MFEM: A modular finite element methods library

• Published in: Computers & mathematics with applications (1987) Vol. 81; no. 1; pp. 42 - 74
• Main 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
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.01.2021; Elsevier BV; Elsevier
• Subjects: Algorithms; Finite element method; Finite element methods; High-order methods; High-performance computing; Libraries; Matrix-free algorithms; Numerical PDEs; Open-source scientific software; Source code; Open-source scientific software; High-order methods; Finite element methods; Matrix-free algorithms; High-performance computing; Numerical PDEs
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2020.06.009

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.