An integral equation method for the Helmholtz problem in the presence of small anisotropic inclusions

DOI10.1080/17476933.2020.1833866zbMath1485.35130OpenAlexW3097608763MaRDI QIDQ5037857

Houssem Lihiou, Abdessatar Khelifi

Publication date: 4 March 2022

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2020.1833866

zbMATH Keywords

Helmholtz equationanisotropic inclusionssmall perturbation of the domain

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Perturbations in context of PDEs (35B20)

Cites Work

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• Helmholtz equation in periodic media with a line defect
• The method of approximate particular solutions for solving anisotropic elliptic problems
• A posteriori error estimation of residual type for anisotropic diffusion-convection-reaction problems
• The mathematical theory of time-harmonic Maxwell's equations. Expansion-, integral-, and variational methods
• Electromagnetic scattering by small dielectric inhomogeneities.
• On the behavior of resonant frequencies in the presence of small anisotropic imperfections
• Reconstruction of small inhomogeneities from boundary measurements
• Polarization tensors and effective properties of anisotropic composite materials
• The factorization method for inverse scattering by a penetrable anisotropic obstacle with conductive boundary condition
• Ellipticity in the Interior Transmission Problem in Anisotropic Media
• Some Remarks on Rellich's Theorem and the Poincaré Inequality
• Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
• Anisotropic Polarization Tensors and Detection of an Anisotropic Inclusion
• Recovery of Small Inhomogeneities from the Scattering Amplitude at a Fixed Frequency
• Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
• Asymptotic expansions for currents caused by small interface changes of an electromagnetic inclusion
• Inverse acoustic and electromagnetic scattering theory
• Boundary Element Methods
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

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