The work is devoted to the problem of scattering of monochromatic electromagnetic waves on heterogeneous dielectric inclusions of arbitrary shapes. For the numerical solution of the problem, the volume integral equation for the electric field in the region occupied by the inclusion is used. Discretization of this equation is carried out by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms. For a regular grid of approximating nodes, the matrix of the discretized problem proves to have the Toeplitz structure, and the matrix-vector product with such matrices can be carried out by the Fast Fourier Transform technique. The latter strongly accelerates the process of the iterative solution of the discretized problem. Electric fields inside a spherical inclusion and its differential cross-sections are calculated and compared with the exact (Mie) solution for various wave lengths of the incident field. Internal electric fields and the differential cross-sections of a cylindrical inclusion are calculated for the incident fields of various directions and wave lengths.
2. Chew, W. C., J.-M. Jin, C.-C. Lu, E. Michielssen, and J. M. Song, "Fast solution methods in electromagnetics," IEE Transactions on Antennas and Propagation, Vol. 45, No. 3, 533-543, 1997.
3. Tsang, L., J. A. Kong, K.-H. Ding, and C. O. Ao, "Scattering of Electromagnetic Waves: Numerical Solutions," John Wiley & Sons, 2001.
4. Samokhin, A. B., Integral Equations and Iterative Methods in Electromagnetic Scattering, VSP, Utrecht, Boston, Koln, Tokyo, 2001.
5. Ewe , W.-B., L.-W. Li, and M.-S. Leong, "Solving mixed dielectric/conducting scattering problems using adaptive integral method," Progress In Electromagnetics Research, Vol. 46, 143-163, 2004.
6. Fan, Z. H., R. S. Chen, H. Chen, and D. Z. Ding, "Weak form nonuniform fast Fourier transform method for solving volume integral equations," Progress In Electromagnetics Research, Vol. 89, 275-289, 2009.
7. Maz'ya, V. and G. Schmidt, "Approximate Approximation, Mathematical Surveys and Monographs," American Mathematical Society, Providence, 2007, Vol. 41.
8. Kanaun, S. and S. B. Kochekseraii, "A numerical method for the solution of 3D-integral equations of electro-static theory based on Gaussian approximation functions," Applied Mathematics and Computation, Vol. 184, 754-768, 2007.
9. Peterson, A., S. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, NY, 1998.
10. Golub, G. and C. Van Loan, Matrix Computations, 3rd Ed., The Johns Hopkins University Press, 1996.
11. Kanaun, S., "On the effective elastic properties of matrix composites: Combining the effective field method and numerical solutions for cell elements with multiple inhomogeneities ," International Journal of Engineering Sciences, Vol. 48, No. 2, 160-173, 2009.