MueLu Overview

MueLu is designed for the parallel solution of large sparse linear systems of equations arising from PDE discretizations. MueLu provides easy-to-use multigrid solvers and preconditioners based on smoothed aggregation algorithms. As a multigrid framework, MueLu supports the design of application-specific multigrid preconditioners. MueLu is extensible and allows for the research and development of novel multigrid preconditioning methods. Finally, MueLu is able to run on virtually all modern CPU and accelerator based architectures.

If you're looking for something ready-to-use, MueLu provides scalable multigrid preconditioners for these problem classes:

Poisson
Elasticity
convection-diffusion
Maxwell’s equations (eddy current formulation)

Features:

Easy-to-use interface: MueLu has a user-friendly parameter input deck which covers most important use cases, with reasonable defaults provided for common problem types.
Modern object-oriented software architecture: MueLu is written completely in C++ as a modular object-oriented multigrid framework, which provides flexibility to combine and reuse existing components to develop novel multigrid methods.
Extensibility: Due to its flexible design, MueLu is an excellent toolkit for research on novel multigrid concepts. Experienced multigrid users have full access to the underlying framework through an advanced XML based interface. Expert users may use and extend the C++ API directly.
Integration with Trilinos: As a package of Trilinos, Muelu is well integrated into the Trilinos environment and uses the Tpetra-based sparse linear algebra stack: Krylov solvers (Belos), algebraic solvers (Ifpack2), sparse direct solvers (Amesos2), and load-balancing (Zoltan2).
Broad range of supported platforms: MueLu runs on wide variety of architectures, from desktop workstations to parallel Linux clusters and accelerator-based supercomputers.
Open source: MueLu is freely available through a simplified BSD license.

If you are interested in using MueLu for your research or want to contribute, please contact the MueLu team through github.

Documentation

Useful views of the Doxygen documentation are:

Browsing the entire class documentation. Choose the Class Index subtab.
Browsing the class documentation organized by logical groups. Choose the Modules tab.

The MueLu User's Guide is located in muelu/doc/UsersGuide and at the MueLu home page.

Tutorial

The MueLu tutorial describes the most important features of MueLu, from beginning information to advanced usage. It contains accompanying exercises where the interested user can do their own experiments with multigrid parameters. The MueLu tutorial is part of the Trilinos repository, and its examples are automatically tested to ensure that they compile and run.

For All Questions and Comments...

Open an issue: https://github.com/trilinos/Trilinos/issues.
Start a discussion: https://github.com/orgs/trilinos/discussions.

Citing

To cite MueLu, please use the following bibliography entry.

@techreport{MueLu, title={Mue{L}u User’s Guide}, author={Luc Berger-Vergiat and Christian A. Glusa and Graham Harper and Jonathan J. Hu and Matthias Mayr and Peter Ohm and Andrey Prokopenko and Christopher M. Siefert and Raymond S. Tuminaro and Tobias A. Wiesner}, number={SAND2023-12265}, year={2023}, institution = {Sandia National Laboratories}, }

Current Developers

Luc Berger-Vergiat, Sandia National Labs
Max Firmbach, University of the Bundeswehr Munich
Christian Glusa, Sandia National Labs
Graham Harper, Sandia National Labs
Jonathan Hu, Sandia National Labs
Matthias Mayr, University of the Bundeswehr Munich
Malachi Phillips, Sandia National Labs
Chris Siefert, Sandia National Labs
Ray Tuminaro, Sandia National Labs

Authors and Contributors

Tom Benson, LLNL
Emily Furst, University of Washington (summer intern, 2015)
Jeremie Gaidamour, INRIA
Axel Gerstenberger, Rolls Royce
Brian Kelley, Sandia National Labs
Andrey Prokopenko, ORNL
Paul Tsuji, LLNL
Peter Ohm, RIKEN
Jerry Watkins, Sandia National Labs
Tobias Wiesner, Leica