A parallel and incremental extraction of variational capacitance with stochastic geometric moments

Authors:
Fang Gong;Hao Yu;Lingli Wang;Lei He
Affiliations:
Department of Electrical Engineering, University of California, Los Angeles, CA;Department of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;State Key Laboratory of Application Specific Integrated Circuits and Systems, Fudan University, Shanghai, China;Department of Electrical Engineering, University of California, Los Angeles, CA
Venue:
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Year:
2012

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Abstract

This paper presents a parallel and incremental solver for stochastic capacitance extraction. The random geometrical variation is described by stochastic geometrical moments, which lead to a densely augmented system equation. To efficiently extract the capacitance and solve the system equation, a parallel fast-multipole-method (FMM) is developed in the framework of stochastic geometrical moments. This can efficiently estimate the stochastic potential interaction and its matrix-vector product (MVP) with charge. Moreover, a generalized minimal residual (GMRES) method with incremental update is developed to calculate both the nominal value and the variance. Our overall extraction flow is called piCAP. A number of experiments show that piCAP efficiently handles a large-scale on-chip capacitance extraction with variations. Specifically, a parallel MVP in piCAP is up to 3 × faster than a serial MVP, and an incremental GMRES in piCAP is up to 15 × faster than non-incremental GMRES methods.