This is a list of software packages that implement the finite element method for solving partial differential equations.
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|Agros2D||Multiplatform open source application for the solution of physical problems based on the Hermes library||University of West Bohemia||3.2||2014-03-03||GNU GPL||Free||Linux, Windows|
|CalculiX||It is an Open Source FEA project. The solver uses a partially compatible ABAQUS file format. The pre/post-processor generates input data for many FEA and CFD applications||Guido Dhondt, Klaus Wittig||2.14||2018-04-27||GNU GPL||Free||Linux, Windows|
|DIANA FEA||General purpose finite element package utilised by civil, structural and geotechnical engineers.||DIANA FEA BV, The Netherlands||10.1||2016-11-14||Paid||Windows, Linux|
|deal.II||Comprehensive set of tools for finite element codes, scaling from laptops to clusters with 10,000+ cores. Written in C++.||Wolfgang Bangerth, Timo Heister, Guido Kanschat, Matthias Maier et al.||9.0||2018-05-12||LGPL||Free||Linux, Unix, Mac OS X, Windows|
|DUNE||Distributed and Unified Numerics Environment, written in C++||DUNE Developer team||2.4.1||2016-02-29||GPL Version 2 with Run-Time Exception||Free||Linux, Unix, Mac OS X|
|Elmer||Open source multiphysical simulation software developed by Finnish Ministry of Education's CSC, written primarily in Fortran (written in Fortran90, C and C++)||CSC||8.2||2016-03-15||GPL||Free||Linux, Mac OS X, Windows|
|FEBio||Finite Elements for Biomechanics||University of Utah (MRL), Columbia University (MBL)||2.7||April, 2018||Custom||Free||Linux, Mac OS X, Windows|
|FEniCS Project||Software package developed by American and European researchers with the goal to enable automated solution of differential equations||FEniCS Team||1.6.0||2015-07-29||LGPL (Core) & GPL/LGPL (Non-Core)||Free||Linux, Unix, Mac OS X, Windows|
|FEATool Multiphysics||MATLAB FEM and PDE multiphysics simulation toolbox||Precise Simulation||1.10||2019-05-17||Free for personal use||Windows, Mac OS X, Linux, Unix|
|FreeFEM||FreeFEM is a free and open-source parallel FEA software for multiphysics simulations. The problems are defined in terms of their variational formulation and can be easily implemented using FreeFEM language. Written in C++.||Sorbonne University and Jacques-Louis Lions Laboratory||4.2.1||2019-06-06||LGPL||Free||Linux, MacOS, Windows, Solaris|
|GOMA||GOMA is an open-source, parallel, and scalable multiphysics software package for modeling and simulation of real-life physical processes, with a basis in computational fluid dynamics for problems with evolving geometry.||Sandia National Laboratories, University of New Mexico||6.1||Aug 28, 2015||GPL Version 2||Free||Linux|
|GetFEM++||A generic finite element library written in C++ with interfaces for Python, Matlab and Scilab. It focuses on modeling of contact mechanics and discontinuities (e.g. cracks).||Yves Renard, Julien Pommier||5.0||2015-07||LGPL||Free||Unix, Mac OS X, Windows|
|Hermes Project||Modular C/C++ library for rapid development of space- and space-time adaptive hp-FEM solvers||hp-FEM group||3.0||2014-03-01||LGPL||Free||Linux, Unix, Mac OS X, Windows|
|Mathematica||General purpose computation software.||Wolfram Research||12.1.1 (June 17, 2020; 27 days ago) [±]||Regularly||Proprietary||Linux, Mac OS X, Windows, Raspbian, Online service.|
|MATLAB Partial Differential Equation Toolbox||MATLAB Toolbox for solving structural, thermal, electromagnetics, and other general PDEs||MathWorks||3.3 (R2019b)||2019-09-11||Linux, Mac OS X, Windows|
|MFEM||MFEM is a free, lightweight, scalable C++ library for finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretizations, and emphasis on usability, generality, and high-performance computing efficiency.||MFEM team||4.1||2020-03-10||BSD||Free||Linux, Unix, Mac OS X, Windows|
|MoFEM JosePH||Mesh Oriented hp-FE code, written in C++||University of Glasgow||0.6.8||2017-11-16||LGPL||Free||Unix, Mac OS X|
|MOOSE||Object Oriented FE framework, written in C++||Idaho National Laboratory||regularly||LGPL||Free||Unix, Mac OS X|
|OOFEM||Object Oriented Finite EleMent solver, written in C++||Bořek Patzák||2.4||2016-02-15||GPL Version 2||Free||Unix, Windows|
|OpenSees||Open System for Earthquake Engineering Simulation||Non Commercial||Free||Unix, Linux, Windows|
|SESAM (FEM)||Software suite for structural and hydrodynamic analysis of ships and offshore structures||DNV GL||regularly||Proprietary, SaaS||Windows, Web browser|
|Range Software||Multiphysics Finite Element Analysis Software||Tomáš Šoltys||3.0||2018-04-30||GPL||Free||Linux, Windows|
|Z88/Z88Aurora||Freeware finite element package; The present version Z88Aurora V4 offers, in addition to static strength analysis modules such as non-linear strength calculations (large displacements), simulations with non-linear materials, natural frequency, static thermal analysis and a contact module.||Frank Rieg||Z88 V15, Z88Aurora V5||2017-07-17, 2019-04-01||GNU GPL, Custom||Free||Linux, Windows, Mac OS X|
|Abaqus||Advanced Franco-USA software from SIMULIA, owned by Dassault Systemes||Abaqus Inc.||2019||2019-12||Linux, Windows|
|CONSELF||CAE simulation from your browser||CONSELF SRL||2.9||2015-10||SaaS||Freemium||Web browser|
|FreeCAD||Parametric 3D modeler with a FEM workbench allowing it to use external solvers like CalculiX, Z88, Elmer, and OpenFoam||FreeCAD Team||0.18||12 March 2019||LGPL 2||Free||Linux, Windows, Mac OS X|
|ADINA||Finite element software for structural, fluid, heat transfer, electromagnetic, and multiphysics problems, including fluid-structure interaction and thermo-mechanical coupling||Adina R&D|
|Advance Design||BIM software for FEM structural analysis, including international design eurocodes||GRAITEC||2014||2013-09|
|Autodesk Simulation||Finite Element software of Autodesk||Autodesk||Windows|
|ANSYS||US-based and -developed full CAE software package||Ansys Inc.||19.2||2018-09-18||Free student version available, up to 32,000 nodes/elements||Windows, Linux|
|COMSOL Multiphysics||COMSOL Multiphysics Finite Element Analysis Software (formerly FEMLAB)||COMSOL Inc.||5.5||2019-11-14||Linux, Mac OS X, Windows, Web browser|
|CosmosWorks||Part of SolidWorks||Dassault Systèmes SolidWorks Corp.||Windows|
|Quickfield||EM, Heat Transfer and Stress Analysis ||Tera Analysis Ltd||6.4 ||2020-04-17||Free Student Edition available||Windows|
|LS-DYNA||Best known for explicit dynamics / crash analysis||LSTC - Livermore Software Technology Corporation||R8.0||2015-03||Linux, Windows|
|Nastran||Originally developed for NASA, now available commercially from several software companies||MSC NASTRAN, Siemens PLM NX Nastran||2014||2014||Linux, Mac OS X, Windows|
|RFEM||3D finite element analysis software||Dlubal Software||5.06||2016-02||Free student license available||Windows|
|SimScale||German 100% web-based CAE platform||SimScale GmbH||14||2013-07||SaaS||Free community version available||Web browser|
|VisualFEA||Finite element software for structural, geotechnical, heat transfer and seepage analysis||Intuition Software||5.11||2016-01||Proprietary software||Free educational version available||Mac OS X, Windows|
|JCMsuite||Finite element software for the analysis of electromagnetic waves, elasticity and heat conduction||JCMwave GmbH||3.6.1||2017-01-27||Linux, Windows|
|JMAG||2D and 3D finite element analysis software for electromagnetic field, thermal, structural||JSOL||18.1||2019-06||Education pack available||Linux, Windows, Web browser|
|StressCheck||Finite element analysis software based on p-FEM with a focus on solid mechanics applications||ESRD, Inc.||10.4||2018-04||Student version available (limited to 15k DOF)||Windows|
|SDC Verifier||An extension for Ansys Mechanical, Femap and Simcenter with out of the box predefined standards on fatigue, stiffener and plate buckling, beam member checks, joint checks and weld. Such as AISC 360-10, API 2A RP, ISO 19902, Norsok N004, DIN15018, Eurocode 3, FEM 1.001, ABS 2004, ABS 2014, DNV RP-C201 2010, DNV CN30/1995, FKM etc.||SDC Verifier||5.3.1||2020-03||Student version available||Windows|
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This table is contributed by a FEA-compare project, which provides an alternative view of this table with the first row and Feature column being fixed for ease of table exploration.
|Feature||COMSOL Multiphysics||MFEM||GetFEM++||deal.II||Range Software||Elmer||MOOSE||FEniCS Project||FEATool Multiphysics|
|license:||Proprietary||BSD||LGPL||LGPL||GPL||GNU (L)GPL||LGPL||GNU GPLLGPL||Proprietary|
|GUI:||Yes||No||No||No||Yes||Yes, partial functionality||Yes||Postprocessing only||Matlab and Octave GUI|
|Documentation:||User guides, reference manuals, API documentation, application libraries with solved examples, online tutorials||examples, miniapps, Doxygen, online documentation||User doc, tutorials, demos, developer's guide||tutorials, video lectures, Doxygen||user manual, tutorials||ElmerSolver Manual, Elmer Models Manual, ElmerGUI Tutorials, etc. LaTeX documentation available in PDFs||Doxygen, Markdown, example codes, test inputs||Tutorial, demos, book||Online FEATool documentation, tutorials, and model examples|
|mesh elements:||Intervals (1D); triangles, quadrilaterals (2D and 3D boundaries); tetrahedra, pyramids, prisms, hexahedra (3d)||segments, triangles, quadrilaterals, tetrahedra, hexahedra, prisms||intervals, triangles, tetrahedra, quads, hexes, prisms, some 4D elements, easily extensible.||intervals (1d), quads (2d), and hexes (3d) only||points(0d), segments (1d), triangles, quadrilaterals (2d), tetrahedra, hexahedra (3d)||intervals (1d), triangles, quadrilaterals (2d), tetrahedra, pyramids, wedges, hexahedra (3d)||Tria, Quad, Tetra, Prism, etc.||intervals, triangles, tetrahedra (quads, hexes - work in progress)||intervals, triangles, tetrahedra, quads, hexes|
|mesh high-order mapping:||Any? Second-order is the default for most cases.||arbitrary-order meshes and NURBS meshes||any order||Yes, for Lagrange elements||(Any - work in progress)|
|mesh generation:||Built-in||meshing miniapps and target-matrix mesh optimization||Experimental in any dimension + predefined shapes + Extrusion.||external+predefined shapes||Yes (TetGen)||Limited own meshing capabilities with ElmerGrid and netgen/tetgen APIs. Internal extrusion and mesh multiplication on parallel level.||Built-in||Yes, Constructive Solid Geometry (CSG) supported via mshr (CGAL and Tetgen used as backends)||Integrated DistMesh, Gmsh, and Triangle GUI and CLI interfaces|
|mesh adaptive-refinement:||Yes, full adaptive mesh refinement (h-refinement); no p-refinement but several higher-order elements are included. Mesh adaptation on the whole or parts of the geometry, for stationary, eigenvalue, and time-dependent simulations and by rebuilding the entire mesh or refining chosen mesh elements.||conforming and non-conforming adaptive refinement for tensor product and simplex meshes||Only h||h, p, and hp for CG and DG||h-refinement for selected equations||h, p, mached hp, singular hp||Only h|
|mesh inputoutput:||STL, PLY, NASTRAN, 3MF, VRML (import only), native format||VTK, Gmsh, CUBIT, NETGEN, TrueGrid, and MFEM format||gmsh, GiD, Ansys||rbm, stl||ExodusII, Nemesis, Abaqus, Ensight, Gmsh, GMV, OFF, TecPlot TetGen, etc.||XDMF (and FEniCS XML)||FeatFlow, FEniCS XML, GiD, Gmsh, GMV, Triangle|
|mesh check:||Avoids inverted and degenerated elements; various mesh quality measures||?||limited features (double nodes, degenerated elements, intersected elements)||intersections (collision testing)|
|CAD files support:||STEP, IGES, others.||No||IGES, STEP (with OpenCascade wrapper)||Yes (stl)||Limited support via OpenCASCADE in ElmerGUI|
|mesh operation:||Merge, copy, refine; convert; boundary layers; extrude, revolve, sweep, loft for 3D geometies||Extrude, rotate, translation, refine||Extrude, rotate, translation, refine||Merge, join, extrude, modular mesh modifier system||Merge, join, extrude, and revolve operations|
|automatic mesh partitioning:||METIS and space-filling curve partitioning||Yes (METIS)||yes, shared (METIS/Parmetis) and distributed (p4est)||No||partitioning with ElmerGrid using Metis or geometric division, internal partitioning in ElmerSolver using Zoltan||Metis, Parmetis, Hilbert (shared and distributed meshes)||Yes (ParMETIS and SCOTCH)|
|MPI:||Yes||Yes||Yes||Yes (up to 147k processes)||No||Yes||Yes||Yes|
|threads:||Supports multithreading||Using OpenMP, RAJA, or OCCA backends||Threading Build Blocks||Yes||threadsafe, some modules threaded and vectorized.||Yes|
|OpenMP:||Yes||Yes||Yes||Yes (vectorization only)||Yes||Yes, partially||Yes|
|OpenCL:||No||Through OCCA backends||No||No||No||No|
|CUDA:||No||Yes||No||since 9.1, see step-64 for matrix-free GPU+MPI example||No||Preliminary API for sparse linear algebra|
|Dimension:||0D, 1D, 2D, 3D (can coexist)||1D/2D/3D||Any, possibility to mix and couple problem of different dimension||1/2/3D||0D/1D/2D/3D (dimensions may coexist)||1D/2D/3D (dimensions may coexist)||1/2/3D||1/2/3D||1/2/3D|
|FE:||Lagrange (order 1-7), Hermite (order 3-7), discontinuous Lagrange (order 0-7), bubble, Gauss point, serendipity, Nedelec||Arbitrary-order Lagrange elements (continuous and discontinuous), Bernstein basis, Nedelec and Raviart-Thomas elements, support for NURBS spaces (IGA)||Continuous and discontinuous Lagrange, Hermite, Argyris, Morley, Nedelec, Raviart-Thomas, composite elements (HCT, FVS), Hierarchical elements, Xfem, easily extensible.||Lagrange elements of any order, continuous and discontinuous; Nedelec and Raviart-Thomas elements of any order; BDM and Bernstein; elements composed of other elements.||Lagrange elements||Lagrange elements, p-elements up to 10th order, Hcurl conforming elements (linear and quadratic) for||Lagrange, Hierarchic, Discontinuous Monomials, Nedelec||Lagrange, BDM, RT, Nedelic, Crouzeix-Raviart, all simplex elements in the Periodic Table (femtable.org), any||Lagrange (1st-5th order), Crouzeix-Raviart, Hermite|
|Quadrature:||Gauss-Legendre, Gauss-Lobatto, and uniform quadrature rules.||Gauss-Legendre, Gauss-Lobatto, midpoint, trapezoidal, Simpson, Milne and Weddle (closed Newton-Cotes for 4 and 7 order polinomials), Gauss quadrature with logarithmic or 1/R weighting function, Telles quadrature of arbitrary order.||Gauss-Legendre (1D and tensor product rules in 2D and 3D) tabulated up to 44th-order to high precision, best available rules for triangles and tetrahedra to very high order, best available monomial rules for quadrilaterals and hexahedra.|
|Transient problems:||Yes, BDF, Runge-Kutta (RK34, Cash-Karp 5, Dormand-Prince 5), and generalized alpha time stepping||Runge-Kutta, SSP, SDIRK, Adams-Bashforth, Adams-Moulton, Symplectic Integration Algorithm, Newmark method, Generalized-alpha method||Any user implemented and/or from a set of predifined. Explicit methods: forward Euler, 3rd and 4th order Runge-Kutta. Implicit methods: backward Euler, implicit Midpoint, Crank-Nicolson, SDIRK. Embedded explicit methods: Heun-Euler, Bogacki-Shampine, Dopri, Fehlberg, Cash-Karp.||Yes||implicit-euler explicit-euler crank-nicolson bdf2 explicit-midpoint dirk explicit-tvd-rk-2 newmark-beta||BE, CN, and Fractional-Step-Theta schemes|
|Predifined equations:||Incompressible Navier-Stokes, heat transfer, convection-diffusion-reaction, linear elasticity, electromagnetics, pressure acoustics, Darcy’s law, and support for custom PDE equations||Miniapps and examples for Laplace, elasticity, Maxwell, Darcy, advection, Euler, Helmholtz, and others||Laplace?||Yes (Incompressible Navier-Stokes, Heat transfer (convection-conduction-radiation), Stress analysis, Soft body dynamics, Modal analysis, Electrostatics, Magnetostatics )||Around 50 predefined solvers||Phase Field, Solid Mechanics, Navier-Stokes, Porous Flow, Level Set, Chemical Reactions, Heat Conduction, support for custom PDEs||Incompressible Navier-Stokes, Heat transfer, convection-diffusion-reaction, linear elasticity, electromagnetics, Darcy's, Brinkman equations, and support for custom PDE equations|
|Visualization:||Built-in||In situ visualization with GLVis. Export to VisIt and ParaView.||External or with the Scilab/Matlab/Python interface. Possibility to perform complex slices.||External (export to *.vtk and many others)||GUI (built-in)||ElmerGUI comes VTK based visualization tool (but Paraview is recommended)||Yes, VTK-based GUI, Python visualizatuion library||Buil-in simple plotting + External||Built-in with optional Plotly and GMV export|
|Output format:||Text and unstructured VTK-file for data.BMP,PNG, GIF, TIFF, JPEG, glTF, Windows clipboard, Microsoft PowerPoint (for images). GIF, Flash, AVI, WebM (for animatios). Touchstone data (for networks).||VisIt, ParaView (VTU), GLVis format||vtk, gmsh, OpenDX.||*.dx *.ucd *.gnuplot *.povray *.eps *.gmv *.tecplot *.tecplot_binary *.vtk *.vtu *.svg *.hdf5||Several output formats (VTU, gmsh,..)||ExodusII, Xdr, etc.||VTK(.pvd, .vtu) and XDMF/HDF5||GMV and Plotly|
|Boundary elements solver:||Yes||No||Yes||Existing but without multipole acceleration (not usable for large problems)||No|
|Use multiple meshes:||Yes including different dimensions and taking account of any transformation.||Yes, autorefined from same initial mesh for each variable of a coupled problem||Continuity of non-conforming interfaces ensured by mortar finite elements||Yes, including non-matching meshes|
|Used libs:||MUMPS, PARDISO, SPOOLES; ARPACK, BLAS, BLIS, Intel MKL, LAPACK||Built-in and integrated with hypre. Optional integrations with PETSc, Ginkgo, SuperLU, Suite Sparse, libCEED, and more||SuperLU, MUMPS, Built-in.||Built-in + Trilinos, PETSc, and SLEPc||No||Built-in, Hypre, Trilinos, umfpack, MUMPS, Pardiso, etc. (optional)||PETSc, Trilinos, LASPack, SLEPc||PETSc, Trilinos/TPetra, Eigen.||Matlab/Octave built-in (Umfpack), supports integration with the FEniCS and FeatFlow solvers|
|Iterative matrix solvers:||GMRES, FGMRES, BiCGStab, conjugate gradients, TFQMR, or any precoditioner. Algebraic and geometric multigrid. Domain decomponsition (Schwarz, Schur)||Krylov methods (CG, MINRES, GMRES, BiCGStab)||All Krylov||All Krylov (CG, Minres, GMRES, BiCGStab, QMRS)||GMRES, CG||Built-in Krylov solvers, Krylov and multigrid solvers from external libraries||LASPack serial, PETSc parallel||Matlab/Octave built-in|
|Preconditioners:||Direct preconditioner, Krylov, SOR, SSOR, SORU, SOR line, SOR gauge, SOR vector, Jacobi, incomplete and hierarchical LU, SAI, SCGS, Vanka, AMS||Algebraic, Geometric, and p-multigrid. Block ILU preconditioning. Support for hypre's AMS and ADS preconditioners for H(curl) and H(div).||Basic ones (ILU, ILUT)||Many, including algebraic multigrid (via Hypre and ML) and geometric multigrid||ILU, Jacobi||Built-in preconditioners (ILU, diagonal, vanka, block) and||LASPack serial, PETSc parallel, algebraic multigrid (via Hypre)||Matlab/Octave built-in|
|matrix-free save memory:||Yes||No||Yes||No|
|Native language:||Primarily C++ and Java||C++||C++||C++||C++||Fortran (2008 standard)||C++||C++||Matlab / Octave|
|Bindings to language:||Full API for Java and Matlab (the latter via add-on product)||PyMFEM||Python, Scilab or Matlab||No||No||Python|
|Predefined equations:||Yes, many predefined physics and multiphysics interfaces in COMSOL Multiphysics and its add-ons.||A large number of Bilinear and Linear forms||Model bricks: Laplace, linear and nonlinear elasticity, Helmholtz, plasticity, Mindlin and K.L. plates, boundary conditions including contact with friction.|
|Coupled nonlinear problems:||Yes||Yes||Yes|
|Binary:||Windows, Linux, macOS||Yes, via OpenHPC. Also available as part of Spack, xSDK, E4S, FASTMath, RADIUSS and CEED.||Linux (Debian/Ubuntu)||Linux, Windows (work in progress), Mac||Windows, Linux (launchpad: Debian/Ubuntu), Mac (homebrew) (all with MPI)||Linux (DebianUbuntu), Mac||Windows, Linux, Mac|
|fullname:||Elmer finite element software|
|Testing:||Comprehensive unit and regression tests. Continuous integration through Travis CI||3500+ tests||More than 700 consistency tests ensuring backward compatibility||4300+ tests, Testing as a service for derived applications|
|scripting:||Full API for Java and, through add-on product, Matlab||Runtime parsed mathematical expression in input files||Fully scriptable in as m-file Matlab scripts and the GUI supports exporting models in script format|
|automatic differentiation:||Yes||Forward-mode for Jacobian computation, symbolic differentiation capabilities|
|multiphysics:||Yes, full custom and predefined multiphysics couplings between all kinds of physics||Arbitrary multiphysics couplings are supported||Arbitrary multiphysics couplings are supported||Arbitrary multiphysics couplings are supported|
|Optimization Solvers:||With the Optimization Module add-on: Coorinate search, Nelder-Mead, Monte Carlo, BOBYQA, COBYLA, SNOPT, MMA, Levenberg-Marquardt||Integration with HiOp. Built-in SLBQP optimizer||Support for TAO- and nlopt-based constrained optimization solvers incorporating gradient and Hessian information.|
|Symbolic derivation of the tangent system for nonlinear problems:||Yes|
|Support for fictitious domain methods:||Yes|
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- ^'Sorbonne Université Lettres, Médecine, Sciences'. www.sorbonne-universite.fr. Retrieved 2018-11-30.
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- ^'Student Products - Free Simulation Software'. Ansys.com. Retrieved 2017-05-28.
- ^'NX Nastran: Siemens PLM Software'. Plm.automation.siemens.com. Retrieved 2017-05-28.
- ^'Free Student License Dlubal Software'. Dlubal.com. Retrieved 2017-05-28.
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- ^GitHub For ease of maintaince of this table, please, first consider to contribute changes directly to the project instead of editing the table below, however, direct wiki edits are also valid and will be backported