Treffer: Multilevel Algorithms for Generating Coarse Grids for Multigrid Methods

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. # This work was supported by NSF CCR-9972519, EIA-9986042, ACI-9982274, by Army Research Office contract DA/DAAG55-98-10441, 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 1