Article 1417

Title of the article



Evstigneev Roman Olegovich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia),
Medvedik Mikhail Yur'evich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia),
Smirnov Yuriy Gennad'evich, Doctor of physical and mathematical sciences, professor, head of sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia),
Tsupak Aleksey Aleksandrovich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia),

Index UDK

517.968, 517.983.37




Background. The aim of this work is to theoretical and numerical study the inverse scalar problem of diffraction by a volume obstacle characterized by a piecewise Hoelder-continuous function.
Material and methods. The original boundary value problem is considered in the quasiclassical formulation and then reduced to a system of weakly singular integral equations; the properties of the latter system are studied using the potential theory and Fourier transform.
Results. The inverse problem of diffraction is given the integral formulation; the theorem on uniqueness of a piecewise constant solution to the integral equation of the first type is proved; a new two-step algorythm for numerical solving the inverse problem is proposed and implemented; several numerical tests have been carried out.
Conclusions. The obtained theoretical and numerical results confirm high efficiency of the proposed method, which can be applied for solving problems of nearfield tomography.

Key words

inverse diffraction problem, reconstruction of refractive index, integral equatons, uniqueness of solutions, integral equations, collocation method

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Дата создания: 06.02.2018 10:52
Дата обновления: 20.04.2018 15:16