Kaydırılmış Frekansta İç Eşdeğerlik Algoritmasının İki Boyutlu Elektromanyetik Saçılma Problemlerinde Başarımının İncelenmesi
Özet
In this thesis, scattering from two dimensional inhomogeneous dielectric bodies is investigated. Radiation and scattering problems involving dielectric objects can be formulated by using surface integral equation (SIE) methods or volume integral equation (VIE) methods. SIE methods employ unknown currents that reside on the surface of the geometry and are employed to formulate problems involving homogeneous bodies. VIE methods, on the other hand, employ unknown current densities that are distributed inside the geometry and allow problems involving inhomogeneous bodies to be solved. Numerical solution to these problems start with the discretization of the integral equations by a method of moments (MoM) scheme. Discretized integral equations are then converted into matrix equations which are solved to obtain unknown current coefficients. Numbers of elements in these matrix equations are closely related to the electrical size of the problem. Since VIE methods use volumetric currents, matrix sizes can quickly become very large. Usually these computationally intensive operations are required in multiple frequencies covering a bandwidth. In this case, a lengthy solution process needs to be repeated for each frequency of interest.
It has been shown earlier that by using Shifted Frequency Internal Equivalence (SFIE), it is not necessary to calculate all of the matrix elements for different incident frequencies. It is possible to reuse volume interactions within a wide frequency band by performing only algebraic manipulations. Only the matrix elements which correspond to surface interactions need to be recalculated for the solution at a different incident frequency. By reusing a large part of the matrix, computational complexity of the matrix filling part of the problem is effectively reduced to that of a homogeneous problem, although the body is inhomogeneous. It is the aim of this thesis to investigate the computational performance of SFIE in terms of accuracy, bandwidth, and required computer resources. In order to assess SFIE, analysis results for different, electrically large inhomogeneous scatterers with slowly and rapidly varying material properties are presented. Near and scattered far fields are calculated to assess the accuracy of SFIE. When possible, comparisons with analytical results are made. When analytical results are not available, comparisons with MoM results are made. It is shown that SFIE produces accurate results within a wide frequency band. Since com- putational complexity of the problem is effectively reduced, it will also be shown that SFIE accelerates the frequency sweeps of the multi-frequency scattering problems.
