pGRASS-Solver: A Graph Spectral Sparsification-Based Parallel Iterative Solver for Large-Scale Power Grid Analysis

With the increase in the complexity of VLSI chips, power grid analysis has become a challenging task, because linear equations of extremely large size need to be solved. Recent graph sparsification-based solvers have shown promising performance for power grid analysis. However, existing graph sparsi...

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Published in:IEEE transactions on computer-aided design of integrated circuits and systems Vol. 42; no. 9; pp. 3031 - 3044
Main Authors: Liu, Zhiqiang, Yu, Wenjian
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Cholesky factorization
Domain decomposition method (DDM)
Domain decomposition methods
Factorization
graph spectral sparsification
Iterative methods
iterative solver
Laplace equations
Linear equations
Mathematical models
Matrix decomposition
parallel computing
power grid analysis
Power grids
preconditioned conjugate gradient (PCG) algorithm
Solvers
Symmetric matrices
Transient analysis
ISSN:0278-0070, 1937-4151
Online Access:Get full text
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Summary:With the increase in the complexity of VLSI chips, power grid analysis has become a challenging task, because linear equations of extremely large size need to be solved. Recent graph sparsification-based solvers have shown promising performance for power grid analysis. However, existing graph sparsification algorithms are implemented in serial computing, while factorization and backward/forward substitution of the sparsifier's Laplacian matrix are hard to parallelize. On the other hand, partition-based iterative methods which are inherently parallel lack a direct control of the relative condition number of the preconditioner and consume more memory. In this work, we propose a novel parallel iterative solver called pGRASS-Solver. We first propose a practically efficient parallel graph sparsification algorithm. Then, the domain decomposition method (DDM) is utilized to solve the sparsifier's Laplacian matrix. To further improve the efficiency, a variant of DDM which employs partial Cholesky factorization and Schur complement matrix sparsification is proposed. Thus, we obtain an efficient parallel preconditioner, which not only leads to fast convergence but also enjoys ease of parallelization. Numerous experiments are conducted to illustrate the superior efficiency of the proposed pGRASS-Solver for large-scale power grid analysis, showing an average <inline-formula> <tex-math notation="LaTeX">6.8\times </tex-math></inline-formula> speedup over a recent parallel iterative solver (Wang et al. 2017). Moreover, it solves a real-world power grid matrix with 0.36 billion nodes and 8.7 billion nonzeros within 20 min on a 16-core machine, which is <inline-formula> <tex-math notation="LaTeX">10.9\times </tex-math></inline-formula> faster than the best result of sequential graph sparsification-based solver (Liu et al. 2022).
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ISSN:0278-0070
1937-4151
DOI:10.1109/TCAD.2023.3235754