Scalable Symbolic Model Order Reduction

Symbolic model order reduction (SMOR) is to reduce the complexity of a model with symbolic parameters. It is an important problem in analog circuit synthesis and digital circuit modeling with process variations. However, existing symbolic model order reduction (SMOR) methods do not scale well with the number of symbols or with the model order. This paper presents a scalable SMOR algorithm, namely S² MOR. We first separate the original multz-port multz-symbol system into a set of single-port systems by superposition theorem, and then integrate them together to form a lower-bordered block diagonal (LBBD) structured system. Each block is reduced independently, with a stochastic programming to distribute the given overall model order between blocks for best accuracy. The entire system is efficiently solved by low-rank update. Compared with existing SMOR algorithms, given the same memory space, S²MOR improves accuracy by up to 78% at a similar reduction time. In addition, the factorization and simulation of the reduced model by S²MOR is up to 17 times faster.