ABSTRACT
Due to the rapid advances of integrated circuit technology, the size of power distribution network (power grid) is becoming larger and larger. There are usually multi-million nodes on a power grid. Analyzing these huge power grids has become very expensive in terms of both time and memory. This paper presents an efficient parallel implementation of the Additive Schwarz Method (ASM) for IR-drop analysis of large-scale power grid. Based on distributed memory system, a new data storage method is proposed to overcome memory bottleneck of traditional methods. Techniques including overlapping in multiple layer and irregular power grid, via detection and grouping are utilized to accelerate the simulation. Moreover, a new communication strategy exhibiting minimum communication overhead is proposed. The proposed method is very accurate in the final solution, with the maximum error less than 0.1mv. Experimental results on industrial medium size benchmarks show that the proposed method achieves more than 110X speedup over a state-of-the-art direct LU solver. The proposed approach can easily solve very large-scale benchmarks, while LU solver fails to obtain the solution because of system memory limitation. It is the first time reported in literature that IR-drop analysis of power grid with over 190M nodes is successfully solved within 5 minutes.
- H. Qian, S. Nassif, and S. Sapatnekar, "Power grid analysis using random walks," Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, vol. 24, no. 8, pp. 1204--1224, aug. 2005. Google ScholarDigital Library
- T.-H. Chen and C. C.-P. Chen, "Efficient large-scale power grid analysis based on preconditioned krylov-subspace iterative methods," in Design Automation Conference, 2001. Proceedings, 2001, pp. 559--562. Google ScholarDigital Library
- C.-J. Wei, H. Chen, and S.-J. Chen, "Design and implementation of block-based partitioning for parallel flip-chip power-grid analysis," Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, vol. 31, no. 3, pp. 370--379, march 2012. Google ScholarDigital Library
- Z. Feng and P. Li, "Multigrid on gpu: Tackling power grid analysis on parallel SIMT platforms," in IEEE/ACM International Conference on Computer-Aided Design, 2008, Nov. 2008, pp. 647--654. Google ScholarDigital Library
- J. D. X. Sherry Li and J. Gilbert, "The superlu website," http://crd.lbl.gov/~xiaoye/SuperLU.Google Scholar
- X. S. James W. Demmel, John R. Gilbert, "An asynchronous parallel supernodal algorithm for sparse gaussian elimination," SIAM J. Matrix Analysis and Applications, vol. 20, no. 4, pp. 915--952, 1999. Google ScholarDigital Library
- V. Voronov and N. Popova, "Parallel power grid simulation on platforms with multi core processors," in International Conference on Computing, Engineering and Information, 2009, April 2009, pp. 144--148. Google ScholarDigital Library
- L. Grigori, J. W. Demmel, and X. S. Li, "Parallel symbolic factorization for sparse lu factorization with static," in Pivoting, in Second International Workshop on Combinatorial Scientific Computing, 2005, p. 2007.Google Scholar
- PETSC, "The petsc website," http://www.mcs.anl.gov/petsc/.Google Scholar
- K. Sun, Q. Zhou, K. Mohanram, and D. Sorensen, "Parallel domain decomposition for simulation of large-scale power grids," in IEEE/ACM International Conference on Computer-Aided Design, 2007, Nov. 2007, pp. 54--59. Google ScholarDigital Library
- A. Klawonn and L. F. Pavarino, "A comparison of overlapping schwarz methods and block preconditioners for saddle point problems." Numerical Linear Algebra with Applications, vol. 7, pp. 1--25, 2000.Google ScholarCross Ref
- T. Peng and J. L. V. Kubilay Sertel, "Convergence of a fully overlapping domain decomposition method," in URSI General Assembly and Scientific Symposium of Internaltional Union of Radio Science(GASS), 2011, August 2011.Google Scholar
- Y. Zhong and M. Wong, "Fast block-iterative domain decomposition algorithm for ir drop analysis in large power grid," in 11th International Symposium on Quality Electronic Design (ISQED), 2010, March 2010, pp. 277--283.Google Scholar
- A. Grama, A. Gupta, and V. Kumar, "Isoefficiency: measuring the scalability of parallel algorithms and architectures," Parallel Distributed Technology: Systems Applications, IEEE, vol. 1, no. 3, pp. 12--21, Aug 1993. Google ScholarDigital Library
- V. Kumar and A. Gupta, "Analyzing scalability of parallel algorithms and architectures," J. Parallel Distrib. Comput., vol. 22, pp. 379--391, September 1994. {Online}. Available: http://dx.doi.org/10.1006/jpdc.1994.1099 Google ScholarDigital Library
Index Terms
- Efficient parallel power grid analysis via additive Schwarz method
Recommendations
A multigrid-like technique for power grid analysis
Modern submicron very large scale integration designs include huge power grids that are required to distribute large amounts of current, at increasingly lower voltages. The resulting voltage drop on the grid reduces noise margin and increases gate delay,...
Fast Poisson solver preconditioned method for robust power grid analysis
ICCAD '11: Proceedings of the International Conference on Computer-Aided DesignRobust and efficient algorithms for power grid analysis are crucial for both VLSI design and optimization. Due to the increasing size of power grids IR drop analysis has become more computationally challenging both in runtime and memory consumption. ...
Power grid analysis with hierarchical support graphs
ICCAD '11: Proceedings of the International Conference on Computer-Aided DesignIt is increasingly challenging to analyze present day large-scale power delivery networks (PDNs) due to the drastically growing complexity in power grid design. To achieve greater runtime and memory efficiencies, a variety of preconditioned iterative ...
Comments