A Reduced Order Modeling Method with Variable-Separation-Based Domain Decomposition for Parametric Dynamical Systems

TL;DR

This paper introduces a novel reduced order modeling technique for parametric dynamical systems that employs variable-separation-based domain decomposition in the frequency domain, enabling efficient online computations independent of spatial discretization.

Contribution

It extends variable-separation domain decomposition to complex-valued elliptic equations in the frequency domain for parametric systems, providing an efficient offline-online solution framework.

Findings

Efficient offline-online computational procedure established.

Method effectively handles parametric dynamical systems with high efficiency.

Demonstrated success on three specific parametric system examples.

Abstract

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing frequency variables and 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. At the offline stage, separate representations of the solutions for the interface problem and the subproblems are constructed. At the online stage, the solutions of the parametric dynamical systems for new parameter values 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 of parametric dynamical systems to demonstrate the effectiveness of the proposed method.