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.
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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 -