Parallel Algorithms for Sparse Linear Systems

Heath, Michael T.; Ng, Esmond G.; Peyton, Barry W.

doi:10.1137/1033099

Cited by 197 publications

(99 citation statements)

References 72 publications

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“…In an implicit scheme, this solution process requires solving a liner system of equations, which usually has dimension of millions and even billions of degrees of freedom. The solution of large sparse linear systems of equations is the main concern in any parallel code [43]. The algorithms to solve these systems are basically grouped into two categories: direct methods and iterative methods.…”

Section: System Of Equationsmentioning

confidence: 99%

Alya: Computational Solid Mechanics for Supercomputers

Casoni

Jérusalem

Samaniego

et al. 2014

Arch Computat Methods Eng

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While solid mechanics codes are now conventional tools both in industry and research, the increasingly more exigent requirements of both sectors are fuelling the need for more computational power and more advanced algorithms. For obvious reasons, commercial codes are lagging behind academic codes often dedicated either to the implementation of one new technique, or the upscaling of current conventional codes to tackle massively large scale computational problems. Only in a few cases, both approaches have been followed simultaneously. In this article, a solid mechanics simulation strategy for parallel supercomputers based on a hybrid approach is presented. Hybrid parallelization exploits the thread-level parallelism of multicore architectures, com- bining MPI tasks with OpenMP threads. This paper describes the proposed strategy, programmed in Alya, a parallel multiphysics code. Hybrid parallelization is specially well suited for the current trend of supercomputers, namely large clusters of multicores. The strategy is assessed through transient non-linear solid mechanics problems, both for explicit and implicit schemes, running on thousands of cores. In order to demonstrate the flexibility of the proposed strategy under advance algorithmic evolution of computational mechanics, a non-local parallel overset meshes method (Chimera-like) is implemented and the conservation of the scalability is demonstrated.

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Section: System Of Equationsmentioning

confidence: 99%

Alya: Computational Solid Mechanics for Supercomputers

Casoni

Jérusalem

Samaniego

et al. 2014

Arch Computat Methods Eng

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“…left-looking, right-looking or multifrontal algorithms. For a detailed introduction into sparse matrix solvers, we refer to [22] and the references therein. Similarly to H-matrices, the factorization phase is the most time consuming step in solving the system.…”

Section: Direct Solversmentioning

confidence: 99%

Performance Of H-Lu Preconditioning For Sparse Matrices

Grasedyck

Hackbusch

Kriemann

2008

Comput. Methods Appl. Math.

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In this paper we review the technique of hierarchical matrices and put it into the context of black-box solvers for large linear systems. Numerical examples for several classes of problems from medium to large scale illustrate the applicability and efficiency of this technique. We compare the results with those of several direct solvers (which typically scale quadratically in the matrix size) as well as an iterative solver (an algebraic multigrid method) which scales linearly (if it converges in O(1) steps).

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“…On overview can be found in Chapter 9 of this Handbook; an actual code is described in [216]. Note that in this framework the notation of parallel granularity (see, e. g., [113]) is different from what we have introduced at the beginning of this section.…”

Section: Clustering Gauss Operationsmentioning

confidence: 99%