Fast transform-based preconditioners for large-scale power grid analysis on massively parallel architectures

Daloukas, Konstantis; Evmorfopoulos, Nestor; Drasidis, George; Tsiampas, Michalis; Tsompanopoulou, Panagiota; Stamoulis, George

doi:10.1145/2429384.2429466

Cited by 6 publications

(2 citation statements)

References 20 publications

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“…On the other hand, iterative solvers, which mainly depend on simple operations such as matrixvector multiplication and inner product of vectors, are more amicable for parallelization, especially on GPU platforms. There are some newly published papers, such as [14,10,37,40,39], which confirm the practicality and effectiveness of iterative solvers in solving large linear dynamic networks like power grid networks.…”

Section: Introductionmentioning

confidence: 81%

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Tan

Zhao

et al. 2016

Integration

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a b s t r a c tIn this paper, we propose an efficient parallel dynamic linear solver, called GPU-GMRES, for transient analysis of large linear dynamic systems such as large power grid networks. The new method is based on the preconditioned generalized minimum residual (GMRES) iterative method implemented on heterogeneous CPU-GPU platforms. The new solver is very robust and can be applied to power grids with different structures as well as for general analysis problems for large linear dynamic systems with asymmetric matrices. The proposed GPU-GMRES solver adopts the very general and robust incomplete LU based preconditioner. We show that by properly selecting the right amount of fill-ins in the incomplete LU factors, a good trade-off between GPU efficiency and convergence rate can be achieved for the best overall performance. Such tunable feature can make this algorithm very adaptive to different problems. GPU-GMRES solver properly partitions the major computing tasks in GMRES solver to minimize the data traffic between CPU and GPUs to enhance performance of the proposed method. Furthermore, we propose a new fast parallel sparse matrix-vector (SpMV) multiplication algorithm to further accelerate the GPU-GMRES solver. The new algorithm, called segSpMV, can enjoy full coalesced memory access compared to existing approaches. To further improve the scalability and efficiency, segSpMV method is further extended to multi-GPU platforms, which leads to more scalable and faster multi-GPU GMRES solver. Experimental results on the set of the published IBM benchmark circuits and mesh-structured power grid networks show that the GPU-GMRES solver can deliver order of magnitudes speedup over the direct LU solver, UMFPACK. The resulting multi-GPU-GMRES can also deliver 3-12 Â speedup over the CPU implementation of the same GMRES method on transient analysis.

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Section: Introductionmentioning

confidence: 81%

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Tan

Zhao

et al. 2016

Integration

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“…When the memory usage of the solver is beyond the capacity of a single machine, hierarchical analysis [21] can be applied to partition the power grid and to distribute the job to multiple machines. For DC analysis where a single time step is of concern, parallel solvers exploiting various feature of power grids and leveraging advanced numerical methods including multigrid [5], [6], fast transform [3], and additive Schwarz method [14], [20] have shown great success over direct solvers based on LU decomposition in both memory usage and running time. However, for transient analysis where the LU decompositions are usually computed at the very beginning, it is very difficult to achieve speed-ups in comparison to the direct solvers when there is enough memory since only a pair of forward and back substitutions are necessary at each time step [12].…”

Section: Introductionmentioning

confidence: 99%

Scalable power grid transient analysis via MOR-assisted time-domain simulations

Wang

Xiong

2013

2013 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Abstract-Time domain power grid simulations provide accurate estimations of power supply noises for design verifications. Despite extensive researches, it remains a very challenging problem to perform the simulations efficiently -the large power grid sizes demand tremendous computational resources and the causality between consecutive time steps hinders parallel implementations. Frequency domain and model order reduction (MOR) techniques promise scalability, though the solution accuracy may become a concern without trading off running time. In this paper, we present a framework for power grid transient analysis where time domain simulations are assisted by MOR techniques for scalability without losing much of the solution accuracy. Utilizing a direct sparse matrix solver and the multinode moment matching technique, we are able to achieve more than 5X speed-up using 16 processor cores distributed over two servers when simulating 1000 time steps for all the six IBM power grid simulation benchmarks, in comparison to the time domain simulations using only the direct solver.

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Parallel power grid analysis using preconditioned GMRES solver on CPU-GPU platforms

Liu¹,

Wang²,

Tan³

2013

2013 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Fast transform-based preconditioners for large-scale power grid analysis on massively parallel architectures

Cited by 6 publications

References 20 publications

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Scalable power grid transient analysis via MOR-assisted time-domain simulations

Parallel power grid analysis using preconditioned GMRES solver on CPU-GPU platforms

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