Frequency based coarse space for FETI method in nonlinear structural dynamic problems

The nonlinear structural dynamic analysis of mechanical assemblies with nonlinearities poses significant computational challenges, especially as the size and complexity of the Finite Element model increases. This is especially true in turbomachinery, where the large Finite Element models of bladed-disk assemblies often require the use of reduced order models to reduce computational cost. However, reduced order models rely on physical assumptions and involve additional solution steps, which may not always be computationally efficient or feasible. To address these challenges, domain decomposition methods offer a promising alternative. They constitute a robust and well-established class of techniques for tackling large-scale problems in the context of High Performance Computing. Among the various domain decomposition strategies, the Finite Element Tearing and Interconnecting (FETI) method is widely recognized for its robustness and efficiency in engineering applications. When applied to nonlinear dynamic problems with localized nonlinearities in the frequency domain, the FETI formulation leads to an indefinite, non-symmetric linear system. Such a system is typically solved iteratively using the GMRES algorithm, whose convergence can be significantly accelerated by introducing coarse spaces. In the FETI framework, state-of-the-art coarse spaces for the solution of static and dynamic problems are typically constructed using the rigid body modes of the individual domains resulting from the Finite Element model decomposition. While this approach performs well for static and time domain dynamic analyses, it loses its effectiveness when applied to frequency domain solutions. This paper introduces a novel coarse space, referred to as the Frequency Based Coarse Space, specifically designed for the solution of nonlinear structural dynamic problems in the frequency domain.