Finite-element simulation of wave propagation in periodic piezoelectric SAW structures

Hofer, M.; Finger, N.; Kovacs, G.; Schöberl, Joachim; Zaglmayr, Sabine; Langer, Ulrich; Lerch, Reinhard

doi:10.1109/tuffc.2006.1642518

Cited by 94 publications

(46 citation statements)

References 16 publications

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“…Due to the nonlinear dependence on the design variables, (62), (63) and (61) represents an inequality constrained nonlinear programming problem. For its numerical solution we use a path-following barrier method as described below.…”

Section: Path-following Barrier Methodsmentioning

confidence: 99%

“…Technologically, they are desirably employed in solid-state circuits [29]. We refer to [39,41,57,61,62,76,99] for finite element approximations of surface acoustic wave propagation in signal processing. For the SAW devices under consideration, however, the occurrence of BAWs is unwanted, since the interference of BAWs with SAWs can lead to a complete loss of functionality of the device.…”

Section: Lemma 43 Under the Assumptions (48b) Andmentioning

confidence: 99%

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Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Antil¹,

Hoppe²,

Linsenmann³

et al. 2012

Progress in Computational Physics (PiCP) Vol: 2 Coupled Fluid Flow in Energy, Biology and Environmental Research

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Microfluidic biochips are devices that are designed for high throughput screening and hybridization in genomics, protein profiling in proteomics, and cell analysis in cytometry. They are used in clinical diagnostics, pharmaceutics and forensics. The biochips consist of a lithographically produced network of channels and reservoirs on top of a glass or plastic plate. The idea is to transport the injected DNA or protein probes in the amount of nanoliters along the network to a reservoir where the chemical analysis is performed. Conventional biochips use external pumps to generate the fluid flow within the network. A more precise control of the fluid flow can be achieved by piezoelectrically agitated surface acoustic waves (SAW) generated by interdigital transducers on top of the chip, traveling across the surface and entering the fluid filled channels. The fluid and SAW interaction can be described by a mathematical model which consists of a coupling of the piezoelectric equations and the compressible Navier-Stokes equations featuring processes that occur on vastly different time scales. In this contribution, we follow a homogenization approach in order to cope with the multiscale behavior of the coupled system that enables a separate treatment of the fast and slowly varying processes. The resulting model equations are the basis for the numerical simulation which is taken care of by implicit time stepping and finite element discretizations in space. Finally, the need for a better efficiency and cost effectiveness of the SAW driven biochips in the sense of a significant speed-up and more favorable reliability of the hybridization process requires an improved design which will also be addressed in this contribution. In particular, the challenge to deal with the resulting large scale optimal control and optimization problems can be met by the application of projection based model reduction techniques.

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Section: Path-following Barrier Methodsmentioning

confidence: 99%

Section: Lemma 43 Under the Assumptions (48b) Andmentioning

confidence: 99%

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Antil¹,

Hoppe²,

Linsenmann³

et al. 2012

Progress in Computational Physics (PiCP) Vol: 2 Coupled Fluid Flow in Energy, Biology and Environmental Research

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show abstract

“…The analysis of rail noise caused by high speed trains also leads to a quadratic eigenproblem (QEP), but one with a complex T -palindromic matrix polynomial. Real and complex T -palindromic QEPs also arise in the numerical simulation of the behavior of periodic surface acoustic wave (SAW) filters [43,85]. Quadratic eigenproblems with T -alternating polynomials arise in the study of corner singularities in anisotropic elastic materials [7,8,70].…”

Section: Definition 8 (Adjoint Of Matrix Polynomials)mentioning

confidence: 99%

Polynomial Eigenvalue Problems: Theory, Computation, and Structure

Mackey

Tisseur

2015

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

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Matrix polynomial eigenproblems arise in many application areas, both directly and as approximations for more general nonlinear eigenproblems. One of the most common strategies for solving a polynomial eigenproblem is via a linearization, which replaces the matrix polynomial by a matrix pencil with the same spectrum, and then computes with the pencil. Many matrix polynomials arising from applications have additional algebraic structure, leading to symmetries in the spectrum that are important for any computational method to respect. Thus it is useful to employ a structured linearization for a matrix polynomial with structure. This essay surveys the progress over the last decade in our understanding of linearizations and their construction, both with and without structure, and the impact this has had on numerical practice.

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“…21 When looking at the case with an alternating electric potential, k = / 2p is used. The piezoelectric problem is solved by a plane formulation obtained by setting S i3 and E 3 as well as T i3 and D 3 equal to zero.…”

Section: The Acoustic Modelmentioning

confidence: 99%

Energy storage and dispersion of surface acoustic waves trapped in a periodic array of mechanical resonators

Dühring

Laude

Khelif

2009

Journal of Applied Physics

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International audienceIt has been shown previously that surface acoustic waves can be efficiently trapped and slowed by steep ridges on a piezoelectric substrate, giving rise to two families of shear-horizontal and vertically polarized surface waves. The mechanisms of energy storage and dispersion are explored by using the finite element method to model surface acoustic waves generated by high aspect ratio electrodes. A periodic model is proposed including a perfectly matched layer to simulate radiation conditions away from the sources, from which the modal distributions are found. The ratio of the mechanical energy confined to the electrode as compared to the total mechanical energy is calculated and is found to be increasing for increasing aspect ratio and to tend to a definite limit for the two families of surface waves. This observation is in support of the interpretation that high aspect ratio electrodes act as resonators storing mechanical energy. These resonators are evanescently coupled by the surface. The dispersion diagram is presented and shows very low group velocities as the wave vector approaches the limit of the first Brillouin zone

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Finite-element simulation of wave propagation in periodic piezoelectric SAW structures

Cited by 94 publications

References 16 publications

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Polynomial Eigenvalue Problems: Theory, Computation, and Structure

Energy storage and dispersion of surface acoustic waves trapped in a periodic array of mechanical resonators

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