Preface to the third volume of Model Order Reduction

The third volume of the Model Order Reduction handbook project offers several remarkable instances of applications of model order reduction (MOR) approaches to the solution of problems arising from themost diverse areas of application. Through these examples, we would like to provide the reader with an overview of thematurity of this emerging field and its readiness to address challenging problems ofmultifaceted complexity. We start with several chapter contributions to classical fields of engineering. The first one, by J. Eason and L. Biegler, is onmodel reduction in the optimization of a variety of heterogeneous chemical processes. In particular, two case studies are presented on CO2 capture using nonlinear programming and NLP filter models. The second chapter, by B. Lohmann et al., is on MOR in mechanical engineering. Four applications are discussed, concerning the reduction of a thermo-mechanical machining tool of a car body and driver’s seat, of an elastic crankshaft, and a leaf spring model. The third chapter, by E. Deckers et al., presents several case studies of MOR for acoustics and vibrations inmechanical applications. Two different viewpoints are developed: the application of MOR from a purely mathematical perspective and a consideration of expected properties of MOR based on physical arguments from the field of mechanics. Two chapters devoted to microelectronics and electromagnetism, a very classical and successful arena for MOR methods, follow. The first of those, by B. Nouri et al., pursues a twofold goal: to describe the context in which the need for MOR arose in microelectronics, and to present an overview of their applications to address the issues of high-speed interconnects in microelectronics at various levels of the design hierarchy. The next chapter, by D. Ioan et al., proposes a computer-aided consistent and accurate description of the behavior of electromagnetic devices at various speeds or frequencies, and describes procedures to generate compact electrical circuits featuring an approximately equivalent behavior. The chapter by M. Yano is on model reduction in computational aerodynamics. The focus is on techniques that are designed to address nonlinearity, limited stability, limited regularity, and a wide range of scales that have been demonstrated successful for multidimensional large-scale aerodynamic flows. The next two chapters address a somehow less conventional field of applications, that of life sciences. The chapter by B. Karasözen is on MOR in neurosciences, more specifically on the exploitation of models of large-scale neuronal networks to provide an accurate and fast prediction of patterns and their propagation in different areas of the brain. The following chapter, by N. Dal Santo et al., introduces MOR methods to face some of the most challenging processes of the cardiovascular system. Two specific