Mathematical models of the scattering dielectric objects

The basic operators are suggested as part of the general functional matrix operator with a block structure to construct mathematical models of complex dielectric objects. Boundary problems in the form of systems of integral equations satisfy the boundary conditions and the Zommerfeld radiation condition. Asymptotic correspondence of three-dimensional and two-dimensional problems of scattering of electromagnetic fields to transform to problems with plane symmetry is used. It is shown that this correspondence extends the mathematical modelling in the scattering of electromagnetic fields on the complex dielectric objects. Basic matrix operator is formulated as a generalization of the system of integral equations for two-dimensional homogeneous region bounded by a smooth contour. A formalized method for forming of functional matrix operators for the study of mathematical models of two-dimensional objects as set of separate homogeneous regions is developed. It is shown that in some cases using functional matrix operators for multi-homogeneous regions, which interpolating inhomogeneous dielectric region, is preferable for the numerical study. The results of solution of problem the test of the scattering of a plane wave on homogeneous dielectric cylinder show the high efficiency of the proposed mathematical model. Due to the block structure of the functional matrix operators is suggested the rational form of the generalized complete matrix of mathematical model.