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We propose an isogeometric solver for Poisson problems that combinesi)low-rank tensor techniques to approximate the unknown solution and the systemmatrix, as a sum of a few terms having Kronecker product structure, ii) aTruncated Preconditioned Conjugate Gradient solver to keep the rank of theiterates low, and iii) a novel low-rank preconditioner, based on the FastDiagonalization method where the eigenvector multiplication is approximated bythe Fast Fourier Transform. Although the proposed strategy is written inarbitrary dimension, we focus on the three-dimensional case and adopt theTucker format for low-rank tensor representation, which is well suited in lowdimension. We show by numerical tests that this choice guarantees significantmemory saving compared to the full tensor representation. We also extend andtest the proposed strategy to linear elasticity problems.

A low-rank isogeometric solver based on Tucker tensors