A review of algebraic multigrid

Stüben, Klaus

doi:10.1016/b978-0-444-50617-7.50015-x

Cited by 147 publications

(193 citation statements)

References 28 publications

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“…On the basis of the flow results, we constructed streamline-oriented grids with 1000 Â 500 cells [Cirpka et al, 1999b] and solved for steady state transport using a cell-centered finite volume method [Cirpka et al, 1999c]. The linear systems of equations resulting from spatial discretization were solved by a conjugate gradient solver with algebraic multigrid preconditioning [Stüben, 2001].…”

Section: Evaluation Of Reaction Enhancement Factors By Numerical Simumentioning

confidence: 99%

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Werth

Cirpka

Grathwohl

2006

Water Resources Research

145

130

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[1] Transverse dispersion across adjacent streamlines can control the amount of mixing and reaction between one or more contaminants and a limiting substrate along the fringes of groundwater plumes. Streamlines in groundwater converge and diverge in heterogeneous porous media, depending on the permeability distribution. When flow is focused in a high-permeability zone, the distance required for a solute to cross a given number of streamlines decreases, and the time allowed for mixing and reaction is reduced. Because the first effect outweighs the latter, the overall result is an enhancement of transverse mixing and reaction. Here we develop a conceptual model of heterogeneous two-dimensional structures facilitating flow focusing. We use the conceptual model to develop simple analytical expressions quantifying the extent to which mixing and reaction are enhanced when flow focusing occurs and compare these to results of numerical simulations. Significant enhancement of transverse mixing and reaction by flow focusing is observed; for the cases considered, flow focusing enhances the amount of reaction by a factor ranging from 1.8 to 11.9. The relatively simple analytical expressions demonstrate that the fraction of the domain height made up by highpermeability inclusions, the fraction of flow that passes through the inclusions, and the fringe bypassing of inclusions determine the amount of mixing and reaction enhancement for the permeability distributions considered. These results partially explain why field-scale dispersivities are larger than laboratory derived dispersivities, where homogeneous and isotropic sediments are typically used. Further work is needed to verify the theoretical results presented here with laboratory and field experiments and to expand the relatively simple analytical expressions to consider more heterogeneous three-dimensional permeability fields.Citation: Werth, C. J., O. A. Cirpka, and P. Grathwohl (2006), Enhanced mixing and reaction through flow focusing in heterogeneous porous media, Water Resour. Res., 42, W12414,

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Section: Evaluation Of Reaction Enhancement Factors By Numerical Simumentioning

confidence: 99%

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Werth

Cirpka

Grathwohl

2006

Water Resources Research

145

130

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“…The three methods are: a LS-based approach, a global matrix approach, and a local neighborhood approach. The first approach is suggested in [9] and fits the near-nullspace modes only approximately. In contrast, our second approach fits the near-nullspace modes exactly in a SA-like fashion by adding additional dofs to the coarse grids.…”

Section: Discussion Of Goals and Strategymentioning

confidence: 99%

“…We begin by noting that the general idea of modifying classical AMG interpolation to better fit a particular set of test vectors was first proposed in the early work [3]. Later, in [9], Stüben discusses improving AMG interpolation specifically for elasticity problems based on using coordinate information. Essentially, he describes a method for improving the interpolation of the RBMs by doing a local LS fit and modifying the initial interpolation weights.…”

Section: Relevant Prior Workmentioning

confidence: 99%

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Improving algebraic multigrid interpolation operators for linear elasticity problems

Baker

Kolev

Yang

2009

Numerical Linear Algebra App

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SUMMARYLinear systems arising from discretizations of systems of partial differential equations can be challenging for algebraic multigrid (AMG), as the design of AMG relies on assumptions based on the near-nullspace properties of scalar diffusion problems. For elasticity applications, the near-nullspace of the operator includes the so-called rigid body modes (RBMs), which are not adequately represented by the classical AMG interpolation operators. In this paper we investigate several approaches for improving AMG convergence on linear elasticity problems by explicitly incorporating the near-nullspace modes in the range of the interpolation. In particular, we propose two new methods for extending any initial AMG interpolation operator to exactly fit the RBMs based on the introduction of additional coarse degrees of freedom at each node. Though the methodology is general and can be used to fit any set of near-nullspace vectors, we focus on the RBMs of linear elasticity in this paper. The new methods can be incorporated easily into existing AMG codes, do not require matrix inversions, and do not assume an aggregation approach or a finite element framework. We demonstrate the effectiveness of the new interpolation operators on several 2D and 3D elasticity problems.

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“…Drop deformation in steady state can be measured by the Taylor [30] with piecewise linear interface construction (PLIC) scheme [31], algebraic multigrid (AMG) approach [32] and k-ε turbulence model [33]. The rupturing, interaction and dispersion of droplets, the essential microscopic mechanisms of the twin-screw extruder, are investigated to improve further our understanding of the rheomixing process.…”

Section: Analysis Of the Twin-screw Rheomixing Processingmentioning

confidence: 99%

Numerical analysis of the hydrodynamic behaviour of immiscible metallic alloys in twin-screw rheomixing process

2006

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A numerical analysis by a VOF method is presented for studying the hydrodynamic mechanisms of the rheomixing process by a twin-screw extruder (TSE). The simplified flow field is established based on a systematic analysis of flow features of immiscible alloys in TSE rheomixing process. The studies focus on the fundamental microstructure mechanisms of rheological behaviour in shear-induced turbulent flows. It is noted that the microstructure of immiscible alloys in the mixing process is strongly influenced by the interaction between droplets, which is controlled by shearing forces, viscosity ratio, turbulence, and shearing time. The numerical results show a good qualitative agreement with the experimental results, and are useful for further optimisation design of prototypical rheomixing processes.

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A review of algebraic multigrid

Cited by 147 publications

References 28 publications

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Improving algebraic multigrid interpolation operators for linear elasticity problems

Numerical analysis of the hydrodynamic behaviour of immiscible metallic alloys in twin-screw rheomixing process

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