Partitioned Balancing Domain Decomposition Method for Heterogeneous Static Structures

This study proposes a partitioned balancing domain decomposition (P‐BDD) method for static analysis of heterogeneous structures. The P‐BDD method may be viewed as a localized version of traditional BDD approaches. Its principal solution vector consists of unassembled partition‐boundary displacements, used to compute the partition‐interior displacements. This differs from existing BDD methods whose primary solution vector consists of the assembled interface displacements along the partition boundaries. Two types of coarse‐space preconditioners, Type‐c and Type‐ci, are introduced to enhance convergence. Numerical experiments demonstrate that the P‐BDD method achieves high accuracy and computational efficiency in solving heterogeneous systems compared with traditional methods. As a byproduct of the P‐BDD method, adopting the framework of localized Lagrange multipliers (LLMs) yields an efficient preconditioner for conventional BDD methods, referred to as LLM‐BDD, which is applicable to nonconformal interface problems.