The optimization and control of systems governed by partial differential equations (PDEs) usually requires numerous evaluations of the forward problem or the optimality system. Despite the fact that many recent efforts, many of which are reported in this book, have been made to limit or reduce the number of evaluations to 5–10, this cannot be achieved in all situations and even if this is possi...

Model order reduction (MOR) is here understood as a computational technique to reduce the order of a dynamical system described by a set of ordinary or differential-algebraic equations (ODEs or DAEs) to facilitate or enable its simulation, the design of a controller, or optimization and design of the physical system modeled. It focuses on representing the map from inputs into the system to its ...

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...

In this paper new sufficient conditions are presented for the existence of a Lyapunov pair with a coupling rank constraint within a H∞ minimization framework derived using the bounded real lemma and the projection lemma. The conditions are then used to propose a Linear Matrix Inequality (LMI) sub-optimal method to solve the model order reduction problem of general non-square LTI systems with a ...

The paper investigates the properties of reduced order models obtained by projection of a high order system. It answers questions such as are any two models of different orders related by a projection? Is it possible to obtain the same reduced order model using different projections? Etc. It is shown that in cases where not all models of a certain reduced order can be obtained by a projection, ...

Model Order Reduction of Nonlinear Dynamical Systems by Chenjie Gu Doctor of Philosophy in Electrical Engineering and Computer Science University of California, Berkeley Professor Jaijeet Roychowdhury, Chair Higher-level representations (macromodels, reduced-order models) abstract away unnecessary implementation details and model only important system properties such as functionality. This meth...

This paper presents an optimal discrete time reduced order Kalman ̄lter. The reduced order ̄lter is used to estimate a linear combination of a subset of the state vector. Most previous approaches to reduced order ̄ltering rely on a reduction of the model order. However, this paper takes the full model order into account. The reduced order ̄lter is obtained by minimizing the trace of the estimat...

In this paper, we have proposed a novel model order reduction technique via rational transfer function fitting and eigenmode analysis considering residues. We define a constant as a key in the sorting algorithm as one of correlations in order to sort the order of eigenvalues. It is demonstrated that the accuracy via eigenmode analysis considering residues is improved. The proposed algorithm is ...

Theoretical and practical aspects of model order reduction techniques for use in the context of circuit simulation are investigated, with particular attention to problems involving clocked analog circuitry and to interconnect and packaging applications. First, an algorithm for the efficient simulation of clocked analog circuits is described and simulation results are presented. Traditional simu...