Fast poisson solvers for thermal analysis

Haifeng Qian, Sachin S Sapatnekar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


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.

Original languageEnglish (US)
Title of host publication2010 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2010
Number of pages5
StatePublished - Dec 1 2010
Event2010 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2010 - San Jose, CA, United States
Duration: Nov 7 2010Nov 11 2010


Other2010 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2010
Country/TerritoryUnited States
CitySan Jose, CA


  • Fast poisson solver
  • Green function
  • Thermal analysis


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