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.

翻译：本文提出了一种用于可压缩线性弹性问题共形多片离散的低秩方法，采用等几何分析实现了该技术。该方法是[M. Montardini, G. Sangalli, and M. Tani. A low-rank isogeometric solver based on Tucker tensors. Comput. Methods Appl. Mech. Engrg., page 116472, 2023.]向多片几何结构的非平凡扩展。我们采用重叠型Schwarz方法处理模型问题，子域可定义为相邻片的并集。随后在每个子域上，分别利用Tucker矩阵和Tucker向量近似线性系统矩阵块与右端向量。我们采用截断预处理共轭梯度法作为线性求解器，并搭配适配的预处理器。数值实验表明该方法在内存存储方面具有优势，且迭代次数对相关参数保持稳健性。