Modern Model Order Reduction for Industrial Applications

2 Dynamic analysis is an important part of modern simulation strategy. However, finite element models are inherently high dimensional and, as a result, their dynamic analysis is computationally expensive. For this reason, it is impossible to include a finite element model directly into system level simulation where a device dynamic model should be simulated as a part of a whole system including driving circuitry. In structural mechanics, model reduction based on mode superposition or Guyan reduction has been in use for long time in order to speed up dynamic simulation [1]. These two techniques can be found nowadays in almost any commercial implementation of the finite element method and they are employed not only for structural mechanics but also for other physical domains. Model reduction can also be considered as a formal mathematical problem to approximate dynamic behavior of a high-dimensional model. Recently mathematicians extensively researched the problem from such a viewpoint [2]. They say that if we look at a model reduction problem formally then neither mode superposition nor Guyan reduction produces an optimal reduced model. The goal of this paper is to introduce modern formal model reduction methods and then present examples of their use for different applications in design and system level simulation (see Fig. 1). We limit ourselves by model reduction for linear models as only in this case the model reduction process can be fully automated. We start by short introduction to linear model reduction. Then we discuss how it can be employed for the second order systems, as mathematicians developed the model reduction theory originally for the first order dynamic systems. After that Modern Model Order Reduction for Industrial Applications