Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations

Labat, Justine; Péron, Victor; Tordeux, Sébastien

doi:10.1016/j.wavemoti.2019.102409

Cited by 5 publications

(4 citation statements)

References 34 publications

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“…Finally, the method we have proposed can be extended to other wave equations. Recently, it has been developed for Maxwell's equations in harmonic regime [25,26]. The time-dependent case is clearly more technical but it is quite possible, at least when considering low order asymptotic models.…”

Section: Discussionmentioning

confidence: 99%

“…To build such a mathematical model, asymptotic methods turn out to be very efficient besides having a rigorous framework for establishing convergence results which ensure that the solution calculated by solving the asymptotic model converges towards the solution of the initial problem. Asymptotic methods have been applied several times to stationary problems (see [13,21,23,26,40,42]) and to the best of our knowledge, Mattesi and Tordeux [32,33] represents the first attempt in the time domain.…”

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confidence: 99%

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Asymptotic behavior of acoustic waves scattered by very small obstacles

et al. 2021

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The direct numerical simulation of the acoustic wave scattering created by very small obstacles is very expensive, especially in three dimensions and even more so in time domain. The use of asymptotic models is very efficient and the purpose of this work is to provide a rigorous justification of a new asymptotic model for low-cost numerical simulations. This model is based on asymptotic near-field and far-field developments that are then matched by a key procedure that we describe and demonstrate. We show that it is enough to focus on the regular part of the wave field to rigorously establish the complete asymptotic expansion. For that purpose, we provide an error estimate which is set in the whole space, including the transition region separating the near-field from the far-field area. The proof of convergence is established through Kondratiev's seminal work on the Laplace equation and involves the Mellin transform. Numerical experiments including multiple scattering illustrate the efficiency of the resulting numerical method by delivering some comparisons with solutions computed with a finite element software.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Asymptotic behavior of acoustic waves scattered by very small obstacles

et al. 2021

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“…The literature on the frequency-domain asymptotic models for various types of wave propagation problems is quite rich; a non-exhaustive list of works exploiting either of the above approaches includes [6,7,24,10,38,11,9,26,27]. It seems that there exist fewer results in the time domain (see the recent monograph by Martin [33]).…”

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confidence: 99%

A New Class of Uniformly Stable Time-Domain Foldy–Lax Models for Scattering by Small Particles. Acoustic Sound-Soft Scattering by Circles

Kachanovska

2024

Multiscale Model. Simul.

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In this work we study time-domain sound-soft scattering by small circles. Our goal is to derive an asymptotic model for this problem valid when the size of the particles tends to zero. We present a systematic approach to constructing such models, based on a well-chosen Galerkin discretization of a boundary integral equation. The convergence of the method is achieved by decreasing the asymptotic parameter rather than increasing the number of basis functions. We prove the second-order convergence of the field error with respect to the particle size. Our findings are illustrated with numerical experiments.

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“…We can cite the variation method, via the maximum principle, as proposed by Maz'ya and Movchan [29] or integral equations as proposed firstly by Ramm [35] for some particular models and scaling regimes, and developed since then by many authors [16][17][18], [32][33][34] and [36][37][38]. We also cite the method of matched asymptotic expansions, see [11,27] and the references therein. Regarding the Maxwell system, apart from [37,38] which are derived more formally with questionable issues, few results are known.…”

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confidence: 99%

The Effective Permittivity and Permeability Generated by a Cluster of Moderately Contrasting Nanoparticles

Cao¹,

Sini²

2021

Preprint

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In a 3D bounded and C 1,α -smooth domain Ω, α ∈ (0, 1), we distribute a cluster of nanoparticles enjoying moderately contrasting relative permittivity and permeability which can be anisotropic. We show that the effective permittivity and permeability generated by such cluster is explicitly characterized by the corresponding electric and magnetic polarization tensors of the fixed shape. The error of the approximation of the scattered fields corresponding to the cluster and the effective medium is inversely proportional to the dilution parameter cr := δ a where a is the maximum diameter of the nanoparticles and δ the minimum distance between them. The constant of the proportionality is given in terms of a priori bounds on the cluster of nanoparticles (i.e. upper and lower bounds on their permittivity and permeability parameters, upper bound on the dilution parameter cr, the used incident frequency and the domain Ω).A key point of the analysis is to show that the Foldy-Lax field appearing in the meso-scale approximation, derived in [14], is a discrete form of a (continuous) system of Lippmann-Schwinger equations with a related effective permittivity and permeability contrasts. To derive this, we prove that the Lippmann-Schwinger operator, for the Maxwell system, is invertible in the Hölder spaces. As a by-product, this shows a Hölder regularity property of the electromagnetic fields up to the boundary of the inhomogeneity.

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Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations

Cited by 5 publications

References 34 publications

Asymptotic behavior of acoustic waves scattered by very small obstacles

Asymptotic behavior of acoustic waves scattered by very small obstacles

A New Class of Uniformly Stable Time-Domain Foldy–Lax Models for Scattering by Small Particles. Acoustic Sound-Soft Scattering by Circles

The Effective Permittivity and Permeability Generated by a Cluster of Moderately Contrasting Nanoparticles

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