NUMERICAL SOLUTION OF THE ELECTROMAGNETIC WAVE DIFRACTION PROBLEM                               ON THE SYTEM OF BODIES AND SCREENS 

Maksimova Marina Aleksandrovna, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
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), _medv@mail.ru
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), mmm@pnzgu.ru
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), mmm@pnzgu.ru

517.3

Background. The aim of this work is numerical solving of the vector problem of electromagnetic wave scattering on obstacles of complex shape, consisting of inhomogeneous bodies and infinitely thin absolutely conducting screens.
Material and methods. Using the methods of the potential theory, the original boundary value problem for Maxwell's equations is reduced to a system of integrodifferential equations in the regions and the surfaces of the scatterer. To obtain an approximate solution to the system the authors suggest the Galerkin method with piecewise linear finite basis functions.
Results. The quasiclassical statement of the diffraction problem by a system of obstacles of various dimensions is proposed; the boundary value problem is reducedto a system of integro-differential equations; the projection method for solving this system is formulated, the piecewise linear basis functions with compact support are introduced; formulas of matrix elements are obtained according to the Galerkin method; numerical results for the diffraction problem on inhomogeneous bodies and piecewise flat screens are obtained.
Conclusions. The proposed method allows to find numerical solutions to the vector problem of electromagnetic diffraction by obstacles of various dimensions. This method can be extended to the case of anisotropic volume scatterers and nonplanar screens.

vector diffraction problem, integro-differential equations, Galerkin method, finite basis functions.

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