MFEM: A modular finite element methods library

Anderson, Robert; Andrej, Julian; Barker, Andrew; Bramwell, Jamie; Camier, Jean Sylvain; Cerveny, Jakub; Dobrev, Veselin; Dudouit, Yohann; Fisher, Aaron; Kolev, Tzanio; Pazner, Will; Stowell, Mark; Tomov, Vladimir; Akkerman, Ido; Dahm, Johann; Medina, David; Zampini, Stefano

MFEM: A modular finite element methods library

Files

Articlefile1.pdf (7.18 MB)

Embargo End Date

2022-07-11

Type

Article

Authors

Anderson, Robert
Andrej, Julian

Barker, Andrew
Bramwell, Jamie
Camier, Jean Sylvain
Cerveny, Jakub
Dobrev, Veselin
Dudouit, Yohann
Fisher, Aaron
Kolev, Tzanio

Pazner, Will
Stowell, Mark
Tomov, Vladimir
Akkerman, Ido
Dahm, Johann
Medina, David
Zampini, Stefano

KAUST Department

Extreme Computing Research Center
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date

2020-07-11

Print Publication Date

2020-07

Date

2020-07-11

Submitted Date

2020-05-15

Abstract

MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM's goal is to provide application scientists with access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers, while enabling researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel and GPU-accelerated settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library.

Citation

Anderson, R., Andrej, J., Barker, A., Bramwell, J., Camier, J.-S., Cerveny, J., … Zampini, S. (2020). MFEM: A modular finite element methods library. Computers & Mathematics with Applications. doi:10.1016/j.camwa.2020.06.009

Acknowledgements

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, LLNL-JRNL-795849.The MFEM project would not have been possible without the help and advice of Joachim Schöberl, Panayot Vassilevski, and all the contributors in the MFEM open-source community, see https://mfem.org/about and https://github.com/orgs/mfem/people. MFEM has been supported by a number of U.S. Department of Energy (DOE) grants, including the Applied Math and SciDAC programs in the DOE Office of Science, and the ASC and LDRD programs in NNSA. MFEM is also a major participant in the co-design Center for Efficient Exascale Discretizations (CEED) in the DOE's Exascale Computing Project. This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.