Model order reduction: Basic concepts and notation

Abstract

This is the first chapter of a three-volume series dedicated to theory and application of Model Order Reduction (MOR). We motivate and introduce the basic concepts and notation, with reference to the two main cultural approaches to MOR: the system-theoretic approach employing state-space models and transfer function concepts (Volume 1), and the numerical analysis approach as applied to partial differential operators (Volume 2), for which projection and approximation in suitable function spaces provide a rich set of tools for MOR. These two approaches are complementary but share the main objective of simplifying numerical computations while retaining accuracy. Despite the sometimes different adopted language and notation, they also share the main ideas and key concepts, which are briefly summarized in this chapter. The material is presented so that all chapters in this three-volume series are put into context, by highlighting the specific problems that they address. An overview of all MOR applications in Volume 3 is also provided.