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Developer(s)Wolfgang Bangerth, Timo Heister, Guido Kanschat, Matthias Maier et al.
Initial release2000; 22 years ago (2000)
Stable release
9.4.0 / 23 June 2022; 9 days ago (2022-06-23)
Written inC++
Operating systemLinux, macOS, Microsoft Windows
TypeFinite element analysis
LicenseGNU Lesser General Public License 2.1 or later

deal.II is a free, open-source library to solve partial differential equations using the finite element method.[1][2]  The current release is version 9.2.0, released in May 2020. It is one of the most widely used finite element libraries, and provides comprehensive support for all aspects of the solution of partial differential equations. The founding authors of the project — Wolfgang Bangerth, Ralf Hartmann, and Guido Kanschat — won the 2007 J. H. Wilkinson Prize for Numerical Software for deal.II.[3] However, it is today a worldwide project with around a dozen "Principal Developers", to which over the years several hundred people have contributed substantial pieces of code or documentation.


The library features

  • dimension independent programming using C++ templates on locally adapted meshes,
  • a large collection of different finite elements of any order: continuous and discontinuous Lagrange elements, Nedelec elements, Raviart-Thomas elements, and combinations,
  • parallelization using multithreading through TBB and massively parallel using MPI. deal.II has been shown to scale to at least 16,000 processors[4] and has been used in applications on up to 300,000 processor cores.
  • multigrid method with local smoothing on adaptively refined meshes[5][6]
  • hp-FEM
  • extensive documentation and tutorial programs,
  • interfaces to several libraries including Gmsh, PETSc, Trilinos, METIS, VTK, p4est, BLAS, LAPACK, HDF5, NetCDF, and Open Cascade Technology.

History and Impact[edit]

The software started from work at the Numerical Methods Group at Heidelberg University in Germany in 1998. The first public release was version 3.0.0 in 2000. Since then deal.II has gotten contributions from several hundred authors[7] and has been used in more than a thousand research publications.[8]

The primary maintainers, coordinating the worldwide development of the library, are today located at Colorado State University, Clemson University, Heidelberg University, Texas A&M University, Oak Ridge National Laboratory and a number of other institutions.[9] It is developed as a worldwide community of contributors through GitHub[10] that incorporates several hundred changes by dozens of authors every month.

See also[edit]


  1. ^ Bangerth, W; Hartmann, R; Kanschat, G. (2007). "deal.II - a general purpose object oriented finite element library". ACM Trans. Math. Softw. 33.
  2. ^ "deal.II Homepage". deal.II Homepage. Archived from the original on 8 June 2012. Retrieved 5 August 2012.
  3. ^ "Developers of Finite Element Library Receive Wilkinson Prize for Numerical Software". Retrieved 5 August 2012.
  4. ^ Bangerth, W.; Burstedde, C.; Heister, T.; Kronbichler, M. (2011). "Algorithms and Data Structures for Massively Parallel Generic Finite Element Codes". ACM Trans. Math. Softw. 38.
  5. ^ Janssen, B.; Kanschat, G. (2011). "Adaptive multilevel methods with local smoothing for H1- and Hcurl-conforming high order finite element methods". SIAM J. Sci. Comput. 33 (4).
  6. ^ Kanschat, G. (2004). "Multi-level methods for discontinuous Galerkin FEM on locally refined meshes". Computers & Structures. 82.
  7. ^ "deal.II Authors". Retrieved 14 June 2019.
  8. ^ "List of Publications". Retrieved 14 June 2019.
  9. ^ "deal.II author list". Retrieved 20 January 2020.
  10. ^ "deal.II github page". Retrieved 14 June 2019.

External links[edit]