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

In this three-part sequence of papers, we outline an architecture for systematically dealing in an efficient and rigorous manner with electromagnetic field 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 unified 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 Tableau equations which combine all of the necessary information. The suggested framework accommodates the use of different analytic/numerical methods (hybridization), the choice of problem-matched alternative Green's function representations, as well as different types of field representations. In the present paper, we focus on the general architecture, various options and their implications, in Part II we furnish formal expressions for the subdomain relationships via alternative Green's functions representations; and in part III, we discuss the connection network properties.