MST MEMS model order reduction: Requirements and benchmarks

Lienemann, Jan; Rudnyi, Evgenii B.; Korvink, Jan G.

doi:10.1016/j.laa.2005.04.002

Cited by 32 publications

(28 citation statements)

References 37 publications

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“…One application for this model is analysis of microelectromechanical systems (MEMS) devices, such as electromechanical radio frequency (RF) filters [42]. Given a simple enough shape, these devices can be modeled as 1D beams embedded in two or three dimensional space.…”

Section: Electrostatically Actuated Beam Examplementioning

confidence: 99%

Construction of energy-stable projection-based reduced order models

Kalashnikova

Barone

Arunajatesan

et al. 2014

Applied Mathematics and Computation

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a r t i c l e i n f o Keywords: Reduced order model (ROM) Proper orthogonal decomposition (POD)/ Galerkin projection Linear hyperbolic/incompletely parabolic systems Linear time-invariant (LTI) systems Numerical stability Lyapunov equation a b s t r a c tAn approach for building energy-stable Galerkin reduced order models (ROMs) for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is developed. This method is an extension of earlier work by the authors specific to the equations of linearized compressible inviscid flow. The key idea is to apply to the PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. For linear problems, the desired transformation is induced by a special inner product, termed the ''symmetry inner product'', which is derived herein for several systems of physical interest. Connections are established between the proposed approach and other stability-preserving model reduction methods, giving the paper a review flavor. More specifically, it is shown that a discrete counterpart of this inner product is a weighted L 2 inner product obtained by solving a Lyapunov equation, first proposed by Rowley et al. and termed herein the ''Lyapunov inner product''. Comparisons between the symmetry inner product and the Lyapunov inner product are made, and the performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.Published by Elsevier Inc.

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Section: Electrostatically Actuated Beam Examplementioning

confidence: 99%

Construction of energy-stable projection-based reduced order models

Kalashnikova

Barone

Arunajatesan

et al. 2014

Applied Mathematics and Computation

View full text Add to dashboard Cite

show abstract

“…The complexity of such models (thousands up to millions of possibly nonlinear equations) causes a long computation time per time step. Thus, methods have been developed to generate compact models automatically, which offer a computation with comparable accuracy but much lower computational effort (Antoulas 2005;Rudnyi and Korvink 2002;Lienemann et al 2006). Model order reduction (MOR) is a method to generate these compact models automatically from the space-discretised, but time-continuous FEM equations.…”

Section: Model Order Reductionmentioning

confidence: 99%

“…Dissipative Particle Dynamics or Smoothed Particle Hydrodynamics (SPH) (Español and Revenga 2003), and the phase field method (Anderson et al 2000), which is already available in commercial tools. In the framework of these investigations, we will also present a new approach to reduce computational expenses, the so called model order reduction (Lienemann et al 2006). In Sects.…”

Section: Introductionmentioning

confidence: 99%

Integrated process simulation of primary shaping: multi scale approaches

et al. 2008

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We investigate simulation approaches for the modelling of the primary shaping processes micro powder injection moulding and micro casting. We could reproduce the segregation during micro powder injection moulding (MicroPIM) with a simulation using particle methods. The phase field method allows for accurate prediction of the dynamics of solidification of a melt, whereby model order reduction is used to limit the computational effort. The results give valuable advice for the process conduct and the dimensioning of the micro parts.

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“…Therefore, the voltage V (m,j ) at the location of each point charge, q (m,i) , should be accounted for in the formulation. If there are 2N tot electrodes, the total electrostatic energy induced by the point charges can then be calculated as follows [10,11]:…”

Section: Formulations Based On Point Chargesmentioning

confidence: 99%

“…It is reported that the charge points at distinct locations on the electrode of a structure can be used to calculate the electrostatic interactions between electrodes [10,11]. If the point charges are defined on the lumped masses, the equations of motion can be easily obtained by expressing the electrostatic forces in terms of their positions and charge values.…”

Section: Introductionmentioning

confidence: 99%

A multibody-based dynamic simulation method for electrostatic actuators

et al. 2007

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A numerical simulation method is developed to analyze the dynamic responses of electrostatic actuators, which are electromechanically-coupled systems. The developed method can be used to determine the dynamic responses of cantilever-type switches, which are an example of typical MEMS (Micro-Electro-Mechanical System) devices driven by an electrostatic force. We propose the approach that adopts a point charge to deal with electric field effects between electrodes. This approach may be considered as a lumped parameter model for the electrostatic interactions. An advantage of this model may be the easy incorporation of the electrostatic effects between electrodes into a multibody dynamics analysis algorithm. The resulting equations contain the variables for position, velocity, and electric charge to describe the motion of the masses and the charges on the electrodes in a system. By solving these equations simultaneously, the dynamic response of an electrostatically-driven system can be correctly simulated. In order to realize this approach, we implement the procedures into RecurDyn, the multibody dynamics software developed by the authors. The developed numerical simulation tool was evaluated by applying it to cantilever-type electrostatic switches in many different driving conditions. The results suggest that the developed tool may be useful for predicting behaviors of electrostatic actuators in testing as well as in design.

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MST MEMS model order reduction: Requirements and benchmarks

Cited by 32 publications

References 37 publications

Construction of energy-stable projection-based reduced order models

Construction of energy-stable projection-based reduced order models

Integrated process simulation of primary shaping: multi scale approaches

A multibody-based dynamic simulation method for electrostatic actuators

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