TY - GEN
T1 - Fast poisson solvers for thermal analysis
AU - Qian, Haifeng
AU - Sapatnekar, Sachin S.
PY - 2010
Y1 - 2010
N2 - 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 non-rectangular 3D domain. This paper presents a class of eigendecomposition- based fast Poisson solvers (FPS) for chiplevel thermal analysis. We start with a solver that solves a rectangular 3D domain with mixed boundary conditions in O(NlogN) 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-functionbased methods. Finally, we propose an FPS method that leverages the preconditioned conjugate gradient method to solve non-rectangular 3D domains efficiently. We demonstrate that this approach solves a system of dimension 5.33e6 in only 11 Conjugate Gradient iterations, with a runtime of 171 seconds, a 6X speedup over the popular ICCG solver.
AB - 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 non-rectangular 3D domain. This paper presents a class of eigendecomposition- based fast Poisson solvers (FPS) for chiplevel thermal analysis. We start with a solver that solves a rectangular 3D domain with mixed boundary conditions in O(NlogN) 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-functionbased methods. Finally, we propose an FPS method that leverages the preconditioned conjugate gradient method to solve non-rectangular 3D domains efficiently. We demonstrate that this approach solves a system of dimension 5.33e6 in only 11 Conjugate Gradient iterations, with a runtime of 171 seconds, a 6X speedup over the popular ICCG solver.
KW - Fast poisson solver
KW - Green function
KW - Thermal analysis
UR - http://www.scopus.com/inward/record.url?scp=78650907870&partnerID=8YFLogxK
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U2 - 10.1109/ICCAD.2010.5654249
DO - 10.1109/ICCAD.2010.5654249
M3 - Conference contribution
AN - SCOPUS:78650907870
SN - 9781424481927
T3 - IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD
SP - 698
EP - 702
BT - 2010 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2010
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2010 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2010
Y2 - 7 November 2010 through 11 November 2010
ER -