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24
Krylov Subspace Techniques for ReducedOrder Modeling of Nonlinear Dynamical Systems
 Appl. Numer. Math
, 2002
"... Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of largescale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bilinearization method, which extends Kry ..."
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Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of largescale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bilinearization method, which extends Krylov subspace techniques for linear systems. In this approach, the nonlinear system is first approximated by a bilinear system through Carleman bilinearization. Then a reducedorder bilinear system is constructed in such a way that it matches certain number of multimoments corresponding to the first few kernels of the VolterraWiener representation of the bilinear system. It is shown that the twosided Krylov subspace technique matches significant more number of multimoments than the corresponding oneside technique.
Model reduction of MIMO systems via tangential interpolation
 SIAM J. Matrix Anal. Appl
, 2004
"... Abstract. In this paper, we address the problem of constructing a reduced order system of minimal McMillan degree that satisfies a set of tangential interpolation conditions with respect to the original system under some mild conditions. The resulting reduced order transfer function appears to be ge ..."
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Abstract. In this paper, we address the problem of constructing a reduced order system of minimal McMillan degree that satisfies a set of tangential interpolation conditions with respect to the original system under some mild conditions. The resulting reduced order transfer function appears to be generically unique and we present a simple and efficient technique to construct this interpolating reduced order system. This is a generalization of the multipoint Padé technique which is particularly suited to handle multiinput multioutput systems.
Perspectives on technology and technologydriven CAD
 Decem ber
, 2000
"... Abstract—Computeraided design (CAD) techniques are absolutely essential to harness the everincreasing complexity of the microsystem design. Similarly, the technology CAD (TCAD) tools played a key role in the development of new technology generations. Although there is a common belief that the TCAD ..."
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Abstract—Computeraided design (CAD) techniques are absolutely essential to harness the everincreasing complexity of the microsystem design. Similarly, the technology CAD (TCAD) tools played a key role in the development of new technology generations. Although there is a common belief that the TCAD tools have been trailing the technology development, the situation has been changing very significantly especially over the last decade. For the deep submicrometer (DSM) devices, these tools provide a better insight than any measurement techniques and they have become indispensable in the new device creation. Moreover, these tools after calibration to a relatively small number of experiments, exhibit very impressive predictive power, which is utilized to speed up the technology integration and transfer to volume manufacturing. This results in very manufacturable highyielding products that can be ramped up much faster than in the past decade, which is absolutely necessary given the huge costs of integrated circuit fabrication lines, short product lifecycles and penalties for being late to the market place. In this paper, we will present our perspective on the semiconductor technology development, and highlight the rapid growth of TCAD and its strategic use in semiconductor industry.
ReducedOrder Modeling of Weakly Nonlinear MEMS Devices with TaylorSeries Expansion and Arnoldi Approach
 TRANSDUCERS MAGAZINE (S&T EDIGEST)
, 2004
"... In this paper, we present a new technique by combining the Taylor series expansion with the Arnoldi method to automatically develop reducedorder models for coupled energy domain nonlinear microelectromechanical devices. An electrostatically actuated fixedfixed beam structure with squeezefilm dam ..."
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In this paper, we present a new technique by combining the Taylor series expansion with the Arnoldi method to automatically develop reducedorder models for coupled energy domain nonlinear microelectromechanical devices. An electrostatically actuated fixedfixed beam structure with squeezefilm damping effect is examined to illustrate the modelorder reduction method. Simulation results show that the reducedorder nonlinear models can accurately capture the device dynamic behavior over a much larger range of device deformation than the conventional linearized model. Compared with the fully meshed finitedifference method, the model reduction method provides accurate models using orders of magnitude less computation. The reduced MEMS device models are represented by a small number of differential and algebraic equations and thus can be conveniently inserted into a circuit simulator for fast and efficient systemlevel simulation.
Model Order Reduction of MEMS for Efficient Computer Aided Design and System Simulation
 MTNS2004, Sixteenth International Symposium on Mathematical Theory of Networks and Systems, Katholieke Universiteit
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Genetic programming for multiscale modeling
 INT. J. OF MULTISCALE COMPUT. ENG
, 2004
"... We propose the use of genetic programming (GP)—a genetic algorithm that evolves computer programs—for bridging simulation methods across multiple scales of time and/or length. The effectiveness of genetic programming in multiscale simulation is demonstrated using two illustrative, nontrivial case s ..."
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We propose the use of genetic programming (GP)—a genetic algorithm that evolves computer programs—for bridging simulation methods across multiple scales of time and/or length. The effectiveness of genetic programming in multiscale simulation is demonstrated using two illustrative, nontrivial case studies in science and engineering. The first case is multitimescale materials kinetics modeling, where genetic programming is used to symbolically regress a mapping of all diffusion barriers from only a few calculated ones, thereby avoiding explicit calculation of all the barriers. The GPregressed barrier function enables use of kinetic Monte Carlo for realistic potentials and simulation of realistic experimental times (seconds). Specifically, a GP regression is applied to vacancyassisted migration on a surface of a binary alloy and predict the diffusion barriers within 0.1–1 % error using 3 % (or less) of the barriers. The second case is the development of constitutive relation between macroscopic variables using measured data, where GP is used to evolve both the function form of the constitutive equation as well as the coefficient values. Specifically, GP regression is used for developing a constitutive relation between flow stress and temperaturecompensated strain rate based on microstructural characterization for an aluminum alloy AA7055. We not only reproduce a constitutive relation proposed in literature, but also develop a new constitutive equation that fits both lowstrainrate and highstrainrate data. We hope these disparate example applications exemplify the power of GP for multiscaling at the price, of course, of not knowing physical details at the intermediate scales.
Order reduction of second order systems
 In Proc. 4th Mathmod
, 2003
"... Abstract. In this article a projection method for order reduction of large systems of linear equations is presented. Such systems arise for instance through the semidiscretization of partial differential equations from the electrical, thermal or mechanical domain. The proposed algorithm extends the ..."
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Abstract. In this article a projection method for order reduction of large systems of linear equations is presented. Such systems arise for instance through the semidiscretization of partial differential equations from the electrical, thermal or mechanical domain. The proposed algorithm extends the efficient nodal order reduction method (ENOR) that was developed for second order systems. Our method ensures an exact solution for the static case and provides good approximations in the frequency and the time domain. The reduced systems can be used for behavioral models for system simulation. Examples from several domains demonstrate the power of our algorithm. 1
MST MEMS compact modeling meets model order reduction: Requirements and Benchmarks
, 2004
"... Needs for model reduction in microsystem technology (MST) are described from an engineering perspective. The MST model reduction benchmarks are presented in order to facilitate further development in this area. The first benchmark application is electrothermal simulation and the second one is an el ..."
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Needs for model reduction in microsystem technology (MST) are described from an engineering perspective. The MST model reduction benchmarks are presented in order to facilitate further development in this area. The first benchmark application is electrothermal simulation and the second one is an electrostatically actuated beam. Model reduction is contrasted with compact modeling, which currently enjoys widespread use among engineers, and important problems to be solved are listed.
VHDLAMS based modeling and simulation of mixedtechnology microsystems: a tutorial $
, 2005
"... This tutorial paper describes different approaches to modeling and simulation of mixedtechnology microsystems that consist of electrical circuits connected to subsystems described by partial differential equations (PDEs), which is a typical situation in many modern integrated circuits and systems. ..."
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This tutorial paper describes different approaches to modeling and simulation of mixedtechnology microsystems that consist of electrical circuits connected to subsystems described by partial differential equations (PDEs), which is a typical situation in many modern integrated circuits and systems. We target this paper towards the audience use of VHDLAMS (a hardware description language suitable for modeling and simulation of such systems). We describe existing approaches to modeling such systems and present three examples accompanied by their VHDLAMS implementations and simulation results. r 2006 Elsevier B.V. All rights reserved. Keywords: VHDLAMS; Modeling; Simulation; Mixedtechnology