Patol75
commented
1 year ago It is not clear to me that you have demonstrated a shortcoming in SciPy's integrate module. However, it seems likely that the Python code you provided is not an accurate translation of the Matlab script you also attached. I would encourage you to start again and be more careful as you work your way through the translation. In particular, try to avoid adding in unnecessary functions and classes until you are sure the code you have written works. You may want to consider the below Python snippet as a new starting point:
import numpy as np
from scipy.constants import N_A, e, epsilon_0, h, k
from scipy.integrate import solve_ivp
from scipy.sparse import spdiags
from scipy.sparse.linalg import spsolve
def ion_conc_equ(t, y):
return
T = 298.15
a_M = 3.5e-10
N_M = 1 / np.sqrt(3) / a_M**2
potential = 0.5 * e / k / T
delta_RP = 1.5 * 2.75e-10
epsilon_RP = 6
epsilon_s = 78.5
D = 1e-9
n0 = N_A
Ld = 1e-4
lambda_d = np.sqrt(epsilon_s * epsilon_0 * k * T / e**2 / n0)
tref = lambda_d * Ld / D
Length_limit = Ld / lambda_d
x_cal_1 = np.linspace(0, 1, 70)
x_cal_2 = np.linspace(1.1, 10, 50)
x_cal_3 = np.linspace(11, 100, 50)
x_cal_4 = np.linspace(110, Length_limit, 20)
xmesh = np.hstack((x_cal_1, x_cal_2, x_cal_3, x_cal_4))
nx = xmesh.size
harray = np.diff(xmesh)
diag0 = np.hstack(
(
-1 / harray[0] - lambda_d * epsilon_RP / epsilon_s / delta_RP,
-2 / harray[1:-1] / harray[:-2],
-2 / harray[-1] / harray[-2],
)
)
diagp1 = np.hstack((1 / harray[0], 2 / harray[1:-1] / (harray[1:-1] + harray[:-2])))
diagm1 = np.hstack(
(
2 / harray[0] / (harray[0] + harray[1]),
2 / harray[1:-1] / (harray[1:-1] + harray[2:]),
)
)
A = np.column_stack((np.pad(diagm1, (0, 1)), diag0, np.pad(diagp1, (1, 0))))
# https://stackoverflow.com/a/31900194/10640534
pot_M = spdiags(A.T, [-1, 0, 1], nx - 1, nx - 1).tocsc()
pot_b = np.zeros(nx - 1)
pot_b[0] = -potential * lambda_d * epsilon_RP / delta_RP / epsilon_s
y0 = np.ones((5, nx))
y0[-1, :-1] = spsolve(pot_M, pot_b)
y0[-1, -1] = 0
t_end = 5
tmesh = np.linspace(0.1, t_end, 101)
tmesh = np.hstack(([1e-10, 1e-8, 1e-6, 1e-4, 1e-2], tmesh))
t_cal = tmesh / tref
sol = solve_ivp(
ion_conc_equ, [t_cal[0], t_cal[-1]], y0.flatten(), method="LSODA", t_eval=t_cal
)It should reproduce the Matlab script until line 74, which is the ode15s call. For example, you could start by making sure that arrays calculated up until there in both languages are identical. Then, you could translate the system's right-hand side into the ion_conc_equ function. Once you are sure that the Python code you have written is an accurate translation of the whole Matlab script, then you can assess if the ODE solvers provided by SciPy are behaving well or not.
MSJavaScript
But I my function, because I solve the poisson equation manually with spsolve, the Jacobian is not sparse matrix anymore. So if I set Jacobian matrix with the form above, it will not work.
Describe your issue.
I am trying to solve pne dimensional Possion-Nernst-Planck (PNP) Equation with solve_ivp, it looks like
Here, $\psi$ is electrode potential, $c_i$ are concentrations of ions.
Here is an example in matlab.
matlab_cc.txt
The function current calculate the currenr density of a reaction. The result will be used to calculate the Robin condition of left boundary. It's a little complex, but jr should decrease during the integration of equation. And ode15s can reach the end of the time span I want to calculate.
I also write a Python version and use solve_ivp to solve this equation. mkm_electro4.py.txt However, the current density jr decrease slowly. If you print the t variable in ions_conc_equ, you will find the time step is very small, t can only reach 8.0e-7. I tried BDF, LSODA solver, but both of them can not reach the end of the time span I want to calculate.
In short, PNP equation is a stiff equation, but BDF or LSODA solver fail to solve it.
Reproducing Code Example
Error message
SciPy/NumPy/Python version information
1.7.1 1.21.2 sys.version_info(major=3, minor=8, micro=10, releaselevel='final', serial=0)