Modeling inductive effects accurately and efficiently is a critical necessity for design verification of high performance integrated systems. While several techniques have been suggested to address this problem, they are mostly based on sparsification schemes for the L or L-inverse matrix. In this paper, we introduce CHIME, a methodology for non-local inductance modeling and simulation. CHIME is based on a hierarchical model of inductance that accounts for all inductive couplings at a linear cost, without requiring any window size assumptions for sparsification. The efficacy of our approach stems from representing the mutual inductive couplings at various levels of hierarchy, rather than discarding some of them. A prototype implementation demonstrates orders of magnitude speedup over a full, flat model and significant accuracy improvements over a truncated model. Importantly, this hierarchical circuit simulation capability produces a solution that is as accurate as the hierarchically extracted circuits, thereby providing a "golden standard" against which simpler truncation based models can be validated.

The increasing size of integrated systems combined with deep submicron physical modeling details creates an explosion in RLC interconnect modeling complexity of unmanageable proportions. Interconnect extraction tools employ hierarchy to manage complexity, but this hierarchy is discarded via eliminating far away coupling terms when the equivalent ARC circuits are Formed. The increasing dominance of capacitance coupling along with the emergence of on chip inductance, however, makes the composite effect of far-away couplings increasingly evident. Even if newly enforced design rules and practices will ultimately obviate the need for modeling these couplings for design verification, some approximation of the "exact" solution is required to validate these rules. This paper proposes an efficient hierarchical equivalent circuit representation of interconnect parasitics that utilizes the efficient hierarchical long-distance modeling already existing within extractors. Results from a prototype simulator based on these hierarchical models demonstrate the simulation inaccuracy incurred when the faraway coupling terms are ignored. Such a form of interconnect modeling may provide the key to hierarchical modeling of electro-magnetic interactions between large components on future gigascale systems.