Mathematical modeling of interaction of H-polarized electromagnetic wave with a system of thin penetrable inclusions

Запропоновано математичну модель взаємодії електромагнітного поля – поляризованої плоскої хвилі з системою тонких діелектричних циліндричних включень у вигляді системи інтегродиференціальних сингулярних інтегральних рівнянь, визначених на середній лінії поперечного перетину розсіювачів. З використанням квадратурних формул інтерполяційного типу за вузлами, що співпадають з коренями полінома Чебишева, числову реалізацію математичної моделі зведено до розв’язання системи лінійних алгебраїчних рівнянь. Наведено результати числового дослідження поперечника розсіяння двох включень.Using the method of integral equations the mathematical model of interwork between the electromagnetic field of H-polarized plane wave and the system of thin dielectric or little conducting cylindrical embedding has been built. For its building the system of two-dimensional integral equations defined on the basis transverse section diffusers was taken. The direct implementation of the available methods for their numerous solving faces numerical difficulties caused by the little thickness of diffuser and are connected with calculus of singular and quasisingular two-dimensional integrals. Taking into consideration the fact that inside the diffuser the field changes its thickness unsufficeintly the mathematical model of interwork between the electromagnetic field of H-polarized plane wave with the system of thin dielectric cylindrical inclusions in the form of the system of integrodifferential singular integral equations defined on the centre line of the diffusers transverse section has been proposed. They were obtained by averaging of the system of integral equations defined the diffusers transverse section area. Using the quadrature formula of interpolatory type by the crosspoints which coincide with the Chebyshev polynomial, roots the numerical realization of mathematical model is redused to the solving of the system of linear algebraic equations. To test the proposed mathematical model the case of whole and cross-cut plate and half-ring shape has been proposed. The research of the influence of the distance between the two parts of infusions and the direction of plane wave propagation on the field in the far-field zone was conducted. The built mathematical model allows conducting research of the field scattered characteristics scattered by the arbitrarily-spaced cylindrical open coverings, the maximum thickness of which is considerably less than the length, the latter being considerably bigger or the same as the length of the explorative electromagnetic wave