Multi-level Order Reduction with Nonlinear Port Constraints

In recent years, congruence transformation based model order reduction methods have proven to be an effective tool in dealing with increasing computational complexities which arise from the simulation of interconnect networks. However, most existing model order reduction methods are only efficient in coping with systems with small number of ports. Moreover, model order reduction methods based on Krylov subspace result in a macromodel which is not optimal. In this paper, a two-level reduction method is proposed to address the above two limitations. In the first level reduction, prior information about the types the loads that can be connected to the ports and their ranges of values is exploited to obtain a reduced macromodel whose size is not very sensitive to the number of ports. Since the first level reduction uses congruence transformation based on Krylov subspace techniques, which contain redundant information. This leads to a second level reduction using singular value decomposition. The proposed method is shown to produce a macromodel which is significantly smaller than standard methods.