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
Dalam kertas kerja ini, kami mencadangkan Kaedah Kolokasi Stokastik Adaptif (MASCM) berasaskan grid bersarang diubahsuai untuk Analisis Masa Statik (SSTA) berasaskan blok. MASCM yang dicadangkan menggunakan strategi penyesuaian yang lebih baik yang diperoleh daripada Kaedah Kolokasi Stokastik Adaptif (ASCM) sedia ada untuk menganggar pengendali utama MAX semasa analisis masa. Berbeza dengan ASCM yang menggunakan grid jarang bersarang dan kuadratur produk tensor untuk menghampiri pengendali MAX masing-masing untuk keadaan lemah dan kuat tak linear, MASCM mencadangkan kuadratur grid jarang bersarang yang diubah suai untuk menghampiri pengendali MAX bagi kedua-dua keadaan tak linear lemah dan kuat. Dalam kuadratur grid jarang bersarang yang diubah suai, mula-mula kami membina titik kuadratur tertib kedua berdasarkan kuadratur Gauss-Hermite yang dilanjutkan dan teknik grid jarang bersarang, dan kemudian membuang titik kuadratur yang tidak menyumbang dengan ketara kepada ketepatan pengiraan untuk meningkatkan kecekapan anggaran MAX. Berbanding dengan kuadratur grid jarang tidak bersarang, kuadratur grid jarang bersarang yang diubah suai yang dicadangkan bukan sahaja menggunakan titik kolokasi yang jauh lebih sedikit, tetapi juga menawarkan ketepatan yang lebih tinggi. Berbanding dengan kuadratur produk tensor, kuadratur grid jarang bersarang yang diubah suai telah banyak mengurangkan kos pengiraan, sementara masih mengekalkan ketepatan yang mencukupi untuk anggaran operator MAX. Hasilnya, MASCM yang dicadangkan memberikan ketepatan yang setanding sementara dengan ketara mengurangkan kos pengiraan berbanding dengan ASCM. Keputusan berangka menunjukkan bahawa dengan ketepatan yang setanding MASCM mempunyai pengurangan 50% dalam masa larian berbanding dengan ASCM.
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Salinan
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
Salinan
@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},}
Salinan
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 -