Model Reduction for RF MEMS Simulation

Bindel, David; Bai, Zhaojun; Demmel, James

doi:10.1007/11558958_34

Cited by 13 publications

(17 citation statements)

References 16 publications

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“…Rational interpolation methods have been extended to bilinear [24,36,37,39,58,92,98,192] and quadratic-in-state systems [37,38,97,114]. Even though these methods have proven effective for a wide range of problem settings, they are most widely used in circuit theory, such as [23,44,90,184,195], e.g., to analyze and predict signal propagation and interference in electric circuits; in structural mechanics, such as [53,106,174,198,211], to study, e.g., vibration suppression in large structures or behavior of micro-electromechanical systems; and in (optimal) control and controller reduction, such as [11,21,126,185,215,231], e.g., in LQR/LQG control design.…”

Section: Applicability Of the Basis Computation Methodsmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

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Section: Applicability Of the Basis Computation Methodsmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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“…Also, because W is a real-valued basis, projection onto the space spanned by W corresponds to a Bubnov-Galerkin discretization of the PML equation with shape functions N reduced I = J W IJ N J . While these facts alone might induce us to use W rather than V as a projection basis [47], we expect projection onto W to yield much better accuracy than standard Arnoldi projection, as we now describe.…”

Section: Efficient Forced Motion Computationsmentioning

confidence: 93%

“…The reflection coefficient in the discrete case can now be defined as r discrete = |c 2 /c 1 |. The coefficients c m are computed by solving (50) using the values for V 1 and V 2 from the numerical solution to (47). Because 1 is an algebraic function of k x h, it can only approximate the transcendental function exp(−ik x h).…”

Section: Model Problem: Discrete Casementioning

confidence: 99%

Elastic PMLs for resonator anchor loss simulation

Bindel

Govindjee

2005

Numerical Meth Engineering

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146

104

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SUMMARYElectromechanical resonators and filters, such as quartz, ceramic, and surface-acoustic wave devices, are important signal-processing elements in communication systems. Over the past decade, there has been substantial progress in developing new types of miniaturized electromechanical resonators using microfabrication processes. For these micro-resonators to be viable they must have high and predictable quality factors (Q). Depending on scale and geometry, the energy losses that lower Q may come from material damping, thermoelastic damping, air damping, or radiation of elastic waves from an anchor. Of these factors, anchor losses are the least understood because such losses are due to a complex radiation phenomena in a semi-infinite elastic half-space. Here, we describe how anchor losses can be accurately computed using an absorbing boundary based on a perfectly matched layer (PML) which absorbs incoming waves over a wide frequency range for any non-zero angle of incidence. We exploit the interpretation of the PML as a complex-valued change of co-ordinates to illustrate how one can come to a simpler finite element implementation than was given in its original presentations. We also examine the convergence and accuracy of the method, and give guidelines for how to choose the parameters effectively. As an example application, we compute the anchor loss in a micro disk resonator and compare it to experimental data. Our analysis illustrates a surprising mode-mixing phenomenon which can substantially affect the quality of resonance.

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“…The goal of this device is to produce a high-frequency bandpass filter, for example, the surface acoustic wave devices used in cell phones [18]. The order of stiffness and mass matrices K and M generated by the FE discretization of 2D elements is 15 258.…”

Section: Checkerboard Filtermentioning

confidence: 99%

High‐frequency response analysis via algebraic substructuring

Ko¹,

Bai²

2008

Numerical Meth Engineering

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SUMMARYHigh-frequency response analysis (Hi-FRA) of large-scale dynamical systems is critical to predict the resonant behavior of modern micro-devices and systems operated over MHz or GHz frequency range. Algebraic substructuring (AS) is a powerful technique to extract a large number of natural frequencies. In this work, we extend the AS technique for FRA between two specified cutoff frequencies min and max . The technique is referred to as ASFRA. ASFRA can be efficiently applied to Hi-FRA, as demonstrated by two examples of microelectromechanical sensors operated at 1-2 and 200-250 MHz ranges. To some extent ASFRA generalizes the underlying numerical algorithm and functionality of commercially viable automated multi-level substructuring (AMLS) technique. AMLS is designed for FRA up to a specific frequency max , starting from the lowest, and is inefficient for Hi-FRA.

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Model Reduction for RF MEMS Simulation

Cited by 13 publications

References 16 publications

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Elastic PMLs for resonator anchor loss simulation

High‐frequency response analysis via algebraic substructuring

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