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PowerRChol: Efficient Power Grid Analysis Based on Fast Randomized Cholesky Factorization

Published: 07 November 2024 Publication History

Abstract

Efficient power grid analysis is critical in modern VLSI design. It is computationally challenging because it requires solving large linear equations with millions of unknowns. Iterative solvers are more scalable, but their performance relies on preconditioners. Existing preconditioning approaches suffer from either high construction cost or slow convergence rate, both resulting in unsatisfactory total solution time. In this work, we propose an efficient power grid simulator based on fast randomized Cholesky factorization, named PowerRChol. We first propose a randomized Cholesky factorization algorithm with provable linear-time complexity. Then we propose a randomized factorization oriented matrix reordering approach. Experimental results on large-scale power grids demonstrate the superior efficiency of PowerRChol over existing iterative solvers, showing 1.51X, 1.93X and 3.64X speedups on average over the original RChol [3], feGRASS [11] and AMG [14] based PCG solvers, respectively. For instance, a power grid matrix with 60 million nodes and 260 million nonzeros can be solved (at a 1E-6 accuracy level) in 148 seconds on a single CPU core.

References

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P. R. Amestoy, T. A. Davis, and I. S. Duff. 1996. An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17, 4 (1996), 886--905.
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C. Chen, T. Liang, and G. Biros. 2021. RCHOL: Randomized Cholesky factorization for solving SDD linear systems. SIAM Journal on Scientific Computing 43, 6 (2021), C411--C438.
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Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam. 2008. Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. ACM Trans. Math. Software 35, 3 (2008), 22.
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Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms, Third Edition. The MIT Press.
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Z. Feng. 2020. GRASS: graph spectral sparsification leveraging scalable spectral perturbation analysis. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 39, 12 (2020), 4944--4957.
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C. Li, C. An, Z. Gao, F. Yang, Y. Su, and X. Zeng. 2023. Unleashing the power of graph spectral sparsification for power grid analysis via incomplete Cholesky factorization. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 42, 9 (2023), 3053--3066.
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Z. Liu and W. Yu. 2022. Pursuing more effective graph spectral sparsifiers via approximate trace reduction. In Proc. DAC. 613--618.
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Z. Liu, W. Yu, and Z. Feng. 2022. feGRASS: Fast and effective graph spectral sparsification for scalable power grid analysis. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 41, 3 (2022), 681--694.
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S. R. Nassif. [n. d.]. IBM power grid benchmarks. https://web.ece.ucsb.edu/~lip/PGBenchmarks/ibmpgbench.html
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J. Yang and Z. Li. [n. d.]. THU power grid benchmarks. http://tiger.cs.tsinghua.edu.cn/PGBench/
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J. Yang, Z. Li, Y. Cai, and Q. Zhou. 2014. PowerRush: An efficient simulator for static power grid analysis. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 22, 10 (2014), 2103--2116.
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W. Yu, T. Zhang, X. Yuan, and H. Qian. 2013. Fast 3-D thermal simulation for integrated circuits with domain decomposition method. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 32, 12 (2013), 2014--2018.
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A. Zharmagambetov and M. A. Carreira-Perpinan. 2022. Semi-supervised learning with decision trees: Graph Laplacian tree alternating optimization. In Proc. NeurIPS, Vol. 35. 2392--2405.

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cover image ACM Conferences
DAC '24: Proceedings of the 61st ACM/IEEE Design Automation Conference
June 2024
2159 pages
ISBN:9798400706011
DOI:10.1145/3649329
This work is licensed under a Creative Commons Attribution International 4.0 License.

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Published: 07 November 2024

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