ShyLU: A Hybrid-Hybrid Solver for Multicore Platforms

Rajamanickam, Sivasankaran; Boman, Erik G.; Heroux, Michael A.

doi:10.1109/ipdps.2012.64

Cited by 62 publications

(28 citation statements)

References 28 publications

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“…Since iterative method [19] requires precondition in each NewtonRaphson iteration, its advantages for circuit simulation need to be proved. A recent solver called ShyLU [20], which combines direct method and iterative method, is not specially targeted at circuit matrices. Other methods, such as conjugate gradient [21] and multigrid [22], are usually used for linear circuit simulation [23], [24].…”

Section: B Iterative Methodsmentioning

confidence: 99%

NICSLU: An Adaptive Sparse Matrix Solver for Parallel Circuit Simulation

Chen

Wang

Yang

2013

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

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The sparse matrix solver has become a bottleneck in simulation program with integrated circuit emphasis (SPICE)-like circuit simulators. It is difficult to parallelize the solver because of the high data dependency during the numeric LU factorization and the irregular structure of circuit matrices. This paper proposes an adaptive sparse matrix solver called NICSLU, which uses a multithreaded parallel LU factorization algorithm on shared-memory computers with multicore/multisocket central processing units to accelerate circuit simulation. The solver can be used in all the SPICE-like circuit simulators. A simple method is proposed to predict whether a matrix is suitable for parallel factorization, such that each matrix can achieve optimal performance. The experimental results on 35 matrices reveal that NICSLU achieves speedups of 2.08× ∼ 8.57× (on the geometric mean), compared with KLU, with 1 ∼ 12 threads, for the matrices which are suitable for the parallel algorithm. NICSLU can be downloaded from http://nicslu.weebly.com.

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Section: B Iterative Methodsmentioning

confidence: 99%

NICSLU: An Adaptive Sparse Matrix Solver for Parallel Circuit Simulation

Chen

Wang

Yang

2013

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

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“…This triangular solve approach is very popular; see [8,14,16,26,41] as the most recent papers on this parallelization based on incomplete Schur complements. Some of the papers recognize that the triangular solve approach is the limitation in the computation of the Schur complement and focus on overcoming it; for example, in [41] the authors try to exploit sparsity during the triangular solves (with no reference to multithreading), while the authors of [26] are concerned in [39] with the multithreaded performance of the sparse triangular solves.…”

Section: Linear Algebra Overviewmentioning

confidence: 99%

“…Some of the papers recognize that the triangular solve approach is the limitation in the computation of the Schur complement and focus on overcoming it; for example, in [41] the authors try to exploit sparsity during the triangular solves (with no reference to multithreading), while the authors of [26] are concerned in [39] with the multithreaded performance of the sparse triangular solves. Downloaded 12/01/14 to 142.244.5.161.…”

Section: Linear Algebra Overviewmentioning

confidence: 99%

An Augmented Incomplete Factorization Approach for Computing the Schur Complement in Stochastic Optimization

Petra¹,

Schenk²,

Lubin³

et al. 2014

SIAM J. Sci. Comput.

138

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We present a scalable approach and implementation for solving stochastic optimization problems on high-performance computers. In this work we revisit the sparse linear algebra computations of the parallel solver PIPS with the goal of improving the shared-memory performance and decreasing the time to solution. These computations consist of solving sparse linear systems with multiple sparse right-hand sides and are needed in our Schur-complement decomposition approach to compute the contribution of each scenario to the Schur matrix. Our novel approach uses an incomplete augmented factorization implemented within the PARDISO linear solver and an outer BiCGStab iteration to efficiently absorb pivot perturbations occurring during factorization. This approach is capable of both efficiently using the cores inside a computational node and exploiting sparsity of the right-hand sides. We report on the performance of the approach on highperformance computers when solving stochastic unit commitment problems of unprecedented size (billions of variables and constraints) that arise in the optimization and control of electrical power grids. Our numerical experiments suggest that supercomputers can be efficiently used to solve power grid stochastic optimization problems with thousands of scenarios under the strict "real-time" requirements of power grid operators. To our knowledge, this has not been possible prior to the present work.

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“…To achieve a high scalability, algebraic domain decomposition methods are commonly employed to split a large size linear system into smaller size linear systems. To achieve this goal, the Schur complement method is often used to design sparse hybrid linear solvers [2], [3], [4], [5].…”

Section: Introductionmentioning

confidence: 99%

“…Section II-A presents the context in more details. Section II-B presents the basics of domain decomposition Schur complement methods, which are common to most sparse hybrid solvers [2], [3], [4], [5]. Sections II-C and II-D present the method used for preconditioning the reduced system in MAPHYS and the parallel implementation of the solver, respectively.…”

Section: Introductionmentioning

confidence: 99%

On the Resilience of Parallel Sparse Hybrid Solvers

Agullo¹,

Giraud²,

Zounon³

2015

2015 IEEE 22nd International Conference on High Performance Computing (HiPC)

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As the computational power of high performance computing (HPC) systems continues to increase by using a huge number of CPU cores or specialized processing units, extreme-scale applications are increasingly prone to faults. Consequently, the HPC community has proposed many contributions to design resilient HPC applications. These contributions may be system-oriented, theoretical or numerical. In this study we consider an actual fully-featured parallel sparse hybrid (direct/iterative) linear solver, MAPHYS, and we propose numerical remedies to design a resilient version of the solver. The solver being hybrid, we focus in this study on the iterative solution step, which is often the dominant step in practice. We furthermore assume that a separate mechanism ensures fault detection and that a system layer provides support for setting back the environment (processes, . . . ) in a running state. The present manuscript therefore focuses on (and only on) strategies for recovering lost data after the fault has been detected (a separate concern beyond the scope of this study), once the system is restored (another separate concern not studied here). The numerical remedies we propose are twofold. Whenever possible, we exploit the natural data redundancy between processes from the solver to perform exact recovery through clever copies over processes. Otherwise, data that has been lost and no longer available on any process is recovered through a so-called interpolation-restart mechanism. This mechanism is derived from [1] by carefully taking into account the properties of the target hybrid solver. These numerical remedies have been implemented in the MAPHYS parallel solver so that we can assess their efficiency on a large number of processing units (up to 12, 288 CPU cores) for solving large-scale real-life problems.

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ShyLU: A Hybrid-Hybrid Solver for Multicore Platforms

Cited by 62 publications

References 28 publications

NICSLU: An Adaptive Sparse Matrix Solver for Parallel Circuit Simulation

NICSLU: An Adaptive Sparse Matrix Solver for Parallel Circuit Simulation

An Augmented Incomplete Factorization Approach for Computing the Schur Complement in Stochastic Optimization

On the Resilience of Parallel Sparse Hybrid Solvers

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