How Can I Speed up a loop that solves a pde?

Hello,

I am solving the 4th order pde for plate vibration and after discretizing the pde and solving for W(x,y,t) or W(k,m,n+1) as a function of W(k,m,n) and W(k,m,n-1) I get a double for loop like

for k=3:K-3
   for m=3:M-3

            Wnp1(k,m)=coe(1,3)*Wn(k-2,m)...
                + coe(2,2)*Wn(k-1,m-1) + coe(2,3)*Wn(k-1,m) + coe(2,4)*Wn(k-1,m+1)...
                +coe(3,1)*Wn(k,m-2) + coe(3,2)*Wn(k,m-1)+coe(3,3)*Wn(k,m)...
                +coe(3,4)*Wn(k,m+1)+coe(3,5)*Wn(k,m+2)...
                +coe(4,2)*Wn(k+1,m-1)+coe(4,3)*Wn(k+1,m)+coe(4,4)*Wn(k+1,m+1)...
                +coe(5,3)*Wn(k+2,m)...
                +cNm1*Wnm1(k,m)+SWW(k,m);
      end
end

where coe is a 5x5 matrix with several zeros that contains the coefficients in the finite difference approximation to the pde and Wn(k,m) represents the displacement at position k,m at time n.

I was hoping to find a way to use matrix multiplication that might speed things up but I am stumped. Does anyone have any suggestions?

Thanks,

Dave

[Jan]

Do you pre-allocate the output Wnp1?

Answer 1

[Zoltán Csáti]

When you did your calculations on paper, you probably wrote the problem as a linear system. Try to create the coefficient matrix in a vectorized manner. Or if you cannot do it, attach an image of the coeff. matrix so that we can see it.