Review: Automatic Model Reduction for Transient Simulation of MEMS‐based Devices

Rudnyi, Evgenii B.; Korvink, Jan G.

doi:10.1002/seup.200211105

Cited by 84 publications

(67 citation statements)

References 84 publications

(89 reference statements)

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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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“…(5), (6) among balanced truncation approximation, singular perturbation approximation, Hankel norm approximation, Guyan reduction and Krylov subspace methods such as Lanczos algorithm and Arnoldi process. Also there are many research works recently on proper orthogonal decomposition (7) or…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation of Dynamic Problem Using Model Order Reduction Technique Highlighting on Tail Probability

Takano

Asai

Okamoto

2012

JCST

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This paper aims at practical Monte Carlo (MC) simulation by finite element method for a dynamic problem where the load condition includes uncertainty factors. A new sampling scheme is proposed to predict an extreme case with high stress by unexpected combination of load parameters, which is involved in the tail probability, to be used in the fatigue life estimation of structures. The proposed scheme, named as stepwise limited sampling (SLS), can provide the expected value of the stress with moderate accuracy and provide reliable results with extremely high stress. In the demonstrative example, the proposed method was computationally cost-effective than usual MC simulation. In addition, a model order reduction (MOR) technique is employed to reduce both the computational cost and the memory requirement. The latter contributed to the fast MC simulation by parallel processing.

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“…It happens that in most cases the trajectory of the state vector can be well approximated by a low-dimensional subspace V, and projecting of ODEs on that subspace yields quite and accurate reduced models [1]. The goal of model order reduction is to find a new system of equations (2)…”

Section: Model Order Reduction For Second Order Systemsmentioning

confidence: 99%

Efficient optimization of transient dynamic problems in MEMS devices using model order reduction

Han

Rudnyi

Korvink

2005

J. Micromech. Microeng.

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Summary One of the main obstacles to including transient dynamic effects into the performance functions of a structural optimization is the high computational cost of each time-dependent simulation. The focus of this paper is on the application of model order reduction techniques to reduce the transient analysis time for the attainable optimization process. The software mor4ansys developed at IMTEK performs model reduction via the Arnoldi algorithm directly to ANSYS finite element models. We adopt a micro accelerometer as an example to demonstrate the advantages of this approach. The harmonic and transient results of a reduced model of the accelerometer yield very good agreement with those from the original high dimensional ANSYS model. The use of model reduction within the optimization iterations produces almost the same results as without order reduction and speeds up the total computation by about an order of magnitude.

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Review: Automatic Model Reduction for Transient Simulation of MEMS‐based Devices

Cited by 84 publications

References 84 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

Monte Carlo Simulation of Dynamic Problem Using Model Order Reduction Technique Highlighting on Tail Probability

Efficient optimization of transient dynamic problems in MEMS devices using model order reduction

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