MFEM explained

MFEM
Latest Release Version:	4.7
Repo:	https://github.com/mfem/mfem
Programming Language:	C++
Operating System:	Linux, MacOS, Microsoft Windows
Genre:	Finite element analysis
License:	BSD

MFEM is an open-source C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore National Laboratory and the MFEM open-source community on GitHub. MFEM is free software released under a BSD license.^[1]

The library consists of C++ classes that serve as building blocks for developing finite element solvers applicable to problems of fluid dynamics,^[2] structural mechanics,^[3] electromagnetics,^[4] radiative transfer^[5] and many other.

Features

Some of the features of MFEM include^[6]

• Arbitrary high order finite elements with curved boundaries.
• H¹, H(curl) and H(div) conforming, discontinuous (L₂), and NURBS finite element spaces.
• Local mesh refinement, both conforming (simplex meshes) and non-conforming (quadrilateral/hexahedral meshes).
• Highly scalable MPI-based parallelism and GPU acceleration.^[7]
• Wide variety of finite element discretization approaches, including Galerkin, discontinuous Galerkin, mixed, high-order and isogeometric analysis methods.
• Tight integration with the Hypre parallel linear algebra library.
• Many built-in solvers and interfaces to external libraries such as PETSc, SuiteSparse, Gmsh, etc.
• Accurate and flexible visualization with VisIt and ParaView.
• Lightweight design and conservative use of C++ templating.
• Documentation in the form of examples and mini-applications.

See also

• List of finite element software packages
• List of numerical analysis software
• List of numerical libraries

Notes and References

1. Auten . Holly . The High Value of Open-Source Software . Science & Technology Review . January/February 2018 . 5–11 .
2. Anderson . Robert W. . Dobrev . Veselin A. . Kolev . Tzanio V. . Rieben . Robert N. . High-Order Multi-Material ALE Hydrodynamics . SIAM Journal on Scientific Computing . 2018 . 40 . 1 . B32–B58 . 10.1137/17M1116453. 2018SJSC...40B..32A . 1474269 .
3. White . D. A. . Stowell . M. L. . Tortorelli . D. A. . Topological optimization of structures using Fourier representations . Structural and Multidisciplinary Optimization . 58 . 3 . 2018 . 1205–1220 . 10.1007/s00158-018-1962-y. 1479078 . 126093513 .
4. Shiraiwa . S. . Wright . J. C. . Bonoli . P. T. . Kolev . T. . Stowell . M. . RF wave simulation for cold edge plasmas using the MFEM library . 22 Topical Conference on Radio-Frequency Power in Plasmas . 23 October 2017 . 157 . 03048 . 10.1051/epjconf/201715703048. 2017EPJWC.15703048S . free . 1721.1/113307 . free .
5. Holec . M. . Limpouch . J. . Liska . R. . Weber . S. . High‐order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics . Numerical Methods in Fluids . 10 April 2017 . 83 . 10 . 779–797 . 10.1002/fld.4288. 2017IJNMF..83..779H . 125947931 .
6. Web site: MFEM Finite Element Discretization Library .
7. Web site: MFEM video: Advanced simulation algorithms for HPC applications. YouTube.