Abstract
In this paper, we investigate the problem of electromagnetic (EM) wave scattering by one and many small perfectly conducting bodies and present a numerical method for solving it. For the case of one body, the problem is solved for a body of arbitrary shape, using the corresponding boundary integral equation. For the case of many bodies, the problem is solved asymptotically under the physical assumptions a d a is the characteristic size of the bodies, d is the minimal distance between neighboring bodies, λ = 2π/k is the wave length and k is the wave number. Numerical results for the cases of one and many small bodies are presented. Error analysis for the numerical method is also provided.
Highlights
Many real-world electromagnetic (EM) problems like EM wave scattering, EM radiation, etc. [1], cannot be solved analytically and exactly to get a solution in a closed form
We investigate the problem of electromagnetic (EM) wave scattering by one and many small perfectly conducting bodies and present a numerical method for solving it
The EM wave scattering problem is solved asymptotically under the physical assumptions: a d λ, where a is the characteristic size of the bodies, d is the minimal distance between neighboring bodies, λ = 2π k is the wave length and k is the wave number
Summary
Many real-world electromagnetic (EM) problems like EM wave scattering, EM radiation, etc. [1], cannot be solved analytically and exactly to get a solution in a closed form. Typical DE methods are: Finite Difference Time Domain (FDTD) developed by Kane Yee (1966) [7], Finite Element Method (FEM) [8], Finite Integration Technique (FIT) proposed by Thomas Weiland (1977) [9], Pseudospectral Time Domain (PSTD) [10], Pseudospectral Spatial Domain (PSSD) [11], and Transmission Line Matrix (TLM) [12]. G. Ramm has developed a theory of EM wave scattering by many small perfectly conducting and impedance bodies. In [25], a numerical method is developed for solving EM wave scattering by many small impedance bodies.
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