The present study reports a family of iterative domain decomposition method for the static structural analysis, labeled as and its variants ( and ), all of which employ a recently developed Displacement-Only (DO) partitioned formulation (Park et al., 2023). The DO partitioned equation () consists of the applied force , the block-diagonal stiffness matrix () for each partition, the coupling projection operator (), and the unknown partitioned displacements (). Numerical experiments with the AFETI-DO and its two variants demonstrate that, while their performance is comparable to existing iterative solution algorithms for homogeneous problems, for highly heterogeneous two and three-dimensional problems the proposed methods yield an accurate convergence threshold compared with the FETI-DP method (Farhat et al., 2001). For fourth-order elasticity problems (i.e., thin plates and shells), the present methods offer a comparable accuracy and computational effort required with the FETI-DP method. In addition, while not extensive, the numerical performance of the proposed AFETI-DO method and its variants appear to exhibit scalability and improved accuracy, provided the preconditioners are paired with the commensurate heterogeneities.

中文翻译：

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采用仅位移分区方程进行准静态结构分析的域分解方法


本研究报告了一系列用于静态结构分析的迭代域分解方法，标记为 及其变体 ( 和 )，所有这些方法都采用了最近开发的仅位移 (DO) 分区公式（Park 等人，2023）。 DO 分区方程 () 由施加的力 、每个分区的块对角刚度矩阵 ()、耦合投影算子 () 和未知分区位移 () 组成。 AFETI-DO 及其两个变体的数值实验表明，虽然它们的性能与现有的同质问题迭代求解算法相当，但对于高度异构的二维和三维问题，与 FETI-DO 相比，所提出的方法产生了准确的收敛阈值。 DP 方法（Farhat 等，2001）。对于四阶弹性问题（即薄板和薄壳），本方法提供了与 FETI-DP 方法所需的相当的精度和计算量。此外，虽然不广泛，但所提出的 AFETI-DO 方法及其变体的数值性能似乎表现出可扩展性和更高的准确性，前提是预处理器与相应的异质性配对。