Inverse vector problem of diffraction by inhomogeneous body with a piecewise smooth permittivity
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Mikhail Y. Medvedik
Abstract
The vector problem of reconstruction of an unknown permittivity of an inhomogeneous body is considered. The original problem for Maxwell’s equations with an unknown permittivity and a given permeability is reduced to the system of integro-differential equations. The solution to the inverse problem is obtained in two steps. First, a solution to the vector integro-differential equation of the first kind is obtained from the given near-field data. The uniqueness of the solution to the integro-differential equation of the first kind is proved in the classes of piecewise constant functions. Second, the sought-for permittivity is straightforwardly calculated from the found solution and the total electric field. A series of test problems was solved using the two-step method. Procedures of approximate solutions’ refining were implemented. Comparison between the given permittivities and the found approximate solutions shows efficiency of the proposed method.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 18-01-00219 A
Funding statement: This work was supported by Russian Foundation for Basic Research [grant No. 18-01-00219 A].
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Articles in the same Issue
- Frontmatter
- Stability properties for a class of inverse problems
- Inverse scattering problem for nonstrict hyperbolic system on the half-axis with a nonzero boundary condition
- Identification of the time-dependent source term in a Kuramoto–Sivashinsky equation
- Direct numerical algorithm for calculating the heat flux at an inaccessible boundary
- The game model with multi-task for image denoising and edge extraction
- On the X-ray transform of planar symmetric tensors
- Inverse vector problem of diffraction by inhomogeneous body with a piecewise smooth permittivity
- Acquiring elastic properties of thin composite structure from vibrational testing data
- Inverse nodal problem for diffusion operator on a star graph with nonhomogeneous edges
- Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces
- A projected gradient method for nonlinear inverse problems with 𝛼ℓ1 − 𝛽ℓ2 sparsity regularization
- Correctness and regularization of stochastic problems
- A layer potential approach to inverse problems in brain imaging
- Inverse problem for Dirac operators with two constant delays
