MFEM is an

open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use and view the source code, design documents, or content of the product. The open source model is a decentrali ...

C++ library for solving

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s using the

finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...

, developed and maintained by researchers at the

Lawrence Livermore National Laboratory Lawrence Livermore National Laboratory (LLNL) is a Federally funded research and development centers, federally funded research and development center in Livermore, California, United States. Originally established in 1952, the laboratory now i ...

and the MFEM open-source community on

GitHub GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug trackin ...

. MFEM is

free software Free software, libre software, libreware sometimes known as freedom-respecting software is computer software distributed open-source license, under terms that allow users to run the software for any purpose as well as to study, change, distribut ...

released under a

BSD license BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. This is in contrast to copyleft licenses, which have share-alike requirements. The original BSD lic ...

. The library consists of C++ classes that serve as building blocks for developing finite element solvers applicable to problems of

fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

structural mechanics Structural mechanics or mechanics of structures is the computation of deformations, deflections, and internal forces or stresses (''stress equivalents'') within structures, either for design or for performance evaluation of existing structures. ...

electromagnetics In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

radiative transfer Radiative transfer (also called radiation transport) is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering process ...

and many other.

Features

Some of the features of MFEM include * Arbitrary high order finite elements with curved boundaries. * H¹, H(curl) and H(div) conforming, discontinuous (L₂), and

NURBS Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analy ...

finite element spaces. * Local

mesh refinement In numerical analysis, adaptive mesh refinement (AMR) is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. When solutions ...

, both conforming (

simplex In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...

meshes) and non-conforming (

quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...

hexahedral A hexahedron (: hexahedra or hexahedrons) or sexahedron (: sexahedra or sexahedrons) is any polyhedron with six faces. A cube, for example, is a regular hexahedron with all its faces square, and three squares around each vertex. There are seven ...

meshes). * Highly scalable

MPI MPI or Mpi may refer to: Science and technology Biology and medicine * Magnetic particle imaging, a tomographic technique * Myocardial perfusion imaging, a medical procedure that illustrates heart function * Mannose phosphate isomerase, an enzyme ...

-based parallelism and

GPU A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal ...

acceleration. * Wide variety of finite element discretization approaches, including Galerkin, discontinuous Galerkin, mixed, high-order and

isogeometric analysis Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. Currently, it is necessary to convert data between CAD and FEA packages to ana ...

methods. * Tight integration with the Hypre parallel linear algebra library. * Many built-in solvers and interfaces to external libraries such as PETSc, SuiteSparse,

Gmsh Gmsh is a finite-element mesh generator developed by Christophe Geuzaine and Jean-François Remacle. Released under the GNU General Public License, Gmsh is free software. Gmsh contains 4 modules: for geometry description, meshing, solving and p ...

, etc. *Accurate and flexible visualization with

VisIt Visit refer as go to see and spend time with socially. Visit may refer to: *State visit, a formal visit by a head of state to a foreign country *Conjugal visit, in which a prisoner is permitted to spend several hours or days in private with a visit ...

and

ParaView ParaView is an open-source multiple-platform application for interactive, scientific visualization. It has a client–server architecture to facilitate remote visualization of datasets, and generates level of detail (LOD) models to maintain in ...

. * Lightweight design and conservative use of C++ templating. * Documentation in the form of examples and mini-applications.

References

External links

* {{DEFAULTSORT:MFEM Project Scientific simulation software C++ numerical libraries Finite element method Finite element software Cross-platform free software Free software for Linux Free software for Windows Free software for macOS Software using the BSD license

Features

See also

References

External links