Showing papers on "Model order reduction published in 2000"

Modeling and transient simulation of planes in electronic packages

Abstract: This paper presents a modeling and simulation approach for ground/power planes in high speed packages. A plane pair structure is first characterized in terms of its impedance (Z) matrix at arbitrary port locations in the frequency domain. This solution is then extended for multiple plane pairs under the assumption that skin effect is prominent at higher frequencies causing isolation between the layers. Since the solutions are in analytical form, the frequency and transient response can be computed efficiently requiring small computational time. To develop spice models, equivalent circuits are constructed using resonator models with passive elements using model order reduction methods. This paper also discusses a method for incorporating decoupling capacitors into the plane models. The simulation results show good correlation with measured data.

Emerging simulation approaches for micromachined devices

Abstract: In this survey paper, we describe and contrast three different approaches for extending circuit simulation to include micromachined devices. The most commonly used method, that of using physical insight to develop parameterized macromodels, is presented first. The issues associated with fitting the parameters to simulation data while incorporating design attribute dependencies are considered. The numerical model order reduction approach to macromodeling is presented second, and some of the issues associated with fast solvers and model reduction are summarized. Lastly, we describe the recently developed circuit-based approach for simulating micromachined devices, and describe the design hierarchy and the use of a catalog of parts.

Macro-elements for efficient FEM simulation of small geometric features in waveguide components

Abstract: This paper introduces a novel class of specially constructed elements aimed at the expedient finite-element modeling of waveguide components containing fine geometric/material features such as dielectric and conducting posts. Instead of utilizing a very fine grid to resolve such fine features, special elements are constructed that capture accurately the electromagnetic properties of the fine features. Since the size of these macro-elements Is commensurate with the size of the elements of the grid used to discretize the volume in which the fine features are embedded, their use results in significant reduction in the number of unknowns in the finite-element approximation of the electromagnetic problem without sacrificing solution accuracy. The numerical implementation and effectiveness of the proposed macro-elements are demonstrated through several numerical experiments.

An algorithm for automatic model-order reduction of nonlinear MEMS devices

Abstract: In this paper, we apply the Arnoldi method to generate accurate reduced-order models for coupled energy domain nonlinear microelectromechanical devices. Besides the traditional application of Arnoldi method to generate reduced-order models for linear systems, we propose a new algorithm by combining the Arnoldi method and Taylor series expansion for carrying out model-order reduction on quadratic or even higher order nonlinear systems. A well-known nonlinear MEMS device, electrostatic actuated fixed-fixed beam device with squeeze-film damping effect, is studied. Simulation results demonstrate that the reduced nonlinear model has a much better accuracy to capture the original device behavior than the simple linearization method. The reduced MEMS device model can be easily connected to a circuit simulator for efficient system level simulations.

Novel closed-form Green's function in shielded planar layered media

Abstract: A new method is proposed for the construction of closed-form Green's function in planar, stratified media between two conducting planes. The new approach does not require the a priori extraction of the guided-wave poles and the quasi-static part from the Green function spectrum. The proposed methodology can be easily applied to arbitrary planar media without any restriction on the number of layers and their thickness. Based on the discrete solution of one-dimensional ordinary differential equations for the spectral-domain expressions of the appropriate vector potential components, the proposed method leads to the simultaneous extraction of all Green's function values associated with a given set of source and observation points. Krylov subspace model order reduction is used to express the generated closed-form Green's function representation in terms of a finite sum involving a small number of Hankel functions. The validity of the proposed methodology and the accuracy of the generated closed-form Green's functions are demonstrated through a series of numerical experiments involving both vertical and horizontal dipoles.

Systematic development of transmission line models for interconnects with frequency-dependent losses

Abstract: This paper presents a systematic methodology for the development of transmission line models for interconnects with frequency-dependent per-unit-length parameters. The proposed methodology is such that a variety of models can be developed for use either in frequency-domain or time-domain simulation of signal propagation in the interconnects. The models derived make no assumption about the frequency dependence of the elements (both diagonal and off-diagonal) of the per-unit-length inductance and resistance matrices. Furthermore, their form is such that model order reduction can be effected using a variety of state-of-the-art methodologies.

Model order reduction techniques applied to electromagnetic problems

Abstract: The modeling of the electromagnetic (EM) behavior of VLSI systems is becoming increasingly important as the clock frequencies increase and as signal rise times decrease. The higher spectral content of the signals and the more complicated structures increase the complexity of the electromagnetic models required. This in turn results in an increase in memory requirements as well as in computer time. For this reason, many researchers have considered the use of model order reduction (MOR) techniques to simplify the analysis of EM models of all types. This paper describes the state of the art of MOR for EM problems. Two practical problems, a 2D problem and a 3D problem, are given to encourage comparison between the methods for similar problems.

Reduced-order design-oriented stress analysis using combined direct and adjoint solutions

Abstract: A new method for extracting accurate stress information from reduced-order structural and aeroelastic models is presented. The method has second-order accuracy when approximate reduced-order direct and adjoint solutions (based on different reduced-order bases) are used simultaneously to obtain approximate stresses. The method is applicable to both static and dynamic linear analysis. A review of four common methods for structural model order reduction [two variants of the mode displacement method (standard mode displacement and the fictitious mass method), the mode acceleration method, and the Ritz vector method] identifies sources of difficulty and causes of errors in stress behavior sensitivity calculations. Considerations used for selection of the reduced-order direct and adjoint bases are discussed. A series of static and dynamic test cases is used to assess accuracy of the new method in an analysis mode. Accuracy studies of sensitivity calculations follow. We hope to contribute to the field of design-oriented structural dynamics in terms of both insight and practice.

Novel Closed-Form Green's Function in Shielded

Abstract: A new method is proposed for the construction of closed-form Green's function in planar, stratified media between two conducting planes. The new approach does not require the a priori extraction of the guided-wave poles and the quasi-static part from the Green function spectrum. The proposed methodology can be easily applied to arbitrary planar media without any restriction on the number of layers and their thickness. Based on the discrete solution of one-dimensional ordinary differential equations for the spectral-domain expressions of the appropriate vector potential components, the proposed method leads to the simultaneous extraction of all Green's function values associated with a given set of source and observation points. Krylov subspace model order reduction is used to express the generated closed-form Green's function representation in terms of a finite sum involving a small number of Hankel functions. The validity of the proposed methodology and the accuracy of the generated closed-form Green's functions are demonstrated through a series of numerical experiments involving both vertical and horizontal dipoles. Index Terms—Green's function, layered media.

Passive model order reduction algorithrrl based on Chebyshev expansion of impulse response of interconnect networks

Abstract: In this paper, we provide a new passive model order reduction algorithm on interconnects, which is based on the Chebyshev expansion of their impulse response The Chebyshev coefficient matrices of the impulse response of the reduced order model up to a given order remain the same as those of the original network, so that the time domain transient response of the reduced order model matches that of the original network well Compared with the model order reduction algorithms based on the frequency domain response, it is more efficient in dealing with complicated transient waveforms of interconnects where strong inductance effects are involved

Parametric generalized singular perturbation approximation for model order reduction

Abstract: A new model reduction technique for the approximation of balanced realization is introduced. The method involves a further generalization of the generalized singular perturbation approximation by adding several parameters that can be tuned according to a specified performance criterion. An a priori bound can be computed guaranteeing the quality of the approximated model in the whole range of parameter variations. Two numerical examples conclude this paper.

Rules for robust generation of accurate reduced-order models for high-speed coupled interconnections

Abstract: Recently, robust algorithms have been established for passive order reduction of electrical models of complex interconnection networks. However, very little is known about the way the order of the reduced model should be chosen to ensure accuracy in subsequent transient simulation studies. In this paper, a rule is derived for the selection of the order of the reduced model for interconnections modeled as transmission lines. It is shown that pulse rise time, interconnection length, and physical properties impact the order of the reduced model. The proposed rule is validated through numerical studies involving both analytic and numerical results from the frequency- and time-domain response of multiconductor transmission line circuits.

Application of Model Order Reduction to Compressor Aeroelastic Models

Abstract: A model order reduction technique that yields low-order models of blade row unsteady aerodyamics is introduced. The technique is applied to linearized unsteady Euler CFD solutions in such a way that the resulting blade row models can be linked to their surroundings through their boundary conditions. The technique is applied to a transonic compressor aeroelastic analysis, in which the high-fidelity CFD forced-response results are better captured than with models that use single-frequency influence coefficients. A low-speed compressor stage is also modeled to demonstrate the multistage capability of the method. These examples demonstrate how model order reduction can be used to systematically improve the versatility, fidelity, and range of applicability of the low-order aerodynamic models typically used for incorporation of CFD results into aeroelastic analyses.Copyright © 2000 by ASME

Arnoldy based passive model order reduction algorithm

Abstract: Many problems in modern interconnect and packaging design require use of "full-wave" modeling in order to obtain good accuracy at high frequencies. In this paper, we introduce a passive Arnoldy based model order reduction algorithm for such systems.

Passive model order reduction of multiport distributed interconnects

Abstract: Signal integrity analysis has become imperative for high-speed designs. In this paper, we present a new technique to advance Krylov-space based passive model-reduction algorithms to include lossy coupled transmission lines described by Telegrapher's equations. In the proposed scheme, transmission line subnetworks are treated with closed-form stamps obtained using matrix-exponential Pade, where the coefficients describing the model are computed a priori and analytically. In addition, a technique is given to ensure that the contribution of these stamps to the modified nodal analysis (MNA) formulation leads to guaranteed passive macromodel.

Model-order reduction of weakly nonlinear MEMS devices with Taylor series expansion and Arnoldi process

Abstract: Presents a new method combining Taylor series expansion and Arnoldi method to develop reduced-order models for weakly nonlinear MEMS devices. A fixed-fixed beam structure with squeeze-film damping effect is studied. Simulation results with the reduced-order models demonstrate good agreement with the data generated from the finite difference simulation but with an order of magnitude reduction in execution time. The reduced-order models have been integrated in a multi-level circuit simulator for composite circuit and micromechanical simulations.

Multipoint Galerkin asymptotic waveform evaluation

Abstract: A novel model order reduction technique is coupled with the finite element method (FEM) to provide solutions to antenna radiation problems. This technique, known as multipoint Galerkin asymptotic waveform evaluation (MGAWE), can be used to reduce matrices describing electromagnetic phenomena generated through the FEM to a smaller space while still accurately approximating the characteristics of the original responses. The resulting solution procedure of using MGAWE to solve FEM equations allows for wideband frequency simulations with a reduction in total computation time. Numerical simulations using this method are shown along with the traditional method of using an LU decomposition at each frequency point of interest. Comparisons in accuracy as well as computation time are also given.

An Application of Robust H2/H infinity Control Synthesis to Launch Vehicle Ascent

Abstract: : This thesis explores the application of H2/H infinity control synthesis methods to launch vehicle ascent, specifically the pitch-plane control of the Kistler Aerospace launch vehicle, K1. A classical single-input, single-output design is also presented in order to assess the true applicability of a modern control synthesis approach to launch vehicle ascent. In addition, the K1 dynamics are developed to include aerodynamic, fuel-sloshing, tail-wags-dog, and body-bending effects. The objective of the modern control synthesis approach is to design compensation for pitch tracking and disturbance rejection. It combines techniques in optimal H2, optimal H infinity, and sub-optimal control synthesis to create pitch control laws that provide 6 dB of gain margin and 30 degrees of phase margin. The sensitivity and high-order of traditional H2/H infinity synthesis are addressed through the implementation of uncertainty in the design model and the application of balanced, model order reduction on the resulting controllers. To reduce the complexity in applying these methods, a hierarchical approach and design strategy is employed. A comparison of the two design methods, classical and modern, reveals that each design architecture is capable of creating controllers of equivalent order with both nominal and robust performance. The advantages of the modern approach are realized in the design process itself. The hierarchical methodology and intuitive nature of the modern approach helps to manage the selection of design parameters. Whereas, classical methods provide less insight into strategies for parameter selection and control design. Additionally, the ability to address disturbances and uncertainty in the modern approach offers a more direct alternative to the ad hoc and iterative nature of classical methods, and although not fully exploited here, the modern approach does allow coupling between channels to be accommodated.

Enhancement of the least-squares Padé method for discrete systems

Abstract: The least-squares Pade method for discrete system order reduction is further enhanced. First, it is shown how the method may be extended to produce true least-squares approximations between the time responses of the full and reduced models. Second, it is shown how different stable reduced degree denominator polynomials can be generated from subsets of the system Markov parameters. Examples are given to illustrate these enhancements to the method.

On Process Model Order Reduction for Controller Design in Discrete Systems

Abstract: This paper studies the model reduction problem with emphasis on closed loop performance. First, the admissible fixed order models are identified as the ones that are simultaneously stabilizable with the high order process. A complete parametrization of this set in terms of stable parameters that satisfy cubic equality constraints is developed. An optimization problem is then formulated so that its solution identifies the fixed order model that satisfies nominal performance specifications, it is simultaneously stabilizable with the actual process and the actual closed loop optimally satisfies the nominal performance specifications. This nonlinear, infinite dimensional optimization problem is solved by means of exact penalty functions and an asymptotic approximation procedure. An illustrative example is also presented.

A higher level algorithm for 2D electromagnetic modelling using an FDTD grid

Abstract: A new method combining a finite difference method together with a model order reduction algorithm is presented for 2D electromagnetic problems. The problem is first subdivided into suitable subdomains. Next, the spatial part of the 2D-FDTD method is applied to obtain a set of first order differential equations describing each subdomain and a model order reduction method (ROM) is used to reduce the number of variables needed to describe the subdomain. In a last step, a time-stepping algorithm is used to solve the ROM equations and subdomains are again connected in an FDTD-way.