References & Citations
Mathematics > Numerical Analysis
Title: A low-rank isogeometric solver based on Tucker tensors
(Submitted on 1 Jun 2023 (v1), last revised 28 Sep 2023 (this version, v3))
Abstract: We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated Preconditioned Conjugate Gradient solver to keep the rank of the iterates low, and iii) a novel low-rank preconditioner, based on the Fast Diagonalization method where the eigenvector multiplication is approximated by the Fast Fourier Transform. Although the proposed strategy is written in arbitrary dimension, we focus on the three-dimensional case and adopt the Tucker format for low-rank tensor representation, which is well suited in low dimension. We show by numerical tests that this choice guarantees significant memory saving compared to the full tensor representation. We also extend and test the proposed strategy to linear elasticity problems.
Submission history
From: Monica Montardini [view email][v1] Thu, 1 Jun 2023 12:54:20 GMT (577kb,D)
[v2] Sat, 3 Jun 2023 07:22:32 GMT (577kb,D)
[v3] Thu, 28 Sep 2023 08:14:10 GMT (505kb,D)
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