Multilevel Algorithms for Generating Coarse Grids for Multigrid Methods, sc

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 al-gorithms, both serial and parallel, for generating a sequence of coarse grids from the original unstruc-tured grid. Our algorithms treat the problem of coarse grid construction as an optimization problem that tries to optimize the overall quality of the result-ing 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 qual-ity of the coarse grids obtained by the serial algo-rithm