Model Reduction of Large-Scale Systems:
An Overview and Some New Results
Direct numerical simulation has become one of few available means for the systematic study of physical or artificial processes for which experiments are expensive and/or time-consuming to perform. But without the aid of systematic strategies for reducing model complexity, the burdens of complex geometries, multi-physics, and operating environments coupled with an ever increasing appetite for accuracy and model fidelity, would likely render simulation an ineffective tool. Model reduction seeks to replace large-scale or infinite-order dynamical systems arising from PDE models with systems of relatively low dimension having similar response characteristics. The goal is to dissipate the fierce computational intensity that the original dynamical system may have required while still maintaining model fidelity. In this talk we will give an overview of projection methods for model reduction and discuss some recent results. Thanos Antoulas, Rice University