An enhanced BDDC preconditioner with weighted Schur complement averaging: Application to flexible multibody systems

While the deluxe balancing domain decomposition by constraints (deluxe BDDC) preconditioner has shown effectiveness in large-scale simulations of flexible multibody systems, its current formulation does not fully utilize local Schur complement information in the treatment of primal (coarse) variables, which may affect convergence behavior in the presence of material heterogeneity. To address this issue, this work proposes a weighted Schur complement averaged BDDC preconditioner. The key innovation lies in applying a weighted average of local Schur complements not only in constructing the scaling operator, but also in forming the primal block via the Schur complement with respect to dual variables. Theoretical analysis confirms that the condition number of the preconditioned system remains uniformly bounded. Numerical experiments demonstrate that the proposed method achieves improved scalability, quasi-optimality, and robustness to material coefficient variations compared to the deluxe BDDC preconditioner. Application to the deployment dynamics of a rectangular solar array further illustrates its effectiveness and computational efficiency. This study contributes to the theoretical foundation for the parallel simulation of flexible multibody systems.