MFEM

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 56 articles , 2 standard articles )

Showing results 1 to 20 of 56.
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  1. Anzt, Hartwig; Cojean, Terry; Flegar, Goran; Göbel, Fritz; Grützmacher, Thomas; Nayak, Pratik; Ribizel, Tobias; Tsai, Yuhsiang Mike; Quintana-Ortí, Enrique S.: \textscGinkgo: a modern linear operator algebra framework for high performance computing (2022)
  2. Kolev, Tzanio; Pazner, Will: Conservative and accurate solution transfer between high-order and low-order refined finite element spaces (2022)
  3. Langer, Ulrich; Schafelner, Andreas: Simultaneous space-time finite element methods for parabolic optimal control problems (2022)
  4. Southworth, Ben S.; Krzysik, Oliver; Pazner, Will: Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs. II: Nonlinearities and DAEs (2022)
  5. Southworth, Ben S.; Krzysik, Oliver; Pazner, Will; De Sterck, Hans: Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs. I: The linear setting (2022)
  6. 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)
  7. Brown et al.: libCEED: Fast algebra for high-order element-based discretizations (2021) not zbMATH
  8. Cao, Shuhao: A simple virtual element-based flux recovery on quadtree (2021)
  9. Dohrmann, Clark R.: Spectral equivalence of low-order discretizations for high-order H(curl) and H(div) spaces (2021)
  10. Fairbanks, Hillary R.; Villa, Umberto; Vassilevski, Panayot S.: Multilevel hierarchical decomposition of finite element white noise with application to multilevel Markov chain Monte Carlo (2021)
  11. Fairbanks, Hillary R.; Villa, Umberto; Vassilevski, Panayot S.: Multilevel hierarchical decomposition of finite element white noise with application to multilevel Markov chain Monte Carlo (2021)
  12. Fortunato, Daniel; Hale, Nicholas; Townsend, Alex: The ultraspherical spectral element method (2021)
  13. Hajduk, Hennes: Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws (2021)
  14. 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)
  15. Jolivet, Pierre; Roman, Jose E.; Zampini, Stefano: KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners (2021)
  16. Li, Ruipeng; Sjögreen, Björn; Meier Yang, Ulrike: A new class of AMG interpolation methods based on matrix-matrix multiplications (2021)
  17. Liu, Yang; Ghysels, Pieter; Claus, Lisa; Li, Xiaoye Sherry: Sparse approximate multifrontal factorization with butterfly compression for high-frequency wave equations (2021)
  18. Liu, Yang; Ghysels, Pieter; Claus, Lisa; Li, Xiaoye Sherry: Sparse approximate multifrontal factorization with butterfly compression for high-frequency wave equations (2021)
  19. Munch, Peter; Kormann, Katharina; Kronbichler, Martin: hyper.deal: an efficient, matrix-free finite-element library for high-dimensional partial differential equations (2021)
  20. Nikl, Jan; Göthel, Ilja; Kuchařík, Milan; Weber, Stefan; Bussmann, Michael: Implicit reduced Vlasov-Fokker-Planck-Maxwell model based on high-order mixed elements (2021)

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Further publications can be found at: http://mfem.org/publications/