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The complicated geometry of high-density interconnect structures in multilayer, planar substrates is one of the major hurdles in the application of finite element methods for their multigigahertz electromagnetic analysis. In addition to compounding the complexity in the generation of the finite element grid, the multilayer nature of the structures and their multiscale attributes result in finite element systems of very large dimension which, more often than not, are not well conditioned. This paper presents a domain decomposition methodology for overcoming these hurdles. More specifically, the proposed methodology utilizes the multiple power and ground planes used in such structures as natural physical boundaries for their decomposition into a set of subdomains, each one of which is meshed and discretized separately from the rest. The electromagnetic interaction between the domains is effected through the enforcement of tangential field continuity conditions at the voids and via holes present at the power and ground planes. In particular, a Krylov subspace model order reduction approach is used to facilitate the broadband solution of the multilayer interconnect structure. The proposed modeling methodology is demonstrated through its application to the electromagnetic analysis of several multilayer interconnect structures.