Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid

Meyerhenke, Henning; Monien,; Schamberger,

doi:10.1109/ipdps.2006.1639295

Cited by 18 publications

(19 citation statements)

References 23 publications

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“…Subsequently, this approach has been used and improved by [148,117,116,115,114]. For example, Schamberger [148] introduced the usage of diffusion as a growing mechanism around the initial seeds and extended the method to weighted graphs.…”

Section: Bubble Frameworkmentioning

confidence: 99%

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High quality graph partitioning

Sanders¹,

Schulz²

2013

Contemporary Mathematics

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Section: Bubble Frameworkmentioning

confidence: 99%

“…Because these algorithms still have a large execution time, approaches using algebraic multigrid techniques were used to improve the running time of the algorithm by Meyerhenke et al [116]. To do so the diffusion process was modified to a disturbed diffusion process.…”

Section: Bubble Frameworkmentioning

confidence: 99%

High quality graph partitioning

Sanders¹,

Schulz²

2013

Contemporary Mathematics

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“…Also note that a parallelization is not easy due to the strictly serial assignment process. Dierent implementations of the framework operations exist, see our previous work [23] for how they have evolved.…”

Section: Bubble Framework and Shape-optimizing Graph Partitioningmentioning

confidence: 99%

“…Diusion is used here within the Bubble framework as a similarity measure that overcomes drawbacks of previous Bubble implementations. For this reason a disturbance based on drain [23] has been introduced into the rst order diusion scheme (FOS) [7] for load balancing to yield the FOS/C algorithm (C for constant drain). FOS/C reaches a non-balanced load distribution in the steady state, which can represent similarities of graph nodes reecting their connectedness.…”

Section: Disturbed Diusion Fos/cmentioning

confidence: 99%

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A new diffusion-based multilevel algorithm for computing graph partitions of very high quality

Meyerhenke

Monien

Sauerwald

2008

2008 IEEE International Symposium on Parallel and Distributed Processing

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Abstract. Graph partitioning requires the division of a graph's vertex set into k equally sized subsets s. t. some objective function is optimized. High-quality partitions are important for many applications, whose objective functions are often N P-hard to optimize. Most state-of-the-art graph partitioning libraries use a variant of the Kernighan-Lin (KL) heuristic within a multilevel framework. While these libraries are very fast, their solutions do not always meet all user requirements. Moreover, due to its sequential nature, KL is not easy to parallelize. Its use as a load balancer in parallel numerical applications therefore requires complicated adaptations. That is why we developed previously an inherently parallel algorithm, called Bubble-FOS/C (Meyerhenke et al., IPDPS'06), which optimizes partition shapes by a diusive mechanism. However, it is too slow for practical use, despite its high solution quality.In this paper, besides proving that Bubble-FOS/C converges towards a local optimum of a potential function, we develop a much faster method for the improvement of partitionings. This faster method called TruncCons is based on a dierent diusive process, which is restricted to local areas of the graph and also contains a high degree of parallelism. By coupling TruncCons with Bubble-FOS/C in a multilevel framework based on two dierent hierarchy construction methods, we obtain our new graph partitioning heuristic DibaP. Compared to Bubble-FOS/C, DibaP shows a considerable acceleration, while retaining the positive properties of the slower algorithm. Experiments with popular benchmark graphs show that DibaP computes consistently better results than the state-of-the-art libraries METIS and JOSTLE. Moreover, with our new algorithm, we have improved the best known edge-cut values for a signicant number of partitionings of six widely used benchmark graphs.

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A bubble‐inspired algorithm for finite element mesh partitioning

Liu

Wang

2012

Numerical Meth Engineering

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SUMMARY This paper presents a bubble‐inspired algorithm for partitioning finite element mesh into subdomains. Differing from previous diffusion BUBBLE and Center‐oriented Bubble methods, the newly proposed algorithm employs the physics of real bubbles, including nucleation, spherical growth, bubble–bubble collision, reaching critical state, and the final competing growth. The realization of foaming process of real bubbles in the algorithm enables us to create partitions with good shape without having to specify large number of artificial controls. The minimum edge cut is simply achieved by increasing the volume of each bubble in the most energy efficient way. Moreover, the order, in which an element is gathered into a bubble, delivers the minimum number of surface cells at every gathering step; thus, the optimal numbering of elements in each subdomain has naturally achieved. Because finite element solvers, such as multifrontal method, must loop over all elements in the local subdomain condensation phase and the global interface solution phase, these two features have a huge payback in terms of solver efficiency. Experiments have been conducted on various structured and unstructured meshes. The obtained results are consistently better than the classical kMetis library in terms of the edge cut, partition shape, and partition connectivity. Copyright © 2012 John Wiley & Sons, Ltd.

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Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid

Abstract: We propose a load balancing heuristic for parallel adaptive finite element method (FEM)

Cited by 18 publications

References 23 publications

High quality graph partitioning

High quality graph partitioning

A new diffusion-based multilevel algorithm for computing graph partitions of very high quality

A bubble‐inspired algorithm for finite element mesh partitioning

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