Abstract
The proposal deals with electromagnetic (EM) wave scattering by one and many small impedance particles of an arbitrary shape. Analytic formula is derived for EM wave scattering by one small impedance particle of an arbitrary shape and an integral equation for the effective field in the medium where many such particles are embedded. These results are applied for creating a medium with a desired refraction coefficient. The proposed theory has no analogs in the literature. (Mathematical Subject Classiffication: 35J05, 35J25, 65N12, 78A25, 78A48.)
Highlights
The proposal deals with electromagnetic (EM) wave scattering by one and many small impedance particles of an arbitrary shape
The first basic result PI proposes to obtain is an analytic, closed-form formula for the EM field scattered by the small impedance body D of an arbitrary shape
The second basic result PI proposes to obtain is a numerical method for solving many-body EM wave scattering problem in the case of M small impedance bodies of an arbitrary shape, where M ranges from
Summary
The first basic result PI proposes to obtain is an analytic, closed-form formula for the EM field scattered by the small impedance body D of an arbitrary shape. The second basic result PI proposes to obtain is a numerical method for solving many-body EM wave scattering problem in the case of M small impedance bodies of an arbitrary shape, where M ranges from. The third basic result PI proposes to derive is an integral equation for the effective field in the medium in which many small impedance bodies (particles) are embedded. This allows PI to derive an analytic formula for the refraction coefficient of the above medium. PI plans to use GMRES method ([18]) for solving such systems and PETSC libraries to do the computations in parallel ([1])
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