Multilevel Algorithms for Generating Coarse Grids for Multigrid Methods

Irene Moulitsas, George Karypis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

27 Scopus citations

Abstract

Geometric Multigrid methods have gained widespread acceptance for solving large systems of linear equations, especially for structured grids. One of the challenges in successfully extending these methods to unstructured grids is the problem of generating an appropriate set of coarse grids. The focus of this paper is the development of robust algorithms, both serial and parallel, for generating a sequence of coarse grids from the original unstructured grid. Our algorithms treat the problem of coarse grid construction as an optimization problem that tries to optimize the overall quality of the resulting fused elements. We solve this problem using the multilevel paradigm that has been very successful in solving the related grid/graph partitioning problem. The parallel formulation of our algorithm incurs a very small communication overhead, achieves high degree of concurrency, and maintains the high quality of the coarse grids obtained by the serial algorithm.

Original languageEnglish (US)
Title of host publicationProceedings of the 2001 ACM/IEEE Conference on Supercomputing, SC 2001
PublisherAssociation for Computing Machinery
Pages45
Number of pages1
ISBN (Electronic)158113293X
DOIs
StatePublished - Nov 10 2001
Externally publishedYes
Event2001 ACM/IEEE Conference on Supercomputing, SC 2001 - Denver, United States
Duration: Nov 10 2001Nov 16 2001

Publication series

NameProceedings of the International Conference on Supercomputing

Conference

Conference2001 ACM/IEEE Conference on Supercomputing, SC 2001
Country/TerritoryUnited States
CityDenver
Period11/10/0111/16/01

Bibliographical note

Funding Information:
∗This work was supported by NSF CCR-9972519, EIA-9986042, ACI-9982274, by Army Research Office contract DA/DAAG55-98-1-0441, by the DOE ASCI program, and by Army High Performance Computing Research Center contract number DAAH04-95-C-0008. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage, and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SC2001 November 2001, Denver (c) 2001 ACM 1-58113-293-X/01/0011 $5.00

Publisher Copyright:
© 2001 ACM.

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