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                Finite Element Discretization Library                               __                   _ __ ___   / _|  ___  _ __ ___                  | '_ ` _ \ | |_  / _ \| '_ ` _ \                  | | | | | ||  _||  __/| | | | | |                  |_| |_| |_||_|   \___||_| |_| |_|                           https://mfem.org

MFEM is a modular parallel C++ library for finite elementmethods. Its goal is to enable high-performance scalable finite elementdiscretization research and application development on a wide variety ofplatforms, ranging from laptops to supercomputers.

We welcome contributions and feedback from the community. Please see the fileCONTRIBUTING.md for additional details about our developmentprocess.

• For building instructions, see the fileINSTALL, or type "make help".

• Copyright and licensing information can be found in filesLICENSE andNOTICE.

• The best starting point for new users interested in MFEM's features is toreview the examples and miniapps athttps://mfem.org/examples.

• Instructions for learning with Docker are inconfig/docker.

Conceptually, MFEM can be viewed as a finite element toolbox that provides thebuilding blocks for developing finite element algorithms in a manner similar tothat of MATLAB for linear algebra methods. In particular, MFEM provides supportfor arbitrary high-order H1-conforming, discontinuous (L2), H(div)-conforming,H(curl)-conforming and NURBS finite element spaces in 2D and 3D, as well as manybilinear, linear and nonlinear forms defined on them. It enables the quickprototyping of various finite element discretizations, including Galerkinmethods, mixed finite elements, Discontinuous Galerkin (DG), isogeometricanalysis, hybridization and Discontinuous Petrov-Galerkin (DPG) approaches.

MFEM includes classes for dealing with a wide range of mesh types: triangular,quadrilateral, tetrahedral and hexahedral, as well as surface and topologicallyperiodical meshes. It has general support for mesh refinement, including localconforming and non-conforming (AMR) adaptive refinement. Arbitrary elementtransformations, allowing for high-order mesh elements with curved boundaries,are also supported.

When used as a "finite element to linear algebra translator", MFEM can take aproblem described in terms of finite element-type objects, and produce thecorresponding linear algebra vectors and fully or partially assembled operators,e.g. in the form of global sparse matrices or matrix-free operators. The libraryincludes simple smoothers and Krylov solvers, such as PCG, MINRES and GMRES, aswell as support for sequential sparse direct solvers from the SuiteSparselibrary. Nonlinear solvers (the Newton method), eigensolvers (LOBPCG), andseveral explicit and implicit Runge-Kutta time integrators are also available.

MFEM supports MPI-based parallelism throughout the library, and can readily beused as a scalable unstructured finite element problem generator. Starting withversion 4.0, MFEM offers support for GPU acceleration, and programming models,such as CUDA, HIP, OCCA, RAJA and OpenMP. MFEM-based applications requireminimal changes to switch from a serial to a highly-performant MPI-parallelversion of the code, where they can take advantage of the integrated linearsolvers from the hypre library. Comprehensive support for other externalpackages, e.g. PETSc, SUNDIALS and libCEED is also included, giving access toadditional linear and nonlinear solvers, preconditioners, time integrators, etc.

For examples of using MFEM, see theexamples/ andminiapps/directories, as well as the OpenGL visualization tool GLVis which is availableathttps://glvis.org.

MFEM is distributed under the terms of the BSD-3 license. All new contributionsmust be made under this license. SeeLICENSE andNOTICE fordetails.

SPDX-License-Identifier: BSD-3-Clause
LLNL Release Number: LLNL-CODE-806117
DOI: 10.11578/dc.20171025.1248