Abstract
The Gauss-Seidel method is effective to solve the traditional sparse linear system. In the paper, we define a class of sparse linear systems in iterative algorithm. The iterative method for linear system can be extended to the dummy sparse linear system. We apply the Gauss-Seidel method, which is one of the iterative methods for linear system, to the thermal model of floorplan of VLSI physical design. The experimental results of dummy sparse linear system are computed by using Gauss-Seidel method that have shown our theory analysis and extendibility. The iterative time of our incremental thermal model is 5 times faster than that of the inverting matrix method.
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References
K. Roy, S. Mukhopadhyay, and H. Mahmoodi-Meimand. Leakage current mechanisms and leakage reduction techniques in deep submicrometer CMOS circuits. Proceedings of the IEEE, 91(2003)2, 305–327.
Z. Li, X. Hong, Q. Zhou, S. Zeng, J. Bian, H. Yang, V. Pitchumani, and C. Cheng. Integrating dynamic thermal via planning with 3D floorplanning algorithm. Proceedings of the 2006 International Symposium on Physical Design, San Jose, CA, April 2006, 178–185.
S. N. Adya and I. L. Markov. Fixed-outline floorplanning: enabling hierarchical design. IEEE Trans. on VLSI, 11(2003)6, 1120–1135.
H.-C. Lee, Y.-W. Chang, J.-M. Hsu, and H. Yang. Multilevel floorplanning/placement for large-scale modules using B*-trees. Proceedings of ACM/IEEE Design Automation Conference, Anaheim, CA, June 2003, 812–817.
J. A. Roy, D. A. Papa, S. N. Adya, H. H. Chan, J. F. Lu, A. N. Ng, and I. L. Markov. Capo: robust and scalable open-source min-cut floorplacer. Proceedings of International Symposium on Physical Design, San Francisco, April 2005, 224–227.
S. N. Adya, S. Chaturvedi, J. A. Roy, D. A. Papa, and I. L. Markov. Unification of partitioning, floorplanning and placement. International Conference on Computer-Aided Design, San Jose, CA, November 2004, 550-557.
Y. C. Chang, Y. W. Chang, G. M. Wu, and S. W. Wu. B-trees: a new representation for nonslicing floorplans. Proceedings of ACM/IEEE Design Automation Conference, Los Angeles, CA, June 2000, 458–463.
Paul E. Black. Sparse matrix. In dictionary of algorithms and data structures. Paul E. Black, ed., U.S. National Institute of Standards and Technology, June 2006, http://www.nist.gov/dads/HTML/sparse-matrix.html.
Michael T. Heath. Science Computing: An Introductory Survey. 2nd ed., New York, McGraw-Hill, 2002.
R. Barrett, M. Berry, T. F. Chan, J. Demmel, et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. 2nd ed., Philadelphia, PA, SIAM, 1994.
C.-H. Tsai and S.-M. S. Kang. Cell-level placement for improving substrate thermal distribution. IEEE Trans. on CAD of Integrated Circuits and Systems, 19(2000)2, 253–266.
K. Skadron, M. R. Stan, W. Huang, S. Velusamy, K. Sankaran-Arayanan, et al. Temperature aware microarchitecture: Extended discussion and results. University of Virginia, Dept. of Computer Science Technical Report CS-2003-08, April 2003.
Noel Black and Shirley Moore. Gauss-Seidel method. From MathWorld_A Wolfram Web Resource, created by Eric W. Weisstein, http://mathworld.wolfram.com/Gauss-SeidelMethod.html.
Tan Tianen,et al. Principles of Chemical Engineering. Beijing, Chemical Industry Press, 2006.
Jack Dongarra. The successive over relaxation method. http://www.netlib.org/linalg/htmltemplates/node15.html.
W. Kahan. Gauss-Seidel methods of solving large systems of linear equations, [Ph.D. dissertation], University of Toronto, 1958.
S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220(1983)4598, 671–680.
Marco GSRC T2 Fabric: Bookshelf Floorplanning Slot, http://www.cse.ucsc.edu/research/surf/GSRC/progress.html.
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Communication author: Xu Ning, born in 1968, male, Ph.d., Associate Professor.
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Xu, N., Jiang, Z. Thermal aware floorplanning using Gauss-Seidel method. J. Electron.(China) 25, 845–851 (2008). https://doi.org/10.1007/s11767-008-0025-8
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DOI: https://doi.org/10.1007/s11767-008-0025-8