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We consider the problem of computing approximate solution of Poisson equationin the low-parametric tensor formats. We propose a new algorithm to compute thesolution based on the cross approximation algorithm in the frequency space, andit has better complexity with respect to ranks in comparison with standardalgorithms, which are based on the exponential sums approximation. Toillustrate the effectiveness of our solver, we incorporate into a Uzawa solverfor the Stokes problem on semi-staggered grid as a subsolver. The resultingsolver outperforms the standard method for $n \geq 256$.

Fast low-rank solution of the Poisson equation with application to the Stokes problem