SUBSTANTIATION OF THE NUMERICAL METHOD FOR SOLVING THE DIFFRACTION PROBLEM ON A SYSTEM OF INTERSECTING BODIES AND SCREENS 

Smirnov Yuriy Gennad'evich, Doctor of physical and mathematical sciences, professor, head of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mmm@pnzgu.ru
Moskaleva Marina Aleksandrovna, Junior research assistant, the research center of “Supercomputer modeling in electrodynamics”, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: m.a.moskaleva1@gmail.com 

517.3 

10.21685/2072-3040-2019-4-1 

Background. The problems of electromagnetic wave diffraction on the intersecting bodies and screens are important for solving applied problems associated, for example, with the study and radio coverage areas estimate in controlled rooms. The objectives of this study are to prove the smoothness of the solutions of the integrodifferential system corresponding to the problem of electromagnetic waves diffraction on a system of intersecting bodies and screens, and to substantiate a numerical method for solving the problem under study.
Material and methods. The problem under investigation is reduced to a system of integro-differential equations using potential theory. The properties of the system are studied using pseudodifferential calculus in Sobolev spaces.
Results. The smoothness of the solutions of the obtained system is proved. The application of the numerical method (Galerkin scheme) for solving a system of integro-differential equations is substantiated.
Conclusions. The results can be applied to solve various applied problems in radiolocation, electronics, and other fields of electrodynamics and technology. 

electromagnetic wave diffraction, inhomogeneous anisotropic bodies, perfectly conducting screens, elliptic operator, a system of integral-differential equations 

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