Efficient large-scale power grid analysis based on preconditioned krylov-subspace iterative methods

Chen, Tsung-Hao; Chen, Charlie Chung‐Ping

doi:10.1145/378239.379023

Cited by 195 publications

(111 citation statements)

References 11 publications

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“…Direct methods such as LU or Cholesky matrix factorizations, or iterative methods [12], [13] can be used for power grid transient analysis according to problem scales. …”

Section: A Power Grid Analysismentioning

confidence: 99%

Hierarchical Cross-Entropy Optimization for Fast On-Chip Decap Budgeting

Zhao

Guo

Chen

et al. 2011

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Abstract-Decoupling capacitor (decap) has been widely used to effectively reduce dynamic power supply noise. Traditional decap budgeting algorithms usually explore the sensitivity-based nonlinear optimizations or conjugate gradient (CG) methods, which can be prohibitively expensive for large-scale decap budgeting problems and cannot be easily parallelized. In this paper, we propose a hierarchical cross-entropy based optimization technique which is more efficient and parallel-friendly. Cross-entropy (CE) is an advanced optimization framework which explores the power of rare event probability theory and importance sampling. To achieve the high efficiency, a sensitivity-guided cross-entropy (SCE) algorithm is introduced which integrates CE with a partitioning-based sampling strategy to effectively reduce the solution space in solving the large-scale decap budgeting problems. Compared to improved CG method and conventional CE method, SCE with Latin hypercube sampling method (SCE-LHS) can provide 2× speedups, while achieving up to 25% improvement on power supply noise. To further improve decap optimization solution quality, SCE with sequential importance sampling (SCE-SIS) method is also studied and implemented. Compared to SCE-LHS, in similar runtime, SCE-SIS can lead to 16.8% further reduction on the total power supply noise.Index Terms-Adjoint sensitivity analysis, cross-entropy optimization, decoupling capacitor budgeting, power grid design, power supply noise.

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“…Direct methods such as LU or Cholesky matrix factorizations, or iterative methods [12], [13] can be used for power grid transient analysis according to problem scales. …”

Section: A Power Grid Analysismentioning

confidence: 99%

Hierarchical Cross-Entropy Optimization for Fast On-Chip Decap Budgeting

Zhao

Guo

Chen

et al. 2011

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…(4) directly. In addition, it is proposed in [4] that the preconditioned conjugate gradient (PCG) method [5], [6] can be employed to compute c l with a proper choice of preconditioner. The stochastic preconditioning technique proposed in [10] is applied in [4] to generate the preconditioner using random walks [11].…”

Section: B Previous Approachesmentioning

confidence: 99%

“…Therefore, for all the nodes, essentially the whole inverse of the power grid matrix is computed in a row-by-row manner. In comparison to [4] where the rows are computed independently by the preconditioned conjugate-gradient (PCG) method [5], [6], we propose a hierarchical algorithm to speed up the matrix inversion by exploiting the fact that there are dependencies among the rows in the inverse of the matrix.…”

Section: Introductionmentioning

confidence: 99%

A hierarchical matrix inversion algorithm for vectorless power grid verification

Xiong¹,

Wang²

2010

2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Abstract-Vectorless power grid verification is a powerful technique to validate the robustness of the on-chip power distribution network for all possible current waveforms. Formulated and solved as linear programming problems, vectorless power grid verification demands intensive computational power due to the large number of nodes in modern power grids. Previous work showed that the performance bottleneck of this powerful technique is within the sub-problem of power grid analysis, which essentially computes the inverse of the sparse but large power grid matrix. In this paper, we propose a hierarchical matrix inversion algorithm to compute the rows of the inverse efficiently by exploiting the structure of the power grid. The proposed algorithm is integrated with a previous dual algorithm addressing an orthogonal sub-problem for vectorless power grid verification. Results show that the proposed hierarchical algorithm accelerates the matrix inversion significantly, and thus makes the overall vectorless power grid verification efficient.

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“…models (from tens of thousands to millions of nodes or circuit elements) renders traditional simulation tools such as SPICE inefficient. Much work has been done to find efficient methods for power grid simulation and optimization [1,4,8,9,[12][13][14]17].…”

Section: Introductionmentioning

confidence: 99%

“…These algorithms model power grids as RC(L) circuits and model currents drawn by transistors and logic gates as ideal time-varying current sources. Nodal voltages can be solved given the waveforms of current sources [1,8,9,12,17]. Yet, such methods are not always feasible for two reasons.…”

Section: Introductionmentioning

confidence: 99%

Efficient trace-driven metaheuristics for optimization of networks-on-chip configurations

Kahng¹,

Lin²,

Samadi³

et al. 2010

2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Vectorless power grid verification algorithms, by solving linear programming (LP) problems under current constraints, enable worstcase voltage drop predictions at an early design stage. However, worst-case current patterns obtained by many existing vectorless algorithms are time-invariant (i.e., are constant throughout the simulation time), which may result in an overly pessimistic voltage drop prediction. In this paper, a more realistic power grid verification algorithm based on hierarchical current and power constraints is proposed. The proposed algorithm naturally handles general RCL power grid models. Currents at different time steps are treated as independent variables and additional power constraints are introduced; this results in more realistic time-varying worstcase current patterns and less pessimistic worst-case voltage drop predictions. Moreover, a sorting-deletion algorithm is proposed to speed up solving LP problems by utilizing the hierarchical constraint structure. Experimental results confirm that worst-case current patterns and voltage drops obtained by the proposed algorithm are more realistic, and that the sorting-deletion algorithm reduces runtime needed to solve LP problems by > 85%.

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Efficient large-scale power grid analysis based on preconditioned krylov-subspace iterative methods

Cited by 195 publications

References 11 publications

Hierarchical Cross-Entropy Optimization for Fast On-Chip Decap Budgeting

Hierarchical Cross-Entropy Optimization for Fast On-Chip Decap Budgeting

A hierarchical matrix inversion algorithm for vectorless power grid verification

Efficient trace-driven metaheuristics for optimization of networks-on-chip configurations

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