An improved incomplete Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
Power supply noise analysis methodology for deep-submicron VLSI chip design
DAC '97 Proceedings of the 34th annual Design Automation Conference
Design and analysis of power distribution networks in PowerPC microprocessors
DAC '98 Proceedings of the 35th annual Design Automation Conference
Full-chip verification methods for DSM power distribution systems
DAC '98 Proceedings of the 35th annual Design Automation Conference
Analysis of performance impact caused by power supply noise in deep submicron devices
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
Proceedings of the 37th Annual Design Automation Conference
Extended Krylov subspace method for reduced order analysis of linear circuits with multiple sources
Proceedings of the 37th Annual Design Automation Conference
Efficient large-scale power grid analysis based on preconditioned krylov-subspace iterative methods
Proceedings of the 38th annual Design Automation Conference
Frequency domain analysis of switching noise on power supply network
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
Power network analysis using an adaptive algebraic multigrid approach
Proceedings of the 40th annual Design Automation Conference
Power grid reduction based on algebraic multigrid principles
Proceedings of the 40th annual Design Automation Conference
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Proceedings of the 42nd annual Design Automation Conference
Fast algorithms for IR drop analysis in large power grid
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Power grid analysis benchmarks
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
ETBR: extended truncated balanced realization method for on-chip power grid network analysis
Proceedings of the conference on Design, automation and test in Europe
Stochastic Preconditioning for Diagonally Dominant Matrices
SIAM Journal on Scientific Computing
Multigrid on GPU: tackling power grid analysis on parallel SIMT platforms
Proceedings of the 2008 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
An adaptive parallel flow for power distribution network simulation using discrete Fourier transform
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
PowerRush: a linear simulator for power grid
Proceedings of the International Conference on Computer-Aided Design
On the preconditioner of conjugate gradient method: a power grid simulation perspective
Proceedings of the International Conference on Computer-Aided Design
Fast Poisson solver preconditioned method for robust power grid analysis
Proceedings of the International Conference on Computer-Aided Design
Power grid analysis with hierarchical support graphs
Proceedings of the International Conference on Computer-Aided Design
Hierarchical analysis of power distribution networks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A multigrid-like technique for power grid analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Power grid analysis using random walks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Power Grid Analysis and Optimization Using Algebraic Multigrid
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Parallel forward and back substitution for efficient power grid simulation
Proceedings of the International Conference on Computer-Aided Design
Parallel power grid analysis using preconditioned GMRES solver on CPU-GPU platforms
Proceedings of the International Conference on Computer-Aided Design
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Iterative linear equation solvers depend on high quality preconditioners to achieve fast convergence. For sparse symmetric systems arising from large power grid analysis problems, however, preconditioners generated by traditional incomplete Cholesky factorizations are usually of low quality, resulting in slow convergence. On the other hand, although preconditioners generated by random walks are quite effective to reduce the number of iterations, it takes considerable amount of time to compute them in a stochastic manner. In this paper, we propose a new preconditioning technique for power grid analysis, named deterministic random walk, that combines the advantages of the above two approaches. Our proposed algorithm computes the preconditioners in a deterministic manner to reduce computation time, while achieving similar quality as stochastic random walk preconditioning by modifying fill-ins to compensate dropped entries. We have proved that for such compensation scheme, our algorithm will not fail for certain matrix orderings, which otherwise cannot be guaranteed by traditional incomplete factorizations. We demonstrate that by incorporating our proposed preconditioner, a conjugate gradient solver is able to outperform a state-of-the-art algebraic multigrid preconditioned solver on public IBM power grid benchmarks for DC power grid analysis, while potentially remaining very efficient for transient analysis.