High frequency scattering and spectral methods

Sammanfattning: This thesis consists of five parts. The first part is an introduction with references to some recent work on 2D electromagnetic scattering problems at high frequencies. It also presents the basic integral equation types for impenetrable objects and the standard elements of the method of moments. An overview of frequency modulated radar at low frequencies is followed by summaries of the papers. Paper I presents an accurate implementation of the method of moments for a perfectly conducting cylinder. A scaling for the rapid variation of the solution improves accuracy. At high frequencies, the method of moments leads to a large dense system of equations. Sparsity in this system is obtained by the modification of the path in the integral equation. The modified path reduces the accuracy in the deep shadow. In paper II, a hybrid method is used to handle the standing waves that are prominent in the shadow for the cylindrical TE case. The shadow region is treated separately, in a hybrid scheme based on a priori knowledge about the solution. An accurate method to combine solutions in this hybrid scheme is presented. In paper III, the surface current in the shadow zone of a convex or a concave scatterer is approximated by extracting the dominant waves. An accurate technique based on the symmetric discrete Fourier transform is used to extract the complex wavenumbers and amplitudes for those waves. The dominant waves constitute a concise form of scaling that is used to improve the performance of the method of moments. The effect of surface curvature on the dominant waves has been investigated in this work. In paper IV, frequency modulated continuous wave radar (FMCW) at low frequency is studied as a way to locate targets that are normally not detected by conventional radar. Three separate platforms with isotropic antennas are used for this purpose. The trilateration method is a way to locate the targets accurately by means of spectral techniques. The problem of ghost targets has been studied for monostatic and multistatic radar. In the case of confluent echoes in the spectra, potentially missing echoes are reinserted in order to locate all targets. The Capon method is used to obtain high resolution spectra and thus reduce the confluence problem. The need for bandwidth is also reduced.