%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% poisson_sor.m
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

x_left = 0.0;
x_right = 1.0; 
y_bottom = 0.0;
y_top = 1.0;

J = 12;
K = 12;
n = 0;
N = 100;

dx = (x_right - x_left)/J;
dy = (y_top - y_bottom)/K;

omega = 2.0/(1.0 + sin(pi/(J+1)));

d = (J+1)*(K+1);

x = linspace(x_left,x_right,J+1);
y = linspace(y_bottom,y_top,K+1);

u = zeros(d);
b = zeros(d);

u_matrix = zeros(J+1,K+1);
B = zeros(J+1,K+1);

u_matrix = boundary_conditions(x,y);

for j = 1:J+1
	for k = 1:K+1
		B(j,k) = dx*dx*(x(j)^2 + y(k)^2.0);
    end
end

for k = 1:K+1
	for j = 1:J+1;
		l = ;
		u(l) = u_matrix(j,k);
    end
end

for l = 1:d
	column = ;
	row = ;
	
	if column ~= 1 && column ~= K+1
		if row ~= 1 && row ~= J+1
			u(l) = .5;
        end
    end
	
	b(l) = B(row,column);
end

for n = 1:N
	for l = 1:d
		column = ;
		row = ;
		
		if column > 1 && column < K+1
			if row > 1 && row < J+1
				index1 = ;
				index2 = ;
				index3 = ;
				index4 = ;
					
				u(l) = 
            end
        end
    end
end

for l = 1:d
	column = ;
	row = ;
	
	u_matrix(row,column) = u(l);
end

surf(x,y,u_matrix')