Description

This folder contains the sources of the dune-dpg library, which allows to solve Partial Differential Equations with Discontinuous Petrov-Galerkin finite elements. It is built upon the finite element package Dune. For further information on the dune-dpg library, we refer to the paper The dune-dpg library for solving PDEs with Discontinuous Petrov-Galerkin finite elements by F. Gruber, A. Klewinghaus and O. Mula.

For build instruction see the accompanying INSTALL.md file. See doc/experiments.md for explanations on how to run the example programs bundled with dune-dpg. If you are interested in an API documentation of dune-dpg, see the instructions in section [Generating API documentation with Doxygen] (INSTALL.md#generating-api-documentation-with-doxygen) in the INSTALL.md file.

Required Software and Libraries

Additional to the Dune libraries, you'll need the following programs and libraries installed on your system:

• Programs:
  • a fully C++17-compatible compiler and standard library (e.g. GCC >= 9)
  • cmake >= 3.1
• Libraries:
  • Boost >= 1.63 (Boost versions as low as 1.61, which introduced Boost::Hana, might work but have not been tested.)
  • Eigen >= 3.2 (http://eigen.tuxfamily.org)
  • UMFPACK (which is part of Suitesparse, www.suitesparse.com)
  • DUNE core libraries 2.8 including the staging modules dune-typetree and dune-functions (https://dune-project.org/releases/2.8.0/)
  • A grid manager. Our examples use dune-uggrid (https://www.dune-project.org/modules/dune-uggrid/) but one could also use other managers, e.g., ALBERTA or YASPgrid. (https://dune-project.org/groups/grid/)
  • for the plot_solution and the ASTI programs, you will also need dune-subgrid (>= 2.7) (https://gitlab.dune-project.org/extensions/dune-subgrid)

Instructions on how to build dune-dpg can be found in INSTALL.md.

Descriptions of our example programs and how to use them to reproduce published results can be found in the file doc/experiments.md.

Citing dune-dpg

If you use dune-dpg in your own scientific work, please consider citing our overview paper (PDF). Here's the BibTeX data for the paper:

@Article{GKM2017,
  author         = {Felix Gruber and Angela Klewinghaus and Olga Mula},
  title          = {The {DUNE-DPG} Library for Solving {PDE}s with {Discontinuous Petrov--Galerkin} Finite Elements},
  journal        = {Archive of Numerical Software},
  year           = {2017},
  volume         = {5},
  number         = {1},
  pages          = {111--128},
  doi            = {10.11588/ans.2017.1.27719},
  keywords       = {discontinuous Petrov-Galerkin; partial differential equations; inf-sup stability; transport equation; finite elements; DUNE},
}

If you are using our ASTI implementation for radiative transfer problems, please also consider citing Felix’ thesis (PDF) and our Math. Comp. paper (arXiv preprint). The BibTeX entries for these are:

@PhdThesis{Gruber2018,
  author    = {Felix Gruber},
  title     = {Adaptive Source Term Iteration: A Stable Formulation for Radiative Transfer},
  school    = {RWTH Aachen University},
  year      = {2018},
  doi       = {10.18154/RWTH-2018-230893},
  keywords  = {DPG transport solver; fast application of scattering operator; iteration in function space},
}

@Article{DGM2020,
  author     = {Wolfgang Dahmen and Felix Gruber and Olga Mula},
  title      = {An Adaptive Nested Source Term Iteration for Radiative Transfer Equations},
  journal    = {Mathematics of Computation},
  year       = {2020},
  doi        = {10.1090/mcom/3505},
  keywords   = {DPG transport solver, iteration in function space, fast application of scattering operator, Hilbert–Schmidt decomposition, matrix compression},
}

If you are using other Dune modules, you might find the corresponding papers here.

License

Licensing information for dune-dpg can be found in the accompanying file COPYING.