Contribution of leaky modes in the modal analysis of unbounded problems with perfectly matched layers

Gallezot, Matthieu; Treyssède, Fabien; Laguerre, Laurent

doi:10.1121/1.4973313

Cited by 13 publications

(15 citation statements)

References 15 publications

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“…2.1, these branch cuts are rotated by an angle equal to −arg(γ) in the case of an infinite PML (for further details, see Ref. [45]). For a PML of finite thickness, this angle becomes equal to −arg(d + hγ) as shown in Ref.…”

Section: Resultsmentioning

confidence: 99%

“…In a recent work [45], the authors have shown that when the surrounding medium is modified by an infinite PML, the forced response can theoretically be obtained with a modal expansion on trapped modes, revealed leaky modes and two continua of radiation modes related to the PML branch cuts. With numerical methods, the PML must yet be truncated to a finite thickness.…”

Section: Context and State-of-the-artmentioning

confidence: 99%

See 1 more Smart Citation

A modal approach based on perfectly matched layers for the forced response of elastic open waveguides

Gallezot¹,

Treyssède²,

Laguerre³

2018

Journal of Computational Physics

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This paper investigates the computation of the forced response of elastic open waveguides with a numerical modal approach based on perfectly matched layers (PML). With a PML of infinite thickness, the solution can theoretically be expanded as a discrete sum of trapped modes, a discrete sum of leaky modes and a continuous sum of radiation modes related to the PML branch cuts. Yet with numerical methods (e.g. finite elements), the waveguide cross-section is discretized and the PML must be truncated to a finite thickness. This truncation transforms the continuous sum into a discrete set of PML modes. To guarantee the uniqueness of the numerical solution of the forced response problem, an orthogonality relationship is proposed. This relationship is applicable to any type of modes (trapped, leaky and PML modes) and hence allows the numerical solution to be expanded on a discrete sum in a convenient manner. This also leads to an expression for the modal excitability valid for leaky modes. The physical relevance of each type of mode for the solution is clarified through two numerical test cases, a homogeneous medium and a circular bar waveguide example, excited by a point source. The former is favourably compared to a transient analytical solution, showing that PML modes reassemble the bulk wave contribution in a homogeneous medium. The latter shows that the PML mode contribution yields the long-term diffraction phenomenon whereas the leaky mode contribution prevails closer to the source. The leaky mode contribution is shown to remain accurate even with a relatively small PML thickness, hence reducing the computational cost. This is of particular interest for solving three-dimensional waveguide problems, involving two-dimensional cross-sections of arbitrary shapes. Such a problem is handled in a third numerical example by considering a buried square bar.

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Section: Resultsmentioning

confidence: 99%

Section: Context and State-of-the-artmentioning

confidence: 99%

A modal approach based on perfectly matched layers for the forced response of elastic open waveguides

Gallezot¹,

Treyssède²,

Laguerre³

2018

Journal of Computational Physics

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“…More details about the spectrum of open systems using perfectly matched layers can be found in Refs. [33,42,43].…”

Section: Open Waveguide Test Case: Bar Buried Into a Solid Matrixmentioning

confidence: 99%

A model reduction method for fast finite element analysis of continuously symmetric waveguides

Treyssède

2021

Journal of Sound and Vibration

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“…Let us first briefly recall some theoretical results by considering the unbounded problem without introducing any PML. Theoretically, the spectrum of an unbounded problem is constituted by a continuum of radiation modes and proper discrete poles [15,[35][36][37].…”

Section: Spectrum Characteristicsmentioning

confidence: 99%

High-frequency leaky whispering-gallery modes in embedded elastic spheres

Treyssède

Gallezot

2021

Phys. Rev. B

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The goal of this paper is to investigate the characteristics of high-frequency whispering-gallery modes in embedded elastic spheres, that is, surrounded by an infinite elastic matrix. Due to several modeling difficulties, the high-frequency regime of embedded spheres has remained unexplored in elasticity. Our approach consists of formulating a specific finite-element method in spherical coordinates. The basic idea is to discretize only the radial coordinate while describing analytically the angular distribution of elastodynamic fields. Then, we also introduce a radial perfectly matched layer to cope with the unbounded nature of the external medium. Our approach yields a linear matrix eigensystem, simple and costless to solve. In order to identify general trends, both stiff and soft configurations are considered, corresponding to a sphere stiffer and softer than the external medium, respectively. Including material loss, our results highlight the behavior of leaky elastic whispering-gallery modes in the high-frequency regime. This work is motivated by the well-known behavior of whispering-gallery modes in optical resonators, reaching high Q factors as the frequency increases. Identifying high-Q-factor whisperinggallery modes in elastic spheres could find promising applications for sensing the mechanical properties of external media.

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Contribution of leaky modes in the modal analysis of unbounded problems with perfectly matched layers

Cited by 13 publications

References 15 publications

A modal approach based on perfectly matched layers for the forced response of elastic open waveguides

A modal approach based on perfectly matched layers for the forced response of elastic open waveguides

A model reduction method for fast finite element analysis of continuously symmetric waveguides

High-frequency leaky whispering-gallery modes in embedded elastic spheres

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