Modelling electromagnetic waves in anisotropic materials

The thesis deals with modelling electromagnetic waves in anisotropic media. In the first part of the thesis, a new method of approximate computation of the electric and magnetic matrix Green's functions in general gyrotropic media has been suggested and investigated. This method is based on the following. The Fourier images of the elements of the electric and magnetic matrix Green's functions with respect to space variables are computed exactly by some matrix transformations and symbolic computations in MATLAB. The element of the Green's functions for electric and magnetic fields are derived approximately by the regularized numerical computation of the inverse Fourier transform of their images obtained on the previous step. The regularization parameters are chosen by comparison the elements of regularized Green's functions for electric and magnetic fields with exact the Green's functions for electric and magnetic fields in the case of an isotropic medium. The computational experiments confirmed the robustness of the method. In the second part of the thesis we suggested a new method of approximate computation of the fundamental solution of time-dependent Maxwell's equations for general anisotropic conductive materials. This method is based on the following. Applying the Fourier transformation with respect to the space variables, the initial value problem is reduced to the Volterra integral equations. The solution of the obtained integral equation is constructed by the method of successive approximations. Finally, the inverse Fourier transform is applied numerically to the fundamental solution for the time-dependent Maxwell's equations. The computational experiments confirmed the robustness of the method.