Convergence Enhancement of the AFETI-DO Parallel Domain Decomposition Method
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Recently, a partitioning method referred to as the PartStiff equation was developed for structural finite element (FE) analysis, which eliminates interface variables (e.g., Lagrange multipliers) to yield partitioned displacement-only (DO) equations. The corresponding DO-based algebraically partitioned FE tearing and interconnecting (AFETI-DO) method was subsequently developed as a parallel iterative solution algorithm, offering significant implementation simplicity and solution accuracy for heterogeneous structures. However, despite these advantages, the scalability of the AFETI-DO method remains an open issue. This paper presents a convergence acceleration technique for the AFETI-DO method by utilizing recent advancements in PartStiff and its complete dual, the PartFlex equation. An element-by-element preconditioner is developed for the quasi-static analysis of heterogeneous structures across various applications. In addition, an interface variant of the AFETI-DO method, labelled as the partitioned balancing domain decomposition (P-BDD) method, is introduced, inheriting a similar implementation simplicity of regularization strategy for heterogeneous problems as that of AFETI-DO.
