Proper Orthogonal Decomposition in the Generation of Reduced Order Models for Interconnects

Abstract

In this paper, reduced order models are generated using the technique of proper orthogonal decomposition (POD), also known as Karhunen-Loeve decomposition (KLD) for the simulations of interconnect problems. Model order reduction is achieved by projecting the state-space of the original problems onto a subspace spanned by a few number of proper orthogonal modes (POMs) extracted by the POD procedure from an ensemble of system responses at a series of selected frequencies. The proper orthogonal values (POVs) corresponding to the POMs indicate the level of the importance of each POM and provide a guidance for the number of POMs to be used in the reduced order models in order to have enough accuracy. Numerical experiment results obtained from the simulations of a two-conductor interconnect and a spiral inductor demonstrate that the reduced order models generated in this way can simulate the original system more effectively and faithfully than those generated with the standard Krylov subspace method with moment matching at a single point.