Haifeng Qian
Sachin S. Sapatnekar
Abstract
Accurate and efficient thermal analysis for a VLSI chip is crucial, both for sign-off reliability verification and for design-time circuit optimization. To determine an accurate temperature profile, it is important to simulate a die together with its thermal mounts: this requires solving Poisson's equation on a nonrectangular 3D domain. This article presents a class of eigendecomposition-based Fast Poisson Solvers (FPS) for chip-level thermal analysis. We start with a solver that solves a rectangular 3D domain with mixed boundary conditions in O(N⋅ logN) time, where N is the dimension of the finite difference matrix. Then we reveal, for the first time in the literature, a strong relation between fast Poisson solvers and Green-function-based methods. Finally, we propose an FPS method that leverages the preconditioned conjugate gradient method to solve nonrectangular 3D domains efficiently. We demonstrate this approach on thermal analysis of an industrial microprocessor, showing accurate results verified by a commercial tool, and that it solves a system of dimension 4.54e6 in only 13 conjugate gradient iterations, with a runtime of 65 seconds, a 15X speedup over the popular ICCG solver.
- Amestoy, P. R., Davis, T. A., and Duff, I. S. 1996. An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 886--905. Google Scholar
Digital Library
- ANSYS Thermal Modeling Reference. 2012. http://www1.ansys.com/customer/content/documentation/121/ans_the.pdf.Google Scholar
- Bagnoli, P. E., Casarosa, C., and Stefani, F. 2007. DJOSER: Analytical thermal simulator for multilayer electronic structures. Theory and numerical implementation. In Proceedings of the International Conference on Thermal Issues in Emerging Technologies, Theory and Applications. 111--118.Google Scholar
- Costa, J. P., Chou, M., and Silveira, L. M. 1999. Efficient techniques for accurate modeling and simulation of substrate coupling in mixed-signal IC's. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 18, 5, 597--607. Google ScholarDigital Library
- Gharpurey, R. and Meyer, R. G. 1996. Modeling and analysis of substrate coupling in integrated circuits. IEEE J. Solid State Circ. 31, 3, 344--353.Google ScholarCross Ref
- Heriz, V. M., Park, J., Kemper, T., Kang, S., and Shakouri, A. 2007. Method of images for the fast calculation of temperature distributions in packaged VLSI chips. In Proceedings of the 13th International Workshop on Thermal Investigation of ICs and Systems. 18--25.Google Scholar
- Huang, W., Ghosh, S., Velusamy, S., Sankaranarayanan, K., Skadron, K., and Stan, M. R. 2006. HotSpot: A compact thermal modeling methodology for early-stage VLSI design. IEEE Trans. VLSI. Syst. 14, 5, 501--513. Google ScholarDigital Library
- Jimenez, V., Gioiosa, R., Kursun, E., Cazorla, F. J., Cher, C., Buyuktosunoglu, A., Bose, P., and Valero, M. 2010. Trends and techniques for energy efficient architectures. In Proceedings of the IEEE/IFIP VLSI System on Chip Conference. 276--279.Google Scholar
- Johnson, T. A., Knepper, R. W., Marcello, V., and Wang, W. 1984. Chip substrate resistance modeling technique for integrated circuit design. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 3, 126--134. Google ScholarDigital Library
- Karypis, G. and Kumar, V. 1995. METIS: Unstructured graph partitioning and sparse matrix ordering system, version 2.0. http://glaros.dtc.umn.edu/gkhome/views/metis.Google Scholar
- Le, H. Q., Starke, W. J., Fields, J. S., O'Connell, F. P., Nguyen, D. Q., Ronchetti, B. J., Sauer, W. M., Schwarz, E. M., and Vaden, M. T. 2007. IBM POWER6 microarchitecture. IBM J. Res. Devel. 51, 6, 639--662. Google ScholarDigital Library
- Li, P., Pileggi, L. T., Ashenghi, M., and Chandra, R. 2004. Efficient full-chip thermal modeling and analysis. In Proceedings of the IEEE/ACM International Conference on Computer-Aided Design (Digest of Technical Papers). 319--326. Google ScholarDigital Library
- Mizunuma, H., Yang, C., and Lu, Y. 2009. Thermal modeling for 3D-ICs with integrated microchannel cooling. In Proceedings of the IEEE/ACM International Conference on Computer-Aided Design (Digest of Technical Papers). 256--263. Google ScholarDigital Library
- Miknejad, A. M., Gharpurey, R., and Meyer, R. G. 1998. Numerically stable green function for modeling and analysis of substrate coupling in integrated circuits. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 17, 4, 305--315. Google ScholarDigital Library
- Saad, Y. 2003. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA. Google ScholarDigital Library
- Sabry, M. M., Coskun, A. K., Atienza, D., Rosing, T. S., and Brunschwiler, T. 2011. Energy-Efficient multiobjective thermal control for liquid-cooled 3-D stacked architectures. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 30, 12, 1883--1896. Google ScholarDigital Library
- Shi, J., Cai, Y., Hou, W., Ma, L., Tan, S. X. D., Ho, P., and Wang, X. 2009. GPU friendly fast poisson solver for structured power grid network analysis. In Proceedings of the IEEE/ACM Design Automation Conference (DAC'09). 178--183. Google ScholarDigital Library
- Sridhar, A., Vincenzi, A., Ruggiero, M., Brunschwiler, T., and Atienza, D. 2010. 3D-ICE: Fast compact transient thermal modeling for 3D ICs with inter-tier liquid cooling. In Proceedings of the IEEE/ACM International Conference on Computer-Aided Design (Digest of Technical Papers). 463--470. Google ScholarDigital Library
- Stolt, B., Mittlefehldt, Y., Dubey, S., Mittal, G., Lee, M., Friedrich, J., and Fluhr, E. 2008. Design and implementation of the POWER6 microprocessor. IEEE J. Solid State Circ. 43, 1, 21--28.Google ScholarCross Ref
- Swarztrauber, P. N. 1977. The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson's equation on a rectangle. SIAM Rev. 19, 3, 490--501.Google ScholarDigital Library
- Wang, B. and Mazumder, P. 2007. Accelerated chip-level thermal analysis using multilayer Green's function. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 26, 2, 325--344. Google ScholarDigital Library
- Xu, C., Gharpurey, R., Fiez, T. S., and Mayaram, K. 2005. A Green function-based parasitic extraction method for inhomogeneous substrate layers. In Proceedings of the IEEE/ACM Design Automation Conference (DAC'05). 141--146. Google ScholarDigital Library
- Zhan, Y. and Sapatnekar, S. S. 2007. High efficiency Green function based thermal simulation algorithms. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 26, 9, 1661--1675. Google ScholarDigital Library
Index Terms
- Fast poisson solvers for thermal analysis
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