An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A green function-based parasitic extraction method for inhomogeneous substrate layers
Proceedings of the 42nd annual Design Automation Conference
Efficient full-chip thermal modeling and analysis
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
IBM Journal of Research and Development
GPU friendly fast Poisson solver for structured power grid network analysis
Proceedings of the 46th Annual Design Automation Conference
Thermal modeling for 3D-ICs with integrated microchannel cooling
Proceedings of the 2009 International Conference on Computer-Aided Design
Hotspot: acompact thermal modeling methodology for early-stage VLSI design
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
3D-ICE: fast compact transient thermal modeling for 3D ICs with inter-tier liquid cooling
Proceedings of the International Conference on Computer-Aided Design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient techniques for accurate modeling and simulation of substrate coupling in mixed-signal IC's
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Accelerated Chip-Level Thermal Analysis Using Multilayer Green's Function
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
High-Efficiency Green Function-Based Thermal Simulation Algorithms
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Energy-Efficient Multiobjective Thermal Control for Liquid-Cooled 3-D Stacked Architectures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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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.