MATLAB: Matrix set up for kron use and speed up.

finite differencekronmatrixsparse

Hi, I am trying an alternative way of doing explicit finite difference method to explore and use other matlab available tools. I am attempting the following algorithm which is
an(j,i)=2*a(j,i)+c1*(a(j+1,i)-2*a(j,i)+a(j-1,i)+a(j,i+1)-2*a(j,i)+a(j,i-1))-ao(j,i);
assuming dx=dy
Unfortunately I run into some problems in the following code.
    % iterative method 2-D
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n=100;
i=2:n-1;
j=2:n-1;
dx=1;
dt=0.1;
c1=dt^2/dx^2;
a=zeros(n,n);
ao=zeros(n,n);
an=zeros(n,n);
CC=2-4*c1;
an(j,i)=CC*a(j,i)+c1*(a(j+1,i)+a(j-1,i)+a(j,i+1)+a(j,i-1))-ao(j,i); 
            % sparse method
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n=100;
dx=1;
dt=0.1;
c1=dt^2/dx^2;
w=zeros(n,n);
wo=zeros(n,n);
wn=zeros(n,n);
CC=2-4*c1;
K = sparse(diag(2*ones(n,1))+diag(-ones(n-1,1),1) + diag(-ones(n-1,1),-1));
I = eye(n);
K2D = kron(c1*I,K)+kron(c1*K,I);
b=[-c1 zeros(1,n-2) -c1 zeros(1,n*n-n-n) -c1 zeros(1,n-2) -c1]'.*wo;  % <-- this line gives me an error
wn = 2*w-K2D*w-wo-b;

Best Answer

Hi, I managed to fix the sparse algorithm, however it is slower than simple iterative method. Have I done something wrong with the sparse method? Can it be optimized further? Is there a way to substitute for for loop ?
    wo=w;
I=eye(n);
e=ones(n,1);
T=spdiags([e -4*e e],[-1 0 1],n,n);
S=spdiags([e e],[-1 1],n,n);
A=(kron(I,T)+kron(S,I))*c1;
for tt=0:dt:200
    wn=2*w+A*w-wo;
       for i=1:n
            wm(i,:)=w((i-1)*n+1:i*n);    % Convert back to matrix
        end
    wo=w; % curent become old
    w=wn; % new become current 
end
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