Generalized Stochastic Collocation Method for Variation-Aware Capacitance Extraction of Interconnects Considering Arbitrary Random Probability
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概要
- 論文の詳細を見る
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.
- （社）電子情報通信学会の論文
- 2009-04-01
著者
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LUO Xu
State Key Lab. of ASIC & System, MOE Key Lab. for Computational Physical Sciences, Fudan University
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ZENG Xuan
State Key Lab. of ASIC & System, MOE Key Lab. for Computational Physical Sciences, Fudan University
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ZHU Hengliang
State Key Lab. of ASIC & System, MOE Key Lab. for Computational Physical Sciences, Fudan University
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CAI Wei
Department of Mathematics, University of North Carolina at Charlotte
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Zeng Xuan
State Key Lab. Of Asic & System Moe Key Lab. For Computational Physical Sciences Microelectronic
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Luo Xu
State Key Lab. Of Asic & System Microelectronics Dept. Fudan Univ.
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Zhu Hengliang
State Key Lab. Of Asic & System Microelectronics Dept. Fudan Univ.
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Cai Wei
Department Of Mathematics University Of North Carolina At Charlotte
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Cai Wei
Department of Applied Physics, Beihang University, Beijing 100191, China
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