A Parallel Multilevel Preconditioning Module for Unstructured Mesh Krylov Solvers

Ray Tuminaro

Sandia National Laboratories, PO Box 969, Livermore, Ca 94551

Charles Tong
Lawrence Livermore National Labs, Livermore CA

John Shadid
Karen Devine
David Day
Sandia National Laboratories Albuquerque, NM 87185


Multilevel methods offer the best promise to attain both fast convergence and parallel efficiency in the numerical solution of partial differential equations. Unfortunately, they have not been widely used, in part, due to implementation difficulties for unstructured mesh solvers. To facilitate use, a multilevel preconditioner software module, ML, has been constructed. Several methods (e.g. smoothed aggregation multigrid and two-level domain decomposition) are provided requiring relatively modest effort from the application developer. We discuss the current status of this software module including the parallel smoothed aggregation method, domain decomposition scheme, and their use with other software packages (e.g. Aztec, ParaSails, Metis, SuperLU, XYT) for outer iterations, smoothers, and coarse grid solvers. We will discuss our experiences in solving problems arising from a few application areas in electromagnetics, elasticity, and computational fluid dynamics (CFD) on the ASCI red machine.