High Performance Inverse Preconditioning

Gravvanis, George A.

doi:10.1007/s11831-008-9026-x

Cited by 36 publications

(38 citation statements)

References 55 publications

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“…Gravvanis et al [14], [15] attempt to accelerate a SAI preconditioned BiCGStab iterative solver on Intel multicore architecture by allocating the computation of each iteration of the iterative solver to a different thread; implementation details on how to accelerate the preconditioner computation on a multicore are not presented in this work. Xu et al [16] accelerate factorized SAI on NVIDIA GPUs.…”

Section: Sai Preconditioningmentioning

confidence: 99%

“…By generating a denser preconditioner, SAI preconditioning can reduce iterations in iterative solvers considerably and be applied to a broad range of applications. Previous work has accelerated the computation of this preconditioner on multiple processors [5], [6], [7], [8], [9], [10], [11], [12], [13] as well as multicore [14], [15] and manycore architecture [16].…”

Section: Introductionmentioning

confidence: 99%

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Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

Dehnavi

Fernández

Gaudiot

et al. 2013

IEEE Trans. Parallel Distrib. Syst.

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Abstract-Accelerating numerical algorithms for solving sparse linear systems on parallel architectures has attracted the attention of many researchers due to their applicability to many engineering and scientific problems. The solution of sparse systems often dominates the overall execution time of such problems and is mainly solved by iterative methods. Preconditioners are used to accelerate the convergence rate of these solvers and reduce the total execution time. Sparse approximate inverse (SAI) preconditioners are a popular class of preconditioners designed to improve the condition number of large sparse matrices. We propose a GPU accelerated SAI preconditioning technique called GSAI, which parallelizes the computation of this preconditioner on NVIDIA graphic cards. The preconditioner is then used to enhance the convergence rate of the BiConjugate Gradient Stabilized (BiCGStab) iterative solver on the GPU. The SAI preconditioner is generated on average 28 and 23 times faster on the NVIDIA GTX480 and TESLA M2070 graphic cards, respectively, compared to ParaSails (a popular implementation of SAI preconditioners on CPU) single processor/core results. The proposed GSAI technique computes the SAI preconditioner in approximately the same time as ParaSails generates the same preconditioner on 16 AMD Opteron 252 processors.

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Section: Sai Preconditioningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

Dehnavi

Fernández

Gaudiot

et al. 2013

IEEE Trans. Parallel Distrib. Syst.

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“…When thread 1 has finished the computation of the element m 7,6 and its symmetric counterpart, then the thread with rank 2 is ready to start the computation of the element m 6,6 . The data dependency pattern follows the antidiagonal motion (wave pattern approach) described in Giannoutakis and Gravvanis (2008), Gravvanis (2009) and Gravvanis and Giannoutakis (2006):…”

Section: Design Of Inverses Using Posix Threadsmentioning

confidence: 99%

On the design and implementation of parallel finite element approximate inverses using POSIX threads on multicore systems

Gravvanis

Matskanidis²,

Giannoutakis³

et al. 2012

Engineering Computations

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Purpose -The purpose of this paper is to propose novel parallel computational techniques for the parallelization of explicit finite element generalized approximate inverse methods, based on Portable Operating System Interface for UniX (POSIX) threads, for multicore systems. Design/methodology/approach -The authors' main motive for the derivation of the new Parallel Generalized Approximate Inverse Finite Element Matrix algorithmic techniques is that they can be efficiently used in conjunction with explicit preconditioned conjugate gradient-type schemes on multicore systems. The proposed parallelization technique of the Optimized Banded Generalized Approximate Inverse Finite Element Matrix (OBGAIFEM) algorithm is achieved based on the concept of the "fish bone" approach with the use of a thread pool pattern. Theoretical estimates on the computational complexity of the parallel generalized approximate inverse finite element matrix algorithmic techniques are also derived. Findings -Application of the proposed method on a two-dimensional boundary value problem is discussed and numerical results are given on a multicore system using POSIX threads. These results tend to become optimum and are favorably compared to corresponding results from multiprocessor systems, as presented in recent work by Gravvanis et al. Originality/value -The proposed parallel explicit finite element generalized approximate inverse preconditioning, using approximate factorization and approximate inverse algorithms, is an efficient computational method that is valuable for computer scientists and for scientists and engineers in engineering computations.

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“…The convergence of iterative methods can be improved by preconditioners such as the Successive Over Relaxation (SOR) preconditioner [23] and sparse approximate inverse preconditioners that are based on factorized sparse approximate inverses or on the minimization of some convenient norm [12,21]. Recently, explicit approximate inverse preconditioners have been introduced for solving sparse linear systems [17,19,20]. In [7], interested readers will find issues for implementing iterative methods in a sequential manner.…”

Section: Related Workmentioning

confidence: 99%

Solving large sparse linear systems in a grid environment: the GREMLINS code versus the PETSc library

2011

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International audienceSolving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids

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High Performance Inverse Preconditioning

Cited by 36 publications

References 55 publications

Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

On the design and implementation of parallel finite element approximate inverses using POSIX threads on multicore systems

Solving large sparse linear systems in a grid environment: the GREMLINS code versus the PETSc library

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