Electromagnetic field representations and computations in complex structures I: complexity architecture and generalized network formulation

Abstract

SUMMARYIn this three-part sequence of papers, we outline an architecture for systematically dealing in an e$cient and rigorous manner with electromagnetic "eld representations and computations in complex structures. The approach is based on the topological partitioning of the complex structure into several subdomains joined together by interfaces. In analogy with network theory, individual subdomains are characterized via subdomain relations, obtained either analytically or numerically, and described in a uni"ed format by using a generalized network formulation; the various subdomains are linked together via connection relations provided by the complex structure topology. Together these two relations yield the ¹ableau equations which combine all of the necessary information. The suggested framework accommodates the use of di!erent analytic/numerical methods (hybridization), the choice of problem-matched alternative Green's function representations, as well as di!erent types of "eld representations. In the present paper, we focus on the general architecture, various options and their implications, in Part II [1] we furnish formal expressions for the subdomain relationships via alternative Green's functions representations; and in part III [2], we discuss the connection network properties.

Electromagnetic field representations and computations in complex structures II: alternative Green's functions

“…Analogous explicit and abstract formulations can be obtained in other vector and coordinate separable con"gurations [2, Chapters 1}3]. The abstract formulation ties the subdomain problem to the architecture in Reference [1].…”

“…In a &transfer' representation, particularly suited on the analysis of cascaded discontinuity structures, the "eld amplitudes on B (or B ) are speci"ed and one seeks to determine the corresponding "eld distribution on B (or B ). In the "rst instance, the appropriate Green's function Z l (r, r) is one which does not disturb the prescribed "eld at B and contributes only to the asymptotic (propagating mode) "eld at zP# R. Inspection of (45) shows that subtraction of the dyadic In this second part of a three-part sequence, we have examined the analytic structure and options pertaining to the subdomain (SD) problem in the overall complexity architecture de"ned in Reference [1]. Emphasis has been placed on problem-matched Green's functions (GFs) which are to be selected so as to (a) &best' model the &correct' wave dynamics; (b) render numerical implementation more e$cient; and (c) form the background kernel in integral equations which relate the vector "elds in an actual physical environment to the analytically tractable problemmatched GF.…”

“…where¸(u) is given in (1), and the prime on a function denotes the derivative with respect to the argument. The bracketed term on the right-hand side of (5),…”

“…In Reference [1], we have presented an architecture that decomposes a complex conglomerate into simpler interactive subdomains. Subdomains (SD) can be treated in a variety of ways ranging from purely numerical methods, such as "nite element or "nite di!erence methods, to analytic approaches based on constructable problem-matched Green's functions (GF).…”

Electromagnetic field representations and computations in complex structures III: network representations of the connection and subdomain circuits

“…Via a systematic approach to electromagnetic "eld computations in complex structures as shown in Reference [2], we divide the geometrical domain into subdomains connected via interfaces. In this way, the task of electromagnetic "eld computations is separated essentially into two parts: (i) characterization of individual subdomains and (ii) description of the topology, i.e.…”