Coarse-grid selection for parallel algebraic multigrid

Cleary, A.; Falgout, Robert D.; Henson, Van Emden; Jones, Jim E.

doi:10.1007/bfb0018531

Cited by 53 publications

(52 citation statements)

References 7 publications

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“…A parallel approach that is independent on the number of processors is suggested in [29,51] for classical coarsening. It is based on parallel independent set algorithms as described by Luby [59] and Jones and Plassmann [53].…”

Section: Parallel Coarsening Strategies For Unstructured Problemsmentioning

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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Section: Parallel Coarsening Strategies For Unstructured Problemsmentioning

confidence: 99%

10. A Survey of Parallelization Techniques for Multigrid Solvers

Chow¹,

Falgout²,

Hu³

et al. 2006

Parallel Processing for Scientific Computing

Self Cite

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“…In addition, it should be possible to apply the operator in parallel in order to ensure scalability. The tested coarsening techniques include the classical Ruge Stueben technique (RGST) (Ruge and Stüben, 1987) using a third pass for correcting inconsistencies on the interprocessor boundaries, the Cleary Luby Jones Plassman scheme (CLJP) (Cleary et al, 1998), the Falgout scheme (FALG) (Henson and Meier Yang, 2002), the hybrid modified independent set technique (HMIS) and the extended coarse grid classification algorithm (ECGC) of Griebel et al (2006b). The RGST method shows a good sequential performance (Griebel et al, 2006a, Section 4) and is often used as a basis for enhanced coarsening techniques.…”

Section: Solvers and Preconditionersmentioning

confidence: 99%

Numerical analysis of computational models for induction heat treatment of complex geometrical parts

Klonk

Bay

2016

IJMMP

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Large scale industrial induction heating models require economical and robust computational methods. There is an increasing demand for efficient models for use in optimisation procedures, where a large number of parameter combinations must be solved. The goal of this work is to demonstrate that the multiphysics model of induction heating can efficiently be described by a weak coupling of the eddy current model with heat transfer and material evolution to derive a numerical model that is both robust and scalable. The solution of the electromagnetic problem is accelerated by using an auxiliary multigrid method. It will be demonstrated that the numerical convergence is mostly unaffected by discontinuities of the magnetic permeability, which can, for instance, be found at material boundary interfaces. A crankshaft will be used as an example for the broad class of problems that can be described by this induction heating model. Keywords: induction heat treatment; auxiliary space preconditioning; algebraic multigrid; edge finite elements.Reference to this paper should be made as follows: Klonk, S. and Bay, F. (2016) 'Numerical analysis of computational models for induction heat treatment of complex geometrical parts', Int.

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“…A completely different way of coarsening is given by the CLJP algorithm [8,12]. It is based on parallel graph coloring methods developed by Luby, Jones and Plassman.…”

Section: Cljp Coarseningmentioning

confidence: 99%

Coarse grid classification: a parallel coarsening scheme for algebraic multigrid methods

Griebel

Metsch

Oeltz

et al. 2006

Numerical Linear Algebra App

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SUMMARYIn this paper we present a new approach to the parallelization of algebraic multigrid (AMG), i.e., to the parallel coarse grid selection in AMG. Our approach does not involve any special treatment of processor subdomain boundaries and hence avoids a number of drawbacks of other AMG parallelization techniques. The key idea is to select an appropriate (local) coarse grid on each processor from all admissible grids such that the composed coarse grid forms a suitable coarse grid for the whole domain, i.e. there is no need for any boundary treatment. To this end, we first construct multiple equivalent coarse grids on each processor subdomain. In a second step we then select exactly one grid per processor by a graph clustering technique. The results of our numerical experiments clearly indicate that this approach results in coarse grids of high quality which are very close to those obtained with sequential AMG. Furthermore, the operator and grid complexities of our parallel AMG are mostly smaller than those obtained by other parallel AMG methods, whereas the scale-up behavior of the proposed algorithm is similar to that of other parallel AMG techniques. However a significant improvement with respect to the speed-up performance is achieved.

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Coarse-grid selection for parallel algebraic multigrid

Cited by 53 publications

References 7 publications

10. A Survey of Parallelization Techniques for Multigrid Solvers

10. A Survey of Parallelization Techniques for Multigrid Solvers

Numerical analysis of computational models for induction heat treatment of complex geometrical parts

Coarse grid classification: a parallel coarsening scheme for algebraic multigrid methods

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