clear all
close all

% Problem domain, in meters.
X = 2;
Y = 1;
D = 0.025;

% Problem domain, in cells.
NX = X/D;
NY = Y/D;

V_last = zeros(NY+1,NX+1);
V_next = zeros(NY+1,NX+1);

% Write boundary conditions into V_last.
V_last(1,:) = -1;
V_last(end,:) = 1;
V_last(:,1) = linspace(-1,1, NY+1);
V_last(:,end) = linspace(-1,1, NY+1);
V_last(1:18,39:41) = -1;
V_last(24:41,39:41) = 1;

ITERATIONS = 800;

for i=1:ITERATIONS
  for iy=2:NY
    for ix=2:NX
      V_next(iy,ix) = 1/4* ( V_last(iy-1,ix) + V_last(iy+1,ix) + V_last(iy,ix-1) + V_last(iy,ix+1) );
    end
  end
  % Write boundary conditions into V_next.
  V_next(1,:) = -1;
  V_next(end,:) = 1;
  V_next(:,1) = linspace(-1,1, NY+1);
  V_next(:,end) = linspace(-1,1, NY+1);
  V_next(1:18,39:41) = -1;
  V_next(24:41,39:41) = 1;
  % Iterate.
  V_last = V_next;
end

x_axis = linspace(0,X, NX + 1);
y_axis = linspace(0,Y, NY + 1);
[x,y] = meshgrid(x_axis, y_axis);
[Ex,Ey] = gradient(-V_last,D,D);
contour(x,y,V_last,20);
hold on
quiver(x,y,Ex,Ey);
hold off
axis equal;
xlabel ('x, meters');
ylabel ('y, meters');
title ('ECE 311 - HW7, Problem 2');
set(gcf,'Color',[1 1 1]);


disp ('Conceptual Question: Dielectric breakdown occurs because the electric');
disp ('field is so large that it can strip electrons even from non-conducting');
disp ('atoms. The most likely place for this to occur is where E is the largest,');
disp ('in the small gap between the conducting fins. Real devices which deliberately');
disp ('create sparks (like spark plugs) are shaped similarly. Two conductors at ');
disp ('different potentials are bent into close proximity, to the spark will occur');
disp ('in the same place in a predictable manner.');