Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core

Guo, Jun; Yan, Guozheng; Cai, Mingjian

doi:10.1155/2015/195460

Cited by 5 publications

(6 citation statements)

References 23 publications

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“…Hence, the generated scattering theorems imply simpler results for sound soft, hard, penetrable or impedance problems. Corresponding scattering theorems can be proved in the case of more general imposed boundary conditions on the core, such as in [23] (resistive and conductive transmission conditions) and in [24] (generalized impedance boundary condition). Applying the derived results, we aim to study inverse scattering problems for multi-layered obstacles in two dimensions.…”

Section: Discussionmentioning

confidence: 99%

On the Far Field Pattern for Acoustic Scattering by a Piecewise Homogeneous Obstacle in Two Dimensions

Athanasiadou¹,

Roupa²

2022

JAMP

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A time-harmonic plane acoustic wave is scattered by a piecewise homogeneous obstacle with a penetrable or impenetrable core. We construct in the close form an integral representation for the far field pattern in which we have incorporated the physical and geometrical characteristics of the scatterer. Through this representation, we obtain the far field pattern for this scatterer. We prove scattering relations between the far field patterns of two scattering problems due to two distinct incident waves on the same scatterer. In particular, we prove reciprocity and general scattering theorems. The optical theorem, connecting the total power that the scatterer extracts from the incident plane wave either by radiation or by absorption with the corresponding far field pattern of an incident plane wave, is recovered as a corollary of the general scattering theorem. Moreover, if we consider incident waves to be both a plane and a spherical, we derive a mixed reciprocity theorem. We define the corresponding far field operators and using these relations, we prove some properties that can be used for solving inverse scattering problems.

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Section: Discussionmentioning

confidence: 99%

On the Far Field Pattern for Acoustic Scattering by a Piecewise Homogeneous Obstacle in Two Dimensions

Athanasiadou¹,

Roupa²

2022

JAMP

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“…In this case, the scattering theorems are simplified as follows. Corresponding relations can be found in [1][2][3]5,9,22].…”

Section: A Special Casementioning

confidence: 93%

“…A mixed reciprocity theorem, i.e., a theorem which connects the far-field pattern of a line source wave and the scattered field of a plane wave, will be proven in this section. This theorem plays a crucial role in studying inverse scattering problems [3,5,22]. Theorem 3.…”

Section: Mixed Reciprocitymentioning

confidence: 96%

“…For the last integral, taking into account the interior elliptic regularity, see Refs. [5,22,28], we have…”

Section: Reciprocity For Line Source Wavesmentioning

confidence: 99%

“…In [20], plane electromagnetic scattering is studied, whereas in [21] line source elastic waves are studied. In [22], a mixed reciprocity principle is proven in two dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Two-Dimensional Scattering of Line Source Electromagnetic Waves by a Layered Obstacle

Athanasiadis,

Roupa

2023

Mathematics

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We consider the scattering problem of line source electromagnetic waves using a multi-layered obstacle with a core, which may be a perfect conductor, a dielectric, or has an impedance surface. We formulate this problem in two dimensions and we prove some useful scattering relations. In particular, we state and prove a reciprocity principle and a general scattering theorem for line source waves for any possible positions of the source. These theorems can be used to approximate the far-field pattern in the low-frequency theory. Moreover, an optical theorem is recovered as a corollary of the general scattering theorem. Finally, we obtain a mixed reciprocity relation which can be used in proving the uniqueness results of the inverse scattering problems.

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Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization

Borges

Rachh

2021

Adv Comput Math

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Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core

Cited by 5 publications

References 23 publications

On the Far Field Pattern for Acoustic Scattering by a Piecewise Homogeneous Obstacle in Two Dimensions

On the Far Field Pattern for Acoustic Scattering by a Piecewise Homogeneous Obstacle in Two Dimensions

Two-Dimensional Scattering of Line Source Electromagnetic Waves by a Layered Obstacle

Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization

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