parGeMSLR :   Parallel Generalized Multilevel Schur Complement Low-Rank Preconditioner   -- (Version 1.0.0)

This version dated : Wed June 2 12:00:00 CDT 2021

pargemslr-logo Welcome to release 1.0.0 of parGeMSLR (the parallel Generalized Multilevel Schur complement Low-Rank preconditioning/solution package). This is a distributed-memory Multilevel Low-Rank Preconditioning and Solution package for the solution of large and sparse (non)symmetric linear systems of equations. Preconditioners provided by parGeMSLR are purely algebraic and are based on a multilevel reordering of the original set of equations/variables, exploiting a hierarchical ordering of the interface variables at each level. Several options for reordering are available. At each given level, parGeMSLR decouples (using, e.g., ParMETIS) the solution of the current linear system into one associated with the interior variables and another associated with the interface ones. The first subproblem is block-diagonal and solved in parallel by applying some form of ILU preconditioning. The recursive nature of the preconditioner appears on the second subproblem where the Schur complement linear system is reconditioned by the interface coupling matrix. The latter is applied by descending to the next level until the last level is reached. In the latter case, the user can choose to use either Block Jacobi acceleration or redundantly solve the problem by (I)LU. Low-rank correction terms can be added at each level to further enhance robustness, and these are applied using the Woodbury formula.
In addition to the documentation that accompanies the package, the technical reports listed below provide details on the techniques used in ParGeMSLR. Online documentation (based on Doxygen) is available - see below.

Related publications


parGeMSLR is a continuing team effort. Developers of the most recent version include: Yousef Saad, Tianshi Xu, Vassilis Kalantzis, Ruipeng Li, Yuanzhe Xi, and Geoffrey Dillon. If you are interested in contributing to the effort contact us.

Download parGeMSLR

Before you download read the COPYRIGHT statement

The package is availiable on the github site:

Yousef Saad    

Documentation :     (Doxygen based)

Documentation :     (pdf)

Work supported by:     NSF