SOME ANALYTICAL METHODS FOR SOLVING A CLASS OF BOUNDARY VALUE PROBLEMS
ILLINOIS UNIV AT URBANA ANTENNA LAB
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A variety of boundary problems, related to basic Wiener-Hopf geometries but of more practical interest, has been solved by a modified residue-calculus technique MRCT, by the generalized scattering matrix technique, or by a combination of the two methods. The MRCT solution is given in a form convenient for computation, not involving numerical integration or solution of large order matrix equations. In addition, the MRCT automatically guarantees satisfaction of the edge condition and includes built-in tests on the convergence of the solution. An additional group of modified Wiener-Hopf geometries in which modal expansions are possible are solved by a combination of the MRCT and the generalized scattering matrix procedure. The analytical methods described in this report are applicable to waveguide discontinuities, including steps, bifurcations, and diaphragms, in both rectangular and circular waveguides to phased arrays of dielectric-filled waveguides with thick walls to a variety of diffraction surfaces and gratings and to many other modified Wiener-Hopf geometries.
- Theoretical Mathematics
- Radiofrequency Wave Propagation