Solve linear tensor equation

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

Answer 1

[Matt J]

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