Hierarchical Krylov subspace reduced order modeling of large RLC circuits

In this paper, we propose a new model order reduction approach for large interconnect circuits using hierarchical decomposition and Krylov subspace projection-based model order reduction. The new approach, called MePrimor, first partitions a large interconnect circuit into a number of smaller subcircuits and then performs the projection-based model order reduction on each of subcircuits in isolation and on the top level circuit thereafter. The new approach can exploit the parallel computing to speed up the reduction process. Theoretically we show hiePrimor can have the same accuracy as the flat reduction method given the same reduction order and it can also preserves the passivity of the reduced models as well. We also show that partitioning is important for hierarchical projection-based reduction and the minimum-span objective should be required to archive best performance for hierarchical reduction. The proposed method is suitable for reducing large global interconnects like coupled bus, transmission lines, large clock nets in the post layout stage. Experimental results demonstrate that hiePrimor can be significantly faster than flat projection method like PRIMA and be order of magnitude faster than PRIMA with parallel computing without loss of accuracy.