Coarse-grid treatment in parallel AMG for coupled systems in CFD applications

Emans, Maximilian

doi:10.1016/j.jocs.2011.08.001

Cited by 7 publications

(7 citation statements)

References 23 publications

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“…Any parallel multigrid or algebraic multigrid solver needs a carefully designed bottom level solver [11]. Typically, only few unknowns per process are left on the coarsest grid, making it difficult, if not impossible, to achieve good scalability for that part of the algorithm.…”

Section: Algorithm Redesignmentioning

confidence: 99%

A massively parallel solver for discrete Poisson-like problems

Notay

Napov

2015

Journal of Computational Physics

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The paper considers the parallel implementation of an algebraic multigrid method. The sequential version is well suited to solve linear systems arising from the discretization of scalar elliptic PDEs. It is scalable in the sense that the time needed to solve a system is (under known conditions) proportional to the number of unknowns. The associate software code is also robust and often significantly faster than other algebraic multigrid solvers. The present work address the challenge of porting it on massively parallel computers. In this view, some critical components are redesigned, in a relatively simple yet not straightforward way. Thanks to this, excellent weak scalability results are obtained on three petascale machines among the most powerful today available.

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Section: Algorithm Redesignmentioning

confidence: 99%

A massively parallel solver for discrete Poisson-like problems

Notay

Napov

2015

Journal of Computational Physics

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“…Moreover, our solver must be robust enough for meshes with a quality typical for industrial applications. We prefer therefore to construct our own solver based on the experience we had with both, segregated (elliptic) problems, see Emans [6,8], and coupled problems of another kind, see Emans [11,13].…”

Section: Numerical Solution Of the Linear Systemsmentioning

confidence: 99%

Velocity–pressure coupling on GPUs

Emans

Liebmann

2012

Computing

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We explore the possibilities to accelerate simulations in computational fluid dynamics (CFD) by additional graphics processing units (GPUs). By examining some examples of stationary incompressible flows from the industrial practice we demonstrate that the potential speedup obtained by deploying GPU accelerated linear solvers alone is limited if standard segregated algorithms are used. However, recently presented velocity-pressure coupling algorithms are an attractive alternative to these segregated algorithms. We present an efficient AMG solver for the coupled linear system of mixed elliptichyperbolic character and show that the GPU-accelerated version of this linear solver accelerates the velocity-pressure coupling scheme by almost 50% compared to a competitive CPU implementation. Compared to standard segregated methods, the computing time of the whole simulation is reduced by up to 75%.

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“…[5,7,16,18,19,21]. In general, the agglomeration methods require a-priori specification of when agglomeration should occur and how aggressive it should be.…”

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confidence: 99%

“…We note that this may in part be due to the problem-and machine-dependent nature of the scalability issues connected with coarse-level solvers. For a range of problems containing less than about 3M unknowns and scaling using up to 32 cores, a comparison of using a parallel LU factorization, an iterative method, and an agglomeration strategy together with algebraic multigrid has indicated that agglomeration is a superior approach [7]. For medium-sized problems containing approximately 25M unknowns on 4096 cores, the benefits of using agglomeration compared to an iterative coarselevel solver combined with smoothed aggregation algebraic multigrid on 4096 cores was demonstrated in [16], with an overall solver speed-up of 1.8 being reported.…”

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confidence: 99%

Extreme-Scale Multigrid Components within PETSc

May

Sanan

Rupp³

et al. 2016

Proceedings of the Platform for Advanced Scientific Computing Conference

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Abstract. Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete PDEs of this type and thus are the method of choice for high-resolution simulations. The scalability and time-to-solution of massively parallel multilevel preconditioners can be adversely effected by using a coarse-level solver with sub-optimal algorithmic complexity. To maintain scalability, agglomeration techniques applied to the coarse level have been shown to be necessary.In this work, we present a new software component introduced within the Portable Extensible Toolkit for Scientific computation (PETSc) which permits agglomeration. We provide an overview of the design and implementation of this functionality, together with several use cases highlighting the benefits of agglomeration. Lastly, we demonstrate via numerical experiments employing geometric multigrid with structured meshes, the flexibility and performance gains possible using our MPI-rank agglomeration implementation.

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Coarse-grid treatment in parallel AMG for coupled systems in CFD applications

Cited by 7 publications

References 23 publications

A massively parallel solver for discrete Poisson-like problems

A massively parallel solver for discrete Poisson-like problems

Velocity–pressure coupling on GPUs

Extreme-Scale Multigrid Components within PETSc

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