Solve linear tensor equation

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Dominique Gorissen
Dominique Gorissen 2023-2-12
编辑： Matt J 2023-2-12
Ran in:
I am building a fem code and want to solve an equation of the form
f= tensorprod(A,u,[2,4],[1,2])
where:
size(A)= n by n by 2 by 2
Size(u) = n by 2
Size(F) = n by 2.
A and f are known, u is to be solved
please note that n is a large number e.g order of 1e4 and this equation has to be solved often
n=5;
A=rand(n,n,2,2);
u=rand(n,2); %u is actually the variable that is to be solved while f is known
f=tensorprod(A,u,[2 4],[1 2])
f = 5×2
2.2134 2.4372 1.8815 2.0397 2.8814 2.2488 2.5063 2.0120 3.1808 1.7589

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Matt J
Matt J 2023-2-12
编辑：Matt J 2023-2-12
Ran in:
n=5;
A=rand(n,n,2,2);
utrue=rand(n,2);
f=tensorprod(A,utrue,[2 4],[1 2]);
A=permute(A,[1,3,2,4]);
A=reshape(A,2*n,2*n);
u=A\f(:); %solve
[u(:), utrue(:)]
ans = 10×2
0.2121 0.2121 0.7296 0.7296 0.3174 0.3174 0.5335 0.5335 0.6222 0.6222 0.8405 0.8405 0.3491 0.3491 0.2908 0.2908 0.8140 0.8140 0.1061 0.1061

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