Matrix-Free Moment-Matching Method for Reduced-Order Modeling of Quadratic-Bilinear Descriptor Systems with Multiple Inputs

Abstract

This paper develops a new moment-matching order reduction method for multi-input quadratic-bilinear descriptor systems. The proposed approach accommodates multiple inputs acting on both the differential and algebraic equations and constructs separate projection spaces associated with different input channels and input combinations. The method uses a matrix-free algorithm, allowing the reduced-order matrices and tensors to be computed without explicitly assembling or storing the full-order system matrices and tensors. This feature makes the proposed method particularly suitable for large-scale computational fluid dynamics problems. Numerical experiments carried out for two-dimensional flow problems demonstrate that the resulting reduced-order models accurately reproduce the transient responses of the full-order models under multiple time-varying inputs.