Approximation by multipoles of the multiple acoustic scattering by small obstacles in three dimensions and application to the Foldy theory of isotropic scattering

DOI10.1007/s00205-015-0915-5zbMath1333.35179OpenAlexW1122910176MaRDI QIDQ5962880

Abderrahmane Bendali, Sébastien Tordeux, Pierre-Henri Cocquet

Publication date: 25 February 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-015-0915-5

zbMATH Keywords

acoustic scatteringasymptotic analysisFoldy's method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Scattering theory for PDEs (35P25) Asymptotic expansions of solutions to PDEs (35C20) Hydro- and aero-acoustics (76Q05)

Related Items

Multiscale analysis of the acoustic scattering by many scatterers of impedance type ⋮ Team organization may help swarms of flies to become invisible in closed waveguides ⋮ Inverse acoustic scattering using high-order small-inclusion expansion of misfit function ⋮ Asymptotic Analysis of Solutions to Transmission Problems in Solids with Many Inclusions ⋮ Numerical robustness of single-layer method with Fourier basis for multiple obstacle acoustic scattering in homogeneous media ⋮ 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 ⋮ Asymptotic behavior of acoustic waves scattered by very small obstacles ⋮ Estimation of the Heat Conducted by a Cluster of Small Cavities and Characterization of the Equivalent Heat Conduction ⋮ Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations ⋮ Analysis of the Acoustic Waves Reflected by a Cluster of Small Holes in the Time-Domain and the Equivalent Mass Density

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiscale analysis of the acoustic scattering by many scatterers of impedance type
• Wave scattering by small bodies and creating materials with a desired refraction coefficient
• The equivalent refraction index for the acoustic scattering by many small obstacles: with error estimates
• Multiple scattering of acoustic waves by small sound-soft obstacles in two dimensions: mathematical justification of the Foldy-Lax model
• Boundary integral equations
• Scattering theory for the d'Alembert equation in exterior domains
• Electromagnetic scattering by small dielectric inhomogeneities.
• Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities
• Reconstruction of small inhomogeneities from boundary measurements
• A Two-Scale Multiple Scattering Problem
• Field behavior near the edge of a microstrip antenna by the method of matched asymptotic expansions
• Asymptotic Analysis and Boundary Layers
• Many-body wave scattering by small bodies and applications
• A Singularly mixed boundary value problem
• Robust and high-order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer
• Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
• Extension of Functions in Sobolev Spaces on Parameter Dependent Domains
• Mathematical Justification of the Rayleigh Conductivity Model for Perforated Plates in Acoustics
• EXTENDED FOLDY–LAX APPROXIMATION ON MULTIPLE SCATTERING
• On the Justification of the Foldy--Lax Approximation for the Acoustic Scattering by Small Rigid Bodies of Arbitrary Shapes
• MUSIC Imaging and Electromagnetic Inverse Scattering of Multiple-Scattering Small Anisotropic Spheres
• Lower and upper bounds for the Rayleigh conductivity of a perforated plate
• Scattering of a scalar time-harmonic wave by N small spheres by the method of matched asymptotic expansions
• Wave Scattering by Small Bodies of Arbitrary Shapes
• Matching of Asymptotic Expansions for Wave Propagation in Media with Thin Slots I: The Asymptotic Expansion
• The Effect of a Thin Coating on the Scattering of a Time-Harmonic Wave for the Helmholtz Equation
• The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers
• Acoustic and electromagnetic equations. Integral representations for harmonic problems