Solving the Problem of Electromagnetic Wave Scattering on Small Impedance Particle by Integral Equation Method

Abstract

The problem of electromagnetic (EM) wave scattering on small particles is reduced to solving the Fredholm integral equation of the second kind. Integral representation of solution to the scattering problem leads to necessity to determine some unknown function contained in integrand of this equation. The respective linear algebraic system (LAS) for the components of this unknown vector function is derived and solved by the successive approximation method. The region of convergence of the proposed method is substantiated. The numerical results show rapid convergence of the method in the wide region of the physical and geometrical parameters of problem. Comparison of the obtained results with Mie type and asymptotic solutions demonstrates high degree of accuracy of the proposed method. The numerical results of scattering on particles of several forms and sizes are presented.

Asymptotic Solution to Scattering Problem on a Set of Small Particles and Application to Creating the Materials with a Peculiar Refractive Index

“…In order to justify the exactness of solution to SLAE (16), which is used for determination of the effective field, we derive some different SLAE, corresponding to limiting Equation (7). Let us divide the domain D, where the small particles are located, into an union of the small non-intersecting cubes p ∆ with centers in points p y ; the diameter of such cubes can be chosen as ( )…”

“…In order to determine the solution to Equation 7, we apply for it the collocation method proposed in [14] and applied successfully to solving the similar SLAR in [15] [16]. In accordance with this method, we obtain such SLAE…”

“…Since the value of d is small, then diameter p ∆ can be of an order larger than distance d between particles. Since P M  , then solving SLAE (17) is much easier than solving SLAE (16) in terms of the number of calculations.…”

“…As a result, we have two different SLAE (16) and (17). Solving both the SLAE, we can compare their solutions and to evaluate the area of accuracy of asymptotic solution (15).…”

“…The values of opt a in the third row correspond to the optimal values of radius a, which guarantees the minimal error for module of solution to Equation (7) and system (16). In the fourth row, × .…”