  In this paper we present a low-rank method for conforming multipatch
discretizations of compressible linear elasticity problems using Isogeometric
Analysis. The proposed technique is a non-trivial extension of [M. Montardini,
G. Sangalli, and M. Tani. A low-rank isogeometric solver based on Tucker
tensors. Comput. Methods Appl. Mech. Engrg., page 116472, 2023.] to multipatch
geometries. We tackle the model problem using an overlapping Schwarz method,
where the subdomains can be defined as unions of neighbouring patches. Then on
each subdomain we approximate the blocks of the linear system matrix and of the
right-hand side vector using Tucker matrices and Tucker vectors, respectively.
We use the Truncated Preconditioned Conjugate Gradient as a linear solver,
coupled with a suited preconditioner. The numerical experiments show the
advantages of this approach in terms of memory storage. Moreover, the number of
iterations is robust with respect to the relevant parameters.
