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Repository files navigation is an efficient, matrix-free finite-element library for solving partial differential equations in two to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal.II to create low-dimensional meshes and to operate on them individually. We combine these meshes via a tensor product on the fly and provide new special-purpose highly optimized matrix-free functions.

The library is freely available under the LGPL 3.0 license. If you use, please cite the release paper:

  title       = { An efficient, matrix-free finite-element library for
                 high-dimensional partial differential equations},
  author      = {Munch, Peter and Kormann, Katharina and Kronbichler, Martin},
  year        = {2021},
  institution = {accepted for publication in ACM Transactions on Mathematical Software}

The paper has been accepted; the preprint can be found online on arXiv (with the corrsponding and deal.II branches). The full list of publications using or related to can be found here.

We provide following useful resources:

  • a WIKI (see here)
  • an online Doxygen documentation (see here)
  • example programs presenting features of in the folder examples

For getting started, check out the following site.

Continuous integration status:

Doxygen Indent GitHub CI


The principal developers are (in alphabetical order):


The library is dedicated explicitly only to algorithms for high-dimensional finite-element methods. However, the close ties to deal.II enable us to use general-purpose FEM features from there. In particular, we are contributing to the deal.II project functionalities that have been developed with high-dimensions in mind, but are also useful for lower dimensions.

Via deal.II, we optionally also have access to other third-party libraries like Trilinos, p4est, Metis, or PETSc. Furthermore, a large variety of efficient off-the-shelf matrix-free physical solvers from the deal.II-based ExaDG project could be used to solve low-dimensional sub-problems and coupled to modules provided by

The library is a community development project. Contributions by new developers are more than welcome! In the case of questions, please contact any of the principal developers listed above.

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