list of finite element software packages

| Proprietary

| BSD

| LGPL

| LGPL

| GNU (L)GPL

| LGPL

| GNU GPL\LGPL

| Proprietary

| Yes

| No

| No

| No

| Yes, partial functionality

| Yes

| Postprocessing only

| Matlab and Octave GUI

| 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

| extensive tutorials, video lectures, Doxygen

| 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

| intervals (1D); triangles, quadrilaterals (2D and 3D boundaries); tetrahedra, pyramids, prisms, hexahedra (3d)

| segments, triangles, quadrilaterals, tetrahedra, hexahedra, prisms, pyramids

| intervals, triangles, tetrahedra, quads, hexes, prisms, some 4D elements, easily extensible.

| intervals (1D); triangles, quadrilaterals (2D and 3D boundaries); tetrahedra, pyramids, prisms, 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

| 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)

|

| Built-in

| meshing miniapps and target-matrix mesh optimization

| experimental in any dimension + predefined shapes + Extrusion.

| external mesh generators via mesh exchange files, internally generated meshes for simple shapes, internal interfaces to gmsh

| 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

| 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-adaptivity for both continuous and discontinuous finite elements

| h-refinement for selected equations

| h, p, mached hp, singular hp

| Only h

|

| STL, PLY, NASTRAN, 3MF, VRML (import only), native format

| VTK, Gmsh, CUBIT, NETGEN, TrueGrid, and MFEM format

| gmsh, GiD, Ansys

| DB, XDA, GMSH, Tecplot, UNV, UCD, Abaqus, VTK, Assimp, ExodusII

|

| ExodusII, Nemesis, Abaqus, Ensight, Gmsh, GMV, OFF, TecPlot TetGen, etc.

| XDMF (and FEniCS XML)

| FeatFlow, FEniCS XML, GiD, Gmsh, GMV, Triangle

| Avoids inverted and degenerated elements; various mesh quality measures

|

| ?

|

|

|

| intersections (collision testing)

|

| STEP, IGES, others.

|

| No

| IGES, STEP (with OpenCascade wrapper)

| Limited support via OpenCASCADE in ElmerGUI

|

|

|

| Merge, copy, refine; convert; boundary layers; extrude, revolve, sweep, loft for 3D geometries

|

| Extrude, rotate, translation, refine

| Extrude, rotate, translation, refine

|

| Merge, join, extrude, modular mesh modifier system

|

| Merge, join, extrude, and revolve operations

|

| METIS and space-filling curve partitioning

| Yes (METIS)

| yes, shared (METIS/Parmetis/Zoltan) and distributed (p4est)

| 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)

|

| Yes

| Yes

| Yes

| Yes (up to 310k processes)

| Yes

| Yes

| Yes

|

| Supports multithreading

| Using OpenMP, RAJA, or OCCA backends

|

| Threading Build Blocks

| threadsafe, some modules threaded and vectorized.

| Yes

|

|

| Yes

| Yes

| Yes

| Yes (vectorization only)

| Yes, partially

| Yes

|

|

| No

| Through OCCA backends

| No

| No

| No

|

|

|

| No

| Yes

| No

| since 9.1, see step-64 for matrix-free GPU+MPI example

| Preliminary API for sparse linear algebra

|

|

|

| 0D, 1D, 2D, 3D (can coexist)

| 1D/2D/3D

| Any, possibility to mix and couple problem of different dimension

| 1/2/3D

| 1D/2D/3D (dimensions may coexist)

| 1/2/3D

| 1/2/3D

| 1/2/3D

| 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, 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

|

| 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 polynomials), 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.

|

|

| 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 predefined. 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.

|

| implicit-euler explicit-euler crank-nicolson bdf2 explicit-midpoint dirk explicit-tvd-rk-2 newmark-beta

|

| BE, CN, and Fractional-Step-Theta schemes

| 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

|

| The tutorial provides examples for many different equations

| 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

|

|

| Yes

|

|

|

| Yes

| Yes

| 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/.vtu and many others)

| 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

| Text and unstructured VTK-file for data. BMP, PNG, GIF, TIFF, JPEG, glTF, Windows clipboard, Microsoft PowerPoint (for images). GIF, Flash, AVI, WebM (for animations). 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

| Yes

|

| No

| Yes

| Existing but without multipole acceleration (not usable for large problems)

|

| No

|

|

|

| 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

|

| 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

| 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

| 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)

| Built-in Krylov solvers, Krylov and multigrid solvers from external libraries

| LASPack serial, PETSc parallel

|

| Matlab/Octave built-in

| 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

| Built-in preconditioners (ILU, diagonal, vanka, block) and

| LASPack serial, PETSc parallel, algebraic multigrid (via Hypre)

|

| Matlab/Octave built-in

| Yes

| Yes

| No

| Yes

| Experimental implementation

|

|

|

|

| Yes

| No

| Yes

|

|

|

|

|

| Yes

| No

| Yes

|

|

|

|

| Primarily C++ and Java

| C++

| C++

| C++

| Fortran (2008 standard)

| C++

| C++

| Matlab / Octave

| Full API for Java and Matlab (the latter via add-on product)

| PyMFEM (Python)

| Python, Scilab or Matlab

| Python bindings to some functionality

|

|

| Python

|

| 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.

|

|

|

|

|

| Yes

| Yes

| Yes

|

|

|

|

|

| Windows, Linux, macOS

| Yes, via OpenHPC. Also available as part of Spack, xSDK, E4S, FASTMath, RADIUSS and CEED.

| Linux (Debian/Ubuntu)

| Linux, Windows, Mac

| Windows, Linux (launchpad: Debian/Ubuntu), Mac (homebrew) (all with MPI)

|

| Linux (Debian\Ubuntu), Mac

| Windows, Linux, Mac

|

| Modular Finite Element Methods

|

|

| Elmer finite element software

|

|

|

|

| Comprehensive unit and regression tests. Continuous integration through Travis CI

|

| 13,000+ tests

| More than 700 consistency tests ensuring backward compatibility

| 4300+ tests, Testing as a service for derived applications

|

|

| 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

| Yes

| Yes

|

| Yes

|

| Forward-mode for Jacobian computation, symbolic differentiation capabilities

|

|

| Yes, full custom and predefined multiphysics couplings between all kinds of physics

| Arbitrary multiphysics couplings are supported

|

| Yes

|

| Arbitrary multiphysics couplings are supported

|

| Arbitrary multiphysics couplings are supported

| With the Optimization Module add-on: Coordinate 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.

|

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| Yes

|

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| Yes

| Yes

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|

|

| Yes

| Yes

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