Sparse approximate inverse smoothers for geometric and algebraic multigrid

Bröker, Oliver; Grote, Marcus J.

doi:10.1016/s0168-9274(01)00110-6

Cited by 41 publications

(22 citation statements)

References 22 publications

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“…Also, incomplete factorization preconditioners have been shown to provide good smoothers for multigrid (see, e.g., [290]). Recent studies [69,70,270] have shown that sparse approximate inverses can also provide effective and robust smoothers for both geometric and algebraic multigrid, especially for tough problems (see also [19,29,30,234] for early work in this direction). Conversely, the ever-increasing size of the linear systems arising in countless applications has exposed the limitations of nonscalable methods (such as incomplete factorization and sparse approximate inverse preconditioners), and it is now generally agreed that the multilevel paradigm must somehow be incorporated into these techniques in order for these to remain competitive.…”

Section: Algebraic Multilevel Variantsmentioning

confidence: 99%

Preconditioning Techniques for Large Linear Systems: A Survey

Benzi¹

2002

Journal of Computational Physics

1,004

659

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This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An extensive bibliography completes the paper. c 2002 Elsevier Science (USA)

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Section: Algebraic Multilevel Variantsmentioning

confidence: 99%

Preconditioning Techniques for Large Linear Systems: A Survey

Benzi¹

2002

Journal of Computational Physics

1,004

659

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“…Some additional theoretical results are given in [23], including for a diagonal approximate inverse smoother, which may be preferable over damped Jacobi. Experimental results in the algebraic multigrid context are given in [22]. Although none of these studies used parallel implementations, parallel implementations of sparse approximate inverses are available [27].…”

Section: Polynomial Smoothingmentioning

confidence: 99%

10. A Survey of Parallelization Techniques for Multigrid Solvers

Chow¹,

Falgout²,

Hu³

et al. 2006

Parallel Processing for Scientific Computing

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This paper surveys the techniques that are necessary for constructing computationally efficient parallel multigrid solvers. Both geometric and algebraic methods are considered. We first cover the sources of parallelism, including traditional spatial partitioning and more novel additive multilevel methods. We then cover the parallelism issues that must be addressed: parallel smoothing and coarsening, operator complexity, and parallelization of the coarsest grid solve.

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“…We remark that similar approaches are used in the field of sparse approximate inverse smoothers, cf. Bröker and Grote in [3]. The construction of interpolation in FAMG is based on the minimization of…”

Section: Norm Minimization and Filter Conditionmentioning

confidence: 99%

Filtering algebraic multigrid and adaptive strategies

Nägel

Falgout

Wittum

2007

Comput. Visual Sci.

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Abstract. Solving linear systems arising from systems of partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. The method is used in an adaptive, selfcorrecting framework and tested numerically.

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Sparse approximate inverse smoothers for geometric and algebraic multigrid

Cited by 41 publications

References 22 publications

Preconditioning Techniques for Large Linear Systems: A Survey

Preconditioning Techniques for Large Linear Systems: A Survey

10. A Survey of Parallelization Techniques for Multigrid Solvers

Filtering algebraic multigrid and adaptive strategies

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