e+03 s Elapsed time so far: 4.1 s
75.5 % 1.1e+03 s Elapsed time so far: 4.1 s
75.9 % 1.1e+03 s Elapsed time so far: 4.1 s
76.2 % 1.1e+03 s Elapsed time so far: 4.1 s
76.5 % 1.1e+03 s Elapsed time so far: 4.1 s
76.9 % 1.2e+03 s Elapsed time so far: 4.1 s
77.2 % 1.2e+03 s Elapsed time so far: 4.2 s
77.5 % 1.2e+03 s Elapsed time so far: 4.2 s
77.9 % 1.2e+03 s Elapsed time so far: 4.2 s
78.2 % 1.2e+03 s Elapsed time so far: 4.2 s
78.5 % 1.2e+03 s Elapsed time so far: 4.2 s
78.9 % 1.2e+03 s Elapsed time so far: 4.2 s
79.2 % 1.2e+03 s Elapsed time so far: 4.2 s
79.5 % 1.2e+03 s Elapsed time so far: 4.2 s
79.9 % 1.2e+03 s Elapsed time so far: 4.2 s
80.2 % 1.2e+03 s Elapsed time so far: 4.2 s
80.5 % 1.2e+03 s Elapsed time so far: 4.3 s
80.9 % 1.2e+03 s Elapsed time so far: 4.3 s
81.2 % 1.2e+03 s Elapsed time so far: 4.3 s
81.5 % 1.2e+03 s Elapsed time so far: 4.3 s
81.9 % 1.2e+03 s Elapsed time so far: 4.3 s
82.2 % 1.2e+03 s Elapsed time so far: 4.3 s
82.5 % 1.2e+03 s Elapsed time so far: 4.3 s
82.9 % 1.2e+03 s Elapsed time so far: 4.4 s
83.2 % 1.2e+03 s Elapsed time so far: 4.4 s
83.5 % 1.3e+03 s Elapsed time so far: 4.4 s
83.9 % 1.3e+03 s Elapsed time so far: 4.4 s
84.2 % 1.3e+03 s Elapsed time so far: 4.4 s
84.5 % 1.3e+03 s Elapsed time so far: 4.4 s
84.9 % 1.3e+03 s Elapsed time so far: 4.4 s
85.2 % 1.3e+03 s Elapsed time so far: 4.4 s
85.5 % 1.3e+03 s Elapsed time so far: 4.4 s
85.9 % 1.3e+03 s Elapsed time so far: 4.5 s
86.2 % 1.3e+03 s Elapsed time so far: 4.5 s
86.5 % 1.3e+03 s Elapsed time so far: 4.5 s
86.9 % 1.3e+03 s Elapsed time so far: 4.5 s
87.2 % 1.3e+03 s Elapsed time so far: 4.5 s
87.5 % 1.3e+03 s Elapsed time so far: 4.5 s
87.9 % 1.3e+03 s Elapsed time so far: 4.5 s
88.2 % 1.3e+03 s Elapsed time so far: 4.5 s
88.5 % 1.3e+03 s Elapsed time so far: 4.5 s
88.9 % 1.3e+03 s Elapsed time so far: 4.6 s
89.2 % 1.3e+03 s Elapsed time so far: 4.6 s
89.5 % 1.3e+03 s Elapsed time so far: 4.6 s
89.9 % 1.3e+03 s Elapsed time so far: 4.6 s
90.2 % 1.4e+03 s Elapsed time so far: 4.6 s
90.5 % 1.4e+03 s Elapsed time so far: 4.6 s
90.9 % 1.4e+03 s Elapsed time so far: 4.6 s
91.2 % 1.4e+03 s Elapsed time so far: 4.6 s
91.5 % 1.4e+03 s Elapsed time so far: 4.7 s
91.9 % 1.4e+03 s Elapsed time so far: 4.7 s
92.2 % 1.4e+03 s Elapsed time so far: 4.7 s
92.5 % 1.4e+03 s Elapsed time so far: 4.7 s
92.9 % 1.4e+03 s Elapsed time so far: 4.7 s
93.2 % 1.4e+03 s Elapsed time so far: 4.7 s
93.5 % 1.4e+03 s Elapsed time so far: 4.7 s
93.9 % 1.4e+03 s Elapsed time so far: 4.7 s
94.2 % 1.4e+03 s Elapsed time so far: 4.7 s
94.5 % 1.4e+03 s Elapsed time so far: 4.8 s
94.9 % 1.4e+03 s Elapsed time so far: 4.8 s
95.2 % 1.4e+03 s Elapsed time so far: 4.8 s
95.5 % 1.4e+03 s Elapsed time so far: 4.8 s
95.9 % 1.4e+03 s Elapsed time so far: 4.8 s
96.2 % 1.4e+03 s Elapsed time so far: 4.8 s
96.5 % 1.4e+03 s Elapsed time so far: 4.8 s
96.9 % 1.5e+03 s Elapsed time so far: 4.8 s
97.2 % 1.5e+03 s Elapsed time so far: 4.8 s
97.5 % 1.5e+03 s Elapsed time so far: 4.9 s
97.9 % 1.5e+03 s Elapsed time so far: 4.9 s
98.2 % 1.5e+03 s Elapsed time so far: 4.9 s
98.5 % 1.5e+03 s Elapsed time so far: 4.9 s
98.9 % 1.5e+03 s Elapsed time so far: 4.9 s
99.2 % 1.5e+03 s Elapsed time so far: 4.9 s
99.5 % 1.5e+03 s Elapsed time so far: 4.9 s
99.9 % 1.5e+03 s Elapsed time so far: 4.9 s
100.0 % 1.5e+03 s Elapsed time so far: 5.0 s
Defining initial values
Defining variational problem
Defining source terms
Defining boundary conditions
Time stepping...
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0.0 % 9.8e-02 s Elapsed time so far: 0.2 s
0.0 % 1.1e-01 s Elapsed time so far: 0.2 s
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0.0 % 2.0e-01 s Elapsed time so far: 0.2 s
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0.0 % 2.5e-01 s Elapsed time so far: 0.2 s
0.0 % 2.7e-01 s Elapsed time so far: 0.2 s
0.0 % 3.0e-01 s Elapsed time so far: 0.2 s
0.0 % 3.3e-01 s Elapsed time so far: 0.3 s
0.0 % 3.6e-01 s Elapsed time so far: 0.3 s
0.0 % 4.0e-01 s Elapsed time so far: 0.3 s
0.0 % 4.4e-01 s Elapsed time so far: 0.3 s
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0.0 % 5.4e-01 s Elapsed time so far: 0.3 s
0.0 % 5.9e-01 s Elapsed time so far: 0.3 s
0.0 % 6.5e-01 s Elapsed time so far: 0.3 s
0.1 % 7.2e-01 s Elapsed time so far: 0.3 s
0.1 % 7.9e-01 s Elapsed time so far: 0.3 s
0.1 % 8.7e-01 s Elapsed time so far: 0.3 s
0.1 % 9.6e-01 s Elapsed time so far: 0.3 s
0.1 % 1.1e+00 s Elapsed time so far: 0.3 s
0.1 % 1.2e+00 s Elapsed time so far: 0.4 s
0.1 % 1.3e+00 s Elapsed time so far: 0.4 s
0.1 % 1.4e+00 s Elapsed time so far: 0.4 s
0.1 % 1.6e+00 s Elapsed time so far: 0.4 s
0.1 % 1.7e+00 s Elapsed time so far: 0.4 s
0.1 % 1.9e+00 s Elapsed time so far: 0.4 s
0.1 % 2.1e+00 s Elapsed time so far: 0.4 s
0.1 % 2.3e+00 s Elapsed time so far: 0.4 s
0.2 % 2.5e+00 s Elapsed time so far: 0.4 s
0.2 % 2.8e+00 s Elapsed time so far: 0.4 s
0.2 % 3.0e+00 s Elapsed time so far: 0.4 s
0.2 % 3.3e+00 s Elapsed time so far: 0.4 s
0.2 % 3.7e+00 s Elapsed time so far: 0.4 s
0.3 % 4.0e+00 s Elapsed time so far: 0.4 s
0.3 % 4.4e+00 s Elapsed time so far: 0.5 s
0.3 % 4.9e+00 s Elapsed time so far: 0.5 s
0.4 % 5.4e+00 s Elapsed time so far: 0.5 s
0.4 % 5.9e+00 s Elapsed time so far: 0.5 s
0.4 % 6.5e+00 s Elapsed time so far: 0.5 s
0.5 % 7.2e+00 s Elapsed time so far: 0.5 s
0.5 % 7.9e+00 s Elapsed time so far: 0.5 s
0.6 % 8.7e+00 s Elapsed time so far: 0.5 s
0.6 % 9.5e+00 s Elapsed time so far: 0.5 s
0.7 % 1.1e+01 s Elapsed time so far: 0.5 s
0.8 % 1.2e+01 s Elapsed time so far: 0.5 s
0.8 % 1.3e+01 s Elapsed time so far: 0.6 s
0.9 % 1.4e+01 s Elapsed time so far: 0.6 s
1.0 % 1.5e+01 s Elapsed time so far: 0.6 s
1.1 % 1.7e+01 s Elapsed time so far: 0.6 s
1.2 % 1.9e+01 s Elapsed time so far: 0.6 s
1.4 % 2.0e+01 s Elapsed time so far: 0.6 s
1.5 % 2.3e+01 s Elapsed time so far: 0.6 s
1.6 % 2.5e+01 s Elapsed time so far: 0.6 s
1.8 % 2.7e+01 s Elapsed time so far: 0.6 s
2.0 % 3.0e+01 s Elapsed time so far: 0.6 s
2.2 % 3.3e+01 s Elapsed time so far: 0.6 s
2.4 % 3.6e+01 s Elapsed time so far: 0.6 s
2.7 % 4.0e+01 s Elapsed time so far: 0.7 s
2.9 % 4.4e+01 s Elapsed time so far: 0.7 s
3.2 % 4.8e+01 s Elapsed time so far: 0.7 s
3.5 % 5.3e+01 s Elapsed time so far: 0.7 s
3.9 % 5.8e+01 s Elapsed time so far: 0.7 s
4.2 % 6.3e+01 s Elapsed time so far: 0.7 s
4.5 % 6.8e+01 s Elapsed time so far: 0.7 s
4.9 % 7.3e+01 s Elapsed time so far: 0.7 s
5.2 % 7.8e+01 s Elapsed time so far: 0.7 s
5.5 % 8.3e+01 s Elapsed time so far: 0.7 s
5.9 % 8.8e+01 s Elapsed time so far: 0.7 s
6.2 % 9.3e+01 s Elapsed time so far: 0.7 s
6.5 % 9.8e+01 s Elapsed time so far: 0.8 s
6.9 % 1.0e+02 s Elapsed time so far: 0.8 s
7.2 % 1.1e+02 s Elapsed time so far: 0.8 s
7.5 % 1.1e+02 s Elapsed time so far: 0.8 s
7.9 % 1.2e+02 s Elapsed time so far: 0.8 s
8.2 % 1.2e+02 s Elapsed time so far: 0.8 s
8.5 % 1.3e+02 s Elapsed time so far: 0.8 s
8.9 % 1.3e+02 s Elapsed time so far: 0.8 s
9.2 % 1.4e+02 s Elapsed time so far: 0.8 s
9.5 % 1.4e+02 s Elapsed time so far: 0.9 s
9.9 % 1.5e+02 s Elapsed time so far: 0.9 s
10.2 % 1.5e+02 s Elapsed time so far: 0.9 s
10.5 % 1.6e+02 s Elapsed time so far: 0.9 s
10.9 % 1.6e+02 s Elapsed time so far: 0.9 s
11.2 % 1.7e+02 s Elapsed time so far: 0.9 s
11.5 % 1.7e+02 s Elapsed time so far: 0.9 s
11.9 % 1.8e+02 s Elapsed time so far: 0.9 s
12.2 % 1.8e+02 s Elapsed time so far: 0.9 s
12.5 % 1.9e+02 s Elapsed time so far: 0.9 s
12.9 % 1.9e+02 s Elapsed time so far: 0.9 s
13.2 % 2.0e+02 s Elapsed time so far: 0.9 s
13.5 % 2.0e+02 s Elapsed time so far: 1.0 s
13.9 % 2.1e+02 s Elapsed time so far: 1.0 s
14.2 % 2.1e+02 s Elapsed time so far: 1.0 s
14.5 % 2.2e+02 s Elapsed time so far: 1.0 s
14.9 % 2.2e+02 s Elapsed time so far: 1.0 s
15.2 % 2.3e+02 s Elapsed time so far: 1.0 s
15.5 % 2.3e+02 s Elapsed time so far: 1.0 s
15.9 % 2.4e+02 s Elapsed time so far: 1.0 s
16.2 % 2.4e+02 s Elapsed time so far: 1.0 s
16.5 % 2.5e+02 s Elapsed time so far: 1.0 s
16.9 % 2.5e+02 s Elapsed time so far: 1.0 s
17.2 % 2.6e+02 s Elapsed time so far: 1.0 s
17.5 % 2.6e+02 s Elapsed time so far: 1.1 s
17.9 % 2.7e+02 s Elapsed time so far: 1.1 s
18.2 % 2.7e+02 s Elapsed time so far: 1.1 s
18.5 % 2.8e+02 s Elapsed time so far: 1.1 s
18.9 % 2.8e+02 s Elapsed time so far: 1.1 s
19.2 % 2.9e+02 s Elapsed time so far: 1.1 s
19.5 % 2.9e+02 s Elapsed time so far: 1.1 s
19.9 % 3.0e+02 s Elapsed time so far: 1.1 s
20.2 % 3.0e+02 s Elapsed time so far: 1.1 s
20.5 % 3.1e+02 s Elapsed time so far: 1.1 s
20.9 % 3.1e+02 s Elapsed time so far: 1.1 s
21.2 % 3.2e+02 s Elapsed time so far: 1.1 s
21.5 % 3.2e+02 s Elapsed time so far: 1.2 s
21.9 % 3.3e+02 s Elapsed time so far: 1.2 s
22.2 % 3.3e+02 s Elapsed time so far: 1.2 s
22.5 % 3.4e+02 s Elapsed time so far: 1.2 s
22.9 % 3.4e+02 s Elapsed time so far: 1.2 s
23.2 % 3.5e+02 s Elapsed time so far: 1.2 s
23.5 % 3.5e+02 s Elapsed time so far: 1.2 s
23.9 % 3.6e+02 s Elapsed time so far: 1.2 s
24.2 % 3.6e+02 s Elapsed time so far: 1.2 s
24.5 % 3.7e+02 s Elapsed time so far: 1.2 s
24.9 % 3.7e+02 s Elapsed time so far: 1.2 s
25.2 % 3.8e+02 s Elapsed time so far: 1.2 s
25.5 % 3.8e+02 s Elapsed time so far: 1.2 s
25.9 % 3.9e+02 s Elapsed time so far: 1.3 s
26.2 % 3.9e+02 s Elapsed time so far: 1.3 s
26.5 % 4.0e+02 s Elapsed time so far: 1.3 s
26.9 % 4.0e+02 s Elapsed time so far: 1.3 s
27.2 % 4.1e+02 s Elapsed time so far: 1.3 s
27.5 % 4.1e+02 s Elapsed time so far: 1.3 s
27.9 % 4.2e+02 s Elapsed time so far: 1.3 s
28.2 % 4.2e+02 s Elapsed time so far: 1.3 s
28.5 % 4.3e+02 s Elapsed time so far: 1.3 s
28.9 % 4.3e+02 s Elapsed time so far: 1.3 s
29.2 % 4.4e+02 s Elapsed time so far: 1.3 s
29.5 % 4.4e+02 s Elapsed time so far: 1.4 s
29.9 % 4.5e+02 s Elapsed time so far: 1.4 s
30.2 % 4.5e+02 s Elapsed time so far: 1.4 s
30.5 % 4.6e+02 s Elapsed time so far: 1.4 s
30.9 % 4.6e+02 s Elapsed time so far: 1.4 s
31.2 % 4.7e+02 s Elapsed time so far: 1.4 s
31.5 % 4.7e+02 s Elapsed time so far: 1.4 s
31.9 % 4.8e+02 s Elapsed time so far: 1.4 s
32.2 % 4.8e+02 s Elapsed time so far: 1.4 s
32.5 % 4.9e+02 s Elapsed time so far: 1.4 s
32.9 % 4.9e+02 s Elapsed time so far: 1.4 s
33.2 % 5.0e+02 s Elapsed time so far: 1.4 s
33.5 % 5.0e+02 s Elapsed time so far: 1.5 s
33.9 % 5.1e+02 s Elapsed time so far: 1.5 s
34.2 % 5.1e+02 s Elapsed time so far: 1.5 s
34.5 % 5.2e+02 s Elapsed time so far: 1.5 s
34.9 % 5.2e+02 s Elapsed time so far: 1.5 s
35.2 % 5.3e+02 s Elapsed time so far: 1.5 s
35.5 % 5.3e+02 s Elapsed time so far: 1.5 s
35.9 % 5.4e+02 s Elapsed time so far: 1.5 s
36.2 % 5.4e+02 s Elapsed time so far: 1.5 s
36.5 % 5.5e+02 s Elapsed time so far: 1.5 s
36.9 % 5.5e+02 s Elapsed time so far: 1.5 s
37.2 % 5.6e+02 s Elapsed time so far: 1.5 s
37.5 % 5.6e+02 s Elapsed time so far: 1.6 s
37.9 % 5.7e+02 s Elapsed time so far: 1.6 s
38.2 % 5.7e+02 s Elapsed time so far: 1.6 s
38.5 % 5.8e+02 s Elapsed time so far: 1.6 s
38.9 % 5.8e+02 s Elapsed time so far: 1.6 s
39.2 % 5.9e+02 s Elapsed time so far: 1.6 s
39.5 % 5.9e+02 s Elapsed time so far: 1.6 s
39.9 % 6.0e+02 s Elapsed time so far: 1.6 s
40.2 % 6.0e+02 s Elapsed time so far: 1.6 s
40.5 % 6.1e+02 s Elapsed time so far: 1.6 s
40.9 % 6.1e+02 s Elapsed time so far: 1.6 s
41.2 % 6.2e+02 s Elapsed time so far: 1.6 s
41.5 % 6.2e+02 s Elapsed time so far: 1.6 s
41.9 % 6.3e+02 s Elapsed time so far: 1.6 s
42.2 % 6.3e+02 s Elapsed time so far: 1.7 s
42.5 % 6.4e+02 s Elapsed time so far: 1.7 s
42.9 % 6.4e+02 s Elapsed time so far: 1.7 s
43.2 % 6.5e+02 s Elapsed time so far: 1.7 s
43.5 % 6.5e+02 s Elapsed time so far: 1.7 s
43.9 % 6.6e+02 s Elapsed time so far: 1.7 s
44.2 % 6.6e+02 s Elapsed time so far: 1.7 s
44.5 % 6.7e+02 s Elapsed time so far: 1.7 s
44.9 % 6.7e+02 s Elapsed time so far: 1.7 s
45.2 % 6.8e+02 s Elapsed time so far: 1.7 s
45.5 % 6.8e+02 s Elapsed time so far: 1.7 s
45.9 % 6.9e+02 s Elapsed time so far: 1.7 s
46.2 % 6.9e+02 s Elapsed time so far: 1.7 s
46.5 % 7.0e+02 s Elapsed time so far: 1.7 s
46.9 % 7.0e+02 s Elapsed time so far: 1.8 s
47.2 % 7.1e+02 s Elapsed time so far: 1.8 s
47.5 % 7.1e+02 s Elapsed time so far: 1.8 s
47.9 % 7.2e+02 s Elapsed time so far: 1.8 s
48.2 % 7.2e+02 s Elapsed time so far: 1.8 s
48.5 % 7.3e+02 s Elapsed time so far: 1.8 s
48.9 % 7.3e+02 s Elapsed time so far: 1.8 s
49.2 % 7.4e+02 s Elapsed time so far: 1.8 s
49.5 % 7.4e+02 s Elapsed time so far: 1.8 s
49.9 % 7.5e+02 s Elapsed time so far: 1.8 s
50.2 % 7.5e+02 s Elapsed time so far: 1.8 s
50.5 % 7.6e+02 s Elapsed time so far: 1.8 s
50.9 % 7.6e+02 s Elapsed time so far: 1.8 s
51.2 % 7.7e+02 s Elapsed time so far: 1.8 s
51.5 % 7.7e+02 s Elapsed time so far: 1.8 s
51.9 % 7.8e+02 s Elapsed time so far: 1.9 s
52.2 % 7.8e+02 s Elapsed time so far: 1.9 s
52.5 % 7.9e+02 s Elapsed time so far: 1.9 s
52.9 % 7.9e+02 s Elapsed time so far: 1.9 s
53.2 % 8.0e+02 s Elapsed time so far: 1.9 s
53.5 % 8.0e+02 s Elapsed time so far: 1.9 s
53.9 % 8.1e+02 s Elapsed time so far: 1.9 s
54.2 % 8.1e+02 s Elapsed time so far: 1.9 s
54.5 % 8.2e+02 s Elapsed time so far: 1.9 s
54.9 % 8.2e+02 s Elapsed time so far: 1.9 s
55.2 % 8.3e+02 s Elapsed time so far: 1.9 s
55.5 % 8.3e+02 s Elapsed time so far: 1.9 s
55.9 % 8.4e+02 s Elapsed time so far: 1.9 s
56.2 % 8.4e+02 s Elapsed time so far: 1.9 s
56.5 % 8.5e+02 s Elapsed time so far: 1.9 s
56.9 % 8.5e+02 s Elapsed time so far: 2.0 s
57.2 % 8.6e+02 s Elapsed time so far: 2.0 s
57.5 % 8.6e+02 s Elapsed time so far: 2.0 s
57.9 % 8.7e+02 s Elapsed time so far: 2.0 s
58.2 % 8.7e+02 s Elapsed time so far: 2.0 s
58.5 % 8.8e+02 s Elapsed time so far: 2.0 s
58.9 % 8.8e+02 s Elapsed time so far: 2.0 s
59.2 % 8.9e+02 s Elapsed time so far: 2.0 s
59.5 % 8.9e+02 s Elapsed time so far: 2.0 s
59.9 % 9.0e+02 s Elapsed time so far: 2.0 s
60.2 % 9.0e+02 s Elapsed time so far: 2.0 s
60.5 % 9.1e+02 s Elapsed time so far: 2.0 s
60.9 % 9.1e+02 s Elapsed time so far: 2.1 s
61.2 % 9.2e+02 s Elapsed time so far: 2.1 s
61.5 % 9.2e+02 s Elapsed time so far: 2.1 s
61.9 % 9.3e+02 s Elapsed time so far: 2.1 s
62.2 % 9.3e+02 s Elapsed time so far: 2.1 s
62.5 % 9.4e+02 s Elapsed time so far: 2.1 s
62.9 % 9.4e+02 s Elapsed time so far: 2.1 s
63.2 % 9.5e+02 s Elapsed time so far: 2.1 s
63.5 % 9.5e+02 s Elapsed time so far: 2.1 s
63.9 % 9.6e+02 s Elapsed time so far: 2.1 s
64.2 % 9.6e+02 s Elapsed time so far: 2.1 s
64.5 % 9.7e+02 s Elapsed time so far: 2.1 s
64.9 % 9.7e+02 s Elapsed time so far: 2.1 s
65.2 % 9.8e+02 s Elapsed time so far: 2.1 s
65.5 % 9.8e+02 s Elapsed time so far: 2.2 s
65.9 % 9.9e+02 s Elapsed time so far: 2.2 s
66.2 % 9.9e+02 s Elapsed time so far: 2.2 s
66.5 % 1.0e+03 s Elapsed time so far: 2.2 s
66.9 % 1.0e+03 s Elapsed time so far: 2.2 s
67.2 % 1.0e+03 s Elapsed time so far: 2.2 s
67.5 % 1.0e+03 s Elapsed time so far: 2.2 s
67.9 % 1.0e+03 s Elapsed time so far: 2.2 s
68.2 % 1.0e+03 s Elapsed time so far: 2.2 s
68.5 % 1.0e+03 s Elapsed time so far: 2.2 s
68.9 % 1.0e+03 s Elapsed time so far: 2.2 s
69.2 % 1.0e+03 s Elapsed time so far: 2.2 s
69.5 % 1.0e+03 s Elapsed time so far: 2.2 s
69.9 % 1.0e+03 s Elapsed time so far: 2.2 s
70.2 % 1.1e+03 s Elapsed time so far: 2.2 s
70.5 % 1.1e+03 s Elapsed time so far: 2.3 s
70.9 % 1.1e+03 s Elapsed time so far: 2.3 s
71.2 % 1.1e+03 s Elapsed time so far: 2.3 s
71.5 % 1.1e+03 s Elapsed time so far: 2.3 s
71.9 % 1.1e+03 s Elapsed time so far: 2.3 s
72.2 % 1.1e+03 s Elapsed time so far: 2.3 s
72.5 % 1.1e+03 s Elapsed time so far: 2.3 s
72.9 % 1.1e+03 s Elapsed time so far: 2.3 s
73.2 % 1.1e+03 s Elapsed time so far: 2.4 s
73.5 % 1.1e+03 s Elapsed time so far: 2.4 s
73.9 % 1.1e+03 s Elapsed time so far: 2.4 s
74.2 % 1.1e+03 s Elapsed time so far: 2.4 s
74.5 % 1.1e+03 s Elapsed time so far: 2.4 s
74.9 % 1.1e+03 s Elapsed time so far: 2.4 s
75.2 % 1.1e+03 s Elapsed time so far: 2.4 s
75.5 % 1.1e+03 s Elapsed time so far: 2.4 s
75.9 % 1.1e+03 s Elapsed time so far: 2.5 s
76.2 % 1.1e+03 s Elapsed time so far: 2.5 s
76.5 % 1.1e+03 s Elapsed time so far: 2.5 s
76.9 % 1.2e+03 s Elapsed time so far: 2.5 s
77.2 % 1.2e+03 s Elapsed time so far: 2.5 s
77.5 % 1.2e+03 s Elapsed time so far: 2.5 s
77.9 % 1.2e+03 s Elapsed time so far: 2.5 s
78.2 % 1.2e+03 s Elapsed time so far: 2.5 s
78.5 % 1.2e+03 s Elapsed time so far: 2.5 s
78.9 % 1.2e+03 s Elapsed time so far: 2.6 s
79.2 % 1.2e+03 s Elapsed time so far: 2.6 s
79.5 % 1.2e+03 s Elapsed time so far: 2.6 s
79.9 % 1.2e+03 s Elapsed time so far: 2.6 s
80.2 % 1.2e+03 s Elapsed time so far: 2.6 s
80.5 % 1.2e+03 s Elapsed time so far: 2.6 s
80.9 % 1.2e+03 s Elapsed time so far: 2.6 s
81.2 % 1.2e+03 s Elapsed time so far: 2.6 s
81.5 % 1.2e+03 s Elapsed time so far: 2.6 s
81.9 % 1.2e+03 s Elapsed time so far: 2.7 s
82.2 % 1.2e+03 s Elapsed time so far: 2.7 s
82.5 % 1.2e+03 s Elapsed time so far: 2.7 s
82.9 % 1.2e+03 s Elapsed time so far: 2.7 s
83.2 % 1.2e+03 s Elapsed time so far: 2.7 s
83.5 % 1.3e+03 s Elapsed time so far: 2.7 s
83.9 % 1.3e+03 s Elapsed time so far: 2.7 s
84.2 % 1.3e+03 s Elapsed time so far: 2.7 s
84.5 % 1.3e+03 s Elapsed time so far: 2.8 s
84.9 % 1.3e+03 s Elapsed time so far: 2.8 s
85.2 % 1.3e+03 s Elapsed time so far: 2.8 s
85.5 % 1.3e+03 s Elapsed time so far: 2.8 s
85.9 % 1.3e+03 s Elapsed time so far: 2.8 s
86.2 % 1.3e+03 s Elapsed time so far: 2.8 s
86.5 % 1.3e+03 s Elapsed time so far: 2.8 s
86.9 % 1.3e+03 s Elapsed time so far: 2.8 s
87.2 % 1.3e+03 s Elapsed time so far: 2.8 s
87.5 % 1.3e+03 s Elapsed time so far: 2.9 s
87.9 % 1.3e+03 s Elapsed time so far: 2.9 s
88.2 % 1.3e+03 s Elapsed time so far: 2.9 s
88.5 % 1.3e+03 s Elapsed time so far: 2.9 s
88.9 % 1.3e+03 s Elapsed time so far: 2.9 s
89.2 % 1.3e+03 s Elapsed time so far: 2.9 s
89.5 % 1.3e+03 s Elapsed time so far: 2.9 s
89.9 % 1.3e+03 s Elapsed time so far: 2.9 s
90.2 % 1.4e+03 s Elapsed time so far: 2.9 s
90.5 % 1.4e+03 s Elapsed time so far: 3.0 s
90.9 % 1.4e+03 s Elapsed time so far: 3.0 s
91.2 % 1.4e+03 s Elapsed time so far: 3.0 s
91.5 % 1.4e+03 s Elapsed time so far: 3.0 s
91.9 % 1.4e+03 s Elapsed time so far: 3.0 s
92.2 % 1.4e+03 s Elapsed time so far: 3.0 s
92.5 % 1.4e+03 s Elapsed time so far: 3.0 s
92.9 % 1.4e+03 s Elapsed time so far: 3.0 s
93.2 % 1.4e+03 s Elapsed time so far: 3.1 s
93.5 % 1.4e+03 s Elapsed time so far: 3.1 s
93.9 % 1.4e+03 s Elapsed time so far: 3.1 s
94.2 % 1.4e+03 s Elapsed time so far: 3.1 s
94.5 % 1.4e+03 s Elapsed time so far: 3.1 s
94.9 % 1.4e+03 s Elapsed time so far: 3.1 s
95.2 % 1.4e+03 s Elapsed time so far: 3.1 s
95.5 % 1.4e+03 s Elapsed time so far: 3.1 s
95.9 % 1.4e+03 s Elapsed time so far: 3.1 s
96.2 % 1.4e+03 s Elapsed time so far: 3.2 s
96.5 % 1.4e+03 s Elapsed time so far: 3.2 s
96.9 % 1.5e+03 s Elapsed time so far: 3.2 s
97.2 % 1.5e+03 s Elapsed time so far: 3.2 s
97.5 % 1.5e+03 s Elapsed time so far: 3.2 s
97.9 % 1.5e+03 s Elapsed time so far: 3.2 s
98.2 % 1.5e+03 s Elapsed time so far: 3.2 s
98.5 % 1.5e+03 s Elapsed time so far: 3.2 s
98.9 % 1.5e+03 s Elapsed time so far: 3.2 s
99.2 % 1.5e+03 s Elapsed time so far: 3.3 s
99.5 % 1.5e+03 s Elapsed time so far: 3.3 s
99.9 % 1.5e+03 s Elapsed time so far: 3.3 s
100.0 % 1.5e+03 s Elapsed time so far: 3.3 s
Comparison with experimental data#
FESTIM reproduces the experimental data over the whole range of temperatures using one set of parameters.
Show code cell source
import plotly.graph_objects as go
import plotly.express as px
fig = go.Figure()
for i, T in enumerate(T_list):
color = px.colors.qualitative.Plotly[i]
FESTIM_data = results[T]
retention = np.array(FESTIM_data[1].data) + np.array(FESTIM_data[0].data)
t = np.array(FESTIM_data.t)
exp = np.loadtxt(f"./content_data/{T-273}.csv", delimiter=",", skiprows=1)
fig.add_trace(
go.Scatter(
x=t / 60,
y=retention * A / N_Ti,
mode="lines",
line=dict(color=color, width=3),
name=f"FESTIM: T={T} K",
)
)
fig.add_trace(
go.Scatter(
x=exp[:, 0],
y=exp[:, 1],
mode="markers",
marker=dict(color=color, size=9),
name=f"Exp.: T={T} K",
)
)
fig.update_yaxes(title_text="Content, H/Ti", range=[0, 0.8], tick0=0, dtick=0.1)
fig.update_xaxes(title_text="Time, min", range=[0, 25], tick0=0, dtick=5)
fig.update_layout(template="simple_white", height=600)
# The writing-reading block below is needed to avoid the issue with compatibility
# of Plotly plots and dollarmath syntax extension in Jupyter Book
# For mode details, see https://github.com/jupyter-book/jupyter-book/issues/1528
fig.write_html("./hirooka_comparison.html")
from IPython.display import HTML, display
display(HTML("./hirooka_comparison.html"))
Fitted parameters#
The table below displays the input parameters which were determined during the optimisation procedure.
Show code cell source
import pandas as pd
pd.set_option("display.float_format", "{:.3e}".format)
prms_list = [k_sb, E_sb, k_bs, E_bs, k_des, E_des]
col_names = [
"k_sb (s^-1)",
"E_sb (eV)",
"k_bs (s^-1)",
"E_bs (eV)",
"k_des (m^2 s^-1)",
"E_des (eV)",
]
data = pd.DataFrame(prms_list).T
data.columns = col_names
data.style.relabel_index(["value"], axis=0).format("{:.2e}".format)
| k_sb (s^-1) | E_sb (eV) | k_bs (s^-1) | E_bs (eV) | k_des (m^2 s^-1) | E_des (eV) | |
|---|---|---|---|---|---|---|
| value | 5.14e+09 | 1.01e+00 | 1.00e+10 | 1.05e+00 | 3.41e-11 | 5.62e-01 |