Hello guys, i´m trying to solve the Poisson´s equation by using the relaxation method to know the potential and electric field matrixs but i have an error that say “index 101 is out of bounds for axis 0 with size 101” and i dont understand what is the problem. ¿Can anyone helpme please?
import numpy as np
import math
SYMBOLS USED IN THIS CODE
E = Total electric field matrix using Poisson’s equation
#% V = Potential matrix
#% Nx = Number of grid points in X- direction
#% Ny =Number of grid points in Y-Direction
#Enter the dimensions
Nx = 101 # Number of X-grids
Ny = 101 # Number of Y-grids
mpx = math.ceil(Nx/2) # Mid-point of x
mpy = math.ceil(Ny/2) #Mid point of y
Ni = 750 #Number of iterations for the Poisson solver
V = np.zeros((Nx,Ny))
T = 0 # Top-wall potential
B = 0 # Bottom-wall potential
L = 0 # Left-wall potential
R = 0 # Right-wall potential
#-------------------------------------------------------------------------
Initializing edges potentials
#-------------------------------------------------------------------------
V[1,:] = L
R= V[Nx,:]
V[:,1] = B
V[:,Ny] = T
#-------------------------------------------------------------------------
Initializing Corner potentials
#-------------------------------------------------------------------------
V[1,1] = 0.5*(V[1,2]+V[2,1])
V[Nx,1] = 0.5*(V[Nx-1,1]+V[Nx,2])
V[1,Ny] = 0.5*(V[1,Ny-1]+V[2,Ny])
V[Nx,Ny] = 0.5*(V[Nx,Ny-1]+V[Nx-1,Ny])
length_plate = 51 # Length of plate in terms of number of grids
lp = math.floor(length_plate/2)
position_plate = 15 # Position of plate on x axis
pp1 = mpx+position_plate
pp2 = mpx-position_plate
for z in range(1,Ni): #Number of iterations
for i in range(2,Nx-1):
for j in range(2,Ny-1):
#The next two lines are meant to force the matrix to hold the
potential values for all iterations
V[pp1,mpy-lp:mpy+lp] = 100
V[pp2,mpy-lp:mpy+lp] = -100
V[i,j]=0.25*(V[i+1,j]+V[i-1,j]+V[i,j+1]+V[i,j-1])
Take transpose for proper x-y orientation
V = np.transpose(V)
[Ex,Ey]=np.gradient(V)
Ex = -Ex
Ey = -Ey
Electric field Magnitude
E= math.sqrt( ExEx + EyEy )
