Integral equations applied to electromagnetic scattering in the resonance region

摘要

In the application of an integral method to the problem of electromagnetic scattering by three-dimensional objects, the electromagnetic problem is formulated in terms of an electric field integral equation for conducting bodies and a combined field integral equation for dielectric or composite objects. The electric and magnetic fields are related to the unknown surface currents by the Green's functions for the scalar and vector potentials. Triangular patches are used to model the scatterer's surface and the basis functions proposed by Rao, Wilton and Glisson, represent the surface current on the scatterer's surface. The application of the method of moments for the solution of the integral equations results in double surface integrals, which are computationally very expensive. Rao, Wilton and Glisson avoided the computation of a double surface integral by approximating the surface integral over the observation triangle by evaluating the integral at the centre of each observation point using a one point Gaussian quadrature scheme. This approach has also been adopted by other workers as it is relatively straightforward to implement since it only requires the field evaluation over the source triangle. In addition, the edge lengths of the triangle patches should be of the order of one-tenth of a wavelength if good results are to be obtained. This simplifies the computational task and it was believed that it decreases the computation time. For electrically large objects, many patches are needed and the order of the system matrices derived from the discretisation of the integral equations becomes large. This thesis investigates whether the approximation used to compute the impedance terms in the reported schemes lead to a computationally efficient scheme. In this thesis, a comparison is made between the use of the EFIE and the CFIE with the full double surface integrals and the original EFIE and the CFIE schemes with the associated approximation. The integrals over the observation and source triangles are both evaluated. The equations of the discretised integral equations for conducting, dielectric and composite objects are derived to enable the impedance terms to be computed efficiently. A method is described of how to minimise the computing time for the evaluation of the double surface integrals and a criterion is presented for obtaining a good compromise between accuracy and total computing time. The proposed formulation has been developed for the EFIE, for scattering by perfect electric conductors only; for the CFIE, for both dielectric/magnetic materials only and also the CFIE for mixed perfect electric conductors and dielectric materials. The scheme has been used to calculate the radar cross- section of conducting, dielectric and mixed objects and the results compared with those based on the RWG formulation and from the literature. The basis of comparison with the RWG formulation is based on accuracy, total computation time and computer memory required. The proposed formulation's results for conducting objects compare well with results from the literature and clearly demonstrate significant computational advantage over the original RWG formulation. For dielectric objects, the proposed formulation shows only some computational advantage over the RWG formulation whereas there is a no Improvement with the mixed objects.