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- Shestopalov, Youri, 1953-, et al.
(author)
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Estimation of Solutions of Helmholtz Problems with Uncertain Data
- 2010
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In: Electromagnetic Theory (EMTS). - : IEEE. - 9781424451555 ; , s. 517-519
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Conference paper (peer-reviewed)abstract
- The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the determination of minimax estimates is reduced to the solution of integro-differential equations in bounded domains. When observations are distributed on a system of surfaces the problem is reduced to solving integral equations on an unclosed bounded surface which is a union of the boundary of the domain and this system of surfaces. Minimax estimation of the solutions to the boundary value problems from point observations is also studied
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| 3. |
- Shestopalov, Youri, 1953-, et al.
(author)
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Existence and uniqueness of solution to the inverse problem of complex permittivity reconstruction of a dielectric body in a waveguide
- 2010
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In: Inverse Problems. - Bristol : IoP. - 0266-5611 .- 1361-6420. ; 26:10
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Journal article (peer-reviewed)abstract
- This paper presents a statement, a proof of uniqueness, and a method of solution to the inverse problem of the determination of permittivity of a lossy dielectric inclusion in a three-dimensional waveguide of rectangular cross-section fromthe transmission characteristics. The approach is based on the solution to a volume singular integral equation (VSIE). The examination of this equationis based on the analysis of the corresponding boundary value problem (BVP) for the system of Maxwell equations and the equivalence of this BVP andVSIE. The existence and uniqueness for VSIE in the space of square-integrable functions are proved. The permittivity reconstruction employs a method ofiterations applied to the solution of VSIE
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| 4. |
- Smirnov, Yury, et al.
(author)
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A Volume Singular Integral Equation Technique for Reconstruction of Complex Permittivity of a Body in a Rectangular Waveguide
- 2010
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In: Proc. of the 26th International Review of Progress in Applied Computational Electromagnetics (ACES 2010), Tampere, Finland, April 25-29, 2010. - : ACES. ; , s. 426-430
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Conference paper (peer-reviewed)abstract
- The theoretical study outlined in this paper is motivated by the growing interest in microwave imaging in closed microwave systems. We present an original approach to the inverse problem of reconstruction of media parameters (complex permittivity) of a body in a waveguide.The consideration is based on the use of a volume singular integral equation and its reduction toan equation which can be solved, using iterations, both numerically and analytically. This resultsin determination, for a given single-mode rectangular waveguide, of complex permittivity from the transmission coe±cient. The approach also yields the proof of uniqueness of reconstruction of complex permittivity in a rectangular waveguide from the transmission characteristics
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