Numerical solution of the problem of shape recovery for a system of impedance surfaces

Soppa, Mikhail

doi:10.1007/bf02677619

Cited by 2 publications

(4 citation statements)

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“…An e¬ective solution algorithm for this equation using discretization and a regularizing smoothing zero-order Tikhonov functional was reported in [8]. Using this approach, one can calculate the incremental change in the Brought to you by | University of Arizona Authenticated Download Date | 6/3/15 1:49 PM impedance ¢W s that causes a given change in the diagram of the scattered eld E. In this way, we de ne the operator ¢W s =F (e 1 exp (i£)):…”

Section: Problem and Its Solution Algorithmmentioning

confidence: 99%

“…A similar mathematical problem for the case in which complete information about the re®ected eld (amplitude and phase) is available was treated in [8].…”

Section: Problem and Its Solution Algorithmmentioning

confidence: 99%

“…To construct the solution, we will use, instead of the boundary conditions (6 0 ), the following modi ed boundary conditions [8]:…”

Section: Problem and Its Solution Algorithmmentioning

confidence: 99%

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Computer diagnostics of surface characteristics of extended cylindrical objects by the active location technique

Лаврентьев¹,

Zharinov²,

Zerkal³

et al. 2003

Journal of Inverse and Ill-posed Problems

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| A computer-diagnostics method for examining characteristics of surface layers in conducting extended solids, based on treating data on radio-wave scattering by these solids in the meter and centimeter bands, is reported. The problem is reduced to solving a system of nonlinear algebraic equations. The computational algorithm and results of numerical experiments are described. The method allows using, as input data, not only asymptotic scattering diagrams, but also amplitude values of the re°ected¯eld measured close to the surface under study. The latter improves solution stability in complex noise-signal situations in which random distortions in receive chains occur. INTRODUCTIONComputer diagnostics is widely used in various elds of research and manufacture, including tomography, introscopy, and nondestructive inspection problems. Under computer diagnostics, we mean a set of algorithms and software resources intended for analyzing characteristics of objects under inspection by treating indirect data about the objects on computers [1]. A fundamental difference between computer and traditional diagnostics consists in the possibility of processing much larger bodies of data about objects under study and in using, in processing data and interpreting results, high-performance computers, advanced calculus-mathematics algorithms, and special-purpose soft-and hardware facilities. The work was supported by the Russian Foundation for Basic Research (grants Nos. 03-07-90060, 03-01-00910). Brought to you by | University of Arizona Authenticated Download Date | 6/3/15 1:49 PM 632 M. M. Lavrent'ev, S. Yu. Zharinov, S. M. Zerkal, and M. S. Soppa At present, computer diagnostics remains the main tool for solving the majority of nondestructive inspection problems. Computer diagnostics enables easy automation of diagnosing, data processing and archiving procedures, and makes it possible to improve inspection and solution quality. Nondestructive inspection allows one to test constructions and mechanisms at the design stage and monitor them during exploitation, thus providing the possibility, using resources of elements in largest possible extent, to replace and repair, in proper time, those of them out of imposed requirements.The present-day availability of high-performance computing facilities stimulates the demand for development and industrial application of novel nondestructive inspection methods that optimally use these fresh possibilities. Another reason for the evergrowing demand for nondestructive inspection methods is that they, if used, are capable of substantially reducing risks of man-caused accidents and catastrophes, thus yielding substantial ecomonical and ecological e¬ects.At present, a great number of computer diagnostics algorithms are available. In most cases, mathematical formulation and solution of a computer-diagnostics problem can be reduced to solving operator equations. Solving such equations often presents an ill-posed problem [2{4]. In searching for approximate solutions, regularization procedures are...

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Section: Problem and Its Solution Algorithmmentioning

confidence: 99%

“…A similar mathematical problem for the case in which complete information about the re®ected eld (amplitude and phase) is available was treated in [8].…”

Section: Problem and Its Solution Algorithmmentioning

confidence: 99%

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Computer diagnostics of surface characteristics of extended cylindrical objects by the active location technique

Лаврентьев¹,

Zharinov²,

Zerkal³

et al. 2003

Journal of Inverse and Ill-posed Problems

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“…In the present paper, we propose an approach which uses a modified impedance boundary condition of the Leontovich type condition [7]. In this case, retrieving the impedance from the total complex-valued scattered field, the initial inverse problem in the differential formulation can be reduced to a linear integral-operator equation which admits effective discretization and regularization.…”

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confidence: 99%

Mathematical modelling of the microwave-diagnostics of impedance surfaces for the reflected signal of unknown phase

Soppa

2008

J Appl Mech Tech Phy

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Numerical solution of the problem of shape recovery for a system of impedance surfaces

Cited by 2 publications

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Computer diagnostics of surface characteristics of extended cylindrical objects by the active location technique

Computer diagnostics of surface characteristics of extended cylindrical objects by the active location technique

Mathematical modelling of the microwave-diagnostics of impedance surfaces for the reflected signal of unknown phase

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