A quantitative performance study for Stokes solvers at the extreme scale

Gmeiner, Björn; Huber, Markus; John, Lorenz; Rüde, Ulrich; Wohlmuth, Barbara

doi:10.1016/j.jocs.2016.06.006

Cited by 69 publications

(85 citation statements)

References 53 publications

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“…These include preconditioned Krylov subspace methods [10,11,24] and multigrid methods [8]. Parallel multigrid methods for the Stokes system have been studied in [13,14]. In this section, we will apply the the GKB iterative solver to two discretizations of the Stokes equations in two and three dimensions.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Parallel Performance of an Iterative Solver Based on the Golub-Kahan Bidiagonalization

Kruse

Sosonkina

Arioli

et al. 2020

Lecture Notes in Computer Science

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We present a scalability study of Golub-Kahan bidiagonalization for the parallel iterative solution of symmetric indefinite linear systems with a 2 × 2 block structure. The algorithms have been implemented within the parallel numerical library PETSc. Since a nested inner-outer iteration strategy may be necessary, we investigate different choices for the inner solvers, including parallel sparse direct and multigrid accelerated iterative methods. We show the strong and weak scalability of the Golub-Kahan bidiagonalization based iterative method when applied to a two-dimensional Poiseuille flow and to two-and three-dimensional Stokes test problems.

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Section: Numerical Experimentsmentioning

confidence: 99%

Parallel Performance of an Iterative Solver Based on the Golub-Kahan Bidiagonalization

Kruse

Sosonkina

Arioli

et al. 2020

Lecture Notes in Computer Science

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“…Two further families are based on using block preconditioning strategies as relaxation schemes, yielding the Braess-Sarazin 10 and Uzawa 11 approaches. Each of these families has been further developed in the recent years, including Braess-Sarazin-type relaxation schemes, 5,10,[12][13][14] Vanka-type relaxation schemes, 5,9,[13][14][15][16][17][18] Uzawa-type relaxation schemes, [19][20][21][22] distributive relaxation schemes, 23,24 and other types of methods. 25,26 The aim of this paper is to analyze block-structured relaxation schemes, including distributive, Braess-Sarazin, and Uzawa relaxation.…”

Section: Introductionmentioning

confidence: 99%

Local Fourier analysis of block‐structured multigrid relaxation schemes for the Stokes equations

MacLachlan

2018

Numerical Linear Algebra App

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Summary Multigrid methods that use block‐structured relaxation schemes have been successfully applied to several saddle‐point problems, including those that arise from the discretization of the Stokes equations. In this paper, we present a local Fourier analysis of block‐structured relaxation schemes for the staggered finite‐difference discretization of the Stokes equations to analyze their convergence behavior. Three block‐structured relaxation schemes are considered: distributive relaxation, Braess–Sarazin relaxation, and Uzawa relaxation. In each case, we consider variants based on weighted‐Jacobi relaxation, as is most suitable for parallel implementation on modern architectures. From this analysis, optimal parameters are proposed, and we compare the efficiency of the presented algorithms with these parameters. Finally, some numerical experiments are presented to validate the two‐grid and multigrid convergence factors.

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“…Also, the unified initialization interface of AMGCL building blocks means it is easy to reuse existing functionality in order to come up with new preconditioning techniques. Notable examples included into the library codebase are CPR [21] and Schur complement pressure correction [20,35] preconditioners. CPR works best in fully implicit black-oil simulations, and Schur complement pressure correction is well-suited for Navier-Stokes-like problems.…”

Section: Extensibilitymentioning

confidence: 99%

AMGCL: An Efficient, Flexible, and Extensible Algebraic Multigrid Implementation

Demidov

2019

Lobachevskii J Math

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The paper presents AMGCL -an opensource C ++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an unstructured grid. The library supports both shared and distributed memory computation, allows to utilize modern massively parallel processors via OpenMP, OpenCL, or CUDA technologies, has minimal dependencies, and is easily extensible. The design principles behind AMGCL are discussed and it is shown that the code performance is on par with alternative implementations. *

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A quantitative performance study for Stokes solvers at the extreme scale

Cited by 69 publications

References 53 publications

Parallel Performance of an Iterative Solver Based on the Golub-Kahan Bidiagonalization

Parallel Performance of an Iterative Solver Based on the Golub-Kahan Bidiagonalization

Local Fourier analysis of block‐structured multigrid relaxation schemes for the Stokes equations

AMGCL: An Efficient, Flexible, and Extensible Algebraic Multigrid Implementation

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