Circuit simulation via matrix exponential method for stiffness handling and parallel processing

Authors:
Shih-Hung Weng;Quan Chen;Ngai Wong;Chung-Kuan Cheng
Affiliations:
University of California San Diego, La Jolla, CA;University of Hong Kong, Hong Kong;University of Hong Kong, Hong Kong;University of California San Diego, La Jolla, CA
Venue:
Proceedings of the International Conference on Computer-Aided Design
Year:
2012

Citing 12
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Abstract

We propose an advanced matrix exponential method (MEXP) to handle the transient simulation of stiff circuits and enable parallel simulation. We analyze the rapid decaying of fast transition elements in Krylov subspace approximation of matrix exponential and leverage such scaling effect to leap larger steps in the later stage of time marching. Moreover, matrix-vector multiplication and restarting scheme in our method provide better scalability and parallelizability than implicit methods. The performance of ordinary MEXP can be improved up to 4.8 times for stiff cases, and the parallel implementation leads to another 11 times speedup. Our approach is demonstrated to be a viable tool for ultra-large circuit simulations (with 1.6M ~ 12M nodes) that are not feasible with existing implicit methods.