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

Asked by David Koenig

David Koenig (view profile)

on 21 Nov 2014
Latest activity Commented on by Jan

Jan (view profile)

on 24 Nov 2014
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

Jan (view profile)

on 24 Nov 2014
Do you pre-allocate the output Wnp1?

Zoltán Csáti (view profile)

Answer by Zoltán Csáti

Zoltán Csáti (view profile)

on 24 Nov 2014

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.