Model Reduction and Frequency Windowing for Acoustic Fem Analysis

Ingel, R. P.; Dyka, C. T.; Flippen, L.D.

doi:10.1006/jsvi.2000.3207

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…Djellouli et al [52] present an approach based on Padé approximation to compute multi-frequency evaluations efficiently by solving a reference scattering problem with multiple excitation vectors and local BGT boundary conditions to characterize frequency derivatives of the scattered field. In [108,166] domain decomposition concepts are combined with interpolation of substructure (subdomain) matrices over frequency bands of interest to accelerate multi-frequency solutions.…”

Section: A Multi-frequency Solution Methodsmentioning

confidence: 99%

A review of finite-element methods for time-harmonic acoustics

Thompson

2006

The Journal of the Acoustical Society of America

302

196

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State-of-the-art finite element methods for time-harmonic acoustics governed by the Helmholtz equation are reviewed. Four major current challenges in the field are specifically addressed: the effective treatment of acoustic scattering in unbounded domains, including local and nonlocal absorbing boundary conditions, infinite elements, and absorbing layers; numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales, and requiring a large computational effort; efficient algebraic equation solving methods for the resulting complex-symmetric (non-Hermitian) matrix systems including sparse iterative and domain decomposition methods; and a posteriori error estimates for the Helmholtz operator required for adaptive methods. Mesh resolution to control phase error and bound dispersion or pollution errors measured in global norms for large wave numbers in finite element methods are described. Stabilized, multiscale and other wavebased discretization methods developed to reduce this error are reviewed. A review of finite element methods for acoustic inverse problems and shape optimization is also given.Running Title: Finite element methods for acoustics

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Section: A Multi-frequency Solution Methodsmentioning

confidence: 99%

A review of finite-element methods for time-harmonic acoustics

Thompson

2006

The Journal of the Acoustical Society of America

302

196

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“…Flippen [49] developed a frequency window version of substructuring methods for degree-of-freedom reduction. Ingel et al [50] extended this into a finite-element environment.…”

Section: Introductionmentioning

confidence: 99%

A Generic Bilevel Formalism for Unifying and Extending Model Reduction Methods

Flippen¹

2000

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. 12b. DISTRIBUTION CODE ABSTRACT (Maximum 200 words)An abstract, algebraic bilevel version of conventional multigrid methods has been developed that formally unifies and extends the reduced basis, substructuring, smoothing/homogenization, and frequency window methods of model reduction. Within the context of this formalism, a given model reduction method synthesizes a reduced model that plays the role of a "coarse grid" model. Another original-model approximation, conjugate to the model reduction method, plays the role of a "fine grid" model. Conventional multigrid methods can be thought of as an extension of the coarse grid model beyond the original scope of its accuracy through the alternating use of "fine-grid-error-smoothing" and "coarse-grid-correction" steps. Analogously fashioned, abstract versions of these steps extend the particular model reduction method used beyond the original scope of its accuracy. In addition to the development of the mathematical formalism, a generic continuation is proposed and developed as the conjugate approximation for use in the abstract version of the fine-grid-error-smoothing step. For generality, the nature of the parameter-embedding of the continuation is deliberately left unspecified; a particular parameter-embedding is chosen by the analyst to complement the particular model and model reduction method (or class thereof) in a given case. As an example, a particular submethod of this formalism is constructed by specializing the parameter-embedding to a temporal, biscale perturbational parameter-embedding for the case of a generic set of coupled ordinary differential equations with constant coefficients. The initial iteration of this submethod is a general, combined transient/frequency-window methodology for linear finite-element method applications. It is shown to encompass both the force derivative and Lanczos/Ritz vector methods for the limiting case of a zero frequency, singlepoint window for the "fast" time scale. To put this in perspective, the force derivative and Lanczos/Ritz vector methods are two leading approaches for extending/replacing modal reduced basis methods. Current frequency window methods, in turn, are very efficient for extensive time-harmonic «analysis of the system.

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“…The main idea of the condensation method is that modal properties of connected subsystems can be reduced to those of a main body retaining the dominant effects of the problem [14,15]. An example is a method of dynamic condensation [20] in which the passive coordinates are represented by the active ones, and the eigenvalue problem is solved by a combined technique of Sturm sequence and subspace iteration.…”

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confidence: 99%

An iterative asymptotic expansion method for elliptic eigenvalue problems with oscillating coefficients

Mehraeen

Chen

2009

Comput Mech

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In this work we propose a method for obtaining fine-scale eigensolution based on the coarse-scale eigensolution in elliptic eigenvalue problems with oscillating coefficient. This is achieved by introducing a 2-scale asymptotic expansion predictor in conjunction with an iterative corrector. The eigensolution predictor equation is formulated using the weak form of an auxiliary problem. It is shown that large errors exist in the higher eigenmodes when the 2-scale asymptotic expansion is used. The predictor solution is then corrected by the combined inverse iteration and Rayleigh quotient iteration. The numerical examples demonstrate the effectiveness of this approach.

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Model Reduction and Frequency Windowing for Acoustic Fem Analysis

Cited by 5 publications

References 7 publications

A review of finite-element methods for time-harmonic acoustics

A review of finite-element methods for time-harmonic acoustics

A Generic Bilevel Formalism for Unifying and Extending Model Reduction Methods

An iterative asymptotic expansion method for elliptic eigenvalue problems with oscillating coefficients

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