LSBRMLeast-Square Boundary Residual Method
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Given the level of accuracy obtainable by our LSBRM model for [[theta].sub.k], we can confidently proceed to compute the various scattering parameters defined in (1) via the following equations [10] (which are derived via the superposition of the output waves portrayed in Figure 3 for all possible eigenmodes [25]):
Hence, it is not surprising to find in Tables 1 and 2 that our LSBRM model requires a large number of modes (with P and Q exceeding 800) before the computed results for [alpha], [beta], [gamma], [tau] and [[lambda].sub.k] converge to [+ or -] 0.001 and [+ or -] 0.1[degrees] for magnitude and phase respectively.
Another useful advantage of the LSBRM is that we can check the level of residual field-mismatch via the parameters [[DELTA].sub.A], [[DELTA].sub.B] and [[DELTA].sub.C] defined in (2)-(4) as stipulated by BC5 and BC6.
The close agreement between the predicted and measured results plotted in Figure 8 for [alpha], [beta], [gamma] and [tau] over the frequency range from 8.2 GHz to 12.4 GHz provides further corroboration that the numerical results generated by our LSBRM model are accurate and reliable for use in computer-aided design.