A Variable-Separation-based Domain Decomposition Method for Parametric Dynamical Systems

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier integral transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing both the frequency variables and the parameters inherited from the original model. To reduce the computational cost of the frequency-variable elliptic equations, we extend the variable-separation-based domain decomposition method to the complex-valued context, resulting in an offline-online procedure for solving the parametric dynamical systems. In the offline stage, separate representations of the solutions for the interface problem and the subproblems are constructed. In the online stage for new parameter values, the solutions of the parametric dynamical systems can be directly derived by utilizing the separate representations and implementing the inverse Fourier transform. The proposed approach is capable of being highly efficient because the online stage is independent of the spatial discretization. Finally, we present three specific instances for parametric dynamical systems to demonstrate the effectiveness of the proposed method.