Fast power grid simulation

Nassif, Sani R.; Kozhaya, J.N.

doi:10.1145/337292.337359

Cited by 117 publications

(105 citation statements)

References 5 publications

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“…From Equation (6), an interpolation formula for each fine node error variable, e i , by its neighboring coarse nodes error variables is defined as e i = j∈Ci w ij e j [9], where…”

Section: Mapping Operator Construction Of Amgmentioning

confidence: 99%

“…The preconditioned conjugate gradient method was applied in [3], and the hierarchical methods were developed in [4] [5]. Multigrid-like methods were developed in [6] [7] to map the original problem to a reduced system by using the geometric property of circuit. However, these geometric multigrid techniques [6] [7] are hard to handle the coupling effects of mutual inductances.…”

Section: Introductionmentioning

confidence: 99%

“…Multigrid-like methods were developed in [6] [7] to map the original problem to a reduced system by using the geometric property of circuit. However, these geometric multigrid techniques [6] [7] are hard to handle the coupling effects of mutual inductances.To deal with the coupling effects, an algebraic multigrid (AMG) [9] based approach was developed in [8]. Generally, the mapping operator of AMG method [9] is determined by each row equation of Ae ≈ 0, where A is the system matrix and e is the error vector of unknown variables.…”

mentioning

confidence: 99%

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An Aggregation-Based Algebraic Multigrid Method for Power Grid Analysis

Huang¹,

Chou²,

Lee³

2007

8th International Symposium on Quality Electronic Design (ISQED'07)

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This paper develops an aggregation-based algebraic multigrid (AbAMG) method to efficiently analyze the power grids. Different from the conventional algebraic multigrid (AMG) scheme, an innovative constructing method of global inter-grid mapping operator is employed to not only enhance the sparsity of coarse grid operator for reducing the computational complexity but also solve the problem with better convergent rate. The proposed method can solve the circuit with size over two millions in 167.6 CPU seconds (including DC analysis, and transient analysis with 50 time steps), and the maximum error is less than 1%. The significant runtime improvement, over 26X faster than the InductWise [1] and over 1.25X faster than the conventional AMG method, and less memory usage, 40% of the memory usage in [1] are demonstrated. IntroductionWith the deep sub-micron technology, several features of chips (such as larger number of transistors and lower supply voltages) have made the quality of power delivery network become a key factor of high performance designs [2]. Generally, the power delivery network contains enormous amounts of circuit elements and efficient analyzers are necessary. Thus, general circuit solvers, such as SPICE/HSPICE, by using direct methods are not practicable for the power delivery analysis. In the past years, various efficient methods have been developed for the power distribution network analysis. The preconditioned conjugate gradient method was applied in [3], and the hierarchical methods were developed in [4] [5]. Multigrid-like methods were developed in [6] [7] to map the original problem to a reduced system by using the geometric property of circuit. However, these geometric multigrid techniques [6] [7] are hard to handle the coupling effects of mutual inductances.To deal with the coupling effects, an algebraic multigrid (AMG) [9] based approach was developed in [8]. Generally, the mapping operator of AMG method [9] is determined by each row equation of Ae ≈ 0, where A is the system matrix and e is the error vector of unknown variables. Although this mapping operator doesn't need the geometric information of circuit, its quality strongly counts on the selection of coarse grids and only contains the local information of A. Therefore, it may lose several important error terms, and degrade the convergent rate. To remedy this undesirable behavior, [8] proposed an adaptive coarse grids choosing method. However, its choosing strategy needs to reconstruct the mapping operator at each time step and may boost the CPU time.To solve above problems, we develop a global mapping operator construction procedure based on aggregation AMG methods [10] [11]. The idea of aggregation originates in economics [12], where products in a large scale system are aggregated to become a small system. This procedure can significantly reduce the problem size, and still maintain the accurate representation of overall behaviors. An algebraic partition is performed to the fine grids and the system matrix is partitioned into sev...

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“…From Equation (6), an interpolation formula for each fine node error variable, e i , by its neighboring coarse nodes error variables is defined as e i = j∈Ci w ij e j [9], where…”

Section: Mapping Operator Construction Of Amgmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

An Aggregation-Based Algebraic Multigrid Method for Power Grid Analysis

Huang¹,

Chou²,

Lee³

2007

8th International Symposium on Quality Electronic Design (ISQED'07)

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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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Wires as Interconnects

Zheng

Tenhunen

Interconnect-Centric Design for Advanced SoC and NoC

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Fast power grid simulation

Cited by 117 publications

References 5 publications

An Aggregation-Based Algebraic Multigrid Method for Power Grid Analysis

An Aggregation-Based Algebraic Multigrid Method for Power Grid Analysis

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

Wires as Interconnects

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