Stochastic Sparse-Grid Collocation Algorithm for Steady-State Analysis of Nonlinear System with Process Variations

Jun TAO; Xuan ZENG; Wei CAI; Yangfeng SU; Dian ZHOU

doi:10.1587/transfun.E93.A.1204

Stochastic Sparse-Grid Collocation Algorithm for Steady-State Analysis of Nonlinear System with Process Variations

Jun TAO, Xuan ZENG, Wei CAI, Yangfeng SU, Dian ZHOU

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In this paper, a Stochastic Collocation Algorithm combined with Sparse Grid technique (SSCA) is proposed to deal with the periodic steady-state analysis for nonlinear systems with process variations. Compared to the existing approaches, SSCA has several considerable merits. Firstly, compared with the moment-matching parameterized model order reduction (PMOR) which equally treats the circuit response on process variables and frequency parameter by Taylor approximation, SSCA employs Homogeneous Chaos to capture the impact of process variations with exponential convergence rate and adopts Fourier series or Wavelet Bases to model the steady-state behavior in time domain. Secondly, contrary to Stochastic Galerkin Algorithm (SGA), which is efficient for stochastic linear system analysis, the complexity of SSCA is much smaller than that of SGA for nonlinear case. Thirdly, different from Efficient Collocation Method, the heuristic approach which may result in "Rank deficient problem" and "Runge phenomenon," Sparse Grid technique is developed to select the collocation points needed in SSCA in order to reduce the complexity while guaranteing the approximation accuracy. Furthermore, though SSCA is proposed for the stochastic nonlinear steady-state analysis, it can be applied to any other kind of nonlinear system simulation with process variations, such as transient analysis, etc.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.6 pp.1204-1214

Publication Date: 2010/06/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E93.A.1204

Type of Manuscript: PAPER

Category: VLSI Design Technology and CAD

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Jun TAO, Xuan ZENG, Wei CAI, Yangfeng SU, Dian ZHOU, "Stochastic Sparse-Grid Collocation Algorithm for Steady-State Analysis of Nonlinear System with Process Variations" in IEICE TRANSACTIONS on Fundamentals, vol. E93-A, no. 6, pp. 1204-1214, June 2010, doi: 10.1587/transfun.E93.A.1204.
Abstract: In this paper, a Stochastic Collocation Algorithm combined with Sparse Grid technique (SSCA) is proposed to deal with the periodic steady-state analysis for nonlinear systems with process variations. Compared to the existing approaches, SSCA has several considerable merits. Firstly, compared with the moment-matching parameterized model order reduction (PMOR) which equally treats the circuit response on process variables and frequency parameter by Taylor approximation, SSCA employs Homogeneous Chaos to capture the impact of process variations with exponential convergence rate and adopts Fourier series or Wavelet Bases to model the steady-state behavior in time domain. Secondly, contrary to Stochastic Galerkin Algorithm (SGA), which is efficient for stochastic linear system analysis, the complexity of SSCA is much smaller than that of SGA for nonlinear case. Thirdly, different from Efficient Collocation Method, the heuristic approach which may result in "Rank deficient problem" and "Runge phenomenon," Sparse Grid technique is developed to select the collocation points needed in SSCA in order to reduce the complexity while guaranteing the approximation accuracy. Furthermore, though SSCA is proposed for the stochastic nonlinear steady-state analysis, it can be applied to any other kind of nonlinear system simulation with process variations, such as transient analysis, etc.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1204/_p

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@ARTICLE{e93-a_6_1204,
author={Jun TAO, Xuan ZENG, Wei CAI, Yangfeng SU, Dian ZHOU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Stochastic Sparse-Grid Collocation Algorithm for Steady-State Analysis of Nonlinear System with Process Variations},
year={2010},
volume={E93-A},
number={6},
pages={1204-1214},
abstract={In this paper, a Stochastic Collocation Algorithm combined with Sparse Grid technique (SSCA) is proposed to deal with the periodic steady-state analysis for nonlinear systems with process variations. Compared to the existing approaches, SSCA has several considerable merits. Firstly, compared with the moment-matching parameterized model order reduction (PMOR) which equally treats the circuit response on process variables and frequency parameter by Taylor approximation, SSCA employs Homogeneous Chaos to capture the impact of process variations with exponential convergence rate and adopts Fourier series or Wavelet Bases to model the steady-state behavior in time domain. Secondly, contrary to Stochastic Galerkin Algorithm (SGA), which is efficient for stochastic linear system analysis, the complexity of SSCA is much smaller than that of SGA for nonlinear case. Thirdly, different from Efficient Collocation Method, the heuristic approach which may result in "Rank deficient problem" and "Runge phenomenon," Sparse Grid technique is developed to select the collocation points needed in SSCA in order to reduce the complexity while guaranteing the approximation accuracy. Furthermore, though SSCA is proposed for the stochastic nonlinear steady-state analysis, it can be applied to any other kind of nonlinear system simulation with process variations, such as transient analysis, etc.},
keywords={},
doi={10.1587/transfun.E93.A.1204},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - Stochastic Sparse-Grid Collocation Algorithm for Steady-State Analysis of Nonlinear System with Process Variations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1204
EP - 1214
AU - Jun TAO
AU - Xuan ZENG
AU - Wei CAI
AU - Yangfeng SU
AU - Dian ZHOU
PY - 2010
DO - 10.1587/transfun.E93.A.1204
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2010
AB - In this paper, a Stochastic Collocation Algorithm combined with Sparse Grid technique (SSCA) is proposed to deal with the periodic steady-state analysis for nonlinear systems with process variations. Compared to the existing approaches, SSCA has several considerable merits. Firstly, compared with the moment-matching parameterized model order reduction (PMOR) which equally treats the circuit response on process variables and frequency parameter by Taylor approximation, SSCA employs Homogeneous Chaos to capture the impact of process variations with exponential convergence rate and adopts Fourier series or Wavelet Bases to model the steady-state behavior in time domain. Secondly, contrary to Stochastic Galerkin Algorithm (SGA), which is efficient for stochastic linear system analysis, the complexity of SSCA is much smaller than that of SGA for nonlinear case. Thirdly, different from Efficient Collocation Method, the heuristic approach which may result in "Rank deficient problem" and "Runge phenomenon," Sparse Grid technique is developed to select the collocation points needed in SSCA in order to reduce the complexity while guaranteing the approximation accuracy. Furthermore, though SSCA is proposed for the stochastic nonlinear steady-state analysis, it can be applied to any other kind of nonlinear system simulation with process variations, such as transient analysis, etc.
ER -