Fast Methods for Extraction and Sparsification of Substrate Coupling

The sudden increase in systems-on-a-chip designs has renewed interest in techniques for analyzing and eliminating substrate coupling problems. Previous work on the substrate coupling analysis has focused primarily on faster techniques for extracting coupling resistances, but has offered little help for reducing the resulting network whose number of resistors grows quadratically with the number of contacts. In this paper we show that an approach inspired by wavelets can be used in two ways. First, the wavelet method can be used to accurately sparsify the dense contact conductance matrix. In addition, we show that the method can be used to compute the sparse representation directly. Computational results are presented that show that for a problems with a few thousand contacts, the method can be almost ten times faster at constructing the matrix.