Modal decompositions and point scatterer approximations near the Minnaert resonance frequencies
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Date
2022-07
Publication Type
Journal Article
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yes
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Abstract
This paper provides several contributions to the mathematical analysis of subwavelength resonances in a high-contrast medium containing N acoustic obstacles. Our approach is based on an exact decomposition formula which reduces the solution of the sound scattering problem to that of an N dimensional linear system, and characterizes resonant frequencies as the solutions to an N-dimensional nonlinear eigenvalue problem. Under a simplicity assumptions on the eigenvalues of the capacitance matrix, we prove the analyticity of the scattering resonances with respect to the square root of the contrast parameter, and we provide a deterministic algorithm allowing to compute all terms of the corresponding Puiseux series. We then establish a nonlinear modal decomposition formula for the scattered field as well as point scatterer approximations for the far-field pattern of the sound wave scattered by N bodies. As a prerequisite to our analysis, a first part of the work establishes various novel results about the capacitance matrix and its symmetry properties, since qualitative properties of the resonances, such as the leading order of the scattering frequencies or of the corresponding far-field pattern are closely related to its spectral decomposition.
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published
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Book title
Journal / series
Volume
149 (1)
Pages / Article No.
164 - 229
Publisher
Wiley
Event
Edition / version
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Software
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Date collected
Date created
Subject
Capacitance matrix; High-contrast medium; Holomorphic integral operators; Modal decomposition; Point scatterer approximation; Subwavelength resonance
Organisational unit
09504 - Ammari, Habib / Ammari, Habib
02500 - Forschungsinstitut für Mathematik / Institute for Mathematical Research