Application of integral equation and finite difference methods to electromagnetic scattering by two-dimensional and body-of-revolution geometries

The theoretical and numerical studies of electromagnetic scattering and radiation from perfectly conducting as well as dielectric bodies are of great importance in the design of various systems, such as airborne targets and antennas. This thesis is an attempt to investigate integral equation and partial differential equation techniques as tools for numerical solution of such problems. These techniques are analyzed and some improvements to existing methods are presented. Some scattering problems involving two-dimensional and body of revolution geometries are solved using these techniques to demonstrate their capabilities and to point out their limitations.The first topic that this thesis addresses is the method of moments technique. To demonstrate the techniques developed, electromagnetic scattering from perfectly conducting as well as dielectric bodies of revolution is considered. There are two major issues addressed in this thesis, in this context. First, the use of quasi-entire-domain basis functions, as an alternative to the more traditional sub-sectional basis functions, is considered. It is shown that using the quasi-entire-domain basis functions results in a reduction in the size of the matrix that needs to be solved. The second major topic that Chapter 2 considers is the problem of electromagnetic scattering from layered and partially coated bodies of revolution. The formulation used to solve these problems as well as some results, are presented.The partial differential equation technique that this thesis considers is the finite-difference method. Chapter 3 discusses the finite-difference method in the frequency domain, while Chapter 4 focuses on the solution of Maxwell's equations in the time domain. Chapter 3 solves the problem of scattering by a conducting body of revolution using the finite-difference method in the frequency domain. The procedure outlined uses the coupled azimuthal potentials introduced by Morgan, Chang, and Mei (20) to obtain two coupled partial differential equations. These equations are then solved over a domain discretized using a boundary-fitted curvilinear coordinate system. The main contribution of this thesis in this respect is the application of the boundary-fitted curvilinear coordinate system to this class of problems. It is demonstrated that using this system eliminates the need for using the staircase approximation that is typically required in the finite-difference methods.Chapter 4 focuses on circumventing the problem of staircase approximation that is traditionally used to model material boundaries in finite-difference time-domain algorithms. In this context, two methods are presented. The first one, referred to in this thesis as the modified stencil approach, allows the use of arbitrarily-shaped quadrilateral grids. The second is similar to the boundary-fitted curvilinear coordinate approach presented in Chapter 3. The methods are compared and contrasted, and the advantages and disadvantages of each method are pointed out.U of I OnlyETDs are only available to UIUC Users without author permissio