Extending DUNE: The dune-xt modules

Rene Milk, Felix Tobias Schindler, Tobias Leibner


Abstract: We present our effort to extend and complement the core modules of the Dis-
tributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested
and structured collection of utilities and concepts. We describe key elements of our four modules
dune-xt-common, dune-xt-grid, dune-xt-la and dune-xt-functions, which aim add further
enabling the programming of generic algorithms within DUNE as well as adding an extra layer
of usability and convenience.



Full Text:



Martin Alkämper, Andreas Dedner, Robert Klöfkorn, and Martin Nolte. The dune-alugrid

module. Archive of Numerical Software, 4(1), 2016.

W. Bangerth, T. Heister, L. Heltai, G. Kanschat, M. Kronbichler, M. Maier, B. Turcksin, and

T. D. Young. The deal.II library, version 8.2. Archive of Numerical Software, 3, 2015.

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and

O. Sander. A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part II:

Implementation and Tests in DUNE. Computing, 82(2–3):121–138, 2008.

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, M. Ohlberger, and O. Sander.

A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part I: Abstract

Framework. Computing, 82(2-3):103–119, 2008.

Peter Bastian, Felix Heimann, and Sven Marnach. Generic implementation of finite element

methods in the distributed and unified numerics environment (dune). Kybernetika, 46(2):294–

, 2010.

M. Blatt and P. Bastian. The iterative solver template library. In B. Kagstrom, E. Elmroth,

J. Dongarra, and J. Waśniewski, editors, Applied Parallel Computing. State of the Art in Scientific

Computing, volume 4699 of Lecture Notes in Computer Science, pages 666–675. Springer Berlin

Heidelberg, 2007.

M. Blatt and P. Bastian. On the generic parallelisation of iterative solvers for the finite element

method. International Journal of Computational Science and Engineering, 4(1):56–69, 2008.

M. D. Buhmann. Radial basis functions. In Acta numerica, 2000, volume 9 of Acta Numer.,

pages 1–38. Cambridge Univ. Press, Cambridge, 2000.

A. Burri, A. Dedner, D. Diehl, R. Klöfkorn, and M. Ohlberger. Advances in High Performance

Computing and Computational Sciences: The 1st Kazakh-German Advanced Research Workshop, Al-

maty, Kazakhstan, September 25 to October 1, 2005, chapter A general object oriented framework

for discretizing non-linear evolution equations, pages 69–87. Springer Berlin Heidelberg,

Berlin, Heidelberg, 2006.

P.G. Ciarlet. The Finite Element Method for Elliptic Problems. North-Holland Publishing Com-

pany, 1978.

J. O. Coplien. Curiously recurring template patterns. C++ Report, 7(2):24–27, 1995.

Andreas Dedner, Robert Klöfkorn, Martin Nolte, and Mario Ohlberger. A generic interface

for parallel and adaptive discretization schemes: abstraction principles and the dune-fem

module. Computing, 90(3):165–196, 2010.

Christian Engwer, Carsten Gräser, Steffen Müthing, and Oliver Sander. The interface for

functions in the dune-functions module. arXiv, 1512.06136, 2015.

D. Gottlieb and S. A. Orszag. Numerical Analysis of Spectral Methods: Theory and Applications.

CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and

Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1977.

Gaël Guennebaud, Benoît Jacob, et al. Eigen v3. http://eigen.tuxfamily.org, 2010.

F. Hecht. New development in freefem++. J. Numer. Math., 20(3-4):251–265, 2012.

J. D. Hunter. Matplotlib: A 2d graphics environment. Computing In Science & Engineering,

(3):90–95, 2007.

Dominic Kempf and Timo Koch. System testing in scientific numerical software frameworks

using the example of dune. In Submitted to the Proceedings of the DUNE User Meeting 2015,

Sep. 28-29, 2015, Heidelberg, Germany, 2016.

B. S. Kirk, J. W. Peterson, R. H. Stogner, and G. F. Carey. libMesh: A C++ Library for

Parallel Adaptive Mesh Refinement/Coarsening Simulations. Engineering with Computers,

(3–4):237–254, 2006.

A. Logg, K.-A. Mardal, and G. Wells, editors. Automated Solution of Differential Equations by

the Finite Element Method, volume 84 of Lecture Notes in Computational Science and Engineering.

Springer Berlin Heidelberg, 2012.

Wes McKinney. Data structures for statistical computing in python. In Stéfan van der Walt

and Jarrod Millman, editors, Proceedings of the 9th Python in Science Conference, pages 51 – 56,

Gerard Meszaros. xUnit test patterns: Refactoring test code. Pearson Education, 2007.

René Milk, Stephan Rave, and Felix Schindler. pymor - generic algorithms and interfaces for

model order reduction. arXiv, 1506.07094, 2015.

Martin Nolte. Efficient Numerical Approximation of the Effective Hamiltonian. PhD thesis,

University of Freiburg, 2011.

C. Prud’homme, V. Chabannes, V. Doyeux, M. Ismail, A. Samake, and G. Pena. FEEL++:

a computational framework for Galerkin methods and advanced numerical methods. In

CEMRACS’11: Multiscale coupling of complex models in scientific computing, volume 38 of

ESAIM Proc., pages 429–455. EDP Sci., Les Ulis, 2012.

K. Urban. Wavelet methods for elliptic partial differential equations. Numerical mathematics and

scientific computation. Oxford University Press Oxford, 2009. ISBN 978-0-19-852605-6.

DOI: https://doi.org/10.11588/ans.2017.1.27720

URN (PDF): http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-277200