ITR: Computational Theory and Tools for Reduced-Order Modeling of Very Large Dynamical Systems and Applications

University Of California-Davis, Davis CA

Investigators

Abstract

The continual and compelling need for accurately and efficiently simulating dynamical behavior of physical systems arising from a wide variety of applications has led to increasingly large and complex models. Reduced-order modeling (ROM), also called model reduction, techniques play an indispensable role in providing efficient computational prototyping tools to replace such large-scale models by approximate smaller models. Such reduced-order models must be capable of capturing critical dynamical behavior and faithfully preserving essential properties of the larger models they approximate. An accurate and effiective reduced-order model can be applied for steady-state analysis, transient analysis, or sensitivity analysis of large-scale models and the physical systems they emulate. Consequently, scientists and engineers can significantly reduce design time and pursue more aggressive design strategies. Designers can try ``what-if" experiments in hours instead of days. In this proposal, we propose a broad range of synergistic research activities on ROM relating to three interlinking strands: computational theory, reliable algorithms, and high-performance software tools. We will also be actively involved with promoting applications of ROM techniques and testing our methods through existing and new collaborations with researchers in circuit simulation, structural dynamics, control systems, and microelectromechanical systems (MEMS). Specifically, our proposed research activities on computational theory and algorithms include: Accuracy estimation in both time and frequency domains. Sensitivity analysis of linear systems using the techniques of ROM and statistical condition estimation. Development of ROM techniques that directly exploit so-called second-order model structures and generate a reduced-order model in second-order form. Exploration of a framework of ROM techniques for certain types of large-scale nonlinear systems of technological importance.