MFEM is a general, modular, parallel C++ library for finite element methods research and development. Conceptually, MFEM can be viewed as a finite element toolbox, that provides the building blocks for developing finite element algorithms in a manner similar to that of MATLAB for linear algebra methods. In particular, MFEM supports a wide variety of finite element spaces in 2D and 3D, including arbitrary high-order H1-conforming, discontinuous (L2), H(div)-conforming, H(curl)-conforming and NURBS elements, as well as many bilinear and linear forms defined on them. It includes classes for dealing with various types of triangular, quadrilateral, tetrahedral and hexahedral meshes and their global and, in the case of triangular and tetrahedral meshes, local refinement (including in parallel). General element transformations, allowing for elements with curved boundaries are also supported. MFEM is commonly used as a ”finite element to linear algebra translator”, since it can take a problem described in terms of finite element-type objects, and produce the corresponding linear algebra vectors and sparse matrices. In order to facilitate this, MFEM uses compressed sparse row (CSR) sparse matrix storage and includes simple smoothers and Krylov solvers, such as PCG, GMRES and BiCGStab. The MPI-based parallel version of MFEM can be used as a scalable unstructured finite element problem generator, which supports parallel local refinement and parallel curved meshes, as well as several solvers from the hypre library. An experimental support for OpenMP acceleration is also included as of version 2.0. MFEM originates from the previous research effort in the (unreleased) AggieFEM/aFEM project. Some examples of its use can be found in the Gallery and Publications pages. We recommend using it together with GLVis, which is an OpenGL visualization tool build on top of MFEM.

References in zbMATH (referenced in 37 articles , 2 standard articles )

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  1. 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 (2021)
  2. Hajduk, Hennes: Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws (2021)
  3. Hapla, Vaclav; Knepley, Matthew G.; Afanasiev, Michael; Boehm, Christian; van Driel, Martin; Krischer, Lion; Fichtner, Andreas: Fully parallel mesh I/O using PETSc DMPlex with an application to waveform modeling (2021)
  4. Jolivet, Pierre; Roman, Jose E.; Zampini, Stefano: KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners (2021)
  5. Sandu, Adrian; Tomov, Vladimir; Cervena, Lenka; Kolev, Tzanio: Conservative high-order time integration for Lagrangian hydrodynamics (2021)
  6. Ambartsumyan, Ilona; Boukaram, Wajih; Bui-Thanh, Tan; Ghattas, Omar; Keyes, David; Stadler, Georg; Turkiyyah, George; Zampini, Stefano: Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs (2020)
  7. Bello-Maldonado, Pedro D.; Kolev, Tzanio V.; Rieben, Robert N.; Tomov, Vladimir Z.: A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics (2020)
  8. Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Rieben, Robert; Tomov, Vladimir: Simulation-driven optimization of high-order meshes in ALE hydrodynamics (2020)
  9. Franco, Michael; Camier, Jean-Sylvain; Andrej, Julian; Pazner, Will: High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners (2020)
  10. Hartwig Anzt, Terry Cojean, Yen-Chen Chen, Goran Flegar, Fritz Göbel, Thomas Grützmacher, Pratik Nayak, Tobias Ribizel, Yu-Hsiang Tsai: Ginkgo: A high performance numerical linear algebra library (2020) not zbMATH
  11. Kaczmarczyk, Łukasz; Ullah, Zahur; Lewandowski, Karol; Meng, Xuan; Zhou, Xiao-Yi; Athanasiadis, Ignatios; Nguyen, Hoang; Chalons-Mouriesse, Christophe-Alexandre; Richardson, Euan J.; Miur, Euan; Shvarts, Andrei G.; Wakeni, Mebratu; Pearce, Chris J.: MoFEM: An open source, parallel nite element library (2020) not zbMATH
  12. Langer, Ulrich; Schafelner, Andreas: Adaptive space-time finite element methods for non-autonomous parabolic problems with distributional sources (2020)
  13. Liu, Ju; Yang, Weiguang; Dong, Melody; Marsden, Alison L.: The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations (2020)
  14. Matteo Giacomini, Ruben Sevilla, Antonio Huerta: HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB (2020) arXiv
  15. Pazner, Will: Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods (2020)
  16. Peng, Zhichao; Tang, Qi; Tang, Xian-Zhu: An adaptive discontinuous Petrov-Galerkin method for the Grad-Shafranov equation (2020)
  17. Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Tomov, Vladimir: The target-matrix optimization paradigm for high-order meshes (2019)
  18. Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Tomov, Vladimir: Towards simulation-driven optimization of high-order meshes by the target-matrix optimization paradigm (2019)
  19. Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander: The DUNE Framework: Basic Concepts and Recent Developments (2019) arXiv
  20. Robert Anderson, Julian Andrej, Andrew Barker, Jamie Bramwell, Jean-Sylvain Camier, Jakub Cerveny, Veselin Dobrev, Yohann Dudouit, Aaron Fisher, Tzanio Kolev, Will Pazner, Mark Stowell, Vladimir Tomov, Johann Dahm, David Medina, Stefano Zampini: MFEM: a modular finite element methods library (2019) arXiv

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