| The utility of any computational electromagnetic method (CEM) depends strongly on both its effectiveness in solving specific problems of interest and its broader applicational scope. Naturally, two obvious schools of thought in approaching research in such a field would be to define a very specific class of CEM problem and then cater a solution methodology towards efficiently solving such problems or to identify common features of a broad class of problem and then to exploit knowledge of such features in arriving at an efficient solution methodology. Of course it is not necessary that one strictly adhere to this dichotomy since a research objective can be defined, to varying degrees of success, concurrently through both avenues. It is more the latter approach that has guided the research described in this report.;The initial research objective of the work described in this report was to arrive at a finite-element boundary-integral (FE-BI) solution method that can be efficiently applied to EM problems that exhibit some sort of repeated structure whether it be periodic, aperiodic, or predominantly periodic in nature. Specifically, the objective was to use the FEM to cast a general EM problem with the characteristic features mentioned into a tractable boundary integral problem using surface impedance/admittance (or general interaction) matrices, which can loosely be thought of as a type of numerical Green's function. A consequence of pursuing this research serendipitously resulted in novel means of coupling the two numerical methods towards some computational benefit for a variety of CEM problems. The surface interaction coupling method is applied to per-unit-length parameter extraction of lossy transmission lines, FE-BI coupling for electrostatic problems, and for computing periodic numerical Green's functions of 2D periodic domains. |
