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

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David Koenig
David Koenig on 21 Nov 2014
Commented: Jan on 24 Nov 2014
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
+ 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)...
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?

Answers (1)

Zoltán Csáti
Zoltán Csáti 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.


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