In this paper, we propose an innovative isogeometric low-rank solver for the linear elasticity model problem, specifically designed to allow multipatch domains. Our approach splits the domain into subdomains, each formed by the union of neighboring patches. Within each subdomain, we employ Tucker low-rank matrices and vectors to approximate the system matrices and right-hand side vectors, respectively. This enables the construction of local approximate fast solvers. These local solvers are then combined into an overlapping Schwarz preconditioner, which is utilized in a truncated preconditioned conjugate gradient method. Numerical experiments demonstrate the significant memory storage benefits and a uniformly bounded number of iterations with respect to both mesh size and spline degree.

翻译：本文针对线性弹性模型问题提出了一种创新的等几何低秩求解器，特别设计用于支持多片区域。我们的方法将计算域分割为若干子域，每个子域由相邻片体的并集构成。在每个子域内部，我们分别采用Tucker低秩矩阵和向量来近似系统矩阵与右端项向量。这一策略使得构建局部近似快速求解器成为可能。这些局部求解器随后被整合到一个重叠Schwarz预条件子中，并应用于截断预条件共轭梯度法。数值实验表明，该方法在内存存储方面具有显著优势，且迭代次数相对于网格尺寸和样条次数均呈现一致有界性。