MFEM swMATH ID: 9043 Software Authors: 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 Description: 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. Homepage: http://mfem.org/ Source Code: https://github.com/mfem/mfem Keywords: arXiv_cs.MS; Numerical Analysis; arXiv_math.NA; C++ library; finite element methods; MFEM Related Software: hypre; PETSc; deal.ii; GitHub; FEniCS; GLVis; BoomerAMG; FreeFem++; Gmsh; libMesh; NGSolve; PCBDDC; Trilinos; METIS; UMFPACK; VisIt; Firedrake; STRUMPACK; SuperLU; CSparse Cited in: 58 Publications Further Publications: http://mfem.org/publications/ Standard Articles 2 Publications describing the Software, including 1 Publication in zbMATH Year MFEM: a modular finite element methods library. Zbl 07288706Anderson, 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 2021 MFEM: a modular finite element methods library 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 2019 all top 5 Cited by 124 Authors 13 Kolev, Tzanio V. 9 Vassilevski, Panayot Spirov 8 Pazner, Will E. 6 Dobrev, Veselin A. 6 Tomov, Vladimir Z. 5 Villa, Umberto E. 4 Rieben, Robert N. 3 Ghysels, Pieter 3 Knupp, Patrick M. 3 Li, Ruipeng 3 Li, Xiaoye Sherry 3 Southworth, Ben S. 3 Zampini, Stefano 2 Andrej, Julian 2 Camier, Jean-Sylvain 2 Claus, Lisa 2 Fairbanks, Hillary R. 2 Krzysik, Oliver A. 2 Kuchařík, Milan 2 Kuzmin, Dmitri 2 la Cour Christensen, Max 2 Langer, Ulrich 2 Liu, Yang 2 Meier Yang, Ulrike 2 Mittal, Ketan 2 Nikl, Jan 2 Saad, Yousef 2 Sandu, Adrian 2 Schafelner, Andreas 2 Tang, Xian-Zhu 2 Weber, Stefan 1 Afanasiev, Michael 1 Akkerman, Ido 1 Ambartsumyan, Ilona 1 Anderson, Robert W. G. 1 Anzt, Hartwig 1 Bäcker, Jan-Phillip 1 Badia, Santiago 1 Bangerth, Wolfgang 1 Barker, Andrew T. 1 Bello-Maldonado, Pedro D. 1 Böhm, Christian 1 Boukaram, Wajih-Halim 1 Bramwell, Jamie A. 1 Bui-Thanh, Tan 1 Bussmann, Michael 1 Cao, Shuhao 1 Cervena, Lenka 1 Červený, Jakub 1 Chacón, Luis 1 Cojean, Terry 1 Comellas, Ester 1 Dahm, Johann P. S. 1 D’Ambra, Pasqua 1 De Luna, Manuel Quezada 1 De Sterck, Hans 1 Dohrmann, Clark R. 1 Dong, Melody 1 Dudouit, Yohann 1 Efendiev, Yalchin R. 1 Ellis, Truman E. 1 Engsig-Karup, Allan P. 1 Fichtner, Andreas 1 Filippone, Salvatore 1 Flegar, Goran 1 Fortunato, Daniel 1 Franco, Michael 1 Ghattas, Omar N. 1 Göbel, Fritz 1 Göthel, Ilja 1 Grützmacher, Thomas 1 Hajduk, Hennes 1 Hale, Nicholas 1 Hapla, Vaclav 1 Hölzl, Matthias M. 1 Huijsmans, G. T. A. 1 Jolivet, Pierre 1 1 Kalchev, Delyan Z. 1 Keyes, David Elliot 1 Knepley, Matthew G. 1 Kormann, Katharina 1 Krischer, Lion 1 Kronbichler, Martin 1 Lashuk, Ilya V. 1 Lee, Chak Shing 1 Liu, Ju 1 Manteuffel, Thomas A. 1 Marsden, Alison L. 1 Martín, Alberto F. 1 Martínez-Frutos, Jesús 1 Munch, Peter 1 Napov, Artem 1 Nayak, Pratik 1 Olson, Luke N. 1 Ortigosa, Rogelio 1 Osei-Kuffuor, Daniel 1 Pamela, S. J. P. 1 Pedregal, Pablo 1 Pelteret, Jean-Paul ...and 24 more Authors all top 5 Cited in 17 Serials 22 SIAM Journal on Scientific Computing 8 Journal of Computational Physics 5 Computers and Fluids 4 ACM Transactions on Mathematical Software 3 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 2 Numerical Linear Algebra with Applications 1 Journal of Computational and Applied Mathematics 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Scientific Computing 1 Applied Mathematical Modelling 1 Advances in Computational Mathematics 1 European Journal of Mechanics. A. Solids 1 Archives of Computational Methods in Engineering 1 Computational Methods in Applied Mathematics 1 Communications on Applied Mathematics and Computation 1 Electronic Research Archive all top 5 Cited in 13 Fields 53 Numerical analysis (65-XX) 17 Partial differential equations (35-XX) 17 Fluid mechanics (76-XX) 5 Mechanics of deformable solids (74-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX) Citations by Year