The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
본 논문에서는 블록 기반 통계적 정적 타이밍 분석(SSTA)을 위한 수정된 중첩 희소 그리드 기반 적응형 확률적 배치 방법(MASCM)을 제안합니다. 제안된 MASCM은 타이밍 분석 중 주요 연산자 MAX를 근사화하기 위해 기존 ASCM(Adaptive Stochastic Collocation Method)에서 파생된 향상된 적응 전략을 사용합니다. 약한 비선형 조건과 강한 비선형 조건에 대해 각각 MAX 연산자를 근사화하기 위해 중첩되지 않은 희소 그리드와 텐서 곱 구적법을 사용하는 ASCM과 달리 MASCM은 약하고 강한 비선형 조건 모두에 대해 MAX 연산자를 근사하기 위해 수정된 중첩 희소 그리드 구적법을 제안합니다. 수정된 중첩 희소 그리드 구적법에서는 먼저 확장된 Gauss-Hermite 구적법 및 중첩 희소 그리드 기술을 기반으로 50차 구적점을 구성한 다음 계산 정확도에 크게 기여하지 않는 구적점을 삭제하여 효율성을 향상시킵니다. MAX 근사치. 중첩되지 않은 희소 그리드 구적법과 비교하여 제안된 수정된 중첩 희소 격자 구적법은 훨씬 적은 수의 배열 점을 사용할 뿐만 아니라 훨씬 더 높은 정확도를 제공합니다. 텐서 곱 구적법과 비교하여 수정된 중첩 희소 그리드 구적법은 계산 비용을 크게 줄이면서도 MAX 연산자 근사에 대한 충분한 정확도를 유지합니다. 결과적으로 제안된 MASCM은 ASCM에 비해 계산 비용을 크게 줄이면서 비슷한 정확도를 제공합니다. 수치 결과는 비슷한 정확도로 MASCM이 ASCM에 비해 런타임이 XNUMX% 감소한 것으로 나타났습니다.
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Xu LUO, Fan YANG, Xuan ZENG, Jun TAO, Hengliang ZHU, Wei CAI, "A Modified Nested Sparse Grid Based Adaptive Stochastic Collocation Method for Statistical Static Timing Analysis" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 12, pp. 3024-3034, December 2009, doi: 10.1587/transfun.E92.A.3024.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.3024/_p
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@ARTICLE{e92-a_12_3024,
author={Xu LUO, Fan YANG, Xuan ZENG, Jun TAO, Hengliang ZHU, Wei CAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Modified Nested Sparse Grid Based Adaptive Stochastic Collocation Method for Statistical Static Timing Analysis},
year={2009},
volume={E92-A},
number={12},
pages={3024-3034},
abstract={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.},
keywords={},
doi={10.1587/transfun.E92.A.3024},
ISSN={1745-1337},
month={December},}
부
TY - JOUR
TI - A Modified Nested Sparse Grid Based Adaptive Stochastic Collocation Method for Statistical Static Timing Analysis
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3024
EP - 3034
AU - Xu LUO
AU - Fan YANG
AU - Xuan ZENG
AU - Jun TAO
AU - Hengliang ZHU
AU - Wei CAI
PY - 2009
DO - 10.1587/transfun.E92.A.3024
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2009
AB - 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.
ER -