A Study On The Fast Approximate Numerical Methods For Electromagnetic Scattering Problems

Integral equation method is one of important methods for solving electromagnetic scattering problems. Because the coefficient matrix of moment method (MM) is a dense matrix and solving the linear system is time-consuming, iterative methods are generally used for the solution. Fast algorithms based on integral equations are concentrating on dealing with the coefficient matrix to reduce the time consuming and memory space. Comparing with the numerical methods, high frequency approximation techniques are much more efficient in solving electromagnetic scattering problems, but it is limited in lower precision and applicability for scatterers with complex structures. Hybrid methods combined numerical methods with high frequency approximation would be better tradeoff between efficiency and applicability.In this thesis, a hybrid technique using electromagnetic integral formulae and numerical iterative technique is investigated based on the regions of illumination and shadow in high frequency approximation. A novel iterative method is presented by combining numerical technique, high frequency approximation and surface integral formulae of the fields, which is called windowed iterative technique.Windowed iterative technique is firstly applied to solve electromagnetic scattering problems of conducting cylinder. A single point measuring equation of a field is determined near the scatterer surface, and the iterative formula is established by use of the boundary conditions and field relationships. A window function is introduced to compress the error of current distribution in the shadow region. The descendent rate should be adjusted according to the scatterer sizes, so Kaiser window function is employed for its adjustable parameter. Parameter determination is discussed. Furthermore, a modified Hanning window is proposed. The scattering from cylinders under the TM and TE incidences are analyzed respectively. In the new technique, the solution is initialized with the physical optical current, and then is modified with the fast multipole method (FMM) to accelerate the matrix-vector multiplication and reduce computational costs. The numerical results demonstrate the efficiency and effectiveness. Sufficient accuracy can be reached after only several iterations which is independent of the sizes of the scatterers. It is can be employed to solve electromagnetic scattering problems of electrically large bodies.Secondly, windowed iterative technique is extended to solve the scattering from homogeneous dielectric cylinders. Both single and double measuring equations are proposed. The results with the former are given.It is concluded from the results that numerical methods and high frequency approximation can be syncretized in the hybrid technique proposed which possesses satisfactory precision, good applicability and less computational operations.