A Modified Nested Sparse Grid Based Adaptive Stochastic Collocation Method for Statistical Static Timing Analysis
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概要
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In this paper, we propose a Modified nested sparse grid based Adaptive Stochastic Collocation Method (MASCM) for block-based Statistical Static Timing Analysis (SSTA). The proposed MASCM employs an improved adaptive strategy derived from the existing Adaptive Stochastic Collocation Method (ASCM) to approximate the key operator MAX during timing analysis. In contrast to ASCM which uses non-nested sparse grid and tensor product quadratures to approximate the MAX operator for weakly and strongly nonlinear conditions respectively, MASCM proposes a modified nested sparse grid quadrature to approximate the MAX operator for both weakly and strongly nonlinear conditions. In the modified nested sparse grid quadrature, we firstly construct the second order quadrature points based on extended Gauss-Hermite quadrature and nested sparse grid technique, and then discard those quadrature points that do not contribute significantly to the computation accuracy to enhance the efficiency of the MAX approximation. Compared with the non-nested sparse grid quadrature, the proposed modified nested sparse grid quadrature not only employs much fewer collocation points, but also offers much higher accuracy. Compared with the tensor product quadrature, the modified nested sparse grid quadrature greatly reduced the computational cost, while still maintains sufficient accuracy for the MAX operator approximation. As a result, the proposed MASCM provides comparable accuracy while remarkably reduces the computational cost compared with ASCM. The numerical results show that with comparable accuracy MASCM has 50% reduction in run time compared with ASCM.
- （社）電子情報通信学会の論文
- 2009-12-01
著者
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Yang Fan
State Key Laboratory Of Electroanalytical Chemistry Changchun Institute Of Applied Chemistry Chinese
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Yang Fan
State Key Lab. Of Asic & System Moe Key Lab. For Computational Physical Sciences Fudan Universit
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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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TAO Jun
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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Tao Jun
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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Yang Fan
State Key Lab. Of Asic & System Fudan Univ.
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Cai Wei
Department of Applied Physics, Beihang University, Beijing 100191, China
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