A review of algebraic multigrid

By K. Stüben. 2001

689 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a16a061673690dd2f7cb8ac46db6132d9d6abcc4

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems (2007, background): “This more general approach is called algebraic multigrid (AMG); see, for example, [76], [86].”
Simulation of Flow and Dispersion on Pore-Space Images (2012, methodology): “To solve the resultant linear systems of equations, an algebraic multigrid technique has been used (Stüben 2001; Hackbusch 1985).”
Analysis of the Parareal Time-Parallel Time-Integration Method (2007, background): “This type of smoother, which operates only on the fine grid points and leaves the coarse points unchanged, is sometimes called an F -smoother; see [30].”
Modeling Soil Processes: Review, Key Challenges, and New Perspectives (2016, methodology): “, 1991), or algebraic multigrid methods like SAMG (Jones and Woodward, 2001; Stuben, 2001).”
Neurobiology of Aging: Contents (2005, neutral): “Hence, it is the preferred choice for Algebraic Multigrid (AMG) algorithms, which only exploit information contained in the coefficient matrix [452, 468].”
Enhanced mixing and reaction through flow focusing in heterogeneous porous media (2006, methodology): “The linear systems of equations resulting from spatial discretization were solved by a conjugate gradient solver with algebraic multigrid preconditioning [Stüben, 2001].”
A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries (2008, methodology): “In contrast, for unstructured body-conformal methods, one has to either resort to algebraic multigrid methods [45,46] or other more complex methods such as agglomeration multigrid [28].”
Computations of Absolute Permeability on Micro-CT Images (2012, methodology): “Therefore, for flow simulations, we use PBM in conjunction with an algebraic multigrid solver to solve for the resultant linear systems of equations (Stüben 2001).”
Impact of sampling volume on the probability density function of steady state concentration (2008, methodology): “The resulting systems of linear equations are solved by a (bi)conjugate gradient method with algebraic multigrid preconditioning [Stüben, 2001].”
A comparison of eigensolvers for large‐scale 3D modal analysis using AMG‐preconditioned iterative methods (2005, background): “Several recent studies have demonstrated the viability of AMG preconditioners for problems in computational mechanics [1, 38] but to the best of our knowledge, there are no comparable studies for vibration analysis.”
A discretization and multigrid solver for a Darcy–Stokes system of three dimensional vuggy porous media (2009, methodology): “Another tool used to deal with varying coefficients is algebraic multigrid [24, 27], in which geometric grids are not considered at all.”
Preconditioning techniques for large linear systems: a survey (2002, methodology): “Notable examples of this trend are Dendy’s black box multigrid [110] and especially Ruge and Stüben’s algebraic multigrid (AMG) method [244] (see also the early papers [62, 159, 266] and the recent survey [267]).”
A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes (2015, methodology): “The system of equations resulting from the finite element method accumulation is solved using the Fraunhofer SAMG Solver (Stüben, 2001).”