A Method for Combining Integral Equation and Asymptotic Techniques for Solving Electromagnetic Scattering Problems
ILLINOIS UNIV AT URBANA ELECTROMAGNETICS LAB
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This paper introduces a new approach for combining the integral equation and high frequency asymptotic techniques, e.g., the geometrical theory of diffraction. The method takes advantage of the fact that the Fourier transform of the unknown surface current distribution is proportional to the scattered far field. A number of asymptotic methods are currently available that provide good approximation to this far field in a convenient analytic form which is useful for deriving an initial estimate of the Fourier transform of the current distribution. An iterative scheme is developed for systematically improving the initial form of the high frequency asymptotic solution by manipulating the integral equation in the Fourier transform domain. A synthetic- aperture-distribution scheme is also developed in which the approximate scattered far-field pattern obtained by asymptotic techniques is improved by systematically correcting the scattered field distribution on an aperture erected in juxtaposition with the obstacle. The introduction of such a planar aperture not only provides an additional degree of freedom in performing improving operations, but also renders the scheme to handle n-dimensional geometries by n - 1-dimensional fast Fourier transform FFT, where n 2, 3, and circumvents the unwieldy three-dimensional FFT, making it a conceptually simple and computationally efficient method.
- Numerical Mathematics
- Radiofrequency Wave Propagation