Thermal Floorplan Base on Conjugate Gradient Solver in HotSpot

Abstract:

In this paper, we introduce an effective iterative method to solve the thermal linear system in HotSpot thermal floorplan, the iterative Conjugate Gradient Method is suitable to solve the traditional sparse matrix linear equations. We define a class of dummy sparse linear systems in iterative thermal floorplan algorithm, the iterative methods for linear system can be extended to apply to other iterative framework algorithm. We apply the conjugate gradient method to solve the thermal model in floorplan of VLSI physical design. The experiments' result shows that thermal floorplan using Conjugate gradient method is effective. The running time of our incremental conjugate gradient thermal solver with Jocabi Precondition is approximate 0.59 comparing with LU decomposition method.

• Periodical: Applied Mechanics and Materials (Volumes 608-609)
• Pages: 908-912
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.608-609.908
• Online since: October 2014
• Authors: Zhong Hua Jiang*, Ning Xu, Chun Xiang Wu
• Keywords: Conjugate Gradient, Floorplan, Hotspot, Linear Systems Computation, Thermal

References

[1] Y.C. Chang Y.W. Chang G.M. Wu, and S.W. Wu, B-trees: A new representation for nonslicing floorplans, in Proc. DAC, 2000, pp.458-463.

[2] K. Skadron, K. Sankaranarayanan, S. Velusamy, D. Tarjan, M.R. Stan, and W. Huang. Temperature-Aware Micro architecture: Modeling and Implementation. ACM Transactions on Architecture and Code Optimization, 1(1): 94-125, Mar. (2004).

DOI: 10.1145/980152.980157

[3] Paul E. Black, ed, sparse matrix, in Dictionary of Algorithms and Data Structures , , U.S. National Institute of Standards and Technology. 27 June 2006. Available http: /www. nist. gov/dads/HTML/sparsematrix. html.

[4] Michael T. Heath. SCIENTIFIC COMPUTING: An Introductory Survey, Second Edition by published by McGraw-Hill, New York, (2002).

[5] 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, vol. 19, pp.253-266, Feb. (2000).

DOI: 10.1109/43.828554

[6] K. Skadron, M. R. Stan, W. Huang, S. Velusamy,K. Sankaranarayanan, and D. Tarjan. Temperature-Aware Micro architecture: Extended Discussion and Results., University of Virginia Dept. of Computer Science Technical Report CS-2003-08, April. (2003).

DOI: 10.1109/mm.2003.1261387

[7] Trefethen, Lloyd N.; Bau, David (1997), Numerical linear algebra, Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-361-9. p.152, (1997).

[8] Conjugate gradient method, From Wikipedia, the free encyclopedia http: /en. wikipedia. org/wiki/Preconditioned_conjugate_gradient_method.

[9] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by Simulated Annealing, Science, vol. 220, no. 4598, May 13, 1983, pp.671-680.

DOI: 10.1126/science.220.4598.671

[10] Preconditioners, Jack DongarraMon Nov 20 08: 52: 54 EST 1995 http: /www. netlib. org/utk/papers/templates/node51. html.

[11] GUO, P. -N., CHENG, C. -K., AND YOSHIMURA, T. 1999. An O-tree representation of non-slicing floorplan and its applications. In Proceedings of the ACM/IEEE Design Automation Conference (California, June), 268¨C273.

DOI: 10.1145/309847.309928

[12] C. H. Tsai and S. M. Kang, Cell-Level Placement for Improving Substrate Thermal Distribution, IEEE Trans. On Computer. -Aided Des, vol. 19, no. 2, pp.253-266, Feb. (2000).

DOI: 10.1109/43.828554

[13] Wenjian Yu, Numerical Analysis and Algorithms, Tsinghua Univ. Press, 2011 (in Chinese), http: /learn. tsinghua. edu. cn: 8080/2003990088/index. htm.