POLYNOMIAL REPRESENTATION OF DIFFRACTION FIELDS AT CRUSTAL IRREGULARITIES.
Final rept. 1 Dec 67-1 Dec 68,
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF ELECTRICAL ENGINEERING
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By means of the Lanczos tau method, polynomial representations are found for the transverse variation of modal solutions of the wave equation. This limits the transverse variation to a finite number of degrees of freedom. While restricted to a finite number, the accuracy in representing modal variation is highly satisfactory, particularly for the lower order modes. Furthermore, major computational advantages materialize in the succeeding analysis. Contour integral representations of solutions of the approximate wave equation no longer involve branch cut integrations-- the only singularity being a family of poles at plus or minus k where k is the propagation constant within the waveguide. Accordingly, Weiner-Hopf problems can be solved almost by inspection inasmuch as the kernel to be factored is a rational function with explicitly displayed poles and zeros. Explicit formulas are given for the entries in the scattering matrix that describes the junction of two dissimilar waveguides. Author
- Numerical Mathematics
- Radiofrequency Wave Propagation