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https://github.com/mfem/mfem

Lightweight, general, scalable C++ library for finite element methods
https://github.com/mfem/mfem

amr computational-science fem finite-elements high-order high-performance-computing hpc math-physics parallel-computing radiuss scientific-computing

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Lightweight, general, scalable C++ library for finite element methods

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README 

        
                    Finite Element Discretization Library

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                               https://mfem.org



[MFEM](https://mfem.org) is a modular parallel C++ library for finite element

methods. Its goal is to enable high-performance scalable finite element

discretization research and application development on a wide variety of

platforms, ranging from laptops to supercomputers.



We welcome contributions and feedback from the community. Please see the file

[CONTRIBUTING.md](CONTRIBUTING.md) for additional details about our development

process.



* For building instructions, see the file [INSTALL](INSTALL), or type "make help".



* Copyright and licensing information can be found in files [LICENSE](LICENSE) and [NOTICE](NOTICE).



* The best starting point for new users interested in MFEM's features is to

  review the examples and miniapps at https://mfem.org/examples.



* Instructions for learning with Docker are in [config/docker](config/docker).



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 provides support

for 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 many

bilinear, linear and nonlinear forms defined on them. It enables the quick

prototyping of various finite element discretizations, including Galerkin

methods, mixed finite elements, Discontinuous Galerkin (DG), isogeometric

analysis, 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 topologically

periodical meshes. It has general support for mesh refinement, including local

conforming and non-conforming (AMR) adaptive refinement. Arbitrary element

transformations, 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 a

problem described in terms of finite element-type objects, and produce the

corresponding linear algebra vectors and fully or partially assembled operators,

e.g. in the form of global sparse matrices or matrix-free operators. The library

includes simple smoothers and Krylov solvers, such as PCG, MINRES and GMRES, as

well as support for sequential sparse direct solvers from the SuiteSparse

library. Nonlinear solvers (the Newton method), eigensolvers (LOBPCG), and

several explicit and implicit Runge-Kutta time integrators are also available.



MFEM supports MPI-based parallelism throughout the library, and can readily be

used as a scalable unstructured finite element problem generator. Starting with

version 4.0, MFEM offers support for GPU acceleration, and programming models,

such as CUDA, HIP, OCCA, RAJA and OpenMP. MFEM-based applications require

minimal changes to switch from a serial to a highly-performant MPI-parallel

version of the code, where they can take advantage of the integrated linear

solvers from the hypre library. Comprehensive support for other external

packages, e.g. PETSc, SUNDIALS and libCEED is also included, giving access to

additional linear and nonlinear solvers, preconditioners, time integrators, etc.



For examples of using MFEM, see the [examples/](examples) and [miniapps/](miniapps)

directories, as well as the OpenGL visualization tool GLVis which is available

at https://glvis.org.



## License



MFEM is distributed under the terms of the BSD-3 license. All new contributions

must be made under this license. See [LICENSE](LICENSE) and [NOTICE](NOTICE) for

details.



SPDX-License-Identifier: BSD-3-Clause 


LLNL Release Number: LLNL-CODE-806117 


DOI: 10.11578/dc.20171025.1248