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The logo of MFEM shows some of its features: curvilinear elements, adaptive mesh refinement and parallel partitioning.
Stable release
4.3 / July 29, 2021; 4 months ago (2021-07-29)
Written inC++
Operating systemLinux, MacOS, Microsoft Windows
TypeFinite element analysis

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.


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


  1. ^ Auten, Holly. "The High Value of Open-Source Software" (PDF). Science & Technology Review. January/February 2018: 5–11.
  2. ^ Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N. (2018). "High-Order Multi-Material ALE Hydrodynamics". SIAM Journal on Scientific Computing. 40 (1): B32–B58. doi:10.1137/17M1116453. OSTI 1474269.
  3. ^ White, D. A.; Stowell, M. L.; Tortorelli, D. A. (2018). "Topological optimization of structures using Fourier representations". Structural and Multidisciplinary Optimization. 58 (3): 1205–1220. doi:10.1007/s00158-018-1962-y. OSTI 1479078. S2CID 126093513.
  4. ^ Shiraiwa, S.; Wright, J. C.; Bonoli, P. T.; Kolev, T.; Stowell, M. (23 October 2017). "RF wave simulation for cold edge plasmas using the MFEM library". 22 Topical Conference on Radio-Frequency Power in Plasmas. 157: 03048. Bibcode:2017EPJWC.15703048S. doi:10.1051/epjconf/201715703048.
  5. ^ Holec, M.; Limpouch, J.; Liska, R.; Weber, S. (10 April 2017). "High‐order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics". Numerical Methods in Fluids. 83 (10): 779–797. Bibcode:2017IJNMF..83..779H. doi:10.1002/fld.4288.
  6. ^ "MFEM Finite Element Discretization Library".
  7. ^ "MFEM video: Advanced simulation algorithms for HPC applications".

External links

  • Official website