A domain decomposition method employing displacement-only partitioned equations for quasi-static structural analysis

The present study reports a family of iterative domain decomposition method for the static structural analysis, labeled as AFETI-DO and its variants (AFETI-DOc and AFETI-DOci), all of which employ a recently developed Displacement-Only (DO) partitioned formulation (Park et al., 2023). The DO partitioned equation (Pdf−Kd=0) consists of the applied force f, the block-diagonal stiffness matrix (K) for each partition, the coupling projection operator (Pd), and the unknown partitioned displacements (d). 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.