# Optimising subdomain aspect ratios for parallel load balancing

Schlimbach, Frank (2000) *Optimising subdomain aspect ratios for parallel load balancing.* PhD thesis, University of Greenwich.

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## Abstract

In parallel adaptive Finite Element simulations the work load 011the individual processors can change frequently. To (re)distribute the load evenly over the processors a load balancing heuristic is needed. Common strategies try to minimise subdomain dependencies by minimising the number of cut edges in the partition. For many solvers this is the most influential factor.

However for example, for certain preconditioned Conjugate Gradient solvers this cutsize can play only a minor role, but their convergence can be highly dependent on the subdomain shapes. Degenerated subdomain shapes can cause them to need significantly more iterations to converge. Common heuristics often fail to address these requirements.

In this thesis a new strategy is introduced which directly addresses the problem of generating and conserving reasonably good subdomain shapes while balancing the load in a dynamically changing Finite Element Simulation. A new definition of Aspect Ratio is presented which assesses subdomain shapes. The common methodology of using adjacency information to select the best elements to be migrated is not considered since it is not necessarily related to the subdomain shapes. Instead, geometric data is used to formulate several cost functions to rate elements in terms of their suitability to be migrated.

The well known diffusive and Generalised Dimension Exchange methods which calculate the necessary load flow are enhanced by weighting the subdomain edges in order to influence their impact on the resulting partition positively. The results of comprehensive tests are presented and demonstrate that the proposed methods are competitive with state-of-the-art load balancing tools.

Item Type: | Thesis (PhD) |
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Additional Information: | uk.bl.ethos.484234 |

Uncontrolled Keywords: | finite element simulation, algorithims, aspect ratio, shapes, mathematics, heuristic |

Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

School / Department / Research Groups: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Computing and Information Systems |

Last Modified: | 20 Aug 2012 10:37 |

URI: | http://gala.gre.ac.uk/id/eprint/6293 |

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