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For variation-aware capacitance extraction, stochastic collocation method (SCM) based on Homogeneous Chaos expansion has the exponential convergence rate for Gaussian geometric variations, and is considered as the optimal solution using a quadratic model to model the parasitic capacitances. However, when geometric variations are measured from the real test chip, they are not necessarily Gaussian, which will significantly compromise the exponential convergence property of SCM. In order to pursue the exponential convergence, in this paper, a generalized stochastic collocation method (gSCM) based on generalized Polynomial Chaos (gPC) expansion and generalized Sparse Grid quadrature is proposed for variation-aware capacitance extraction that further considers the arbitrary random probability of real geometric variations. Additionally, a recycling technique based on Minimum Spanning Tree (MST) structure is proposed to reduce the computation cost at each collocation point, for not only "recycling" the initial value, but also "recycling" the preconditioning matrix. The exponential convergence of the proposed gSCM is clearly shown in the numerical results for the geometric variations with arbitrary random probability.

- Publication
- IEICE TRANSACTIONS on Electronics Vol.E92-C No.4 pp.508-516

- Publication Date
- 2009/04/01

- Publicized

- Online ISSN
- 1745-1353

- DOI
- 10.1587/transele.E92.C.508

- Type of Manuscript
- Special Section PAPER (Special Section on Low-Leakage, Low-Voltage, Low-Power and High-Speed Technologies for System LSIs in Deep-Submicron Era)

- Category

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Hengliang ZHU, Xuan ZENG, Xu LUO, Wei CAI, "Generalized Stochastic Collocation Method for Variation-Aware Capacitance Extraction of Interconnects Considering Arbitrary Random Probability" in IEICE TRANSACTIONS on Electronics,
vol. E92-C, no. 4, pp. 508-516, April 2009, doi: 10.1587/transele.E92.C.508.

Abstract: For variation-aware capacitance extraction, stochastic collocation method (SCM) based on Homogeneous Chaos expansion has the exponential convergence rate for Gaussian geometric variations, and is considered as the optimal solution using a quadratic model to model the parasitic capacitances. However, when geometric variations are measured from the real test chip, they are not necessarily Gaussian, which will significantly compromise the exponential convergence property of SCM. In order to pursue the exponential convergence, in this paper, a generalized stochastic collocation method (gSCM) based on generalized Polynomial Chaos (gPC) expansion and generalized Sparse Grid quadrature is proposed for variation-aware capacitance extraction that further considers the arbitrary random probability of real geometric variations. Additionally, a recycling technique based on Minimum Spanning Tree (MST) structure is proposed to reduce the computation cost at each collocation point, for not only "recycling" the initial value, but also "recycling" the preconditioning matrix. The exponential convergence of the proposed gSCM is clearly shown in the numerical results for the geometric variations with arbitrary random probability.

URL: https://global.ieice.org/en_transactions/electronics/10.1587/transele.E92.C.508/_p

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@ARTICLE{e92-c_4_508,

author={Hengliang ZHU, Xuan ZENG, Xu LUO, Wei CAI, },

journal={IEICE TRANSACTIONS on Electronics},

title={Generalized Stochastic Collocation Method for Variation-Aware Capacitance Extraction of Interconnects Considering Arbitrary Random Probability},

year={2009},

volume={E92-C},

number={4},

pages={508-516},

abstract={For variation-aware capacitance extraction, stochastic collocation method (SCM) based on Homogeneous Chaos expansion has the exponential convergence rate for Gaussian geometric variations, and is considered as the optimal solution using a quadratic model to model the parasitic capacitances. However, when geometric variations are measured from the real test chip, they are not necessarily Gaussian, which will significantly compromise the exponential convergence property of SCM. In order to pursue the exponential convergence, in this paper, a generalized stochastic collocation method (gSCM) based on generalized Polynomial Chaos (gPC) expansion and generalized Sparse Grid quadrature is proposed for variation-aware capacitance extraction that further considers the arbitrary random probability of real geometric variations. Additionally, a recycling technique based on Minimum Spanning Tree (MST) structure is proposed to reduce the computation cost at each collocation point, for not only "recycling" the initial value, but also "recycling" the preconditioning matrix. The exponential convergence of the proposed gSCM is clearly shown in the numerical results for the geometric variations with arbitrary random probability.},

keywords={},

doi={10.1587/transele.E92.C.508},

ISSN={1745-1353},

month={April},}

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TY - JOUR

TI - Generalized Stochastic Collocation Method for Variation-Aware Capacitance Extraction of Interconnects Considering Arbitrary Random Probability

T2 - IEICE TRANSACTIONS on Electronics

SP - 508

EP - 516

AU - Hengliang ZHU

AU - Xuan ZENG

AU - Xu LUO

AU - Wei CAI

PY - 2009

DO - 10.1587/transele.E92.C.508

JO - IEICE TRANSACTIONS on Electronics

SN - 1745-1353

VL - E92-C

IS - 4

JA - IEICE TRANSACTIONS on Electronics

Y1 - April 2009

AB - For variation-aware capacitance extraction, stochastic collocation method (SCM) based on Homogeneous Chaos expansion has the exponential convergence rate for Gaussian geometric variations, and is considered as the optimal solution using a quadratic model to model the parasitic capacitances. However, when geometric variations are measured from the real test chip, they are not necessarily Gaussian, which will significantly compromise the exponential convergence property of SCM. In order to pursue the exponential convergence, in this paper, a generalized stochastic collocation method (gSCM) based on generalized Polynomial Chaos (gPC) expansion and generalized Sparse Grid quadrature is proposed for variation-aware capacitance extraction that further considers the arbitrary random probability of real geometric variations. Additionally, a recycling technique based on Minimum Spanning Tree (MST) structure is proposed to reduce the computation cost at each collocation point, for not only "recycling" the initial value, but also "recycling" the preconditioning matrix. The exponential convergence of the proposed gSCM is clearly shown in the numerical results for the geometric variations with arbitrary random probability.

ER -