This paper is concerned with model order reduction of large scale dynamic systems that have sparse matrix representations, particularly systems with large numbers of input/output ldquoports.rdquo We present an algorithm that combines the advantages of widely-used approaches such as PRIMA and TICER but avoids many of the drawbacks of both. The resulting algorithm is capable of high-order rational approximation, exploits network sparsity, preserves passivity, can be extended to general non-symmetric systems, and can be applied to networks with hundreds or thousands of ports. We develop a common mathematical framework that can encompass all three algorithms, show mathematical relations between them, and point out certain special cases where they are equivalent. We show examples from analysis of industrial on-chip RC/RLC networks that demonstrate performance advantages of more than three orders of magnitude.

In this paper, we present a technique for automatically extracting nonlinear macromodels of biomedical microelectromechanical systems devices from physical simulation. The technique is a modification of the recently developed trajectory piecewise-linear approach, but uses ideas from balanced truncation to produce much lower order and more accurate models. The key result is a perturbation analysis of an instability problem with the reduction algorithm, and a simple modification that makes the algorithm more robust. Results are presented from examples to demonstrate dramatic improvements in reduced model accuracy and show the limitations of the method.

In this paper we are concerned with developing more reliable model reduction algorithms. We have focused on less common, but real, examples that fail to be effectively reduced by almost all of the currently popular model reduction methods. The failure of these popular methods is due to the fact that they all separately examine controllability and observability. We then present a new method based on several modifications and extensions of the recently developed AISIAD algorithm. The modified AISAID method is demonstrated on a wide variety of examples, including electrical interconnect, micromachined devices, and heat flow to show that the method is reliable. Our modified AISAID method is either nearly equivalent or far superior to any of the other reduction methods suitable for large scale problems.

In this paper we propose a method for generating reduced models for a class of nonlinear dynamical systems, based on truncated balanced realization (TBR) algorithm and a recently developed trajectory piecewise-linear (TPWL) model order reduction approach. We also present a scheme which uses both Krylov-based and TBR-based projections. Computational results, obtained for examples of nonlinear circuits and a micro-electro-mechanical system (MEMS), indicate that the proposed reduction scheme generates nonlinear macromodels with superior accuracy as compared to reduction algorithms based solely on Krylov subspace projections, while maintaining a relatively low model extraction cost.