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：本文提出一种针对可压缩线弹性问题协调多片离散化的低秩方法，该方法采用等几何分析。所提出的技术是[M. Montardini, G. Sangalli, 和 M. Tani. 基于Tucker张量的低秩等几何求解器. Comput. Methods Appl. Mech. Engrg., 页码116472, 2023.] 向多片几何的非平凡扩展。我们利用重叠型Schwarz方法处理模型问题，其中子域可定义为相邻片的并集。随后在每个子域上，分别采用Tucker矩阵和Tucker向量逼近线性系统矩阵及右端向量中的分块。我们使用截断预条件共轭梯度法作为线性求解器，并配以合适的预条件子。数值实验展示了该方法在内存存储方面的优势，同时迭代次数对相关参数具有鲁棒性。