Abstract
An analysis of the extensions and improvements of GTD since its early time is given. Especially the theoretical foundations of two powerful methods, namely the Boundary Layer Method and the Uniform Asymptotic Expansion Method, are outlined. Aspects of these theories which are of growing interest at present, for solving electromagentic diffraction and radiation problems are pointed out. The resulting solutions are described in a general framework including perfectly conducting and imperfectly conducting objects condition. Their limitations are discussed and indications for further improvements are given. Some new non published results on higher-order edges and coated metallic bodies are also included. The author concludes with a brief description of future trends in the development of GTD.
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