Large-scale numerical simulations, a significant portion of the total computational cost is spent on solving linear systems. Iterative solvers are commonly employed due to their high parallel efficiency; however, their convergence behavior strongly depends on the conditioning of the system matrix. Consequently, the design of effective preconditioners is crucial for achieving both robustness and performance in large-scale parallel computations. Representative preconditioning techniques for large-scale problems include multigrid methods, domain decomposition methods, and deflation-based approaches [1]. Multigrid methods can provide excellent convergence properties, but geometric multigrid is constrained by mesh structure, while algebraic multigrid does not always fully exploit geometric information. Domain decomposition methods are well suited for parallel environments, yet they often rely on mesh-based frameworks and impose restrictions on partitioning strategies. Deflation preconditioning, on the other hand, is attractive because it allows flexible selection of basis vectors, enabling adaptation to problem-specific characteristics. For these reasons, this study focuses on deflation-based preconditioning. The objective of this research is to develop a flexible linear solver framework that is independent of specific numerical discretization schemes. To this end, computational domains are represented using graph structures, allowing the proposed solver to be applied independently of the underlying numerical method. Furthermore, hierarchical domain decomposition is introduced to enable independent specification of domains used for parallel computation and those used for preconditioning. This decomposition scheme provides additional flexibility in balancing parallel efficiency and preconditioning effectiveness. In this presentation, parallel structural analysis based on the finite element method is considered as a representative application. Eigenvectors are employed as basis vectors for deflation, and the convergence behavior and computational time of the proposed method are evaluated. The performance of the proposed approach is compared with existing methods, including multigrid-based pre- conditioners, to demonstrate its effectiveness in large-scale parallel simulations.