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
GPU friendly fast Poisson solver for structured power grid network analysis
Proceedings of the 46th Annual Design Automation Conference
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
Proceedings of the International Conference on Computer-Aided Design
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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 non-rectangular 3D domain. This paper 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(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-function-based 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.