fork download 
  1. import numpy as np
  2. import matplotlib.pyplot as plt
  3.  
  4. def solve_poisson_boltzmann(charge_density, epsilon, kappa, dx, max_iter=1000, tol=1e-6):
  5.     """
  6.     Solve the Poisson-Boltzmann equation in 1D with Dirichlet boundary conditions.
  7.  
  8.     Args:
  9.     - charge_density (ndarray): Array containing the charge density.
  10.     - epsilon (float): Dielectric constant of the medium.
  11.     - kappa (float): Inverse Debye length.
  12.     - dx (float): Grid spacing.
  13.     - max_iter (int): Maximum number of iterations for the solver.
  14.     - tol (float): Tolerance for convergence.
  15.  
  16.     Returns:
  17.     - potential (ndarray): Array containing the electrostatic potential.
  18.     """
  19.     n = len(charge_density)
  20.     potential = np.zeros(n)
  21.     for _ in range(max_iter):
  22.         old_potential = np.copy(potential)
  23.         for i in range(1, n - 1):
  24.             potential[i] = 0.5 * (old_potential[i - 1] + old_potential[i + 1] +
  25.                                   dx**2 / epsilon * charge_density[i] -
  26.                                   kappa**2 * np.sinh(old_potential[i]))
  27.         if np.max(np.abs(potential - old_potential)) < tol:
  28.             break
  29.     return potential
  30.  
  31. # Parameters
  32. charge_density = np.array([0, 1, 0, -1, 0])
  33. epsilon = 1.0
  34. kappa = 0.1
  35. dx = 1.0
  36.  
  37. # Solve Poisson-Boltzmann equation
  38. potential = solve_poisson_boltzmann(charge_density, epsilon, kappa, dx)
  39.  
  40. # Plotting
  41. plt.figure()
  42. plt.plot(np.arange(len(charge_density)), charge_density, label='Charge Density')
  43. plt.plot(np.arange(len(potential)), potential, label='Potential')
  44. plt.xlabel('Position')
  45. plt.ylabel('Value')
  46. plt.legend()
  47. plt.show()
Success #stdin #stdout 0.85s 55540KB
comments (?)
stdin 
Standard input is empty
stdout 
Standard output is empty
https://ideone.com/SoshCH
language:
Python (cpython 2.7.16)
created:
14 days ago
visibility:
public

Share or Embed source code

Discover > Sphere Engine API

The brand new service which powers Ideone!

Discover > IDE Widget

Widget for compiling and running the source code in a web browser!